Gas Turbine Operation Offshore

Journal of Mechanics Engineering and Automation Volume 4, Number 12, December 2014 (Serial Number 42)

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Publication Information: Journal of Mechanics Engineering and Automation is published monthly in hard copy (ISSN 2159-5275) and online (ISSN 2159-5283) by David Publishing Company located at 240 Nagle Avenue #15C, New York, NY 10034, USA. Aims and Scope: Journal of Mechanics Engineering and Automation, a monthly professional academic journal, particularly emphasizes practical application of up-to-date technology in realm of Mechanics, Automation and other relevant fields. And articles interpreting successful policies, programs or cases are also welcome. Editorial Board Members: Adel Abdel-Rahman Megahed (Egypt), Curtu Ioan (Romania), Ionel Staretu (Romania), Isak Karabegovic (Bosnia and Herzegovina), Jianhua Zhang (China), Khalid Alzebdeh (Sultanate of Oman), Konstantin Samsonovich Ivanov (Kazakhstan), Mihai Valentin Predoi (Romania), Mohammad Mehdi Rashidi (Iran), Najim Ameer Saad (Iraq), Pak Kin Wong (Macao), Peng-Sheng Wei (Taiwan), Sergio Baragetti (Italy), Valentina Emilia Balas (Romania), Wei Min Huang (Singapore), Yuping He (Canada), Zhumadil Baigunchekov (Kazakhstan), Zhijun Peng (United Kingdom) Manuscripts and correspondence are invited for publication. You can submit your papers via web submission, or E-mail to [email protected]. Submission guidelines and web submission system are available at http://www.davidpublishing.com. Editorial Office: 240 Nagle Avenue #15C, New York, NY 10034, USA Tel: 1-323-984-7526, 323-410-1082; Fax: 1-323-984-7374, 323-908-0457 E-mail: [email protected] Copyright©2014 by David Publishing Company and individual contributors. All rights reserved. David Publishing Company holds the exclusive copyright of all the contents of this journal. In accordance with the international convention, no part of this journal may be reproduced or transmitted by any media or publishing organs (including various websites) without the written permission of the copyright holder. Otherwise, any conduct would be considered as the violation of the copyright. The contents of this journal are available for any citation. However, all the citations should be clearly indicated with the title of this journal, serial number and the name of the author. Abstracted / Indexed in: Google Scholar Chinese Database of CEPS, Airiti Inc. & OCLC Chinese Scientific Journals Database, VIP Corporation, Chongqing, China CSA Technology Research Database Database of EBSCO, Massachusetts, USA Norwegian Social Science Data Services (NSD), Norway Summon Serials Solutions Ulrich’s Periodicals Directory Subscription Information: Price (per year): Print $520; Online $320; Print and Online $600 David Publishing Company 240 Nagle Avenue #15C, New York, NY 10034, USA Tel: 1-323-984-7526, 323-410-1082; Fax: 1-323-984-7374, 323-908-0457 E-mail: [email protected] Digital Cooperative Company: www.bookan.com.cn

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Journal of Mechanics Engineering and Automation Volume 4, Number 12, December 2014 (Serial Number 42)

Contents Techniques and Methods 919

Advantages of Multi-body Simulation within the Design Process of Heavy Drivetrains Jennifer Papies, Christoph Lohmann, Jörg Hermes and Markus Wöppermann

924

Test Rig Effect on Performance Measurement for Low Loaded Large-Diameter Fan for Automotive Application Manuel Henner, Bruno Demory, François Franquelin , Youssef Beddadi and Zebin Zhang

937

A Theoretical Dynamic Analysis of a Regenerative Heat Exchanger Assembly in a Fluctuating Flow Regime Franck Mulumba Senda and Robert Thomas Dobson

945

Gas Turbine Operation Offshore: Online Compressor Wash Operational Experience Stian Madsen and Lars E. Bakken

960

Simulating the Inverse Kinematic Model of a Robot through Artificial Neural Networks: Complementing the Teaching of Robotics José Tarcísio Franco de Camargo, Estéfano Vizconde Veraszto and Gilmar Barreto

Investigation and Analysis 969

Measurement Module for Young for Thermal Insulation Composite Polymeric Jacques Cousteau da Silva Borges, Manoel Leonel de Oliveira Neto and George Santos Marinho

975

Model of the Reliability Prediction of Masonry Walls in Buildings Beata Nowogońska

981

Mathematical Modeling and Computational Semiotics: Methodological Approach to Formalization of Semiotic Concepts Silvia Regina dos Santos Coelho and Ricardo Matos Chaim

1001 Innovation and Education: Construction of Interactivity Indicators to Collaborative and Immersive Learning Estéfano Vizconde Veraszto, Gilmar Barreto, Sérgio Ferreira do Amaral and José Tarcísio Franco de Camargo 1008 Standardization of Work for Setting the Tone of Ceramics José Víctor Galaviz Rodríguez, Miguel Terrón Hernández, Vicente Flores Lara and Jorge Bedolla Hernández

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Journal of Mechanics Engineering and Automation 4 (2014) 919-923

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Advantages of Multi-body Simulation within the Design Process of Heavy Drivetrains Jennifer Papies1, Christoph Lohmann1, Jörg Hermes2 and Markus Wöppermann2 1. Ruhr University Bochum, Bochum 44801, Germany 2. SEW-EURODRIVE GmbH & Co. KG, Bruchsal 76646, Germany Received: September 03, 2014 / Accepted: September 25, 2014 / Published: December 25, 2014. Abstract: For the further design of the particular gearbox components, the alternating cycles of the respective application mean an often insufficient knowledge of the actual loads occuring in use. Especially for the application within lifting units, such dynamic load cycles are very difficult to pre-estimate. The so-called slack rope test represents the most critical point in the load cycle and provides a special challenge for the gearbox design. Because of this missing expert knowledge, a test bench of such an application is installed and applied to practical movement cycles. Besides the test bench, a multi-body simulation model of the whole system is mapped within the MBS (multi-body simulation) environment SIMPACK. To verify this simulation model, the results are compared with the respective measurements of the test bench. These comparisons show very good agreements. Thus, one of the major advantages of using such simulation tools is the possibility to re-evaluate the internal and external loads during the whole design process. Finally, these simulations serve as a clarification of the load spectrum of the different drivetrain components. Gearbox series or different modifications of the design can now be analyzed prospectively without extensive testing. Key words: Comparison of test bench and simulation results, dynamic behavior of lifting units, multi-body simulation.

1. Introduction The insufficient knowledge of the actual loads occuring in use provides a problem for the design of the particular gearbox components. The dynamic load cycles can be determined properly either by means of test benches or by simulating the dynamic load cycles. The results of such investigations can then be converted into a load spectrum and contribute a basis for a life time prediction based on the rules of fatigue strength for each individual component. Thereby, the transfer into the digital environment offers a major cost and time advantage and also provides additional information which can be hardly determined by conventional measurements. For instant analysis, a test bench of a complete lifting unit is installed and applied to practical movement cycles to estimate the dynamic load conditions of this concrete application. Multi-body simulation Corresponding author: Jennifer Papies, Dipl.-Ing., research field: multi-body simulation. E-mail: [email protected].

models are used additionally to assess the critical load situations due to the overall system dynamics. With the aid of such simulation models, a further analysis can be performed of the load acting inside the gearbox and within the different gearbox components. This allows to determine the load of all gears, shafts and bearings within the gearbox considering all specifications of this concrete application. In addition to the test bench configuration, this paper shows the modeling of the different test bench components in MBS (multi-body simulation). Furthermore, a detailed comparison is made of the results to demonstrate the potential of such simulation methods for use in gearbox design and development. The paper is organized as follows: Section 2 describes the installed test bench as well as the measuring points of the respective signals; Section 3 introduces modeling of the multi-body simulation model of the whole test bench configuration; Section 4 presents the comparison and the discussion of the results; and Section 5 provides conclusions to this investigation.

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Advantages of Multi-body Simulation within the Design Process of Heavy Drivetrains

2. Test Bench For this investigation, a test bench of the lifting unit is installed which consists of typical components. Basically, these components are the support structure, a motor, the gearbox unit on which this concrete investigation focus, a rope drum, four ropes, and a lifting beam. The asynchronous motor with an output of 75 kW drives the lifting unit, and a frequency converter controls the speed. The gear unit is a 4-stage spur gear system of SEW-Eurodrive (type X4FR160) which offers a gear ratio of i = 100.04. Motor and gear units are connected with an elastic coupling to absorb potential torque impulses. An additional measure adapter at this point measures the motor torque. The torque is transmitted to the support structure by a torque bracket. The force between torque bracket and support structure is measured with a load cell. The output torque is specified with the aid of the measured force and the torque of the torque bracket. The output shaft has to carry the housing of the motor and the gear unit. To eliminate the weight of these components, the value of the load cell is zeroed at standstill without load torque. The output torque is transmitted via a rigid coupling at the output shaft to a pin of the rope drum. The rope drum is a hollow shaft, which is carried by a pin on each end. These pins serve as a connection between the rope drum and a bearing block, and between the output coupling and the rope drum. They are mounted by two spherical roller bearings. The rope drum converts the torque into a force, which is transmitted to the lifting beam by four ropes. This means the ropes are rolling up side by side and not on top of each other. Consequently, the ratio between torque and force remains constant. Because the rope drum and the lifting beam are located on the same level, the rope is diverted to the deviating roller in a height of circa 8 m. Between the becket and the lifting beam, four plate springs are arranged to form a spring column, which provide additional damping to lessen further impulses. Altogether the lifting beam has a total weight of m = 19,960 kg. This test bench is shown in Fig. 1.

The entire application is applied to practical movement cycles. The most decisive load case for the gearbox design is the so-called slack rope test. During this test, the lifting beam is lowered to the ground until the ropes get unloaded. By unwinding the ropes further at the end of the cycle, the drivetrain accelerates at the beginning of the next cycle without load torque so that the ropes get stretched at maximum lifting speed and the lifting beam is lifted. It suggests itself that this represents the most critical point of the whole operating cycle.

3. Model Description In addition to this test bench, a MBS model is mapped within the mbs environment SIMPACK (Version 8.904) to assess critical load situations of this drivetrain and its components due to the previous overall system dynamics. This model [1] allows to determine the load of all gears, shafts and bearings within the gearbox considering all specifications of this concrete application. The entire model is a rigid body system and consists of several subsystems which are representative for the real test bench components. Gearbox and housing are combined to one mass point considering the mass and inertia properties of all non-rotating components. The

Fig. 1

Overview of the real test bench.


supporting structure is also assumed to be rigid. The electric motor is represented by its torque-drive characteristic. The controller of the frequency converter [5], which has a major influence on the whole system dynamics, is considered in the model also with a closed loop control. The elastomer coupling between motor and gear unit reflects the resilience of the elastomer with its non-linear stiffness characteristic given by the respective catalogs. The discretization of all shafts within the drivetrain leads to a realistic model of the deflection of the shafts. For the modeling of the involute gear contacts, the SIMPACK dedicated force element is used within the model. Bearings including a non-linear characteristic [7] and clearance are also implemented within the model. More influence on the whole system dynamics has the resilience of the ropes for this application [6]. For this purpose, a unilateral spring damper element is used which can only contain tensile forces. The respective load elongation characteristic is given by the rope manufacturer. At this point, it is important that this characteristic is based on the averaging of different measurements which combine different rope diameters, different load and decompression curves as well as different tensile strengths. Therefore, the scattering rage of this curve is very large. Because of this correlation in the further comparison of the simulation and measurement results, a differentiation is made between the results of the original rope resilience and an optimized characteristic which is indicated with an additional “adapted” in the diagrams. An overview of the dynamic model is given in Fig. 2.

Fig. 2

921

Overview of mbs model.

4. Results and Discussion

Fig. 3 Force comparison (slack rope test—lifting, original rope characteristic).

The respective forces of the most critical point of the operation cycle, the so-called slack rope test, are shown in the further comparison of the simulation and measurement results. The decay behavior fits very well with the decay of the lifting unit (Fig. 3). Differences can be seen in the

first three amplitudes during unloading whereas the amplitudes of the loading signals are more consistent. This effect can be traced back to the rope model approach due to the unilateral spring damper elements used. These elements build a force only for a positive moving direction. But during unloading, the velocity

922

Advantages of Multi-body Simulation within the Design Process of Heavy Drivetrains Classification in load classes

Tension calculation for each stressed part in the gear box and comparison with Whoehler curve

Definition of a minimum gear box service factor for this application Load cycles [Mio.]

part 2 part 3

Application type

Tension

part 1

0.5

1.0

2.0

1

0.6

1.0

1.5

2

1.2

1.5

1.7

Load cycles

Fig. 5

Fig. 4 Force comparison (slack rope test—lifting, adapted rope characteristic).

between rope and rope drum is negative, and therefore, no resulting damping force is set up at this point. The maximum occurring load is larger by 3% compared to the measurement results which indicate a softer drivetrain than that of the modeled one (Fig. 3). The frequency analysis shows an oppositional trend. These results are acceptable due to the high generalization of the rope stiffness characteristic. By adjusting this characteristic (within the given parameters), the results can be further harmonized (Fig. 4). Small differences at the build-up of the force can also be identified. The linear values assumed in most spring damper elements lead to a stiffer model at small loads. This linearity does not reflect the real behavior at small loads because most components have a progressive spring characteristic. But at this point, the effort to adapt the spring characteristic is much higher than the benefit of improved quantitative results. For the interpretation of fatigue strength of the different gearing components, shafts and housing the obtained data is used in particular calculation models. With this approach, the different gearbox components can be classified and traced back to a tension for each stressed part within the gearbox. Then each part can be compared to the Whoehler curve. Thus, this procedure leads to a definition of a minimum service factor for this application (Fig. 5). Based on the forces known from the simulation results, the deformation of the

Further processing with the simulation results.

housing and the twisting of the individual gear wheel sets can be evaluated in a further FEM analysis. The precise knowledge of all forces and contact conditions allows for a relative accurate prediction of the product life cycle.

5. Conclusions The comparison between the simulation and measurement results allows to evaluate the information level of this model:  A nearly identical trend can be identified for the measured and simulated vibrations at the flange and the load cell;  The deviations of the frequencies between the model and the measurements range between 0.03 s and 0.07 s. This amount can still be eliminated even further by a parameter optimization (Fig. 4);  The maximum deviation of the amplitudes amounts to 4%;  The existing deviations can be partially attributed to the lack of the consideration of the efficiency of the system, for the most part the friction of the rope. As a conclusion, this investigation has shown that the internal and external loads can be re-evaluated with the aid of such simulation tools. The analysis provides the load of each respective component of the drivetrain and serves, therefore, as a clarification of the load spectrum for this concrete application. Without extensive testing, gearbox series or different modifications can be analyzed in advance. For this reason, the multi-body simulation provides a major cost and time advantage compared to the conventional approach, and collects an information content which, in this way, was hardly possible in previous investigations.


References [1]

[2]

[3]

Lohmann, C. 2012. “Simulation der Systemdynamik Eines Hubwerks in MKS.” M.Sc. thesis, Ruhr University Bochum. Papies, J., Lohmann, C., Hermes, J., and Wöppermann, M. 2013. “Gearbox for Lifting Unit Applications-Life Time Prediction Based on Multi-body Simulation.” Presented at the International Conference on Gears, Munich. Dresig, H. 2001. Schwingungen Mechanischer Antriebssysteme. Modellbildung, Berechnung, Analyse,

[4] [5] [6] [7] [8]

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Synthese. Berlin: Springer. Dresig, H., and Holzweissig, F. 2005. Maschinendynamik. 6. Aufl. Heidelberg: Springer. SEW Eurodrive. 2012. Movidrive Drehzahlregelung. Hg. v. Bruchsal: SEW Eurodrive. Verreet, R. 1997. Casar Spezialdrahtseile. Hg. v. Casar: Technische Eigenschaften. Schaeffler Technologies AG & Co. 2012. KG: Steifigkeitskennlinien Wälzlager. Herzogenaurach. DIN 3990. 1987. Tragfähigkeitsberechnung von Stirnrädern. Beuth Verlag.

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Test Rig Effect on Performance Measurement for Low Loaded Large-Diameter Fan for Automotive Application Manuel Henner, Bruno Demory, François Franquelin , Youssef Beddadi and Zebin Zhang Valeo Thermal Systems- 8, La Verrière 78321, France Received: August 20, 2014 / Accepted: September 16, 2014 / Published: December 25, 2012. Abstract: Large diameter fans with low solidity are widely used in automotive application for engine cooling. Their designs with small chord length help reducing the torque on the electrical motor and providing a good aerodynamic compromise between several operating conditions, some of these being at high flow rate. Their global performances are measured according to the ISO standard DP 5801, which allows comparison of results from different facilities. However, some variations in global performances are observed when considering results from two different test rigs. On a fan selected for the purpose of this study, up to 6 % of efficiency is lost on the worst case. As efficiency is more than ever a key factor to select a component, some experimental and numerical investigations were conducted to analyze the fan behavior on each facility. Two sets of measurement and simulation are performed and compared. Geometries considered for the domain of computation include the test rig plenum, the torquemeter, the ground and a large domain for the atmospheric conditions. The exact fan geometry with tip clearance and under-hub ribs is also considered. Numerical results show a good agreement with experiment in both cases when convergence is reached and for low flow rate when computations are switched to unsteady mode. Comparisons show that simulations are able to capture the different fan behaviors depending on the configuration and those efficiency losses previously observed are correctly predicted. These results are further analyzed to perform some post-processing. Blade loading remains identical for both cases but disparities appear in the wake and its interaction with the surrounding. Tiny details that are often neglected during experiment and/or simulation appear to be the cause of slight variations. Position of the torquemeter and shape of the plenum are among the parameters that various and that have cumulative effects. Efficiency being a ration of pressure and torque, variations are rather important. Finally, these results are discussed in terms of rules for conception and a new geometry less sensible to loss of efficiency is proposed. Key words: Fan, performance measurements, test rig, validation, torque, uncertainty.

1. Introduction Fan systems are used on vehicles to force the air flow through heat exchangers when the vehicle is at rest or running at low speed. The design of the engine cooling system follows the current trend which is to provide more compact and lighter components, and should help reducing the on-board electrical power consumption. Large diameter fans with small axial length are increasingly used to meet these constraints since they provide large airflow rate and they cover a large surface of the stacking of heat exchangers. Their low Corresponding author: Manuel Henner, Ph.D., research fields: fan systems, automotive thermal management. E-mail: [email protected].

serration allows them to be lightly loaded and therefore, do not require a significant torque (or power). However, their conception has to be revisited to ensure good turbomachinery efficiency despite the drawback of this low serration. During a long time, fan design for automotive application was based on an iterative process, which allowed with some experience to achieve the required aerodynamics performance. Fans were ultimately validated by a test on a test rig in accordance with the ISO standard DP 5801, which ensures the measurement validity [1]. In recent years, the specifications have been tightened for the reasons of energy efficiency, and it is not uncommon that fans have to be reworked to gain 1% of efficiency (static efficiency is usually in

Test Rig Effect on Performance Measurement for Low Loaded Large-Diameter Fan for Automotive Application

a range of 50% to 55%). In addition, it is not simply asked to reach a performance at a nominal point, it is also required that the pressure rise stays positive at high flow rate. Several studies have been conducted to describe the aerodynamics of the fan, showing that the actual blade loading is somehow quite different from the theoretical one. Different phenomena may affect operation: the back flow of the tip clearance, the contraction of the fluid with the hub, and the effect of radial equilibrium on the blade loading. Some of these effects have been studied by Refs. [2, 3] in term of blade load. Another study [4] shows that the blade curvature (or blade sweep) influences the load distribution from hub to tip. It has some interesting properties for performance, especially with the backward sweep which seems to be good for global efficiency. Other improvements were proposed by modifying the contouring on the hub in order to partially correct some default on blade loading at blade root [5]. Some other investigations were also devoted to these fans with experimental measurements, and served as a validation campaigns for the numerical methodologies used for performance predictions [6-8]. Some uncertainties quantifications have also been conducted around the simulation methodology which allows to predict both aerodynamics and aeroacoustics performances [9]. These studies highlight the difficulty to use low loaded fan, with a high specific speed in a confined environment such as in an automotive under-hood. A previous study [10] with an extreme concept of low loaded fan showed that only 45% of static efficiency can be reached. The blade is subject to insufficient load from bottom to top, and moreover, is destabilized by the tip clearance recirculation, as explained in Ref. [11]. These difficulties to find good compromises have to be replaced in the current context of the automotive industry, where the increase pressure exerted by end-users or legislators to improve the energy efficiency is gradually re-assigned to all components.

925

The fan system is no exception. High efficiencies are expected and must be guaranteed by reliable numerical and experimental results. The paper is organized as follows: Section 2 presents the objectives; Section 3 describes the experimental facilities; Section 4 introduces the numerical simulation and presents the results; Section 5 introduces the test rig effect; Section 6 compares test rig effects on two different fans; and Section 7 gives conclusions and perspectives.

2. Objectives The new trend for large diameter fan systems with low torque has led to question about the ability of test facilities to measure aerodynamic performances, and about the ability of numerical simulation methods to predict these performances. This information is essential in the light of new energy efficiency requirement. They also provide information about the capacity that is provided to engineers to develop virtually components thanks to CFD (computational fluid dynamics). For these reasons, a fan that meets the latest requirements of low torque and subjects to difficult blade loading conditions (tip clearance recirculation, blade bottom not filled correctly) has been tested on two facilities and the results were compared. A set of different simulations with various changes in the environment were conducted to measure the impact on performance. All experimental and numerical results serve as a basis for comparison and are used to establish some cross-validation. A second type of fan, slightly more loaded was numerically tested in order to assess the effect of the fan characteristics on its stability regarding variations of test conditions. In summary, investigations presented in this paper cover the following points:  Uncertainty quantification of experimental results to evaluate the capability of test rig facilities to deliver reliable results;

926

Test Rig Effect on Performance P M Measuremen t for Low Loa aded Large-D Diameter Fan for Auttomotive App plication

 Compaarison betweeen numerical and a experimeental results to asssess accuracyy of fan simullation;  Evaluattion of diffferent effecct of test rig configuratioon on low loadded fan;  Fan beehavior compparison with a slightly more m loaded fan.

3. Experim mental Resu ults A large diiameter fan of o 440 mm diiameter is useed to compare results obtaineed from twoo test rigs. This seven bladee fan is preseented in Fig.. 1. The average chord lengthh of only 5 cm m leads to a quite q low soliddity. Results weree obtained forr the rotationnal speed of 2,100 rpm on bothh test rigs, annd some addiitional tests were w conducted on o one of them m at 1,800 rpm m and 2,400 rpm. It has been verified andd first, resultts are repeataable, and secondd, performaance curvess are perfeectly homothetic with the speeed variation and no Reynnolds effect was detected. The two test t rig facilitties that weree used are loccated respectively at LVR (La Verrière) in France F and att the University of o Siegen in Germany. Both B of them m are equipped wiith an additioonal high pow wer fan aimeed to force the flow f rate, coonnected to a measurem ment nozzle andd a plenum m. This lattter includes a honey-combb panel whhich homogeenizes the flow f before it arrrives on the fan to be tessted. A sketch of the LVR tesst rig facilityy is presentedd in Fig. 2, annd a general view w is presentedd in Fig. 3. Some diffferences exisst between thhe two faciliities. For the LVR R one, two nozzles are ussed to controll the flow rate, reespectively beelow 800 m3/hh and above. The plenum has a square sectiion of 2.4 m × 2.4 m, wheereas the Siegen plenum p has a cylindrical shhape (as it caan be seen in Fig. 4 with the vieew of the testt rig). Its diam meter of 1.1 m is juust at the low wer limit of thhe specificatioon. Some othher geometriical differennces might have h some effectss on fan behaavior. At Sieggen Universitty, a frame is useed at the outleet (Fig. 4) to support four thin arms that ceenter the torqquemeter shaaft and avoid any vibration and resonance during d operattion.

Fig. 1 View of th he 440 mm-diiameter fan ussed for test rigg com mparison.

Fig.. 2

Layout off LVR facility.

Fig.. 3

General view v of LVR faacility.

Fig.. 4

View of Siiegen facility.


9277

On the LV VR test rig, the t fan is moounted on a plate p that is not directly d conneected to the square s sectioon of the plenum:: a reduced section s of 1..2 m × 0.6 m is positioned on o the center of the exit wall w as presented in Fig. 5. S and LV VR Measurements 3.1 Compariison between Siegen Aerodynaamics perform mances are presented in Figs. F 6-8 respectively for the pressure risee, the torque and the efficienccy as functionns of the flow w rate. Resultss are obviously quuite similar but not identiccal. In Fig. 6, the pressure curve is alm most linear forr the LVR resultss, whereas it can be seenn a change inn the slope occurrring around 3,200 m3/h forr Siegen’s ressults. It results inn a higher level of pressuure rise betw ween 3 3 2,000 m /h and 3,000 m /h for LVR R measuremeents, and a lower flow rate forr the zero preessure point. The discontinuityy observed after a 3,000 m3/h at Siegeen is discussed laater in this paaper with resuults of numerrical investigationn.

Fig. 5

Shapee of the reduceed section at th he plenum exit

(LVR).

Fig. 6

Presssure rise P = f(Q). f

Fig.. 7

Torque = f(Q). f

Fig.. 8

Efficiencyy = f(Q).

In n Fig. 7, onee can see thaat the torque measured att Sieg gen is lowerr than that at LVR (~-0 0.1N·m, i.e.,, -10%), but both curves are quuite parallel and a show thee sam me behavior. The T torque iss smaller at high h flow ratee than n that at low flow f rate. Both B effects of o pressure annd torque lead d to identicall effeects on the sttatic efficienccy curve pressented in Fig.. 8. A change iss observed bbetween 3,00 00 m3/h andd 3,20 00 m3/h for Siegen’s S resullts, whereas the t efficiencyy look ks like a smoooth bell for L LVR’s experrimental data.. A maximum m deeviation of 6% % in efficien ncy occurs att 3 3,20 00 m /h: it reesults from tthe pressure discontinuityy observed on thee Siegen faciility after 3,0 000 m3/h andd the lower measuured torque. These T differennces in resultts are quite im mportant andd justtify some invvestigations: uuncertainty quantification q n and d further CFD D analysis oof both facillities will bee pressented to provvide some exxplanations.

928

Test Rig Effect on Performance Measurement for Low Loaded Large-Diameter Fan for Automotive Application

3.2 Experimental Uncertainty Quantification Uncertainty quantifications on experimental results were conducted by identifying factors that are used in the measurement process. These factors are those presented in the formula for flow rate calculation and those related to the pressure and the torque measurement. One pressure sensor is located in the nozzle for measuring the flow rate, and another one is located in the plenum to provide the fan performance. Other uncertainties are related to the dimensional accuracy of the nozzle and variations of temperature and ambient pressure. For the flow rate, Eq. (1) is used:

Qnozzle  A  S   0  Pnozzle 

T0 Tambient



Patm

(1)

P0

where, A is a calibration constant, S = πD²/4 the

0

surface area and

is proportional to

Patm Tambient

exact geometries of both test rig facilities. Computational domains include the plenum, starting at the position of the honeycomb panel, the fan mounted on the torquemeter, and the external domain to figure the atmospheric conditions. A 5-m diameter sphere is used to ensure a correct dissipation of the wake before the outlet condition. These domains are presented in Figs. 9 and 10, where one can see the great attention paid to accurately reproduce the facility geometries. Details like the torquemeter, the step on the ground and the equipment on the side reproduce the LVR context. The external frame is modeled for the Siegen test rig. The exact fan geometry is considered, and simulations include the tip clearance between the rotating ring of the fan and the plenum wall at rest. The ribs inside the hub are also taken into account in the simulation as presented in Fig. 11.

.

The relative uncertainty of flow rate can be obtained by Eq. (2):

Q Q

 2

D D



Patm Patm



Tambient Tambient

 0.5 

Pnozzle Pnozzle

(2)

where, accuracies on measurements have been accessed to ±0.4° on Tambient, ±5 Pa on Patm and ±0.1 mm on the nozzle diameter (D). Others uncertainties are ±0.05 N·m on the torque (Tq), ±2% on pressure measurement (P) and ±3 rpm on rotational speed (N). Finally, uncertainty on efficiency is given by Eq. (3):







D P Tq N    D P Tq N

Fig. 9

LVR’s computational domain.

(3)

Performance uncertainties obtained by this process will be presented in the next section, simultaneously with CFD results.

4. Numerical Results Numerical simulations were performed using the

Fig. 10 Siegen’s computation domain (without torquemeter).


In Figs. 9 and 10, thhe inlet domaain is colored in green (plenuum), where a volume flow w rate is impoosed. The fan (redd) is located inn the rotationnal domain which w uses either MRF M (movinng reference frame) f for steeady simulation or o RBM (rigiid body motiion) for unsteeady simulation. 3D CFD calculationss were carrieed out with the CD-Adapco solver Sttar CCM+ Version 7.04. 7 Turbulence is modeled with w the classiical two equaation model k-ω SST S from Meenter, and a tw wo layer moddel is used to accuurately predicct the boundarry layer on walls. w About 15 million m polyhhedral cells are used in the simulation, mainly m conceentrated arounnd the fan annd in cell extrusioon from fan walls. w All simullations were run steady at a first, and then unsteady wiith a least onne fan rotatioon. Convergennces were checkeed in any caases by monnitoring residduals and global performancces (pressurre and torqque). Differences between steady and unssteady simulaation are mainly observed o at loow flow rate when separaation on fan bladee are at their higher levell and cause some unsteady phenomena. Comparissons betweenn experimenntal results and simulations are presenteed in Figs. 12-14 for LVR L results, and in Figs. 15-177 for Siegen. The solid cuurves named Max and Min reppresent the meeasured valuees to which uncertainty vallues have been b addedd or subtracted reespectively. For pressuure curves (F Figs. 12 and 15), CFD ressults are close too experimentaal one for booth test rigs, and even with a good matchiing with Sieggen measurem ment. Discrepanciees where sim mulation ressults are outtside uncertainty ranges r come from high fllow rates at LVR L 3 (above 4,0000 m /h), annd from the slope changge at Siegen arounnd 3,200 m3/hh. Numericaal results forr the torque show a perrfect matching with w experim mental data for the Sieegen configuratioon (Fig. 13), whereas ressults obtained at LVR are abbout 10% higgher than thee prediction (Fig. ( 16). This difference d reeminds of course c the 10% experimentaal deviation already estaablished betw ween

9299

LVR R and Siegenn results. Finally, F for the efficienncy which depends onn unccertainties off both pressuure and torqu ue, numericall valu ues are outsidde the uncertaainty range of o experimentt for LVR configguration at high flow rate, r and forr 3 Sieg gen configuraation at ~3,2000 m /h (Figss. 14 and 17) . It has to be notedd that maxim mum efficiency y uncertaintyy is ±5%. ±

Fig. 11 Ribs insid de the fan hub (exact geometrry of the fan).

