Line-coordinated
optimisation of strip geometry and surface properties by using model-based predictive technologies (Linecop)
Research and Innovation
EUR 25858 EN
EUROPEAN COMMISSION Directorate-General for Research and Innovation Directorate G — Industrial Technologies Unit G.5 — Research Fund for Coal and Steel E-mail:
[email protected] [email protected] Contact: RFCS Publications European Commission B-1049 Brussels
European Commission
Research Fund for Coal and Steel Line-coordinated optimisation of strip geometry and surface properties by using model-based predictive technologies (Linecop)
M. Jelali, A. Wolff VDEh-Betriebsforschungsinstitut (BFI) Sohnstraße 65, 40237 Düsseldorf, GERMANY
J. Bathelt, P. Foerster ArcelorMittal Eisenhüttenstadt GmbH: Dep. VZA Postfach 7252, 15872 Eisenhüttenstadt, GERMANY
M. Nevot ArcelorMittal ESPAÑA: Dep. Innovation and Research PO Box: 90, 33480 Aviles-Asturias, SPAIN
J. Ordieres, I. Ortiz UPM: EscuelaTécnica Superior de IngenierosIndustrieales Av. Ramiro de Maeztu 7 s/n, 28040 Madrid, SPAIN
Grant Agreement RFSR-CT-2006-00037 1 July 2006 to 30 June 2010
Final report Directorate-General for Research and Innovation
2013
EUR 25858 EN
LEGAL NOTICE Neither the European Commission nor any person acting on behalf of the Commission is responsible for the use which might be made of the following information. The views expressed in this publication are the sole responsibility of the authors and do not necessarily reflect the views of the European Commission.
Europe Direct is a service to help you find answers to your questions about the European Union Freephone number (*):
00 800 6 7 8 9 10 11 (*) Certain mobile telephone operators do not allow access to 00 800 numbers or these calls may be billed.
More information on the European Union is available on the Internet (http://europa.eu). Cataloguing data can be found at the end of this publication. Luxembourg: Publications Office of the European Union, 2013 ISBN 978-92-79-28947-7 doi:10.2777/63992 © European Union, 2013 Reproduction is authorised provided the source is acknowledged. Printed in Luxembourg Printed on white chlorine-free paper
Table of contents 1. 2.
3. 4. 5.
Final summary ............................................................................................................................... 5 Scientific and technical description of the results ..................................................................... 15 2.1 Objectives of the project ................................................................................................... 15 2.2 Comparison of initially planned activities and work accomplished ................................. 16 2.3 Description of activities and discussion ............................................................................ 17 WP 1: Characterisation of Transfer/Final Strip Quality and Data Acquisition ............... 17 Task 1.1. Overview of processing/strip-quality problems and customer requirements [ARCELOR ESPAÑA, EKO] ............................................................................ 17 Task 1.2. Strip-quality characterisation (hot, cold, galvanised) following the needs of internal users and final customers [ALL PARTNERS]..................................... 18 Task 1.3. Configuration and installation of a mobile shape measurement system [BFI, AMEH] .............................................................................................................. 21 Task 1.4. Acquisition and pre-processing of data samples [ALL PARTNERS] .............. 26 WP 2: Development of Integrated Model ......................................................................... 32 Task 2.1. Enhancement of existing flatness model for cold rolling [BFI, FQZ] .............. 32 Task 2.2. Development of models for hot-dip galvanising [BFI, FQZ] ........................... 39 Task 2.3. Construction of total strip-quality predictor [BFI, FQZ] .................................. 40 Task 2.4. Use collected data and perform plant-based trials to verify predictions [BFI, AMEH, FQZ] .................................................................................................... 49 Task 2.5. Model adaptation/self-tuning [BFI] .................................................................. 57 WP 3: Development of Through-Process Monitoring and Optimisation.......................... 59 Task 3.1. Correlation and operating-range analysis [BFI, FQZ, ARCELOR ESPAÑA, UPM] ................................................................................................................. 59 Task 3.2. Hot-dip galvanising entry-coil-quality monitoring [ARCELOR ESPAÑA, UPM] ................................................................................................................. 68 Task 3.3. Through-process strip-quality optimisation over cold rolling and galvanising [BFI, AMEH] .................................................................................................... 79 WP 4: Algorithms and Interfaces Implementation ........................................................... 94 Task 4.1. Definition of systems functionality [ALL PARTNERS] .................................. 94 Task 4.2. Methods & system for Hot-dip galvanising entry coil quality monitoring [AME, UPM] ................................................................................................................. 96 Task 4.3. Methods & system for line-coordinated optimisation of cold rolling and galvanising lines [BFI, AMEH] ...................................................................... 101 WP 5: Systems Integration, Testing and Evaluation....................................................... 107 Task 5.1. Galvanising line at ACERALIA / HDG-entry coil quality monitoring [AME, UPM] ............................................................................................................... 107 Task 5.2. Cold rolling and galvanising lines at EKO STAHL / Line-coordinated quality prediction and optimisation [BFI, AMEH]...................................................... 109 Task 5.3. Guidelines for best through-process monitoring and optimisation [ALL PARTNERS] ................................................................................................... 116 2.4 Conclusions..................................................................................................................... 117 2.5 Exploitation and impact of the research results .............................................................. 119 List of acronyms......................................................................................................................... 121 List of figures and tables ........................................................................................................... 123 List of references ........................................................................................................................ 127
3
1.
Final summary
The core idea of the project is that, knowing the operating characteristics and monitoring the current conditions and output of a processing stage, the transfer specifications are adjusted (by the setup and control systems) such that the desired objectives of the downstream process are met, the strip quality of the final customer is ensured, and simultaneously the process disruption and the energy/material consumption is minimised. This is also motivated by the fact that, despite the equipment of most steel production plants with powerful automation systems, many quality defects reported by the steel producers cannot be corrected locally within the process where they appear. Thus, the only appropriate way to fight with these quality defects and problems is to handle them from the through-process viewpoint proposed in this project. Figure 1 gives an overview of the project objectives/deliverables. Line-coordinated Strip Quality Optimisation • Strip quality predictor • Optimiser of shape/flatness and zinc-layer thickness
Hot rolling
Automation
Automation
Automation
Cold rolling
Hot-dip galvanising
Temper rolling
Transfer StripQuality Characterisation HDG-Entry-Coil Quality Monitoring Coil Rejection Measur. thickness profile, tempreture, etc.
Shape/Flatness measur.
Zinc layer measur.
Task 1.1. Overview of processing/strip-quality problems and customer requirements [ARCELOR ESPAÑA, EKO] Detailed studies of the current situation at the different plants were carried out. The different components of the investigated plants were identified and the available process and quality parameters were registered. Out of the available variables, the relevant ones were detected by means of the knowledge of the shift managers and technicians. The results of this first step are used to define demands to the data infrastructure. Based on that, concepts for the necessary enhancement of existing databases or the components, which have to be established, were developed. Here, for example, necessary network connections to quality measurement devices, databases or server computers are mentioned. According to the project objectives, the main quality parameters considered were: a) Galvanised strip: homogeneity of the zinc layer, strip flatness. b) Cold-rolled strip: strip flatness, tension-stress state after cold rolling (offline flatness). After several meetings with the facilities technicians it was decided to focus the research project in following main areas: Cold-rolled strip flatness, tension-stress state after cold rolling (offline flatness); relation to homogeneity of the zinc layer, strip flatness. Quality surface problems (like zinc grains, blisters, scale, etc.). Mechanical characterization of the raw material, after being processed.
5
Task 1.2. Strip-quality characterisation (hot, cold, galvanised) following the needs of internal users and final customers [ALL PARTNERS] During this task, preliminary test analyses were performed in order to get better understanding of different parameters relevant for the project. Different initial attributes were gathered and initial tests regarding their integrity across different facilities were performed. Within a close work between BFI, AMEH (and FQZ), the parameters for the description of the strip quality in terms of flatness and zinc-layer thickness have been discussed. Also, all process and plant parameters influencing these target variables were specified, and their sources within the distributed data acquisition and automation systems at the facilities. A total database has been developed for the analysis of the process chain cold rolling – galvanising, including online process data and plant parameters for two cold rolling mill and two galvanising lines. The selected variables at AME were: length, width, thickness, maximum, minimum and average flatness, maximum, minimum and average speed of galvanizing line, mechanical parameters related to the quality of coils. WeKa® software has been used, including special variance analysis and algorithms ('BestFirst'). The first interest was to identify some breaks in information flows and to identify relevant variables in the amount of tables from different databases involved in the project. Task 1.3. Configuration and installation of a mobile shape measurement system [BFI, EKO] Work by BFI and AMEH has focused on designing the layout, installing and integrating a topometrical flatness measurement system at the entry of AMEH’s HDG line no. 2. The interfaces of the measurement systems have been specified. After finishing the laboratory design, the prepared construction and computer system have been transferred to the HDG plant, installed, calibrated, adapted to the on-site conditions, and commissioned. A major effort was also spent in the integration of the system in the automation platform to ensure continuously gathered and synchronised data. Task 1.4. Acquisition and pre-processing of data samples [ALL PARTNERS] The objective of this task was double. First, it was relevant to provide an infrastructure capable of gathering data and provide them to the research teams in a smooth way. Main difficulties here where the different data bases storing relevant data in different facilities as well as the security services required to bring out the approved datasets. Then, following target consisted in trying to produce as much automatic pre-processing as possible, including rule based identification of potentially damaged patterns, in order to avoid storing invalid data making not possible its use. Regarding software, at design laboratory level it was decided to use mainly open source tools, like SNNS (Stuttgart Neural Network Simulator) for NN developing and testing. R (www.r-project.org) for statistical analysis and WeKA (http://www.cs.waikato.ac.nz/ml/weka/) for CART technology, mainly because the interest in releasing models developed as source code, in order to make easier the implementation at plant level. First analysis revealed that material tracking and assignment from cold rolling mills to the galvanising plants is difficult and not possible with available tools, particularly, when having in mind that the project aims to monitor the strip quality in quasi-real time (from one coil to the next). Therefore, special emphasis and work was spent during this project period on implementing proper algorithms for “coil assembling”, i.e. to track and assign data of cold-rolled strips trimmed or welded together before coat-
6
ing. A further challenge was to collect the data from different plants and different archives and formats, which all have been merged and integrated into a new database, which is able to gather data on demand, synchronise, and present them to the user. Task 2.1. Enhancement of existing flatness model for cold rolling [BFI, FQZ] Physically-based shape models for cold rolling have been extended, considering the hot strip properties (thickness, profile, temperature) and the coiling process. The accuracy of the model has also been improved by detailed finite-element (FE) model predictions. The coiling process after cold rolling is a process that may affect the strip shape. BFI has analysed the impact of coiling on the flatness of the final cold coil condition, considering the findings of previous EU-funded work. The analysis within the present project has been done by physically-based approaches, taking the strip thickness profile and the coiling tension into account to calculate coil stresses and deformations, as well as by data-based methods, taking the measured flatness at the exit of the cold mill coiler and at the entry of the galvanising line into account. The flatness model for coiling and de-coiling consists of three sub-models: Coiling model. Air-cooling model. De-coiling model. Some simulations studies have been performed. The resulting flatness profile due to coiling for the thinner strip shows a combination of centre buckles and wavy edges after coiling. The maximum of the centre buckles is reached in the first third of the coil, which is due to the bending of the strip around the mandrel and the developing coil set. But the maximum of the wavy edges is reached at the end of the strip, due to the fact that the coil set has its larges value there. In contrast to thinner strips, thicker strips show higher centre buckles at the beginning, which decline with increasing coil radius. From these simulations, one can conclude that the flatness error due to coiling does increase with the strip thickness and varies along the strip length. Therefore, the flatness reference for the flatness controller at the tandem mill has to be varied along the strip length and with strip thickness to compensate the effect of the coiling process. Task 2.2. Development of models for hot-dip galvanising [BFI, FQZ] The annealing process does not contribute much to the post-rolling flatness, and most of the postrolling flatness is introduced already at the coiling operation. Also, it was decided in an earlier stage of the project that the modelling of hot-dip galvanising process should not be a core area of the project due to the non-availability of stored data that can be analysed or used for model validation. Instead, more effort was spent in analysing and controlling the strip flatness over the cold tandem rolling process with emphasis placed on the modelling of the coiling process that dominates in changing strip flatness. Moreover, the uniformity of the coating (Zinc) thickness has been analysed to find out possible correlation between flatness defects and non-homogeneity of coating thickness for two processing routes. Also, the mean spreading of the Zinc coating thickness over the strip width was analysed. Two superposed distributions were found in the data: the first has its center at 0.3g/m2 can be related to “flat” strip, whereas the second distribution with a center at 1.2g/m2 corresponds to strips with more or less local flatness defects. The skewness of this distribution may result from stronger flatness defects in the entering cold rolled strips.
