Parametric Reliability Sensitivity Analysis Using Failure Probability Ratio Function

2016 ◽  
Vol 13 (04) ◽  
pp. 1641005 ◽  
Author(s):  
Pengfei Wei ◽  
Zhenzhoug Lu
Keyword(s):  
Sensitivity Analysis ◽  
Importance Sampling ◽  
Failure Probability ◽  
Probability Ratio ◽  
Sensitivity Indices ◽  
Analysis Technique ◽  
Parametric Reliability ◽  
Reliability Sensitivity ◽  
Reliability Sensitivity Analysis ◽  
Distribution Parameters

Reducing the failure probability is an important task in the design of engineering structures. In this paper, a reliability sensitivity analysis technique, called failure probability ratio function, is firstly developed for providing the analysts quantitative information on failure probability reduction while one or a set of distribution parameters of model inputs are changed. Then, based on the failure probability ratio function, a global sensitivity analysis technique, called R-index, is proposed for measuring the average contribution of the distribution parameters to the failure probability while they vary in intervals. The proposed failure probability ratio function and R-index can be especially useful for failure probability reduction, reliability-based optimization and reduction of the epistemic uncertainty of parameters. The Monte Carlo simulation (MCS), Importance Sampling (IS) and Truncated Importance Sampling (TIS) procedures, which need only a set of samples for implementing them, are introduced for efficiently computing the proposed sensitivity indices. A numerical example is introduced for illustrating the engineering significance of the proposed sensitivity indices and verifying the efficiency and accuracy of the MCS, IS and TIS procedures. At last, the proposed sensitivity techniques are applied to a planar 10-bar structure for achieving a targeted 80% reduction of the failure probability.

scholarly journals Reliability Sensitivity Analysis Method for Mechanical Components

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yan-Fang Zhang ◽  
Yan-Lin Zhang
Keyword(s):  
Sensitivity Analysis ◽  
Failure Probability ◽  
Reduction Method ◽  
Dimension Reduction Method ◽  
Edgeworth Series ◽  
Reliability Sensitivity ◽  
Reliability Sensitivity Analysis ◽  
Distribution Parameters ◽  
Mechanical Components ◽  
Univariate Dimension Reduction Method

Based on the univariate dimension-reduction method (UDRM), Edgeworth series, and sensitivity analysis, a new method for reliability sensitivity analysis of mechanical components is proposed. The univariate dimension-reduction method is applied to calculate the response origin moments and their sensitivity with respect to distribution parameters (e.g., mean and standard deviation) of fundamental input random variables. Edgeworth series is used to estimate failure probability of mechanical components by using first few response central moments. The analytic formula of reliability sensitivity can be derived by calculating partial derivative of the failure probability P f with respect to distribution parameters of basic random variables. The nonnormal random parameters need not to be transformed into equivalent normal ones. Three numerical examples are employed to illustrate the accuracy and efficiency of the proposed method by comparing the failure probability and reliability sensitivity results obtained by the proposed method with those obtained by Monte Carlo simulation (MCS).

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

2019 ◽  
Vol 233 (6) ◽  
pp. 943-957 ◽  
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.

scholarly journals Reliability sensitivity analysis using axis orthogonal importance Latin hypercube sampling method

2019 ◽  
Vol 11 (3) ◽  
pp. 168781401982641 ◽  
Author(s):  
Wei Zhao ◽  
YangYang Chen ◽  
Jike Liu
Keyword(s):  
Sensitivity Analysis ◽  
Importance Sampling ◽  
Failure Probability ◽  
Random Variables ◽  
Latin Hypercube Sampling ◽  
Sampling Point ◽  
Latin Hypercube ◽  
Sensitivity Estimation ◽  
Reliability Sensitivity ◽  
Reliability Sensitivity Analysis

In this article, a combined use of Latin hypercube sampling and axis orthogonal importance sampling, as an efficient and applicable tool for reliability analysis with limited number of samples, is explored for sensitivity estimation of the failure probability with respect to the distribution parameters of basic random variables, which is equivalently solved by reliability sensitivity analysis of a series of hyperplanes through each sampling point parallel to the tangent hyperplane of limit state surface around the design point. The analytical expressions of these hyperplanes are given, and the formulas for reliability sensitivity estimators and variances with the samples are derived according to the first-order reliability theory and difference method when non-normal random variables are involved and not involved, respectively. A procedure is established for the reliability sensitivity analysis with two versions: (1) axis orthogonal Latin hypercube importance sampling and (2) axis orthogonal quasi-random importance sampling with the Halton sequence. Four numerical examples are presented. The results are discussed and demonstrate that the proposed procedure is more efficient than the one based on the Latin hypercube sampling and the direct Monte Carlo technique with an acceptable accuracy in sensitivity estimation of the failure probability.

scholarly journals Global Sensitivity Analysis of Fuzzy Distribution Parameter on Failure Probability and Its Single-Loop Estimation

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Lei Cheng ◽  
Zhenzhou Lu ◽  
Luyi Li
Keyword(s):  
Sensitivity Analysis ◽  
Failure Probability ◽  
Global Sensitivity Analysis ◽  
Computational Cost ◽  
Single Loop ◽  
Global Sensitivity ◽  
Sensitivity Indices ◽  
Distribution Parameters ◽  
Input Variables ◽  
Sampling Probability

An extending Borgonovo’s global sensitivity analysis is proposed to measure the influence of fuzzy distribution parameters on fuzzy failure probability by averaging the shift between the membership functions (MFs) of unconditional and conditional failure probability. The presented global sensitivity indices can reasonably reflect the influence of fuzzy-valued distribution parameters on the character of the failure probability, whereas solving the MFs of unconditional and conditional failure probability is time-consuming due to the involved multiple-loop sampling and optimization operators. To overcome the large computational cost, a single-loop simulation (SLS) is introduced to estimate the global sensitivity indices. By establishing a sampling probability density, only a set of samples of input variables are essential to evaluate the MFs of unconditional and conditional failure probability in the presented SLS method. Significance of the global sensitivity indices can be verified and demonstrated through several numerical and engineering examples.

A Fast Approximate Method for Reliability Sensitivity Based on Markov Chain Simulation

2007 ◽  
Vol 353-358 ◽  
pp. 1005-1008
Author(s):  
Xiu Kai Yuan ◽  
Zhen Zhou Lu
Keyword(s):  
Sensitivity Analysis ◽  
Monte Carlo ◽  
Markov Chain ◽  
Weighted Regression ◽  
Analysis Method ◽  
Reliability Sensitivity ◽  
Reliability Sensitivity Analysis ◽  
Failure Region ◽  
Sensitivity Analysis Method ◽  
Distribution Parameters

On the basis of Markov chain simulation, an efficient method is presented to analyze reliability sensitivity of structure. In the presented method, Markov chain is employed to draw the samples distributed in the failure region, and these samples are fitted in a form of hyperplane by the weighted regression. By use of the regressed hyperplane, it is convenient to complete the sensitivities of the failure probability with respect to the distribution parameters of basic random variables by the available method. The presented method is applied to some examples to validate its accuracy and efficiency. The obtained results show that the presented reliability sensitivity analysis method is far more efficient than Monte Carlo based method.

Sign in / Sign up

Export Citation Format

Share Document