Numerical Method For Structural Reliability Analysis Based On Statistical Moments

In the design of engineering structure,it is necessary to follow the principles of safety,reliability,applicability,aesthetics and durability,etc.Whether the structure is safe and reliable or not only affects the normal use of the structure,but also relates to the safety of people.Therefore,the analysis of structural reliability is particularly important to guarantee the overall safety of the structure.The moment method is a reliability theory based on the statistical moments of random system response in the existing reliability analysis methods,that is widely used because it is simple and does not need to calculate the gradient of the performance function.The reliability analysis based on moment method is to calculate the statistical moment of structural performance function according to the known distribution of basic random variables,and to obtain the failure probability by integrating the probability density function over the failure domain by fitting the probability density function through the parametric distribution model.In this paper,the numerical methods for the statistical moments assessment of performance functions are studied according to the distribution of input random variables,and the probability density function(PDF)of performance functions is constructed by using the shifted generalized lognormal distribution(SGLD)model,so as to find a more accurate and efficient result reliability analysis method.The main research work is as follows:An adaptive trivariate dimension-reduction method based on High-order unscented transformation(HUT)is proposed for the problem of the huge number of three-dimensional integrals and the quadrature points in numerical integrals.H ighorder unscented transformation is a simple and efficient method to estimate the high-order moments of output variables,the basic idea of that is to select a set of points and corresponding weights to match the high-order moments of the input variables,and then estimate the statistical moments of the output variables through the nonlinear transformation and weights of the points,thus providing a new way to calculate the high-dimensional integrals.The cross term criterion is introduced to reduce the n umber of high-dimensional integrals to improve the computational efficiency.The structural reliability analysis of explicit and implicit performance function proves the feasibility of the adaptive trivariate dimension-reduction method based on HUT for accuracy and efficiency.A statistical moment assessment method based on the fifth-degree cubature formula with free parameters is proposed,named improved fifth-degree cubature formula.The method first needs to input the precise first four moments of the random variable.Then,the first-four central moments of the input variables are approximated by using the integral points of the fifth-degree cubature formula with free parameters in the selected parameter range,and the optimal parameters are determined by the moment error minimization.Finally,the optimal parameters are substituted into the fifth-degree cubature formula to obtain the statistical moment of the performance function.Compared with the traditional fifth-degree cubature formula,this method introduces a free parameter to make the integral points match with the input variable better,which could reduce the error of estimating the statistical moment of performance function and improve the calculation accuracy.However compared with the sevent hdegree cubature formula,the improved fifth-degree cubature formula has less computational work on the basis of maintaining the accuracy,especially in the case of a large number of variables.