Global sensitivity analysis-enhanced surrogate (GSAS) modeling for reliability analysis

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• 作者：Zhen Hu ; Sankaran Mahadevan
• 关键词：Surrogate model ; Reliability analysis ; Sensitivity analysis ; Design of experiments
• 刊名：Structural and Multidisciplinary Optimization
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：53
• 期：3
• 页码：501-521
• 全文大小：1,788 KB
• 参考文献：Basudhar A, Missoum S (2008) Adaptive explicit decision functions for probabilistic design and optimization using support vector machines. Comput Struct 86(19):1904–1917CrossRef
  Basudhar A, Missoum S, Harrison Sanchez A (2008) Limit state function identification using support vector machines for discontinuous responses and disjoint failure domains. Probabilistic Eng Mech 23(1):1–11CrossRef
  Bichon BJ, Eldred MS, Swiler LP, Mahadevan S, McFarland JM (2008) Efficient global reliability analysis for nonlinear implicit performance functions. AIAA J 46(10):2459–2468CrossRef
  Blatman G, Sudret B (2010) An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis. Probabilistic Eng Mech 25(2):183–197CrossRef
  Borgonovo E (2007) A new uncertainty importance measure. Reliability Eng System Safety 92(6):771–784CrossRef
  Bourinet J-M, Deheeger F, Lemaire M (2011) Assessing small failure probabilities by combined subset simulation and support vector machines. Struct Saf 33(6):343–353CrossRef
  Du X, Hu Z (2012) First order reliability method with truncated random variables. J Mech Des 134(9):091005CrossRef
  Dubourg V, Sudret B (2014) Meta-model-based importance sampling for reliability sensitivity analysis. Struct Saf 49:27–36CrossRef
  Dubourg V, Sudret B, Deheeger F (2013) Metamodel-based importance sampling for structural reliability analysis. Probabilistic Eng Mech 33:47–57CrossRef
  Echard B, Gayton N, Lemaire M (2011) AK-MCS: an active learning reliability method combining Kriging and Monte Carlo simulation. Struct Saf 33(2):145–154CrossRef
  Echard B, Gayton N, Lemaire M, Relun N (2013) A combined importance sampling and kriging reliability method for small failure probabilities with time-demanding numerical models. Reliability Engineering & System Safety 111:232–240CrossRef
  Faravelli L (1989) Response-surface approach for reliability analysis. J Eng Mech 115(12):2763–2781CrossRef
  Gayton N, Bourinet J, Lemaire M (2003) CQ2RS: a new statistical approach to the response surface method for reliability analysis. Struct Saf 25(1):99–121CrossRef
  Gomes HM, Awruch AM (2004) Comparison of response surface and neural network with other methods for structural reliability analysis. Struct Saf 26(1):49–67CrossRef
  Haldar A, Mahadevan S (2000) Probability, reliability, and statistical methods in engineering design, John Wiley & Sons, Incorporated
  Jacques J, Lavergne C, Devictor N (2006) Sensitivity analysis in presence of model uncertainty and correlated inputs. Reliability Eng System Safety 91(10):1126–1134CrossRef
  Kaymaz I (2005) Application of kriging method to structural reliability problems. Struct Saf 27(2):133–151CrossRef
  Kbiob D (1951) A statistical approach to some basic mine valuation problems on the Witwatersrand, Jnl Chem Met Min Soc S Afr
  Kiureghian AD, Stefano MD (1991) Efficient algorithm for second-order reliability analysis. J Eng Mech 117(12):2904–2923CrossRef
  Kleijnen JP (2009) Kriging metamodeling in simulation: a review. Eur J Oper Res 192(3):707–716MathSciNet CrossRef MATH
  Li G, Rabitz H, Yelvington PE, Oluwole OO, Bacon F, Kolb CE, Schoendorf J (2010) Global sensitivity analysis for systems with independent and/or correlated inputs. J Phys Chem A 114(19):6022–6032CrossRef
  Lophaven SN, Nielsen HB, Søndergaard J (2002) DACE-A Matlab Kriging toolbox, version 2.0. Technical University of Denmark, Lyngby
  Mara TA, Tarantola S (2012) Variance-based sensitivity indices for models with dependent inputs. Reliability Eng System Safety 107:115–121CrossRef
  McRae GJ, Tilden JW, Seinfeld JH (1982) Global sensitivity analysis—a computational implementation of the Fourier amplitude sensitivity test (FAST). Comput Chem Eng 6(1):15–25CrossRef
  Paffrath M, Wever U (2007) Adapted polynomial chaos expansion for failure detection. J Comput Phys 226(1):263–281MathSciNet CrossRef MATH
  Rajashekhar MR, Ellingwood BR (1993) A new look at the response surface approach for reliability analysis. Struct Saf 12(3):205–220CrossRef
  Rasmussen CE (2006) Gaussian processes for machine learning, The MIT Press
  Saltelli A, Tarantola S, Chan K-S (1999) A quantitative model-independent method for global sensitivity analysis of model output. Technometrics 41(1):39–56CrossRef
  Santner TJ, Williams BJ, Notz W (2003) The design and analysis of computer experiments. Springer, New YorkCrossRef MATH
  Schueremans L, Van Gemert D (2005) Benefit of splines and neural networks in simulation based structural reliability analysis. Struct Saf 27(3):246–261CrossRef
  Simpson TW, Mauery TM, Korte JJ, Mistree F (2001) Kriging models for global approximation in simulation-based multidisciplinary design optimization. AIAA J 39(12):2233–2241CrossRef
  Sobol’ IM (2001) Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math Comput Simul 55(1–3):271–280MathSciNet CrossRef MATH
  Song S, Lu Z, Qiao H (2009) Subset simulation for structural reliability sensitivity analysis. Reliability Eng System Safety 94(2):658–665CrossRef
  Stein ML (1999) Interpolation of spatial data: some theory for kriging, Springer
  Sudret B (2008) Global sensitivity analysis using polynomial chaos expansions. Reliability Eng System Safety 93(7):964–979CrossRef
  Sudret B, Der Kiureghian A (2000) Stochastic finite element methods and reliability: a state-of-the-art report, Department of Civil and Environmental Engineering, University of California
  Vinh NX, Chetty M, Coppel R, Wangikar PP (2011) GlobalMIT: learning globally optimal dynamic bayesian network with the mutual information test criterion. Bioinformatics 27(19):2765–2766CrossRef
  Wagner HM (1995) Global sensitivity analysis. Oper Res 43(6):948–969MathSciNet CrossRef MATH
  Wand MP, Jones MC (1994) Kernel smoothing, Crc Press
  Xiong Y, Chen W, Apley D, Ding X (2007) A non‐stationary covariance‐based Kriging method for metamodelling in engineering design. Int J Numer Methods Eng 71(6):733–756CrossRef MATH
  Xiu D, Karniadakis GE (2002) The Wiener--Askey polynomial chaos for stochastic differential equations. SIAM J Sci Comput 24(2):619–644MathSciNet CrossRef MATH
  Xiu D, Karniadakis GE (2003) Modeling uncertainty in flow simulations via generalized polynomial chaos. J Comput Phys 187(1):137–167MathSciNet CrossRef MATH
  Xu C, Gertner G (2007) Extending a global sensitivity analysis technique to models with correlated parameters. Comput Statistics Data Analys 51(12):5579–5590MathSciNet CrossRef MATH
  Zhao H, Yue Z, Liu Y, Gao Z, Zhang Y (2014) An efficient reliability method combining adaptive importance sampling and Kriging metamodel, Applied Mathematical Modelling
  