7
Task 2.3. Construction of total strip-quality predictor [BFI, FQZ] The models developed in the previous tasks can easily be linked together to simulate a (physicallybased) through-process evolution of flatness over the considered processing stages, considering the relevant strip-input properties and process parameters. The total model can serve for prediction of shape development from entry of cold rolling mills to entry of the continuous annealing lines. It can also be extended by models for prediction of flatness through hot-dip galvanising lines. However, such a total model is a very complicated and computationally time-consuming, so that it is not suitable for use in fast calculations or online applications. Moreover, the model validation and parameter adaptation is a huge task. Nevertheless, the techniques described in Task 2.4 can be used for this purpose. Instead of the physically-based model, the alternative way of data-driven (back-box) modelling was also taken in this task. This means that the prediction of the post-rolling flatness can be made by fitting a regression model to measured variables from the cold rolling mill and from hot rolling. For data-based modelling of flatness, neural networks have been evaluated. At a first stage, the most important input variables have been selected by using self-organising maps (SOM). From twenty one (21) potential influence variables, seven input variables have been selected as the most important ones. The data sets were separated for three material groups, to get material-dependent models. Task 2.4. Use collected data and perform plant-based trials to verify predictions [BFI, AMEH, FQZ] Data analysis performed later in Task 3.1 and 5.2 reveals that the coiling process does heavily affect the strip flatness. A central observation is that the post-rolling flatness often shows edge waves at the head of the strip, but these disappear over the strip length, and are overtaken by center buckles. A possible explanation for this behavior is found to be a combination of the effects of strip crown and the mandrel profile (diameter). Two effects can be be obeserved: 1. The egde waves are showing up and they disappear after the fist 20‒30 laps of the coil. 2. With increasing strip tension center buckles / W-shaped flatness are showing with increasing magnitude towards the end of the coil. Comparing the simulated flatness evolution with the measured one, a good (at least qualitative) agreement between the model predictions and measurements can be concluded. In this context, it should be noted that rough estimates for strip profile and mandrel crown were taken. Considering the results of the input-variables selection process, both linear regression and artificial neural networks (MLP: multi-layer perceptron) have been trained to predict the post-rolling flatness from the (seven) most important input. The conclusion is that the prediction quality of MLP is superior than that obtained using the linear regression model. This confirms the mappings between the input data and the post-rolling flatness is nonlinear. Therefore, it can be said that data-based (MLP) modelling is a suitable approach for the prediction of post-rolling flatness from measured variables from the cold tandem mill. Task 2.5. Model adaptation/self-tuning [BFI] From different techniques available for parameter adaptation, the recent approach of unscented Kalman filter (UKF) was proposed to overcome several limitations of other adaptation methods like the extended Kalman filter (EKF). Conceptually, the UKF process is identical to the standard KF process with the prediction–estimation recursive loop. The main difference is that UKF uses the sigma points and the nonlinear equations to compute the predicted states and measurements and the associated covariance matrices.
8
Task 3.1. Correlation and operating-range analysis [BFI, FQZ, ARCELOR ESPAÑA, UPM] Different analyses were performed in order to look for structural relationships and also in order to get correct connection between dataset representing the same coil at different facilities along its transformation. These initial studies show that in many cases the interest questions like factors explaining some defect types or particular conditions related to flatness properties were not clearly separated. These particular things make very complex the construction of models explaining the facts and sometimes require reformulating the interest questions just in order to increase the separability of evidences provided by the sensors and data. Data from AMEH’s cold-rolling/galvanising route have been collected for several representative coils. These data sets have been visually and systematically analysed, to check data consistency, remove artifacts from data, and find out first correlation relationships. The following observations can be stated (based on data acquired by the first version TopPlan system): The flatness is significantly modified from exit of tandem mill to entry of galvanising plant. After decoiling some coils have waves, while they show no flatness defects after cold rolling before coiling. The process that can be responsible for these changes is the coiling process. The flatness changes differ quantitatively and qualitatively. The difference between online and post-rolling flatness mainly depends on the strip geometry and material. Edge waves often appear at the entry of the HDG line, which decay over the strip length: for some coils (coil no. 1 and no. 2), the waves disappear earlier or later (coil no. 3), but may also persist over the whole strip length for other coils (coil no. 4). To evaluate the evolution of flatness, the flatness distributions (acquired by the final version of the TopPlan system) have been decomposed into orthogonal parts using Gram polynomials. The data analysis reveals that the coiling operation introduces an asymmetrical flatness defect seen at the C1 signals. In the first part over the coil length, edge waves appear and superpose the C2 component, but decay along the strip length. This is confirmed by the value of the correlation coefficient. It seems that the wider strip the higher is the correlation, and the smaller are the edge waves generated by the coiling process. A strip that has been subjected to the coil crown effect usually has long edges on the head end, which is overtaken by full center that persist until the tail. Many examples of flatness evolution have been found that may be (more or less) caused by the coil crown effect, but sometimes partly supposed by other flatness defects. From the analysis of C2 signals, it can also be concluded that a perfect online flatness is not necessarily optimal for the final flatness. A higher C2 online flatness would be better in this case, at least over 2/3 of the strip length. Moreover, a varying reference flatness curve should be used to compensate for the coiling process effects and produce consistent flatness over the whole strip length. The current practice of keeping the reference flatness constant is not the optimum from the through-process viewpoint. Task 3.2. Hot-dip galvanising entry-coil-quality monitoring [ARCELOR ESPAÑA, UPM] In order to provide enough technical capability to the project different algorithms with very different technologies were used. These include classical linear models, support vector machines, partial least squares regression tools, multi adaptive spline regression, neural networks and other similar tools.
9
In addition to these techniques other approaches have been considered too, like, classification and regression trees, J48 based classifiers, clara, decision trees, random forest and many other classifying techniques. In all the cases the datasets used were preprocessed further than the automatic processes do. Then specific random set were defined by partition of datasets and in many cases cross validation was used in order to avoid bias or over fitting. In short there was not only one type of algorithm bringing out the complete solution but the selection strongly depended on the problem considered, that is, the involved datasets. Due to this particular issue, a very big effort was spent in these areas as they are core for the final performance of the developed system and some gained knowledge from these areas was properly disseminated in scientific journals and conferences. Task 3.3. Through-process strip-quality optimisation over cold rolling and galvanising [BFI, AMEH] Measures have been developed by BFI and AMEH to improve the through-process flatness quality: Prediction of interstand flatness and use it to trim bending at each stand This gives a qualitative figure of how the flatness evolves throughout the mill and allows operators to adjust tilting or bending to affect the flatness quality and the strip guiding between the stands. Also, an automatic trimming of bending is included to anticipate changes in entry profile and rolling force at each stand. Compensation of asymmetrical coiler movement Longer observations of the mill operation revealed that operators often switched off the automatic tilting. The reason for the coiler movement is that the coiler at that mill is of the cantilever design, which implies that it has vertical support only on the drive side. As the strip is coiled, the weight of the coiler will increase continuously. The coiler could then deflect such that the operator side of the strip will have a bigger strain than the drive side. The operator side of the strip would then be plastically elongated more than the drive side during coiling. A compensation solution has now been developed and realised as part of the flatness controller. For this purpose, the coiler movement has been measured by laser distance sensors for different strip characteristics. An online algorithm has been developed that compensates for the drawdown of the coiler depending on coiler weight and tension. The parameters of the compensation algorithms have been identified from measured signals. The compensation module is now in operation leading to the fact that automatic mode of tilting is used as default and trims of the operators have been reduced significantly. Modification of flow ratio basic to selective cooling and adaptation of the flatness controller. In 2008, it was decided to change the ratio cooling to 75/25: 75% of cooling medium (emulsion) is provided by the selective cooling; 25% by the basic permanent cooling. For this purpose, a Selectrospray® roll cooling system has been installed by Lechler: a third switchable spray header has been added to each cooling system. This revamping took place within a plant shutdown. The flatness controller has then been adapted to the new situation and re-commissioned by BFI and AMEH. The result of this measure was a substantial improvement in flatness.
10
More precise adaptation of flatness reference curves to strip characteristics considering the effect of coiling on flatness One possible measure to compensate flatness changes through coiling and ensure consistent flatness over the strip length at the entry of galvanising plants is to adapt the flatness reference curve in a length-dependent manner. For this purpose, an iterative learning control (ILC) strategy has been proposed. Task 4.1. Definition of systems functionality [ALL PARTNERS] The focus of this task was to make clear the users of the system and its functionality. Objectives of this task were the development and installation of a through-process flatness optimisation system (BFI, AMEH) and a HDG entry-coil-quality monitoring system trying to avoid poor surface properties (AME, UPM), based on the strategies developed in WP3. Depending on the required reaction time, the information about the entry-coil-quality gained in this project was used in two directions: Information to the planning department. This way is used when a medium term reaction is required. Information to the line about the quality of the incoming coils. This way is used when an immediate reaction of the line could be required. Both strategies were tested and evaluated in the galvanizing line of Aviles.
