基于自适应Kriging代理模型的交叉熵重要抽样法

doi:10.7527/S1000-6893.2019.23123

Abstract

Abstract: To solve the reliability analysis of the coupling of complex failure domain and small failure probability, an improved method shortened as CE-IS-AK is proposed by combining Cross-Entropy Importance Sampling (CE-IS) with the Adaptive Kriging (AK) model on the existing CE-IS. In the proposed CE-IS-AK, the Gaussian mixed model suitable for complex failure domain is used to approximate the optimal Importance Sampling Density Function (IS-DF), and in the approximation process, the AK model is used to iteratively update the parameters of the Gaussian mixed model, so the efficiency of CE-IS is improved by the modification. In addition, the convergence criterion of the existing CE-IS is improved by CE-IS-AK for avoiding redundant iterations and expanding the applicability of the existing CE-IS. Since the AK model is nested into the CE-IS, the efficiency of constructing IS-DF is improved by the CE-IS-AK while ensuring the accuracy. Compared with the widely applicable AK based on Monte Carlo Simulation (AK-MCS), the size of the candidate sample pool for training AK in the CE-IS-AK is greatly reduced due to the variance-reduced strategy of IS in the case of that the number of training samples keeps almost equivalent, and the introduction of the Gaussian mixed model makes the proposed CE-IS-AK applicable for the multiple complex failure domain. The presented examples demonstrate the superiority of the CE-IS-AK.

Key words: failure probability, cross-entropy, importance sampling, Gaussian mixed model, adaptive Kriging

CLC Number:

V19
TB114.3

SHI Zhaoyin, LYU Zhenzhou, LI Luyi, WANG Yanping. Cross-entropy importance sampling method based on adaptive Kriging model[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2020, 41(1): 223123-223123.

References 26

[1]	吕震宙, 宋述芳, 李洪双, 等. 结构机构可靠性及可靠性灵敏度分析[M]. 北京:科学出版社, 2009:91-167. LYU Z Z, SONG S F, LI H S, et al. Reliability and sensitivity analysis of structural mechanism[M]. Beijing:Science Press, 2009:91-167(in Chinese).
[2]	ZHAO Y G, ONO T. A general procedure for first/second-order reliability method (FORM/SORM)[J]. Structural Safety, 1999, 21(2):95-112.
[3]	SCIUVA M D, LOMARIO D. A comparison between Monte Carlo and FORMs in calculating the reliability of a composite structure[J]. Composite Structures, 2003, 59(1):155-162.
[4]	HOHENBICHLER M, GOLLWITZER S, KRUSE W, et al. New light on first- and second-order reliability methods[J]. Structural Safety, 1987, 4(4):267-284.
[5]	DONLINSKI K. First-order second-moment approximation in reliability of structural systems:Critical review and alternative approach[J]. Structural Safety, 1982, 1(3):211-231.
[6]	MELCHERS R E. Importance sampling in structural systems[J]. Structural Safety, 1989, 6(1):3-10.
[7]	HARBITZ A. An efficient sampling method for probability of failure calculation[J]. Structural Safety, 1986, 3(2):109-115.
[8]	AU S K. Probabilistic failure analysis by importance sampling Markov chain simulation[J]. Journal of Engineering Mechanics, 2004, 130(3):303-311.
[9]	MELCHER S R E. Search-based importance sampling[J]. Structural Safety, 1990, 9(2):117-128.
[10]	吴斌, 欧进萍, 张纪刚, 等. 结构动力可靠度的重要抽样法[J]. 计算力学学报, 2001, 18(4):478-482. WU B, OU J P, ZHANG J G, et al. Importance sampling technique in dynamical structural reliability[J]. Chinese Journal of Computational Mechanics, 2001, 18(4):478-482(in Chinese).
[11]	PRIEBE C E, MARCHETTE D J. Adaptive mixture density estimation[J]. Pattern Recognition, 1993, 26(5):771-785.
[12]	AU S K, BEEK J L. A new adaptive importance sampling scheme for reliability calculations[J]. Structural Safety, 1999, 21(2):135-158.
[13]	DUBOURG V, SUDRET B, DEHEEGER F. Metamodel-based importance sampling for structural reliability analysis[J]. Probabilistic Engineering Mechanics, 2013, 33(1):47-57.
[14]	CADINI F, SANTOS F, ZIO E. Passive systems failure probability estimation by the meta-AK-IS 2 algorithm[J]. Nuclear Engineering & Design, 2014, 277(1):203-211.
[15]	KURTZ N, SONG J. Cross-entropy-based adaptive importance sampling using Gaussian mixture[J]. Structural Safety, 2013, 42(4):35-44.
[16]	CIARLET P G. The finite element method for elliptic problems[M]. Philadelphia:SIAM, 2002, 106-176.
[17]	KAYMAZ I, MCMAHON C A. A response surface method based on weighted regression for structural reliability analysis[J]. Probabilistic Engineering Mechanics, 2005, 20:11-17.
[18]	CHENG J, LI Q S, XIAO R C. A new artificial neural network-based response surface method for structural reliability analysis[J]. Probabilistic Engineering Mechanics, 2008, 23(1):51-63.
[19]	PAN Q, DIASS D. An efficient reliability method combining adaptive support vector machine and Monte Carlo simulation[J]. Structural Safety, 2017, 67:85-95.
[20]	BLATMAN G, SUDRET B. Adaptive sparse polynomial chaos expansions based on least angle regression[J]. Journal of Computational Physics, 2011, 230(6):2345-2367.
[21]	ZHENG P J, WANG C M, ZONG Z H, et al. A new active learning method based on the learning function U of the AK-MCS reliability analysis method[J]. Engineering Structures, 2017, 148:185-194.
[22]	LIU H T, CAI J F, ONG Y S. An adaptive sampling approach for Kriging metamodeling by maximizing expected prediction error[J]. Computers & Chemical Engineering, 2017, 106:171-182.
[23]	BICHON B J, ELDRED M S, SWILER L P, et al. Efficient global reliability analysis for non-linear implicit performance functions[J]. AIAA Journal, 2008, 46:2459-2468.
[24]	ECHARD B, GAYTON N, LEMAIRE M. AK-MCS:An active learning reliability method combining Kriging and Monte Carlo Simulation[J]. Structural Safety, 2011, 33(2):145-154.
[25]	LU Z Y, LU Z Z, WANG P. A new learning function for Kriging and its application to solve reliability problems in engineering[J]. Computers & Mathematics with Applications, 2015, 70:1182-1197.
[26]	SUN Z L, WANG J, LI R, et al. LIF:A new Kriging based learning function and its application to structural reliability analysis[J]. Reliability Engineering & System Safety, 2017, 157:152-165.

Cross-entropy importance sampling method based on adaptive Kriging model

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