structural models in multilayer simulation system of ...

STRUCTURAL MODELS IN MULTILAYER SIMULATION SYSTEM OF SUBMERGED ARC FURNACE Janis K. Tenteris~ Esko K. Juuso and Kauko Leiviski. Department of Process Engineering, University of Oulu, SF-90570 Oulu, Finland

ABSTRACT A simulation and structural modeling system for ferroa.lloy p~ ceases in a submerged arc furnace is described. It includes subsystems of multilevel simulation and structural (topological) modeling. The simulation subsystem provides a decomposition procedure that coven reaction space with an arbitrary degree of details. On the basis of the zone balance model of simulation subsystems, a structural modeling of metallurgical processes is carried out. The structural models represent interactions between main phenomena in a one electrode cylindrically symmetrical furnace in a form of directed graph and allow the selection of most important processes as well as to form an optimal set of externally observable signals.

tion, the combined simulation and expert system contains procedures for developing simplified fuzzy modela on the basis of simulation experiment1. Since these models, together with rule-based linguistic models, are embedded in the expert systems, there are a total of five levels of simulation. In the applications there is a trade-off between the depth of the capabilities that are needed and the scope of the process that the system must support.

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It is a part of a more extensive system which is developed for usage in several different ways - in production and operation planning, in process design, in process research, in multilevel optimization, diagnostics and process control. /

INTRODUCTION The joint application of multilevel simulation and structural modeling in this signal processing system has the aim of versatile description and investigation of ferroalloy processes in a submerged arc furnace. In these investigations such aspects as process research, process control and diagnostics are emphasized. The simulation system provides a method for comparing the production alternative& of metallurgical processes. The system was originally developed for the Outokumpu ferroalloy smelter (Juuso 1980,Juuso and Uronen 1989]. Expert systems are developed for ferroa.lloy processes in order to im· prove the application facilities of an extensive, hierarchical simulation system (Juuso 1989a). The task of optimal proce88 control and diagnostics is based on external signals that can be observed by the process control system. These signals provide the possibility to recognize different stages of ferroalloy processes as well aa considerable deviations from their optima.I condition [Grundspenkis, Markovich and Osis 1972]. Besides, structural models make it possible to select a minimal set of externally observable signals. Another usage of structural models allow us to carry out structural analysis of processes in furnace and use the results of this analysis for simulation subsystem. In this case, joint application of multilevel simulation and structural modeling allows an increase in the precision of results and a decrease in labour because the most important processes and volume elements can be chosen as a result of structural analysis [Grundspenkis 1983).

MULTILAYER SIMULATION The multilayer structure based on a decomposition procedure is very efficient in an iterative, gradually refining optimization scheme used in design applications. In addition to the deterministic simula.-

Zones of subprocesses

Subprocesses

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~

~

I~~ Volume element

Rectanaular arid

Figure 1: The levels of simulation. The multilayer aimulation ayatem is designed for the off-line optimization of production alternatives by using deterministic steady state model1. The system is primarily used in deaign and planning applications. Production planning here is divided over three levels of the multilevel process control: operative planning is performed on the optimization level, tactical planning can be included in the coordination level, and finally, strategical planning belongs to the management level. In order to gradually increase the amount of detail in selected parts of the process, a decomposition procedure (Fig. 1) is used. On the first level, the process is decomposed into smaller subsystems, e.g. preheating, feeding ring, and electric furnace. The decomposition is continued on the second level by dividing the subsystems into zones (Fig. 1). On the third level, spatial dependence is taken into consideration by using a rectangular grid (Juuso 1980]. On the fourth level, detailed simulation models are applied to a volume element. The size of this element can range from very small to the entire zone area. The level of decomposition can be chosen quite flexibly, e.g. in the descending burden element model the volume element level is used before the grid level calculations. In the simulation system there is also a level where the chemical reaction equilibrium is calculated under isothermal conditions (Juuso 1988]. In this model the molten zone of the electric furnace is treated as a volume element. 1 Pr-nt oddr-: Department of Management Information Sy1teme, Riga Polytechnic, Riga 226355, Latvia

Lumped parameter models are developed for testing ideas on several levels of production control. If detailed calculations corresponding to process design, process studies and process development are needed, distributed parameter models are used in refining the estimated output values of the lumped parameter models. A lumped parameter version developed for the descending burden element model and one-dimensional heat-flow calculation models are links between balance models and detailed simulation models [Juuao 1989b].

