Point Estimation Method For Reliability And Its Application

The safety of engineering structures has always been an important issue in the field of civil engineering.Reliability analysis of engineering structures plays an important role in structural design and safety assessment.After continuous exploration,researchers have developed many reliability methods,such as numerical simulation methods,first/second-order reliability methods,response surface methods and high-order moment methods.Each method has its own advantages and disadvantages.The numerical simulation method has a simple analysis process,but the calculation cost is too large for complex structures;the first/second-order reliability method and the response surface method involve the solution of design points,but there are problems such as non-convergence of design point and multiple design points.In addition,the degree of polynomials in the response surface method and whether cross terms are considered will affect the accuracy of the calculation;the high-order moment method still has problems such as the scope of application and the selection of distribution types.Therefore,the basic idea of this paper is to transform the failure probability into probability integral,and then use the point estimation method to calculate the structural reliability,and propose the concept of the point estimation method for reliability analysis,trying to find a simple,easy and accurate reliability analysis methodThe study found that for the existence of independent linear random variables in the performance function(for the reliability of actual engineering structures,the component function of the load variable is usually linear),the failure probability of the structure can be directly expressed as the probability integral of the linear variable,and then the point estimation method is used to calculate the failure probability of the structure.Therefore,this paper introduces the factorized dimension-reduction approximation,cross-term judgment and the point estimation method based on the optimal reference variable,and proposes a reliability point estimation method based on the adaptive factorized dimension-reduction approximation.This method does not rely on design points,the analysis process is simple,and the calculation accuracy is good.The above method is suitable for the situation with obvious independent linear variables,but is not suitable for the complex or implicit performance function.Therefore,in order to expand the scope of application of the point estimation method for reliability analysis,the anisotropic response surface method and exact vector dimension-reduction are first introduced.The performance function can be decomposed into two parts: the linear component function and the component function of the residual vector.Then,the univariate factorized dimension-reduction approximation and point estimation method are introduced,and a new reliability analysis method is proposed: reliability point estimation method based on the univariate dimension-reduction approximate response surface and integral,and the feasibility and high accuracy of the new method are verified through calculation examples.In this paper,the reliability point estimation method based on univariate adaptive factorized dimension-reduction approximation and the reliability point estimation method based on univariate dimension-reduction approximate response surface are applied to the reliability analysis of a reinforced concrete frame structure.A finite element model was established based on ANSYS,and modal analysis was performed to study the internal force and deformation laws of the structure under earthquake action;combined with the equivalent extreme event theory and incremental dynamic analysis method,the dynamic reliability analysis of the high-rise building was performed,and the analysis results were consistent with In practice,it can provide theoretical support for engineering design.