Fig.. 12 P = f(Q Q) LVR.

Fig.. 13

Torque = f(Q) LVR.

930

Fig. 14


Efficciency = f(Q) LVR. L

Fig.. 17

Efficienccy = f(Q) Siegen n.

Others O differeences betweenn LVR and Siegen S resultss hav ve been, how wever, invesstigated numerically, andd resu ults from thhis study aree presented in the nextt paraagraph.

5. Test T Rig Efffect

Fig. 15

Dp = f(Q) Siegen.

Fig. 16

Torq que = f(Q) Sieggen.

All in all, numerical results r are abble to predictt fan performancees with resultts that are moost of the tim me in the uncertaiinty range of the experim mental faciliities, except for some s LVR reesults. These differences have h triggered soome further investigationns that are still running on the chain of measuremennt and calibraation procedures at a LVR.

CFD C results from f the two test rigs are presented inn Figs. 18-20. Pressure P rise,, torque an nd efficiencyy curv ves are quitee similar, exccept at 3,200 0 m3/h wheree the slope changge occurs inn the Siegen n context. Itt resu ults in a diff fference of ppeak efficienccy of 4% att 3 3,49 90 m /h. Post-processin P ng of simullation perforrmed at thiss critical flow ratee of 3,490 m3/h are preseented in Figs.. 21 and 22 to asssess the effecct of the test rig. In thesee grap phs, circumfferential aveeraging of the velocityy com mponents is plotted p along the blade spaan, as well ass the total pressuure from blaade bottom to top. Thee curv ves show thee magnitude of these scallars extractedd from m a plane behhind the trailling edge (Fig g. 21) and inn fron nt of the leadiing edge (Figg. 22). Itt is clearly obbserved from the axial velocity that thee maiin flow is located l closee to the blaade tip. Thee tang gential velocity is close to zero at inleet, and fairlyy con nstant from bottom b to toop at outlet. It might bee exp plain by two opposite effe fects along th he blade, i.e.,, on one o hand, thee peripheral sspeed which increases, onn the other hand thhe solidity whhich decreasees. The radiall velo ocity at inlet shows the contraction of the flow w com ming from thhe whole vollume of the plenum, andd

931


the trailing edge. The T test rig context doees not chan nge the loadd disttribution on blades, b and thhe fan produces the samee fluiid deflection between the leading and trailing t edge.. Thiis explains whhy the torquee is the same, and it showss thatt the measurred pressuree difference comes from m lossses in other parts of the doomain. To T identify root causes of global performancee diffferences betw ween the two facilities, sev veral changess werre made in the domainn of simulaation. Thesee Fig. 18

Q). Presssure rise = f(Q

mod difications shhould help m measuring th he impact off threee elements: 

meter locatedd in the fan wake; w The torquem



The shape of o the LVR pplenum with its change off

secttion; 

o the outer fface of Siegen n plenum. The frame on

5.1 Effect of the Torquemeterr Results R of num merical simullations are co ompared withh or without w torquuemeter and aare shown in Figs. 23 andd 24, respectivelyy for LVR and Siegeen test rigs.. moving Rem Fig. 19

Torq que = f(Q).

thee

torquemeeter

frees

the

spacee

dow wnstream of the fan, butt does not fu undamentallyy chaange the perfoormance. Som me slight diffference existss but remains beloow experimeental uncertain nties: for thee R facilities reesults are quuite similar, except for thee LVR torq que that is slightly decreaased without torquemeter.. On the Siegen test rig, a higher presssure level iss obtaained at highh flow rate, w whereas some few Pascall of pressure p are lost at low fflow rate wh hen removingg the torquemeter.. p shappe at LVR 5.2 Effect of the plenum

Fig. 20

Efficciency = f(Q).

becomes lesss important at fan exit. Finally, F the total t pressure at outlet is annother evidennce of the loower loading at bottom b sincee values alonng the span vary v from ~20 to ~100 Pa. These posst-processinggs for both coontexts LVR and Siegen show w that the faan exactly beehaves the same s way, the onnly differencee comes from m the pressurre at

The T LVR tesst rig is equippped with a plenum thatt has a change in its section, aas presented in the sketchh of Fig. F 5. Simulations S o the LVR faacility are conducted withh on a siimplified plennum which iis just a cubee without thee redu uced sectionn. Results presented in Fig. 255 dem monstrate thaat it has noo influence on the fann perfformance.

932


Fig. 21

Distribution of circumferential averaged a veloccity componentts and total preessure at trailiing edge (3,490 0m3/h).

Fig. 22

Distribution of circumferential averaged a veloccity componentts and total preessure at leadin ng edge (3,490 0m3/h).

Test Rig Effect on Performance P Measurement for Low Loa aded Large D Diameter plication Fan for Auttomotive App

Fig. 23 Prressure rise = f(Q) LVR with or witthout torquemeter.

Fig. 24 E Efficiency = f(Q) f Siegen with or witthout torquemeter.

5.3 Effect off the Frame at a Siegen Last compparisons are conducted c to assess the efffect of the framee that is mouunted on the external wall of the test rig (Fig. 2). Neew simulationns are conduucted without fram me and withoout torquemetter and compared with Siegen and LVR iniitial results. Results R presented v in Fig. 25 shhow that the pressure currve becomes very similar to the one obtaineed at LVR. t simulattions is presented A post-prrocessing of these in Fig. 26 inn order to shhow the differrences in thee fan wake. Veloccity vectors arre presented in i a cross-secction of the simullation domainn that containns the fan axiis of rotation. Thhe torquemeteer and its shaaft are visiblle in the center, and a the fan is located at thee bottom. Forr the Siegen context, the cut in i the frame is visible onn the left and righht side.

Fig. 25 nozzzle.

9333

ure rise = f(Q) LVR with h or withoutt Pressu

The T frame thaat is used at Siegen confiines the flow w and d a recirculation on the lefft can be seen n between thee walll and the maain stream. It has for effecct to contractt the wake, in coontrast of L LVR and Sieegen withoutt fram me that prooduces simiilar flow pattern. p Thiss pheenomenon occcurs when thhe flow rate in ncreases, andd wheen the wake direction d chaanges from raadial to axial,, 3 i.e.,, between 3,0000 m /h to 3,600 m3/h. The fan exitt flow w progressiveely detaches from the fraame and thiss inteeraction correesponds to thhe change of slope for thee presssure curve measured m at S Siegen.

6. Fan F Compaarison The T fan testedd is sensitive to the changee imposed byy the two facilitties and it shows som me lack off “rob bustness” in its behavior.. It was foun nd interestingg to see s whether thhese differennces are repro oducible withh ano other type off fan. A neew fan geom metry with a backward blade sweep is useed to reprodu uce the samee typee of comparisson. The initiial fan (nameed Fan 1) andd the new one (nam med Fan 2) aare presented in Fig. 27. Their T performaances are com mpared for thee two test rigss in Figs. F 28 and 299 (pressure annd efficiency, respectively).. It can c be noticeed that the F Fan 2 does not n show anyy diffference in performance p caused by a differentt con ntext. The prressure curvve is linear without anyy chaange of slopee around the nominal opeerating pointt (clo ose to 3,200 m3/h). It provvides a curve of efficiencyy whiich outperform ms Fan 1 by 44% around 3,000 m3/h.

934


Flow patternn on LVR test rig r Fig.. 28

Pressuree rise = f(Q).

Fig.. 29

Efficienccy = f(Q).

Flow pattern on o SIEGEN tesst rig

7. Conclusion C ns

EN test rig withhout frame and Flow paattern on SIEGE torqquemeter Fig. 26 Veloocity vectors in n horizontal secctions: comparrisons between LV VR, Siegen with w and witthout frame and torquemeter.

Fig. 27

View w of initial Fan n 1 and new Faan 2.

A low soliddity fan haas been testted on twoo exp perimental faacilities, i.e.., at Siegen n Universityy (Geermany) andd at La Veerrière (Fran nce). Resultss showed some significant s ddifferences th hat triggeredd inveestigations. At first, annalysis of the t test rigg capabilities shoowed that efficiency measurement m t can nnot be guaaranteed wiith less thaan ±5% off unccertainties beecause of thhe cumulativ ve effect off erro ors on pressurre and torquee. Other O differennces of relativvely low amp plitudes havee theiir origins in some geomeetrical differeences on thee testt benches. Foor instance, thhe frame used d to hold thee torq quemeter shafft at Siegen pproduces som me effects thatt alteer the slope of the pressuree curve. A seecond changee is noticed n with the t presence of the torqueemeter whichh is lo ocated in thee downstream m flow. Thesee changes aree

9355


deteect small diffferences causeed by tiny details. From F these elements, e it iis planned to o conduct ann unccertainty quanntification off simulation results. Thiss step p is necessaary to ensure the qualitty of virtuall dev velopments

on

our

pproducts

by y

numericall

sim mulation.

Acknowledgm ments

Flow pattern onn LVR test rig Fan 2

This T work would not havve been posssible withoutt the help of SIEG GEN’s Univerrsity. The sup pport of Prof.. Tho omas Caroluss in the earliier stages off the work iss grattefully acknoowledged.

References [1]

[2]

F Flow pattern onn Siegen test rigg Fan 2 Fig. 30 Veloocity vectors in n horizontal secctions: comparrisons between LVR R and Siegen forr Fan 2.

of very low w amplitude, less than the t measurem ment uncertaintiess, but their efffects can be cumulative. c Other diffferences havve found anyy explanationn, at first the torqque measuredd at LVR whiich is 10% higher than that of Siegen and simulation ressults, and second, the weaker pressure leveel at high floow rate for LVR L measuremennts. These aspects are a still unnder investigationn. A third element e highhlights the diifficulty to make m fine comparrisons, since two fans prroducing a priori equivalent performancees do not show s the same s variation in performance from one tesst rig to the otther. This effect confirms thhe need forr caution beefore driving a coorrelation studdy between different d facillities or between test t and simulation. In concluusion, it is veery importantt to note thatt the numerical reesults are verry close to exxperimental ones. o Comparisonns showed thhat the simullation is able to provide a good perform mance predictiion, and eveen to

[3]

[4]

[5]

[6]

[7]

[8]

ISO Standdard DP 5801 1997 7. Industriall Fans—Perforrmance Testting Using Standardizedd Airways. Hurault, J., Kouidri, S., B Bakir, F., and Rey, R. 2010.. “Experimentaal and Numericcal Study of thee Sweep Eﬀectt on Three-Dim mensional Flow w Downstream of Axial Flow w Fans.” Jouurnal of F Flow Measu urement andd Instrumentatiion 21: 155-65. Vad, J. 2008. “Aerodynamic Effects of Blade Sweep andd w-Speed Axiall Flow Rotors at the Designn Skew in Low Flow Rate: An A Overview.” JJournal of Pow wer and Energyy 222 (A1): 69--85. Zayani, M., Caglar, S S., and Gabii, M. 2012.. xial Fans forr “Aeroacoustiical Investigattions on Ax Automotive Cooling System ms.” Presented d at Fan 2012,, Senlis, France. K and Caroluus, T. 2012. “O Optimization off Bamberger, K., Axial Fans with w Highly Sw wept Blades with w Respect too Losses and Noise N Reductioon.” Presented d at Fan 2012,, Senlis, France. D Henner, M., and Moreau, S. 2007. “Vallidation of 3D ne Cooling Fann Rotor-Stator URANS in Auutomotive Engin nal Symposium m Systems.” Prresented at the 8th Internation on Exxperimental and Computationall Aerothermoddynamics of Inteernal Flows, Ly yon, France. Henner, M., Moreau, S., and Brouckaerrt, J. F. 2009.. “Comparisonn of Experimenntal and Numeriical Flow Fieldd in an Automootive Engine C Cooling Modulee.” Presented att the 8th Eurropean Turbom machinery Con nference, Graz,, Austria. D 2005. “3D D Henner, M.,, Moreau, S., and Neal, D. Rotor-Stator Interaction in Automotive Engine E Coolingg Fan System ms.” Presented at the 6th 6 Europeann Turbomachinnery Conferencee, Lille, France.

936 [9]

Test Rig Effect on Performance Measurement for Low Loaded Large Diameter Fan for Automotive Application

Christophe, J., Moreau, S., Hamman, C. W., Witteveen, J. A. S., and Iaccarino, G. 2010. “Uncertainty Quantification for the Trailing-Edge Noise of a Controlled-Diffusion Airfoil.” Presented at the 17th AIAA/CEAS Aeroacoustics Conference, Portland, Oregon, USA. [10] Henner, M., Demory, B., Beddadi, Y., Bonnet, P. A., Pengue, F., and Zangeneh, M. 2013. “Low Weight, High

Speed Automotive Fan Design by 3D Inverse Design Method.” Presented at the 10th European Turbomachinery Conference, Lappeenranta, Finland. [11] Soulat, L. 2010. “Définition, Analyse et Optimisation Aérodynamique d’un Nouveau Concept de Traitement de Carter au Moyen D’outils Numériques. Application aux Turbomachines Basse Vitesse.” Ph.D. thesis, Ecole Centrale Lyon.

D


DAVID

PUBLISHING

A Theoretical Dynamic Analysis of a Regenerative Heat Exchanger Assembly in a Fluctuating Flow Regime Franck Mulumba Senda1 and Robert Thomas Dobson2 1. Mechanical Engineering Services, the South African Nuclear Energy Corporation, Pelindaba 0240, South Africa 2. Mechanical and Mechatronics Engineering, Stellenbosch University, Stellenbosch 7602, South Africa Received: August 19, 2014 / Accepted: September 21, 2014 / Published: December 25, 2014. Abstract: A fluctuating flow was used to investigate the thermo-fluid characteristic of a regenerative heat exchanger assembly designed, modelled, built and constructed for the used in Stirling engines applications. Vibration of the regenerative heat exchanger assembly was a problem to deal with during the experimental investigation. Hence, a dynamic analysis of the regenerative heat exchanger assembly was undertaken. The main sources of excitation in vibrations of the regenerative heat exchanger assembly were investigated and calculated based initially on the empirical correlations provided in the literature. Thereafter, a mathematical model of the regenerative heat exchanger assembly was developed based on the energy equations for each moving part of the assembly. The kinetic and potential energy equations were formulated for each moving part of the regenerative heat exchanger assembly. From the kinetic and potential equations, the Lagrange operator was defined, and then the Lagrange formulations were used to derive the differential equations representing the dynamic behavior of each moving part of the assembly. The differential equations were integrated to determine the system natural frequencies. These were then compared to the frequency on excitation in vibrations in order to predict the regenerative heat exchanger working conditions despite the existence of vibration in the system. Key words: Regenerative heat exchanger, vibrations, natural frequencies, dynamic behavior, Stirling engines.

1. Introduction When a mechanical component is subject to the action of external forces or torques, it deforms by developing internal stresses. These stresses may totally or partially balance the external forces. If partially balanced, a dynamic and/or thermodynamic state is reached. In this analysis, it is assumed that all deformations are elastic and linear. Any dynamic behavior is a source of vibrations in components, particularly in mechanical systems. Vibrations of mechanical systems cause noise, premature wear and fatigue [1]. Fatigue of material is a process of the generation and development of cracks, leading finally the breakage of components [2]. Due to frictions of mechanical components, fatigue causes energy dissipation that is harmful to the system efficiency [3]. Corresponding author: Franck Mulumba Senda, M.Sc., research fields: heat transfer and heat conversion. E-mail: [email protected].

It is important to reduce vibrations in a system by either resisting against their effects with a passive isolation or resisting against their causes by a good design of components or, if necessary, a good design of the entire mechanical system. Resisting against vibration in a mechanical design may be elaborated as follows: detect the main source causing vibrations of a mechanical system; analyze the transmissions of vibration in the system, and then predict the resonance possibilities, or design ways of reducing all vibrations, if possible [4]. The transmission of vibrations and the prediction of resonance may be done by the use of modal analysis [5]. Regenerative heat exchangers consist with three heat exchangers, namely, the heater, the regenerator and the cooler. The heater transfers heat from an external source to the working fluid contained in the expansion space. The cooler absorbs heat from the engine working fluid in the compression space and

938

A Theoretical Dynamic Analysis of a Regenerative Heat Exchanger Assembly in a Fluctuating Flow Regime

rejects it into the atmosphere through a coolant. Regenerators act as thermal sponges by alternatively accepting heat from the working fluid and rejecting heat back into the working fluid. The working fluid flows through the heater, regenerator and cooler in an irreversible process, because, it is largely affected by the pumping losses [6]. Pumping losses are generally described in terms of the flow’s viscous friction [7]. In Stirling engines applications, heat exchangers comprise the dead volume of the engine. They reduce the nominal output power by decreasing the engine compression ratio. In order to investigate the regenerative heat exchanger performances, a reciprocating system operating with a three-phase, asynchronous electric motor and a crankshaft was designed and built. The reciprocating system was subjecting all the assembly to numerous vibrations which required a particular attention. Thus, a preliminary dynamic analysis was developed to predict the stability of the regenerative heat exchanger experimental set-up assembly with respect to fatigue and indefinite life. The paper is organized as follows: Section 2 discusses the design and mechanical arrangement of the regenerative heat exchanger assembly; Section 3 discusses, first, the modal analysis of a mechanical system thereafter introduces the regenerative heat exchanger assembly main sources of vibrations before analyzing its dynamic behavior; and Section 4 gives conclusions of the findings.

2. Regenerative Heat Exchanger Assembly Fig. 1 shows the regenerative heat exchanger assembly that was used to evaluate the regenerative heat exchanger performances for the use in Stirling engine applications. This assembly comprises a regenerative heat exchanger and a reciprocator. In addition to the heat exchanger design, the reciprocator was designed to simulate the Stirling engine oscillating flow behaviour through the heat exchangers. It displaces air back and forth through the

Fig. 1

Regenerative heat exchanger assembly.

regenerative heat exchanger. The reciprocator was made using a stainless steel pipe of 300 mm internal diameter, 180 mm length and 10 mm wall thickness and containing an aluminium piston of 300 mm diameter and 45 mm width. The reciprocator piston was designed to displace 4 litres of air through the heat exchanger at a maximum operating frequency and pressure of 40 Hz and 300 kPa, respectively. The piston shaft is supported by the reciprocator closures through two SKF YAR2082F linear bearings. The linear motion of the piston shaft is obtained using an eight pole, 380 V/415 V or 525 V, three-phase, 50 Hz and 7.5 kW squirrel cage electrical motor (Weg made in Brazil, permit number: 4754/6862) through a crankshaft mechanism, mechanically linked to the flywheel. The flywheel shaft is supported by two SKF SYK40TR bearings fitted in housing units, and mechanically linked to the electrical motor shaft through an Arpex ARF-6 coupling. The crankshaft then converts the angular motion received from the flywheel into a linear motion directly transmitted to the piston shaft though a connector. The regenerative heat exchanger is a heater-regenerator-cooler assembly. The heater and cooler were manufactured and assembled in the same configuration. The heater and cooler are made of a grade 304 stainless steel shell tube of 133 mm external diameter, 135 mm length and 5 mm wall thickness (Fig. 2). The shell tube contains 10 copper pipes of


939

measurements. The analytic modal analysis establishes the theoretical or mathematical modelling for the dynamic behavior of a mechanical system, allowing the frequencies response analysis through an appropriate mathematical tool [2]. 3.1 Analytical Analysis

Fig. 2

Heater and cooler details.

20 mm internal diameter, 100 mm length and 1 mm wall thickness. The regenerator is made of a grade 304 stainless steel tube of 125 mm internal diameter, 100 mm length and 7.5 mm wall thickness. The regenerator is filled with 303 60-mesh offset woven copper wire laminating screens. The heater, cooler and regenerator flanges are bolted together with M8 stainless bolts. All flanges have a 40-durometer, peroxide cured, and high-temperature-resistant silicone rubber compound gasket sandwiched between them. The heat exchanger is fitted to the assembly support with M8 bolts, through a bracket.

3. Modal Analysis of a Mechanical System Modal analysis is a tool that offers knowledge of the characteristics of a machine, a structure or a mechanical system. Through modal analysis, the operating conditions and factors influencing the vibration behavior of a mechanical system may also be determined. It allows predicting any eventual damage of a particular component in the system and/or the entire system. At the stage of a preliminary design for a new mechanical system, modal analysis allows for the sizing and the definition of its optimal operating conditions. There are two types of modal analysis, the experimental and the analytical modal analysis. Experimental modal analysis requires the realization of prototypes, from which, representative tests are performed to deduce a mathematical model corresponding to the theoretical model of the system. Experimental modal analysis must include vibration

A mechanical system may be considered as a system of n degrees of freedom, possessing n natural frequencies. To each natural frequency, there corresponds a natural vibration, the displacements of which define normal modes of vibration [4]. Normal modes of vibrations depend on masses, stiffness and their distributions on the system. A mechanical system may vibrate in a normal mode if only appropriate initial conditions of vibrations are reached. But if the system is subject to some external force, such as torque, vibrations comprising all system normal modes will exist [5]. Forced vibrations of a mechanical system in a simple harmonic excitation occur at a frequency of excitation. If there is coincidence between one of the natural frequencies and one of the excitation frequencies, there is resonance. Resonance causes damage in any mechanical system, therefore, a damper should be added to the system to reduce the amplitude of vibration by creating a phase shift of the response of the system [2]. 3.2 Main Sources of Vibrations To comprehend the analysis of the dynamic behavior of a mechanical system, special attention must be paid to major sources of excitation in vibration, the components of liaison and components containment of the system. In the case of the Regenerative heat exchanger experimental assembly, the main sources of excitation in vibration are: the shafts and couplings, the bearings and the electrical motor and the heat exchanger working spaces. 3.2.1 The Shafts and Couplings Not only do shafts transmit vibrations, they are also sources of vibrations. Notwithstanding the care given

940


to the construction of a mechanical system, it is not possible to align the shaft axis of rotation with the centre of gravity of each of its parts. The deformation of the shaft during rotation results in vibrations. Generally, the vibrations arise from machining defects, shaft installation or assembly. During operation, shafts may also deform due to an asymmetric heat distribution [3]. Couplings may also be sources of vibrations due to, bad centring of plates: a defect of parallelism and a failure of alignment of axis in rotation defined by two angles. These two angles are the angle of inclination corresponding to a deviation angle in the plane of the rotation axis, and the angle of deviation in the plane normal to the previous [8]. The shaft and coupling failure results in vibrations of the system in rotation; it therefore vibrates at the frequency of rotation as given in Eq. (1) with N is the number of revolution per minute. (1) It is convenient to consider the frequencies of excitation in vibration for the shafts and couplings equal to the double, and sometimes, even to the triple and quadruple, of the frequency of rotation ω [5]. Table 1 summarizes the values of the frequency of excitation in vibration for the shaft and the coupling. 3.2.2 The Bearings Bearings are a compulsory passage of vibrations. The failure mode in bearings is often explained by the degradation process. Indeed, bearing degradation generally results in a subsurface or a surface fatigue of one of the ball-races. Thus fatigue cracks occur and propagate until failure occurs. Shocks due to bearings failure excite defective frequencies, which depend on the number of rolling elements Nb, the rotational speed ω = 149.2 rad/s and the geometrical dimension of the bearing, such as, the rolling element diameter d, the bearing pitch diameter D and the contact angle φ . The bearings frequencies of excitation in vibration as given in Table 2 may be determined as [9]:

Table 1 Frequency of excitation in vibration of shaft and coupling. Type of component Shaft and coupling Table 2

ω (rad/s)

2ω (rad/s) 3ω (rad/s) 4ω (rad/s)

149.2

298.5

447.7

596.9

Frequency of excitation in vibration of bearings.

N

d (mm) D (mm)

ω1 (rad/s) ω2 (rad/s) ω3 (rad/s)

33

40

1514.5

90

3409.9

932.2

For the outer race defect: 1

cos

(2)

1

cos

(3)

cos

(4)

For the inner race defect:

For the rolling defect: 1

3.2.3 The Electrical Motor The electromagnetic actions of parasitic induction forces in the electrical motor generally originate due to a deficiency in the gap and a failure of the stator and/or the rotor. The electrical motor failures generate vibrations with excitation frequencies as summarized in Table 3. The excitation frequencies given in Table 3 are computed as [10]: The vibration frequency: (5) The asynchronous speed: 1

(6)

The synchronous speed: (7) where, f is the frequency, poles, is the slip and

is the number of pairs of is the number of poles.

3.2.4 The Heat Exchanger The excitation in vibration in the heat exchanger is due to the gas-spring effect and the viscous effect in the heat exchanger working spaces. All dynamic gas spring spaces, including reciprocators vibrate at the

A Theoretical Dynamic Analysis of a Regenerative Heat Exchanger Assembly in a Fluctuating Flow Regime Table 3

Frequency of excitation of the electrical motor.

f (Hz) 50

2

5

(rpm) ω (rad/s)

(rpm)

(%) 4

1,500

1425

31.42

Table 4 Frequency of excitation in vibration of the heat exchanger. Control volume Expansion Heater Regenerator Cooler compression

Pmax (Pa 114,000 113,100 111,800 110,250 109,100

(m) 0.03 0.03 0.03 0.03 0.03

Ap m2 0.1029 0.023 0.049 0.023 0.1029

m (kg) 0.0034 0.0001 0.0003 0.0002 0.0034

ω (rad/s) 10724.1 29446.7 24671.6 20557.8 10491.1

natural frequency of gas. At the point of vibration, the displacement and the resulting pressure amplitude is maximum. The frequency of vibration in the heat exchanger is summarized in Table 4. The heat exchanger natural frequencies are computed as [11]:

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forces acting on the system. The Lagrange formulations will be applied to the heat exchanger assembly model shown in Fig. 3 to develop its dynamic behaviour characteristic equations in the form of Eq. (9). Lagrange’s formulation allows the derivation of all the equations of motion of the system, from three scalar equations: the kinetic energy, the potential energy and the virtual work due to non-conservative forces. From the kinetic and potential energy of each of the moving parts of the heat exchanger assembly model shown in Fig. 3, the Langrage operator will be defined. Thereafter, from the Lagrange operator definition, a Lagrange formulation will be established to determine the dynamic behavior equations of the system. The dynamic equations of the system will be simplified considering the following assumptions. As

(8)

all shafts in rotation are short and rigid, only

where, Pmax is the maximum pressure, is the displacement, is the working fluid mass and Ap

deformation in torsion will be considered. Bending deformation defined by the deformation ycr and the

is the heat exchanger cross sectional area. 3.3 The Dynamic Behavior of the Regenerative Heat Exchanger Modelling of a continuous system (mass and stiffness distributed throughout the element) provides analytical results based on continuum mechanics and analytical mechanics. These analytical results are general, but necessary in the design of a mechanical system. However, the vibrations of complex structures admit a large number of degrees of freedom and require the use of a computer program to solve their characteristic differential equations. Differential equations characterizing the dynamic behavior of a mechanical system are summarized by the way of the following equations [2]:

angle of bending deformation θcr will be considered for the crankshaft. As the piston shaft is short and very rigid, its bending deformation is neglected, and it will only be considered as a connecting element between the piston and the crankshaft, and therefore characterized only by its stiffness [2, 12]. Considering the regenerative heat exchanger assembly mathematical model as shown in Fig. 3, the kinetic and potential energy equations for each moving part of the regenerative heat exchanger assembly are derived in Eqs. (10)-(23) as follow. The kinetic energy of the electrical motor and shaft:

(9) where, x, x and x are the displacement, velocity and acceleration, respectively. [M], [C] and [K] are the matrix mass, damping and stiffness, respectively, and f(t) is a vector representing the effect of the external

Fig. 3 Dynamic model of regenerative heat exchanger assembly.

