Response Analysis Of Stochastic System And Its Application

Point estimate method(PEM) is one of the simplest and most efficient approaches for the stochastic system or reliability analysis. The precision of results and the efficiency of implement are two indexes to evaluate the performance of the point estimate algorithm, and precision is more important. Studies have shown that PEMs can’t ensure the accuracy when calculate higher non-linear or moments. To improve the precision of PEM, this article is concentrated on the degree judgement of non-linear, the dimension-reduction of response function and the numerical calculation.Choosing the number and co-ordinate of points are major parts of PEMs. Present PEMs translate random variables into standard normal space by adopt Rosenblatt transformation or Nataf transformation, then the co-ordinates are integral nodes under standard normal density function and the number is determined by degree judgment of non-linear. In 3rd chapter, two PEMs based on convergence principle have been proposed: One is the direct iterative point estimate method(DIPEM), in which all probability moments from different nodes are compared step by step until the results converge. The other is the adaptive iterative point estimate method(AIPEM), in which the degree of nonlinear for function is deduced via the difference of lower statistical moments from different nodes, then the number of necessary points is determined rationally and the corresponding moments are obtained. The improved iterative point estimate method(IIPEM) is proposed to raise the efficiency, which utilize points from the judgment by Gauss-Hermite quadrature with several preassigned nodes developed in chapter 2nd.On the other hand, improve efficiency and keep precision need a reasonable approximation of the response function and dimensionality reduction method is a theoretical support for that. But, univariate dimension-reduction method is not accuracy enough to keep precision even the precision is extremely productive, present bivariate dimension-reduction method and generalized dimension-reduction method can effectively improve the calculation accuracy, but the efficiency is drastically reduced. In chapter 4th, a judgment of the existence of cross terms has developed for dimensional decomposition optimization, and a PEM based on adaptive bivariate dimension-reduction is proposed.Finally, the explicit approximation for response function is different from PEM, but also high efficiency for stochastic response analysis, preliminary research just in 5th chapter. In this part, adopting the univariate dimension-reduction method to simplified function, judging non-linear degree of component function, approximating component function by Hermite orthogonal polynomial, then calculating the statistical moments. Research shows that the efficiency of stochastic response analysis based on approximation by orthogonal polynomial is much higher than IIPEM.