Abstract
This article presents new sensitivity measures in reliability-oriented global sensitivity analysis. The obtained results show that the contrast and the newly proposed sensitivity measures (entropy and two others) effectively describe the influence of input random variables on the probability of failure Pf. The contrast sensitivity measure builds on Sobol, using the variance of the binary outcome as either a success (0) or a failure (1). In Bernoulli distribution, variance Pf(1 − Pf) and discrete entropy—Pfln(Pf) − (1 − Pf)ln(1 − Pf) are similar to dome functions. By replacing the variance with discrete entropy, a new alternative sensitivity measure is obtained, and then two additional new alternative measures are derived. It is shown that the desired property of all the measures is a dome shape; the rise is not important. Although the decomposition of sensitivity indices with alternative measures is not proven, the case studies suggest a rationale structure of all the indices in the sensitivity analysis of small Pf. The sensitivity ranking of input variables based on the total indices is approximately the same, but the proportions of the first-order and the higher-order indices are very different. Discrete entropy gives significantly higher proportions of first-order sensitivity indices than the other sensitivity measures, presenting entropy as an interesting new sensitivity measure of engineering reliability.
Highlights
Classical sensitivity analysis focuses on the model output, whereas the reliability-oriented sensitivity analysis (ROSA) generally deals with reliability measures, usually the failure probability
Distribution-oriented SA based on discrete entropy [80] is known but has never been presented in the context of the ROSA of Pf
The condition of reliability in Equation (15) is studied using five input random variables, where two variables are on the load side A and three variables are on the resistance side R
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Classical sensitivity analysis focuses on the model output, whereas the ROSA generally deals with reliability measures, usually the failure probability. Methods [27,28] oriented to the reliability index β cannot analyze the interaction effects of input variables. Reliability and sensitivity analyses should work in tandem with a common focus on Pf. The goal of the ROSA should be Pf , including all interaction effects from input random variables. This article presents new global sensitivity measures oriented to Pf , building on Sobol [14,15] on the path from variance [11,12,13] to entropy and other measures. The research presents case studies with induction from results starting from the particular to the more general
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