942

A Theoretical Dynamic Analysis of a Regenerative Heat Exchanger Assembly in a Fluctuating Flow Regime 1

Ek,m = Jm φ2m

(10)

2

The potential energy of the electrical motor and shaft: 1

Ep,m = kt,m φ2m

(11)

2

The kinetic energy of the coupling: 1

Ek,co = Jco φ2m

Ek = Ek,m

φ2a

2

Ep,co = kc,co φm

1

2

Ep = Ep,m

The potential energy of the shaft: 1

Ep,a = kt,a φ2a

(15)

2

1

L

2

2

Ek,fw = Jfw φ2a

2

(16)

The potential energy of the flywheel: 1

L

2

2

Ep,fw = ke,fw φa

2

θcr

(17)

The kinetic energy of the crankshaft: 1

L

2

2

Ek,cr = mcr y2cr

2

1

L

2

2

Ep,cr = kb,cr ycr + θcr

2

(19)

The kinetic energy of the piston: mp x2p

(20)

The potential energy of the piston: 1

kc,c kb,ps

2 kc,c kb,ps

1

Ek,g = mg

x2p

xg xp x2p 3

2

(21)

(22)

The potential energy of the gas: 1

Ep,g = kg x2g 2

Ep,p

Ep,g

L = Ek

Ep,a

Ep,co

Ep,fw

(23)

Ep

(26)

The Lagrange formulations of the regenerative heat exchanger assembly are given as: d

∂L

∂L

∂W

dt ∂xj

∂xj

∂xj

= fj t

(27)

where, ∂xj and ∂xj are the change in the vector displacement and velocity, ∂L is the change in the Lagrange operator, ∂W is the change in the dissipation vector and fj t is a vector representing the system external forces. For a no dissipative system, the Lagrange formulations may be reduced as [2]: d

∂L

∂L

dt ∂xj

∂xj

= fj t

(28)

Substituting Eq. (26) into Eq. (28) and rearranging, the equations of motion for each component of the system are derived as: ∂L d ∂L = Jm Jco φm kt,m kc,co φm ∂φm dt ∂φm kc,co φa = θmax sin ωt Table 5 assembly. Torsion

The kinetic energy of the gas: x2g

Ep,cr

is:

(18)

The potential energy of the crankshaft:

Ep,p =

Ek,a

(25)

The kinetic energy of the flywheel:

mps

Ek,g

(13)

(14)

2

2

Ek,p

Using Eqs. (24) and (25), the Lagrange operator

Ek,a = Ja φ2a

1

Ek,cr

(24)

The kinetic energy of the shaft:

Ek,p =

Ek,fw

The total potential energy is:

φa

2

Ek,co

(12)

The potential energy of the coupling: 1

The mass and mass inertia of the regenerative heat exchanger components are calculated from their geometry while the stiffness of components are calculated as summarized in Table 5. From Eqs. (10)-(23) of the regenerative heat exchanger assembly, the total kinetic energy is:

πGd4j kt,j = 32Lj

(29)

Stiffness calculation summary exchanger Compression or extension πEd2j kc,j = 4Lj

Bending kb,j =

3πEd4j

4L3j Bending Crankshaft 6EWH3j kb,j = L3j

943


d ∂L dt ∂φa kt,a d ∂L dt ∂θcr

∂L = Jfw ∂φa ke,fw

kc,co φa

L 2

L

θcr = 0

k y 2 b,cr cr

kb,cr ycr

d ∂L dt ∂xp

kc,co φm (30)

L k φ 2 e,fw a =0

kb,cr

(31)

L θ =0 2 cr (32)

ω 2 JM

kM

-kc,co 0

ω 2 JA ke,fw

0

0

0

0

0

0

6

d ∂L dt ∂xg

L 2

mg xg

kc,c kb,ps x = kc,c kb,ps p

∂L 1 = mg xg ∂xg 3

1 mx 6 g p

0

0

0

0

0

0

0

0

k 2 b,cr

k 2 b,cr kb,cr ω2 mcr

0

0

0

0

ke,fw

L

2 2

kFW

ω JFW L

0

4. Conclusions The frequencies of excitation in vibration of the regenerative heat exchanger assembly were calculated. The dynamic behavior analysis of the assembly was discussed based on the analytical modal analysis. It was found that all the regenerative heat exchanger assembly excitations in vibration frequencies are small compared to the smallest natural frequency—ω1 = 35,000 rad/s. The system vibrations will not reach resonance, therefore, the design is safe. There is resonance only when there is coincidence between one of the excitation frequencies in vibration and one of the natural frequencies of the system [12]. The reason why the natural frequency is so high is that the stiffness of the materials used in the design of the regenerative heat exchanger is high. Vibrations dealt with during testing would not damage the assembly. It is also noticed that the frequency of excitation in vibration for the regenerative heat exchanger working spaces is too high compared to the frequency of

1 m x 3 g p

mp

0

(33) kg xg = 0

(34) The determinant of the characteristic matrix of Eqs. (15)-(20) as given in Eq. (35) gives the frequency equation of the system. The first solution of the frequency equation gives the smallest system natural frequency—ω1 = 35,000 rad/s.

0

-kc,co kA

∂L = mps ∂xp 1

Jfw θcr

ke,fw θcr

∂L = mcr ycr ∂ycr

Jco φa ke,fw

∂L L2 = m 4 cr ∂θcr kb,cr

d ∂L dt ∂ycr

Ja

L

kc,c kb,ps kc,c +kb,ps

ω2 M

mg ω2 6

0

ω2 kg

(35) mg 6

mg ω2 3

excitation in vibration of other moving parts. This means that high frequencies will be required to excite the heater, cooler and regenerator working fluid in vibration, therefore, vibrations at low frequency will not affect the working fluid dynamic behavior in the heat exchanger.

Acknowledgments The author’s thanks go to Necsa for financial support and Stellenbosch University for academic guidance.

References [1] [2]

[3] [4]

Mulapi, W. 2002. Cours d’equilibrage et Vibration des Machines. Mbuji-Mayi: Universite de Mbuji-Mayi. Del, P. M., and Pahud, P. 1988. Mechanique Vibratoire, System Discrets Lineaires. Lausanne: Presses Polytechniques et Universitaires Romandes. Morel, J. 1979. “Surveillance Vibratoireet Maintenance Predictive.” Technique de l Ingenieur 6 (100): 1-20. Senda, F. M. 2004. Analyse Dynamique du Reducteur de Vitesse Hassen Patent a la Commande pour Transporteur

944

[5]

[6] [7]

[8]

A Theoretical Dynamic Analysis of a Regenerative Heat Exchanger Assembly in a Fluctuating Flow Regime a Bande, Cas du Transporteur n˚3 de l Usine Central de la Miba. Mbuji-Mayi: Universite de Mbuji-Mayi. Courrech, J., and Ronald, L. 2002. Conditioning Monitoring of Machinery. Harris’ Shock and Vibration Handbook. New York: McGraw Hill. Urieli, I. 1977. “A Computer Simulation of the Stirling Cycle Machine.” Ph.D. thesis, University of the Witwatersrand. Minassians, A. D. 2007. “Stirling Engines for Low-Temperature Solar Thermal Electric Power Generation.” Ph.D. thesis, University of California. Blanc, H. 2004. Dynamique des Rotor en Torsion-Type d Excitation Permenante. Accessed January 16, 2011.

http://www. techniques-ingenieur.fr/. Kilundu, B., Dehombreux, P., and Chiementin, X. 2009. “Early Detection of Bearing Damage by Means of Decision Trees.” Journal of Automation, Mobile Robotics & Intelligent Systems 3 (3):70-4. [10] Briget, R. 1980. Vibration des Machines Tournantes et des Structures, Tome II. Technique et documentation. [11] Smith, G. R. 2006. “Building, Testing and Modelling of a Pulse Tube Cryogenic Cooler.” M.Sc. thesis, University of Stellenbosch. [12] Meirovitch, L. 2001. Fundamentals of Vibrations. New York: McGraw-Hill. [9]

D


DAVID

PUBLISHING

Gas Turbine Operation Offshore: Online Compressor Wash Operational Experience Stian Madsen1 and Lars E. Bakken2 1. Statoil ASA, Trondheim N-7005, Norway 2. Department of Energy and Process Engineering, Norwegian University of Science and Technology, Trondheim N-7491, Norway Received: August 08, 2014 / Accepted: August 28, 2014 / Published: December 25, 2014. Abstract: Online compressor wash for six GE LM2500PE engines at a Statoil North Sea offshore field is analyzed. Three engines are generator drivers whilst three engines are compressor drivers. Two of the compressor drive engines are running at peak load (T5.4-control), hence production rate is limited by the available power from these engines. All the six engines analyzed run continuously without redundancy, hence gas turbine uptime is critical for the field’s production and economy. The performance and operational experience with on-line wash at different water-to-air ratios and engine loads, as well as economy potentials related to successful on-line wash are given. This work is based on long-term operation with on-line wash, where operational data are collected and performance analyzed, over a 4-5 year period. All engines are operated with four-month intervals between maintenance stops, where off-line crank-wash is performed as well as other necessary maintenance and repairs. On-line wash is performed daily between the maintenance stops at full load (i.e., normal operating load for the subject engine). To keep the engine as clean as possible and reduce degradation between maintenance stops, both an effective on-line water wash system as well as effective air intake filter system, are critical factors. The overall target is to maintain high engine performance, and extend the interval between maintenance stops through effective on-line wash. It is of vital importance to understand the gas turbine performance deterioration. The trending of its deviation from the engine baseline facilitates load-independent monitoring of the gas turbine’s condition. Engine response to water injection at different loads and water-to-air ratios, as well as engine response to compressor deterioration is documented and analyzed. Instrument resolution and repeatability are key factors required in order to obtain reliable performance analysis results. Offshore instrumentation on older installations is often limited to the necessary instruments for machine control/protection, and additional instruments for effective performance monitoring and analysis are often missing or, if installed, have less accuracy. As a result of these analyses, a set of monitoring parameters is proposed for effective diagnosis of compressor degradation. Avenues for further research and development are proposed in order to further increase the understanding of the deterioration mechanisms and the gas turbine performance and response. Key words: Gas turbine performance, water wash, inlet air filter system.

Nomenclature N1 N2 P PS T RH

GG rotor speed (rpm) LPT rotor speed (rpm) Pressure (mbar or bar) Pressure static (bar) Temperature (°C or K) Relative humidity (%)

Subscripts c

Corrected parameter

Corresponding author: Lars E. Bakken, professor, research field: thermal turbomachinery. E-mail: [email protected].

i p η κ h

Isentropic Polytropic Efficiency Real air heat capacity ratio (kappa) Mass specific enthalpy

LM2500 Gas Turbine Station Numbers 0 1 2 3 5.4 8

Ambient condition Intake plenum condition HPC inlet condition HPC discharge condition LPT inlet condition LPT discharge condition

Gas Turbine Operation Offshore: Online Compressor Wash Operational Experience

946

Acronyms GG HPC HPT LPT PT CDP GE RR OEM R-MC VSV ISO WHRU SAC DLE MCS PLC ASME

Gas generator High pressure compressor High pressure turbine Low pressure turbine Power turbine Compressor discharge pressure General Electric Rolls-Royce Original equipment manufacturer Rivenæs motor-clean Variable stator vanes International Organization for Standardization Waste heat recovery unit Standard annular combustor Dry low emission Maximum continuous speed Programmable logic controller American Society of Mechanical Engineers

1. Introduction Oil and gas production on several Statoil North Sea offshore installations is limited by the gas turbine power available, and any deterioration in gas turbine performance directly affects production rates. Fouling in the compressor section of the gas turbines is the main cause of performance deterioration, and the fouling is removed by water wash. The most important finding from previous research work [1-3] is that the water-to-air ratio (by mass) during online washing should be increased compared to current online water wash systems. Water-to-air ratios of up to 3% (mass fraction) have been tested for online water wash on a GE J85-13 jet engine, and the tests revealed that online water wash at such high water-to-air ratios gave a significant increase in the power recovery after online water wash compared to online water wash at lower water-to-air ratios. Efficient online water wash will reduce the gas turbine performance deterioration caused by contaminants in the intake air, hence the power available and the efficiency of the gas turbine will increase. The reduction in performance deterioration will allow for extended intervals between stoppages for offline water

wash. Efficient online water wash will increase the production in installations where the oil and gas production rates are limited by power, by increasing the average power available. The benefit from efficient online water wash in installations with 100% gas turbine redundancy will mainly be increased efficiency which implies lower fuel consumption and exhaust emissions and hence lower costs for fuel, CO2 and NOx taxes and reduced environmental impact. In order to minimize compressor fouling, it is important that both intake air system and water wash are evaluated as equal important factors. Previous research [4, 5] on offshore intake air filters has shown large variations in efficiency for various filter systems as currently used in the North Sea. This demonstrates the importance of an efficient intake air filter system, in

terms

of

optimum

design,

operation

and

maintenance routines to minimize compressor fouling and degradation. The paper is organized as follows: Section 2 is the review of Statoil online wash experience; Section 3 is the engine description; Section 4 describes water wash system; Section 5 describes engine response to deterioration and water ingestion; Section 6 introduces process simulations; Section 7 states the performance trends/analysis; Section 8 depicts instrumentation; Section 9 introduces the economical aspects; Section 10 gives conclusions; and Section 11 gives the recommendations for further work.

2. Review of Statoil Online Wash Experience Statoil has extensive operating experience of both offline and online water wash regimes. Offline wash is generally very efficient in terms of regaining efficiency, if the engine does not have any mechanical damage (e.g., blade tip rub) that reduces performance. The performance gain can be clearly seen on HPC efficiency trends. Typically a detergent solution (R-MC), mixed with water, is used. It is injected at a 3 min low-speed crank-sequence, followed by one to two sequences with clean water, and a final drying


sequence. Both the detergent/water mix and the clean water are pre-heated to approximate 60 °C before injection. Pre-heating of the water to this temperature level is carried out for both offline and online water wash, and is based on experience. Pre-heated water yields a much more efficient compressor cleaning compared to cold/ambient water temperatures. The disadvantage of frequent offline/crank-washing is obviously that production has to be halted for several hours, if operating without redundancy. With redundancy, the engine down-time for offline wash is of less importance. An offline wash is normally conducted in combination with other necessary maintenance tasks, such as bore scope inspection, intake air filter change, exhaust duct inspection. Online water wash discussed in this paper is defined as water injection at full load (i.e., normal operating load for the subject engine), and not idle wash (typically 5,000 rpm GG-speed for LM2500), which is another online wash regime. The advantages of online wash at full load are that there is no impact on engine downtime and production can therefore be maintained. Idle washing implies downtime not only during the wash sequence itself, but also for a time-consuming period during the ramping-up and -down of the load on the train and production wells. Depending on the train/process/well configuration, this may take several hours, especially on compressor trains. But for installations that run frequent offline wash intervals and/or have redundancy, idle washing might represent a preferable and economical washing regime in addition to offline washing. Statoil has some operational experience of idle washing from test periods offshore, with typical intervals of 1,000 running hours (offline/crank-wash interval 3,000 h). These tests have shown a potential for power recovery since the water-to-air ratio is high (fixed water flow rate). However, due to the disadvantage of engine downtime, idle washing has not been taken further to offshore operational routines in Statoil. Online water wash is not widely used on Statoil

947

North Sea offshore fields, but a couple of installations have extensive operating experience of online wash at full load on GE LM2500PE and RR RB211-24G engines, respectively. The operating hours accumulated by online wash are to date well above 100,000 running hours, and the LM2500 engines by far have the highest portion of these operating hours. The water-to-air ratios have been 0.5%-1.0% (mass fraction), which is in the range of maximum recommended water from the OEM (GE/RR) guidelines. The general improvement has been cleaner engine on bore scope inspections and during visual observations of the engine intake. The performance gain has been documented by overall compressor efficiency trends in some operating periods, particularly when the load and other parameters are stable (e.g., no anti-icing bleed). But when these factors vary, it is more challenging to evaluate compressor efficiency and to obtain repeatable results between operation intervals. In the absence of conclusive results from offshore online water wash, Statoil has funded extensive research and experimental testing to determine the fundamental mechanisms of axial compressor performance deterioration and recovery through online washing.

3. Engine Description All engines analyzed are two-shaft LM2500PE type, with GE six-pack LPT. Depending on the load, the GG operates in the speed range 8,500-9,500 rpm, and LPT in the speed range 3,300-3,700 rpm. The generator drive engines, have a direct drive configuration from the LPT to generator, and operate at 3,600 rpm. These engines use compressor bleed air (CDP 16stg compressor air) for anti-icing protection. The bleed air for anti-icing is controlled by an on/off valve controlled by ambient temperature and humidity. Moreover, an orifice is used in order to minimize the bleed air consumption. The bleed air is finally routed to an anti-icing manifold upstream of the intake air filter vane separators. The generator engines seldom

948


run in T5.4 control, only occasionally when droop mode is used (T5.4 is set manually at a fixed value for one engine, while the other engine(s) handle load variation). Otherwise, isochronous-mode is the normal operating condition with equal load-sharing between the generators. The compressor drive engines have a speed-increasing gearbox between the LPT and compressor. The MCS and over-speed limit for the process compressor is normally set at the LPT shaft speed control (N2-control compensated for gear ratio), thus a margin is set for the LPT speed limit when choosing gear ratio in order to obtain MCS at the process compressor before the LPT speed limit occurs. These engines use the heating medium from the WHRU-system for anti-icing protection, a much more energy-efficient solution than that used in the generator engines described above. 3.1 Available Power and Control Modes The power available from the engine is highly dependent on ambient temperature. At low temperatures, the air density increases, hence the air mass flow increases. This again leads to more air feed to the combustion chamber and more power output is generated from the turbine. At very low temperatures, however, shaft power will decrease slightly. Anti-icing influences the curve when ambient temperature is below 4.4 °C and air humidity is high (Fig. 1). The typical power

Fig. 1

characteristics shown in Fig. 2 do not include anti-icing. Anti-icing will increase T2 and therefore reduce power output. Thus, the most energy-efficient operation point for North Sea ambient temperature is just above the upper anti-icing limit, since average relative humidity is typically above 70 %. The characteristics given in Figs. 3-5 for PS3, N1c and T5.4, respectively, are all at engine base load condition. Control limit for compressor discharge pressure (PS3), shown in Fig. 3, only occurs at very low ambient temperatures, below the typical annual ambient temperature range in the North Sea. Control limit for N1c speed (corrected GG speed) is shown in Fig. 4. This typically occurs at the same ambient temperature (and lower) as maximum PT shaft power. At very low ambient temperatures, the N1c speed will drop below the control limit. Control limit for T5.4 shown in Fig. 5, is the most common engine limitation for the typical annual ambient temperature range in the North Sea. At very low ambient temperature, T5.4 is not a limitation. However, at higher ambient temperature, T5.4 is the limiting parameter for the engine. The control limit of T5.4 is typically set in the range of 832-840 °C. For ambient temperature and operational conditions in the North Sea, the most common control limits are:  T5.4 control (835 °C);  N1-control (GG speed);  N2-control (MCS process compressor speed).

Icing conditions, function of ambient temperature and relative humidity.


Fig. 2 PT shaft power, function of ambient temperature.

Fig. 3

PS3, function of ambient temperature.

Fig. 5

T5.4, function of ambient temperature.

Fig. 6

Layout of the gas turbine intake air system.

949

for water that reaches the filters to be drained out on the upstream side of the filter elements. These filters are the final barrier before the airflow enters the gas turbine compressor and are promoted with an M6 rating in accordance with the European EN-779 standard [6]. The gas turbines have 30 filter elements arranged in five rows of six elements for combustion air and an additional row of six filter elements for cooling air to the gas turbine enclosure.

4. Water Wash System Fig. 4 Corrected GG speed, function of ambient temperature.

3.2 Inlet Air Filter Configuration The layout of the gas turbine intake air system is illustrated in Fig. 6. These systems rely on an efficient vane separator to remove the vast majority of water and humidity from the airflow before it reaches the high-efficiency filters. The high-efficiency filters are especially designed to withstand moisture, and seals on the bottom of each filter bag are intended to allow

Water supply is taken from platform fresh water distribution, which is produced from seawater by evaporators. Further, the water is led through a set of DI-filters (de-ionization or de-mineralization) and a final particle filter before entering the water wash skid, in order to achieve the OEM water quality specification for online water wash. The layout is shown in Fig. 7. The water wash skid has two tanks (each with a 200 liter capacity), one tank for clean water (used for online wash and offline cleaning after crank soak


950

Water wash skid DI Particle filter filter

Discharge to bellmouth Fig. 7

Layout of the water wash system.

wash) and one tank for detergent/water mix (only used for offline wash). Thus, the risk of contamination of the clean water tank is avoided. The water is further pre-heated to 60 °C, before ingestion to the engine from the pressure outlet connection to the water wash nozzles assembled at the engine’s bell mouth. One water wash skid is typically used for several engines in the same platform module; hence a sequence of logic for solenoid valves, heaters and pump is programmed into the unit’s PLC. The unit is operated semi-automatically (local manual trigging of the sequence), in order to minimize the time consumption for platform operators to operate the system. A fully integrated system is also possible with the platform process control system, i.e., one which enables remote system operation from the platform control room, or by a programmed timer function. But a fully integrated system adds complexity to the system, as well as the risk of malfunction, and the operators lose hands-on operation of the system.

5. Engine Respons to Deterioration and Water Ingestion The control modes discussed previously in this paper are valid when the engine is in new condition (i.e., overhauled/after offline water wash cleaning). When the compressor section becomes deteriorated by deposits, the control modes will change. Engines typically compensate for a deteriorated compressor by increasing N1-speed to keep N2-speed/power output at the same level. In particular engines initially running in

T5.4-control (T5.4 maximum), will climb up against the N1-control limit. Thus the N1-control limit can occur before T5.4 maximum. This is typical when engines are not operated with online water wash. Thus, the target for online wash is to avoid such cases and run at T5.4-control limit continuously. However, if an N1-control limit occurs, some power margin can normally be gained by adjusting the VSV schedule to reach the maximum T5.4 limit again (if the VSV schedule is close to the overspeed side). This requires an adjustment of the VSV micro-adjust (or bracket in some cases) which is an on-engine manual adjustment (for base SAC engines). Thus, this operation requires ramping down to idle speed, or shutting down the engine, in order to enter the turbine enclosure compartment, which implies downtime. If the engine is stopped, an offline wash can be done simultaneously. If the engine is not stopped, the VSV adjustment is just a temporary compensation until the next offline water wash. Risks to be considered when running online wash are:  Cooled HPC casing, risk of rub;  Flame out;  Icing at HPC inlet (cold ambient conditions);  Long-term effects corrosion/erosion;  Staging/burning mode change (DLE engines). Four cases with actual operating data are analyzed:  Case #1: low water rate/part-load operation;  Case #2: low water rate/peak-load operation;  Case #3: high water rate/part-load operation;  Case #4: high water rate/peak-load operation. Two sets of water wash nozzles are used, one for low rate and one for high rate. High water rate is 30 liter/min which yields approximate 0.75% water-to-air ratio (by mass fraction) at engine base load. Corresponding ratio at low water rate is approximate 0.45%, by water rate of 18 liter/min. The water rate is fixed through the pump/nozzle configuration; hence, the water-to-air ratio will increase at part-load operation. Thus, the highest water-to-air ratio at approximate 1.00% is for case #3.


Discussion The operational experience with online wash of LM2500 Base SAC engines at these water rates has not shown any disadvantageous impact on the operation of the engine/train. The transient conditions described in the analyzed cases, are handled well by

951

the impact of temperature-drop (particularly T3) is less than in part-load operation. When the engine is running at T5.4 control (T5.4 maximum) prior to water ingestion (case #2), and the T5.4 drops during water wash, the control system demands more power from the turbine, hence, T5.4 will increase slightly to compensate for the initial drop.

the control system and do not influence the output N2-speed or power demand in a manner that poses a

6. Process Simulations

risk for the operation (e.g., engine trip). When water

A process simulation model of the LM2500 compressor is established in Aspen HYSYS, with humid air inlet to simulate real inlet air conditions offshore, as well as added water for online washing. The process simulation analysis is performed to validate the compressor response in order to compute the response when the water-to-air ratio is further increased (up to 3%, future target based on previous research [1-3]) and inlet conditions vary (T2, P2, RH). The analysis is even more important for DLE engines, with a more sophisticated fuel and control system, thus the risk of distribution of the burning-modes/staging during water ingestion. Each of the empirical cases in the previous section in this paper is simulated in steady state condition, in order to compare results of how the HPC discharge condition is affected during water ingestion. The EOS (equation of state) used is the SRK (Soavo-RedlichKwong), further, real air heat capacity ratio (κ) and correction factors are derived using the ASME and Schultz methods [7].

ingestion is shut off, the engine stabilizes at the initial condition as before the online wash sequence. Online wash is operated without any restrictions (e.g., fixed parameters) in the control system. However, as a precaution, the trip level for T5.4 has been increased, to avoid trips in transient conditions during online water wash, in particular when the water is shut off. N1-speed tends to increase during the wash sequence, ref. Fig. 8 below, but stabilizes close to initial condition after the water is shut off. The same transient pattern is observed for all four cases (Figs. 9-20); T3 decreases, PS3 increases slightly and T5.4 decreases during water ingestion. The higher the water ratio, the higher the temperature drops of T3 and T5.4. The T3 and T5.4 temperature drop is in accordance with the thermodynamic theory, since the energy to evaporate the water is extracted from the air through the compressor. Thus, the PS3 increases due to higher mass flow through the compressor. When engine load is high,

Fig. 8

Variation of N1-speed during water ingestion.

952


Case #1

Fig. 9

Variation of T5.4 during water ingestion.

Fig. 10

Variation of T3 during water ingestion.

Fig. 11

Variation of PS3 during water ingestion.

Table 1

Engine parameters and water wash parameters.

Water injection T: 60 °C P: 60 bar Rate: 18 liter/min Duration: 3 min

Engine data T2: 10.8 °C P2: 1,001 mbar RH: 87.6% T3: 351 °C PS3: 11.7 bar T5.4: 686 °C N1: 8,474 rpm

Change T5.4: ~30 °C T3: ~30 °C PS3: ~0.15 bar


Case #2

Fig. 12


Fig. 13


Fig. 14


Table 2



Engine data T2: 11.1 °C P2: 978 mbar RH: 78.1% T3: 417 °C PS3: 15.9 bar T5.4: 834 °C N1: 8,986 rpm

Change T5.4: ~25 C° T3: ~7 °C PS3: ~0.40 bar

953

954


Case #3

Fig. 15


Fig. 16


Fig. 17


Table 3






Case #4

Fig. 18


Fig. 19


Fig. 20


Table 4





955

956


Summary of simulation results are shown in Table 5. An iterative method have been performed in order to optimize and tune the model to compensate for the added water and speed variations during the water sequence. A single performance point is established based on operating data for each cases, further, the performance point above and below (at fixed speed) is set based on experience and iterations to established a performance map around the operating point. The T3 simulated values are within 0.7% deviation of for all cases. PS3 values are slightly over-predicted in the simulations, except for case #3 (which has the highest water-to-air ratio).

Table 5 Case 1 2 3 4

Summary of simulation results.

T3 sim. (°C) 320 409 282 394

T3 dev (%) -0.6% -0.5% +0.7% -0.3%

PS3 sim. (bar) 13.5 17.8 11.4 16.5

PS3 dev. (%) +4.5% +3.5% -4.2% +1.9%

Sensitivity Analysis Compressor air flow is a calculated value based on the energy balance of the GG (iterative method), from the performance software used on the subject offshore field. In the simulations, inlet air humidity is assumed to be equal to ambient condition (in the absence of an inlet plenum RH measurement), hence the inlet air filter system (vane separators/filters) is assumed to remove large droplets and not change the humidity significantly. Furthermore, compressor head and efficiency are calculated using empirical data input to Aspen HYSYS in steady-state condition without water ingestion, and a compressor operating point/map is established. In the water ingestion simulations, the HPC discharge pressure and temperature are calculated values based on the given compressor map, thus an error in air flow and humidity implies uncertainties in the HPC discharge calculations. Furthermore, the operating point/map will change to some degree when water is added during water ingestion. Since the above mentioned parameters introduce some uncertainties to the simulation model, a sensitivity analysis is performed for inlet air flow and humidity for case #1. A deviation of ±1% for inlet air flow and ±10% for inlet RH, is applied in the simulation model to determine the effect on HPC

Fig. 21

Variation of T3/PS3 vs. air flow.

Fig. 22

Variation of T3/PS3 vs. air humidity.

discharge condition (T3, PS3). As shown in Figs. 21 and 22, deviation of air flow implies the largest effects on HPC discharge condition, in particular for T3.

7. Performance Trends/Analysis In the performance software tools used in the subject offshore field, gas turbine compressor efficiencies are derived from the following relations:


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Offline wash

Isentropic enthalpie (h3i) is derived as a function of the T3i-value, furthermore, kappa (κ) for air is calculated using the mean temperature over the compressor (T2, T3). The efficiency trends analyzed are based on relative change from a baseline, since the absolute value can vary from one engine to another and thus, are not of such interest. The baseline is defined as a clean engine after offline/crank wash, and is set at 0. Further, the HPC efficiency is ISO-corrected against T2. However, this type of ISO-correction does not result in any significant difference compared to the HPC efficiency without the correction, thus, this parameter is not very useful in this kind of analysis [8].

Fig. 23

HPC efficiency—no online wash.

Offline wash

Fig. 24

HPC efficiency—online wash low rate.

Long Term Trend Data Fig. 23 shows the trend data for HPC efficiency from an engine operated without online wash. The degradation over an operational period of four months between offline washes is approximate 4.5% from the baseline. The efficiency gain of approximate 4% after offline wash can be clearly seen in the figure as well. Fig. 24 shows the trend data for HPC efficiency from an engine operated with a daily online wash at low water rate over a four-month period between offline washes. The degradation is approximate 3%. Fig. 25 shows the trend data for HPC efficiency from an engine operated with daily online wash at high water rate over a four-month period among offline washes. The degradation is approximate 2%. Again, the efficiency gain of approximate 2% after offline wash can be clearly seen in the figure. These long-term trends document that a high water-to-air ratio is advantageous for achieving

Offline wash

Fig. 25

HPC efficiency—online wash high rate.

compressor degradation as low as possible, hence, the potential to extend shut-down interval for offline/crank wash. This is in accordance with previous research [1-3]. However, not all operational periods (four-month intervals) yield conclusive and repeatable results. In particular when engine load and ambient conditions vary, it is challenging to evaluate compressor efficiency and obtain repeatable results between operation intervals. Load-independent correction factors/algorithms should be further investigated, as well as correction factors for bleed air from the compressor (e.g., anti-icing, rig air and

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engine cooling). The traditional ISO correction for standard ambient conditions is not sufficient for this type of performance analysis [8].

8. Instrumentation Instrumentation on older offshore installations is often limited to the necessary instruments for machine control/protection, and additional instruments for effective performance monitoring and analysis are often missing or, if installed, have less accuracy. LM2500 SAC engines are quite flexible regarding fuel flow/composition. These values are typically programmed once in the fuel controller during commissioning, thus, there is no requirement for measuring online gas-flow for fiscal quality, nor is there a need for a gas chromotograph/calorimeter to gauge online fuel-gas composition (as is required for DLE engines). Inlet depression as well as inlet plenum temperature, pressure and humidity are other typical parameters which are not available. Thus, inlet air flow calculation implies inaccuracy, which in the next phase implies inaccuracy for compressor head and efficiency calculations. In order to achieve more accurate air flow and compressor head calculations, it is recommended to have absolute pressure transmitters for P2 (mbar) and PS3 (bar), with high resolution and as short impulse tubing lines as possible (in addition to inlet depression measurement). The above mentioned monitoring parameters are suggested for effective diagnosis of compressor degradation.

9. Economical Aspects The economic potential of running online water wash is dependent on several factors, such as field layout, engine/train configuration, the number of engines running at peak load, whether the performance gain is utilized by longer intervals between maintenance stops (offline wash), or if the performance gain alone is utilized by keeping the same maintenance stop interval.

