Structural Reliability Evaluation And Optimization Design Based On Copula Functions

Structural reliability evaluation and optimization design method are extensively applied to various industrial fields.The purpose is to ensure that the mechanical structural can be lightweight as much as possible and prolong the life length on the premise of accomplishing the prescribed functions.Meanwhile,the uncertainties of load,structure size,material attributes and the correlation of design variables also affect the structural reliability index and optimization results,which can be not ignored.Copula function,as a tool for describing the dependency mechanism among variables,contains almost all the dependency information of random variables.In this paper,Copula function is introduced to make the description of the correlation among design variables more perfect.Firstly,a reliability evaluation method based on Copula functions is proposed to improve the method of solving the reliability problem with correlated evidence variables.The method introduces deterministic optimization on the basis of the existing reliability evaluation method.By a small number of iterations,the extreme point on the focal element is solved,and the reliability interval is obtained by the method of evidence theory.The calculation results of numerical examples show that this method avoids the error caused by the improper selection of the step length,and this method has satisfactory calculation results for the linear,nonlinear and implicit functions of the limit state function.And the proposed method improves the calculation efficiency under the condition of ensuring the calculation accuracy.Secondly,a reliability decoupling optimization method based on threshold factor and tail correlation between optimization design variables is proposed in the second part of this paper,which aims to improve the computational efficiency and reduce the calculation errors caused by the independence assumption in the capturing process.This method makes full use of the capability of capturing optimization variables tail dependencies of Copula functions to study the joint extreme motion among optimization variables.This method gives the extreme events of variables in the form of Copula function,and embeds the threshold factor into the limit state function of reliability optimization models.The numerical examples show that Archimedean Copula function family has certain advantages in the process of studying tail correlation of optimization design variables.It can describe tail correlation of upper tail correlation,lower tail correlation and mixed tail correlation,and its application process is simple and changeable.