New Importance Measures Based on Failure Probability in Global Sensitivity Analysis of Reliability

Mathematics

Zdeněk Kala¹ 

[1] Department of Structural Mechanics, Faculty of Civil Engineering, Brno University of Technology, 602 00 Brno, Czech Republic;

关键词: sensitivity analysis;    reliability analysis;    failure probability;    entropy;    uncertainty;    importance measure;   

DOI  :  10.3390/math9192425

来源: DOAJ

【 摘 要 】

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 P_f. 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 P_f(1 − P_f) and discrete entropy—P_fln(P_f) − (1 − P_f)ln(1 − P_f) 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 P_f. 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.

【 授权许可】

Unknown