Moment-independent importance measure of basic variable and its state dependent parameter solution

Li, Luyi; Lü, Zhenzhou; Feng, Jian; Wang, Bintuan

doi:10.1016/j.strusafe.2012.04.001

Cited by 121 publications

(35 citation statements)

References 18 publications

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“…Sobol indices in the context of ROSA can be derived as in [20], by introducing the binary random variable 1 (failure) or 0 (success) as the quantity of interest [21], where the basis of this transformation is the importance measure between P f and conditional P f defined in [22]. Indices can be derived in different variants, depending on whether the square of the importance measure [20] or the absolute value of the importance measure [23,24] is considered, but only the variant [20] after Sobol is based on decomposition, with the sum of all indices equal to one.…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

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

Kala

2020

Symmetry

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“…In order to further illustrate the engineering applicability of the proposed method, a plane truss structure [31] is introduced. The structure contains 10 bars as shown in Figure 6.…”

Section: Example 4: a Planar Truss Structurementioning

confidence: 99%

An Improved Structural Reliability Analysis Method Based on Local Approximation and Parallelization

Xie

2020

Mathematics

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The Kriging-based reliability method with a sequential design of experiments (DoE) has been developed in recent years for implicit limit state functions. Such methods include the efficient global reliability analysis, the active learning reliability method combining Kriging and MCS Simulations. In this research, a novel local approximation method based on the most probable failure point (MPFP) is proposed to improve such methods. In this method, the MPFP calculated in the last iteration is the center of the next sampling region. The size of the local region depends on the reliability index obtained by the First Order Reliability Method (FORM) and the deviation distance of the standard deviation. The proposed algorithm, which approximates the limit state function accurately near MPFP rather than in the whole design space, can avoid selecting samples in regions that have negligible effects on the reliability analysis results. In addition, a multi-point enrichment technique is also introduced to select multiple sample points in each iteration. After the high-quality approximation of limit state function is obtained, the failure probability is calculated by the Monte Carlo method. Four numerical examples are used to validate the accuracy and efficiency of the proposed method. Results show that the proposed method is very effective for an accurate evaluation of the failure probability.

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“…不确定性分析 [13,14] [15,16] [17][18][19][20][21][22] 、导数法 [23][24][25][26][27][28] 、方差灵敏度分析法 [29][30][31][32][33][34] 、矩独立灵敏度分析法 [35][36][37][38][39][40] 、基于失效概率的灵敏度分析 [41,42] . 基本效 [17] .…”

Section: 甚至冲突信息进行合理描述和处理较好地符合了人unclassified

A review of global sensitivity analysis for uncertainty structure

Xiao¹,

Lv²,

Wang³

2017

Sci. Sin.-Phys. Mech. Astron.

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Moment-independent importance measure of basic variable and its state dependent parameter solution

Cited by 121 publications

References 18 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

An Improved Structural Reliability Analysis Method Based on Local Approximation and Parallelization

A review of global sensitivity analysis for uncertainty structure

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