Metamodel-based collaborative optimization framework

This paper focuses on the metamodel-based collaborative optimization (CO). The objective is to improve the computational efficiency of CO in order to handle multidisciplinary design optimization problems utilising high fidelity models. To address these issues, two levels of metamodel building techniques are proposed: metamodels in the disciplinary optimization are based on multi-fidelity modelling (the interaction of low and high fidelity models) and for the system level optimization a combination of a global metamodel based on the moving least squares method and trust region strategy is introduced. The proposed method is demonstrated on a continuous fiber-reinforced composite beam test problem. Results show that methods introduced in this paper provide an effective way of improving computational efficiency of CO based on high fidelity simulation models.

[1]  George E. P. Box,et al.  Empirical Model‐Building and Response Surfaces , 1988 .

[2]  Ilan Kroo,et al.  Implementation and Performance Issues in Collaborative Optimization , 1996 .

[3]  Vassili Toropov,et al.  Parameter Identification for Nonlinear Constitutive Models: Finite Element Simulation — Optimization — Nontrivial Experiments , 1993 .

[4]  Kroo Ilan,et al.  Multidisciplinary Optimization Methods for Aircraft Preliminary Design , 1994 .

[5]  F. Jose,et al.  Convergence of Trust Region Augmented Lagrangian Methods Using Variable Fidelity Approximation Data , 1997 .

[6]  Alastair S. Wood,et al.  Use of Global Approximatio ns in the Collaborative Optimization Framework , 2004 .

[7]  Vassili Toropov,et al.  Modelling and Approximation Strategies in Optimization — Global and Mid-Range Approximations, Response Surface Methods, Genetic Programming, Low / High Fidelity Models , 2001 .

[8]  Vassili Toropov,et al.  The use of simplified numerical models as mid-range approximations , 1996 .

[9]  N. M. Alexandrov,et al.  Analytical and Computational Properties of Distributed Approaches to MDO , 2000 .

[10]  Raphael T. Haftka,et al.  Analysis and design of composite curved channel frames , 1994 .

[11]  G. Gary Wang,et al.  Review of Metamodeling Techniques in Support of Engineering Design Optimization , 2007 .

[12]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[13]  Jaroslaw Sobieszczanski-Sobieski,et al.  Optimization by decomposition: A step from hierarchic to non-hierarchic systems , 1989 .

[14]  John E. Dennis,et al.  On Alternative Problem Formulations for Multidisciplinary Design Optimization , 1992 .

[15]  J. -F. M. Barthelemy,et al.  Approximation concepts for optimum structural design — a review , 1993 .

[16]  Raphael T. Haftka,et al.  CORRECTION RESPONSE SURFACE APPROXIMATIONS FOR STRESS INTENSITY FACTORS OF A COMPOSITE STIFFENED PLATE , 1998 .

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

[18]  Jaroslaw Sobieszczanski-Sobieski,et al.  Multidisciplinary design optimisation - some formal methods, framework requirements, and application to vehicle design , 2001 .

[19]  Ilan Kroo,et al.  Aircraft design using collaborative optimization , 1996 .

[20]  Klaus Hinkelmann,et al.  Design and Analysis of Experiment , 1975 .

[21]  Ren-Jye Yang,et al.  Approximation methods in multidisciplinary analysis and optimization: a panel discussion , 2004 .

[22]  M. D. McKay,et al.  A comparison of three methods for selecting values of input variables in the analysis of output from a computer code , 2000 .

[23]  Vassili Toropov,et al.  Multi-Fidelity Multidisciplinary Design Optimization Based on Collaborative Optimization Framework , 2002 .

[24]  Sobieszczanski Jaroslaw,et al.  Bi-Level Integrated System Synthesis (BLISS) , 1998 .

[25]  Vassili Toropov,et al.  Simultaneous model building and validation with uniform designs of experiments , 2007 .

[26]  Beom-Seon Jang,et al.  Managing approximation models in collaborative optimization , 2005 .

[27]  John E. Dennis,et al.  Problem Formulation for Multidisciplinary Optimization , 1994, SIAM J. Optim..

[28]  Raphael T. Haftka,et al.  Design of Shell Structures for Buckling Using Correction Response Surface Approximations , 1998 .

[29]  T. Simpson,et al.  Computationally Inexpensive Metamodel Assessment Strategies , 2002 .

[30]  Bernard Grossman,et al.  Variable-Complexity Multidisciplinary Design Optimization Using Parallel Computers , 1995 .

[31]  T Haftka Raphael,et al.  Multidisciplinary aerospace design optimization: survey of recent developments , 1996 .

[32]  P. A. Newman,et al.  Optimization with variable-fidelity models applied to wing design , 1999 .

[33]  Panos Y. Papalambros,et al.  Analytical Target Cascading in Automotive Vehicle Design , 2001 .

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