A new sampling-based RBDO method via score function with reweighting scheme and application to vehicle designs

Abstract Sampling-based methods are general but time consuming for solving a reliability-based design optimization (RBDO) problem. However, one of the major drawbacks of using Monte Carlo simulation (MCS) to compute the sensitivities of reliability functions is computation intensive. In order to alleviate the computation burden, score function together with the MCS method is exploited to compute the stochastic sensitivities of reliability functions. Furthermore by reweighting an initial set of samples, the objective and constraint functions become smooth functions of changes of the parameters of probability distribution, rather than the stochastic functions obtained using MCS. A new sampling-based RBDO method by using score function with reweighting scheme is proposed to perform sensitivities analysis of reliability functions to improve the computational efficiency and accuracy. Several numerical examples are used to show the advantages of the proposed method. Comparisons to the conventional methods are made and discussed. Two large-scale industrial vehicle design problems are solved to demonstrate the feasibility of the proposed method.

[1]  Urmila M. Diwekar,et al.  Better Optimization of Nonlinear Uncertain Systems (BONUS): A New Algorithm for Stochastic Programming Using Reweighting through Kernel Density Estimation , 2004, Ann. Oper. Res..

[2]  Xiaoping Du,et al.  Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design , 2004, DAC 2002.

[3]  Kyung K. Choi,et al.  Design Potential Method for Robust System Parameter Design , 2001 .

[4]  K. K. Choi,et al.  Enriched Performance Measure Approach (PMA+) for Reliability-Based Design Optimization , 2004 .

[5]  Jin Cheng,et al.  Reliability analysis of structures using artificial neural network based genetic algorithms , 2008 .

[6]  Timothy K. Hasselman,et al.  Reliability based structural design optimization for practical applications , 1997 .

[7]  S. Rahman.  Stochastic sensitivity analysis by dimensional decomposition and score functions , 2009 .

[8]  Rajib Chowdhury,et al.  Enhanced high‐dimensional model representation for reliability analysis , 2009 .

[9]  Ren-Jye Yang,et al.  Experience with approximate reliability-based optimization methods II: an exhaust system problem , 2005 .

[10]  G. Schuëller,et al.  Uncertainty analysis of complex structural systems , 2009 .

[11]  Jack P. C. Kleijnen,et al.  Optimization and Sensitivity Analysis of Computer Simulation Models by the Score Function Method , 1996 .

[12]  Jason H. Goodfriend,et al.  Discrete Event Systems: Sensitivity Analysis and Stochastic Optimization by the Score Function Method , 1995 .

[13]  Klaus Schittkowski,et al.  More test examples for nonlinear programming codes , 1981 .

[14]  Yu Zhang,et al.  Metamodeling development for reliability-based design optimization of automotive body structure , 2011, Comput. Ind..

[15]  T. Hesterberg,et al.  Weighted Average Importance Sampling and Defensive Mixture Distributions , 1995 .

[16]  Timothy W. Simpson,et al.  Sampling Strategies for Computer Experiments: Design and Analysis , 2001 .

[17]  K. Choi,et al.  Sampling-Based Stochastic Sensitivity Analysis Using Score Functions for RBDO Problems with Correlated Random Variables , 2011, DAC 2010.

[18]  Kyung K. Choi,et al.  Sampling-Based RBDO Using the Dynamic Kriging (D-Kriging) Method and Stochastic Sensitivity Analysis , 2010 .

[19]  K. Choi,et al.  Sampling-based RBDO using the stochastic sensitivity analysis and Dynamic Kriging method , 2011 .

[20]  B. Youn,et al.  Enriched Performance Measure Approach for Reliability-Based Design Optimization. , 2005 .

[21]  Zissimos P. Mourelatos,et al.  A Single-Loop Approach for System Reliability-Based Design Optimization , 2006, DAC 2006.

[22]  Ping Zhu,et al.  A method for selecting surrogate models in crashworthiness optimization , 2012 .