Abstract
An extending Borgonovo’s global sensitivity analysis is proposed to measure the influence of fuzzy distribution parameters on fuzzy failure probability by averaging the shift between the membership functions (MFs) of unconditional and conditional failure probability. The presented global sensitivity indices can reasonably reflect the influence of fuzzy-valued distribution parameters on the character of the failure probability, whereas solving the MFs of unconditional and conditional failure probability is time-consuming due to the involved multiple-loop sampling and optimization operators. To overcome the large computational cost, a single-loop simulation (SLS) is introduced to estimate the global sensitivity indices. By establishing a sampling probability density, only a set of samples of input variables are essential to evaluate the MFs of unconditional and conditional failure probability in the presented SLS method. Significance of the global sensitivity indices can be verified and demonstrated through several numerical and engineering examples.
Highlights
Two different uncertainty sources are involved in reliability engineering: aleatory uncertainty and epistemic uncertainty [1,2,3]
The moment independent sensitivity index δi proposed by Borgonovo is widely extended in global SA (GSA): Castaings et al [20], Plischke et al [21], and Luo et al [22] developed methods for moment independent indices recently; the moment independent model was applied to environmental models [23] and climate model [24] et al.; Wei et al [25] and Borgonovo et al [26] brought up new moment independent indices
Based on the fuzzy set theory which models the epistemic uncertainty as a fuzzy variable represented by membership functions (MFs), some methods have been developed for evaluating the importance of fuzzy variables [29,30,31, 33], among which Song et al [33] proposed a generalized Borgonovo’s sensitivity indicator to analyze the effect of fuzzy-valued variables on the output response, and optimization techniques are employed to calculate the MF of output response [34]
Summary
Two different uncertainty sources are involved in reliability engineering: aleatory uncertainty and epistemic uncertainty [1,2,3]. Based on the fuzzy set theory which models the epistemic uncertainty as a fuzzy variable represented by MF, some methods have been developed for evaluating the importance of fuzzy variables [29,30,31, 33], among which Song et al [33] proposed a generalized Borgonovo’s sensitivity indicator to analyze the effect of fuzzy-valued variables on the output response, and optimization techniques are employed to calculate the MF of output response [34]. A global sensitivity analysis is proposed to estimate the effect of fuzzy-valued distribution parameters on failure probability. 2. Global Sensitivity Indices for Fuzzy Distribution Parameter Based on Failure Probability. For knowing about the detailed property of moment-independent sensitivity index, one could refer to [45, 46]
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