Task 4.2. Methods & system for Hot-dip galvanising entry coil quality monitoring [AME, UPM] Different classes of coil quality affectations were considered: Coils with severe defects, affecting a big area of the coil.
Coils with severe defects, concentrated on the coil ends.
Coils with severe but isolated defects located in the central part of the coil.
Different objectives were under consideration for all these cases. These objectives include: a) To develop predicting methods about the impact in the galvanizing product in terms of defect survival. b) To predict evolution of mechanical properties inside the coil as a tool helping the decision making for cutting or delivering tasks. c) To analyze different influences combined throughout model interactions. The software built help the users in these directions by implementing convenient algorithms according to the modeling processes carried out in WP3. According to the specific performance the system was built by using very different tools pending on the type of prediction expected. The user interface was tested extensively in order to provide a common access way to the system functionalities. Task 4.3. Methods & system for line-coordinated optimisation of cold rolling and galvanising lines [BFI, AMEH] Some features of the thorough-process flatness optimisation strategy developed in Task 3.3 have been implemented in the flatness controller module on the ABB Controller AC800PEC platform. To enable the tandem mill staff to parameterise and adapt the coiler-droop compensation algorithm, a user-friendly (offline) software tool has been implemented. When new data are generated, they can be loaded and used for parameter adaptation. The coefficients identified can then set in the flatness controller interface. The user has also the option of looking at the internal results of the fitting algorithm.
11
Also, work was focused on completing data analysis through the processing route cold rolling / galvanising. Specifically, the topometrical flatness measurement system TopPlan has been revamped by implementing a new routine for accurate edge detection. Moreover, much effort has been spent to create a new (improved) version of the measurement software tailored to the strip and environment conditions at the entry of AMEH’s galvanising line no. 2. The main features of the new measurement algorithm are: Accurate edge detection using special transformation and segmentation
Three-dimensional computation to consider strip movement
Decomposition of height surface into windable and unwindable parts; only the unwindable part does contribute to flatness.
The modified measurement system has been first implemented and calibrated at the BFI testbed. The implementation and commissioning of the software at AMEH’s galvanising line was then. A simulation platform has been designed to test the iterative learning control algorithm with given data from the plant. Task 5.1. Galvanising line at ACERALIA / HDG-entry coil quality monitoring [AME, UPM] Developed algorithms have been combined in different ways, under different user interfaces, in order to fulfil the final user requirements. In addition to this, specific features were implemented in order to fulfil specific user wishes and to provide to them with the required information, including hierarchical analyses for specific user types. In particular, specific tool helping coil grading application includes a full monitoring into the hot dip galvanizing line as well as the comparison with the system prediction for the evolution of the coil, in order to provide to operators with a global view about how the prediction for coil quality actually performs. This interface promotes operator learning too, as it is possible to have a look on these specific areas of defect across different facilities as well as to ask the active model responsible for the prediction about what were main rules fired and explaining the prediction. This functionality is only available if the involved model is a rule based decision tool. Task 5.2. Cold rolling and galvanising lines at EKO STAHL / Line-coordinated quality prediction and optimisation [BFI, AMEH] Trials for measuring coiler drawdown A measurement equipment consisting of two laser sensors has been installed at the coiler of the tandem mill of AMEH to acquire the drawdown of the coiler. The influence of the drawdown on flatness has been analysed. It is clearly observed how the coiler is moving in both directions, particularly in the vertical (Y) direction. This leads to continuous increase of the flatness (linear) error, as can be seen in the top part of the figure. Trials for evaluation of the through-process optimisation features A number of experiments have been conducted to get data, from which a sensitivity analysis can be made, to find out whether the post-rolling flatness can be affected by some mill actuators or strip parameters.
12
Trials have been performed to get insight into the influence of the strip tension on the online and postrolling flatness. It can be concluded that the higher tension the strip is coiled with, the worse is the post-rolling flatness. The purpose of the next experiment was then to investigate to what extent the online flatness in the rolling process can be used for controlling the post-rolling flatness. In this experiment, the amplitude of the reference flatness has been changed in steps that can later be tracked in the post-rolling flatness registered by the TopPlan system. The general conclusion is that the reference flatness curve can be used to affect the post-rolling flatness. Moreover, the flatness reference should be varied with the strip length, to compensate for changing flatness figures, i.e. edge waves at that head of this strip that are overtaken by full centers over the last ac. 2/3 of the coil. Selective roll cooling can also be used to improve the flatness quality, as has been confirmed by the experiments carried out on this actuator. Task 5.3. Guidelines for best through-process monitoring and optimisation [ALL PARTNERS] Different measures and strategies should be taken to ensure best flatness over the chain cold rolling / hot-dip galvanizing: Consider the entry profile information for profile feedforward control that acts on the bending at the first stand of a tandem cold mill. Use a line-coordinated control strategy compensates for any flatness disturbance as early as possible, e.g. roll force changes. Have in mind that post-rolling flatness will be often different from that obtained online during the cold rolling process. Avoid or keep at minimum any misalignment between the rollgap, flatness roll (shapemeter) and coiler. Do not believe that differences detected between online flatness and post-rolling flatness are due incorrectness of the shapemeter readings. If the misalignment cannot be avoided, e.g. coiler droop in a tandem mill, it is absolutely necessary to compensate for this movement depending on coiler weight and tension. Without coiler-drawdown compensation, it is usually hopeless to use the automatic tilting operation. Do not wonder if you get degraded flatness. Take into account that the coiling process does contribute substantially to changes between online flatness and post-rolling flatness. Use a control strategy that acts on the actuators from through-process viewpoint, to ensure best flatness over the whole strip length at the entry of galvanizing plants. Consider an appropriate scheduling strategy, a length-dependent reference flatness curve, reduced coiler tension and optimized cooling strategy, as possible features for optimal through-process flatness.
Avoid on-sided edge waves at the entry in the annealing process.
13
2.
Scientific and technical description of the results
2.1
Objectives of the project
The core idea of the project is that, knowing the operating characteristics and monitoring the current conditions and output of a processing stage, the transfer specifications are adjusted (by the setup and control systems) such that the desired objectives of the downstream process are met, the strip quality of the final customer is ensured, and simultaneously the process disruption and the energy/material consumption is minimised. This is also motivated by the fact that, despite the equipment of most steel production plants with powerful automation systems, many quality defects reported by the steel producers cannot be corrected locally within the process where they appear. Thus, the only appropriate way to fight with these quality defects and problems is to handle them from the through-process viewpoint proposed in this project. Figure 1 gives an overview of the project objectives/deliverables. Line-coordinated Strip Quality Optimisation • Strip quality predictor • Optimiser of shape/flatness and zinc-layer thickness
Hot rolling
Automation
Automation
Automation
Cold rolling
Hot-dip galvanising
Temper rolling
Transfer StripQuality Characterisation HDG-Entry-Coil Quality Monitoring Coil Rejection Measur. thickness profile, tempreture, etc.
Shape/Flatness measur.
Zinc layer measur.
Figure 1. Overview of the line-coordinated optimisation system and its components to be developed within the scope of the project.
LINECOP develops line-coordinated strip-quality assessment, monitoring and optimisation systems for cold rolling and hot-dip galvanising (incl. continuous annealing and temper rolling), based on an integrated model for the whole processing route. The main and secondary objectives can be summarised in following items: 1.) Development and installation of a HDG entry-coil-quality-monitoring system to improve the knowledge about the coil quality conditions in the entry of the galvanising process. It helps to determine whether the coil has the minimum quality to go on process or not (coil rejection), based on collected and pre-processed data samples from HDG line and upstream processes, using an intelligent (predictive) data-mining strategy. 2.) Establishment of a model-based line-coordinated shape- and coating-thickness optimiser, i.e. a technological analysis and advisory package for providing immediate knowledge for diagnosis of shape and coating thickness problems. It includes suggestions for intervention measures (processing practice, setup/control systems modifications) to reduce/avoid these problems. 2.1 Development of an integrated quality model for the (stage by stage) prediction of the evolution of shape/flatness in cold rolling and of coating thickness variations in HDG lines, incl. continuous annealing and temper rolling. - Data acquisition for a large sample of coils over the production route, installing appropriate additional instrumentation where necessary, establishing changes occurring at the considered production stages, and quantification of the degree of interaction between
15
-
the processes by comprehensive analysis. New instrumentation will be required to measure shape changes at entry of EKO’s hot-dip galvanising (HDG) line. Suggestion and implementation of appropriate self-tuning/learning algorithms for parameter adaptation of the through-process quality predictor.
2.2 Development of a through-process optimisation system, which uses the quality prediction model and considers the HDG-entry-coil-quality-monitoring to optimise the corresponding strip-quality parameters in cold rolling and galvanising lines. - Unified through-process strip quality characterisation (hot, cold, galvanised) to generate simply and meaningful indications to the internal users and final customers. 3.) Generation, realisation and test of an online-capable version of the shape- and coating-thickness optimiser to run automatically during the production to minimise strip-quality variations over strip length and width. 4.) Working out guidelines/rules for strip-quality monitoring and optimisation over the whole production route based on the results and experience gained from the developments of the project. 2.2
Comparison of initially planned activities and work accomplished
The initially scheduled work was carried out mainly as expected, in spite of the economical crisis that was affecting in some individual tasks the project’s performance. Globally the project were requiring more man-hours that those initially estimated, mainly because of the complexity of models, algorithms and the difficulties for finding all the relevant information for specific defects at different facilities and, sometimes, the difficulties in having clear relationship between coil parameters. Indeed, the project showed how relevant is the assessment of the databases and, as far as it is not an easy task due to the big amount of sensors involved and the specifically heavy conditions of these facilities, strong recommendations for developing and implementing smart software agents able to notify maintenance people about ‘unexpected’ values in different parameters is a clear additional value of technology carried out during this project. As mentioned in the last technical report (no. 2), Task 1.1 of the project (Configuration and installation of a mobile shape measurement system) has slowed down. Due to internal production reasons (need for preparation of the measuring location, provision with setup data, integration into the automation system), and some supplier delay, the installation and commissioning of the flatness measurement system TOPPLAN at the entry of the AMEH’s hot-dip galvanising (HDG) line no. 2 could not be performed as planned in the work programme. That has produced a delay of at least 6 months in the project work. This delay affects all subsequent project tasks, e.g. model derivation and verification, correlation and operating data analysis, construction of the quality predictor, etc. Revamping work at AMEH was carried out to couple the tandem cold rolling mill with the pickling line no. 2 since 2007, and has continued until end of 2008 (coupling and commissioning phase, originally planned for end of 2007, now postponed to the second half of 2008). There are also revamping work at the annealing plant of the HDG line. All these circumstances created a new situation (product quality, process conditions) for the project, which makes a before-after comparison not possible. Therefore, knowledge gained and concepts proposed based on data before coupling are useless, and do not promise any benefit for the industrial user. Consequently, complete measurement campaigns and trials by BFI and AMEH could not be carried out as planned in the project work programme. By this, a delay of at least 6 months has been caused.
