Surrogate-based evolutionary optimization for friction stir welding

Friction Stir Welding (FSW) is an innovative manufacturing process, which is used to join two pieces of metal with frictional heating and plastic deformation due to stirring action. Melting is avoided during the process, therefore problems related to microstructure phase transformation (i.e., cooling from the liquid phase) are avoided. The temperature distribution in the weld zone, as a function of the heat generation, highly affects the evolution of the residual stresses in the work piece, hence the performance of the final product. Therefore, thermal models play a crucial role in detailed analysis and improvement of this process. In this study, a previously developed and validated three-dimensional steady state thermal model of FS welding of AA2024-T3 plates has been used for evaluating the quality of the candidate solutions. It should be noted that this is a computationally expensive model and closed form formulations (i.e. analytical equations) for the underlying physics are not available, which forces us to use them sparingly during the optimization procedure. A mathematical correlation model, a surrogate in other words, is iteratively constructed to replace the FSW simulations and guide the search towards feasible and promising regions. A new surrogate-based optimization algorithm named EICTS, Expected Improvement with Constrained Tournament Selection has been developed. The striking difference of EICTS from other surrogate based constrained optimization methodologies that it needs to construct only two surrogates, i.e. one for the objective function and another one to handle all constraint functions (i.e., instead of approximating each of them individually). EICTS is first tested on some well-known engineering problems with multiple constraints and finally on the FSW problem briefly mentioned above. Its runtime and convergence performances are compared with EIPF (Expected Improvement with Probability of Feasibility) method and found very promising.

[1]  Lihui Wang,et al.  Multi-objective Evolutionary Optimisation for Product Design and Manufacturing , 2011 .

[2]  Felipe A. C. Viana,et al.  Multiple surrogates for prediction and optimization , 2011 .

[3]  Yaochu Jin,et al.  Surrogate-assisted evolutionary computation: Recent advances and future challenges , 2011, Swarm Evol. Comput..

[4]  William J. Welch,et al.  Computer experiments and global optimization , 1997 .

[5]  Yuh J. Chao,et al.  Numerical simulation of transient temperature and residual stresses in friction stir welding of 304L stainless steel , 2004 .

[6]  Jesper Henri Hattel,et al.  Thermal modelling of friction stir welding , 2008 .

[7]  Xinhai Qi,et al.  Thermal and Thermo-Mechanical Modeling of Friction Stir Welding of Aluminum Alloy 6061-T6 , 1998 .

[8]  Joseph D. Robson,et al.  Microstructural Modelling for Friction Stir Welding of Aluminium Alloys , 2007 .

[9]  R. Haftka,et al.  Multiple surrogates: how cross-validation errors can help us to obtain the best predictor , 2009 .

[10]  Cem Celal Tutum,et al.  Numerical optimisation of friction stir welding: Review of future challenges , 2011 .

[11]  Zhili Feng,et al.  Modelling of residual stresses and property distributions in friction stir welds of aluminium alloy 6061-T6 , 2007 .

[12]  Andy J. Keane,et al.  Enhancing infill sampling criteria for surrogate-based constrained optimization , 2012, J. Comput. Methods Sci. Eng..

[13]  Paul A. Colegrove,et al.  3-Dimensional CFD modelling of flow round a threaded friction stir welding tool profile , 2005 .

[14]  Philip J. Withers,et al.  Global mechanical tensioning for the management of residual stresses in welds , 2008 .

[15]  Thomas J. Santner,et al.  The Design and Analysis of Computer Experiments , 2003, Springer Series in Statistics.

[16]  Cem Celal Tutum,et al.  State-of-the-Art Multi-Objective Optimisation of Manufacturing Processes Based on Thermo-Mechanical Simulations , 2011, Multi-objective Evolutionary Optimisation for Product Design and Manufacturing.

[17]  Masao Fukushima,et al.  Derivative-Free Filter Simulated Annealing Method for Constrained Continuous Global Optimization , 2006, J. Glob. Optim..

[18]  Yaochu Jin,et al.  A comprehensive survey of fitness approximation in evolutionary computation , 2005, Soft Comput..

[19]  Kalyanmoy Deb,et al.  Multi-Criteria Optimization in Friction Stir Welding Using a Thermal Model with Prescribed Material Flow , 2013 .

[20]  Thomas Bäck,et al.  A New Repair Method For Constrained Optimization , 2015, GECCO.

[21]  Cem Celal Tutum,et al.  Optimisation of process parameters in friction stir welding based on residual stress analysis: A feasibility study , 2010 .

[22]  K. Deb.  An Efficient Constraint Handling Method for Genetic Algorithms , 2000 .

[23]  Efrén Mezura-Montes,et al.  Empirical analysis of a modified Artificial Bee Colony for constrained numerical optimization , 2012, Appl. Math. Comput..

[24]  R. Haftka.  Combining global and local approximations , 1991 .

[25]  R. A. Cuninghame-Green,et al.  Applied geometric programming , 1976 .

[26]  Sonja Kuhnt,et al.  Design and analysis of computer experiments , 2010 .

[27]  Z. Ma,et al.  Friction Stir Processing Technology: A Review , 2008 .

[28]  Donald R. Jones,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998, J. Glob. Optim..

[29]  R. Mishraa,et al.  Friction Stir Welding And Processing , 2005 .

[30]  D. Krige.  A statistical approach to some basic mine valuation problems on the Witwatersrand, by D.G. Krige, published in the Journal, December 1951 : introduction by the author , 1951 .

[31]  R. Regis.  Constrained optimization by radial basis function interpolation for high-dimensional expensive black-box problems with infeasible initial points , 2014 .

[32]  Jesper Henri Hattel,et al.  Modelling heat flow around tool probe in friction stir welding , 2005 .

[33]  R Kovacevic,et al.  Parametric finite element analysis of stress evolution during friction stir welding , 2006 .

[34]  Andy J. Keane,et al.  Recent advances in surrogate-based optimization , 2009 .

[35]  Raphael T. Haftka,et al.  Surrogate-based Analysis and Optimization , 2005 .

[36]  Kalyanmoy Deb,et al.  Hybrid Search for Faster Production and Safer Process Conditions in Friction Stir Welding , 2010, SEAL.

[37]  H. Bhadeshia,et al.  Recent advances in friction-stir welding : Process, weldment structure and properties , 2008 .

[38]  Michael James Sasena,et al.  Flexibility and efficiency enhancements for constrained global design optimization with kriging approximations. , 2002 .