• 作者单位：Zhen Hu (1)
  Sankaran Mahadevan (1)
  
  1. Department of Civil and Environmental Engineering, Vanderbilt University, 272 Jacobs Hall, VU Mailbox: PMB 351831, Nashville, TN, 37235, USA
  
• 刊物类别：Engineering
• 刊物主题：Theoretical and Applied Mechanics
  Computer-Aided Engineering and Design
  Numerical and Computational Methods in Engineering
  Engineering Design
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1615-1488

文摘

An essential issue in surrogate model-based reliability analysis is the selection of training points. Approaches such as efficient global reliability analysis (EGRA) and adaptive Kriging Monte Carlo simulation (AK-MCS) methods have been developed to adaptively select training points that are close to the limit state. Both the learning functions and convergence criteria of selecting training points in EGRA and AK-MCS are defined from the perspective of individual responses at Monte Carlo samples. This causes two problems: (1) some extra training points are selected after the reliability estimate already satisfies the accuracy target; and (2) the selected training points may not be the optimal ones for reliability analysis. This paper proposes a Global Sensitivity Analysis enhanced Surrogate (GSAS) modeling method for reliability analysis. Both the convergence criterion and strategy of selecting new training points are defined from the perspective of reliability estimate instead of individual responses of MCS samples. The new training points are identified according to their contribution to the uncertainty in the reliability estimate based on global sensitivity analysis. The selection of new training points stops when the accuracy of the reliability estimate reaches a specific target. Five examples are used to assess the accuracy and efficiency of the proposed method. The results show that the efficiency and accuracy of the proposed method are better than those of EGRA and AK-MCS.