16
In summary, the main objectives of the project have been achieved despite the problems and delays mentioned above. Due to the fact that the development of the TopPlan system has taken more effort and that no data were available for AMEH galvanising plants, more emphasis was placed on monitoring and optimising the flatness over the cold rolling processes until the entry of the galvanising line, at the expense of reduced modelling effort for the galvanising process. 2.3
Description of activities and discussion
WP 1: Characterisation of Transfer/Final Strip Quality and Data Acquisition Task 1.1. Overview of processing/strip-quality problems and customer requirements [ARCELOR ESPAÑA, EKO] Detailed studies of the current situation at the different plants were carried out. The different components of the investigated plants were identified and the available process and quality parameters were registered. Out of the available variables, the relevant ones were detected by means of the knowledge of the shift managers and technicians. The results of this first step are used to define demands to the data infrastructure. Based on that, concepts for the necessary enhancement of existing databases or the components, which have to be established, were developed. Here, for example, necessary network connections to quality measurement devices, databases or server computers are mentioned. According to the project objectives, the main quality parameters to be considered are: c) Galvanised strip: homogeneity of the zinc layer, strip flatness. d) Cold-rolled strip: strip flatness, tension-stress state after cold rolling (offline flatness). When producing galvanised sheet for automotive industry, the conditions of the galvanising lines have to be almost perfect. For these end-users, it is essential to guarantee a minimum zinc-layer thickness for the galvanised strip; a violation of the lower value is however not allowed. Therefore, the setup and control systems have to minimise the variance of the zinc-layer thickness, usually measured at two locations, i.e. the hot and cold gauges. This condition is hard to guarantee and requires reliable process control and monitoring systems. There are many reasons that avoid ensuring good conditions in the line, for example, coils with bad flatness, thickness, in many cases, the chemical composition of a specific steel grade may vary slightly, due to the large number of steel grades produced in the steel plant. Besides the saving of zinc, the uniformity of the zinc layer leads to fulfilling the ever increasing demands of customers, in particular the automotive industry for „galvannealed“ strips. Specifically, AMEH (formerly EKO) produces galvanised products with 8 different variants of reference zinc-layer thickness between 70 and 275 g/m2, at two different HDG lines, one with a vertical annealing facility, the other with a horizontal annealing facility. The analysis of current quality for the whole range of products is thus a difficult task. Moreover, the quality of the galvanised strips inherently depends on the strip geometry, material, and the flatness produced in the downstream processes, i.e., hot and cold. The flatness inheritance from cold rolling to galvanising and its effect on the zinc-layer thickness and zinc consumption is a key component of the project studies to be carried out by BFI and AMEH. An in-depth analysis of flatness and zinc-layer thickness over the strip width and length for different product classes and plants will be performed. The next point processed during this task is the study of the current applied methods for classifying the product quality. In intensive discussions with the experts of the quality and production departments, their experiences were collected as well as their demands to be developed during the project. A brainstorming for gathering information about the parameters upstream and their influences have been done. During these meetings key factors of the hot strip mills, pickling lines and cold rolling mills have been collected.
17
After that several meetings with the facilities technicians it was decided ARCELORMITTAL ESPANA to focus the research project in following main areas: Flatness. Quality surface problems (like zinc grains, blisters, scale, etc.). Mechanical characterization of the raw material, after being processed. Specific algorithms and products must be carried out in order to deal with these specific issues in such a way that can be useful for different roles at the galvanizing line in an integrated way [13]. Task 1.2. Strip-quality characterisation (hot, cold, galvanised) following the needs of internal users and final customers [ALL PARTNERS] As the project tries to take a look at the “global quality of coils” coming to the hot dip galvanising lines, we start by considering parameters from previous facilities, like the hot-strip mills and cold rolling mills, and from the galvanising facilities themselves. Strip characterisation at ARCELORMITTAL EISENHÜTTENSTADT Within a close work between BFI, AMEH (and FQZ), the parameters for the description of the strip quality in terms of flatness and zinc-layer thickness have been discussed. Also, all process and plant parameters influencing these target variables were specified, and their sources within the distributed data acquisition and automation systems at the facilities. Besides the different data sources and formats, a major problem to be solved before starting the data analysis at the mills of AMEH is to establish the correct coil allocation; see Figure 2. This is due to different processing/sequencing in the cold rolling mills and galvanizing mills. Also, coils (parts) are welded together, and other parts are trimmed, so that it is not easy to track and compare the quality attributes directly. A substantial effort and time has therefore been spent by AMEH (and FQZ) to develop and implement an appropriate procedure for data synchronisation, exploiting all information available in existing databases. A total database has been developed at AMEH for the analysis of the process chain cold rolling – galvanising, planned within project. A (draft) list of the data and parameters to be considered is given below. A) Cold rolling mills (tandem mill & reversing mill) Strip speed (after the last stand) Strip thickness (reference and actual for each stand) Strip width (after the last stand) Rolling force (drive/operator side; for each stand) Roll bending force (for each stand) Strip tension (between each two stands) Hydraulic position (drive/operator side; for each stand) Roll (peripheral) speed (for each stand) Strip flatness distribution (reference and actual) Status of the selective cooling sprays (at the last stand) Coil diameter (Coiler)
18
B) Galvanising lines B1) Homogeneity of zinc layer Strip thickness and width Strip speed, temperatures, and tensions Roll system of the zinc bath Process parameters at the air knives (pressure, distance, etc.) Evaluation indices for the homogeneity of zinc layer (hot and cold gauges) B2) Flatness of galvanised strip Strip speeds at skin-pass mill and leveller Strip tensions at skin-pass mill and leveller Elongation at skin-pass mill and leveller Roll system of leveller r Rolling and bending forces at leveller
Figure 2. Data bases, formats and streams at the considered facilities of AMEH
C) Characterisation of hot strip Thickness profile (measured after pickling) Strip thickness Strip flatness at the exit of the hot finishing mill Cooling conditions (finishing temperature, coiler temperature) Strip characterisation at ARCELORMITTAL ESPANA During Task 1.2 different tools were installed at plant level, based on a Linux middleware running php, configured with some database drivers and allowing linking several databases relevant to the galvanizing process.
19
Other target of this task was to analyze the coherence of first sample of data, and in order to test installation of tools. For this, the speed of individual coils in hot dip galvanizing line has been studied by considering mainly the flatness produced in tandem line. The selected variables were: 1. Length 2. Width 3. Thickness 4. Maximum, minimum and average flatness 5. Maximum, minimum and average speed of galvanizing line WeKa® software has been used, including special variance analysis and algorithms ('BestFirst'), with attribute evaluation with 'WrapperSubSetEval' and 'M5Rules'. See as an example Table 1. Table 1. Diagram showing variable relevance according BestFirst strategy Evaluator: weka.attributeSelection.WrapperSubsetEval -B weka.classifiers.rules.M5Rules -F 5 -T 0.01 -R 1 -- -M 4.0 Search: weka.attributeSelection.BestFirst -D 1 -N 5 Relation: linecop-weka.filters.unsupervised.attribute.Remove-R12-18,21-32 Instances: 668 Attributes: 13 Longitud Ancho Espesor Peso Planitud.med Planitud.max Menor.5pct Menor.10pct Menor.20pct Menor.30pct Menor.50pct Vel.linea.med PRO_STC Evaluation mode: 10-fold cross-validation === Attribute selection 10 fold cross-validation seed: 1 === number of folds (%) attribute 0( 0 %) 1 Longitud 0( 0 %) 2 Ancho 10(100 %) 3 Espesor 0( 0 %) 4 Peso 3( 30 %) 5 Planitud.med 2( 20 %) 6 Planitud.max 1( 10 %) 7 Menor.5pct 1( 10 %) 8 Menor.10pct 0( 0 %) 9 Menor.20pct 2( 20 %) 10 Menor.30pct 4( 40 %) 11 Menor.50pct 10(100 %) 13 PRO_STC
This approach allows to select in an independent way (with cross validation), what variables are more suitable for explaining speed variation and in what order, showing that thickness is much more relevant that flatness what is much more relevant that coil length or width regarding this particular issue. Discriminant analyses were also produced in order to identify classes inside the data (see Figure 3). In this figure it can be seen agglomerative distribution of samples in classes for previous data related to speed against flatness and geometrical structure of coils. Each color means one class, according to discrimination suggested by LD algorithm. It was drawn two main components (LD1 and LD2) for Linear Discriminant plane and samples projection of data into.
20
Figure 3. Classes inside the data, according discriminant analysis
Task 1.3. Configuration and installation of a mobile shape measurement system [BFI, AMEH] Work by BFI and AMEH has focused on designing the layout, installing and integrating a topometrical flatness measurement system at the entry of AMEH’s HDG line no. 2; see Figure 4. However, due to many revamping activities, the progress of this work has been slowed down. The interfaces of the measurement systems have been specified. Then, the laboratory design and testing phase has been initiated. Once finished, the prepared construction and computer system have been transferred to the HDG plant, installed, calibrated, adapted to the on-site conditions, and commissioned. A major task was also the integration of the system in the automation platform to ensure continuously gathered and synchronised data. BFI and AMEH have completed the layout design, installation and integration of the topometrical flatness measurement system (TopPlan) at the entry of AMEH’s HDG line no. 2. The following steps have been carried out. 15/16 June 2008:
Training course VisionLab (programming environment) at IMS; hand-over of software July 08: Specific training Vision Lab on the TopPlan software; New Version VisionLab Inspection of completed construction (support frame, camera, projector) at IMS test lab; see Figure 5. Setup of TopPlan at BFI test filed; software installation Software calibration Transport of the system to AMEH
21
Figure 4. View of the entry side of the HDG line, where the flatness measurement system was temporarily installed.
2124 July 2008: Installation of TopPlan at the entry of AMEH’s HDG line no. 2; see Figure 6 and Figure 7. Calibration and storage; see Figure 8. 4 August 2008: Further tests Mid September 2008:
Construction of protection barrier
22
Figure 5. Layout of the TopPlan system
23
Camera
Frame
Figure 6. View of the TopPlan system installed at entry side of the HDG line
Cabinet Image
Frame
Figure 7. View of the installed hardware and software of TopPlan.
