A local adaptive sampling method for reliability-based design optimization using Kriging model

Reliability-based design optimization (RBDO) in practical applications is hindered by its huge computational cost during structure reliability evaluating process. Kriging-model-based RBDO is an effective method to overcome this difficulty. However, the accuracy of Kriging model depends directly on how to select the sample points. In this paper, the local adaptive sampling (LAS) is proposed to enhance the efficiency of constructing Kriging models for RBDO problems. In LAS, after initialization, new samples for probabilistic constraints are mainly selected within the local region around the current design point from each optimization iteration, and in the local sampling region, sample points are first considered to be located on the limit state constraint boundaries. The size of the LAS region is adaptively defined according to the nonlinearity of the performance functions. The computation capability of the proposed method is demonstrated using three mathematical RBDO problems and a honeycomb crash-worthiness design application. The comparison results show that the proposed method is very efficient.

[1]  E. Nikolaidis,et al.  Reliability based optimization: A safety index approach , 1988 .

[2]  T. Cruse,et al.  Advanced probabilistic structural analysis method for implicit performance functions , 1990 .

[3]  M. D. Stefano,et al.  Efficient algorithm for second-order reliability analysis , 1991 .

[4]  John Dalsgaard Sørensen,et al.  Reliability-Based Optimization in Structural Engineering , 1994 .

[5]  Ramana V. Grandhi,et al.  Reliability based structural optimization - A simplified safety index approach , 1994 .

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

[7]  Gerhart I. Schuëller,et al.  Reliability-Based Optimization of structural systems , 1997, Math. Methods Oper. Res..

[8]  R. Grandhi,et al.  Reliability-based structural optimization using improved two-point adaptive nonlinear approximations , 1998 .

[9]  E. Polak,et al.  An Outer Approximations Approach to Reliability-Based Optimal Design of Structures , 1998 .

[10]  Kyung K. Choi,et al.  A NEW STUDY ON RELIABILITY-BASED DESIGN OPTIMIZATION , 1999 .

[11]  Johannes O. Royset,et al.  Reliability-based optimal structural design by the decoupling approach , 2001, Reliab. Eng. Syst. Saf..

[12]  Y.-T. Wu,et al.  Safety-Factor Based Approach for Probability-Based Design Optimization , 2001 .

[13]  G. Kharmanda,et al.  Efficient reliability-based design optimization using a hybrid space with application to finite element analysis , 2002 .

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

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

[16]  Wei Chen,et al.  An integrated framework for optimization under uncertainty using inverse Reliability strategy , 2004 .

[17]  Johan Haarhoff,et al.  Kriging Response Surfaces as an Alternative Implementation of RBDO in Continuous Casting Design Optimization , 2004 .

[18]  J. Tu,et al.  A Single-Loop Method for Reliability-Based Design Optimization , 2004, DAC 2004.

[19]  Kyung K. Choi,et al.  A new response surface methodology for reliability-based design optimization , 2004 .

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

[21]  B. Youn,et al.  Adaptive probability analysis using an enhanced hybrid mean value method , 2005 .

[22]  G. Cheng,et al.  A sequential approximate programming strategy for reliability-based structural optimization , 2006 .

[23]  Sankaran Mahadevan,et al.  A direct decoupling approach for efficient reliability-based design optimization , 2006 .

[24]  Kyung K. Choi,et al.  Dimension reduction method for reliability-based robust design optimization , 2006 .

[25]  L. Watson,et al.  An inverse-measure-based unilevel architecture for reliability-based design optimization , 2007 .

[26]  Jianye Ching,et al.  Transforming reliability limit-state constraints into deterministic limit-state constraints , 2008 .

[27]  A. Basudhar,et al.  Adaptive explicit decision functions for probabilistic design and optimization using support vector machines , 2008 .

[28]  Byung Chai Lee,et al.  Reliability-based design optimization using a moment method and a kriging metamodel , 2008 .

[29]  Tae Hee Lee,et al.  A sampling technique enhancing accuracy and efficiency of metamodel-based RBDO: Constraint boundary sampling , 2008 .

[30]  G. Gary Wang,et al.  Reliable design space and complete single-loop reliability-based design optimization , 2008, Reliab. Eng. Syst. Saf..