Subprocess Level The charge calculation model generates production alternatives on the basis of design restrictions. The energy balance model takes into account the process constraints by checking realizability for these alternatives. The zone balance model divides the mass and energy balance into several zone balances suitable for detailed simulation model application [Juuso and Uronen 1989]. The descending burden element model is applied to the calculation of chemical reactions in the reaction zone [Juuso 1989b].

the submerged arc furnace as well as the external signals between the furnace and its control system and other facilities of metallurgical plant. In this application of structural models, special emphasis is on the control and diagnostical problems of ferroalloy processes. That motivates the choice of several types of topological models {TM) pr viding control and diagnostic possibilities. The TM can be represented as directed graphs {digraphs). The application of TM in this signal processing aystem provides functional and parametricaJ analysis (Fig. 2). Both types of analysis are based on the joint procedure of model formation [Grundspenkis, Markovich and Osis 1972], however, usage of separate models obtained during this procedure is adapted to the needs of signal processing system.

Functionot modelinQ Formation of morpholo9ical •tructure

Porametrical modelini;

F"ormotlon of porometricol

•truc:ture

Zone Balance Model The zone balance model divides the mass and energy balance into several zone balances suitable for detailed simulation model application [Juuso 1989a]. The zone balance model forms a link between mass and energy balances and the detailed simulation models. On this level, several simultaneous reactions between binary components are taken into consideration in selected zones of the subsystems. Here the programs are based on sequential modular architecture. Only the most important independent reactions, e.g. in the ferrochromium process reduction reactions of Cr 2 0 3 , Fe 20 3 , FeO, Si01 , SiO and Al203 oxides, are employed [Juuso 1988]. The estimates of the final extents for these reactions are given in the input data.

Distributed Parameter Models

Formation of function al

etru · · · > r~.r > · · · > r::.ar• z!,;,. < · · · < ~;,. < · · · < z;:.,,., a.nd z!.az > · · · > z!s.z > · · · > Z~ar·

The next step towards functional modeling is the formation of functional structure. The functional structure of the submerged arc furnace was obtained from the morphological structure as a result of the formal substitution of all furnace elements by the corresponding processes [Grundspenkis, Markovich and Osis 1972). Thus nodes of functional structure represent the most important functional processes and features while arcs have the meaning of causal links or sequence between these processes.

where

STRUCTURAL MODELING Structural models are used widely as a tool for interdisciplinary investigations of complex systems and processes. In comparison with other models they have such advantages as simplicity and visuality, they are easy-tgrasp and easy-ti>interpret, they reveal the internal structure of object and represent in a joint model all its subsystems even if they have different physical nature [Lendaris 1980]. In the construction of structural models it is possible to use both numerical and verbal information about the object. These models represent interactions between system elements with arbitrary degree of details as well as interactions between the object and environment [Grundspenkis et al. 1988). The latter ability of structural models motivates their usage in a signal processing system of ferroalloy pr ceases. In this case these models represent the main processes inside

Model Specification. A computer program INP in PCMATLAB has been developed for formation of structural models. The program provides a possibility to create and input a new structural model in matrix form as well as to correct an earlier stored model. The following optional information can be added to each structural model:

• weighu of nodea; each node weight can be evaluated as the weighted sum of up to 5 separate components. If the node weight has a meaning of measurability of corresponding process or parameter, the evaluation of measurability includes such comp nents as accessibility for measuring, time necessary for measuring, costs of measuring, objectivity (or accuracy) of measurements, undesirability (risk) of measuring etc.

• weight& of arc& that can be interpreted as strength of influence between adjacent nodes; arc weights from interval (0,1] specify structural model as a fuzzy graph;

can be used if they are stored in the same MATLAB environment. Different vectors of node weights can be used as well.

• lowest and highest estimated values of arc weights; these values together with the average or mean value of arc weight as a matter of fact specify triangular distribution of arbitrary arc weight for fuzzy structural model.

