A metamodel optimization methodology based on multi-level fuzzy clustering space reduction strategy and its applications

This paper proposes metamodel optimization methodology based on multi-level fuzzy-clustering space reduction strategy with Kriging interpolation. The proposed methodology is composed of three levels. In the 1st level, the initial samples need partitioning into several clusters due to design variables by fuzzy-clustering method. Sequentially, only some of the clusters are involved in building metamodels locally in the 2nd level. Finally, the best optimized result is collected from all metamodels in the 3rd level. The nonlinear problems with multi-humps as test functions are implemented for proving accuracy and efficiency of proposed method. The practical nonlinear engineering problems are optimized by suggested methodology and satisfied results are also obtained.

[1]  Timothy W. Simpson,et al.  Metamodels for Computer-based Engineering Design: Survey and recommendations , 2001, Engineering with Computers.

[2]  A. J. G. Schoofs,et al.  Crash worthiness design optimization using multipoint sequential linear programming , 1996 .

[3]  J. H. Starnes,et al.  Construction of Response Surface Approximations for Design Optimization , 1998 .

[4]  Jaroslaw Sobieszczanski-Sobieski,et al.  Multidisciplinary aerospace design optimization - Survey of recent developments , 1996 .

[5]  T. Simpson,et al.  A Study on the Use of Kriging Models to Approximate Deterministic Computer Models , 2003, DAC 2003.

[6]  T. Simpson,et al.  Fuzzy clustering based hierarchical metamodeling for design space reduction and optimization , 2004 .

[7]  Donald R. Jones,et al.  Global versus local search in constrained optimization of computer models , 1998 .

[8]  Farrokh Mistree,et al.  Statistical Approximations for Multidisciplinary Design Optimization: The Problem of Size , 1999 .

[9]  Farrokh Mistree,et al.  Statistical Experimentation Methods for Achieving Affordable Concurrent Systems Design , 1997 .

[10]  Timothy W. Simpson,et al.  On the Use of Statistics in Design and the Implications for Deterministic Computer Experiments , 1997 .

[11]  Hakim Naceur,et al.  Recent developments on the analysis and optimum design of sheet metal forming parts using a simplified inverse approach , 2000 .

[12]  V. Markine,et al.  Refinements in the multi-point approximation method to reduce the effects of noisy structural responses , 1996 .

[13]  Cristina H. Amon,et al.  An engineering design methodology with multistage Bayesian surrogates and optimal sampling , 1996 .

[14]  John E. Renaud,et al.  Adaptive experimental design for construction of response surface approximations , 2001 .

[15]  Wang Hu,et al.  Optimization of sheet metal forming processes by adaptive response surface based on intelligent sampling method , 2008 .

[16]  Uwe Schramm.  Multi-disciplinary optimization for NVH and crashworthiness , 2001 .

[17]  Timothy M. Mauery,et al.  COMPARISON OF RESPONSE SURFACE AND KRIGING MODELS FOR MULTIDISCIPLINARY DESIGN OPTIMIZATION , 1998 .

[18]  Aimo A. Törn,et al.  Global Optimization , 1999, Science.

[19]  Douglas C. Montgomery,et al.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .

[20]  George E. P. Box,et al.  Evolutionary Operation: A Statistical Method for Process Improvement , 1969 .

[21]  James C. Bezdek,et al.  Pattern Recognition with Fuzzy Objective Function Algorithms , 1981, Advanced Applications in Pattern Recognition.

[22]  J. Jakumeit,et al.  Parameter optimization of the sheet metal forming process using an iterative parallel Kriging algorithm , 2005 .

[23]  Inci Batmaz,et al.  Small response surface designs for metamodel estimation , 2003, Eur. J. Oper. Res..

[24]  Ren-Jye Yang,et al.  Optimization of car body under constraints of noise, vibration, and harshness (NVH), and crash , 2000 .

[25]  Raphael T. Haftka,et al.  Optimization and Experiments: A Survey , 1998 .

[26]  F. A. Lootsma,et al.  Numerical methods for non-linear optimization , 1974 .

[27]  Koetsu Yamazaki,et al.  Maximization of the crushing energy absorption of tubes , 1998 .

[28]  Henry P. Wynn,et al.  Screening, predicting, and computer experiments , 1992 .

[29]  G. Matheron.  Principles of geostatistics , 1963 .

[30]  R. Germundsson,et al.  Mathematica Version 4 , 2000 .

[31]  J. S. Hunter,et al.  Statistics for experimenters : an introduction to design, data analysis, and model building , 1979 .

[32]  L. Watson,et al.  Reduced Sampling for Construction of Quadratic Response Surface Approximations Using Adaptive Experimental Design , 2002 .

[33]  Hasan Kurtaran,et al.  Crashworthiness design optimization using successive response surface approximations , 2002 .

[34]  van Dh Dick Campen,et al.  Optimization of Multibody Systems Using Approximation Concepts , 1996 .

[35]  N. M. Alexandrov,et al.  A trust-region framework for managing the use of approximation models in optimization , 1997 .

[36]  Ren-Jye Yang,et al.  Multidisciplinary Design Optimization of A Full Vehicle With High Performance Computing , 2001 .

[37]  Jerome Sacks,et al.  Designs for Computer Experiments , 1989 .

[38]  Eiji Nakamachi,et al.  Development of optimum process design system for sheet fabrication using response surface method , 2003 .

[39]  Sang-Moon Hwang,et al.  Finite element analysis and design in stainless steel sheet forming and its experimental comparison , 2001 .

[40]  M. Natalia.  On Managing the Use of Surrogates in General Nonlinear Optimization and MDO , 1998 .

[41]  H. H. Rosenbrock,et al.  An Automatic Method for Finding the Greatest or Least Value of a Function , 1960, Comput. J..

[42]  G. Box,et al.  On the Experimental Attainment of Optimum Conditions , 1951 .

[43]  Enying Li,et al.  Development of metamodeling based optimization system for high nonlinear engineering problems , 2008, Adv. Eng. Softw..

[44]  Uwe Schramm,et al.  CRASHWORTHINESS DESIGN USING STRUCTURAL OPTIMIZATION , 1998 .

[45]  J. Renaud,et al.  New Adaptive Move-Limit Management Strategy for Approximate Optimization, Part 2 , 1998 .

[46]  John E. Renaud,et al.  Concurrent Subspace Optimization Using Design Variable Sharing in a Distributed Computing Environment , 1996 .