Estimation of quantile oriented sensitivity indices

Maume-Deschamps, Véronique; Niang, Ibrahima

doi:10.1016/j.spl.2017.10.019

Cited by 22 publications

(13 citation statements)

References 13 publications

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“…Although contrasts are of a different type, similarities between the results of QSA and SSA have been observed in the task of SA of the resistance of a building load-bearing element [35]. Other numerical illustrations of contrast Q indices are presented in [38,39].…”

Section: Specific Properties Of Contrasts Associated With Quantilesmentioning

confidence: 94%

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

Kala

2020

Symmetry

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In structural reliability analysis, sensitivity analysis (SA) can be used to measure how an input variable influences the failure probability Pf of a structure. Although the reliability is usually expressed via Pf, Eurocode building design standards assess the reliability using design quantiles of resistance and load. The presented case study showed that quantile-oriented SA can provide the same sensitivity ranking as Pf-oriented SA or local SA based on Pf derivatives. The first two SAs are global, so the input variables are ranked based on total sensitivity indices subordinated to contrasts. The presented studies were performed for Pf ranging from 9.35 × 10−8 to 1–1.51 × 10−8. The use of quantile-oriented global SA can be significant in engineering tasks, especially for very small Pf. The proposed concept provided an opportunity to go much further. Left-right symmetry of contrast functions and sensitivity indices were observed. The article presents a new view of contrasts associated with quantiles as the distance between the average value of the population before and after the quantile. This distance has symmetric hyperbola asymptotes for small and large quantiles of any probability distribution. Following this idea, new quantile-oriented sensitivity indices based on measuring the distance between a quantile and the average value of the model output are formulated in this article.

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Section: Specific Properties Of Contrasts Associated With Quantilesmentioning

confidence: 94%

“…Equation (36) can be interpreted using Equation (39). The key idea is to introduce l 2 as a variance.…”

Section: New Quantile-oriented Sensitivity Indices For Small and Largmentioning

confidence: 99%

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

Kala

2020

Symmetry

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“…[31] compute variance-based sensitivity indices for a probability of failure conditional on distribution parameters using importance sampling and the FAST algorithm for estimating the sensitivity indices. Alternative sensitivity measures for rare event probabilities include the use of quantiles [32] or perturbation of input densities [33] to globally quantify influence of model inputs on rare event probabilities.…”

Section: Reliability Analysismentioning

confidence: 99%

A framework for global reliability sensitivity analysis in the presence of multi-uncertainty

Ehre

Papaioannou

Straub

2020

Reliability Engineering & System Safety

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In reliability analysis with numerical models, one is often interested in the sensitivity of the probability of failure estimate to changes in the model input. In the context of multi-uncertainty, one whishes to separate the effect of different types of uncertainties. A common distinction is between aleatory (irreducible) and epistemic (reducible) uncertainty, but more generally one can consider any classification of the uncertain model inputs in two subgroups, type A and type B. We propose a new sensitivity measure for the probability of failure conditional on type B inputs. On this basis, we outline a framework for multi-uncertainty-driven reliability sensitivity analysis. A bi-level surrogate modelling strategy is designed to efficiently compute the new conditional reliability sensitivity measures. In the first level, a surrogate is constructed for the model response to circumvent possibly expensive evaluations of the numerical model. By solving a sequence of reliability problems conditional on samples of type B random variables, we construct a level 2-surrogate for the logarithm of the conditional probability of failure, using polynomial bases which allow to directly evaluate the variance-based sensitivities. The new sensitivity measure and its computation are demonstrated through two engineering examples.

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“…Yun, Lu, Zhan, & Jiang, 2018b;Xiao & Lu, 2017), which measure the effect of each model input variable on the failure probability, have been developed with this motivation. In cases where reliability is given by exceeding the quantile value, sensitivity measurements based directly on the quantiles of model outputs may be more appropriate (Maume-Deschamps & Niang, 2018;Kala, 2019a;Kucherenko, Song, & Wang, 2019).…”

Section: Introductionmentioning

confidence: 99%

Global sensitivity analysis of failure probability caused by fatigue crack propagation

Kala

2019

Modern Building Materials, Structures and Techniques (MBMST)

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The probability of failure of a load bearing steel member is investigated using a new type of global sensitivity analysis subordinated to contrasts. The main objective of the probability-oriented sensitivity analysis is structural reliability. The structural reliability methodology uses random variables as inputs. The subject of interest is the identification of those random variables that are most important when the limit state of a steel bridge member is reached. The limit state is defined by the occurrence of brittle fracture, which results from stress changes caused by multiple repeated loads. The propagation of a single-edge crack from initial to critical size is analysed using linear fracture mechanics. The failure probability and sensitivity indices are calculated using sampling-based methods. The sensitivity indices are estimated using double-nested-loop simulation of the Latin Hypercube Sampling method. New findings indicate that interaction effects among input variables strongly influence the probability of failure especially at the beginning of the operating period.

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Estimation of quantile oriented sensitivity indices

Abstract: Abstract. The paper concerns quantile oriented sensitivity analysis. We rewrite the corresponding indices using the Conditional Tail Expectation risk measure. Then, we use this new expression to built estimators.

Cited by 22 publications

References 13 publications

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

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

A framework for global reliability sensitivity analysis in the presence of multi-uncertainty

Global sensitivity analysis of failure probability caused by fatigue crack propagation

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