[31]  Lei Jiang,et al.  A sequential approximate programming strategy for performance-measure-based probabilistic structural design optimization , 2008 .

[32]  Zissimos P. Mourelatos,et al.  A single-loop method for reliability-based design optimisation , 2008 .

[33]  Kyung K. Choi,et al.  Reliability-Based Design Optimization Using Response Surface Method With Prediction Interval Estimation , 2008 .

[34]  M. Eldred,et al.  Efficient Global Reliability Analysis for Nonlinear Implicit Performance Functions , 2008 .

[35]  Zhenzhou Lu,et al.  Subset simulation for structural reliability sensitivity analysis , 2009, Reliab. Eng. Syst. Saf..

[36]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[37]  Kyung K. Choi,et al.  Response Surface Method Using Sequential Sampling for Reliability-Based Design Optimization , 2009, DAC 2009.

[38]  Byeongdo Kim,et al.  Comparison study on the accuracy of metamodeling technique for non-convex functions , 2009 .

[39]  Dong-Hoon Choi,et al.  Construction of the radial basis function based on a sequential sampling approach using cross-validation , 2009 .

[40]  Teresa Wu,et al.  An accurate penalty-based approach for reliability-based design optimization , 2010 .

[41]  Kuei-Yuan Chan,et al.  A Modified Efficient Global Optimization Algorithm for Maximal Reliability in a Probabilistic Constrained Space , 2010 .

[42]  Victor Picheny,et al.  Adaptive Designs of Experiments for Accurate Approximation of a Target Region , 2010 .

[43]  Zissimos P. Mourelatos,et al.  System RBDO With Correlated Variables Using Probabilistic Re-Analysis and Local Metamodels , 2010, DAC 2010.

[44]  Gerhart I. Schuëller,et al.  A survey on approaches for reliability-based optimization , 2010 .

[45]  Alaa Chateauneuf,et al.  Benchmark study of numerical methods for reliability-based design optimization , 2010 .

[46]  Zissimos P. Mourelatos,et al.  A Re-Analysis Methodology for System RBDO Using a Trust Region Approach with Local Metamodels , 2010 .

[47]  Qing Li,et al.  A two-stage multi-fidelity optimization procedure for honeycomb-type cellular materials , 2010 .

[48]  Chang Yong Song,et al.  Role of Conservative Moving Least Squares Methods in Reliability Based Design Optimization: A Mathematical Foundation , 2011 .

[49]  Kyung K. Choi,et al.  Equivalent Standard Deviation to Convert High-Reliability Model to Low-Reliability Model for Efficiency of Sampling-Based RBDO , 2011, DAC 2011.

[50]  Tomas Dersjö,et al.  Reliability Based Design Optimization Using a Single Constraint Approximation Point , 2011 .

[51]  Kyung K. Choi,et al.  Metamodeling Method Using Dynamic Kriging for Design Optimization , 2011 .

[52]  T. Cho,et al.  Reliability-based design optimization using convex linearization and sequential optimization and reliability assessment method , 2011 .

[53]  Nicolas Gayton,et al.  AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation , 2011 .

[54]  Gerhart I. Schuëller,et al.  Efficient strategies for reliability-based optimization involving non-linear, dynamical structures , 2011 .

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

[56]  Hae Chang Gea,et al.  A Modified Reliability Index Approach for Reliability-Based Design Optimization , 2011, DAC 2009.

[57]  Yi Lu,et al.  Analysis and Determination of Associated Linkage, Redundant Constraint, and Degree of Freedom of Closed Mechanisms With Redundant Constraints and/or Passive Degree of Freedom , 2012 .

[58]  Xiaotian Zhuang,et al.  A Sequential Sampling Strategy to Improve Reliability-Based Design Optimization With Implicit Constraint Functions , 2012 .

[59]  D. Choi,et al.  Reliability-based design optimization using an enhanced dimension reduction method with variable sampling points , 2012, International Journal of Precision Engineering and Manufacturing.

[60]  Liang Gao,et al.  An optimal shifting vector approach for efficient probabilistic design , 2013 .

[61]  Zhenzhong Chen,et al.  An adaptive decoupling approach for reliability-based design optimization , 2013 .