Structural Reliability Analysis And Optimization Design Based On Parametric Density Estimation

Nowadays the chief content of reliability theory includes structural reliability analysis and reliability-based design optimization.This paper presents two efficient reliability analysis methods,an active learning function based on probability integral and take the proposed reliability analysis method into reliability-based design optimization.The main research contents are following:An adaptive mixture distribution based on normal-inverse Gaussian distribution is put forward to deal with the problem of the applicability of single distribution model and mixture distribution.In this paper,a limited condition is proposed to decide to choose which distribution we will use,a single distribution model or mixture distribution model.The proposal calculates the unknown parameters of distribution by matching the discrete values of Laplace transform,then reconstructs the probability density function of performance function.Five examples demonstrate the proposal can accurately predict failure probability of performance function,especially in rare events.An improved saddlepoint approximation method based on polynomial expansion is presented to deal with the inflexible assumption about cumulative generating function.The proposed approach which stems from the idea of iteration approximates the cumulative generating function of performance function by keeping increasing the number of terms of polynomial expansion.The unknown parameters of cumulative generating function are determined by solving system of the nonlinear equations at discrete values in cumulative generating function,the failure probability can easily be obtained by saddlepoint approach after obtaining cumulative generating function.When the change rate of the reliability index in the iteration is lower than given threshold for three consecutive times,the iteration is stopped and the final reliability index is output.For static problems,this paper considers a mixture cubature formula as numerical integral method.For dynamic problems,a numerical sampling based partially stratified sampling is used to calculate related numerical quadrature.The results illustrate that the proposed method can predict small failure probability in both static problems and high-dimensional dynamic structure.A new sequential experimental design point method in Bayesian Quadrature is presented to tackle the problem of expensive computation in reliability analysis.The new method of selecting training sample point is made by two parts,the first part deduces the error source that affects the result by the formula of Bayesian Quadrature,the second part presents a distance function that can measure the distance between a new sample point and training pool.A new selecting point method is presented based on these two parts.The results demonstrate this approach has a good trade-off in accuracy and efficiency compared to deterministic integral methods and sampling method.Besides,it can quantify the uncertainty of the value of integral while other methods cannot do.A sequential reliability-based design optimization based on quantile is used to calculate the design problem and the above-mentioned adaptive mixture distribution is applied to reconstruct cumulative distribution function of the probability constraint function in optimization and the corresponding quantile,the probabilistic constraint surface is replaced by a deterministic constraint surface by moving the limit state surface.When the change value of the optimization target before and after the two times is less than the given threshold value,if so,output the result,if not,continue the decoupling optimization,repeat the above operations until the conditions are met.Three examples demonstrate the proposed method is more efficient than other classical reliability-based design optimization methods.