24
Figure 8. View of from calibration process
25
Task 1.4. Acquisition and pre-processing of data samples [ALL PARTNERS] Data Acquisition at ARCELORMITTAL EISENHÜTTENSTADT The concept for establishing the necessary data bases at AMEH, described in the last reports has now been realised. The total database was developed for the analysis of the process chain cold rolling – galvanising, planned within project. The resulting data files have been transferred to BFI for carrying out the required analysis. Visual Basic and MATLAB Codes have been created to read the data; see Figure 9.
Figure 9. Visual Basic mask for data reading
This task aims to specify hardware and software architectures needed to collect all needed process and quality data, taking into account a proper and continuous link with the various existing data sources, a flexible data-base structure and management, a flexible rules management, flexible and easy reporting facilities, and the system integration in the existing company IT (Information Technology) environments. Moreover, data-measurement campaigns planned, and data pre-processing will be carried out. First analysis revealed that material tracking and assignment from cold rolling mills to the galvanising plants is difficult and not possible with available tools, particularly, when having in mind that the project aims to monitor the strip quality in quasi-real time (from one coil to the next). This implies higher demands on the availability of the data and the accuracy of material tracking. Therefore, special emphasis and work was spent during this project period on implementing proper algorithms for “coil assembling”, i.e. to track and assign data of cold-rolled strips trimmed or welded together before coating. A further challenge was to collect the data from different plants and different archives and formats, which all have been merged and integrated into a new database, which is able to gather data on demand, synchronise, and present them to the user. A typical task is to present and analyse shape related parameters from entry of cold rolling to the exit of galvanising; see Figure 10. Such figures, yet assembled manually, can now be generated and analysed automatically and continuously after completion of the work in Tasks 1.3 and 1.4.
26
Thickness profile at entry of cold tandem mill (traversing measurement; exit pickling)
Flatness profile at exit of cold tandem mill (flatness roll)
Flatness profile at entry galvanising line no. 2 (TopPlan)
Flatness at exit of galvanising line no. 2 (Shapeline)
Figure 10. Through-process tracking and presentation of shape-related data
Based on the integrated data, through-process quality defects and problems over the chain rolling– galvanising have been analysed. Particular interest was on the diagnosis of shape-induced coating thickness problems/defects. A typical problem in this area is the effect of entry strip-shape defects (which can be produced in hot rolling or cold rolling) on the annealing operation, and on the uniformity of the coating thickness; see Figure 11. The use of through-process optimisation approaches promises to figure out the source of such quality faults and to provide hints about reducing/eliminating them, thus leading to decreasing the material (zinc) consumption.
27
Figure 11. Distribution of coating thickness over the strip width at top and bottom side when shape defects occur near the air knives.
The concept for establishing the necessary databases at AMEH, described in Task 1.1 has now been realised. The total database has been developed for the analysis of the process chain cold rolling – galvanising, planned within project. The database part for the processing route tandem cold mill/HDG line no. 2 has now been completed, consisting of 91 process data signals from the cold mill and 193 signals from HDG. Also, the TopPlan flatness data were included in the database. In the first stage, three data files are provided to BFI for carrying out the required analysis: a description excel file, a database (plant and setup data) and a binary data file containing the process data. Just as examples, some data generated are plotted in Figure 12 and Figure 13.
Figure 12. An example of length-based data included in the database of AMEH’s cold tandem mill
28
Figure 13. An example of length-based data included in the database of AMEH’s hot-dip galvanising line no. 2
Data pre-processing at ARCELORMITTAL ESPANA By using different passive agents, compatible with AME’s firewall policies, data gathered are put together inside an oracle database located for research purposes, in the UPM laboratory. The architecture of the system can be visualized as described in Figure 14.
Figure 14. Conceptual graphs for architecture (left); architecture Framework of the database system (right)
The system has been built as a robust system tolerant to difficulties or fortuities like shutdowns in any element of the system [2, 1]. The database & interface allow the use MySQL admin as well as specific tools like RMySQL and ODBC gateways.
29
Regarding the hardware to be used, it is required a NAS system allowing to store 6TB of information (regarding samples, defects, laboratory analysis and other similar data sets). In order to produce models being validated at plant level, a farm of powerful systems is required. For the project it was used 6 dual core opteron with two CPU and 16 GB of RAM each one. Regarding software, at design laboratory level it was decided to use mainly open source tools, like SNNS (Stuttgart Neural Network Simulator) for NN developing and testing, R (www.r-project.org) for statistical analysis and WeKA (http://www.cs.waikato.ac.nz/ml/weka/) for CART technology, mainly because the interest in releasing models developed as source code, in order to make easy the implementation at plant level. Specific campaigns of data capturing were conducted in addition to the general one, looking to specific purposes. Just as an example, the database built for blister analyses includes smart pre-processing in an automatic way: 77 patterns were removed because some variables had either not available or erroneous data. 161 observations were removed because their values were zero in some variables: BF.SAN_GRL_TMP_DSANG, CC.DIS_TND_WGT_REM, CC.GRL_GRL_SPD_AV, CC.OXI_GRL_HGT_MEN, MS.GRL_GRL_TMP_ULT, MS.EVN_GRL_TIM_TRAT, DIS_BUZ_FLW_MED, DIS_BUZ_PRE_MED, DIS_MLD_FLW_ACE_MED MSRH.DIS_TRM_CNT_VIDA_ESTE, MSRH.DIS_TRM_CNT_VIDA_OESTE and MSRH.DIS_VAS_CNT_VIDA. Some variables were removed from the dataset because they were equal to zero: CC.DIS_AAC_CMP_CD_2, CC.DIS_AAC_CMP_H_2, CC.DIS_AAC_CMP_MG_2, CC.DIS_AAC_CMP_O2_2, CC.DIS_AAC_CMP_ZN_2, CC.DIS_TRR_TIM_ESP, MSRH.TRL_GRL_CMP_PPM_ENT and MSRH.TRL_GRL_TIM_TRAT. Specific variable were removed because it was constant and equal to one. In other cases, the number of zeros and/or not available (NA) data was very high in comparison with the number of patterns in the dataset. In this particular case, the final dataset contained 690 patterns and 118 variables that were feed to the modelling phase. In some cases the automatic pre-processing required specific human conducted approach because the automatic tools do not provide enough discriminant capability, like in the case shown in Figure 15. In this case PCA projection with normalized independent variables illustrates the absence of different clusters. Linear discriminant analysis (LDA) seeks the linear combination of features which best separate two or more classes of objects or events (in this case, the presence or absence of defects after the pickling line). The resulting combination may be used as a linear classifier or, more commonly, for dimensionality reduction before later classification. Figure 16 shows the LDA projection of data. The overlap of data indicates that the data is not linearly separable, and therefore it is difficult to predict the true labels of instances in the overlap. In these cases, specific treatment was required in order to improve, by means of nonlinear techniques, the response after data pre-processing.
30
Figure 15. PCA projection
Figure 16. LDA projection
31
WP 2: Development of Integrated Model Task 2.1. Enhancement of existing flatness model for cold rolling [BFI, FQZ] At BFI, a (physically-based) shape model for cold rolling exists [12, 7]. The hot strip properties (thickness, profile, temperature) will be considered as input parameters/data. The model has been enhanced within this project, i.e. particularly extended with sub-models of coiling/uncoiling. The accuracy of the model has also been improved by detailed finite-element (FE) model predictions. FE modelling of shape
contact pressure [MPa]
Different strategies are possible in FE modelling. A 3-dimensional FE-simulation model for AMEH’s four-stand cold rolling mill describing shape effects has been developed by BFI; see Figure 17.
contact area [mm]
strip width [mm]
Figure 17. Three-dimensional finite-element model with elastic rolls, strip and boundary conditions and calculated contact-pressure distribution
Modelling of shape changes induced by the coiling process The coiling process after cold rolling is a process that may affect the strip shape. During coiling, the strip is bent in tension over the pinch roll. Strip deformation in coiling is similar to the deformation that occurs during levelling [8]. In levelling, the material is bent over a roll of sufficiently small diameter to cause plastic deformation in the material. The bottom pinch roll, in this case, has a relatively small diameter, usually around 20 inches, and serves the same purpose. When the strip is bent in tension over the pinch roll, it undergoes non-uniform through-thickness plastic deformation with the maximum tensile deformation at the top surface. Such a strain distribution creates positive coil set and helps to keep the coil tight by minimizing the springback effect [17]. BFI has analysed the impact of coiling and de-coiling on the flatness of the final cold coil condition, considering the findings of previous EU-funded work [16, 4, 20]. The analysis within the present project has been done by physically-based approaches, taking the strip thickness profile and the coiling tension into account to calculate coil stresses and deformations, as well as by data-based methods, taking the measured flatness at the exit of the cold mill coiler and at the entry of the galvanising line into account.
32
The flatness model for coiling and de-coiling consists of three sub-models: Coiling model. Air-cooling model. De-coiling model. The classical coiling model and the integration of the strip bending have already been described in [16, 4]. The integration of the effect of strip crown has been further developed and implemented to the shape calculation routines. Model of stress-strain behaviour of the material For the calculation of the resulting stresses the material properties described by the stress strain curve of the material have to be considered. The stress-strain curve at elevated temperatures [9, 10] has been given by the following equations:
F , , A , p0
B
with the material depending parameters:
A , a0 a1 a2 log a3 log
B b0 b1
The given relation is valid for reductions > 0.002. The transition from the quasi-elastic deformation to the plastic deformation is defined at the reduction = 0.002. The method of modelling the curve in the complete elastic-plastic region is schematically shown in Figure 18.
E (T ) F ( , , T ) m( g ) ( g , g , T ) F ( , , T )
s s g g
with [21]
d F ( , , T ) d g , g ,T
m
V
s
x
m g ( g , g , T ) E (T ) m
E (T ) 2.14 105 52T 4.7 102 T 2
33
Figure 18. Model of the stress-strain-curve in the complete elastic-plastic region
Model of strip deformation by the coiler tension The calculation starts with an assumed flatness profile of the strip exiting the last stand to which no coiler tension is applied:
IU
L( x) L0 5 10 L0
L( x) L0 L0
The relation between the true strain and the local elongation ε is given by:
ln(
L ) ln( 1) L0
Stress in the outer lap The stress in the outer lap of the coil as seen in Figure 19 is manly induced by Strip crown. Strip flatness. Strip tension. Bending of the strip around the coil. This will be described in some details in this paragraph.
Figure 19. Effect of strip crown on the shape of the coil and on the stress distribution
34
The strip crown may be described by
h( z ) h0 (1 z /( w / 2 ) n
where h0 is the nominal thickness, the crown ratio ( 0.52 % ), and N the crown exponent (2, 4, 6). The radius of the coil after i windings
R( z, i) R0 i h( z) The tangential strain of winding i is:
t ( z , i, a )
R( z, i 1) a uz a a 0
R( z, i 1) a 0 R( z, i 1) a 0
Next the effect of bending the strip around the coil is investigated; see Figure 20.
