Reliability Sensitivity Analysis Method for Mechanical Components

Yan-Fang Zhang,Yan-Lin Zhang,Arturo J Fernández

doi:10.1155/2021/7867003

Abstract

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).

Highlights

E numerical simulation method can be divided into many different methods due to different sampling methods including importance sampling, direction sampling, line sampling, subset simulation, and low-discrepancy sampling [5,6,7,8,9,10]. ese different simulation methods are all based on Monte Carlo simulation but have different sampling methods
Analytic methods for reliability sensitivity analysis are always based on analytic reliability methods. ese reliability analysis methods are the mean-value first-order reliability method (MVFORM)/mean-value second-order reliability method (MVSORM) [11, 12], JC method, mean-value firstorder saddlepoint approximation (MVFOSA) [13], and moment method
A feasible method to compute the sensitivity of failure probability with respect to distribution parameters of basic random input variables is proposed. e method can be applied to estimate failure probability and reliability sensitivity based on Edgeworth series. e proposed reliability sensitivity analysis method includes the following steps

Summary

Response Origin Moments and Response Sensitivity

Where μ1 is the mean of ln X, and σ1 is the standard deviation of ln X. e kernel function of lognormal variable X with respect to μ1 and σ1 can be derived from equation (12) directly and can be written as follows: ln(x) −. Zσ zσ e kernel function of the lognormal distributed variable X with respect to its mean and standard deviation can be written as follows:. E kernel function of the Weibull distributed variable X with respect to scale parameter α and shape parameter β can be derived from equation (12) directly, which can be written as follows:. E kernel function of the Weibull distributed variable X with respect to its mean and standard deviation can be written as follows:. Where kα and kβ are the kernel functions with respect to scale parameter and shape parameter, respectively. α and β are the scale parameter and shape parameter of the two parameter Weibull distributed X, respectively

Reliability and Reliability Sensitivity Based on Edgeworth Series

Example 1

Example 2

Example 3