Parametrical modeling

The INP program includes a lot of comments and is saved as a PC-MATLAB 1cript file with identifier INP.M. The structural model formed by this program i1 1aved as a matrix f. Node weights are presented in vector vw. Lowest and highest estimated values of arc weight• are saved as matrices fl and fh. Further development of this input program includes its usage together with another MATLAB program for selection of different combinations of fuzzy arc weights. Thi• program provides detaHed investigation of the processes to be mod· elled taking into consideration possible fuzziness of each interaction between nodes. Seledion of moat 1igniflcant 1ubproceuea. The selection of the most significant subprocesses is necessary for detailed inve&· tigation by the simulation subsystem. In this step structural analysis of the functional structure graph was carried out. For this purpose all nodes were compared and ranked by several criteria. The ranking program can be carried out by MATLAB program ACYC that performs structural analysis of acyclic graphs. The program ACYC provides structural analysis according 4 criteria: (1) out-degree of nodes (number of leaving arcs for every node); (2) degree of nodes (number of incident arcs); (3) number of outgoing (leaving) walks for every node; ( 4) number of walks comprising each node. The criteria mentioned can also be used for graphs with cycles, therefore notion of walks is used in the 3rd and 4th criterion. In the ca.-e of acyclic graphs these criteria are calculated according to the number of outgoing paths and all paths of the structural model. The program user can select any subset of criteria and calculate generalized significance of nodes within that subset. Every criterion in such subset can have different weights (significance).

The parametrical modeling has been carried out in order to select optimal parameters for control and diagnostics of processes in furnace. The selection stage is preceded by following steps: • formation of parametrical structure; • inclusion of external signals, poesible defects and their symptoms in the structural model; • weighting of elements (nodes and area). Formation of Parametrjgl Structure. The parametrical structure has been formed according to two different methodologies. In the first methodology (Grundspenkis, Markovich and Osi1 1972], the functional structure i1 used as a basis for parametrical structure. In this case every functional process is supplemented with the main parameters describing the conditions of this process. The functional processes themselves are substituted by the most important parameter. This parametrical model contains also an important subset of structural parameters describing the physical, chemical, electrical and geometrical properties of separate details and units. Due to structural parameters this model represents the technical condition of the system. However, usage of this methodology for parametrical model formation is insufficiently formalized, therefore the model contains rel· atively much subjective information that can decrease the reliability of results. The second methodology (Zulis 1985] uses the morphological structure as the basis for parametrical structure. In this case special attention is paid to the most important measurable parameters of flows between elements in the furnace. The properties of electri· cal, charge, gas and heat flows have been described by such param· eters as power (productivity), current, speed, temperature and the amount (percentage) of different components (dust, volatiles, molten compounds) in the flow.

Structural analy1is and the ranking of nodes can be carried out alao for a fuzzy graph (with fuzzy arc weights) as well as for non· fuzzy graph. A non-fuzzy graph can also be created from an earlier fuzzy graph. In this case all arc weights exceeding 0 are taken as equivalently significant with a weight value 1.

The modeling procedure was quite formal and a considerable part of it i1 computer-aided (Grundspenk.is et al. 1988], but the main disadvantage of this methodology is the redundancy of the model. Thia model does not describe the structural properties (technical con· dition} of the system in a direct, obvious form, therefore more efforts are needed in the following steps of structural modeling. In order to reduce this disadvantage, possible defects were also added to this parametrical structure model.

Ranking of nodes can be carried out proportionally to the node weights. Such a method of 1tructural analysis is reasonable if the meaning of node weights is the significance of the corresponding el· ement. Results of such analysis provide motivated choice of more important subprocesses and zones of subprocesses for detailed inves· tigation by simulation subsystem.

External Signala, Defect. and Their Symptoms. During this step the following activities are carried out: (1) the most probable defects of elements, deviations of parameters, are added to the parametrical structure as separate nodes; (2) external signals charac· terizing the process performance and symptoms of defects are added to the model (Grundspenk.i1, Markovich and Osis 1972].

The results of the structural analysis program ACYC are plotted as bar charts. The criteria of each group (both degrees as one group or both numbers of walks as another group) are presented in one plot. The calculation and plotting of generalized criterion (as a weighted sum of separate criteria) can be carried out and repeated with dif· ferent subsets and different weights of separate criterion. Generalized criterion can be obtained both for fuzzy and corresponding non-fuzzy models. The values of this criterion are presented in normalized form.

