Efficient sampling methods for global reliability sensitivity analysis

Systems with random variables and random excitations exist widely in various engineering problems. Extending the traditional global reliability sensitivity to this double-stochastic system has important guiding significance for its design optimization. However, because there is a certain coupling between the randomness of variables and the randomness of excitation, this coupling mechanism is difficult to determine in practical projects. Therefore, it is difficult to extend the traditional reliability sensitivity analysis method to this double-stochastic system. In this research, it is assumed that there is no correlation between variables and excitations. Then, combining the first-passage method–based dynamic strength formula and the variance-based sensitivity analysis method, an approximate global reliability sensitivity analysis method for this double-stochastic system is proposed. In order to improve the computational efficiency, a nested loop method based on seven-point estimation is proposed for reliability sensitivity analysis. In order to verify the accuracy and efficiency of the proposed method, a Monte Carlo simulation is given as a reference. Three examples are studied and discussed to illustrate the practicality and feasibility of the proposed method.

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Structural reliability and reliability sensitivity analysis of extremely rare failure events by combining sampling and surrogate model methods

Proceedings of the Institution of Mechanical Engineers Part O Journal of Risk and Reliability ◽

10.1177/1748006x19844666 ◽

2019 ◽

Vol 233 (6) ◽

pp. 943-957 ◽

Cited By ~ 4

Author(s):

Pengfei Wei ◽

Chenghu Tang ◽

Yuting Yang

Keyword(s):

Sensitivity Analysis ◽

Monte Carlo ◽

Markov Chain ◽

Markov Chain Monte Carlo ◽

Failure Surface ◽

Sensitivity Indices ◽

Parametric Reliability ◽

Reliability Sensitivity ◽

Reliability Sensitivity Analysis ◽

Global Reliability Sensitivity

The aim of this article is to study the reliability analysis, parametric reliability sensitivity analysis and global reliability sensitivity analysis of structures with extremely rare failure events. First, the global reliability sensitivity indices are restudied, and we show that the total effect index can also be interpreted as the effect of randomly copying each individual input variable on the failure surface. Second, a new method, denoted as Active learning Kriging Markov Chain Monte Carlo (AK-MCMC), is developed for adaptively approximating the failure surface with active learning Kriging surrogate model as well as dynamically updated Monte Carlo or Markov chain Monte Carlo populations. Third, the AK-MCMC procedure combined with the quasi-optimal importance sampling procedure is extended for estimating the failure probability and the parametric reliability sensitivity and global reliability sensitivity indices. For estimating the global reliability sensitivity indices, two new importance sampling estimators are derived. The AK-MCMC procedure can be regarded as a combination of the classical Monte Carlo Simulation (AK-MCS) and subset simulation procedures, but it is much more effective when applied to extremely rare failure events. Results of test examples show that the proposed method can accurately and robustly estimate the extremely small failure probability (e.g. 1e–9) as well as the related parametric reliability sensitivity and global reliability sensitivity indices with several dozens of function calls.

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Reliability sensitivity analysis method for time-dependent problem based on first-passage method

Proceedings of the Institution of Mechanical Engineers Part E Journal of Process Mechanical Engineering ◽

10.1177/0954408918809596 ◽

2018 ◽

Vol 233 (4) ◽

pp. 787-802

Author(s):

Wenxuan Wang ◽

Hangshan Gao ◽

Changcong Zhou ◽

Wanghua Xu

Keyword(s):

Sensitivity Analysis ◽

Time Dependent ◽

Sensitivity Index ◽

Analysis Method ◽

First Passage ◽

Reliability Sensitivity ◽

Reliability Sensitivity Analysis ◽

Sensitivity Analysis Method ◽

Global Reliability Sensitivity ◽

The Impact

The sensitivity index plays a critical role in the design of product and is used to quantify the impact degree of the uncertainty of the input variable to the uncertainty of the interest output. This paper presents a new local reliability sensitivity method and a global reliability sensitivity analysis method of time-dependent reliability problems. Firstly, according to the Poisson's assumption-based first-passage method, the local reliability sensitivity index is directly obtained by calculating the partial derivative of the failure probability to the distribution parameters of input random variable. Then, the moment-independent global reliability sensitivity index of the time-dependent problems is derived based on the concept of moment-independent. Finally, the efficiency and accuracy of the proposed method are verified with the reference results of Monte Carlo simulation.

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