A FUZZY LOGIC APPROACH FOR OPTIMAL CONTROL OF CONTINUOUS CASTING PROCESS

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1 A FUZZY LOGIC APPROACH FOR OPTIMAL CONTROL OF CONTINUOUS CASTING PROCESS Tomáš MAUDER a, Čeněk ŠANDERA a, Josef ŠTĚTINA a, Miloš MASARIK b a)brno University of Technology, Faculty Mechanical Engineering, Technická 2, Brno, Czech Republic, ymaude00@stud.fme.vutbr.cz,stetina@fme.vutbr.cz, b)evraz VÍTKOVICE STEEL a.s., Štramberská 2871/47, Ostrava, Czech Republic, milos.masarik@cz.evraz.com Abstract Nowadays the continuous casting is used for providing almost one hundred percent of world steel production. A wide range of steel grades is continuously cast with high-quality achievements. The solidifying steel, during its pass through the caster, is subjected to variable thermal conditions and mechanical loading, both of which contribute to the material stresses and strains, the main sources of the defects. Some of these defects might be eliminated by a preceding computer simulation, optimization and subsequent control of the casting process. This paper describes an original algorithm for obtaining such control parameters which ensure the high production rate and the high quality of products as well. This algorithm is based on the keeping surface and core temperatures in the specific ranges corresponding with ductility of steel. The core of the algorithm is our original three-dimensional numerical model of temperature field where heat and mass transfer phenomenon including phase changes is deal with. Geometry and specifications of the caster are taken from the real caster operating in EVRAZ VÍTKOVICE STEEL, a.s. This model is verified by pyrometers measurements. The optimization part lies above the numerical model and iteratively improves the input parameters (casting speed and cooling rates) in order to reach desired surface and core temperatures. The optimization algorithm is performed by our fuzzy-logic interface and runs in off-line version. Its results can be used as a preparation tool for the real casting process. Key Words: Fuzzy optimization, temperature field, continuous casting, secondary cooling 1. INTRODUCTION In steel industry the continuous casting process provides the formation of solidified metal called slabs or billets that are obtained by the passage of liquid steel through several cooling zones. The quality of the final products plays one of the most significant roles for final customers, and thus to satisfy them and maintain the highest possible productivity are a key goals for each steelmaker. Emphasis on a quality control is a prerequisite and it cannot be achieved without a proper knowledge of the main physical influences in the casting process, i.e. the solidification [1], micro and macro segregations, the crack formation etc. Without loss of generality, we can assume that the final quality of solidified slab depends on its thermal history during its passing through different cooling zones. It is well documented that steel has a reduced ductility over specific temperature ranges dependent on a steel composition [2], which has important implications for crack formation. Therefore, it is necessary to lead the cooling according to the casting events, variations of thermal loss, casting speed, and different heat and mass dissipations. From the physical point of view, the continuous casting is a transient coupled thermo-structural problem. Nevertheless we can use the assumption, that the relatively slow deformation speed does not influence the temperature distribution. Conducting of industrial trials is very expensive, time-consuming and in some cases even impossible, which makes the computer simulation the only suitable option. Numerical simulations and optimization algorithms are widely used tools for tuning of the casting processes. Mathematical and computer optimization can be done in many different ways and each of them has its advantages and

2 drawbacks. Therefore, to ensure the correctness of the algorithm, it is highly required to validate the simulation output by the real measured data. Previous works dealing with the optimal control of continuous casting process were generally based on simplified 1D or 2D temperature field models and were optimized by mathematical programming or heuristic methods, e.g. genetic algorithm [3], firefly algorithm [4] or by neural networks [5]. Many of these models are based on simplified assumptions, and therefore they describe the casting process very roughly and not satisfactorily. We developed our original numerical model of the temperature field for the real caster geometry in 3D and its results have been validated by temperature measurements performed by pyrometers. This more precise model simulates the process controlled by several numerical parameters and the goal is to find their values such that the resultant temperature field is optimal. The algorithm is partly inspired by our previous research [4, 6]. This new algorithm is enhanced by a fuzzy logic inference mechanism which makes its behaviour more robust and its setting easier to adjust. 2. PROBLEM DESCRIPTION The natural effort of every steelmaker is to cast as fast as possible but with a preservation of the required material quality. The properties of the final material are highly dependent on the course of temperatures reached during the casting. For instance the temperature stability is very important, especially for casting crack-sensitive steel grades. The temperature at the embedding point must be out of low ductility range [3, 5] that is characterized by a high level of surface oxidation that generates a disturbance of the surface temperature. Hence we need to adjust the caster parameters in such a way that the temperature field is optimal in steel quality point of view. Casting process can be control by regulating many factors such as the speed of casting, rate of water flow through mold, the casting temperature control, changes of cooling intensities for each coolant circuit (a group of nozzles) etc. In order to simplify the problem, the control parameters (input parameters) in this paper are considered to be the casting speed and the cooling rates in the secondary cooling zone. Before the optimization starts, it is necessary to define the temperature field which leads to the optimal material and mechanical properties. This optimal temperature courses are defined by experts (casting operators, material scientists, etc.) and they differ with the chemical composition of steel. For finding the optimal cooling intensities and the highest possible casting speed, an original heuristic algorithm based on fuzzy-logic was created and it can be briefly sketched in the following manner. To describe the optimal temperature field, the experts define a set of points along of the caster and prescribe their optimal temperature ranges. Then the algorithm randomly generates values for all the variable parameters and simulates the temperature field for such casting process. After comparing the computed temperatures with the prescribed ones, the algorithm decides which nozzles need to be adjusted and how to change the casting speed. Particular decisions for changing the values are taken by the fuzzy inference logic. These steps are iteratively repeated until the optimal temperatures are successfully reached. The simulation and optimization parts are described in the subsequent separate sections but for the detailed explanation of fuzzy logic and fuzzy inference we recommend to read a reference [7]. Investigations and verifications in this paper are provided on the steel grade S235J D NUMERICAL MODEL OF TEMPERATURE FIELD AND ITS VERIFICATION The 3D numerical model was developed which computes the formation of solidification and the distribution of temperature of strand. The temperature field is described by the Fourier-Kirchhoff equation [1, 2, 4, 6] H k eff ( T) T v z H, z (1)