For the typical North Sea gas/condensate field analyzed in this paper, an annual production gain of some 50 MSm3 of gas and some 400,000 barrels of condensate can be achieved, just by increasing maintenance stop intervals from four to six months. With a current EU gas sale price of 40 US cents/Sm3 and USD 110/barrel of condensate, this implies some USD 64 million in annual savings. This is considered to be a conservative estimate, as maintenance cost savings (labor hours/spare parts) and daily production gains through higher power availability are not included in the calculations, nor are fuel and CO2/NOx tax savings.

10. Conclusions Online water wash has shown great potential in keeping turbine performance high and increasing compressor efficiency. It is, therefore, possible to increase offline wash intervals without running the compressor into a severe fouling condition. However, great care has to be taken when choosing the water wash system design, particularly the water flow rate, but also the water temperature and pressure as well as the system design which must include proper freezing protection for North Sea conditions. Inlet air filter systems, as well as operation and maintenance routines, are of equal importance in achieving the best possible results in keeping the engine clean. The operational experience analyzed in this paper, documents that a high water flow rate (water-to-air ratio) is a key parameter to achieve increased power recovery and reduce long-term deterioration. However, running at too high rates may cause operational issues, as well as long-term effects such as erosion/corrosion to the engine components. At the water rates analyzed in this paper, no such negative long-term effects have been seen. Finally, the correct monitoring parameters and performance software tools, as used to analyze the engines, are of vital importance to obtain the correct


overview of engine condition and evaluate the effect of online washing.

11. Recommendations for Further Work Process simulation software, such as Aspen HYSYS, is a very useful analytical tool in the evaluation and understanding of the fundamental mechanisms of axial compressor performance deterioration and recovery through online washing. The simulation model used for analysis in this paper, should be further developed to include the HPT and LPT turbines (and possibly the complete train), in order to obtain a better understanding for evaluating and optimize online water wash systems. In addition, each particular engine should be individually tuned in the simulation model. Online water wash testing at higher water-to-air ratios (above 1%) is recommended in order to document the engine response and ascertain whether increased power recovery can be achieved without compromising engine integrity. But long-term effects such as erosion/corrosion issues due to the high water-rate, in particular hot corrosion (HPT blades/nozzles and combustion chamber), need to be further evaluated. Load-independent correction factors/algorithms should be further investigated, as well as correction factors for bleed air from the compressor (e.g., anti-icing, rig air and engine cooling). Air inlet filter systems should be further evaluated and optimized. An upgrade to a higher filter class (F7 rating), is currently being evaluated for the subject

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offshore field analyzed in this paper, with future plans for field testing and comparison with the current M6 filter class.

Acknowledgments Colleagues in Statoil ASA are acknowledged for their valuable support and contributions to this paper.

References [1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

Syverud, E. 2007. “Axial Compressor Performance Deterioration and Recovery through Online Washing.” Ph.D. thesis, NTNU. Syverud, E., and Bakken, L. E. 2005. “Online Water Wash Tests of GE J85-13.” Presented at the 2005 ASME Turbo Expo: Power for Land, Sea and Air, Nevada, USA. Syverud, E., Bakken, L. E., Langnes, K., and Bjørnås, F. 2003. “Gas Turbine Operation Offshore; On-line Compressor Wash at Peak Load.” Presented at the 2003 ASME Turbo Expo: Land, Sea and Air, Atlanta, USA. Brekke, O. 2011. “An Experimental Investigation of Offshore Gas Turbine Intake Air Filter Performance.” Ph.D. thesis, NTNU. Brekke, O., and Bakken, L. E. 2010. “Performance Deterioration of Intake Air Filters for Gas Turbines in Offshore Installations.” Presented at the 2010 ASME Turbo Expo: Power for Land, Sea and Air, Glasgow, UK. EN-779. 2012. “Particulate Air Filters for General Ventilation—Determination of the Filter Performance.” CEN (European Committee for Standardization), Brussels, Belgium. Schultz, J. M. 1962. “The Polytropic Analysis of Centrifugal Compressors.” Journal of Engineering for Gas Turbines and Power 84 (1): 69-82. Krampf, F. M. 1992. “A Practical Guide for Gas Turbine Performance Field and Test Data Analysis.” Presented at the International Gas Turbine and Aeroengine Conference And Exposition, Cologne, Germany.

D


DAVID

PUBLISHING

Simulating the Inverse Kinematic Model of a Robot through Artificial Neural Networks: Complementing the Teaching of Robotics José Tarcísio Franco de Camargo1, Estéfano Vizconde Veraszto2 and Gilmar Barreto3 1. Department of Compouter Engineering, Regional Universitary Center of E. S. do Pinhal, E. S. do Pinhal 13990-000, Brazil 2. Department of Natural Sciences, Mathematics and Education, Federal University of Sao Carlos, Araras 13604-900, Brazil 3. School of Electrical and Computing Engineering, State University of Campinas, Campinas 13083-852, Brazil Received: November 11, 2014 / Accepted: November 21, 2014 / Published: December 25, 2014. Abstract: Teaching robotics necessarily involves the study of the kinematic models of robot manipulators. In turn, the kinematics of a robot manipulator can be described by its forward and reverse models. The inverse kinematic model, which provides the status of the joints according to the desired position for the tool of the robot, is typically taught and described in robotics classes through an algebraic way. However, the algebraic representation of this model is often difficult to obtain. Thus, although it is unquestionable the need for the accurate determination of the inverse kinematic model of a robot, the use of ANNs (artificial neural networks) in the design stage can be very attractive, because it allows us to predict the behavior of the robot before the formal development of its model. In this way, this paper presents a relatively quick way to simulate the inverse kinematic model of a robot, thereby allowing the student to have an overview of the model, coming to identify points that should be corrected, or that can be optimized in the structure of a robot. Key words: Robotics, artificial neural networks, engineering education.

1. Introduction The motion described by a manipulator robot can be represented through its direct and inverse kinematic models according to Ref. [1]. Obtaining the direct kinematic model is relatively simple, being defined by a set of transformations among the reference systems and their joints (or degrees of freedom). Through this model, we can determine the position of the tool at the free end of the robot knowing the position of its joints. The inverse kinematic model, in turn, allows us to determine the state of the joints of a robot according to the desired position for its tool. In this way, when we define a path for the tool, it is possible to determinate the set of positions of the joints that will allow the Corresponding author: José Tarcísio Franco de Camargo, Ph.D., research fields: computer graphics, automation and education. E-mail: [email protected].

robot to describe the desired motion. Obtaining the inverse kinematic model, however, is much more complex than obtaining the direct kinematic model, since it involves the solution of a nonlinear system of equations that can accept more than one solution. Even in relatively simple cases, as for the planar robot with two DOF (degrees of freedom) described below, the definition of the inverse kinematic model is not trivial. Thus, being able to predict the behavior of a robot, in a relatively simple way, before the formal development of its inverse kinematic model, may become a crucial factor for the success of a project. Through the use of ANNs (artificial neural networks), it is possible to simulate the behavior of a robot, by determining with relative precision the state of its joints, depending on the desired position for its tool, allowing that design failures can be detected, and

Simulating the Inverse Kinematic K Mo odel of a Robo ot through Artificial Neura al Networks: Com mplementing g the Teaching of Robotics s

points with possible optiimization cann be identifieed as well. So, as meentioned, thiss paper aims to introducee the subject of ANNs A in the context of teeaching robootics, aiming to contribute to t the form mation of fuuture professionalls that may bee interested inn this subjectt and also being able a to prediict and simullate situationns in this area, in order too discover faults and also optimizationn opportunitiees in projects. This papper is organnized as folllows: Sectioon 2 presents the basics for the kinematics of a planar robot; Section 3 shhows the basics for a multtilayer percepptron network annd an algoritthm for its implementattion; Section 4 exposes ressults and deetails about the implementattion of the kinematic k moodel for a pllanar robot basedd on a mulltilayer percceptron netw work; finally, Secttion 5 discussses the resullts obtained with w this work.

2. Direct and Inverse Kinem matics for the Motion off a Robot The studdy of the diirect and innverse kinem matic models in roobotics can bee introduced, in a simple way, w through a planar p manipuulator robot, as presented in Fig. 1. In this strructure, theree is a manipuulator robot with w two degreess of freedom,, being its baase locked inn the referential coordinate sysstem and its tool t free to move m over the plaane (X, Y). Thhis robot is composed c by two arms with leengths L1 andd L2. Associated with each arm, there is a rottational joint,, with rotational angles θ1 and θ2, respectivvely. The freee end of this robot lies inn the position P(X X, Y) of the pllane. The direcct kinematic model of this t manipulaator, which indiccates the poosition of the t robot’s tool regarding thhe angles of the rotational joints, cann be indicated, inn a simple waay through Eqqs. (1) and (2)): . cos . sin

. cos

(1)

. sin

(2)

where, XP annd YP are thee coordinates of the point P(X, P Y) where thee tool is posittioned.

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Fig.. 1 Structuree of a planar robot with tw wo degrees off freeedom [1].

In n turn, the innverse kinem matic model of o this robot,, whiich indicatess the angles θ1 and θ2 of o the jointss regaarding the desired d posittion of the tool, t can bee described, accorrding to Ref. [1], through Eqs. (3) andd (4):: cos – tan n–

(3)) (4))

In n this modell, the angle θ2 can assum me positive orr neg gative valuess, depending on the possition of thee elbo ow of the robbot (up or dow wn). Itt is notable thhat, through tthe observatio on of Eqs. (33) and d (4), the innverse kinem matic model really has a con nsiderable coomplexity, evven for a ro obot that hass only y two degrees of freedom in the planarr space. In n this case, an a ANN can bbe built in succh a way thatt its inputs are fed f by the desired posiition for thee robot’s tool, being b indicaated in its outputs thee resp pective valuees of its degreees of freedom m (angles, inn the case of rotaational jointss). Through this t strategy,, the ANN mighht be initially trained with w a set off refeerential patteerns determiined through h the directt kineematic model. After the trraining stage,, the networkk willl be able to determinatee the desired d informationn (deg grees of freeddom regardinng the desired d position forr the tool). An A appropriaate ANN moodel for this study is thee ML LP (multilayeer perceptronn). Through a MLP, it iss possible to studdy the inversse kinematics of a robott

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without thee explicit determination d n of its moodel, allowing thaat particular behaviors may m be identiified by the ANN N. This way, thhe study in roobotics presented here is focused on the usse of a MLP as an alternaative to the conveentional methhods for the determinatioon of the inverse kinematic k moodel of a roboot.

3. Neural Networks N a Robotiics and An ANN N may be coonsidered a system, usuually abstract, thaat can be usedd in several applications, a s such as those preesented in Reefs. [2-5]. To do so, beforre its use, in manyy cases, the ANN must be b “trained” with w patterns. This way, in its training stagge, the networrk is presented too several inpuut patterns and a its respecctive desired outpput patters, in a way to learrn the “formaation law” that correlates each input pattern to its correspondinng output paattern. After this t initial phhase, it is expecteed that, if prresented an innput pattern that does not bellong to the traaining set, the network is able to infer a proobable outputt pattern. A very interesting i A ANN model that fits in this proposal is the network composed by b perceptronns in multiple layers or MLP [6].

Fig.. 2

Symbolic model of a perrceptron.

The T external stimuli receiived by a peerceptron cann be originated from outpuuts exported d by otherr percceptrons or from f the inpuut of the netw work or, yet,, from m a bias signnal of the ow wn neuron. According A too Reff. [10], the biias signal haas great impo ortance in thee noisse control of the data pressented to the network. Alll sign nals that arrrive to a neeuron (or, in i this case,, percceptron) are weighted w by tthe synaptic weight w of thee con nnection that carries c this siignal to the neeuron. The T mathemaatical modelling that forrmalizes thiss mod del takes intoo account thhat the input stimuli havee theiir effects added in a weighhted way. Thaat is: n

   i  xi  b

(5))

i 1

3.1 The Percceptron A MLP network is com mposed by thhe organizatioon in layers of thee computationnal element called c percepttron. A perceptroon, in turn, is i characterizzed by trying to express a syymbolic (and mathematicaal) representaation of a biologiical neuron. Fig. 2 presennts the symbbolic model of a perceptron, which w is widdely discusseed in Refs. [6-8]]. Refs. [6, 8, 9] allso present the backpropagaation algorithhm in detail, which willl be discussed fuurther. In this model, m there is i a node that representss the body of thee neuron, fedd by several external stim muli through synnaptic connections. Thee result of the computationn of the exterrnal stimuli by b the percepptron is exported through t an ouutput synaptic connection that will forwarrd this signnal to the input of other o perceptrons (or neurons) of the network.

wheere, v is the weighted w sum m of input stiimuli, wi·xi iss the product betw ween an inputt signal x and d the synapticc weiight w of the connection that forwards the signal too the neuron, b is the t bias signaal of this neurron. The T perceptroon response too the received d stimuli is a function of the weighted w sum m of these. That is: (6)) y = φ(v) wheere, y is the response off the neuron, φ(v) is thee actiivation functiion of the neeuron, that correlates c thee outp put to the inpput stimuli. The T activationn function φ((v) of the perceptron mustt be non-linear, in i such a waay to allow the ANN too reprresent non-linnear functionns, being also o continuouss and d “smooth”, being b differenntiable in all its i interval off con nsideration (fo for the calcullation of the parameter δ,, whiich is used in i the backprropagation allgorithm andd willl be presentedd ahead).


9633

where, α is a constant thaat, according to Ref. [11],, has in 1.7159 a suitable s valuee. In this casse, the derivaative of the acctivation funcction φ(v) is givenn by: (8) φ'(v) = α·φ(v).(1 - φ(v))

indiicates how many m layers a network must m have, orr eveen how manyy neurons eacch layer should contain. Itt is only o possiblee to state thaat a network k with a bigg num mber of layerss can better aassimilate a formation fo law w whiich is intendeed to teach ((but with a possibly p highh com mputational coost). On the oother hand, networks withh a reeduced numbber of layers containing a sufficientt num mber of neeurons may be able to t obtain a high h-performancce learningg. Such observations, o , how wever, are purrely empiricaal.

3.2 Layered Neural Netw works

3.3 The Backproopagation Alggorithm

M is com mposed by the As menttioned, a MLP association of layered perceptrons. p F 3 presennts a Fig. model for a MLP. In this arrchitecture we have an innput layer, where w the input sttimuli of thee network arre applied, being propagated layer by layyer until the network outtput, from the firrst hidden layer of neuroons to the ouutput layer of the network, whhich will pressent the resuult of all the proccessing of the t network to the exteernal environmentt. It should also be notedd that, in a MLP, M the inputts of a given neuuron are connnected to thhe outputs off all neurons in the layer im mmediately previous and, the output of thiis neuron, is connected too all inputs off the neurons of thhe immediateely followingg layer. There is no well-ddefined form mation rule that

During D the learning phasee, so that the network cann learrn the desiredd behavior, a recursive alg gorithm, suchh as the t backpropaagation algoriithm, can be used. u In n this algorithm, during the training stage of thee netw work, an inpput pattern “x” is preseented to thee netw work, being propagated p tow ward the outpu ut, generatingg an output “o” in i this, whicch is comparred with thee desired value “dd” for the inpuut pattern con ncerned. The T differencce “d-o” betw ween the desired patternn and d the actuallyy obtained at the network output is thee erro or “e” of this learning stagge for this patttern. If e = 0, 0 then n we can connclude that the network haas learned thee inpu ut pattern “xx”. If e ≠ 0, then the erro or should bee backpropagated from the outtput layer tow ward the firstt hidd den layer to adjust the w weights of thee connectionss amo ong neurons of o the layers.

An exam mple of a com mmon activaation functionn in MLP networrks is the logistic functionn, presented inn Eq. (7): – ν

Fig. 3

Basicc model for a MLP. M

(7)

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Formally,, we have erroor signal: ej = dj – oj (9) where, “ej” is an elemennt of the obtaiined error vecctor, “dj” is an ellement of thee desired outpput vector forr the input patterrn presented,, “oj” is an element off the obtained ouutput vector with the proopagation off the input vector. Accordingg to Ref. [12], to minim mize the trainning difficulties of an ANN,, the error function fu must be non-linear. Thus, T for thee presented input i pattern,, we define the innstantaneous sum of the squared s errorrs in the output off the networkk by:

1 2

m

    e2j

(10)

j 1

where, m is the number of o elements of o the error veector (which equaals the numbber of neurons in the ouutput layer of the network). n If we connsider all inpuut patterns too be presenteed in the training stage, we caan determine the mean sqquare error for theese patterns during d an epooch (we givee the name of “eppoch” to each propagation--backpropagaation performed for all inpuut patterns presented p to the network in its training staage). Thus:

 QM 

1 N    ( n) N n 1

(11)

where, N is the number of training patterns presented work, ε(n) is i the obtainned error while w to the netw presenting thhe pattern n. Thereforee, the smallerr the value off the mean sqquare error (εQM), much better was the learnning of the innput patterns by the t network at a a given epoch. This waay, if εQM = 0, thee network leaarned with abbsolute preciision all presentedd patterns. So, a propposal for trainning a MLP can c be: (1) While εQM is not loow enough: a. For eacch training paattern:  Propagate this patteern, toward the t output, layer l by layer;  Calculaate the erroor “e” between the dessired

outp put and the obbtained outpuut;  Backpropaggate the errorr, from the ou utput towardss the input, correecting the syynaptic weig ghts of eachh con nnection;  End. b. b Update the value of εQM M; c. c End. (2 2) End. In n the algoriithm above, the error co orrection forr adju usting the syynaptic weighhts can be performed p byy the delta rule. Thhis adjustmennt in the synaaptic weightss is crucial c to thhe learning of the ANN N, since thee kno owledge acquuired by the network is condensed c inn thesse. Consider the connectiion between two neuronss in consecutive c laayers, as pressented in Fig. 4. In n this case, thhe updating oof the synapttic weight ωjii betw ween these neurons, n from m one iteration to another,, willl be given by:

 ji (t  1)   ji (t )   ji

(12))

wheere, ωji(t) iss the currennt value of the synapticc weiight, Δωji is thhe correctionn of the synap ptic weight too be applied, a ωji(t + 1) is the uupdated valuee (next value)) of the t synaptic weight. w The T calculatioon of the corrrection of thee value of thee syn naptic weightt (ωji) shoulld come in the oppositee direection to the gradient of the accumulated error inn the propagationn of an epocch of the in nput sampless (traaining set). Thus, T accordiing to the deelta rule, thee corrrection of thee synaptic weight can be given g by:

 ji     j  yi

(13))

wheere, η is the learning l rate oof the neuron n (0 < η < 1),, who ose value, arrbitrated by tthe network user, definess how w fast the neetwork will cconverge to the point off min nimum; δj is the t local graddient of the neeuron j for

Fig.. 4 Interconn nection betweeen two neuro ons and theirr para ameters.

Simulating the Inverse Kinematic Model of a Robot through Artificial Neural Networks: Complementing the Teaching of Robotics

the error correction, calculated according to the error backpropagated by the network; yi is the output value of the neuron i. The value of the local gradient δj for the neuron j can be calculated as follows:

 j   'e j , if neuron j belongs to the output layer;

or

 j   '  k   kj , if neuron j belongs to a k

hidden layer. In order to improve the convergence of the delta rule, we may use a momentum factor (μ) that will consider the value of Δωji of the previous iteration to calculate the next value:

 ji (t )     ji (t  1)     j (t )  yi (t ) (14) being μ arbitrated between 0 and 1. In a simplified manner, the process of creation and training of a neural network can be described as: Creation of the ANN: (1) Define the size of the input vector of the network, i.e., the number of nodes of the input layer of the network; (2) Define the size of the output vector of the network, i.e., the number of neurons in the output layer of the network; (3) Define the number of hidden layers of the network; (4) Define the number of neurons in each hidden layer of the network; (5) Assign random values (between -1 and 1) for the bias signal of each neuron; (6) Assign random values (between -1 and 1) for the synaptic weights of each connection of the ANN; (7) Define the activation function of the neurons and its derived; (8) End. Network training: (1) Define the values for η and μ; (2) Define the threshold value for εQM; (3) While εQM is not low enough:

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a. For each training pattern:  Apply the pattern to the input x of the ANN;  Calculate the output y of each neuron in the first hidden layer, applying these outputs to the inputs of the next layer, also calculating the outputs of this layer until the output layer (propagation of the input signal);  Calculate the error (e) for this pattern, comparing the desired value for the output (d) and the value obtained at the output (o) for the applied input;  From the output layer, toward the input layer of the network (error backpropagation): - Calculate the local gradient (δ) of each neuron of each layer.  From the output layer toward the input layer of the network: - Calculate Δω of each synaptic connection; - Update ω of each synaptic connection.  End. b. Update the value of εQM for this epoch; c. End. (4) End. After training the network, its use is performed just by presenting an input pattern, which is propagated toward the output the network, where the network response can be observed.

4. Implementation for the Case of the Planar Robot The implementation and simulation of a MLP network can be accomplished through the development of computer programs in different languages. These authors performed the implementation of ANNs through the use of “SciLab” programming language (http://www.scilab.org). According to Refs. [13, 14], an ANN with a single hidden layer is enough to approximate any continuous function. In turn, Ref. [15] states that any mathematical function can be modeled by an ANN with, at most, two hidden layers. For the planar robot model presented in this paper, all simulations were performed with ANNs endowed

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Simulating the Inverse Kinematic Model of a Robot through Artificial Neural Networks: Complementing the Teaching of Robotics

presented by the simulation are, mostly, relatively close to the values of the training, which can justify the use of this method as a tool for analyzing the behavior of a robot, prior to the final design of its inverse kinematic model by algebraic methods.

improbable, but underfitting can occur (the network does not converge during its training). Finally, the applicability of this proposal in the classroom is justified by the need to provide to students of engineering new tools for the study of problems in robotics. In this way, the use of ANN seeks to excite students to research new and better tools for solving problems, considering the inseparability of teaching and research. Specifically, in the case of these authors, the method presented throughout this text was introduced during the classes of “artificial intelligence”. This proposal was presented with the intention of encouraging students, beyond the use of this method, to constantly develop new researches, as a way to continually seek improvement of solutions for engineering problems.

5. Final Conclusions

References

with two hidden layers. In the simulation shown in Appendix, it was used an ANN with two neurons in the input layer (associated with the desired position for the tool: XP and YP), two hidden layers with six neurons each and two neurons in the output layer (associated with the angles θ1 and θ2 of the joints). In this simulation, it was used a learning rate (η) equal to 0.1 and a momentum factor (μ) equal to 0.3. It was also used a logistic activation function. Appendix presents the results for the simulation performed. As can be seen from Appendix, the results

Through this work, it can be seen that the application of ANNs in robotics produces satisfactory results for the previous simulation of the behavior of robots, allowing the detection of design failures or optimization opportunities. The major disadvantage in the use of the ANNs in robotics lies in the difficulty of finding the most suitable network topology for each case to be simulated. Using a large number of layers is not recommended because each time the error measured during training is propagated to the previous layer, it may eventually become higher. The number of nodes in the hidden layers of an ANN strongly depends on the distribution of the training patterns. The use of many neurons may facilitate the storage of training patterns, however, this will limit the ability of extracting the general features that allow the generalization or pattern recognition unseen during training (this problem is called overfitting). On the other hand, a very small number of nodes may force the network to spend too much time trying to find an excellent representation. If the number of patterns is much greater than the number of connections among the nodes, the overfitting is

[1]

[2]

[3]

[4]

[5] [6] [7] [8]

[9]

Craig, J. J. 1989. Introduction to Robotics: Mechanics and Control, 2nd edition. New York: Assison-Wesley Publishing Company. Burke, H., Rosen, D., and Goodman, P. 1995. “Comparing the Prediction Accuracy of Artificial Neural Networks and Other Statistical Models for Breast Cancer Survival.” In Neural Information Processing Systems 7, edited by Tesauro, G., Touretzky, D. S., and Leen, T. K. Massachusetts: MIT Press. Mighell, D. A., Wikinson, T. S., Goodman, J. W. 1988. “Back Propagations and Its Application to Handwritten Signature Verification.” In Advances in Neural Information Processing Systems 2, edited by Lippmann, R. P., Moddy, J. E., and Touretzky, D. S. Massachusetts: Morgan Kaufmann. Reategui, E., and Campbell, J. A. 1994. “A Classification System for Credit Card Transactions.” In Proceedings of the 2nd European Workshop on Case-Based Reasoning, 167-74. Yoda, M. 1994. Predicting the Tokyo Stock Market. New York: John Wiley & Sons. Haykin, S. 2001. Redes Neurais—Princípios e Prática, 2nd edition. Porto Alegre: Bookman. Lippmann, R. P. 1987. “An Introduction to Computing with Neural Nets.” IEEE ASSP Magazine 4: 4-22. Hush, D. R., and Horne, B. G. 1993. “Progress in Supervised Neural Networks—What’s New Since Lippmann?” IEEE Signal Processing Magazine 1: 8-39. Fahlman, S. E. 1988. “An Empirical Study of Learning

Simulating the Inverse Kinematic Model of a Robot through Artificial Neural Networks: Complementing the Teaching of Robotics Speed in Backpropagation Networks.” Technical report, Carnegie Mellow University. [10] German, S., Bienestock, E., and Doursat, R. 1992. “Neural Networks and the Bias-Variance Dilemma.” Neural Computation 4: 1-58. [11] LeCun, Y. 1989. Generalization and network design strategies. Technical report CRG-TR-89-4, Department of Computer Science, University of Toronto, Canada. [12] Andrews, R., and Geva, S. 1994. “Rule Extraction from a Constrained Error Backpropagation MLP.” In Proceedings of the 5th Australian Conference on Neural Networks, 9-12.

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[13] Hertz, J., Krogh, A., and Palmer, R. G. 1991. Introduction to the Theory of Neural Computation, volume Lecture Notes. Vol. 1 of Santa Fe Institute Studies in the Science of Complexity. Massachusetts: Addison-Wesley. [14] Cybenko, G. 1989. “Approximation by Superpositions of a Sigmoid Function.” Mathematic of Control, Signals and Systems 2: 303-14. [15] Cybenko, G. 1988. “Continuos Valued Neural Networks with Two Hidden Layers Are Sufficient.” Technical report, Department of Computer Science, Tufts University.

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Simulating the Inverse Kinematic Model of a Robot through Artificial Neural Networks: Complementing the Teaching of Robotics Appendix: Results for the Simulation of the Planar Robot

Training and simulation of the inverse kinematics of a planar robot through a MLP Length of the arm L1 = 3 un.

Length of the arm L2 = 2 un.

Training patterns Inputs

Simulation results Outputs

Inputs

Outputs

Xp

Yp

θ1

θ2

Xp

Yp

θ1

θ2

Dif. θ1

Dif. θ2

(un.)

(un.)

(deg.)

(deg.)

(un.)

(un.)

(deg.)

(deg.)

(deg.)

(deg.)

5.0

0.0

0.0

0.0

5.0

0.0

0.0

0.0

0.0

0.0

4.7

1.0

0.0

30.0

4.7

1.0

0.0

30.4

0.0

0.4

4.0

1.7

0.0

60.0

4.0

1.7

2.2

58.5

2.2

1.5

3.0

2.0

0.0

90.0

3.0

2.0

6.0

93.4

6.0

3.4

2.6

3.5

30.0

60.0

2.6

3.5

29.9

59.7

0.1

0.3

1.6

3.2

30.0

90.0

1.6

3.2

29.9

92.9

0.1

2.9

0.9

2.5

30.0

120.0

0.9

2.5

29.5

115.2

0.5

4.8

0.6

1.5

30.0

150.0

0.6

1.5

30.5

153.5

0.5

3.5

-0.2

3.6

60.0

90.0

-0.2

3.6

58.9

93.0

1.1

3.0

-0.5

2.6

60.0

120.0

-0.5

2.6

57.8

116.2

2.2

3.8

-0.2

1.6

60.0

150.0

-0.2

1.6

57.0

150.0

3.0

0.0

0.5

0.9

60.0

180.0

0.5

0.9

58.5

175.2

1.5

4.8

-1.7

4.0

90.0

60.0

-1.7

4.0

90.6

58.7

0.6

1.3

-1.7

2.0

90.0

120.0

-1.7

2.0

87.8

120.7

2.2

0.7

-1.0

1.3

90.0

150.0

-1.0

1.3

90.0

153.2

0.0

3.2

-3.5

2.6

120.0

60.0

-3.5

2.6

122.5

57.4

2.5

2.6

-3.2

1.6

120.0

90.0

-3.2

1.6

120.3

93.0

0.3

3.0

-1.5

0.6

120.0

150.0

-1.5

0.6

126.2

152.4

6.2

2.4

-0.5

0.9

120.0

180.0

-0.5

0.9

121.1

173.7

1.1

6.3

-4.6

1.5

150.0

30.0

-4.6

1.5

145.6

25.1

4.4

4.9

-4.3

0.5

150.0

60.0

-4.3

0.5

153.2

63.5

3.2

3.5

-3.6

-0.2

150.0

90.0

-3.6

-0.2

149.0

85.1

1.0

4.9

-2.6

-0.5

150.0

120.0

-2.6

-0.5

144.2

119.0

5.8

1.0

-0.9

0.5

150.0

180.0

-0.9

0.5

149.5

174.5

0.5

5.5

-5.0

0.0

180.0

0.0

-5.0

0.0

180.0

5.2

0.0

5.2

-4.7

-1.0

180.0

30.0

-4.7

-1.0

179.1

29.5

0.9

0.5

-4.0

-1.7

180.0

60.0

-4.0

-1.7

178.0

60.7

2.0

0.7

-3.0

-2.0

180.0

90.0

-3.0

-2.0

180.0

91.1

0.0

1.1

-2.0

-1.7

180.0

120.0

-2.0

-1.7

180.0

121.0

0.0

1.0

-1.3

-1.0

180.0

150.0

-1.3

-1.0

179.8

150.0

0.2

0.0

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Measurement Module for Young for Thermal Insulation Composite Polymeric Jacques Cousteau da Silva Borges1, Manoel Leonel de Oliveira Neto1 and George Santos Marinho2 1. Physics Laboratory, IFRN (Instituto Federal de Educ. Ciência e Tecnologia do Rio Grande do Norte), Natal-RN 59015-000, Brazil 2. Laboratory of Heat Transfer, UFRN (Universidade Federal do Rio Grande do Norte), Natal-RN 59078-970, Brazil Received: October 18, 2014 / Accepted: November 07, 2014 / Published: December 25, 2014. Abstract: To analyze the feasibility of application of composite material as the insulating material, it is necessary to have knowledge of some of its mechanical properties. An insulating material may suffer from the most different efforts, but the major applications suggest mechanical bending and compression tests because the insulation can be applied on roofs of homes, liners similar to, in the form of plates. Thus, the product is continually flexed. When the material is used on a floor, it suffers constant compressions over its use. For tests performed in this study, we used the ASTM D695-96 for compression, an example of literature. Using such a standard test, specimens were produced for compression test, with specimens made of cylindrical shapes, respecting the condition that the height of the specimen corresponds to twice the diameter of the base. Polyurethane castor without charge vermiculite and mass loads of 10%, 15% and 20% matrix: four specimens for each type of material were produced. The composites were tested in a universal testing machine at a speed of 2 mm/s. The results are average values of four test samples, and initially show the behavior of castor oil polyurethane during the compression test, which is detailed in the stress versus strain curve. The achieved results are promising, and detailed in this paper. Key words: Thermal properties, mechanical properties, composite polymeric.