Figure 20. Effect of bending on the stresses across strip thickness
The most inner fibre in strip thickness direction (x) will be compressed and the most outer fibre will be stretched.
B ( x, z, i)
x 2 R( z , i )
for h x h 2 2
The total strain caused by shrinking of the outer lap and bending of the lap around the coil is:
tot ( x, z, i, a) t ( z, i, a) B ( x, z, i)
t E tot taking into account the equilibrium of the force
Fz
w/ 2 h / 2
( z, x, i, a)dxdz 0 t
w / 2 h / 2
35
For the further calculation an average tangential stress is defined as
t ( z, i)
h/2
1 t ( x, z, i, a )dx h h / 2
Stress in the coil (coil on the mandrel) Subsequently the Tangential stress (coil on the mandrel):
t (ri , z) t (ri , z) (ri , z) 02 ra r dr t(ri , z ) 1 2 t (r , z ) 2 ri ri r 02 and radial stress
02 ra r dr r (ri , z ) 1 2 t (r , z ) 2 ri ri r 02 in the coil is calculated due to the pressure of the out lap. In this case the coil is still on the mandrel. Stress in the coil (coil off the mandrel) If the coil is taken off the mandrel the stress within the coil will be redistributed because the pressure between the mandrel and the inner lap will disappear. Therefore, the tangential stress is given by:
t ,relax (r, z) t (r, z) ~t (r, z)
~t (r , z ) r ( R0 , z )
R0 2 RA R02
R2 1 2A r
and radial stress is given by
r ,relax (r, z) r (r, z) ~r (r , z)
~r (r , z ) r ( R0 , z )
R0 RA2 1 2 RA2 R02 r
This model has been implemented in MATLAB for offline use. To speed up the computation, the model has also been transferred to C. Simulation results At BFI, the coiling model described in the mid-term report has been simulated to predict the effect of the coiling process on the flatness of cold rolled strips. The flatness evolution due to coiling has been simulated for two different strips: One with 0.52 mm thickness as seen in Figure 21. The other with 1.51 mm as seen in Figure 23. The resulting flatness profile due to coiling for the thinner strip is shown in Figure 22. In contrast to the initial centre buckles of the strip, as shown in Figure 21, the strip shows a combination of centre buckles and wavy edges after coiling. The maximum of the centre buckles is reached in the first third of the coil, which is due to the bending of the strip around the mandrel and the developing coil set. But the maximum of the wavy edges is reached at the end of the strip, due to the fact that the coil set has its larges value there.
36
In contrast to the thinner strip, the thicker strip shows higher centre buckles at the beginning, which decline with increasing coil radius, as shown in Figure 24 and Figure 25. From these simulations, one can conclude that the flatness error due to coiling does increase with the strip thickness and varies along the strip length. Therefore, the flatness reference for the flatness controller at the tandem mill has to be varied along the strip length and with strip thickness to compensate the effect of the coiling process.
Figure 21. Initial flatness and temperature profile before the strip is coiled (h = 0.52mm)
Figure 22. Resulting flatness after coiling
37
Figure 23. Initial flatness and temperature profile before the strip is coiled (h = 0.52mm)
Figure 24. Resulting flatness after coiling
Figure 25. Resulting flatness after coiling
38
Task 2.2. Development of models for hot-dip galvanising [BFI, FQZ] It was reported in some studies that the annealing process does not contribute much to the post-rolling flatness, and that most of the post-rolling flatness is introduced already at the coiling operation. The annealing process rather may have a smoothing effect on flatness; see [26], for instance. Other researchers [18, 23] claimed that the batch annealing process may be an origin of post-rolling out-of-flatness. These can be induced when the proof stress of the material falls sharply as the temperature is increased between 100–200°C. At this low value, the tensions inside the coil even out at expense of plastically deforming the strip, i.e. post-rolling out-of-flatness is introduced. Dai et al. [5] pointed out that a remarkable change of strip shape can be seen at the exit of the annealing furnace, no matter what the flatness is at its entrance. The transverse stress distribution of the strip is most even while the entry strip shape shows symmetrical double edge waves. On the contrary, single side waves at the entrance of the annealing furnace are the most unsuitable defects. As mentioned earlier in the report, no flatness data base was available at the exit of annealing/galvanising line considered, so that the analysis of flatness evolution over these processes could not be carried out. Instead, more effort was spent in analysing and controlling the strip flatness over the cold tandem rolling process with emphasis place on the modelling of the coiling process that dominates in changing strip flatness. Moreover, the uniformity of the coating (Zinc) thickness has been analysed to find out possible correlation between flatness defects and non-homogeneity of coating thickness. Figure 26 shows the relative occurrence of mean Zinc coating thickness deviation for strips processed in the tandem mill (QT) and the reversing six-high mill (RG). Verteilung der Differenz der Zinkauflage QT- bzw. RG-gewalzter Bänder (VZA2, Sollauflage 50 g/m**2) 30
QT-gewalzt
RG-gewalzt
relat. Anteil Bänder [%]
25
20
15
10
5
0
und größer
3.18
2.74
2.29
1.85
1.41
0.96
0.52
0.07
-0.37
-0.81
-1.26
-1.70
-2.15
Differenz MW Zinkauflage in Bandmitte (Bandoberseite - Bandunterseite) [g/m**2]
Figure 26. Relative occurrence of mean Zinc coating thickness deviation (reference value: 50 g/m2)
More important is to analyse the coating thickness over the strip width, to detect its possible correlation to (local) flatness defects; see Figure 11. For this purpose, the mean spreading (3) of the Zinc coating thickness over the strip width is plotted in Figure 27. It can be seen that two superposed local distributions appear. The first distribution has its center at 0.3g/m2 can be related to “flat” strip, whereas the second distribution with a center at 1.2g/m2 corresponds to strips with more or less local flatness defects. The skewness of this distribution may result from stronger flatness defects in the entering cold rolled strips.
39
35
Verteilung der mittleren Streuung (3s) der Zinkauflage über die Bandbreite für QT- und RG-gewalzte Bänder QT-gewalzt
RG-gewalzt
rel. Anteil Bänder [%]
30 25 20 15 10 5 0
und größer
5.1
4.8
4.5
4.2
3.9
3.6
3.3
3
2.7
2.4
2.1
1.8
1.5
1.2
0.9
0.6
0.3
0
Mittelwert Streuung (3s) Zinkauflage (für Sollwert 50 g/m**2)
Figure 27. Distribution of mean spreading of Zinc coating thickness (reference value: 50 g/m2)
Task 2.3. Construction of total strip-quality predictor [BFI, FQZ] The models developed in the previous tasks can easily be linked together to simulate a (physicallybased) through-process evolution of flatness over the considered processing stages, considering the relevant strip-input properties and process parameters. The total model can serve for prediction of shape development from entry of cold rolling mills to entry of the continuous annealing lines. It can also be extended by models for prediction of flatness through hot-dip galvanising lines. However, such a total model is a very complicated and computationally time-consuming, so that it is not suitable for use in fast calculations or online applications. Moreover, the model validation and parameter adaptation is a huge task. Nevertheless, the techniques described in Task 2.4 can be used for this purpose. Instead of the physically-based model, the alternative way of data-driven (back-box) modelling was also taken in this task. This means that the prediction of the post-rolling flatness can be made by fitting a regression model to measured variables from the cold rolling mill and from hot rolling.
40
Table 2. Input and output variables used for SOM No.
Output variable
1
C1_VZ
2
C2_VZ
3
C3_VZ
4
C4_VZ
5
C5_VZ
6
C6_VZ
No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Input variable BandPos C1_QT C2_QT C3_QT C4_QT C5_QT C6_QT vh1 nh1 h4 BZ_Ab_G1 BZ_G1_G2 BZ_G2_G3 BZ_G3_G4 BZ_G4_Aufh CDM_Aufh WK_G1 WK_G2 WK_G3 WK_G4 VB BESTM Anstellung_dif
Explanation Flatness at entry galvanising (C1) Flatness at entry galvanising (C2) Flatness at entry galvanising (C3) Flatness at entry galvanising (C4) Flatness at entry galvanising (C5) Flatness at entry galvanising (C6) Explanation Strip length Flatness at exit tandem (C1) Flatness at exit tandem (C2) Flatness at exit tandem (C3) Flatness at exit tandem (C4) Flatness at exit tandem (C5) Flatness at exit tandem (C6) Strip thickness at entry stand 1 Strip thickness at exit stand 2 Strip thickness at exit stand 4 Tension at entry stand 1 Tension at exit stand 1 Tension at exit stand 2 Tension at exit stand 3 Tension at exit stand 4 Coiler diameter Roll force stand 1 Roll force stand 2 Roll force stand 3 Roll force stand 4 Strip speed Material group Tilting
For data-based modelling of flatness, neural networks have been evaluated. At a first stage, the most important input variables have been selected by using self-organising maps (SOM). This allows one to reduce the dimensionality of the multivariate data set while maintaining most of the information within the set. Twenty one (21) potential influence variables (Table 2) have been presented to the network, and nonlinear correlation coefficients have been calculated. The data sets were separated for three material groups, to get material-dependent models.
41
Figure 28. Component plane of SOM for C1_VZ (group 1)
Figure 29. Calculated nonlinear correlation coefficients for C1_VZ (group 1)
42
Figure 30. Component plane of SOM for C2_VZ (group 1)
Figure 31. Calculated nonlinear correlation coefficients for C2_VZ (group 1)
43
Figure 32. Component plane of SOM for C1_VZ (group 2)
Figure 33. Calculated nonlinear correlation coefficients for C1_VZ (group 2)
44
Figure 34. Component plane of SOM for C2_VZ (group 2)
Figure 35. Calculated nonlinear correlation coefficients for C2_VZ (group 2)
45
Figure 36. Component plane of SOM for C1_VZ (group 3)
Figure 37. Calculated nonlinear correlation coefficients for C1_VZ (group 3)
46
Figure 38. Component plane of SOM for C2_VZ (group 3)
Figure 39. Calculated nonlinear correlation coefficients for C2_VZ (group 3)
Table 3 contains a summary of the correlation analysis results for the output C2_VZ (parablic Gram coefficient of the flatness at the entry of HDG line). The sum of correlation coefficient for the three groups (graphically iluustrated in Figure 40) is taken to select the most important input variables that should be included in the model identification.
47
Surprisingly, according to this analysis, the flatness at the exit of the tandem mill and the coiling tension seem to have minor influence on the post-rolling flatness. This effect will be further investigated in Tasks 3.1 and 3.2. From the resulting order of importance, it may concluded that the scheduling strategy (i.e. the reduction and tension distribution over the tandem mill) can be used to control the post-rolling flatness. Table 3. Summary of correlation analysis results for the output C2_VZ
Figure 40. Sum of correlation coefficients for C2_VZ over the three groups
The results of the data-based modelling can be found in the next section (Task 2.4).