Thia parametrical structure includes information about poasibilitie1 to control inner processes in the furnace from external signals that can be registered from ou taide. In order to select the most preferable signals for proces& control the evaluation of the model elements must be done in the following step.

This program is saved as a script file AC.M. It is supposed to use earlier created structural model presented as a matrix f. Some other structural models with different identifiers of corresponding matrices

One possible usage for the parametrical structure is the structural analysis of it. Principles of structural analysis in this case are similar to those described above and provide selection of most significant parameters. However, these principles do not take into account the possibilities to measure the parameters, therefore further devel· opment of the model is desirable.

Weighting of Elements. The weighting of elements of parametrica.I structure (Markovich a.nd Markovich 1972] consists of two parts. The weight of the node represents the accessibility of corresponding parameter for control (controllability). The arc weight of the parametrica.I model represents a closeness of interaction (strength of influence) between parameters. The weight of node includes such factors u time and coats of control, objectivity of results, undesirability risk of control etc. Another possibility, direct evaluation of node weights wu used in this case for parametrical structures of the submerged arc furnace. In this evaluation the following principles were taken into consideration. Node weights M; were given values from interval (0,1]. Thia interval wa.a divided into several zones: a) M; = 0.95 - 1.0, if an effective measuring device for the given parameter :r; already exists; b) M; = 0.8 - 0.95, if such a device can easily be installed;

=

c) M; 0.5 - 0.8, if the measuring device exists, but it is compli· cated a.nd difficult to apply;

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d) M; 0.2- 0.5, if the measuring device does not exist but can be developed; e) M; = 0 - 0.2, if you see practically no possibilities to measure this parameter. In the weighting of arcs of the parametrica.I model, weights are also taken from the interval (O, l). This interval is used to evaluate arc weight a(:r;/z;+t) between nodes :r; and :r;+l in the following way: a) a(:r;/z;+il = 0.9 - 1.0, if every change in parameter :r; causes proportional changes in parameter z;+ 1 ; b) a(x;/x;+i) = 0.1- 0.9, if the influence of parameter :r; on param· eter z;+ 1 is not absolute (unilateral), the strength of influence in a considerable extent depends also on other factors; c) a(:r;/z;+ 1 )

=0 -

0.1, if parameter :r;+l does not depend on :r;.

Analysis of Functional Models Morphological atructure. The morphological structure has been developed on the basis of the zone balance model of the furnace. Nodes of it describe separate elements and furnace zones while arcs have the meaning of electrical, charge, gas and heat flows. Such morphological structures have been developed in different levels of detail. In the lea detailed model one node represents each of the following zones: meta.I zone, slag zone, gu zone, molten reaction zone, partly molten reaction zone, electrode and furnace lining. The more detailed models represent reaction zones and lining u a group of interconnected nodes. All models represent interactions between furnace elements and external subsystems (electrical supply system, charge feeding system, ventilation system, cooling system and tapping device). The formation of the morphological structure has been carried out on the basis of principles of computer-aided structural synthesis (Grundspenkia and Tenteria 1980). Because there are several types of arcs between nodes of one particular pair, the morphological structure can be considered as multigraph. These multiple arcs are significant during formation of parametrical structure model. For the structural analysis of the morphological structure an ordinary graph is used. It can be formed as a result of substitution of all multiple arcs by one complex arc. The analysis of the number of incident arcs for every node in· dicates the partly molten reaction zone as a central element of the system. Such a result was obtained for morphological structures on different levels of detail and therefore the next step of structural modeling has been carried out for the less detailed morphological structure. fupctjopal atructure. The functional structure of the furnace wu obtained from the morphological structure in a formal way [Grundspenki1, Markovich and 01i1 1972]. This functional model describes causal links between the 32 m011t important processes and functional features that take place in the functioning of the furnace. Before the functional structure analysis, a problem oriented simpli· fication (reduction) of the corresponding graph was carried out. It included the selection and deletion of transitive nodes having exactly one entering and one leaving arc. Such nodes do not influence the results of the structural analysis as they do not represent branching, combining and other structurally significant properties of flows.