3 that describes a transient heat and mass transfer, where k eff [W/mK] is the effective thermal conductivity, T [K] is the temperature, H [J/m 3 ] is the volume enthalpy and [s] is time. The velocity component v z [m/s] is considered only in the direction of casting. Phase and structural changes are included in the model by the latent heat accumulation method [1, 4, 6] where the enthalpy is used as the primary variable and the temperature is calculated from a defined enthalpy-temperature relationship. Thermo-physical parameters such as the thermal conductivity, the density, the specific heat, the enthalpy and their temperature dependence are computed from a specific chemical composition of steel by using the solidification analysis package IDS. The results of IDS for steel grade S235J0 can be seen in Fig. 1. Fig. 1 Thermo-physical properties for steel S235J0 In order to have a well-posed problem, initial and boundary conditions must be provided. The boundary conditions include the heat flux in the mould and under the rollers, the forced convection under the nozzles, and the free convection and the radiation in the tertiary cooling zone [2, 6]. The model in this paper obtains its heat transfer coefficients from measurements of the spraying characteristics of all nozzles used by the caster on a so-called hot plate in an experimental laboratory [8] and for a sufficient range of operational pressures of water and a sufficient range of casting speeds of the blank. The equation (1) is discretized by the finite difference method [1, 4, 6] using an explicit formula for the time derivative. The mesh for the finite difference scheme is non-equidistant in all direction and its nodes are adapted to the real rollers and nozzles positions. The numerical results including the verification for steel S235J0 are shown in Fig Casting parameters were chosen according to the measurement: casting speed 0.79 m/min, casting temperature 1549 C, heat flux in mould is kw/m 2 (wide size) and kw/m 2 (narrow size). Water flows are shown in Tab. 1. Tab 1 Water flows in the secondary cooling zone Fig. 4 illustrates the unrolled temperature field along the longitudinal cross-section through the entire blank, where the shades of blue represent solidified steel, the shades of dark red represent liquid steel and the light red represents the mushy zone. Fig. 5 shows the temperature history in six points of the cross-section of the slab. Furthermore, the graph indicates two surface temperatures where the pyrometers were positioned (top side of strand).

4 Fig. 3 Temperature distribution in 3D Fig. 4 Liquid and solid zones U X L U X L Fig. 5 Temperature distributions and verification by two pyrometers 4. DESCRIPTION OF FUZZY ALGORITHM The algorithm searches for the optimal values of the control parameters. The inputs to the algorithm are the required temperature ranges in the points along the caster and the maximal metallurgical length. For each circuit the maximal possible cooling intensity is defined. The initial value for each control parameter is uniformly distributed from the permitted range, put into the model and consequently evaluated by its simulation. From the computed result, errors are determinated as a difference between temperatures in the controlled points and prescribed values. The metallurgical length is computed as a distance between meniscus and the point where the liquid material is fully solidified. With this information the algorithm infer the modifications for all control parameters. Tab. 2 The dependences of adjective 3 on adjective 1 and adjective 2. The abbreviations stand for VerySmall, Small, Medium, Big, and their fuzzy sets are equidistantly distributed along the corresponding universes. adj2 / adj1 VS S M B S VS VS S S M VS VS S M B VS S M B