48
Task 2.4. Use collected data and perform plant-based trials to verify predictions [BFI, AMEH, FQZ] Main emphasis was placed on the validation of the process models developed in Tasks 2.1 (coiling process model) and Task 2.3 (data-based through-process flatness model). Verification of coiling process model Data analysis performed later in Task 3.1 and 5.2 reveals that the coiling process does heavily affect the strip flatness. A central observation is that the post-rolling flatness often shows edge waves at the head of the strip, but these disappear over the strip length, and are overtaken by center buckles. A possible explanation for this behavior is presented in the following simulation results. Two cases have been simulated with different cold rolled flatness. The results of the first case are shown in Figure 43, and those for the second case in Figure 44. In both cases, it was assumed that the diameter of the maderel has a profile as shown in the lower subplot of Figure 41 und Figure 42, respectively. In both cases, the strip tension was increased from 68 to 88kN. Two effects can be be obeserved: 3. The egde waves are showing up and they disappear after the fist 20‒30 laps of the coil. 4. With increasing strip tension center buckles / W-shaped flatness are showing with increasing magnitude towards the end of the coil. A possible reason for the first effect is that mandrel profile does elongate the strip edeges during the first few laps. The mandrel profile will be compensated through the ring coil set. The coil set is caued by the strip corwn. After 20‒30 laps, the mandrel profile is fully compensated by the coil set, so that the edge waves disapear. As the coil set increases with increasing coil diameter, the center of the strip will be elongated. Therefore, center buckles are showing up. This effect depends on the material stength and the strip tension. Comparing the simulated flatness evolution with the measured one, a good (at least qualitative) agreement between the model predictions and measurements can be concluded. In this context, it should be noted that rough estimates for strip profile and mandrel crown were taken.
49
Thickness profile and flatness (input)
IUnits
10
0
-10
-600
-400
-200
0
200
400
600
-600
-400
-200
0
200
400
600
-600
-400
-200
0 Width [mm]
200
400
600
Thickness [mm]
0.65
0.6
Mandrel offset [mm]
0.55
0.4 0.2 0
Figure 41. Initial flatness, thickness profile and offset on mandrel rod diameter for coil no. 847990 Thickness profile and flatness (input)
IUnits
10 0
Thickness [mm]
-10
-600
-400
-200
0
200
400
600
-600
-400
-200
0
200
400
600
-600
-400
-200
0 Width [mm]
200
400
600
0.65
0.6
Mandrel offset [mm]
0.55
0.4 0.2 0
Figure 42. Initial flatness, thickness profile and offset of mandrel rod diameter for coil no. 8480007
50
a) 380 400
16
420
14 12
460 10 480 8
IUnits
Coil radius [mm]
440
500 6
520 540
4
560
2
580 -600
-400
-200
0
200
400
0
600
Width [mm]
b) 380 20 400 18 420 16 440
12 480 10 500
IUnits
Coil radius [mm]
14 460
8
520
6
540
4
560
2
580 -600
-400
-200
0
200
400
600
0
Width [mm]
c) 380
400 20
420
15
460
IUnits
Coil radius [mm]
440
480
10
500
520
540
5
560
580 -600
-400
-200
0
200
400
600
Width [mm]
Figure 43. Resulting post-rolling flatness due to initial condition as shown in Figure 41 for different strip tensions: a) T = 68kN; b) T = 78kN; c) T = 88kN. Note: mean-free flatness distributions are plotted in the left sides.
51
a) 380 20 400 18 420 16 440
12 480 10 500
IUnits
Coil radius [mm]
14 460
8
520
6
540
4
560
2
580 -600
-400
-200
0
200
400
600
0
Width [mm]
b) 380
400 20
420
15
460
IUnits
Coil radius [mm]
440
480
10
500
520
540
5
560
580 -600
-400
-200
0
200
400
600
0
Width [mm]
c) 380
400
25
420
20
460 15
480
500 10 520
540 5 560
580 -600
-400
-200
0
200
400
600
Width [mm]
Figure 44. Resulting post-rolling flatness due to initial condition as shown in Figure 42 for different strip tensions: a) T = 68kN; b) T = 78kN; c) T = 88kN. Note: mean-free flatness distributions are plotted in the left sides.
52
IUnits
Coil radius [mm]
440
Figure 45. Comparison of online flatness (left) and post-rolling flatness (right) for coil no. 847990; the lower subplots show the average flatness over the strip length
Figure 46. Comparison of online flatness (left) and post-rolling flatness (right) for coil no. 8480007; the lower subplots show the average flatness over the strip length
53
Results and Verification of data-based through-process flatness model In this section, the data-based modelling started in Task 2.3 will be continued. Considering the results of the input-variables selection process, both linear regression and artificial neural networks (MLP: multi-layer perceptron) have been trained to predict the post-rolling flatness from the (seven) most important input variables found in Table 3 and Figure 40. Just as an example, the results of the training (Figure 47 and Figure 48) and validation (Figure 49 and Figure 50) stages for C2_VZ (Group 1) will be presented. For MLP, the Levenberg-Marquardt algorithm was used for adaptation of the network weights. The data set for training consists of data from 18 coils; for validation, 11 coils were taken. It can be clearly seen that the prediction quality of MLP is superior than that obtained using the linear regression model. This confirms the mappings between the input data and the post-rolling flatness is nonlinear. Nevertheless, some outliers can be observed in data; see Figure 48 (lower/left subplot). As a conclusion, it can be said that data-based (MLP) modelling is a suitable approach for the prediction of post-rolling flatness from measured variables from the cold tandem mill.
54
Figure 47. Results of linear regression training for C2_VZ
Figure 48. Results of MPL model training for C2_VZ
55
Figure 49. Results of linear regression validation for C2_VZ
Figure 50. Results of MPL model validation for C2_VZ
56
Task 2.5. Model adaptation/self-tuning [BFI] As model performance (i.e. prediction accuracy) is critical to the success of the suggested throughprocess optimisation strategy, and each processing stage is subject to unknown disturbances, parameter adaptation techniques are useful and necessary as well. The approach is to take measurements to update the models at different stages. The revised estimates of parameters are then used to recalculate the setup for subsequent processing of similar strips and for processing of the current strip in downstream stages. Different techniques are available for parameter adaptation, such as model inversion, least-square minimisation, Kalman filtering and similar methods. As the considered processes are nonlinear and the measured signals are often corrupted with noise, advanced Kalman filter techniques should be applied. One approach to Kalman filtering for nonlinear systems is the so-called extended Kalman filter (EKF). It is based on the linearization of the model around the current state. Two disadvantages of this method are that (a) it needs time-consuming computation, and (b) its performance may deteriorate drastically when systems under consideration are highly nonlinear. A more recent approach, known as the unscented Kalman filter (UKF) [11], was developed to overcome several limitations of EKF. The UKF is based on the unscented transform, which uses a set of sigma points to approximate the actual statistical properties of random variable after nonlinear propagation with second order accuracy. These sigma points are transformed to a new set of points using the nonlinear model. System states and associated error covariance matrices are determined numerically based on the mean and covariance values of the transformed sigma points. Conceptually, the UKF process is identical to the standard KF process with the prediction–estimation recursive loop. The main difference is that UKF uses the sigma points and the nonlinear equations to compute the predicted states and measurements and the associated covariance matrices. Mathematically, the UKF process can be described as presented in [25] using the structure shown in Figure 51. For applying the UKF for parameter estimation/adaptation, the flatness model has to be reformulated as a general model of non-linear discrete-time systems:
f ( x , u , t ) wk k 1 k k k yk h( x , u ) vk k k
x
where f is the non-linear system function (i.e. flatness prediction function), h is the non-linear measurement function, x is the state vector, y is the system output, u is the system input, w is the process noise and v is the measurement noise. The process noise matrix Q and the measurement noise matrix R are the expected values (the sum of the probability of each possible consequence of the experiment multiplied by its value) of process noise vector w and measurement noise vector v, respectively. Parameters that have to be estimated by the UKF are included in the model by extending the state vector:
k 1
(i.e. are assumed constant) k
57
Figure 51. Block diagram structure of the UKF [24]
58
WP 3: Development of Through-Process Monitoring and Optimisation Task 3.1. Correlation and operating-range analysis [BFI, FQZ, ARCELOR ESPAÑA, UPM] Correlation analysis for AMEH’s cold production line Data from AMEH’s cold-rolling/galvanising route have been collected for several representative coils. In a first step, these data sets have been visually analysed, to check data consistency, remove artifacts from data, and find out first correlation relationships. The flatness evolution in coloured maps for four coils is shown in Figure 52–Figure 55: the upper subplot illustrates the flatness as measured by the Shapemeter at the exit of stand no. 4; the lower subplot contains the flatness as measured by the topometrical system at the entry of the HDG line. The following observations can be stated (based on data acquired by the first version TopPlan system): The flatness is significantly modified from exit of tandem mill to entry of galvanising plant. After decoiling some coils have waves, while they show no flatness defects after cold rolling before coiling. The process that can be responsible for these changes is the coiling process. The flatness changes differ quantitatively and qualitatively. The difference between online and post-rolling flatness mainly depends on the strip geometry and material. Edge waves often appear at the entry of the HDG line, which decay over the strip length: for some coils (coil no. 1 and no. 2), the waves disappear earlier or later (coil no. 3), but may also persist over the whole strip length for other coils (coil no. 4).
Figure 52. Flatness evolution for coil no. 1
59
Figure 53. Flatness evolution for coil no. 2
Figure 54. Flatness evolution for coil no. 3
60
Figure 55. Flatness evolution for coil no. 4
To evaluate the evolution of flatness, the flatness distributions (acquired by the final version of the TopPlan system) have been decomposed into orthogonal parts using Gram polynomials. Figure 56 shows an example of the analysed flatness data: The coiling operation introduces an asymmetrical flatness defect clearly seen at the C1 signal. In the first part over the coil length, edge waves appear and superpose the C2 component, but decay along the strip length. This is confirmed by the value of the correlation coefficient (R2 for C2): when the whole strip length is considered, we get R2 = 0.53 (middle correlation), but for second half of coil length, the parabolic flatness signals (C2) are highly correlated (R2 = 0.96). A more precise analysis shows that for this coil only the first 600m of the strip are affected by the edge waves.
61
Figure 56. Comparison of online and post-rolling flatness for coil no. 145116
Similar situation and results can be seen in Figure 57 for wider coil of different material. It seems that the wider strip the higher is the correlation, and the smaller are the edge waves generated by the coiling process.
