Restoration of the cooling conditions in a three-dimensional continuous casting process using artificial intelligence algorithms

Abstract In this study, we propose a procedure for restoring the cooling conditions in a crystallizer and in the secondary cooling zone of a three-dimensional continuous casting process. The additional information required to solve the inverse problem is given by temperature measurements at selected points. The appropriate direct problem is solved using the alternating phase truncation method. The ant colony optimization algorithm and the artificial bee colony algorithm are used to minimize a functional that defines the error of the approximate solution. We compare usefulness of these two algorithms for solving this type of problem.

[1]  Damian Słota,et al.  Solving the inverse Stefan design problem using genetic algorithms , 2008 .

[2]  Jacek Smolka,et al.  Application of Bezier surfaces to the 3-D inverse geometry problem in continuous casting , 2011 .

[3]  Roger Van Keer,et al.  Finite-element Solutions For A Direct Problem InContinuous Casting And For Its Inverse , 1997 .

[4]  Aleksander Nawrat,et al.  Identification of the heat fluxes and thermal resistance on the ingot-mould surface in continuous casting of metals , 2009 .

[5]  Aleksander Nawrat,et al.  Inverse approach and sensitivity analysis for identification of ingot-mould thermal resistance in continuous casting of metals , 2005 .

[6]  Dervis Karaboga,et al.  A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm , 2007, J. Glob. Optim..

[7]  David J. Browne,et al.  Use of experiment and an inverse method to study interface heat transfer during solidification in the investment casting process , 2000 .

[8]  Damian Słota,et al.  Application of swarm intelligence algorithms in solving the inverse heat conduction problem , 2017 .

[9]  R. Gupta,et al.  Optimisation of continuous casting process using genetic algorithms: studies of spray and radiation cooling regions , 2003 .

[10]  Amauri Garcia,et al.  The use of a heuristic search technique for the optimization of quality of steel billets produced by continuous casting , 2001 .

[11]  D. Słota.  Identification of the Cooling Condition in 2-D and 3-D Continuous Casting Processes , 2009 .

[12]  Dervis Karaboga,et al.  A comparative study of Artificial Bee Colony algorithm , 2009, Appl. Math. Comput..

[13]  Damian Słota,et al.  Application of the Swarm Intelligence Algorithm for Investigating the Inverse Continuous Casting Problem , 2013 .

[14]  L. Tarchi,et al.  Application of the inverse analysis for boundary condition retrieval , 2009 .

[15]  J. Kacur,et al.  Computing An Optimal Cooling Strategy ForContinuous Casting Of Steel , 1997 .

[16]  J. A. Spim,et al.  Evaluation of heat transfer coefficients along the secondary cooling zones in the continuous casting of steel billets , 2006 .

[17]  D. Karaboga,et al.  On the performance of artificial bee colony (ABC) algorithm , 2008, Appl. Soft Comput..

[18]  Damian Słota.  Restoring boundary conditions in the solidification of pure metals , 2011 .

[19]  Heinz W. Engl,et al.  Some inverse problems for a nonlinear parabolic equation connected with continuous casting of steel: Stability estimates and regularization ∗ , 1990 .

[20]  Aleksey V. Nenarokomov,et al.  Uncertainties in parameter estimation: the inverse problem , 1995 .

[21]  Andrzej J. Nowak,et al.  Identification of phase change fronts by Bezier splines and BEM , 2002 .

[22]  Damian Słota,et al.  Identification of the Heat Transfer Coefficient in the Inverse Stefan Problem by Using the ABC Algorithm , 2012 .

[23]  Joel C. W. Rogers,et al.  The Alternating Phase Truncation Method for Numerical Solution of a Stefan Problem , 1979 .

[24]  Thomas Stützle,et al.  The Ant Colony Optimization Metaheuristic: Algorithms, Applications, and Advances , 2003 .

[25]  Jacek Smolka,et al.  An effective 3-D inverse procedure to retrieve cooling conditions in an aluminium alloy continuous casting problem , 2010 .

[26]  R. Van Keer,et al.  On the optimal cooling strategy for variable‐speed continuous casting , 2002 .

[27]  Heinz W. Engl,et al.  Numerical solution of an inverse problem connected with continuous casting of steel , 1985, Z. Oper. Research.

[28]  Nirupam Chakraborti,et al.  A study of the continuous casting mold using a pareto-converging genetic algorithm , 2001 .

[29]  J. A. Spim,et al.  Mathematical modeling and optimization strategies (genetic algorithm and knowledge base) applied to the continuous casting of steel , 2003 .

[30]  M. Duran Toksari,et al.  Ant colony optimization for finding the global minimum , 2006, Appl. Math. Comput..

[31]  J. A. Spim,et al.  The use of artificial intelligence technique for the optimisation of process parameters used in the continuous casting of steel , 2002 .

[32]  Heinz W. Engl,et al.  On an Inverse Problem for a Nonlinear Heat Equation Connected with Continuous Casting of Steel , 1987 .

[33]  M. Krishnan,et al.  Determination of the interfacial heat transfer coefficient h in unidirectional heat flow by Beck`s non linear estimation procedure , 1996 .

[34]  Andreas Binder,et al.  Optimal cooling strategies in continuous casting of steel with variable casting speed , 1996 .

[35]  Damian Slota,et al.  Inverse Continuous Casting Problem Solved by Applying the Artificial Bee Colony Algorithm , 2013, ICAISC.

[36]  Marco Dorigo,et al.  Ant colony optimization theory: A survey , 2005, Theor. Comput. Sci..