Structural Reliability Analysis And Stochastic Optimization Based On Cross Entropy Method

Structural reliability analysis and optimization attract considerable attention to researchers.Reliability and importance analysis can hardly achieve high efficiency and accuracy at once in small failure probability problems considering uncertainties especially in aeronautic and aerospace engineering.Meanwhile in the field of structural optimization,stochastic optimization methods are highly appreciated.Therefore exploring and improving a general method to deal with both the two kinds of problems have become an important topic in modern engineering community.Cross entropy method is a new kind of reliability analysis method which is efficient and adaptive in small failure probability problems and is also a stochastic optimization method with high efficientcy and strong global searching ability.However,cross entropy method will not make full use of all the random samples because part of the samples are located outside the region of interest and there is almost no application of cross entropy method in importance analysis.Additionally,cross entropy method may fail when solving complex optimization problems with high dimension and multiple constraints.Improved cross entropy methods for solving reliability analysis,importance analysis and stochastic optimization are studied in this thesis to overcome the shortcomings of the traditional one.A Gaussian mixture model is introduced to enhance the sample utilization by means of distributing samples adaptively around the region of interest and this model is also innovatively applied to importance analysis.In stochastic optimization problems,a new strategy for updating algorithm parameters is established on the base of current elite samples and global elite samples.Furthermore,variation operation is also used to avoid prematurity.The improved cross entropy method shows better computing performance in both reliability analysis and stochastic optimization.