5 The temperature courses at the controlled points are dominantly influenced by the two preceding coolant circuits. The closer circuit has a bigger influence. Therefore, each coolant circuit defines a numerical value for each controlled point that describes how much coolant circuit impacts temperature at the controlled point. These values are expertly estimated (range from 0 to 10) and they are strongly related to the distance from the controlled points. The fuzzy rules for the modification of cooling intensities have the following form: "IF error IS adj1 AND impact IS adj2 THEN modification IS adj3" and they are described in Tab. 2. These rules give the value of modification for each circuit. Sometimes one circuit can get several different modifications and if it happens the algorithm takes the one with the highest absolute value. The defuzzification method is the standard centre of the gravity function. If the maximal absolute value of all the temperature errors does not exceed the given limit the modification of the casting Tab. 3 The dependences of adjective 6 on adjective 4 and adjective 5. The abbreviations stand for VerySmall, Small, OK, Big, VeryBig and MOre, LittleMore, LittleLess, Less, Nothing, and their fuzzy sets are equidistantly distributed along the corresponding universes. adj4 / adj5 VS S OK B VB S MO LM LM LL L M LM N N N LL speed is computed. The reason of introducing the limit is that if the maximal error is too big (i.e. the solution is far from the optimum), we have no information whether the speed is high or not, and at first, it is better to stabilize the process and then to infer the speed modification. The rules for the modification of the casting speed are in the form: "IF maximal_error IS adj4 AND metalurgical_length IS adj5 THEN modification IS adj6" (Tab. 3). 5. RESULTS OF SIMULATION The numerical model is designed and verified for the radial slab caster operating in EVRAZ VÍTKOVICE STEEL, a.s. The caster contains 13 coolant circuits and the cross-section of the investigated slab has 1550 x 250 mm. The examined grade of steel was S355J0H. The expertly defined temperature ranges in the controlled points are depicted in Fig. 6 (the grey rectangles). Fig. 6 Temperature distributions after fuzzy regulation The crucial reason for defining these temperatures ranges in this way is that approximately first half of caster is curved, and therefore for decreasing of mechanical stresses it is better to keep the temperature above the certain level (1000 C). The controlled points are placed on the top and bottom surfaces, and the end of each coolant circuit. The value of impacts of each circuit to the controlled point is chosen to 8 for the closest previous circuit and 2 for the circuit placed one before (except the last controlled point where the distance to the second closest circuit is much longer and the values are 9 and 1, respectively). The value for the

6 maximal metallurgical length is 20 m (came up from the practice) and the casting temperature 1550 C. Reaching temperature courses on surface ensures that the mechanical and material qualities of the final material can satisfy required demands. The optimization results including the optimal values for control parameters can be seen in Fig Usually the most important indicator characterizing the efficiency of iterative optimization algorithms is the number of evaluations of the model. The computation of the numerical model is very time-consuming, thus each repetition can significantly prolong the computations. Our algorithm is able to find the optimal input parameters in 50 evaluations in average. The tests ran several times for different grades of steel and the number of evaluations never exceeded 65. Computation time takes approximately 17 hours in Intel Core 2 CPU 2.40GHz 4 GB RAM. 6. CONCLUSION Fig. 7 Liquid and solid zones The problem of the optimization of continuous casting process and finding its optimal parameters can be efficiently solved by our algorithm. This algorithm based on heuristics and incorporating the fuzzy logic behaves very robustly and it is easily adaptable to any grade of steel and caster geometry. The number of evaluations of included numerical model is very low (approximately 50 iterations) thereby the algorithm proves its high efficiency. Further work will be focused on placing the algorithm into steel company system. ACKNOWLEDGEMENT The authors gratefully acknowledge a financial support from the project GACR P107/11/1566 founded by the Czech Science, Foundation, project ED0002/01/01 - NETME Centre and Specific research FSI-J REFERENCES [1] STEFANESCU, D. M. Science and Engineering of Casting Solidification, Second Edition, New York, Springer Science, 2009, 402 p., ISBN [2] BIRAT, J. P., et al., The Making, Shaping and Treating of Steel: Casting Volume: 11th. EDITION. ALAN W. CRAMB. Pittsburgh, PA, USA: The AISE Steel Foundation, s. ISBN [3] SANTOS, C. A., SPIM, J. A., GARCIA, A. Mathematical modeling and optimization strategies (genetic algorithm and knowledge base) applied to the continuous casting of steel, Engineering Applications of Artificial Intelligence,16, 2003, pp , ISSN-1: [4] MAUDER, T., SANDERA, C., STETINA, J., SEDA, M. Optimization of Quality of Continuously Cast Steel Slabs by Using Firefly Algorithm. Materiali in tehnologije (4). p ISSN [5] BOUHOUCHE, S, LAHRECHE, M, BAST, J. Control of Heat Transfer in Continuous casting Process Using Natural Networks. ACTA AUTOMATICA SINICA. 2008, 34, s ISSN [6] MAUDER, T., STETINA, J., SANDERA, C., KAVICKA, F., MASARIK, M. An optimal relationship between casting speed and heat transfer coefficients for continuous casting process. In METAL 2011 Conference proceedings. Metal. Ostrava, Tanger p ISBN [7] NGUYEN, H. T., WALKER, E. A. A First Course in Fuzzy Logic, CRC Press, 1999, 392 p., ISBN [8] HORSKY, J., RAUDENSKY, M. Measurement of Heat transfer Characteristics of Secondary Cooling in Continuous Casting. In Metal, Ostrava, TANGER, pp. 1-8.