Copula-based decomposition approach for the derivative-based sensitivity of variance contributions with dependent variables

Wang, Pan; Lü, Zhenzhou; Zhang, Kaichao; Xiao, Sun; Yue, Zhufeng

doi:10.1016/j.ress.2017.09.012

Cited by 33 publications

(11 citation statements)

References 30 publications

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“…They can be derived easily from the constructed PCE model, which are shown in Eqs. (19) and (20), respectively.…”

Section: Sensitivity Analysis Of Input Random and Interval Uncertamentioning

confidence: 99%

“…Many different SA techniques have been proposed to calculate the local and global sensitivity indices for the uncertainty design of complex physical systems in the last several decades. The major SA techniques are classified into the variance-based method [16], screening method [17], [18], derivative-based SA method [19], and moment-independent SA method [20], [21], as well as SA based on failure probability [22], [23]. In these SA technologies, output performances at some sampling points are analyzed and Monte Carlo simulation (MCS) technology, which is straightforward and easy to implement, is the most conventional method used to do this.…”

Section: Introductionmentioning

confidence: 99%

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Sensitivity Analysis of Random and Interval Uncertain Variables Based on Polynomial Chaos Expansion Method

et al. 2019

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The problem of characterizing the sensitivity indices of structural performance considering random and interval uncertainty variables simultaneously is analyzed. Data-driven polynomial chaos expansion (PCE) is established to treat random variables with arbitrary input uncertainty information, and subsequently extended to consider interval uncertainty variables simultaneously. An adaptive-sparse polynomial chaos expansion calculation algorithm is proposed to determine the appropriate polynomial coefficients based on the available uncertainty information of random and interval uncertainty variables. Subsequently, the local and total sensitivity indices of random and interval uncertainty variables are calculated directly using the constructed PCE model. Two numerical and engineering examples are presented to demonstrate the effectiveness of the proposed approach. Compared with the results of the Monte Carlo simulation method, the proposed approach yields excellent results with significantly reduced computational effort in the three examples. INDEX TERMS Sensitivity analysis, polynomial chaos expansion, random variables, interval variables.

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“…They can be derived easily from the constructed PCE model, which are shown in Eqs. (19) and (20), respectively.…”

Section: Sensitivity Analysis Of Input Random and Interval Uncertamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sensitivity Analysis of Random and Interval Uncertain Variables Based on Polynomial Chaos Expansion Method

et al. 2019

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“…Jiang et al proposed a vine‐copula‐based approach for the reliability analysis in multidimensional correlation problems. Wang et al proposed a copula‐based decomposition approach for the derivative‐based sensitivity of variance contributions with dependent variables.…”

Section: Introductionmentioning

confidence: 99%

Generalized F‐discrepancy‐based point selection strategy for dependent random variables in uncertainty quantification of nonlinear structures

Yang

Tao

Sudret

et al. 2019

Numerical Meth Engineering

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Summary In the performance evaluation of structures under disastrous actions, for example, earthquakes, it is important to take into account the randomness of structural parameters. Generally, these random parameters are treated either as independent or perfectly dependent, but practically they are partly dependent. This article aims at developing a point selection strategy for uncertainty quantification of nonlinear structures involving probabilistically dependent random parameters characterized by copula function. For this purpose, the point selection strategy for structures involving independent basic variables is first revisited. As an improvement, a generalized F‐discrepancy diminishing oriented iterative screening algorithm is proposed. Then, combining with the conditional sampling method, a conditional point set rearrangement method and a conditional iterative screening‐rearrangement method are proposed for probabilistically dependent variables. These new point selection strategies are readily incorporated into the probability density evolution method for uncertainty quantification of nonlinear structures involving dependent random parameters, which is characterized by copula function. The proposed methods are illustrated by two examples including a shear frame with hysteretic restoring forces and a reinforced concrete frame structure with the damage constitutive model of concrete, where the material parameters are probabilistically dependent. The results demonstrate the effectiveness of the proposed method. Problems to be studied are discussed.

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“…Another limitation of the presented method is that the reliability sensitivity analysis based on the line sampling requires an accurate estimation of the optimal direction, while the reliability analysis based on the line sampling does not have this requirement . Application of subset simulation and decomposition methods for obtaining reliability and RBS results has received due attention . However, as well as the score function approach, estimation of sensitivities by these approaches requires derivation of PDFs and satisfying the regularity conditions to provide results.…”

Section: Introductionmentioning

confidence: 99%

System‐level reliability sensitivity analysis by using weighted average simulation method

Rashki

Moghaddam

Miri

2019

Quality & Reliability Eng

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In addition to reliability analysis, investigation of the uncertainties' effect on the safety of structures can be regarded as one of the great concerns in engineering fields. The present study provides an efficient perturbation-based reliability sensitivity analysis approach based on weighted average simulation method (WASM) to attain uncertainties effects on the structures safety. Without asking additional samplings and/or requiring to function derivation (that is necessary in score function method), the proposed approach simultaneously uses the finite difference and weight flexibility feature of WASM to estimate the parameter sensitivities of a reliability problem. The proposed method has also been successfully applied to the improved version of WASM to obtain reliability based sensitivity results with very few samples. The accuracy and efficiency of the proposed method is examined by solving five analytical and engineering examples with highly nonlinear performance functions and system-level reliability problems. For each example, results are compared with those obtained by Monte Carlo simulation and common reliability methods. It is shown that the method is capable of solving real world system-level engineering problems efficiently and accurately.

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Copula-based decomposition approach for the derivative-based sensitivity of variance contributions with dependent variables

Cited by 33 publications

References 30 publications

Sensitivity Analysis of Random and Interval Uncertain Variables Based on Polynomial Chaos Expansion Method

Sensitivity Analysis of Random and Interval Uncertain Variables Based on Polynomial Chaos Expansion Method

Generalized F‐discrepancy‐based point selection strategy for dependent random variables in uncertainty quantification of nonlinear structures

System‐level reliability sensitivity analysis by using weighted average simulation method

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