1. Introduction Previous work [1] analyzed the thermophysical properties and the thermal performance of polymer composite polyurethane matrix derived from the oil of castor seed and load-clay mineral vermiculite. Based on the results obtained, it was concluded that the polyurethane derived from castor seed oil can also be used as thermal insulation of building systems such as roofs and vertical locks. The thermal performances were comparable to commercial thermal insulators employed on a large scale, such as rock wool and glass wool. In a comparison with this wool, polyurethane castor shows a much more attractive material, as mentioned herein other than wool, it combines good mechanical resistance and the ability to be able to assume any shape, since it is an expanding resin moldable [2-4]. Corresponding author: Jacques Cousteau da Silva Borges, M.Sc., research fields: instrumentation, control and properties of new materials. E-mail: [email protected].

Furthermore, polyurethane castor showed an insulator with a better performance when compared to its non-revolving relative the petrochemical PU (polyurethane). At this point, the castor plays a key role because it becomes a biodegradable substitute for renewable raw material, and with many improved thermal performances [5]. Just like her mother (polyurethane castor), the composite developed has characteristics which accredit applications that crave good condition of thermal insulation. All ratios tested (10%, 15% and 20%) showed a good thermal performance. The composites studied exhibited better thermal performance than polyurethane matrix without charge. Although the composite to 10% maintains a behavior closer to the matrix, its thermal behavior closely approximates the behavior of glass wool, which is a material widely used in thermal insulation market. Already the composite to 20%, consistent with the results presented rockwool, reaching the best

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Measurement Module for Young for Thermal Insulation Composite Polymeric

insulation values between the studied materials. Finally, to analyze the feasibility of implementing a composite as insulating material, it is necessary to have knowledge of some of its mechanical properties, as a material of thermal insulation may be subjected to a variety of efforts. However, the main applications suggest mechanical bending tests and compression, because the insulation can be applied in the form of plates on the roofs of homes, being constantly flexed, or can be used on a floor, under constant compression along its use. Thus, the standards have been employed by the ASTM (American Society for Testing and Materials): ASTM D790-96 and D695-96 respectively for compression and flexure tests were employed, the example of the literature [6, 7]. The paper is organized as follows: Section 2 discusses the beding test; Section 3 details the methodology of the compression test; Section 4 presents results and discussions; Section 5 gives conclusions.

2. Beding Test The bending test of the composite and the polyurethane resin castor were performed according to standard ASTM D790-96 [8] on a universal testing machine at a speed of 1 mm/min. Adopted the test method I (loading in three points) with L/d = 16, where, L is the length of the span between supports and d is the thickness of the specimen (Fig. 1). Four specimens were tested for each analyzed situation. The same test procedure was employed by Wild Child [2] to perform bending test with composite resin polyurethane castor with carbon fibers, and also by Silva [3], who performed the tests on the composite polyurethane castor and sisal and coconut fibers. Both works are doctoral theses.

Tecnologia do Rio Grande do Norte). For molding of the test specimens, MDF (medium-density fiberboard) molds 15 mm thick (Fig. 2) were constructed with the dimensions: 130 mm × 50 mm × 15 mm. With the aim of facilitating the undercut, the forms were coated with plastic material, preventing the adhesion of the composite to the walls of the container. The width of the mold (50 mm) is well above the minimum required for making four specimens. Each specimen must have an average thickness of 3.2 mm according to the standard. Thus, a thickness of 15 mm would be enough for four samples after cutting. We opted for the width of 50 mm: (a) collect sample the central region of the mold, because in that way, we can disregard the effects caused during expansion and the edges of the container; (b) perform cutting more than one sample, and use only the four specimens that show a better state. The polyol and isocyanate regents component A and component B, respectively, were employed to construct the expansive array of polyurethane castor. The vermiculite was added in the ratio by mass of 10%, 15% and 20%. Table 1 shows the amounts in weight of each component used. According to PROQUINOR [5], manufacturer of the resin, the ratio (by volume) of component A relative to component B is from 1 part of A to 1.63 Part B. Fig. 3 shows the measurement procedure the densities of the resin components, allowing to find the ratio by weight of the components shown in Table 1.

Fig. 1 Dimensions in millimeters of specimens for bending test—ASTM D790-96.

2.1 Preparation of Specimens The molds, as well as the making of the specimens were made in the Physics and Chemistry laboratories of IFRN (Instituto Federal de Educação Ciência e

Fig. 2

Mold specimen flexion.

Measurement Module for Young for Thermal Insulation Composite Polymeric Table 1 Proportion of mass components of the specimens—flexion. Comp. A

Comp. B

Vermiculite

Matrix 10% 15%

2.92 g 2.63 g 2.48 g

6.08 g 5.47 g 5.17 g

0.90 g 1.35 g

Total mass 9g 9g 9g

20%

2.34 g

4.86 g

1.80 g

9g

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slices with thickness values between 7 mm and 10 mm. Recalling that the thickness should be around 3.2 mm. To achieve this value, the material is sanded in only one direction in two stages. Initially, with the help of sandpaper circular No. 80, is an accomplished sanding at high speed until it reaches a thickness of 5 mm. In the second step, the test piece is hand sanded with No. 150 sandpaper until it reaches the thickness required by the technical standard. The slices from the outlying regions were disregarded. Finally, the material is cut into rectangular pattern. Among the specimens produced, the four are selected that have minimal manufacturing defects, such as bubbles in large sizes, cracks and other irregularities. These four specimens were tested in bending mode.

3. Testing Mechanical—Compression

Fig. 3 Measurement of densities of the resins polyol and pre-polymer.

Defined masses of each component, the mold was placed on an electronic scale accurate to 0.01 g and reading in the range from 0.01 g to 300 g. It was then inserted in the mold, the mass corresponding to the vermiculite mixture. In the next step, component A was added, observing the value corresponding to its mass, expressed as values in Table 1 done, withdrew the mold of the balance to perform the homogenization of pre-vermiculite + polyol (homogenization 1) . The mold with the pre-mixture was again brought to the balance, where it finally incorporated to the prepolymer mixture. Finally, the mold with the complete mixture is again homogenized for about 1 min (homogenization 2). The reaction ceased to expand under normal atmospheric pressure was awaited the process of polymerization for 24 h. The compounds were demolded, and then performed the appropriate treatments for their stay dimensions compatible with those required by the standards. First, after the undercuts, the bodies are cut into

To analyze the feasibility of application of composite material as the insulating material, it is necessary to have knowledge of some of its mechanical properties. An insulating material may suffer from the most different efforts, but the major applications suggest mechanical compression tests because the axial force on the quasi-static insulating covers most situations, for example, be employed in a floor or slab, under constant compression along its use. Using this standard, the specimens were produced for compression test on cylindrical shapes, where the height of the specimen corresponds to twice the diameter of the base. Polyurethane castor without charge vermiculite and mass loads of 10%, 15% and 20% matrix: four specimens for each type of material were produced. For the preparation of test specimens used in this test, a cylindrical mold made from PVC (polyvinyl chloride) pipe, 50 mm in diameter and 45 cm long was used. Therefore, the height of the cups test corresponds to 100 mm. The mold was coated internally with a plastic film to prevent adhesion of the material to the mold. The mold has sufficient to produce four specimens length. As each specimen must have a height of 10 cm,

972


2.5 cm were discarded at the ends of the part produced, leaving only 40 cm. These ends are disregarded due to the effects of expansion in the region of the edges of the container. To complete filling of the mold, became a total mass of 90g material, calculated as the filled volume after expansion of the mixture. Thus, the specimens were prepared in accordance with the values presented in Table 2. In procedures for making these specimens, the final mixture is directly inserted in the mold (tube) and has not prepared the inside thereof. These procedures were performed in the laboratories of physics and chemistry IFRN, and for weighing the material, an electronic precision balance 0.01 g was used. After measuring the weight polyol-vermiculite inserts in accordance with the values of Table 2 then homogenising container of the polyol blend is made, vermiculite. In another container, mass of the corresponding prepolymer is weighed. The final blend is held in the first container where the mixing process takes place already during the insertion of the prepolymer. The homogenization process proceeds for about 1 min. Afterwards, the mixture is inserted into the mold for the expansion of the composite material occurs. After 8 h, the undercut is made. Before that, the PVC pipe, filled by the material is cut into 10 cm, 2.5 cm excluding the extremities. With these small tubes in hand, the removal of material by means of a “plunger” that pipe adapted to 50 mm is performed. After extraction of the specimen remains only to remove the plastic covering it and perform the final finish, only consisting of a planning bases, due to possible defects during cutting. Finally, each specimen is identified and too heavy to check specifies the mass of each. Done all these procedures, the four specimens of each of the three ratios of composite material (Fig. 4), plus four of the polyurethane matrix are ready to perform the compression test.

Table 2 Proportion of mass components of the specimens—compression. Material

Comp. A

Comp. B

Vermiculite

Matrix 10% 15% 20%

29.2 g 26.3 g 24.8 g 23.4 g

60.8 g 54.7 g 51.7 g 48.6 g

9.0 g 13.5 g 18.0 g

Fig. 4

Fig. 5 test.

Total mass 90 g 90 g 90 g 90 g

Specimens for compression test.

Universal testing machines used in compression

The test was conducted at the Laboratory of Materials Technology Center Gas—CTGás using a universal testing machine (Fig. 5), 2,500 N load cell and a test speed of 2 mm/s.

4. Results The more matrix composite materials were tested in a universal testing machine at a speed of 2 mm/s. The


results are average values of four test samples, and initially show the behavior of castor oil polyurethane during the compression test, which is detailed in the voltage curve versus this deformation in Fig. 6. You can see that the behavior of the polyurethane can be detailed in two areas. An elastic zone and a plastic zone, and the region near the point of maximum tension the border these two behaviors. In the cosmetic area, the specimen subject to an axial compression stress tends to increase its cross-section insofar as the applied load increases. As the tension is

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composites also exhibit a much higher flow area, i.e., the change of elastic to plastic behavior occurs more gradually, while the matrix is most immediate effect. This statement notes with greater ease in a comparative analysis of the curves in Fig. 7. Can be obtained with some precision in the compressive strength of the plastic flow limit (the highest curve point), and wherein deforming it occurs.

given by the ratio between the instantaneous load and the area increasing applied load entails an increase in the resistance of polyurethane. That is, the material flatten until it becomes a disc, no breaking at any time. Therefore, it is impossible to determine the maximum tolerable load the material. What can be determined with some precision, are some properties in the elastic range, because in this region, the material obeyed Hooke’s law, it is possible to calculate the elastic modulus of polyurethane in this area, which is given by the slope that characterizes this elastic behavior in Fig. 7. The same considerations can be made for composite

Fig. 6 Curve of the compression test of the sample of polyurethane.

materials in the proportions 10%, 15% and 20% by weight vermiculite. Fig. 7 shows the results of compression testing for composites, the more the polyurethane matrix castor. Although composites exhibit mechanical similar to a polyurethane matrix castor behavior, have a lower mechanical resistance to compression, as when vermiculite is incorporated into the mixture. The inclusion of vermiculite in the polyurethane matrix castor oil reduces the density of the material, making it more susceptible to deformation at low loads, relative to the polyurethane matrix. However, all materials exhibit elastic region, followed by a plastic region. This occurs by elastic deformation region close to 5% in all four cases. Thus, it is possible to finish the modulus of elasticity in this region using Hooke’s law. It can be seen that

Fig. 7 Curve of the compression test samples of composite material.


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Table 3 Values of the mechanical properties obtained in compression tests. Material Matrix Comp. 10% Comp. 15% Comp. 20%

Module elasticity 12.03 GPa 8.76 GPa

Resistance Compression1 484 kPa 350 kPa

6.78 GPa

320 kPa

9.0%

6.21 GPa

265 kPa

10%

Strain 3.3% 6.2%

Thus, it is possible to define a threshold of pressure applied to the material and acceptable deformation. Table 3 depicts these values. The unloaded matrix has a higher modulus of elasticity, also deforms least up to the maximum yield stress. As already discussed, the increase of vermiculite not only reduces the compressive strength, but also increases the deformation of the elastic limit of the material.

This increased expansion influences the mechanical properties at least with respect to an axial compression, since this was the only mechanical tests performed. From this test, it can be concluded that the material is ductile, the same as its matrix, and has an elastic phase, which follows Hooke’s law, and a plastic phase, after attaining the yield. As the vermiculite content inside the composite is increased, the modulus of elasticity as well as the maximum voltage limit of the flow reduces. To better describe the mechanical behavior of the composite material, other mechanical tests, such as bending strength, impact resistance, and others are needed.

References [1]

5. Conclusions Polyurethane castor showed an insulator with a better

performance

when

compared

to

its

[2] [3]

non-renewable relative, PU oil. At this point, the castor plays a key role because it becomes replaced a

[4]

biodegradable, renewable raw materials, and much more efficient thermal performance.

[5]

Just like her mother (polyurethane castor), the composite developed has characteristics that indicate

[6]

that this is a likely application material as insulation, and the thermal conductivity of the material inversely proportional to the ratio of the mass of employed vermiculite.

[7]

This effect is explained by the reduction in density of the material, which becomes 30% less justified by the increased expanded volume after curing already

[8]

at best expansion can reach up to 40% higher, is observed ratio between the volume filled and the maid mass. 1

1

Values in yield strength

[9]

Borges, J. C. S, Heifer, H. A. D., and Marine, G. S. 2007. “Substitution of PU by Biodegradable Foam Applied to Thermal Insulation.” Presented at the 6th Brazilian MRS Meeting, Natal-RN, Brazil. Canevarolo, J., Sebastian, V. 2003. Characterization Techniques Polímeros. Sao Paulo: Artliber Publisher. Cavalcanti, E. 2001. “Vermiculite” Summary Mineral. DNPM, pp. 117-8. Chui, Q. S. 2005. “Using Vermiculite as Paulistana Massapé Adsorvedora Metals.” Sanitary Engineering and Ambiental 10 (1): 58-63. Cangemi, J. M. 2006. “Biodegradation of Polyurethane Derived from Castor Oil.” Ph.D. thesis, University of Sao Paulo. Silvestre, F. 2001. “GD Mechanical Behavior Polyurethane Castor Oil Derivative Reinforced by Carbon Fiber: Contribution to the Hip Implant Rods Project.” M.Sc. thesis, Escola de Engenharia de São Carlos. Silva, R. V. 2003. “Resin Composite Polyurethane Derived from Castor Oil and Vegetable Fibers.” Ph.D. thesis, USP. ASTM (American Society for Testing and Materials). 1996. D695-96: Standard Test for Compressive Properties of Rigid Plastics. PROQUINOR, Produtos Químicos do Nordeste LTDA. CD Interativo da PROQUINOR, 2009

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Model of the Reliability Prediction of Masonry Walls in Buildings Beata Nowogońska Institute of Building Engineering, University of Zielona Góra, Zielona Góra 65-516, Poland Received: July 26, 2014 / Accepted: August 18, 2014 / Published: December 25, 2014. Abstract: The suitable repair forecasting is needed for proper maintenance of the buildings. The appropriate maintenance planning should be based on the prognostic analysis of the repair needs. However, in Poland, maintenance planning is currently not seen as a long-term system. Repairs are understood as extemporary work and are carried out exclusively on the basis of intermittent inspections and controls. One of the numerous factors determining maintenance planning is exploitation reliability conditioned by durability. This article presents a proposal to determine the prediction of operational reliability of the building constructed using traditional technology. The method of behaving and changing the reliability of the building throughout its use will be useful in planning renovations. The presented analysis includes apartment buildings erected in a traditional technology and regards them as technical objects. For such approached buildings, it is proposed to apply rules applied for mechanical and electrical objects. The probability of the exploitation of a building without any breakdowns in a given period of time is defined as exploitation reliability. Key words: Exploitation reliability, prediction, degree of technical wear.

1. Introduction The presented analysis includes apartment buildings erected in a traditional technology and regards them as technical objects. For such approached buildings, it is proposed to apply rules applied for mechanical and electrical objects. The probability of the exploitation of a building without any breakdowns in a given period of time is defined as exploitation reliability. The examined material comprises 260 residential buildings performed in the traditional technology, situated within the area of the town of Gorzow Wlkp. (Lubuskie Voivodeship in Poland). The applied building materials and the structural solutions are similar in all the buildings. The masonry walls were made of solid bricks; the floors over the ceilings—masonry, Klein type; the remaining floors—wooden beams; the stairs and the roof structure—wooden, rafter framing—purlin-collar-tie Corresponding author: Beata Nowogońska, Ph.D., research fields: building diagnostics, reliability of a building, renovation of historical buildings. E-mail: [email protected].

type and in some cases—collar-beam type; and roofing—flat tiles or roofing paper. The technical states of all the buildings were periodically inspected by experts. The periodic monitoring, consisting in the examination of technical wear, resulted in the reports containing the information on the percentage wear of 25 components of the buildings. The paper is organized as follows: Sections 2 depicts the background; Section 3 introduces the adaptation models in buildings; Section 4 states the exploitation reliability of components building; Section 5 describes the prediction of the degree of technical wear of masonry walls; and Section 6 gives conclusions.

2. Background Issues related to the reliability of technical objects are presented both in the literature on exploitation of mechanical, electrical, electronic appliances and building structures. Frankel [1] defines reliability as

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Model of the Reliability Prediction of Masonry Walls in Buildings

probability of non-occurrence of any of the unacceptable ultimate states of a whole structure and its components in the assumed operational period. The reliability of a system is the probability that the system will not fail during a specified time period under given operation conditions, while the risk of failure is the probability that the system will fail during that period and operating conditions. Also according to Kolowrocki, the reliability is defined as the probability of non-occurrence of any damage to a device or a system during its exploitation in time period t, in certain conditions and environment [2]. Unlike quality, reliability is dependent on time—quality is evaluated when an object is being put into use, whereas reliability is evaluated during its exploitation period. Reliability is connected with durability which is a measure of the reliability of systems. Kolowrocki defines reliability function Q(t) as the survival function, which decreases with time. Nowak and Collins, who deal with reliability in the design and analysis of structures, defines reliability [3] as the ability to perform certain requirements (load-bearing capacity, stability, usability, durability, etc.) within an assumed period of usage. He provides indicators of reliability designed to achieve the appropriate level of the target on an example of bridges. Methods for reliability analysis uncover the real safety reserves in structures. Moan defines reliability [4] in a general context as the ability of a structure to perform the designed functions within a certain time of its exploitation (the condition of a structure) and in mathematical context—as the probability of failure of a structure to maintain certain states within an assumed period of exploitation. The sufficient reliability of a structure is achieved when any damage to an object or an end of its further exploitation result in economically and socially acceptable consequences and when there is sufficiently small probability of any hazards to life and health. The reliability of electronic devices, as their specific feature, was presented by Fouchera et al. [5].

The essence of the wear of objects, by Cempel and Natke is an increase in damage and partial defects [6]. A prognostic ally elaborated curve of life of a vibro-acoustic machine is based on the reliability of symptoms. Młynczak and Nowakowski [7] analysed the research on the reliability of mechanical objects, mainly vehicles and machines, on the basis of which he developed its own computerised advisory system. Niziński et al. [8] understands a technical object as a subject of diagnosis. He believes that the rational exploitation of technical appliances is possible only after the exploitation characteristics of an object that are known. A joint committee of CIB and RILEM has produced a report [9] which analyses the shortcomings of much durability testing, identifies the problems facing reliable service life prediction, offers a methodology for approaching those problems and lists the key research needs. The object’s reliability is defined as the ability to fulfill the task resulting from the purpose. It means that the object is demanded to fulfill a determined function in determined time t in determined conditions of operation. The measure of the reliability of an object, in terms of the task, is the probability of the task completing. Such determined reliability measure is a function of time of the building’s reliable performance and is called reliability function [10].

3. Methods To model a situation for the needs of the survival analysis, when the probability changes in time, the Weibull distribution is most frequently used as a distribution of random variable of the time of the building’s usefulness [11-15]. The probability density function for the Weibull distribution is determined with the relation: f(t) = ··t-1exp[-(t)] for t  0 (1) where, t is the exploitation period,  is scale parameter (a real number) when  > 0, β is the shape parameter (a real number) when  > 0.


Parameter  of the distribution determines the probability of a breakdown in time:  For  < 1, the probability of breakdown decreases in time, which suggests that, when the object breakdown is modeled, some specimen may have production defects and slowly fall out of the population;  For  = 1 (exponential distribution), the probability is constant, it indicates the fact that breakdowns are caused by external random events;  For  > 1, the probability grows in time, which suggests that time-related technical wear of elements is the main cause of breakdowns;  For  = 2 (the Rayleigh distribution), the probability grows linearly in time. Distribution parameter β is a coefficient characterising the rate of the reliability obsolescence: β = 1/TR (2) where, TR denotes the period of the object durability. The distribution function for the Weibull distribution obtained after integration: F(t) = 1 – exp[-(t)] (3) In the literature, the distribution function is called the probability of damage, a destruction function, breakdown or a failure function and is determined with the relation: F(t) = P (t < TR) = 1 – R(t) (4) where, TR is the period of object durability and R(t) is the reliability function, also called the probability of proper operation, or durability function. Inefficient or failure-free operations are opposite events that exclude one another, therefore, Eq. (4) may be applied. The object’s reliability is defined as the ability to fulfil the task resulting from the purpose that it was intended for. It means that the object is demanded to fulfil a determined function in determined time t in determined conditions of operation. The measure of the reliability of an object, in terms of the task, is the probability of the task completing. Such determined reliability measure is a function of time of the

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building’s reliable performance and is called reliability function. Exponential distribution is a particular case of the Weibull’s distribution, where shape parameter α = 1. Exponential distribution is frequently used in the examination of a proper performance time [16, 17]. The relation defining the reliability functions for the i-th component of a building for known parameters  and  may take the form: Ri(t) = exp[-(t/TRi)] (5) where, Ri(t) is the exploitation reliability for the i-th component of a building, t is the exploitation time and TRi is the durability period of the i-th element of a building. Another particular case of Weibull distribution, where α = 2 is the Rayleigh distribution. The application of the Rayleigh distribution for buildings seems to be the best choice. All buildings and their components are subject to technical wear and the Rayleigh distribution is applied when the object’s wear increases in time. For this case, the reliability function takes the form: Ri(t) = exp[-(t/TRi)2] (6)

4. Exploitation Reliability of Components Building To determine the exploitation reliability of a building with the use of Eq. (6), the building, erected in the traditional technology, was divided into 25 components. A determined material-structure solution with characteristic theoretical average durability periods TRi (TRi by Ref. [18]) was assumed for each component. Eq. (6) was applied to examine the change in the exploitation reliability of all the components within the assumed a 100-year period of exploitation. The selected results of calculations are presented in Figs. 1 and 2. Methods derived from the theory of exploitation of machines and electrical appliances were applied to examine the properties of apartment buildings. The results obtained at the present stage of the realisation


978 1 0.8 0.6 0.4 0.2 0 0

10

20

30

40

R śr

50

60

70

R min

80

90 100

R max

Fig. 1 Exploitation reliability of masonry walls according to the Rayleigh distribution. 1 0.8 0.6 0.4 0.2 0 0

10

20

30

40

R śr

50

60

R min

70

80

90 100

R max

Fig. 2 Exploitation reliability of wooden floors according to the Rayleigh distribution.

of the exploitation reliability problem may be helpful in maintenance planning.

4. Prediction of the Degree of Technical Wear of Masonry Walls The bibliography on reliability of electronic devices attributes the intensity of failure to technical [17] wear as described in Eq. (7). S

z



t



λ (t ) d t

(7)

0

The technical wear, according to the exponential distribution where the intensity of failure is constant, is expressed with a linear function: Sz = t/TR (8) where, Sz is the degree of technical wear of an object expressed in percentage, t is the age of the object and TR is the expected durability period of an object expressed in years. For the Rayleigh distribution, where α = 2, β = 1/TR, the degree of technical wear equals:

Sz = t2/TR2 (9) For each building element, it is possible to determine the prediction of the technical wear in any arbitrary exploitation period, the prediction of the degree of technical wear may be obtained according to the exponential distribution and the Rayleigh distribution. For brick masonry walls, the durability period is determined within the limits of 130-150 years. The degrees of technical wear were determined for the minimum (130) and the maximum (150) values, with the use of the exponential distribution (Eq. (8)) and according to Rayleigh distribution (Eq. (9)). The obtained results are presented in Table 1 and Fig. 3. The time of exploitation during which the components lose their exploitation properties depends on many Table 1 Average values of technical wear of load bearing walls obtained during periodic inspections, and predicted theoretical values of the degree of wear. Real values Predicted values Value of the degree of wear according Age of Average to distribution the values of building the degree Exponential (8) Rayleigh (9) of wear min max min max 0

0.000

0.0000

0.0000

0.0000

0.0000

5

0.000

0.0333

0.0385

0.0011

0.0015

10

0.002

0.0667

0.0769

0.0044

0.0059

15

0.014

0.1000

0.1154

0.0100

0.0133

20

0.022

0.1333

0.1538

0.0178

0.0237

25

0.044

0.1667

0.1923

0.0278

0.0370

30

0.048

0.2000

0.2308

0.0400

0.0533

35

0.062

0.2333

0.2692

0.0544

0.0725

40

0.082

0.2667

0.3077

0.0711

0.0947

45

0.188

0.3000

0.3462

0.0900

0.1198

50

0.184

0.3333

0.3846

0.1111

0.1479

55

0.188

0.3667

0.4231

0.1344

0.1790

60

0.220

0.4000

0.4615

0.1600

0.2130

65

nd

0.4333

0.5000

0.1878

0.2500

70

nd

0.4667

0.5385

0.2178

0.2899

75

0.324

0.5000

0.5769

0.2500

0.3328

80

0.328

0.5333

0.6154

0.2844

0.3787

85

0.420

0.5667

0.6538

0.3211

0.4275

90

0.440

0.6000

0.6923

0.3600

0.4793

95

0.464

0.6333

0.7308

0.4011

0.5340

100

0.488

0.6667

0.7692

0.4444

0.5917


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1 0.9 0.8

Technical wear

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

85

90

95

100

Subsequent years of exploitation technical wear of load-bearing walls according to exponentail distribution min technical wear of load-bearing walls according to exponentail distribution max technical wear of load-bearing walls according to Rayleigh's distribution min technical wear of load-bearing walls according to Rayleigh's distribution max technical wear of load-bearing walls in Gorzow Wlkp

Fig. 3 Comparison between the degrees of technical wear of masonry walls according to exponential and Rayleigh distributions and the average results obtained in the evaluation.

factors: the material quality, the structure solutions, the performance quality of the building erection works, the influence of the environment, the way and conditions of building exploitation. The factors may occur with various frequency and intensity. Due to the complexity of the phenomena, the durability periods are the time periods of various lengths. For respective building components and solutions, average durability periods TRi may be assumed. They are values for average performance quality of the building erection works and building exploitation as well as average environmental conditions. Average values of technical wear of load-bearing walls of buildings in Gorzów were also marked in order to verify the proposed methods. It is possible to determine the current year of its exploitation after having known the time of the building erection. The degrees of technical wear obtained in periodic monitoring were averaged and marked in the figures for comparison.

The values of the degree of wear of the walls by the Rayleigh distribution were verified using student test. Assuming a 5% chance of error in applying (p = 0.05), and the number of degrees of freedom is 19, the critical value of the test is 2.0930. The test result in the study was 2.16817, which means that the results are statistically significant for the level of p = 0.05.

6. Conclusions The results of technical wear of buildings in Gorzow Wlkp confirm the effectiveness of the proposed method of the determination of the degree of technical wear with the use of Rayleigh distribution. The average values of the degree of technical wear determined in situ inconsiderably varied from the proposed charts in Rayleigh distribution. The prediction of the degree of wear of the walls is an example of the methodology of prediction of technical condition of building elements. In an analogous way, it is possible to elaborate predictive changes in


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the degree of wear of all building components. Methods derived from the theory of exploitation of machines and electrical appliances were applied to examine the properties of apartment buildings. The results obtained at the present stage of the realisation of the exploitation reliability problem may be helpful in maintenance planning. In order to program the repair and renovation works, the prognostic determination of the scope of work in terms of the kind and quantity is necessary. The repairs should include preventive actions aiming at assuring that no damages will occur to the building. The reliability analysis may be applied for predicting the dates of the repairs of the components of a building erected in the traditional technology. The course of the exploitation reliability of elements over the subsequent years of their exploitation may be used in prognostic planning of inter-repair cycles for the whole building. The obtained results may be helpful for administrators of residential buildings. Predictive diagnostics is one of the fundamental problems in the process of planning the proper operation of buildings.

