Global sensitivity analysis: A Bayesian learning based polynomial chaos approach

Bhattacharyya, Biswarup

doi:10.1016/j.jcp.2020.109539

Cited by 11 publications

(2 citation statements)

References 54 publications

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“…The VBI versions of PCE have been investigated in the literature to perform global sensitivity analysis and time-invariant reliability analysis. 20,21 In these formulations, the problem is simplified in such a way that the residual (truncated error of PCE) follows a Gaussian distribution. The simplification might lead to results which are less robust, for example, with respect to outliers on the dataset when the numerical model is not available, but only a pre-existent data, or when the underlying assumption of a Gaussian distribution for the residual is not realistic.…”

Section: Introductionmentioning

confidence: 99%

Variational Bayesian inference-based polynomial chaos expansion: Application to time-variantreliability analysis

Zhou

Lü

Yan

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part O:

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In the time-variant systems, random variables, stochastic processes, and time parameter are regarded as the inputs of time-variant computational model. This results in an even more computationally expensive model what makes the time-variant reliability analysis a challenging task. This paper addresses the problem by presenting an active learning strategy using polynomial chaos expansion (PCE) in an augmented reliability space. We first propose a new algorithm that determines the sparse representation applying statistical threshold to determine the significant terms of the PCE model. This adaptive decision test is integrated into the variational Bayesian method, improving its accuracy and reducing convergence time. The proposed method uses a composite criterion to identify the most significant time instants and the associated training points to enrich the experimental design. By simulations, we compare the performance of the proposed method with respect to other existing time-variant reliability analysis methods.

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Section: Introductionmentioning

confidence: 99%

Variational Bayesian inference-based polynomial chaos expansion: Application to time-variantreliability analysis

Zhou

Lü

Yan

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part O:

View full text Add to dashboard Cite

show abstract

“…GSA is divided into three indices: index based on non-parametric method, moment-independent index and variance-based index. Bhattacharyya (2020) proposed a novel sparse polynomial chaos expansion (PCE) which combining variational Bayesian (VB) inference and automatic relevance determination (ARD) with the PCE model. To understand the influence of uncertainties on nuclear reactor systems, Gregory et al (2020) used surrogate models to perform both global and local sensitivity analyses.…”

Section: Introductionmentioning

confidence: 99%

Dynamic reliability and variance-based global sensitivity analysis of pipes conveying fluid with both random and convex variables

Chen

Wang

Guo³

et al. 2020

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Purpose This paper aims to solve the problem that pipes conveying fluid are faced with severe reliability failures under the complicated working environment. Design/methodology/approach This paper proposes a dynamic reliability and variance-based global sensitivity analysis (GSA) strategy with non-probabilistic convex model for pipes conveying fluid based on the first passage principle failure mechanism. To illustrate the influence of input uncertainty on output uncertainty of non-probability, the main index and the total index of variance-based GSA analysis are used. Furthermore, considering the efficiency of traditional simulation method, an active learning Kriging surrogate model is introduced to estimate the dynamic reliability and GSA indices of the structure system under random vibration. Findings The variance-based GSA analysis can measure the effect of input variables of convex model on the dynamic reliability, which provides useful reference and guidance for the design and optimization of pipes conveying fluid. For designers, the rankings and values of main and total indices have essential guiding role in engineering practice. Originality/value The effectiveness of the proposed method to calculate the dynamic reliability and sensitivity of pipes conveying fluid while ensuring the calculation accuracy and efficiency in the meantime.

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An uncertainty propagation method for multimodal distributions through unimodal decomposition strategy

Xie

Huang

Zhang

et al. 2023

Struct Multidisc Optim

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Global sensitivity analysis: A Bayesian learning based polynomial chaos approach

Cited by 11 publications

References 54 publications

Variational Bayesian inference-based polynomial chaos expansion: Application to time-variantreliability analysis

Variational Bayesian inference-based polynomial chaos expansion: Application to time-variantreliability analysis

Dynamic reliability and variance-based global sensitivity analysis of pipes conveying fluid with both random and convex variables

An uncertainty propagation method for multimodal distributions through unimodal decomposition strategy

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