Selection of control and diagnoatical parameten. The Selection of control and diagn011tical parameters is the final step in this subsystem of structural modeling. This selection procedure (Osis et al. 1990] provides selection of an optimal set of control parameters under contradictioua demands · sensitivity and reliability of control from one side and minimal time, costs and amount of detectors from the other side. During this procedure, first, restricted components of reachability and restricted syndromes for every malfunction causing defects of parametrical structure must be calculated. In the second stage of this procedure a special table of overlapping is used. All nodes are ranked in it according to their weight, observability (ba.aed on closeneH of nodes) and distinguishability (ba.aed on the length of paths between symptoms and defects). The optimal set of control and diagnoatical parameters is selected from the upper part of the table.

APPLICATION Application of the described methods to the multilayer simulation system of the submerged arc furnace is discussed in two sections based on the functional and parametrica.I models respectively.

Figure 3: Reduced functional structure.

The reduced functional structure, presented in Fig. 3, was used aa a bui1 for the structural &nalysis of the functional model (functional analysis). This model consists of 15 nodes:

300 200

l. The source of electricity

100

2. The heating of a partly molten charge 3. Source of charge

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4. Charge feed 5. Heating of molten charge

Figure 6: Out-going walks.

6. Partial reactions 7. The formation of gu 8. Ventilation of the furnace 9. Electrical .1. connection 10. Complete reactions 11. Metal storage 12. Slag storage 13. Heat transfer

Figure 7: Number of walks.

14. Cooling system

15. Electrical Y connection

The functional analysis was carried out according to 4 criteria: (1) out-degrees of nodes; (2) degrees of nodes; (3) number of out-

going walks of each node; (4) number of walks comprising the node [Harary, Norman and Cartwright 1965]. An adjacency matrix of the reduced digraph and several variants of reachability matrix were used for calculation of values of these criteria. Results are presented in Figures 4 ... 7 as bar charts characterizing the significance of every node. Normalized values of these criteria were used for calculation of generalized criterion of significance of nodes. All 4 criteria mentioned are considered as equally significant.

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The generalized criterion, presented in Fig. 8, points out the partly molten reaction zone, source of electricity and reaction zones as the most significant components of the furnace, therefore they are recommended to a more detailed investigation by the multilevel simulation subsystem. Nevertheless, it is important to pay enough attention to the cooling system as well because the 4th criterion (number of walks comprising the particular node) points it out as one of the most significant. Calculations and the representation of results of the functional analysi1 were carried out by interactive programs INP and ACYC written in PC-MATLAB. The characteristics of PC-MATLAB [Moler, Little and Bangert 1987] made it poesible to d~cribe ~~ realize these complicated and labour consuming calculations within a file of about 340 command1.

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Figure 4: Out-degree of nodes.

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Figure 5: Degree of nodes. Figure 8: Generalized significance of nodes.

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Analy11i11 of Parametrical Models A similar procedure of structural analysis was carried out for both types of parametrical structures mentioned. Aa a result of the first method a parametric&) model containing 64 main parameters and interactions between them was developed. On the basis of the second method, a model describing interactions between 90 parameters was fOrmed. The presentation of these results would take too much space. In order to take into consideration accessibility of the parameters, further development is going on in two different directions. The first of them provides more refined methods of structural analysis for the parametric&) model. The main idea is the usage of fuzzy values of element weights given by experts. A special MATLAB procedure developed for this purpose allows the expert to select separate weights of the model elements and carry out further calculations based on combinations of fuzzy-discretized values of the selected parameters (Juuso 1989a]. The second direction for further development provides investigations for optimal choice of control and diagnostical parameters. In this case the usage of an overlapping table is the most promising approach (Markovich and Markovich 1972]. This approach has such advantages as a possibility to select the minimal set of control parameters and account for different possible defects and failures that should be di• tinguished in the tasks of diagnostics. It is also worth mentioning the good theoretical motivation of this parameters selection procedure as it guarantees optimal results for the given parametrical model (Osis et al. 1990].

CONCLUSIONS The joint usage of multilevel simulation and structural modeling in a signal processing system is rather efficient. It allows the registration and investigation of several aspects of functional processes in a submerged arc furnace. The main attention is paid to the system and structure features. It is provided by structural analysis of functional and parametrical models of the object. The structural modeling subsystem includes methods and computer programs for the following tasks:

• input and evaluation of different types of structural models; • structural analysis of acyclic structural models with the aim to find the most significant elements for further analysis; • selection of a minimal set of diagnostic parameters for use in diagnostics or optimal control.