Figure 57. Comparison of online and post-rolling flatness for coil no. 131716 The distributions in Figure 58 show another strip with a stronger R2-correlation between online flatness and post-rolling flatness. The local bad flatness around 500m may be due to local crown effects leading to a high build-up of diameter of the rewound coil. A build-up will result in a non-uniform tension distribution in the strip, which affects the flatness through more plastic strain, where the tension is higher. The non-uniform tension distribution within the coil may also contribute to abrasion damage in post rolling handling of the coil [15, 26].
62
Figure 58. Comparison of online flatness to post-rolling flatness coil no. 848125 A strip that has been subjected to the coil crown effect usually has long edges on the head end, which is overtaken by full center that persist until the tail end [26]. Figure 59 shows examples of flatness evolution that may be (more or less) caused by the coil crown effect, but sometimes partly supposed by other flatness defects. Nevertheless, the principal effect is always visible. Looking at the C2 signals in Figure 58, it can also be concluded that a perfect online flatness is not necessarily optimal for the final flatness. A higher C2 online flatness would be better in this case, at least over 2/3 of the strip length. Moreover, a varying reference flatness curve should be used to compensate for the coiling process effects and produce consistent flatness over the whole strip length. The current practice of keeping the reference flatness constant is not the optimum from the through-process viewpoint. The same conclusion can be drawn from data for another coil shown in Figure 60. The data representation in Figure 61 also confirm the above-mentioned observation (the lower figures now show the average values computed over the strip length): although the online flatness is nearly perfect, the post-rolling flatness shows one-sided edge waves, which are highly undesirable for the galvanizing process.
63
Figure 59. Flatness evolutions that may be basically induced by the coil-crown effect
64
Figure 60. Comparison of online flatness to post-rolling flatness coil no. 848131
Figure 61. Comparison of online flatness to post-rolling flatness coil no. 847963
65
Correlation analysis for ARECELOMITTAL ESPANA’s hot-dip galvanising line Initially preliminary analyses were carried out regarding relationship between flatness and HDGL’s speed.
Figure 62. Relationship between flatness and speed Figure 62 shows outliers (red marked samples) as well as the nonlinear structure between flatness deviations and coil’s speed, as clear reference about no consideration for flatness in rules during normal operation. Also a relative distribution of flatness dispersion will be considered as “flatness reference” about 9 units (green line). Below of it relies most of usual production. In parallel, a complete exploratory data analysis in order to identify relevant aspects has been performed; see Figure 63.
Figure 63. Plot showing Exploratory Data Analysis (EDA)
66
In Figure 63, one can see intrinsic structure of data as well as correlations between variables and local structures or underlying models, like huge relation between thickness and speed, but also, strong nonlinear relationship between average flatness and percentage of flatness under 5% of deviance (similar to a “z”). It is also possible to identify very low relation between speed and width or between speed and weight. Also specific and initial studies regarding flatness, width, and line speed were performed in order to understand latent structure of data; see Figure 64.
Figure 64. Averaged variables against time In Figure 64, it is possible to identify different policies along time, regarding speed of coils as well as flatness evolution and other geometrical parameters, like width. It is clear how, when relevant losses of flatness are produced, reduction of speed is normally involved but, this type of qualitative analysis cannot present highest resolution power, like the previous tool, from where it is possible to derive strong relationship between speed and thickness, for example. Additional activities involved to produce a structural data analysis in order to identify major classes, trying to preserve initial data structure were performed, providing the research team with convenient software sensors for the operating rage parameters at different facilities
67
Task 3.2. Hot-dip galvanising entry-coil-quality monitoring [ARCELOR ESPAÑA, UPM] It is possible to realize that the strategy of speed inside the HDGL as well as the quality of data involved and tools installed are good enough but with special attention to be paid to the integrity of some variables across facilities. The second aspect to be considered is the requirement of specific analysis in order to identify particular classes of coils from quality point of view. Also, specific analyses were done in order to identify structural variation in coating, taking into account frequencies in dataset; see Figure 65. Figure 65 presents family variation of Zinc coating (g/m2) against steel grade, where it is really easy to identify relevant variance of coating inside each grade, sometimes depending on final uses of coils and sometimes due to some unstabilities of process parameters.
Figure 65. Zn coating classification by steel grade Specific analyses have been also conducted regarding specific defect relationship, as key knowledge supporting the global strategy under consideration. In what follows, some details are provided, just as an example, of the treatment required for modelling blisters. Possibility of defect prediction with the casting parameters or earlier detection by means of one ultrasound equipment installed at the pickling line. This is a good example of damage crossing several facilities.
68
Main interest here was to discover more knowledge about a very difficult to manage defect that, sometimes, becomes visible on the surface of the coil. There are several theories about its occurrence as well as about its relevance, because sometimes they become visible and sometimes they do not. The first point was to set main objectives for the analysis. From here, a range of classes was adopted, because that it is no matter about to predict the exact number of this type of defects are present inside a particular coil. Adopted classes, according to the process experts, are shown in Table 4. Table 4. Recognised quality classes by attending to the measured number of inclusions in a coil ODL
ODL.CLASS
COLOR
SYMBOL
< 20 (20, 100]
LOW MEDIUM
Green Blue
o ∆
(100, 300]
HIGH
Cyan
+
> 300
VERY.HIGH
Magenta
x
The goal is try to identify the main variables responsible for those numbers of inclusions. The second point was to be able for using an instrument capable for counting number of inclusions. This type of machine was a lamb-wave-based measuring system. It brings online information about inclusions. Visualizing the data in a 111-dimensional space, corresponding to the 111 input variables used in this work, is difficult. To overcome this problem, the original data was compressed by using projection techniques which project m-dimensional data onto a d-dimensional space (usually d = 2 since the resultant data configuration can easily be evaluated by human), preserving as far as possible the original data structure. The resulting visualization depicts clusters in input space as groups of data points mapped close to each other in the output plane. Thus, the inherent structure of the input signals can be told from the structure detected in the 2-dimensional visualization. These techniques can be divided into two main groups, namely, linear and non-linear techniques. The most common non-linear technique is Sammon mapping, whereas principal component analysis (PCA) is the most popular linear projection. Sammon mapping is an iterative method that uses a gradient descent algorithm to minimize an error function, which represents how well the present configuration of the data in the d-dimensional space fits the original data in the m-dimensional space. Sammon mapping attempts to minimise this error by positioning the points in the lower dimensional space so that the distance between the points is as close as possible to distance between the corresponding points in the higher dimensional space. On the other hand, PCA transforms a set of correlated variables into a number of uncorrelated variables, called principal components, which are ordered by reducing variability. The uncorrelated variables are linear combinations of the original variables. It can also be seen as a rotation of the existing axes to new positions in the space defined by the original variables. In this new rotation, there will be no correlation between the new variables defined by the rotation. The first new variable contains the maximum amount of variation; the second new variable contains the maximum amount of variation unexplained by the first and orthogonal to the first, etc.
69
Because the range of attributes (features) values differs, some features might overpower the other ones. The solution of this problem is normalization: scaling data values in a range such as [0…1] to prevent outweighing with large range over features with smaller range. Sammon and PCA projection with normalized independent variables (Figure 66a and Figure 67a) could reveal the existence of two clusters in the data. As Figure 66b and Figure 66b illustrate, these clusters contained coils with different number of inclusions.
Figure 66. Sammon projection. X and Y axis are not related to physical variables In order to observe differences between the classes detected by Sammon and PCA projections, boxplots were used because they are a way of summarizing a distribution: in comparing the boxplots across groups, a simple summary is to say that the box area for one group is higher or lower than that for another group. To the extent that the boxes do not overlap, the groups are quite different from one another. It is shown that some chemical elements (for example, Aluminium, Manganese, Phosphorus, Silicon, Titanium and Vanadium) and some process variables were different in both clusters, for example, MSRH.PAT_COD_COD_GAS and MSRH.PAT_COD_COD_HOMOG.
70
Figure 67. PCA projection of patterns. X axis is the first eigenvector of the correlation matrix and Y axis is the second eigenvector of the same matrix Clustering is a discovery process that groups similar objects into the same cluster. Various clustering algorithms have been designed to fit various requirements and constraints of application. In this study, a well-known k-medoid algorithm, CLARA, was used. This algorithm works on a randomly selected subset of the original data and produces near accurate results at a faster rate than other clustering algorithms.
Figure 68. Bivariate plot of data partitioned into 2 (left) and 4 (right) clusters
71
Figure 68 describes the patterns with their interrelations, and at the same time shows the clusters returned by the CLARA algorithm. In this figure, all observations are represented by points in the plot, using principal components, and the clusters as ellipses. These ellipses are based on the average and the covariance matrix of each cluster, and their size is such that they contain all the points of their cluster. Figure 68 illustrates how the CLARA algorithm could not divide the data into k nonoverlapping clusters, i.e. these clusters could not be considered as dissimilar. Furthermore, Figure 69 shows that these clusters contained coils with different number of inclusions.
Figure 69. Bivariate plot of data partitioned into 4 clusters with points coloured according to the number of detected inclusions Decision trees [3] are powerful and popular tools for classification and prediction. The attractiveness of decision trees is due to the fact that, in contrast to neural networks, decision trees represent rules. Rules can readily be expressed so that humans can understand them. Briefly, a decision tree is a classifier in the form of a tree structure, where each node is either a leaf node or a decision node. A leaf node indicates the value of the target attribute (class) of examples. A decision node specifies some test to be carried out on a single attribute-value, with one branch and sub-tree for each possible outcome of the test. A decision tree can be used to classify an example by starting at the root of the tree and moving through it until a leaf node, which provides the classification of the instance. There are a variety of algorithms for building decision trees that share the desirable quality of interpretability. In this work, the C4.5 learning algorithm, a well-known and frequently-used over the years, was taken. When the 111 input variables were introduced to the learning algorithm, the generated decision tree could correctly classify the 68.26% of the instances. The performance of this tree was not good at all since both the overall and class accuracy was quite poor. The following parameters show a summary of classification results; see Table 5.
72
Table 5. Initial trial for a decision tree with all potential variables considered === Stratified cross-validation === === Summary === Correctly Classified Instances Incorrectly Classified Instances Kappa statistic Mean absolute error Root mean squared error Relative absolute error Root relative squared error Total Number of Instances
471 219 0.3093 0.1752 0.3683 72.9849 % 106.5004 % 690
68.2609 % 31.7391 %
=== Detailed Accuracy By Class === TP Rate FP Rate Precision Recall F-Measure ROC Area 0.835 0.455 0.795 0.835 0.815 0.706 0.41 0.166 0.439 0.41 0.424 MEDIUM 0.132 0.035 0.179 0.132 0.152 0.634 0.389 0.012 0.467 0.389 0.424 VERY.HIGH
Class LOW 0.621 HIGH 0.786
=== Confusion Matrix === a 391 85 12 4
b 62 68 19 6
c 12 10 5 1
d 3 3 2 7
| | | |
