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).

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 Fatigue Reliability Sensitivity Analysis of Complex Mechanical Components under Random Excitation

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Hao Lu ◽  
Yimin Zhang ◽  
Xufang Zhang ◽  
Xianzhen Huang
Keyword(s):  
Sensitivity Analysis ◽  
Random Excitation ◽  
Design Parameters ◽  
State Function ◽  
Fourth Moment ◽  
Fatigue Reliability ◽  
Random Load ◽  
Reliability Sensitivity ◽  
Reliability Sensitivity Analysis ◽  
Mechanical Components

Fatigue failure is the typical failure mode of mechanical components subjected to random load-time history. It is important to ensure that the mechanical components have an expected life with a high reliability. However, it is difficult to reduce the influence of factors that affect the fatigue reliability and thus a reliability sensitivity analysis is necessary. An approach of fatigue reliability sensitivity analysis of complex mechanical components under random excitation is presented. Firstly, load spectra are derived using a theoretical method. A design of experiment (DOE) is performed to study the stresses of dangerous points according to the change of design parameters of the mechanical component. By utilizing a Back-Propagation (BP) algorithm, the explicit function relation between stresses and design parameters is formulated and thus solves the problem of implicit limit state function. Based on the damage accumulation (DA) approach, the probability perturbation method, the fourth-moment method, the Edgeworth expansion is adopted to calculate the fatigue reliability and reliability-based sensitivity. The fatigue reliability sensitivity analysis of a train wheel is performed as an example. The results of reliability are compared with that obtained using Monte Carlo simulation. The reliability sensitivity of design parameters in the train wheel is analyzed.

Reliability sensitivity of automobile components with arbitrary distribution parameters

2005 ◽  
Vol 219 (2) ◽  
pp. 165-182 ◽  
Author(s):  
Y M Zhang ◽  
X D He ◽  
Q L Liu ◽  
B C Wen ◽  
J X Zheng
Keyword(s):  
Sensitivity Analysis ◽  
Design Theory ◽  
Arbitrary Distribution ◽  
Reliability Based Design ◽  
Edgeworth Series ◽  
Sensitivity Theory ◽  
Reliability Sensitivity ◽  
Distribution Parameters ◽  
Automobile Components ◽  
First Four Moments

Techniques from the perturbation method, the Edgeworth series, the reliability-based design theory, and the sensitivity analysis approach are employed to present a practical and efficient method for the reliability sensitivity of automobile components with arbitrary distribution parameters. On the condition of first four moments of original random variables known, the reliability sensitivity theory and case studies are researched. The respective program can be used to obtain the reliability sensitivity of automobile components with arbitrary distribution parameters accurately and quickly.

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.

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.

Reliability and Sensitivity Analysis of Mechanical Structures Based on Dimension Reduction Method

2014 ◽  
Vol 635-637 ◽  
pp. 411-416
Author(s):  
Shu Xin Zhang ◽  
Kai Chao Yu
Keyword(s):  
Sensitivity Analysis ◽  
Dimension Reduction ◽  
Reduction Method ◽  
Random Variables ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Dimension Reduction Method ◽  
Distribution Parameters ◽  
Analytic Derivation ◽  
Random Responses

This paper presents a method for probabilistic sensitivity analysis of mechanical components or structural systems subject to random uncertainties in loads, material properties and geometry. The bi-variate dimension reduction method is applied to compute the response moments and their sensitivities with respect to the distribution parameters of basic random variables. Saddlepoint approximations with truncated cumulant generating functions are employed to estimate the probability density functions and cumulative distribution functions of the random responses. The rigorous analytic derivation of the sensitivities of the probability of failure of the systems under consideration with respect to the distribution parameters of basic random variables is derived. Finally, the practicality and efficiency of the proposed method are demonstrated by an application example.

scholarly journals Reliability sensitivity analysis of coherent systems based on survival signature

2018 ◽  
Vol 232 (6) ◽  
pp. 627-634 ◽  
Author(s):  
Xianzhen Huang ◽  
Frank PA Coolen
Keyword(s):  
Sensitivity Analysis ◽  
Lifetime Distribution ◽  
Relative Importance ◽  
Rank Distribution ◽  
Coherent Systems ◽  
Reliability Improvement ◽  
Reliability Sensitivity ◽  
Reliability Sensitivity Analysis ◽  
Distribution Parameters ◽  
Overall Reliability

The reliability sensitivity can be used to rank distribution parameters of system components concerning their impacts on the system’s reliability. Such information is essential to purposes such as component prioritization, reliability improvement, and risk reduction of a system. In this article, we present an efficient method for reliability sensitivity analysis of coherent systems using survival signature. The survival signature is applied to calculate the reliability of coherent systems. The reliability importance of components is derived analytically to evaluate the relative importance of the component with respect to the overall reliability of the system. The closed-form formula for the reliability sensitivity of the system with respect to component’s distribution parameters is derived from the derivative of lifetime distribution of a component to further investigate the impacts of the distribution parameters on the system’s reliability. The effectiveness and feasibility of the proposed approaches are demonstrated with two numerical examples.

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