References [1] [2]

[3] [4]

[5]

Frankel, E. G. 1984. Systems Reliability and Risk Analysis. Netherlands: Springer. Kolowrocki, K. 1999. On Limit Reliability Functions of Large Systems. Part I. Statistical and Probabilistic Models in Reliability. Boston: Birkhäuser Boston, Nowak, A. S., and Collins, K. R. 2000. Reliability of Structures. New York: Mc Graw-Hill. Moan, T. 2011. “Life-Cycle Assessment of Marine Civil Engineering Structures.” Structure and Infrastructure Engineering: Maintenance, Management, Life-Cycle Design and Performance 7: 11-32. Fouchera, B., Boulliéa, J., Mesletb, B., and Dasb, D. 2002. “A Review of Reliability Prediction Methods for Electronic Devices.” Microelectronics Reliability 42 (8): 1155-62.

[6]

[7]

[8]

[9] [10] [11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

Cempel, C., and Natke, H. G. 1993. “Damage Evolution and Diagnosis in Operating Systems.” In Safety Evaluation Based on Identification Approaches Related to Time-Variant and Nonlinear Structures. Germany: Vieweg+Teubner Verlag. Młynczak, M., and Nowakowski, T. 2006. “Rank Reliability Assessment of the Technical Object at Early Design Stage with Limited Operational Data—A Case Study.” International Journal of Automation and Computing 3 (2): 169-76. Nizinski, S., and Pelc, H. 1990. Diagnosis of Mechanical Equipment. Warszawa: Publisher of Science and Technology. Moubray, J. 2007. RCM II—Reliability Centred Maintenance. Oxford: Industrial Press. Andrews, J. D., Moss, T. R. 1993. Reliability and Risk Assessment. New York: John Wiley. Walpde, R. E., and Myers, R. H. 1985. Probability and Statistics for Engineers and Scientists. London: Macmillan Publishing Company. Khelassi, A., Theilliol, D., and Weber, P. 2011. “Reconfigurability Analysis for Reliable Fault-Tolerant Control Design.” International Journal of Applied Mathematics and Computer Science 21 (3): 431-9. Cordeiro, G., Ortega, M., and Lemonte, A. 2013. “The Exponential-Weibull Lifetime Distribution.” Journal of Statistical Computation and Simulation 84 (12): 1-15. Runkiewicz, L. 1998. “Evaluation of the Quality of Materials in Historic Buildings.” Presented at the IV Conference on Scientific and Technological Sciences and PZITB on “Engineering Problems of the Old Town Historic Restoration”, Cracow, Poland. Zaidi, A., Bouamama, B., and Tagina, M. 2012. “Bayesian Reliability Models of Weibull Systems: State of the Art.” International Journal of Applied Mathematics and Computer Science 22 (3): 585-600. Nowogońska, B. 2011. “Reliability of Building Determined by the Durability of Its Components.” Civil Environmental Engineering Reports 6: 173-80. Salamonowicz, T. 2001. “Models Reliability Serviceable Objects of Preventive Service.” The Journal Issues Machine Operation 2. Ściślewski, Z. 1995. Life Building. Kielce: Kielce University of Technology Press.


D

DAVID

PUBLISHING

Mathematical Modeling and Computational Semiotics: Methodological Approach to Formalization of Semiotic Concepts Silvia Regina dos Santos Coelho1 and Ricardo Matos Chaim2 1. Faculty of Engineering Gama, University of Brasília, Brasília, Brazil 2. Faculty of Engineering Gama, University of Brasília, Brasília, Brazil Received: September 01, 2014 / Accepted: September 22, 2014 / Published: December 25, 2014. Abstract: This paper aims to conduct a research on the state of the art of artificial intelligence techniques to investigate the relationships between cognitive actions addressed in steps of mathematical modeling and computational semiotics activities. It also briefly reviews the main techniques of artificial intelligence, with particular emphasis on intelligent systems techniques. Such analysis uses semiotic concepts in order to identify the use of new techniques for modeling intelligent systems through the integrated use of mathematical and computational tools. At last, once understood that semiotics can bring contributions to the study of intelligent systems, a methodology for modeling computational semiotics based on the semiotic concepts formalization extracted from the semiotic theory of Charles Sanders Peirce is proposed. Key words: Intelligent systems, mathematical modeling, computational semiotics.

1. Introduction1 The consulted literature points out that in the last two decades there has been a rapid growth in interest in research and applications of the techniques of “computational intelligence”. It is worth noting that the term “artificial intelligence” was motivated to distinguish these researches from those surveys called “classical artificial intelligence”, which emerged in the mid 1950s as a study proposal for the development of machines capable of using language and performing tasks as human beings. At the end of the 1960s, the first theorem provers who developed expert systems in 1970s came up. Technology became commercial in 1980s with the so-called “shells” of expert systems. In the area of computational intelligence, techniques such as Fuzzy logic and systems, artificial Corresponding author: Silvia Regina dos Santos Coelho, M.Sc., research fields: information science and management. E-mail: [email protected].

neural networks and evolutionary computation (genetic algorithms, among others) have been studied, giving significant contributions to the understanding of human intelligence nature. It is noteworthy that in parallel, the humanities have also sought a model for intelligence and intelligent behavior, given that in general, human beings have some cognitive disabilities that hinder the understanding of intelligent systems functioning and many of these difficulties stem from linear and mechanistic thinking characteristic of western education. More recently, partial aspects of intelligence, such as reasoning using vague or incomplete knowledge, learning and prediction have been studied in the area of computational intelligence. According to the consulted literature, intelligence is an inherently human capacity. It is said that it is the characteristic that distinguishes us from other animals. Often, the word “intelligence” or the adjective

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Mathematical Modeling and Computational Semiotics: Methodological Approach to Formalization of Semiotic Concepts

“intelligent” is used to value any product that contains some degree of automation. However, for the purposes of this research, an intelligent system can be seen and studied as a semiotic system, where the processing of signs can be seen as the source of intelligence displayed by the system. The intelligence of this system, therefore, will depend on the amount and types of signs that it is able to process. Currently, the mathematical modeling of these systems is a major focus of interest of many researchers studying the interaction between semiotics and intelligent systems. In this respect, it is worth highlighting the study of Peirce to design a semiotic philosophy based on universal categories of perception and thought. Peirce thinking is an operation that takes place exclusively through signs [1]. In this sense, Peirce agreed in saying that “something is a sign only because it is interpreted as a sign of something by an interpreter” [1]. Therefore, it can be said, and are routinely references to these words, one does not have a thought, but if you are in thought—the thought is not an object but a semiotic process, which means that is semiosis. Peirce semiosis (sign action) is an irreducibly triadic phenomenon (indecomposable three-term relation) that relates a sign (S) to its object (O) for an interpretant (I), or effect on an interpreter [1]. The sign is determined by the object relative to the interpretant, and determines the interpretant in reference to the object, so as to produce the interpretant to be determined by the object through the mediation of the sign. According to Peirce, sign is something that produces in the mind of the interpreter, the same idea (interpretant) that would be produced by something else (object), if it were presented to the interpreter [1]. The sign is formed by “object” (anything, feeling, event that can generate an idea in the mind of the interpreter), “interpretant” (an idea in the mind of the interpreter) and “meaning” (which is passed to the

interpreter by the sign when causes the generation of the interpretant in the mind of the interpreter). The “interpreter” is the key element to the understanding of a sign processing and therefore, the operation of an intelligent system. While designating an object, the interpreter provides an assessment of the object significance and the smart system predisposes to an action that corresponds to a reaction to the cognition of the sign, interpreted within the context. These three tasks of the interpreter are highly interconnected. To Silveira (apud Oliveira), what Peirce does, through its semiotic conception, is to promote the essential integration of logic in the context of the experience, giving it as an object, not merely ideal forms, as are the objects of mathematics. The signs, however, are phenomenologically manifest as thought [2]. Another aspect to be highlighted is that the semiotics studies the levels of meaning, that is to say, studying the other direction, the implicit meaning, or the meaning behind the words, or beyond words, different fields of semantic structure, since it is static, while the semiotic significance levels are dynamic and variable. It is known that the meaning as semiotic function, that is, dependency relationship between a content plan and the expression plan, is an intrasemiotics relationship, which therefore cannot be transcoded, whereas the information as a set of operated cultural clippings about the semantic amorphous continuum can be treated by any code filter [3]. Therefore, the interlingual transcoding of a message does not reflect a meaning, but a designatum, a sense. What can be translated is the substance of the content, not the form of it, that is why it is up to us to ask under what conditions two words, two statements, and even two texts belonging to two different languages, are semantically equivalent to the point we can say that both are mutually translate.


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Thus, the content of designative dimension is a coded representation of the interpreted object. The exact determination of this object, that is, the interpretation of the designative dimension of the sign will depend on the relationship between the sign and the object. From this perspective, it is possible to realize that the translation of a text into another language is a process of equivalence in a conceptual level [4]: Fig. 1

Therefore, the speaking subject initially decodes the m1 message in terms of the LN1 natural language, thereby arriving at a conceptual schema, which is then encoded in the LN2 natural language, resulting in a new m2 message, m1 translation.

Input of a sign in the system [5].

Designati

Apraisive

Prescritive

Input

The entry of a sign in the system corresponds to an encoding of the information from the external world by means of sensors. This encoding is then compared to the coding prototypes of objects that match the intelligent system vocabulary, and the internal sign that is most similar to the input sign is called the sign interpretant. To Gudwin and Gomide, the entry of a sign in the system corresponds to an encoding of the information from the external world by means of sensors [5]. This encoding is then compared with the coding prototypes of objects that match the vocabulary of the intelligent system, and the internal sign that is most similar to the input sign is called the sign interpretant. Note that this interpretation is given here only in level of designative dimension. This mechanism can be seen in the following figure. Another interesting observation according to Gudwin and Gomide is that the whole interpretation process is dynamic [5]. That is to say, the box which is called external sign can be considered as such, if the interpretation occurs effectively. The intelligent

Fig 2 Interrelationships between the dimensions of an interpretant [5].

system is continuously flooded with system data, and only certain data combinations are significant. Given these considerations, it is important to note that today, the semiotic earned dimensions that exceed the human field and can be seen as a research area that extends the semiotics of architecture, biosemiotics or cartosemiotics to zoosemiotics, and thus may be defined in a very general way as the science of signs and signification processes (semiosis) in nature and in culture. In short, it is in this context that is presented the work developed in this paper to propose a methodology for mathematical modeling based on the formalization of semiotic concepts from the semiotic theory of Peirce drawing upon the bibliographical review to support the theoretical model [1]. This methodological approach allows the use of new techniques for modeling intelligent systems through the integrated use of mathematical and computational tools.

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This paper is organized as follows: Section 2 presents “dynamic systems” as a methodology that makes use of the concept of systems thinking to solve problems and to study systems; Section 3 shows the process of self-organization in the context of dynamic self-organization; Section 4 formulates the hypothesis that there is a relationship between the concepts of self-organization and the logic semiotics of Charles Sanders Peirce [6]; Section 5 presents the concepts of logical reasoning categories from the point of view of Peirce’s pragmatism, namely, deduction, induction abduction, which was developed by Peirce [6] as a new category of logical reasoning; Section 6 presents the systems of semiotic representation and mathematical modeling as a high school methodology that enables the students the effectiveness of cognitive activities with regard to the representation, treatment and conversion between semiotic registers; Section 7 describes the construction process of the interaction of subject-object (tool) model, due to semiotic elements; finally, Section 8 presents our conclusions.

2. System Dynamics: Methodology for Investigating Cognitive Actions Addressed in Steps of Modeling Activities To achieve the objective of this research, we adopt the methodology of “system dynamics” created by Jay Forrester [7] in the 1950s. This methodology is based on the General Systems Theory [8] and uses computer simulation to relate the structure of a system with its behavior over time [9]. Currently, it is used in various research centers, and various software structures that comprise the system dynamics have been developed. Through such software, it is possible to analyze the behavior of complex systems, including all relevant relationships of cause and effect, delays and feedback loops. Originally, the methodology was used in the industrial environment, but afterwards applications have been identified in other areas of knowledge, such as physics, biology, social sciences and ecology [9]. To Sousa, the DS (dynamic systems) are a rigorous

modeling method that uses computer simulations to define more effective organizations and policies [10]. Such tools in the design of Sterman [11] allow the creation of management simulators—virtual worlds where space and time can be compressed and decelerated so as to allow experimentation with long term side effects, learning, and structures design and high performance strategies. In the context of cognitive science, van Gelder (apud Oliveira) [2] provides the dynamics hypothesis of cognition as opposed to the computational hypothesis, stating that cognitive agents can be: (1) considered as dynamical systems ontologically; (2) described as dynamic systems. Thus, the dynamic perspective of cognition inaugurates a third paradigm in cognitive science, artificial intelligence beyond. According to Ref. [12], dynamic systems are systems whose state (or instantaneous description) changes in time. The state of a system at a given instant of time is the instantaneous description of him, needed to determine the values of its internal variables. The state in the following instant depends only on the state on its current instant, without needing the previous states. The space formed by all possible system states is defined as the state space of the dynamic system. But beyond the system state, its inputs are also needed to determine their future status and from these two facts, the rule of system evolution will determine the future state. More formally, Beer [13] states that a dynamical system can be defined as a triple consisting of an ordered set of time instants T, a state space S and an evolution operator _t: S! S, which transforms the state xt1 _ S _ T in time t1 in the state xt2 _ S _ t2 to time T. The space S can have finite or infinite dimension, can be numeric or symbolic, if numeric can be continuous or discrete. The time T can be discrete or continuous. The _t rule can be defined explicitly or implicitly, and addressed by time or events, may be linear or


nonlinear, deterministic or stochastic, autonomous (not time dependent) or not autonomous. Models examples of dynamical systems are differential equations, cellular automata and finite state machines. Among dynamical systems, a class of systems has gained increasing attention: the complex dynamic systems. But a precise and consensual definition of them has not been obtained yet, containing several authors, elaborated proposals to define this class of systems. It is still possible to define them with less formality by some common characteristics. First, complex systems are systems composed of a large number of different interacting elements [14]. Interactions between components are the effects that one component causes on the other and in the system, that is, changes in the state or structure of components or system. The relationships established by these interactions are responsible for the system characterization, they cannot be ignored or overlooked, preventing that the system could be decomposed, without being mischaracterized. This impossibility of reducing the system to its components is a consequence of the nonlinearity of the interactions, the effects (in the system) are not the simple sum of the causes (on the components). The interactions are necessarily circular processes [15], where the interaction effects are its own causes, retroactive effects on causes. As examples of complex systems, we can mention the human brain, consisting of billions of neurons, interacting electrochemically by synapses; computational systems, constructed with a large number of electronic components such as transistors and logic gates; social and economic systems, obviously composed of several components; and language. When the complex system has the ability to modify its structure and dynamics, either by his action and behavior or evolutionary change, it is called a CAS (complex adaptive system).

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When the system adapts autonomously, it gets the name of self-organizing system. Kelso (apud Oliveira) [2] postulates that every dynamical system displays order (or collective variables) and control parameters. Very briefly in, it is possible to place an order parameter as a behavior that emerges in a dynamic system and, once established, shall direct the behavior of the system itself in a kind of circular causality. An order parameter can be described as a macro property or an emergent property of the interaction of the elements of a system. A control parameter is a condition in which, or the state in which a collective variable emerges, and it is not dependent on another state or condition and can be quite specific and not caused by external events. Therefore, in the case of dynamical systems, their behavior and properties can change due to particular events (control parameters) which result in settings or emergent behaviors (order parameters) that start to drive or restrict the system itself in its behavior.

3. Dynamical and SOSs (Self-organizing Systems) Since its initial formulation, the concept of self-organization is continuously used in several theoretical proposals in many areas of knowledge, ranging from computational modeling to philosophy. It is worth mentioning that self-organizing systems are complex systems in which global standards are produced through local interactions, without central or external control. Global information can be used to enforce global constraints to the system, although they do not act directing the system to “how” it must reach a state of order. The concept of order is the opposite of entropy, for being a process by which a system tends to exhaustion, disorganization and disintegration, and finally to death. In this sense, an orderly system has invariance, redundancies, the freedom degrees of the system are restricted (the responsible parameter is called the

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order parameter). SOSs cannot be seen like isolated systems, not dependent on the environment, which they constantly adapt their dynamics. SOS examples are found in various social, economic, physical, biological and chemical areas. SOSs have characteristics that distinguish them from conventional systems, such as global order, local interactions, positive and negative feedbacks, order from noise, nonlinearity, distributed control, robustness, lock, emergency, and unpredictability. The components of “lower level” interact, subject to local restrictions, spontaneously creating a global configuration ordered. The dynamics of SOS is strongly based on mechanisms of positive feedback and negative feedbacks, and in a circular relationship in which each component affects the others, and is affected by others non-linearly. Positive feedback amplifies fluctuations exploring new settings, while negative feedback stabilizes the system to reduce deviations in the system state. This keeps the system to the “edge of chaos” between balance and chaotic activity. The dynamics of self-organization of the system depends on fluctuations or noise, so that the system can be moved from its current state and eventually leading up to a new state of order. The noise source can be internal, generated by the system itself, or external, from the environment. The feedback loops make them robust and resilient SOS, since the deviations can be suppressed, bringing the system back to an original ordered state. The robustness of SOS, which is characterized by its fault tolerance comes from the distributed control between the system components, through which he self corrects its behavior when its unspoilt parts recompose the activity of non-functional parts. Although not subjected to central controllers, SOS components should be observed as belonging to a coherent whole, and self-sufficient, cannot be analyzed in isolation. Another feature of SOS is its unpredictability. It is a consequence of the intrinsic non-linearity of the

system and probabilistic trajectories that can drive the system from an initial state to any of the various stable states. Briefly, SOS is formed, in most cases, from various parts that interact by distributed manner, not predictable, non-linear, probabilistic, making it extremely difficult to analyze its parts. These properties suggest that a synthetic approach, rather than an analytical, can be an interesting strategy to study the SOS, and computer simulations play an important role when we want to design, model and experiment with SOS. Because of the difficulty of predicting the behavior of SOS, computer simulations are a useful tool to conduct “thought experiments” and to better understand how these systems work [16]. From this perspective, another fundamental question is “where does the order come from”? According to the general laws of thermodynamics, it seems that the dynamic processes tend to follow the paths of least energy consumption until the system is able to find a balance where it will remain until it has suffered disruption. There are many examples in nature of systems and organisms that present high energy and internal organization in apparent defiance of the laws of physics. Some of them are: (1) Iron filings particles that align along the lines of force of the magnetic field to which they are subjected; (2) Water particles that when suspended in air form clouds; (3) Ants or bees that grow from a zygote to form a complex system of cells which then in turn participates in a highly structured and hierarchical society. Thus, the organization arises spontaneously from disorder and it does not seem to be driven by known physical laws. Somehow, the order arises from multiple interactions between the component units and the laws that may govern this behavior are not well known.


The behavioral perspective of a SOS could reveal how spatial and temporal patterns, such as roads, boundaries, cycles and succession could arise in complex heterogeneous communities. Understanding the mechanisms of self-organization may lead to the construction of more informative and accurate models. According to Ref. [17], it is necessary for a system to satisfy various pre-conditions and make use of various mechanisms to promote self-organization. Such mechanisms are in some way redundant and poorly defined. However, they allow intuitively assessment for the potential of systems’ self-organization. They are: (1) Thermodynamics aperture: firstly, the system (a recognizable unit as an organization, an organism or a population) should exchange energy and/or mass with its environment. In other words, there must be a non-zero energy flow through the system; (2) Dynamic behavior: if a system is not in thermodynamic equilibrium, the only option left for its behavior is to assume some type of dynamic, meaning that the system is continuously changing; (3) Local interaction: since all natural systems inherently have local interactions, this condition seems to be an important mechanism for self-organization and as such should be incorporated into models that represent it; (4) Nonlinear dynamics: a system with bands of positive and negative feedback is modeled with nonlinear equations. Self-organization can occur when there are feedback loops between the system components parts and between these components and the structures that emerge at higher hierarchical levels; (5) Large number of independent components: since the origin of self-organization lies in the connections, interactions and feedback loops between the systems parts, it becomes clear that SOS must have a large number of components; (6) General behavior independent of the components internal structure: this means that no matter what or how are made the system components,

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since they do the same things. In other words, this means that the same property will arise emerging in completely different systems; (7) Emergence: emergence is probably the least known among the notions that relate to self-organization. The emergence theory says that the whole is greater than the sum of the parts and the whole displays patterns and structures that emerge spontaneously from the conduct of the parties; (8) General conduct organized and well defined: disregarding the internal structure of a complex system and seeing it only as an emergent phenomenon, it is observed that its behavior is quite accurate and regular; (9) Effects at multiple scales: the emergence also points to interactions and effects on SOS between multiple scales. The small-scale interactions produce the large-scale structures which in turn modify the activity on a small scale. Based on these assumptions, for purely didactic purposes, we describe the example of Pereira [18]—three possible systems based on the logic of meanings production: (1) first, considered low complexity, performs its meaning productions without the participation of a creative memory; (2) second, which admits a median complexity and, just like the first, would be carrying a memory, but in this case already with creative dimensions, although of medium complexity; and (3) third, with high rates complexity, concierge highly creative memory and can thereby generate meanings rich in diversity, even ambiguous. From this angle, Pereira [18] states that differentiated systems as the degrees of low, medium and high complexity possessed some complexity proportional to their degree of complexity memories, varying as to their production of meaning, the mere possibility of recognizing elements which they can interact (recall stored information that enables recognition) to the possibility of furthering their operations with mnemonic content, and this may create new meanings in the face of information with which they interact.

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It is also important to observe that the latter system models, by their richness of its variability of semiotic productions can sometimes within the set of self-organization, promote disorders within the system as an effect of over-complexity. Such excess may form themselves into new content for a growing organization in terms of complexity, or in some cases, promote a radical disruption of the system itself. Thus, the higher the rates of creative memory and complexity, the greater the possibility of meanings produced are rich and varied, organizing, expanding and complexifying the system further. And on the other hand, the excess of significant possibilities of the system itself produces a greater willingness to instability and chaos, which may or may not be the resumption of the eternal game of self-organization. In this sense, Peirce [1] advances on the dynamic view. Therefore, closely related to the notion of representation, the role of interpretation is explicit in his semiotics theory. That is, through interpretation, a meaning to the sign is joined. In addition, representations are subject to additional representations of operations on the representations, the interpretations that become successively new representations and so on. Therefore, in designing Nadin [19] once known objects levels and interpretants, the sign is no longer a synchronic entity, which means, the sign comes to life, in the sense that the process of interpreting injects dynamic to their reality. To Nadin [19], we never deal with signs, but with representations, aggregates of signs whose dynamic meaning is a function of the context, not the alphabet. Thus, under this assumption, we can infer that beyond a representation to be able to cause the generation of different meanings, each sign in turn can generate meanings from themselves. And this chain of ideas continues until the receiver is satisfied or until a new chain idea begins. Peirce’s semiotics in this chain of attribution of meaning is known as unlimited semiosis.

From this perspective, it is necessary to emphasize that the representation of dynamic and non-linear systems, a properly systemic language should be used, given that our linear language and Cartesian is insufficient. And as language shapes the perception, a new language would bring new ways of thinking that would facilitate the understanding of complex dynamic systems. Thus, there would be a break with linear thinking, which mirrors our written and spoken language and presupposes cause and effect relations that prevent the perception of situations involving dynamic complexity. Therefore, if the thesis that dynamic systems and semiotic systems are correlated is relevant, the property of self-organization as a property of dynamical systems should also manifest in semiotic processes.

4. Semiotic Systems and the Systems Dynamics In this paper, we postulate that a semiotic system is a dynamic system. The arguments set forth herein is proposed on the assumption that there is a relationship between the concepts of self-organization and the semiotics of Peirce logic from the premises of Gonzalez and Haselager [20] which established a relationship between the concepts of self-organization and Peirce’s semiotics logic, Peirce’s in the study of creativity in natural and artificial systems. A system receives information from the environment through inputs, and can act in this environment through outputs; A semiotic system is a system that generates, transmits and interprets signs of different types. This system is subdivided into “iconic, indexical and symbolic semiotic systems”. In terms, summarily iconic, indexical and symbolic semiotic systems use signs as means for communication of similarity patterns, correlations, timelines and legal relations. These systems exhibit self-correcting behavior, or some kind of activity driven by a purpose.


The effectiveness of a sign process corresponds to the execution of an interpretation, that is, a function that takes a particular sign facing a given context, to an interpretant. In some cases, this function can be a simple function. The interpretant is only a function of some coordinates of the input vector, normally finding very complex functions, where the interpretants could fuel the input vector, create interpretation chains, where a sign refers to an interpretant, which in turn leads to another interpretant and so on.

5. The Categories of Logical Reasoning and Adaptive Computational Methods The pragmatism of Peirce points to the conceptualization of three categories of logical reasoning: deduction, induction and abduction. Abduction is the process of constructing a hypothesis for the generation of an initial model as an attempt to understand and explain a perceived phenomenon. Induction tests this model as opposed to other factual information and performs the necessary adjustments. Deduction applies the established model of the observed phenomenon. This model will be used by deductive reasoning until new information will put the credibility of this model at risk, or that the reality represented by this model is changed. At this time, a new process of abduction, induction and deduction starts, where a new model of thinking is established. Deduction corresponds to deterministic methods, which can present predictable solutions to a problem. The induction relates to the statistical methods, since they not only have a single, but also a range of possible solutions to the same problem as well as

Fig. 3

System and Environment [5].

Fig. 4

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Process signic scheme in an Intelligent System [5].

abduction that relates to adaptive methods, which can be automatically reset and recreated based on new understandings of the problem that they are modeling, or on its dynamic change. Usually, theories of cognitive science rely on inductive-deductive inferential models. However, the originality of Peirce’s conception of thought comes primarily by abduction, sometimes called retroduction or hypothetical inference.

6. Semiotic Representation Systems and Mathematical Modeling Although computational representations are similar to the semiotic representations, they are not of the same nature. Semiotic representations are conscious representations, closely linked to the idea that we have anything as a result of the action of the object, while the computational representations are internal and independent representations of the vision that one has regarding the object. A computational internal representation can be conscious or not, whereas a conscious semiotic representation can be or not externalized. Every semiotic register of representation is supported on the most important semiotic system. That is, the “natural language”. It could be added that the role of this natural language is decisive and structuring on the other records that are part of formal languages. Normally, there are four types of sign systems in which language operates: (1) semantic systems that constitute the semantic structure of a sentence; (2) semiotic systems that produce the senses by the levels of semiotic significance; (3) logic systems whose

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senses are processed by meaning levels and the logical relationship, for example, the mathematical operation and (4) symbolic systems. In this regard, in relation to mathematical language, Peirce [1] denies that mathematics is a branch of logic by indicating that this knowledge involves a semiotic problem that exceeds the notional subject of writing. In this sense, the consulted literature indicates that no formal language is sufficient enough to entirely sustain from the nature of mathematical doing, since its character is “diagrammatic”, which clearly articulates its own internal logic. Therefore, the diagrams are the main, if not the only, way to acquire new information about spatial relationships. Thus, diagrams and graphs, which represent their objects through the relationships between the constituent parts of them, are semiotic artifacts designed to reveal information about relationships. Although a description of spatial relations can be based on linguistic structures, for example, we know that the best technology is based on the manipulation of lines, arcs, and vertices. Overall, in mathematics, the aspects related to representation are of great importance, for this reason, several authors claim that there is no mathematical knowledge that could be mobilized by a person without the aid of a representation. However, the existence of multiple semiotic registers of representation for the same object, and the inability to access the objects perceived by the materials (requiring a representation) uniquely define their own cognitive activity proper of mathematical procedures, determining their learning. In his manuscript entitled “The Essence of Mathematics”, Peirce (apud Campos) [21] presents two definitions of mathematics. Initially, like his father, Benjamin Peirce, defines mathematics as “the science that draws necessary conclusions”. The following defines it as the study of what is true of the hypothetical state of things. These two definitions contain the essence of the concept of Peirce (apud

Campos) [21] in mathematics. To Hookway [22], the thought of Peirce [1] about math is systemic, considering that he sees mathematics as the core discipline in the classification of the sciences, and this fundamental position of mathematics is a result of his method of reasoning. The mathematical thinking proposed by Peirce [1], which forms a diagram or model of the problem to study and experiment on him, may be employed in any science that is at a lower hierarchical level, and in fact, such reasoning is required for lower sciences while pure mathematical reasoning must remain free of the individual methods of the sciences below it. According to Ref. [22], Peirce [1] considers the virtually foolproof mathematical method, producing certain conclusions and pre-logical, in other words, not subject to logical criticism. The mathematical reasoning is a priori in the sense that its objects of study are entia rationis—we create the objects, namely, mathematical forms. Their findings are right, even when experimentation and observation are inductive, that is, are not reactive, thus the diagrammatic instances are the objects of study. Namely, the math is not subject to the error than the study of perceived truths introduce in our scientific reasoning, since by understanding the meaning of diagrammatic instance we immediately understand the form of general mathematical relationship being studied. For these reasons, the pure mathematical reasoning is fundamental to Peirce [1]. From this perspective, numeration systems, geometric figures, and formal algebraic writings, graphical representations and natural language itself, are examples of semiotic representations. In this sense, Almeida, Tortola and Merli [23] based on Duval [24] admit the “semiotic representation” as part of a semiotic system, a system composed of signs. To Almeida, Tortola and Merli [23], these different semiotic representations constitute from the use of different languages, and thus are associated with different language games whose meanings are


mediated by signs or instruments that represent them. According to Ref. [25], the use of different semiotic representations, that is to say, the plurality of semiotic systems enables diversification of representations of the same object. This fact contributes to a reorganization of the person’s thinking and influences his cognitive activity. Semiotic representations are essential to the understanding of mathematical concepts. According to Ref. [26], the registers of semiotic representation are characterized by three cognitive tasks: the first is the formation of an identifiable representation, that is, when it is possible to recognize this representation of what it represents, within a system of signs socially established; the second is the treatment, which is a transformation that takes place within one system record, for example, solving a system of equations; the third is the conversion, which is the transformation of representation of a mathematical object into another representation of the same object. Conversions are transformations of representations that consist in changing registry keeping the same objects denoted: for example, to move the algebraic writing a function to its graphical representation. According to what Rosa [27] claims, the conversion is generally considered a simple operation, whose finality lies in finding a record in which the treatment is more economical. However, in general, it does not happen. To perform conversions, it is necessary to make joints between the cognitive variables that may be specific to the operation of each records system. These are variables which allow to determine which unit of relevant meaning should be taken into account in each of them. There are many factors that influence the success of a conversion, as the phenomenon of congruence, the order of conversion, the record’s nature and the knowledge that the student has of the records. Thus, the conversions can be more or less complex,

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depending on these factors. To deepen the analysis of cognitive activity required for mathematics, the author deepens the analysis in relation to the different registers of semiotic representation, since they are of different natures. Such nature is important in the conversion process of the records. In this context, Duval [26] ranks the representation registers in multifunctional, monofunctional and its forms in discursive and non-discursive. These records are characterized by their form of treatment: the monofunctional have treatments that can be my made by using algorithms, that is, they are derived and specialized in some kind of therapy and have formal characteristics while the multifunctionals are used in different fields of cultural and social means. They cannot be made by algorithms. For a representation record to be in the discursive form, it needs to allow arguments, deductions, symbolic writing (natural language, numerical system, algebraic) while the non-discursive form is the geometries and Cartesian graphs. For example, writings in natural language is a multifunctional record of discursive representation and a fraction is a monofunctional recording of discursive representation. According to Ref. [26], in solving a problem, one record can appear more privileged than the other, but the important thing is the existence of a possibility of mobilizing at least two records of representation at the same time, or the possibility of constantly interchanging the register and to see, in different registers, the same mathematical object represented. That is, having the coordination between records. To the author, it is the articulation and the coordination of at least two records which constitute a condition of access to understanding in mathematics. In general, mathematical modeling activities involve several steps. The first begins when the individual is faced with a problem situation that it wants to investigate. Then, the action follows to the identification of the characteristics and variables that directly influence the problem.

