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Structural and Multidisciplinary Optimization

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31-03-2020 | Research Paper

An efficient method for estimating time-dependent global reliability sensitivity

Authors: Chunyan Ling, Zhenzhou Lu, Xiaobo Zhang, Suting Zhou

Published in: Structural and Multidisciplinary Optimization | Issue 2/2020

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Abstract

Time-dependent global reliability sensitivity can quantify the effect of input variables in their whole distribution ranges on the time-dependent failure probability. To efficiently estimate it to help researchers control the time-dependent failure probability, a novel method is proposed. The proposed method transforms the estimation of unconditional-conditional time-dependent failure probabilities into that of the unconditional-conditional probability density functions (PDFs) of the minimum of time-dependent performance function. Firstly, the minimum of time-dependent performance function is evaluated by adaptive Kriging, and its unconditional-conditional fractional moments are estimated by multiplicative dimensional reduction method (M-DRM). Then, the maximum entropy (MaxEnt) constrained by these fractional moments is used to estimate the unconditional-conditional PDFs, on which the unconditional-conditional time-dependent failure probabilities can be obtained. Finally, the one-dimensional Gaussian quadrature is applied to estimate the time-dependent global reliability sensitivity indices. Due to the high efficiency of adaptive Kriging for estimating the minimum of time-dependent performance function, the avoidance of dimensional curse by M-DRM, and the high efficiency of MaxEnt constrained by fractional moments for estimating PDF, the proposed method can reduce the computational cost dramatically.

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Acar E, Haftka RT (2005) Reliability based aircraft structural design optimization with uncertainty about probability distributions. In Proceedings of the 6th World Congress on Structural & Multidisciplinary Optimization

Andrieu-Renaud C, Sudret B, Lemaire M (2004) The PHI2 method: a way to compute time-variant reliability. Reliab Eng Syst Saf 84(1):75–86CrossRef

Aven T (2016) Risk assessment and risk management: review of recent advances on their foundation. Eur J Oper Res 253:1–13MathSciNetMATHCrossRef

Borgonovo E (2007) A new uncertainty importance measure. Reliab Eng Syst Saf 92:771–784CrossRef

Campolongo F, Saltelli A, Cariboni J (2011) From screening to quantitative sensitivity analysis. A unified approach. Comput Phys Commun 182(4):978–988MATHCrossRef

Chen JB, Li J (2007) The extreme value distribution and dynamic reliability analysis of nonlinear structures with uncertain parameters. Struct Saf 29(2):77–93CrossRef

Cui LJ, Lu ZZ, Zhao XP (2010) Moment-independent importance measure of basic random variable and its probability density evolution solution. SCIENCE CHINA Technol Sci 53(4):1138–1145MATHCrossRef

Dubowsky S, Norris M, Aloni E, Tamir A (1984) Analytical and experimental study of the prediction of impacts in planar mechanical systems with clearances. J Mech Transm Autom Des 106(4):444–451CrossRef

Dupac M, Beale DG (2010) Dynamic analysis of a flexible linkage mechanism with cracks and clearance. Mech Mach Theory 45(12):1909–1923MATHCrossRef

Feng KX, Lu ZZ, Pang C, Yun WY (2018) An efficient computational method of a moment-independent importance measure using quantile regression. Mech Syst Signal Process 109:235–246CrossRef

Hu Z, Du XP (2013) Time-dependent reliability analysis with joint upcrossing rates. Struct Multidiscip Optim 48(5):893–907MathSciNetCrossRef

Hu Z, Du XP (2015) Mixed efficient global optimization for time-dependent reliability analysis. J Mech Des 137(5):051401CrossRef

Hu Z, Mahadevan S (2016) A single loop Kriging surrogate modeling for time-dependent reliability analysis. J Mech Des 138(6):061406CrossRef

Jiang C, Wei XP, Huang ZL (2017) An outcrossing rate model and its efficient calculation for time-dependent system reliability analysis. J Mech Des 139:1–10

Jones DR, Schonlau M, Welch WJ (1998) Efficient global optimization of expensive black-box functions. Kluwer Acad Publ 13(4):455–492MathSciNetMATH

Kuschel N, Rackwitz R (2000) Optimal design under time-variant reliability constraints. Struct Saf 22(2):113–127MATHCrossRef

