Sensitivity Analysis in Probabilistic Structural Design: A Comparison of Selected Techniques

Abstract

Although more and more reliability-oriented sensitivity analysis (ROSA) techniques are now available, review and comparison articles of ROSA are absent. In civil engineering, many of the latest indices have never been used to analyse structural reliability for very small failure probability. This article aims to analyse and compare different sensitivity analysis (SA) techniques and discusses their strengths and weaknesses. For this purpose, eight selected sensitivity indices are first described and then applied in two different test cases. Four ROSA type indices are directly oriented on the failure probability or reliability index beta, and four other indices (of a different type) are oriented on the output of the limit state function. The case study and results correspond to cases under common engineering assumptions, where only two independent input variables with Gaussian distribution of the load action and the resistance are applied in the ultimate limit state. The last section of the article is dedicated to the analysis of the different results. Large differences between first-order sensitivity indices and very strong interaction effects obtained from ROSA are observed for very low values of failure probability. The obtained numerical results show that ROSA methods lack a common platform that clearly interprets the relationship of indices to their information value. This paper can help orientate in the selection of which sensitivity measure to use.

From Probabilistic to Quantile-Oriented Sensitivity Analysis: New Indices of Design Quantiles

“…It can be noted that Sobol's first-order indices are equal to the squares of α F and α R : [19]. By applying α F and α R according to Equation (6), Equation (5) can be written with formally separated random variables as…”

“…Sensitivity indices subordinated to contrasts associated with probability (in short, contrast P f indices) are based on quadratic-type contrast functions [25]. However, contrast P f indices can be defined more easily based on the probability of failure and the conditional probabilities of failure [19]. A formula that does not require the evaluation of contrast functions can be used for practical computation.…”

“…A formula that does not require the evaluation of contrast functions can be used for practical computation. For practical use, the first-order probability contrast index C i can be rewritten in the form of [19]…”

“…In the interval Pf ∈ [0.1, 0.9], the first-, fourth-, and fifth-order indices generally have higher values than the second-and third-order indices. In civil engineering, the target values of Pf for reliability classes RC1, RC2, and RC3 taken from [4] are 8.5 × 10 −6 , 7.2 × 10 −5 , and 4.8 × 10 −4 (also see [19]). Figure 11b shows the contribution of all 31 indices for target value Pf = 7.2 × 10 −5 .…”

“…SSA is attractive for a number of reasons, e.g., it measures sensitivity across the whole input space (i.e., it is a global method), and it is capable of dealing with non-linear responses, as well as measuring the effect of interactions in non-additive models. However, SSA is based on the decomposition of variance of the model output, without a direct reference (only with partial empathy) to reliability [19].…”