The single-loop Kriging model combined with Bayes’ formula for time-dependent failure probability based global sensitivity

Lei, Jingyu; Lü, Zhenzhou; He, Liangli

doi:10.1016/j.istruc.2021.03.019

Cited by 4 publications

(3 citation statements)

References 53 publications

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“…with which it is possible to go back to the path of Sobol's decomposition; see Equations ( 21) and (22), etc.…”

Section: Sensitivity Measure Based On Entropymentioning

confidence: 99%

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

Kala

2021

Mathematics

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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.

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“…with which it is possible to go back to the path of Sobol's decomposition; see Equations ( 21) and (22), etc.…”

Section: Sensitivity Measure Based On Entropymentioning

confidence: 99%

“…The same indices can be obtained using the contrast function [13] where Pf is a minimizer. The rationality of sensitivity indices [11][12][13] has been shown in many applications [16][17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

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

Kala

2021

Mathematics

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“…Other types of SA include quantile-oriented methods [28][29][30][31][32][33], probability of failure [34][35][36][37][38][39][40][41], or decision-making approaches [42][43][44][45]. The subject of interest of these types of SA is the reliability of the system, which cannot be examined using SA distribution types.…”

Section: Introductionmentioning

confidence: 99%

Global Sensitivity Analysis Based on Entropy: From Differential Entropy to Alternative Measures

Kala¹

2021

Entropy

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Differential entropy can be negative, while discrete entropy is always non-negative. This article shows that negative entropy is a significant flaw when entropy is used as a sensitivity measure in global sensitivity analysis. Global sensitivity analysis based on differential entropy cannot have negative entropy, just as Sobol sensitivity analysis does not have negative variance. Entropy is similar to variance but does not have the same properties. An alternative sensitivity measure based on the approximation of the differential entropy using dome-shaped functionals with non-negative values is proposed in the article. Case studies have shown that new sensitivity measures lead to a rational structure of sensitivity indices with a significantly lower proportion of higher-order sensitivity indices compared to other types of distributional sensitivity analysis. In terms of the concept of sensitivity analysis, a decrease in variance to zero means a transition from the differential to discrete entropy. The form of this transition is an open question, which can be studied using other scientific disciplines. The search for new functionals for distributional sensitivity analysis is not closed, and other suitable sensitivity measures may be found.

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Neural network-based chaotic crossover method for structural reliability analysis considering time-dependent parameters

Dong

Zhang

et al. 2023

Structures

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The single-loop Kriging model combined with Bayes’ formula for time-dependent failure probability based global sensitivity

Cited by 4 publications

References 53 publications

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

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

Global Sensitivity Analysis Based on Entropy: From Differential Entropy to Alternative Measures

Neural network-based chaotic crossover method for structural reliability analysis considering time-dependent parameters

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