The Study On Structural Reliability Algorithm Based On Random Variable Correlation And Failure Mode Correlation

In the reliability analysis of mechanical structure,there are two kinds of correlation problems: one is the correlation between random variables in single failure mode of a part,the other is the correlation between failure modes of mechanical structure system.Most of the existing reliability calculation methods,however,are based on the assumption that random variables and failure modes are independent of each other,and these calculation methods ignoring the correlation problem may have a great influence on the results of reliability analysis.Therefore,the problem of structural reliability considering different forms of correlation needs to be further studied.In this work,a series of researches are carried out on the reliability analysis considering the correlation between random variables in single failure mode and the correlation between failure modes in multiple failure modes.The main content of this dissertation is as follows:(1)The background and present situation of structural reliability research are reviewed.The importance and necessity of this work and the problems to be solved are proposed.The basic concepts of reliability theory and the commonly used reliability calculation methods as well as the analysis methods about the correlation are introduced,which lays a theoretical foundation for the follow-up study.(2)For the structure with explicit limit state function under the single failure mode,a mapping transformation method based on Nataf transformation is proposed when considering the correlation between random variables.The Non-normal distribution variables are first transforms into normal distribution variables by mapping transformation with this method,the Nataf transformation to describe the correlation between the random variables are then introduced and the structural reliability is calculated through First Order and Second Moment method.In addition,when the structure limit state function has strong nonlinearity,a Laplace asymptotic method considering the correlation of random variables is presented in this work,in which the two order partial derivative of the nonlinear performance function is introduced and the calculation precision of the reliability is improved.For structures with implicit limit state functions,an improved weighted response surfacemethod based on continuous interpolation sampling and a random response surface method based on Nataf transformation are proposed.For the first method,the continuous interpolation sampling method is used to obtain the new sampling point,then assigns different weights to the sampling points and obtains the response surface function by least square fitting;the mapping transformation method based on Nataf transformation is then applied to get the reliability of the function when considering the correlation between random variables.For the second method,the high-order Hermite polynomial is used to fit the response surface,and the correlation between random variables is considered at the match point stage;the sample points in the independent standard normal space are then selected based on the Nataf transformation,and the reliability of the fitting response surface function using Monte Carlo simulation is finally computed.In addition,considering the dynamic behavior of random loads,this paper derives the Performance function of structural dynamic reliability,then the function is fitted by the random response surface method,and the random response surface method is extended to the field of dynamic reliability.This two improved response surface methods provide a new way to solve the implicit structural reliability analysis with the correlation between random variables.(3)The reliability of the system with failure-dependent modes is analyzed in the context of multiple failure modes existing in the system.By using the mixed Copula function,the analysis model of system reliability is established when considering the correlation of failure modes.Firstly,aiming at the limitation of common Copula functions in describing the correlation of failure modes,a more flexible mixed Copula function is proposed by integrating the commonly used Copula functions by using linear weighting.The penalty release function of the mixed Copula function is then constructed,and the mathematical expression of the mixed Copula function is obtained from the parameter estimation of the penalty release function by using EM algorithm.Further,the system reliability analysis is finally carried out.In addition,and considering the correlation of each failure mode,a time-varying fuzzy reliability calculation method of the system is presented when considering the fuzziness and time-varying nature of the structural parameters and the correlation between the failure modes of components.