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The second step is the simplification of variables. Afterwards, the stage where they are introduced to the formal mathematical concepts and notations; this step is the abstraction, which involves the selection of mathematical objects needed to represent the situation under study. The next step involves the manipulation with the representations of mathematical objects in order to obtain a model. Finally, the last step is the model validation and interpretation of the response found, taking into account the initial problem situation. To Bassanezi [28], more important than the answer to the problem and the mathematical model are the discussions promoted during the development of the activity, both on mathematical objects as on the actual situation itself. The modeling process can be described by the diagram shown in Fig. 5. In this sense, for example, we are going to describe here one of mathematical modeling activities that was developed by a group of students from the first year of high school, during math classes at a public school in the state of Paraná, Brasil. Which, for example, we extracted from Rosa’s [27] text. Firstly, the group of students sought a topic of their interest. They found an article on the benefits and evils of the use of photocopies, which featured the title “Xerox: a necessary evil”. The story relates the millionaire dispute between publishers and copiers. From there, the group decided to research prices of copies in various copiers from the city. Table 7 shows some proposals found by them, although in order to preserve traders, the names of their copiers were changed.

Fig. 5

Modeling a problem [29].

Fig. 6

Semiotic representations of content [29].

Table 1 Data collected by students on July 13, 2008 in Sarandi, PR [27]. Copier Copier A Copier B Copier C Copier D Copier E Copier F

Prices R$0,20 each and R$0,15 each, up to 100 copies R$0,15 each up to 300 copies; R$0,05 for each copy beyond 300 copies R$0,15 each and R$0,10 each, up to 10 copies R$0,20 each and R$0,15 each, up to 10 copies R$0,10 for any number of copies R$0,15 each and R$0,10 each, up to 50 copies

According to what Rosa [27] argues in analyzing the data, it becames clear that the curiosity of the group in relation to the copier “B”, thus came the problem to be investigated from many copies: is it financially feasible to use the copier “B”? Since the number of copiers, the group decided to choose only two to be analyzed: the copier “B”, for its characteristics, and the copier “E”, for having the lowest price for a small number of copies. This was the step that the group presented more difficulties, supporting Duval’s [26] argument that the congruence phenomenon and the fact that the difference in the nature of records of a conversion determines the degree of difficulty that students face to perform the conversion. The next step of the activity of mathematical modeling is the formulation of hypotheses. They considered that the growth rate against the number of copies for the two copiers was linear. And so, they considered doing two functions, one to represent each copier, and then they would discover the number of copies that would equalize the price charged by the two copiers. Rosa (2009) mentions that when observing the formulation of hypotheses by the group, she noted that


when they referred to the “representation of a function to each copier”, they were referring to the same algebraic record, thus identifying at that time, the mathematical object “function” by their algebraic representation. To obtain the model, they began by the copier “E”, and set off a record tabular. From the data in Table 2, the group held a congruent conversion of the registration tab to the algebraic registry because the output (tabular) registry reveals the arrival record (algebraic). The nature of the two records in this case is monofunctional and the two representations are discursive. The difficulty encountered by students at this stage was in relation to the characterization of the function domain, given that they were unaware of the numerical sets. The complete characterization of the algebraic function to the copier “E” prices passed to the copier “B”, using the same procedures. In Rosa’s [27] opinion, this first part happened analogously to the previous one, namely a conversion of the registration tab to the algebraic register, congruent, an activity of simple coding records of the same nature. The second part started the same way, first the tab record, then the algebraic tabular record. For Rosa [27], that conversion did not happen the same way as the previous ones, because the author found that the degree of difficulty was higher, influenced, in her view, by the level of knowledge of students. Therefore, we have: Copier E: VE (n) = 0,10.n ;’ (1) Copier B: (n) =

0,15. ; 0,15. ;

300 300

+;

(2)

Thus, Rosa [27] states that once defined the functions that represent the copier “E” situation and the copier “B” situation, the group went to the next step, the validation of models. Numerical records were used, obtained with the development of models and presenting the results in the form of tabular records. By comparing the observed values and the values estimated by functions, the group concluded that the two models referring to Tables 1 and 2 represent both

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“E” and “B” copiers’ situation respectively. To answer the original question—from how many copies is it feasible to use the copier “B”? The group drew up Table 3. According to Rosa [27], based on the calculations shown in Table 6, the group concluded that from 600 copies, it was worth using the services of the copier Table 2 Conversion between record tabular and algebraic entry—copier “E” [27]. N

v

0 1 2 3 4 5 6 … n

0 1. 0,10 2. 0,10 3. 0,10 4. 0,10 5. 0,10 6. 0,10 … n. 0,10

V(n)=0,10n Conversion 2

DOM(V)={n/n

Z +}

Table 3 Conversion between algebraic and tabular log record (for a number less or equal to 300 copies)—copier “B” [27]. n 0 1 2 3 4 … 300

v 0 0,15 2. 0,15 3. 0,15 4. 0,15 … 300.0,15

V(n) = 0,15n Conversion 3

N ≤ 300

Table 4 Conversion between algebraic and tabular log record (for a larger number than 300 copies)—copier “B” [27]. n

v

301 … 350 … 400 … 600 … 700

300.0,15 + 0,05 … 300.0,15+0,05.50 … 300.0,15+100.0,05 … 300.0,15+300.0,05 … 300.0,15+400.0,05

n

300.0,15+0,05 (n300)

Conversion 3

V(n) = 0,05.n + 30 n > 300

994 Table 5

Mathematical Modeling and Computational Semiotics: Methodological Approach to Formalization of Semiotic Concepts Validation of models [27].

Real Number of data Function: copies copier e V(n):=0.10.n in R$ 0 0 0,10.0 = 0 0,10.1 = 1 0,10 0,10 0,10.2 = 2 0,20 0,20 … … … 0,10.50 = 50 5,00 5,00 0,10.100 = 100 10,00 10,00 0,10.200 = 200 20,00 20,00 0,10.300 = 300 30,00 30,00 0,10.400 = 400 40,00 40,00 0,10.500 = 500 50,00 50,00 0,10.540 = 540 54,00 54,00 0,10.56 = 560 56,00 56,00 Table 6 N 0 2 200 300 400 500 600 700 800 900 1,000

Real data copier b Function in R$ 0

0

0,15

0,15.1 = 0,15

0,30

0,15.2 = 0,30

…

…

7,50

0,15.50 = 7,50

15,00 30,00 45,00 50,00 55,00 57,00 58,00

0,15..100 = 15,00 0,15.200 = 30,00 0,15.300 = 45,00 0,05.400+30 = 50,00 0,05.500 + 30 = 45,00 0,05.540 + 30 = 57,00 0,05.560 + 30 = 56,00

Calculations to answer the initial question [25]. Related function copier “E” (R$) 0 0,10.2 = 0,20 0,10.200 = 20,00 0,10.300 = 30,00 0,10.400 = 40,00 0,10.500 = 50,00 0,10.600 = 60,00 0,10.700 = 70,00 0,10.800 = 80,00 0,10.900 = 90,00 0,10.1000 = 100,00

Related function copier “B” (R$) 0 0,15.2 = 0,30 0,15.200 = 30,00 0,15.300 = 45,00 0,05.400 + 30 =50,00 0,05.500 + 30 = 55,00 0,05.600 + 30 = 60,00 0,05.700 + 30 = 65,00 0,05.800 + 30 = 70,00 0,05.900 + 30 = 75,00 0,05.1000 + 30 = 80,00

Worth E E E E E IGUAIS B B B B

“B”. Here, another conversion took place (from the registration tab to the record in natural language). As none of the group members “thought” in using graphic recording to find the problem solution, or even to visualize the function behavior, Rosa [27] suggested them to do a graph sketch of each function found and to show the solution graphically. In this respect, Rosa [27] noted that, in Fig. 1, copier “E”, the starting point entered as a point belonging to the function, and, in graph 2, copier “B”,

Graphic 1 Graphical representation of the copier “E” function [27].

Graphic 2 Initial graphical representation for function [27].

copier “B”

beyond the initial point belonging to the function, they failed to make the function graph defined by sentences. For the construction of these charts they used the records of Tables 2-4, namely there was a conversion of the registration tab to the graphic record. Graph 2 shows that they failed to graph the algebraic function found for the copier “B”, since Graph 2 does not have the characteristics of a “set of sentences”. For Rosa [27], this fact shows that the students failed to understand that the registration of the algebraic function (2) and the chart record shown in Fig. 2 represented the same function. Therefore, they need to preserve some features. So we can say that there was no full apprehension of mathematical object under study, because according to Ref. [26], to be apprehension of the mathematical object by the student, he needs to make coordination between records. In summary, Rosa [27] states that she found seven conversions in the activity of mathematical modeling “Xerox: a necessary evil”.

Mathematical Modeling and Computational Semiotics: Methodological Approach to Formalization of Semiotic Concepts Table 7

Conversions performed by the group [27].

Conversion Output record Record in natural 1 language 2 Tabular record 3 Tabular record 4 Tabular record 5 Tabular record 6 Tabular record 7 Tabular record

Arrival record Algebraic record Algebraic record Algebraic record Algebraic record Record in natural language Graphic record Graphic record

Regarding the conversions performed by the students, described in the table above, Rosa [27] claims to have verified much difficulty by the students, fact which can be evidenced mainly in the error occurred in the conversion 7, when converting one tabular record for the chart record for copier “B”. Given these considerations, Rosa [27] states that in the undergoing preparation and problem-solving process, it was found that each member of the group of students felt somewhat responsible, referring to the activity as “my problem”; states the author, students seemed to be solving something particular and of self-interest. This demonstrated interest influenced in the development of the activity, since they “wanted” to solve the problem. In this sense, Rosa [27] says that from the diversity of records that emerged during the development of the activity, the focus of their study was the analysis of the conversions performed during the stages development of mathematical modeling activity that approached the mathematical object “function”. Taking into account all these aspects, Rosa [27] noted that in general, students do not make coordination between records as well as being clearly the choice of algebraic record, while the graphic record is not even remembered (unless when they are suggested). Thus, the success of the conversion activity can be compromised and consequently a conversion is not always carried naturally by the students. In this regard, we note that it is in the conversions where are present the major cognitive difficulties students.

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Ref. [30] presents the explanation of the difficulty in conversions when he introduces the idea of figural concept with two components: conceptual and figural. The conceptual component, varying its degree of formalism from top to bottom is presented in natural and/or symbolic language; the figural component is visual in nature (shape, position, size), and is expressed through drawing. It is the proper fusion of these components that ensures the construction of geometrical ideas. The idea of Fischbein [30] brings advances in understanding the complexity of the mathematics learning process, because his theory shows that it is the work with many conversions between different records that will subsidize the knowledge construction. Therefore, Rosa [27] concludes that student involvement in activities which nurture a diversity of records and the coordination between them is essential for learning the concepts involved. Given these considerations, we agree with Ernest [31] that, semiotics being the signs study which participates in different contexts of human activities, it is natural to consider the process of learning mathematics also from this perspective. Ernest [31] advances in defining what would be a semiotic system in the specific context of mathematics, highlighting three components: a set of symbols that are expressed through speech or text, and design; a set of production rules of signs, including, here, those that deal with the organization of discourse that makes use of the signs composition; a set of relationships between signs and their meanings. This definition seeks to embrace the texts, symbols and designs characteristics that integrate the logical discourse that produces and crystallizes mathematical knowledge. It is important to note that the development of mathematical knowledge depends on representation systems that crystallize and generate new concepts and ideas, but it is these same representation systems

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that must be learned by the student, so that he can have access to mathematical knowledge. That is, on one side, there is the mathematics professor in the teaching process of representations that convey ideas and mathematical procedures; and on the other hand, there is the student in the position of apprentice concepts and procedures that depend on understanding the representation systems. In short, these reflections made in the light of Peirce’s semiotic theory, we believe that the development of a mathematical modeling activity relates to a “quality” (a phenomenon), a “reaction” (the identification of a problem and setting goals resolution) and a “representation” (associated with the solution for the identified problem). In this sense, we can associate this development to the phenomenological categories established by Peirce [6] (Firstness, Secondness and Thirdness) and, consequently, the levels of identified relationships for signs (meaning, objectification and interpretation).

7 Interaction Model Subject—Computing Environment

Text

In this topic, we present a model made by Behar [32] to analyze both logical and infralogical operations, as well as the subject and the computational tools. One study goal is to show the model construction process of the subject-object interaction (tool), arising from semiotics elements. Note that the terms “logical and infralogical operations” have the following meaning conceived by Piaget [33]: “Logic operation is the one which deals with individual objects considered as invariant and merely assemble them or relate them regardless of their neighborhoods and spatiotemporal distances that separate them”. Infralogical operation consists in making the object through its own elements, not achieving classes nor independent spatial relations, but, overall objects of different types. It deals with, for example, gathering

the parts of an object in an all or putting them in a certain succession order. Infralogical operation, in general terms, the infralogical operation consists of “composing the object through its own elements, not achieving classes nor independent spatial relations, but, overall objects of different types”. It deals with, for example, gathering the parts of an object in an all or putting them in an order of certain succession [33]. For the author, by using a graphical editor, we can highlight the logical operations that are found in a text development, in which regards to the parts relationship of a text with their final product, the sequence should be followed in a text to arrange a coherent whole, the correspondence that should exist between the same parts, among others. According to her interpretation, when a subject, for example, develops an activity in which the graphical editor is working on the representational space, forming an overall figure through their parts. This means that he will be operating, mainly in an infralogical level, composing, from the partial objects, entire objects. This does not mean that the person is not making logical operations. For sure he will be. From the formal standpoint, there is no superiority of logic level in relation to the infralogical. These two does not only mutually assume themselves, but also deal with the same operational system, namely, the group applied to different operational modes with the objects. Therefore, regarding the operative analysis of computational tools, the proposed study by Behar [32] shows one of the paths found as to how they can be seen in relation to the logical and infralogical operations. Given these considerations, it is worth highlighting that in this topic, in order to better illustrate the interactional model construction subject—computing environment, we reproduced below the extracted sample of Behar [32]. In this sense, Behar [32] states that, in order to view


the simplest interactional subject (S) model with a computational environment (C) which, in this case is the object (O), shall be a first draft of the same in Fig. 7. The object in question (C) consists of the FC (computational tool), that is, the system itself (hardware environment) and the representation that the subject performs on the computer (RC—software environment). This figure is detailed as follows. To define the elements that are part of the subject, Behar [32] took into account the mental factor of the same which is formed according to Ref. [34] by three inseparable aspects: structural (cognitive), energetic (affective) and symbol (symbolic) systems, serving to these significant operational structures or to these individual values. Thus, it can be said that a subject is composed of affective, cognitive and symbolic structures. Affective structures relate to the values of the subject. The cognitive ones refer to the object itself, that is, they are responsible for the operations carried out in relation to objects, such as ratings, measurements, seriations, sum, subtraction. Finally, the symbolic structures are the ones who give representative meaning to the objects, using, for this, the signals, like the speech. Inherent in these structures are also the mental image of the subject, which will not be presented schematically. This model can be seen in Fig. 9. For Behar [32], these objects, plus those arising from semiotics, gave rise to the necessary elements for the construction of the interactional model that is used to perform the operative analysis of the computational tools for individual and collective use. Therefore, the result of the composition of Figs. 8 and 9 can be seen in the model of Fig. 10. Fig. 7 External view of the subject—computational environment [32].

interaction

Fig. 8 Internal viewing of subject—computational environment [32].

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Fig. 9 Structures that make up an individual subject [32]. Si: individual subject; EA: affective structure; EC: cognitive structure; ES: symbolic structure; V: values; O: objects and L: language.

Fig. 10

Individual interaction assisted by computer [32].

When the subject has to use some kind of computational tool to represent anything, he is led to think about his thinking in order to then be able to transcribe or express his ideas. At the moment in which this one has to express in writing or figurative manner of his thought, he can reflect on it and often restructure it, by building or rebuilding his mental image. This process may lead the subject to construct new knowledge, but everything will depend on how the subject relates to the environment. That is why we used a bidirectional arrow connecting the values, objects and language to the computer. As the mental image of the subject is inherent in the structures, through interacting with the tool and/or the computational representation, this image can be changed constantly. In the model defined in Fig. 10, other elements that are part of the interactional model were added, using the notation of “Petri nets” to detail the elements that are active (ð) and/or passive (O) in the environment in question. This result is shown in Fig. 11. Importantly, Petri nets or simply PNs were created from the doctoral thesis of Carl Adam Petri, entitled

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Fig. 11 General interactive model subject—computing environment [32]. S: subject (subject User and/or programmer); FC: computational tool; L: language used for the computational representation; RC: computational representation (value, object and/or language represented in the form of textual/figural graphical image); RIM: representing the mental image; IM: mental image and T: communication channel: screen, keyboard, image.

“Kommunication mit Automaten” (Communication with Automata), presented at the University of Bonn, Germany in 1962. From the beginning, PN aimed modeling systems with competing components [35]. Therefore, according to what Behar [32] claims, this model can be understood as follows: Relying on the mental picture (IM), the subject (S) has in relation to “something” which wants be to represented, it can be values, objects and/or a particular language, it uses a language (L) for representing your IM. This language, which may be its natural language (drawing or writing) or computer language, allows the representation of this “something” on your computer (RC). To accomplish this representation, the subject uses the computational tool (FC) manipulated via the keyboard, screen, etc. In summary, this is the general model that was built by Behar [32] as one of the ways found to explain the interactional process of a subject and its structures with any computational tool, on the individual level.

8. Results and Future Work This study had two main objectives: first, to conduct an analysis of the state of the art regarding the techniques of intelligent computational systems. Also, to present the theoretical foundations in order to identify the use of new techniques for modeling intelligent systems through the integrated use of

mathematical and computational modeling. During the process of conducting, this research we looked through the consulted literature that the basic triad of semiotics, that is, the triple (sign, object, interpretant) can be mapped in models of artificial intelligence as stated by Gudwin [36]. In the semiotics triple, the sign is used to represent the object, whose understanding by an intelligent mind corresponds to the interpretant. That is to say, the interpreter is the intellectualization of the object. In triple of artificial intelligence, a phenomenon of the environment (which corresponds to the triple object of semiotics), interpreted as knowledge about the environment is represented by a model of knowledge representation, which corresponds to the sign. We also saw that “semiotic representation” consists of signs belonging to a given semiotic system, which gives it a particular meaning within a given context. How different records will be accepted, that is, different semiotic systems referred to the same content, you must consider that the various systems are part of a compound semiotic system, referred to the same content (or slight variations of a same content), endowed with conversion rules between different records. In this sense, the same content can be represented in different records, each recognizing different representations. This relationship between representations of the same object in different records is what Duval [26] calls “conversion” between records. Thus, in a given record, it can be constructed different representations related to each other. Duval [26] calls them “treatment”. The didactic use of Duval’s [26] theory assumes that the student may not have fully appropriated himself of the represented content, and it can treat a representation as a game without clearly understand the terms meanings. Everything happens as if the understanding that the vast students majority had of content was limited to the form of the representation used.


For this reason, the use of an appropriate representation avoids continuous symbols remissions to their meaning, saving the thinking job through the purely symbolic treatment and this is one of the main pragmatic representational functions, under the domain hypothesis of the associated content, transforming the reasoning in a “calculation”. But at the same time, a single representation reduces the concept to a symbolic calculus. Based on these arguments, we believe that the construction of intelligent systems semiotically inspired or not, constitutes a great challenge to computer science and other sciences, because scientific and technological evidence points to the increased interaction between computing and virtually all areas of human knowledge. However, for the hypothetical promise of technological impact is performed, it is necessary that researchers and practitioners are prepared to change and adapt their work practices. This supports the need for further research practices, requiring multidisciplinary and strong fundamental scientific knowledge teams. In our opinion, this knowledge is essential to allow the construction of artificial intelligent computer systems.

9. Acknowledgments The authors thank the teachers Ricardo Matos Chaim, Rita de Cássia and Maria Alzira Araújo Nunes, from the Specialization Course on Modeling of Complex Systems of the Faculty of Engineering (UnB Gama) at the University of Brasilia. And also thank for the stimulus and the contribution to their academic trajectory culminating in this work.

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Peirce, C. S. 1976. The New Elements of Mathematics. Netherlands: Mouton Publishers. Oliveira, L. F. 2012. “Dynamical Systems, Self-organization and Meaning Music.” http://www.academia.edu/1520997/Sistemas_Dinamicos_ Auto-organizacao_e_Significacao_Musical. Hjelmslev, L. 1975. Prolegomena to a Theory of

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Language. Sao Paulo: Perspectiva. Pottier, B. 1974. General Linguistics: Theory and Description. Paris: Klincksieck. Gudwin, R. R., and Gomide, F. A. C. 1996. Semiotic Intelligent Systems According to Behaviourist Semiotics of Charles Morris. Technical report, DCA/FEE/UNICAMP, Campinas. Peirce, C. S. 1977. Collected Papers (1931-1958), Semiotic. Sao Paulo: Perspectiva. Forrester, J. W. 1971. World Dynamics. Cambridge: Wright-Allen Press. Bertalanffy, L. V. 1977. General Systems Theory. Sao Paulo: Vozes. Forrester, J. W. 1961. Industrial Dynamics. New York: John Wiley & Sons. Sousa, G. W. L. 2006. “System Dynamics.” http://www.numa.org.br/conhecimentos/conhecimentos_p ort/pag_conhec/System%20Dynamics.html#instrucao. Sterman, J. 2000. Business Dynamics: Systems Thinking and Modelling for a Complex World. Boston: Irwin McGraw-Hill. Loula, A. C. 2004. “Symbolic Communication between Artificial Creatures: An Experiment in Artificial Life.” M.Sc. thesis, State University of Campinas. Beer, R. 2000. “Dynamical Approaches to Cognitive Science.” Trends in Cognitive Sciences 4 (3): 91-9. Weisbuch, G. 1990. Complex Systems Dynamics. Redwood: Addison-Wesley. Bresciani, E., and D’Ottaviano, I. M. L. 2000. “Conceitos Básicos de Sistêmica.” In Self-organization: Interdisciplinary Studies, edited by Debrun, M. M., Gonzalez, M. E. Q., and Pessoa, O. Campinas: UNICAMP. Camazine, S. 2002. Self-organizing Systems. New York: Nature Publishing Group. Nicolis, G., and Prigogine, I. 1989. Exploring Complexity. New York: W.H. Freeman. Pereira, V. A. 2000. “Cyberspace: A Step of Semiotic Dance of the Universe.” Magazine of Master in Communication, Imaging and Information UFF, Contracampo (4). http://souzaesilva.com/Website/portfolio/webdesign/siteci beridea/vinicius/textos/ciberespaco.pdf. Nadin, M. 2011. “Semiotic Processes and Information Semiotics of Computing.” Graduate Program in Technology Intelligence. (5). http://www4.pucsp.br/pos/tidd/teccogs/dossies/2011/edic ao_5/1-processos_semioticos_e_de_informacao-a_semiot ica_da_computacao-mihai_nadin.pdf. Gonzalez, M. E. Q., and Haselager, W. F. G. 2003. “Creativity and Self-organization: Contributions from Cognive Science and Semiotics.” SEED 3 (3): 61-70.

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[21] Campos, D. G. 2007. “Poietic Creation and Mathematical Reasoning in Peirce.” Cognitio-studies: Electronic Journal of Philosophy 4 (2): 81-92. [22] Hookway, C. 1985. Peirce. London: Routledge. [23] Almeida, L. M. W., Tortola, E., and Merli, R. F. 2012. “Mathematical Modeling: What We Are Dealing with: Different Models or Different Languages?” Acta Scientiae 14 (2): 215-39. [24] Duval, R. 2011. “Registers of Semiotic Representation and Cognitive Functioning in Understanding in Mathematics.” In Learning Mathematics: Records Representation Semiotics, edited by Alcantara, S. D. Campinas: Papirus. [25] Duval, R. 2008. “Records of Semiotic Representation and Cognitive Functioning in Understanding in Mathematics.” In Learning Mathematics: Records Representation Semiotics, edited by Machado, S. D. A. Campinas: Papirus. [26] Duval, R. 2003. “Records of Semiotic Representation and Cognitive Functioning of Understanding in Mathematics.” In Learning in Mathematics, edited by Machado, S. D. A. Campinas: Papirus. [27] Rosa, C. C. 2009. “The Registers of Semiotic Representation and Mathematical Modeling: Performing Conversions in an Activity in High School.” Diálogos & Saberes 5 (1): 111-24.

[28] Bassanezi, R. C. 2002. Teaching and Learning with Mathematical Modeling: A New Strategy. Sao Paulo: Contexto. [29] Silveira, M. A. 2005. “A Pedagogical Analysis of Modeling Dynamic Systems.” Presented at the XXXIII Brazilian Congress of Engineering Education, Campina Grande, PB. [30] Fischbein, E. 1994. “The Theory of Figural Concepts.” Educational Studies in Mathematics 24 (2): 139-62. [31] Ernest, P. A. 2006. “Semiotic Perspective on Mathematical Activity.” Educational Studies in Mathematics 61: 67-101. [32] Behar, P. A. 1999. “The Operative Logic and Computing Environments.” Presented at the X Brazilian Symposium on Computing in Education, Porto Alegre, Brazil. [33] Piaget, J. 1971. Reflective Abstraction. Porto Alegre: Artes Médicas Sul. [34] Piaget, J. 1973. Sociological Studies. Rio de Janeiro: Forense. [35] Marranghello, N. 2005. “Petri Nets: Concepts and Applications.” UNESP, São Paulo, http://www.dca.fee.unicamp.br/projects/artcog/files/wtdia 04-loula-4248.pdf. [36] Gudwin, R. R. 1996. “Contributions to the Mathematical Study of Intelligent Systems.” Ph.D. thesis, State University of Campinas, Campinas.


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Innovation and Education: Construction of Interactivity Indicators to Collaborative and Immersive Learning Estéfano Vizconde Veraszto1, Gilmar Barreto2, Sérgio Ferreira do Amaral2 and José Tarcísio Franco de Camargo3 1. Department of Natural Sciences, Mathematics and Education, Federal University of Sao Carlos, Araras 13604-900, Brazil 2. School of Electrical and Computing Engineering, State University of Campinas, Campinas 13083-852, Brazil 3. Department of Computer Science, Regional Universitary Center of E. Santo do Pinhal, E. S. do Pinhal 13990-000, Brazil Received: November 11, 2014 / Accepted: November 21, 2014 / Published: December 25, 2014. Abstract: Technological innovation, driven towards the educational context, has favored the concept of interactive technological environments that may significantly contribute towards the teaching-learning processes. In that sense, mapping interactivity indicators that consider technical and operational aspects, supported by the available technical literature and based on the perspective of undergraduate engineers and teachers, becomes a fundamental activity in order to build interactive environments that may in fact adequately contribute for the professional education of our students, mainly the ones in engineering courses. Specifically, this paper shows preliminary studies within this perspective, showing how technological innovation may be understood and applied in the educational context. The study also shows the first interactivity indicator for a collaborative learning perspective, obtained from data collected through a qualitative content analysis methodology. Key words: Engineering, statistical indicators, innovation, immersive environments.

1. Introduction Society has gone through significant changes over the last years, thanks to the technological developments. We live in an age in which different sectors of society are trying to constantly reinvent themselves in the sense of developing skills in the most different areas. Technological innovation has contributed to create processes that are able to create and administer knowledge, and the market has shown how it is possible to learn through the interaction with the environment in the sense of attending the social needs and demands [1]. In line with that, this study tries to show introductory guidelines as to how innovation may be faced within the educational context, from different premises, in an attempt to consolidate a guiding perspective. That is because we know that there is a Corresponding author: Estéfano Vizconde Veraszto, Ph.D., research fields: education and new technologies statistics. E-mail: [email protected].

lack of guidelines as to how technological resources should be employed at school in order to actually assure learning. And in order for such resources to be used within the educational scenario, it is fundamental to understand the individual and collective needs associated with the teaching-learning process. In parallel, it is also necessary to know how the resources that come from technological innovations may be efficiently used within this context [2]. In fact, we may go a little further, and question: what is actually innovative in terms of education? The world around us creates innovative technological products, but which of these resources may be used in such a way that they actually contribute toward the educational process? It is in that sense that this study is developed. Here, we will map and analyze indicators for the management of ITE (interactive technological environments) with the purpose of bringing technical aspects and educational needs together.