Li J, Chen JB, Fan WL (2007) The equivalent extreme-value event and evaluation of the structural system reliability. Struct Saf 29(2):112–131CrossRef

Ling CY, Lu ZZ (2020) Adaptive Kriging coupled with importance sampling strategies for time-variant hybrid reliability analysis. Appl Math Model 77:1820–1841MathSciNetMATHCrossRef

Ling CY, Lu ZZ, Zhu XM (2019) Efficient methods by active learning Kriging coupled with variance reduction based sampling methods for time-dependent failure probability. Reliab Eng Syst Saf 188:23–35CrossRef

Miller RA (1997) Thermal barrier coatings for aircraft engines: history and directions. J Therm Spray Technol 6(1):35–42CrossRef

Nielsen UD (2010) Calculation of mean outcrossing rates of non-Gaussian processes with stochastic input parameters–reliability of containers stowed on ships in severe sea. Probabilistic Eng Mech 25(2):206–217CrossRef

Saltelli A, Tarantola S, Campolongo F, Ratto M. (2004) Sensitivity analysis in practice: a guide to assessing scientific models. John Wiley & Sons

Shi Y, Lu ZZ, Cheng K, Zhou YC (2017) Temporal and spatial multi-parameter dynamic reliability and global reliability sensitivity analysis based on the extreme value moments. Struct Multidiscip Optim 56(1):117–129MathSciNetCrossRef

Sobol IM (2001) Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math Comput Simul 55:271–280MathSciNetMATHCrossRef

Venter G, Sobieszczanksi SJ (2004) Multidisciplinary optimization of a transport aircraft wing using particle swarm optimization. Struct Multidiscip Optim 26(1–2):121–131CrossRef

Wang Z, Wang P (2012) A nested extreme response surface approach for time-dependent reliability-based design optimization. J Mech Des 134(12):12100701–12100714CrossRef

Wang ZQ, Wang PF (2015) A double-loop adaptive sampling approach for sensitivity-free dynamic reliability analysis. Reliab Eng Syst Saf 142:346–356CrossRef

Wei PF, Song JW, Lu ZZ, Yue ZF (2016) Time-dependent reliability sensitivity analysis of motion mechanisms. Reliab Eng Syst Saf 149:107–120CrossRef

Xiao SN, Lu ZZ (2017) Structural reliability sensitivity analysis based on classification of model output. Aerosp Sci Technol 71:52–61CrossRef

Xiao SN, Lu ZZ, Wang P (2018) Multivariate global sensitivity analysis for dynamic models based on energy distance. Struct Multidiscip Optim 57:279–291MathSciNetCrossRef

Yun WY, Lu ZZ, Zhang KC, Jiang X (2017a) An efficient sampling method for variance-based sensitivity analysis. Struct Saf 65:74–83CrossRef

Yun WY, Lu ZZ, Jiang X (2017b) A modified importance sampling method for structural reliability and its global reliability sensitivity analysis. Struct Multidiscip Optim 57(6):1–17MathSciNet

Yun WY, Lu ZZ, Jiang X (2018a) An efficient sampling approach for variance-based sensitivity analysis based on the law of total variance in the successive intervals without overlapping. Mech Syst Signal Process 106:495–510CrossRef

Yun WY, Lu ZZ, Jiang X, Zhang LG (2018b) Borgonovo moment independent global sensitivity analysis by Gaussian radial basis function meta-model. Appl Math Model 54:378–392MathSciNetMATHCrossRef

Zhang XF, Pandey MD (2013) Structural reliability analysis based on the concepts of entropy, fractional moment and dimensional reduction method. Struct Saf 43(9):28–40CrossRef

Zhang KC, Lu ZZ, Wu DQ, Zhang YL (2017) Analytical variance based global sensitivity analysis for models with correlated variables. Appl Math Model 45:748–767MathSciNetMATHCrossRef

Title: An efficient method for estimating time-dependent global reliability sensitivity
Authors: Chunyan Ling
Zhenzhou Lu
Xiaobo Zhang
Suting Zhou
Publication date: 31-03-2020
Publisher: Springer Berlin Heidelberg
Published in: Structural and Multidisciplinary Optimization / Issue 2/2020
Print ISSN: 1615-147X
Electronic ISSN: 1615-1488
DOI: https://doi.org/10.1007/s00158-020-02541-3

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