An Effective Approach for Reliability-Based Sensitivity Analysis with the Principle of Maximum Entropy and Fractional Moments

• Published in: Entropy (Basel, Switzerland) Vol. 21; no. 7; p. 649
• Main Authors: Zhang, Xufang, Liu, Jiankai, Yan, Ying, Pandey, Mahesh
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.07.2019; MDPI
• Subjects: Approximation; Design optimization; Entropy; fractional moments; Investigations; Maximum entropy; Monte Carlo simulation; multiplicative dimensional reduction method; Multivariate analysis; Performance evaluation; Probability distribution; Random variables; Reduction; Reliability analysis; reliability-based sensitivity analysis; Sensitivity analysis; Simulation; Standard deviation; Structural failure; Structural models; the principle of maximum entropy
• ISSN: 1099-4300; 1099-4300
• DOI: 10.3390/e21070649

The reliability-based sensitivity analysis requires to recursively evaluate a multivariate structural model for many failure probability levels. This is in general a computationally intensive task due to irregular integrations used to define the structural failure probability. In this regard, the performance function is first approximated by using the multiplicative dimensional reduction method in this paper, and an approximation for the reliability-based sensitivity index is derived based on the principle of maximum entropy and the fractional moment. Three examples in the literature are presented to examine the performance of this entropy-based approach against the brute-force Monte-Carlo simulation method. Results have shown that the multiplicative dimensional reduction based entropy approach is rather efficient and able to provide reliability estimation results for the reliability-based sensitivity analysis of a multivariate structural model.