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Innovation and Education: Construction of Interactivity Indicators to Collaborative and Immersive Learning

It is not about specifying one or more artifacts, but a set of technological resources that are able to support the agents of the educational process for the construction of knowledge. It is fundamental that such agents understand and know how to apply in a practical manner the influence that technology has over the production, storage and transmission of knowledge. And, in that sense, we also highlight the importance for this technological set to be interactive, bearing in mind that nowadays, society creates, consumes and demands information, systems and processes that essentially allow the individual to interact with the environment, other individuals, and information and knowledge in general [3, 4]. We must also consider that it is under this perspective that the most complex innovation processes aimed at the social demands are promoted. Therefore, throughout this study, the choice for such aspects will be justified as the guidelines to map the ITE indicators oriented toward management and education will also be shown. 1.1 Delimiting the Problem This study tries to investigate how ITE may ally characteristics of the own innovation process in the educational context. In the case of this specific study, the work shows efforts in the sense of defining what is innovation at school and tries to answer the following question: which indicators of interactive technologies may be used in education under a collaborative learning perspective? 1.2 Objectives and Justification From the context briefly presented earlier, whose bases were previously published in Ref. [4], in a very specific manner, this article tries to define the concept of innovation at school. Hereafter, a preliminary survey of interactive technologies and environments that may contribute for the teaching-learning process is conducted. With such discussions, we expect to

create bases for further studies with the purpose of verifying how can the technological innovation offer subsides for the ITE management and the educational context. By suggesting innovation aspects at school, Ref. [5] states that in the traditional education, there is a lack of methodological proposals that are able to promote a learning environment up to the current technological scenario. In that sense, they state that fun and playfulness are key aspects to draw the attention of the student. In addition to that aspect, there is also the dialogical characteristic that a teaching activity must have—offering effective dialogues within a group. This factor would break the conventional monologue that is such a major part of the traditional classes. Finally, there is also the challenge aspect, added to the teaching strategies as a fuel for the student to overcome trouble-making situations. With technological innovation aspects in education, the agents involved may benefit from the use of ITE in the teaching and learning process, since these resources allow information and knowledge to be shared. And in order to know how to manage such resources, it is necessary to know them better, under different aspects, such as the ones related with didactic situations, the cognitive design and ergonomy. In order to approach didactic situations, it is necessary to bear in mind that the challenge to produce more and better has been replaced with the permanent challenge of creating new products, services, processes, and managerial systems. On the other hand, individuals have been increasingly searching for constantly learning, at the same time in which they present more creative characteristics [1]. This paper is organized as follows: Section 2 presents the methodology of the work; Section 3 shows the theoretical grounds; Section 4 exposes the interactivity indicators; Section 5 presents the development of indicators to evaluate interactive technological environments, and then discusses the


obtained results; and finally, Section 6 exposes the final conclusions.

2. Methodology This study adopts a content analysis process in order to classify and categorize data from national and international articles, books, and documents. For such, the texts were selected according to a predefined criterion: they should contain information about interactive technological resources that could be used in the teaching-learning process in a collaborative manner. According to the theory presented in Ref. [6], the work is divided into three stages: (1) The first stage (pre-analysis): organizing the collected material and skimming the text in order to categorize the data obtained; (2) The second stage (exploring the material): consisting in the systematic management of the decisions made; (3) The third stage (processing the results and interpretation): combining reflection, intuition, and empirical data in order to establish relations with the results from raw data and making them significant and valid. From this process, the data went through a codification process. From the organized data, the material was categorized based on the theoretical references. This ordination strategy was adopted in order for a simplified representation of raw data to be catalogued for the final analysis process.

3. Theoretical Grounds Before moving forward, it is necessary to define how the innovation concept may be understood and employed within the educational scenario. And that is made below. From the economic point of view, innovation means a new product, a new production method, a new market, a new source for raw materials and inputs, and a new market in an industry [7]. This perspective tends to emphasize innovation as market experiments

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and to search for broad and extensive changes that have restructured industries and markets [8, 9]. In education, how are innovation processes understood? May the same definition from economy be employed or do new subsides need to be aggregated in order to understand how could innovation and school walk together? In order to create bases for a deeper discussion on this issue, it is necessary to consider that the technological cycle has been increasingly shorter than the professional career of the individuals. That makes people search for ongoing improvement in order to update their concepts, techniques, expertise and methodologies. An educational system, that aims to promote the insertion of students in the workplace with such profile, needs structural reformations. It is necessary to rethink about theories and methods based on a new learning paradigm that is able to combine intellectual and creative activities, simply letting the actions follow a direction in the search for improved production processes [9]. Educational institutions need to understand and absorb the innovation process in order to exercise it and stimulate it on them day-by-day. The innovative learning becomes a means to prepare the individual to face new situations, and it is a mandatory requirement to solve global issues. For this reason, it is up to the educational institution: the macro management and incorporation of this new concept. For such, the concept of interdisciplinarity is essential and it needs to be used in the sense of exercising and stimulating creativity and entrepreneurship. According to Ref. [10], there are different concepts of innovation in the educational context. Therefore, it is possible to consider innovation: (1) In an accidental manner, as superficial changes that never affect the essence of the purposes and methods professed in education. Under this perspective, innovation is a synonym for a superficial touch-up;

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(2) As a way to essentially change the educational methods and manners; (3) As the use of other media that are added to the conventional media, being combined with them or replacing them. As with both previous conceptions, innovation is understood as a function of the educational apparatus, with no reference to the context. The difficulties of education are always attributed to the own educational context and, as a consequence, the solutions are suggested within this process, without questioning the purposes of education, since they are extrinsically defined, that is, on the level of social organization, that produces the educational organization; (4) As the use of education for new purposes, for the structural change of society. Therefore, starting from the traditional education, innovation may reach four levels: (1) Keeping the institution and the purposes of education intact and giving the method superficial touch-ups; (2) Keeping the institution and the purposes of education and substantially changing the methods; (3) Keeping the purposes of education, but the institutions and conventional methods, whether they have been changed or not, must be followed by extra-institutional and/or non-institutionalized methods; (4) Changing the own purposes of education, by searching for more adequate and efficient means to reach new objectives.

4. Interactivity Indicators In order for this study to discuss ITE, it is fundamental to indicate, even if briefly, the historical aspects on the conception of the term interactivity, and a broad view on its importance toward educational management. 4.1 Interactivity The transformation of the term interaction to

interactivity occurred when computer science re-elaborated a term that derives from physics, and that acquired different connotations by permeating sociology and then social psychology [11]. According to Ref. [12], the term interactivity was created within the context of the criticisms made to the one-directional communication means and technologies, starting in the 1970s, and being broadly employed currently. However, the theme was seen for the first time in the 1960s, when scholars from the area of Computer Sciences searched for a new meaning for the communication between computers and men, based on improved quality on their relationship, regarding agility, user-friendliness and great possibilities of communication [13]. It is also common to find the term interactivity employed as a synonym for digital interaction. Interactivity only means an exchange, reducing the concept in a very superficial manner in relation to the whole field of meaning that it encompasses [12]. Usually, the term interactivity relates to cyberculture. Most studies focus on computers and give priority to the capacities of the machine, making human being and social relations mere co-actors [14]. 4.2 Preliminary Indicators of Interactivity Considering a complex and intricate discussion on the theme, the authors of this article tried to classify and categorize different studies [11-23], according to content analysis techniques [6]. The result is shown in Table 1, where the elements that are considered as primordial in order to belong to an interactive technology that should be applied to education are shown. In that sense, the study considers that ITE must allow exchanges between the machine, software and users, through peripherals or audiovisual menus and links, providing learning, entertainment, acquisition of information and real-time or remote communication. Therefore, interactivity needs the virtual system to be dynamic, to provide several possibilities of choices


and feedback, with the aid of animations, movies, songs, hypertext, games, simulations, holographs and likelihood with the actual environment and allow the user to be able to be immersed in the virtual environment whether in a passive or active, individual or collective manner, with options to transform the virtual environment freely and according to their will and preferences, believes and values [24, 25]. And all these points considered may be leveraged as long as they are used under a collaborative perspective. In general, collaboration may be understood as a social action in which people share objectives and learn together, with the purpose of overcoming challenges and building knowledge [26]. In that sense, the own elements of innovation may be incorporated by the school from the time that different methodologies are developed, giving priority to a stricter relationship between educational theories and the use of technological resources in the routine of the school.

5. Developing Indicators to Evaluate ITE From the discussion shown in this article and from the results previously shown, the research partnership initially described has the purpose of reaching higher goals. Among these goals, we may highlight:  Mapping interactive technological environment indicators, considering technical and operational aspects;  Considering engineers and teachers (mainly from the areas of nature sciences), creating a research instrument to map expectations by interactive technological environments and to map the demand for interactive technological environments;  Confronting the information and suggesting ITE management strategies;  Establishing an introductory discussion on how to use the results found, in a future study, in order to elaborate didactical situations from ITE, considering technical, epistemological and cognitive aspects; and to investigate the learning process, mapping interactive technological environment indicators, considering technical and operational aspects.

Table 1

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Interactivity indicators (preliminary studies).

1. Exchange across machines 2. Exchanges across users and software 3. Learning possibilities 4. Entertainment 5. Acquisition of information 6. Real-time communication 7. Remote communication

Interativity indicators 8. Dynamic 15. Holographic system simulations 9. Power to 16. Likelihood with choose (decision) the real thing 17. Passive 10. Feedbacks immersion 18. Active 11. Animations immersion 12. Movies and 19. Individual songs immersion 20. Collective 13. Hypertext immersion 21. Transformations 14. Games of the of the virtual environment

5.1 Stage 1: Elaborating Criteria to Build Indicators The first point in order to map the indicators is about the technical and operational characteristics of ITE. Regarding this aspect, indicators on the versatility, configuration, audiovisual resources, usability, connectivity, compatibility with didactical situations, interactivity, playful aspects, among others, are surveyed. These indicators will work as the basis to build the research instrument for the second stage of the research. 5.2 Stage 2: Elaborating the Research Instrument The indicators mapped in the previous stage will work as the basis to build the research instrument to be applied, focusing on undergraduate engineers and teachers as the target audience (mainly from the areas of nature sciences). The instrument will be built based on the search for the actual educational needs derived from the introduction of ITE in the educational context. In general, data are on:  Technology in education;  Interactivity and learning;  Learning in virtual environments. Such data will be surveyed and classified from the point of view of engineering professors and students, and also for the area of undergraduate nature sciences teachers. Within this context, a broader instrument, now based on a quantitative methodology will be used

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to investigate samples comprised by students, professors and professionals that work in the areas of engineering and education. The initial option to analyze the school will be the use of the statistical method known as factorial analysis [27], which is a way to determine the nature of patterns that are involved in a large amount of variables. It is particularly adequate in researches where the objective of the investigators is to make an “ordered simplification” of the number of inter-related variables [28]. That is, we are looking for the smallest possible set of factors by gathering premises according to the same statistical correlation trend, in order to judge aspects with the same relevance regarding the set of assertions. With such analysis, we may separate and aggregate elements that are oftentimes unidentified, and obtain an integral view of the previous conceptions of the respondents. In addition, such analysis may reveal which are the expectations from teachers and students regarding the suggested issue. 5.3 Stage 3: Teaching Engineering and ITE Management

The comparison between the technical indicators and the actual demand and expectation from the agents involved in the educational aspect may be used as a basis for a better management not only of ITE, but also in relation to knowledge in general. These data will work as a first step toward the development of proposals for didactic situations that consider for their conception, not only technical aspects, but also epistemological and cognitive aspects. Therefore, from the research results, the paper showed introductory aspects that will serve as the basis for a new and further research that will try to elaborate a casual model involving conglomerates of indicators. Another possibility that may be opened by the results of this investigation consists in developing didactic situations that consider the technical and desired characteristics of ITE, as well as the improvement of the project upon an assessment of the teaching-learning process from cognitive theories.

References [1]

The instrument described in the previous stage will try to map the demands from the teachers and the

[2]

expectations from the students regarding the use of interactive technologies in the classroom, considering

[3]

technological innovation applications in education. The main purpose of this instrument is to show which technical aspects are really desirable and applicable under didactic situations. With the data surveyed, the

[4]

research will move forward to the conclusion.

6. Final Conclusions With the data collected, the main objective of this

[5]

study will be tackled, that is, efforts will be made with the purpose of contributing for the ITE management within the educational context, based on the

[6] [7]

technological innovation applied to the educational context. This search will occur due to the entanglement between the technical indicators and the indicator derived from the research with the selected sample.

[8]

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D

DAVID

PUBLISHING

Standardization of Work for Setting the Tone of Ceramics José Víctor Galaviz Rodríguez1, Miguel Terrón Hernández1, Vicente Flores Lara2 and Jorge Bedolla Hernández2 1. Engineering and Industrial Operations/Industrial Maintenance Engineering, Technological University of Tlaxcala, Huamantla 90500, México 2. Metal-Mechanical Department, Apizaco Institute of Technology, Apizaco 90300, México Received: October 11, 2014 / Accepted: November 04, 2014 / Published: December 25, 2014. Abstract: Leading Company in the field of ceramic floor and wall, has different areas of workforce development, in this research, we will focus the tone adjustment area that is committed to the quality of the final product because this depends on the tone and color appearance tile. Since there is a need to standardize the procedure of work in the area pitch adjustment so that the head of the area and adjusters have precise specifications when developing the activities. To standardize the procedure proposed and implemented tools and formats to help in practical ways to the adjuster also raised the activities of the head of the area and the setting of tone and adjusters. Key words: Tone, standardize, adjuster, specification, procedure.

1. Introduction The screen inks or pastes are more or less viscous liquids, consisting of a contogether of solid particles dispersed in a fluid carrier, plus any additional substances other, easily transferable to the printing surface where they form a deposit in the order of one-tenth of a millimeter thick. The solid phase consists of dyes that are transformed into glass baking. They are essentially mixtures of crystalline oxides or flux and color pigments prepared by wet grinding and drying. The liquid phase of the ink, which acts as a vehicle for the dyes is usually constituted by products like ethylene glycol and polyglycols, characterized by a high wetting power with respect to the support. Furthermore, this stage must also possess good qualities as binder, plasticizer and stabilizer. Vehicles with higher adhesion, particularly suitable for single firing, can be prepared with carboximetil celluloses an activated polyvinyl alcohol, glycols or polyglycols Corresponding author: José Víctor Galaviz Rodríguez, Ph.D., research field: process optimization of manufacturing SMEs state of Tlaxcala. E-mail: [email protected].

solution [1]. A color can stick on the following screen when the two applications are too close, or if the ink has a first time over drying. Inaccurate and/or incomplete decorations may originate in defective screens, too great a distance between fabric and tile, tile guide out of level. Thickness differences occur in the device by speed differences expulsion variable thickness tiles, worn screen, variations in the composition and/or the viscosity of the ink. Other defects that may arise are: differences by using reactive colors, caused by the lack of parallelism between the planes of the screen and the terminal; 206 stripes applied ceramic technology that can be caused by an improperly sharpened strip or a worn tissue. Decoration under cover: such decoration is applied directly onto the substrate, which should be clean and well preventively lightly sprayed with water, to ensure wettability and the uniform absorption of water. In addition to the above, under cover screen printing is also suitable preparation apply a background as a basis to screen printing ink [2]. If the amount is small to make a glaze, put the more (within the limit of 15%) plus opacifier. Performance range of each is a function

Standardization of Work for Setting the Tone of Ceramics

opacifying of its temperature of operation, for leaded glazes also often used arsenic trioxide (As2O3) but due to its high toxicity is very limited use in a proportion of 6%, and antimony. Los opacifier should have a RI (refractive index) substantially different from the system. On the contrary, brightness can be achieved in a system of choice for components with similar refractive indices [3]. Fried bright: transparent and viscous (commonly called co-crystal). Chips are low fusibility, composed of a high percentage of SiO2 (50%-60%) and with a low percentage of flux elements (20%-25% Na2O-K2O-PbO-B2O3). The remainder of the composition is constituted by elements stabilizing (Al2O3-ZnO-CaO-BaO-MgO) are almost always presented in all singularly low percentages (7%-9% max.). Frits bright, transparent medium fusibility: they differ from the viscous crystal in that fuses are thus silica decreases 35%-50% and increases the percentage of the flux elements (Na2O-K2O-PbO-B2O3-Li2O) up to 30%-40%. They are used in most low temperature glazes and occasionally have been used in some particular type glazes fired at high temperature and pearl leather. Fried fluxes (leaded and aplumbicas): these chips are fitted with high fusibility, hence the name fluxes can be leaded (lead silicate), or aplumbicas (boron fluxes-alkali or alkaline earth-boron). They are used in some nail in small proportion as a corrective, for the purpose of adding a flux component, since these elements cannot be introduced as raw material in that they are water soluble (alkali and boron) or toxic (lead). Fried reactive fluxes: this group’s lead borosilicate fluxes and fluxes aplumbicas to lithium. For lead borosilicate recall the Fried monoboro and iridescent. Excessive fusibility and reactivity are manifested by a marked tendency to react and permeate in the raw material. Colored frits melt: it differs from the preceding groups only in the coloring, however, can be classified as type in groups 3 and 4. Some dyes used elements are iron, cobalt, manganese, copper, cadmium, and selenium [4]. Vehicles huecografía: designed to keep in suspension

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color even in low viscosity and extended storage of the inks. Provide adequate download to get an excellent definition and intensity. Allow to stable the density and viscosity during production, preventing key changes occur. Vehicles flat screen: inks provide good fluidity during application and a good definition on the part. Its high dispersion produces high color rendering. Their high stability allows the application of several consecutive screens and hassle resected. Additives enamels: range is specially commissioned to modify the rheological conditions and glazes screen-prints. Liquid is supplied to facilitate addition in the production line. Spray additives: its use improves the mechanical properties and rheology modifying all kinds of ceramic (porcelain, porous sandstone). Slip: applied on the glazed tile and after cooking oil provides a significant increase in non-slip nature of its surface. Its main feature is that it allows for non-slip finish with soft texture and hardly changes the original key of the piece [5]. Pigments: they are insoluble in water, organic solvents and dilute acids and bases, this division belong the materials we use in the ceramic industry. Ceramic pigments: they are inorganic colored complexes obtained after mixing and calcination of oxides at high temperatures (900 °C-1,300 °C), is insoluble in acids and bases. The color of the glaze is due to the presence of coloring ions within glaze. These ions do not dissolve in the glaze, but remain in suspension by coloring by opacification, i.e., intercepting the light passing through the enamel and reflecting cations of transition elements such as cobalt, iron, copper, among others [6]. The discoloration of the enamel depends on other factors in addition to the dyes ions such as its size, the oxidizing atmosphere or reducing burn, temperature, cooling rate. Viscosity serigraphs: is having fluency screening to keep moving, the higher the viscosity unless the movement. Density (ρ symbol) is a scalar based on the amount of mass contained in a given volume of a substance. The average density is the ratio of the mass of a body and the volume it occupies. Color space: just keep in mind

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Standardiization of Wo ork for Setting g the Tone off Ceramics

that the hum man eye percceives colors according too the wavelength of the light that hits it. The light which w contains the entire spectrrum of color appears as white w light, while the t absence of o light is senssed by our eyees as black. Hoowever, coolor properrties may be mathematicaally defined using u a “colorr mode” so thhat it can be captuured and sorteed [7]. There are a basically four color modess: HSB (huee, saturation and brightneess), RGB (red, green g and bllue), CMYK (cyan, mageenta, yellow and black) and the t L * a * way b *. Some distinguish two dimensiions in colorr: a sensory and other objectiive. In responnse to the firstt of the meaniings, the color would w dependd very personnal and even our own state off mind. As foor the second could be deffined suffered by the as physical modification m t light colooring agents, percceived by humans h andd processed and interpreted in the braiin eye (doees not seem m so objective). However, H it seems to bee consensus that involved: (aa) a light source; (b) an object illuminnated by it; (c) Thhe human eyye, with the brain HSB color c based on thhe way the human eye perceives coolor, therefore, it is the most “natural” “ wayy and serves three t fundamentall characterisstics: hue (hhue or nuannce): normally, thhis feature is confused c withh the name off the color in queestion and refers to the wavelength w off the reflected or emitted by ann object lightt. To measuree the color tone off a “wheel off color” or “coolor bar” standard where the thhree primaryy colors (red, green and blue) b with the seccondary colorrs (cyan, maggenta and yelllow) are arrangedd in a circle is i used equiddistant from each e other and alternating primary and seecondary so that each color is located at a the oppossite pole off the circumference occupiedd by its coomplement, i.e., blue-yellow,, red-cyan, grreen-magentaa. Any applicaation of retouchinng, working in this way adds color too an image, reduucing its coomplement, for f examplee, to increase thee green, maggenta that is lowered. In this system, or toone color modde is measured in degrees from f 0° to 360° acccording to thheir position in i the color wheel. w Chroma (satturation): this is the color inntensity is rellated to the hue, measured m as a percentage from f 0% to 1000%

(fulll saturation). Value (brightness): con nsists of thee ligh htness or darkkness on eveery shade of color and iss also o measured as a percenttage from 0% % (black) too 100 0% color L * a * b: This mode is based on o a standardd (wh hite). Also in percentage ffrom 0% (blaack) to 100% % colo or L * a * b: b This modee is based on a standardd dev veloped by the t Cie and designed to o be “devicee indeependent”, i.ee., making it ppersistent and d colorfast byy meaans of image output, eitherr a printer or monitor. Thee stan ndard color. In existence since 1976 when it wass defi fined by the Cie C Lab (Com mmission Internationale dee l’Ecclairage) and was the “collor mode” Ciee L * a * b, a num merical representation of all visible co olors, from a base mathematiccal created inn 1931 by thee same body,, the Cie when the digital proccessing of thee images wass not even a dream m (Fig. 1). Color C space L * a * b: this is a “lu uminance” orr ligh htness compoonent (L) along the tw wo chromaticc com mponents “a” that goes from m green to red and the “b”” thatt goes from bllue to yellow, practically what w happenss with h the opposite colors of thhe “color wheeel” [8].

2. Developme D ent Knowledge K of how addjusters worrk. For thee stan ndardization of the proocedure with hin the tonee adju ustment areaa, first the w way of work king of eachh adju uster in turn described. d Proocedure to low wer densitiess seriigraphs (% inntensity). The following tab ble shows thee perccentage of inntensity adjuusters added to replenishh colo or when adjusted high dennsities (Table 1). White Green

Yeellow

Blue

Red Chromatic range Black

Fig.. 1

Color space.

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Table 1

Proocedure for low wer density.

Perccentage of intennsity that applyy one point losss at Adjuster highh density screenn prints 3% intensity, if thee amount of collor in data sheeets is 1 highh, and 4% if thee amount of coloor is low 2 3.5% % intensity 3

3%

4

3%

Tab ble 2

Con ntainers/Boats

Getting drry grams: prooducing dry grrams, to calcuulate the percentaage of color that will bee added to loower density is ann important point, p a datum m required forr this calculation is the volum me to be scrreen printingg, to calculate thhe liters off single addjusters sepaarate containers making an approximatioon and havve a j Presentss the different ideea of the abillity of these jars. different coontainers thaat exist withhin the comppany which do noot have a gradduation in literrs to be precise at the time of obtaining thee data, this afffects the tim me of the calculation if the appproximationn is larger liiters, more pigmennt is added orr vice versa (Table 2). Summaryy procedure performs p the adjuster forr the start of a new w design lines, the way thaat each adjustter is to make thee process of starting s a new w design shoown, and this resuults in a problem in workiing conditions, as you reach thhe relay will do d otherwise and so begann the pitch variation. Reliabilityy of density, viscosity andd slip applicaation and databasee recorded inn data table by b operators. The adjuster must m review the data densities d in the registration of operators, sometimess operators only o spend densitty was recordded the previoous shift, perhhaps because it was w improviseed the end off turn, and soo the

Differen nt containers.

1 2 3 4 1 2 3 4 1

Contentt as adjusters (liters) 60 60 70 70 100 120 130 100 200

2

220

3

200

4

230

Adjuster

ligh hting day or night n creatingg metamerism m as you cann see well in the prroduction areea but when czech is in thee quaality design may m be out of tune (Fig. 2).. Amount A of water w to disssolve the pig gment. Eachh adju uster adds waater as you seee fit is impo ortant to set a paraameter of waater to grams oor kilograms certain colorr and d get the exppected tone. Density and viscosity off seriigraphs: loweering density should take into accountt the viscosity off the printingg, before add ding water too disssolve the piggment. Physiccal conditions of the areaa and d tools to imprrove. The areaas and tools are a physicallyy and d improvemeents are propposed. Area of pigmentt disp plays the piggments used tto adjust ton nes. It can bee seen n that there iss no proper seequence (Fig.. 3). Itt is proposedd to organizee the pigmen nts based onn “color space L * a * b”, wiith illustrativee image as a guid de when makking adjustm ments, and haave a clearerr visiion of wheree the tone is turned if th hey add suchh

unsuspectingg adjuster callculates to sett density baseed on who has registered. This causes one of o many factors to the variationn in tone. Cheeck controls. Turn the adjuuster should moniitor what is occurring o in thhe correspondding shift to com mpare tone with w master’ss quality conntrol.

Fig.. 2

Lighting quality q and prooduction area.

Fig.. 3

Area of piigment.

Sometimes, the gap betw ween the production area and o compareed against master m which is i in the quality only production line. l In this arrea, another factor f that caauses problem waas detected: thhe lighting of the quality and production area does not n have a sttandard lampp or

1012


color. Fact sheets: it is proposed too modify foldders, arranged alpphabetically by discardinng obsolete data sheets designns for producction. As welll as giving a more m pleasing othhers appearancce (Fig. 4). Containerrs: it is propoosed to adappt Flexometroo for each type of o boat or tuubs labor useed in producction lines that serrve as feasiblle to make acccurate data liters l when adjussted densities, test or adjust a serigraaphs booking andd no longer taake the recordd so liters of way “about”. Thee following figures f show the types of tubs and pots thaat exist withinn the companyy are shown (Fig. ( 5). Excess pigment: you can c see the coolor bags left over mileage whhen productioon is finisheed designs. It I is proposed thhat adjusters, before distrributing colorr on each turn, ask supervissor lines witth mileage what w remains to produce p and distribute d it based b on the bags b as needed (F Fig. 6). The Adjuusters line to enter on thee bag how many m grams of eaach color addded and bringg it to mills too be added to sillkscreen or bases, b or get adjusted to that color and design d with the t help of some s tintometer. Settings glazzes. When deeveloping a new n design in line you start to adjust a to this foundation sllips and makiing a record that shows the cheemical compoonents of diffeerent types of glaazes and com mpatibility with w the colorrs is proposed. Blog: B it is prroposed to seerve as a forrmat supported by b log workk to bring an a order of the adjustments made in shiifts and one for testing att the beginning off a new desiggn. The tone adjustment a areea is mainly baseed on visual inspection. A more feasiblle to automate thhis inspectionn would use the colorim meter way, which is based on thhe L * a * b inndicating to what w

Fig.. 5

Inks used to slip or basee.

Fig.. 6

Remaining pigments.

colo or the tone gooes, this woulld give us a more m concretee way y to set the tone when ooff the stand dards set forr quaality control. 100% autom mating the pro ocess so thatt therre is actually a variation of tone depend ds on variouss facttors such as raaw materials (clays), oven temperature,, but this can be im mproved by 770% photo ceeramics usingg prin nters that havve control oveer color paletttes and colorr inteensity.

3. Results R Im mproved toools: to improvve the workiing tools andd mak ke them takiing in order activities, th he followingg imp provements are proposeed. The taape measuree disccloses the actuual capacity oof different co ontainers thatt exisst within thee ceramics coompany; thiss is due to a grad duated tape measure taailor for eacch containerr (Taable 3). Tab ble 3

Actual capacity c of con ntainers.

Typ pe of containerss

Capacity

70 liters

Fig. 4

Datassheets binder.

Standardization of Work for Setting the Tone of Ceramics

4. Conclusions The project carried forth one of the problems that other companies are you really the staff follow the instructions of these procedures? Do you have the proper tools for their development? Based on what proposed in the article. Standardization of the procedure in setting tone area. It seeks to achieve waste reduction in the final product by varying tone. By standardizing the procedure adjuster’s work in each shift in the same way, the adjuster is responsible for the most important factor about the tone of ceramics; this

the company. Therefore, the underlying causes this defect and proceeds to the standardization of the procedure and tools are highlighted. The lack of dynamism by managers or department heads to improve various business areas of the company, were reason for the discussion in this work is not carried out within the company and only remains as proposed in the procedure for tone adjustment area. The main disinterest to improve working areas within companies is the cause automatism by workers to develop activities marked as work procedures.

has control of the use of pigments to adjust to master’s

References

tone quality, density screen prints, bases and slips. So

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the proposed standardized to 100% replacement of pigments and of the working tools. The starting point was to look for the causes why does not develop properly adjusting procedure tone, so it was found that the working tools lack a standardization regarding the ability of content different boats that are used to screen prints, order and discipline to start a new design, the department of production and quality department does not have the same brightness controls for checking. Also, staff area that has worked in the business for years has created its own way of performing activities. This creates a destabilization of the conditions of matter, and when the finished product is compared against master’s is a defect called “off key”, which causes the material to be sent to seconds or otherwise, it is rejected by the client, this is not suitable for personal tone and much less for

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Padoa, L. 2012. Firing Ceramic Products. Barcelona: Omega. Abelard, P., Baxte, J., and al, D. B. Proceedings of the 5th Conference and Exhibition of the European Ceramic Society (ECERS V), Versailles, Francia. Ceramic Associates. 2004. Handbook of Applied Ceramic Technology vol. 1. San Luis Potosí: Faenza Editrice Ibérica. Biffi, G. 2007. The Formulas That Have Made Ceramics an Industrial Product and Art. Raw Materials, Bodies, Glazes and Colorant. Faenza: Publishing Group). Ferro, M. 2013. Manual Process of Ceramic Pigment. Celaya: Guanajuato. American, N. 2007. Practical Guide to Industrial Control Systems Burners. Cleveland OH: North American MFG Corporation. Holand, W., and Beall, H. G. 2012. Glass Ceramic Technology, 2nd edition. Hoboken New Jersey: John Wiley & Sons. Van, G. A. T. 2004. Handbook of Applied Ceramic Technology vol. 2. San Luis Potosí: Faenza Editrice Ibérica.