Further investigations should be carried out for wider use of the parametrical model, especially the selection of the optimal parameter set can be useful together with this or other general purpose simulation systems. The methods of using and processing fuzzy information are quite adequate in this system. They should be further developed and used as a component of the expert system for the fuzzy simulation of ferroalloy processes. The programs were realized in PC-MATLAB. They contain a lot of comments and helpful hints for the user not familiar with structural modeling. Possibilities of interactive program PC-MATLAB are sufficient and adequate to such tasks including methods of data and structure analysis in the matrix form.

REFERENCES Grundspenkis J. A. 1980. "The synthesis and analysis of structure in computer-aided desi~.· In Computer Applirotiona in Production and Enginttring, North Holland, Amsterdam, 301-316. Grundspenkis J. A.; M. P. Kirikova; J. K. Tenteris; and V. J. Zulis. 1988. "Man-machine system SATOM for the structural modeling in CAD." AMSE &mew 6, no. 3: 1-11. Grundspenkis J. A.; Z. P. Markovich; and J. J. Osis. 1972. "Formation of topological model of object." In CJ1bemetia and Diagnoatics. Vol. 5, Riga, 1~35. In Russian. Grundspenkis J. A. and J. K. Tenteris. 1980. "Computer-aided formation of topological model or diagnostics problems in complex systems." In HJ1l>rid Computers and Syatema. Vol.3, Naukova Dumka, Kiev, 88-93. In Russian. Harary F., R. Z. Norman, and D. Cartwright. 1965. Structural Mode/a: an introduction to the theory of dirttted gropha. Wiley, New York. Juuso E. 1980. "A computer analysis of temperature distribution and energy consumption in a submerged arc furnace used in the production of high-carbon ferrochromium." Acta Universitatia Ouluensia, Series C Technica No. 17, Techniro Proceuionum No. 3. Juuso E. K. 1988. "Multilayer simulation of chemical reactions in metallurgical processes." In C. C. Barnett and W. M. Holmes, editors, Procttdinga of the Summer Computer Simulation Conference (Seattle, USA, July !5-!8}, SCS International, San Diego, USA, 330-335. Juuso E. K. 1989&- "An expert system and multilayer simulation of electrical flow in a submerged arc furnace." In G. Iazeolla, A. Lehmann, and H. J. van den Herik, editors, Simulation Methodologiea, Language• and Architecture• and Al and Graphics for Simulation, Procttdings of the 1989 European Simulation Multiconference (Rome, /talJI, June 7-9), SCS International, Ghent, Belgium, 16~174. Juuso E. K. 1989b. "Multilayer simulation of heat flow in a submerged arc furnace used in the production of ferroalloys." In A. El Jai and M. Amouroux, editors, Preprinta of the Fifth Symposium on Control of Diatributed Parameter Systema (Perpignan, France, June !6-!g}, IFAC, CNRS, Universite de Perpignan, 485-490. Juuso E. K. and P. Uronen. 1989. "Hierarchical simulation of ferroalloy processes." In V. Koppel, editor, 6th Symposium on Automation in Mining, Mineral and Metal Proct!aaing. Preprints of the Sympoaium, Buenoa A.irea, Argentina, 4-8 September 1989, IFAC, 245-250. Lendaris G. 1980. "Structural modeling - a tutorial guide." IEEE 'lhinsactiona on SJ1atem, Man and Cybemetica 10, no. 12: 807849. Markovich I. V. and Z. P. Markovich. 1972. "Formalized selection of symptoms for differential diagn011tica." In C71bemetics and Diagnostic•. Vol 5, Riga, 37-45. In Russian. Moler C.; J. Little; and S. Bangert. 1987. PC-MATLAB for MSDOS Peraonal Computera. Uaer'a Guide. The Math Works, Inc. Osis J. J.; J. A. Gelfandbein; z. P. Markovich; and N. V. Novozshilova. 1990. Automation of Aoiation Technology Diagnoatica on the Btuia of Graph Models. Transport, Moecow. In Russian, to appear. Zulis V. J. 1985. "Formalization of significance evaluation of the designed system elements using fault-tree." In Methods and Systema of Deciaion Making in Control and Design, Riga, 140-145. In Russian.