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.

Extending the global reliability sensitivity analysis to the systems under double-stochastic uncertainty

2018 ◽  
Vol 22 (3) ◽  
pp. 626-640 ◽  
Author(s):  
Wenxuan Wang ◽  
Hangshan Gao ◽  
Changcong Zhou
Keyword(s):  
Sensitivity Analysis ◽  
Stochastic System ◽  
Dynamic Strength ◽  
Point Estimation ◽  
Coupling Mechanism ◽  
Analysis Method ◽  
Reliability Sensitivity ◽  
Reliability Sensitivity Analysis ◽  
Sensitivity Analysis Method ◽  
Global Reliability Sensitivity

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.

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.

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

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.

Reliability-Based Sensitivity Design of Mechanical Components with Arbitrary Distribution Parameters

2008 ◽  
Vol 44-46 ◽  
pp. 885-892
Author(s):  
Zhou Yang ◽  
Yi Min Zhang ◽  
Li Sha Zhu
Keyword(s):  
Sensitivity Analysis ◽  
Random Parameter ◽  
Design Parameters ◽  
Arbitrary Distribution ◽  
Fourth Moment ◽  
Analysis Method ◽  
Mechanical Joints ◽  
Reliability Sensitivity ◽  
Sensitivity Analysis Method ◽  
Distribution Parameters

In the reliability-based analysis of mechanical joints, as each factor has different effect on the failure of mechanical joints, the effects of design parameters on reliability of the mechanical joints are determined with the reliability-based sensitivity analysis method. Furthermore, the reliability of mechanical joints can be effectively designed. As a matter of fact, if a change of a certain random parameter has great effect on the reliability of mechanical joints, the parameter must be strictly controlled in the course of design and manufacture to ensure reliability. Whereas if a change of a certain random parameter has unobvious effect on the reliability of mechanical joints, it can be treated as a deterministic value to reduce the complexity of the analysis. In this paper, based on the reliability design theory, the sensitivity analysis method and the fourth moment technique, the reliability sensitivity of the mechanical joints with arbitrary distribution parameters is extensively discussed and a numerical method for reliability sensitivity design is presented. The variation regularities of reliability sensitivity are obtained and the effects of design parameters on reliability of the mechanical joints are studied. The method presented in this paper provides reasonable and necessary reliability basis for the design, manufacture, use and evaluation of the mechanical joints.

Sensitivity Analysis and Numerical Simulation of the Planar Mechanism Kinematic Accuracy

2012 ◽  
Vol 605-607 ◽  
pp. 1460-1464
Author(s):  
Rui Jun Zhang ◽  
Qing Xuan Jia ◽  
Liu Meng ◽  
Ji Wei Qiu
Keyword(s):  
Numerical Simulation ◽  
Sensitivity Analysis ◽  
Simulation Method ◽  
Analysis Method ◽  
Planar Mechanism ◽  
Kinematic Accuracy ◽  
Reliability Sensitivity ◽  
Reliability Sensitivity Analysis ◽  
Sensitivity Analysis Method ◽  
Mechanism Kinematic

A kind of accuracy sensitivity analysis and numerical simulation method about the mechanism kinematic is proposed for the purpose of getting the reliability sensitivity of the planar mechanism. Combining with the reliability sensitivity analysis method and the computer simulation technology, this method is on the basis of the research of the kinematics equations and the mechanism kinematic accuracy model. Taking the kinematic accuracy sensitivity analysis of the planar four-bar mechanism as an example, the results verify the effectiveness and feasibility of the method.

Reliability-Based Sensitivity Design of Beam Structure with Non-Normal Distribution

2007 ◽  
Vol 353-358 ◽  
pp. 2459-2462
Author(s):  
Xiang Dong He ◽  
Yi Min Zhang ◽  
Yu Chun Xue ◽  
Bang Chun Wen
Keyword(s):  
Sensitivity Analysis ◽  
Normal Distribution ◽  
Design Theory ◽  
Design Parameters ◽  
Analysis Method ◽  
Beam Structure ◽  
Reliability Based Design ◽  
Reliability Sensitivity ◽  
Sensitivity Analysis Method ◽  
Distribution Parameters

Based on the reliability-based design theory and sensitivity analysis method, the reliability-based sensitivity design of beam structure with non-normal distribution parameters is extensively researched and a numerical method for reliability-based sensitivity design is presented. The variation regularities of reliability sensitivity are obtained and the effects of design parameters on reliability of beam structure are studied. The method presented in this paper provided the theoretic basis for the reliability-based design of beam structure with non-normal distribution parameters.

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