Research On Efficient Statistical Moment Estimation And Reliability Analysis Method Based On Bivariate Dimension-reduction Model

When estimating statistical moment for complex random systems,the bivariate dimension-reduction method can alleviate the curse of dimension to some extent.However,there will be many bivariate component functions for high-dimension random system,which makes the estimation infeasible.For the stochastic system whose response function is implicit or complex,the adaptive dimension-reduction model based on orthogonal polynomial expansion is much more efficient than the existing orthogonal polynomial dimension-reduction model.However,when the system has a high degree of nonlinearity,the calculation efficiency is still not ideal.So,firstly,an efficient point estimations for moments is proposed in this paper,in which the dimension-reduction model is modified based on the Kriging approximation model.Then,we combines nonlinear degree judgment and cross-term judgment theorem to further improve the calculation efficiency.Finally,improving the existing dimension-reduction model based on orthogonal polynomial expansion which by introducing active dimension judgment criterion and the Kriging approximation model,and then we get the adative additive polynomial dimension-reduction model,the adative factorized polynomial dimension-reduction model and the adative hybrid polynomial dimension-reduction model.(1)Point estimations for statistical moments based on bivariate dimension-reduction model and Kriging approximation.Firstly,considering the characteristic of function approximation and abscissas of numerical integration,serveral point-selection strategies are proposed.Based on this point-selection strategy,a Kriging approximation model of the bivariate component function is developed.Then,replacing each bivariate component functions in the bivariate dimension-reduction model for original function or its moment function with their corresponding Kriging approximations,two modified methods for moments estimation are presented.Finally,through several examples,the efficiency and accuracy of several point selection strategies proposed in this paper are compared and analyzed,and a more preferred point selection strategy is obtained.Correspondingly,the statistical moment estimation of the proposed methods achieves comparable accuracy with the existing methods,but fewer function evaluations are required.(2)Point estimations for statistical moments based on adaptive-bivariate dimension reduction model and kriging approximation.First,introduce the nonlinear judgment method into the existing adaptive-bivariate dimension reduction model to determine the order of each variable,and then determine the number of integration nodes according to the order.Then,according to the combination of different integration node numbers,the corresponding point selection strategy is proposed,and based on this,developed he bivariate component function based on the Kriging approximation model.Then,replacing each bivariate component functions in the bivariate dimension-reduction model for original function or its moment function with their corresponding Kriging approximations,two modified methods for moments estimation are presented.Finally,the efficiency and accuracy of the proposed methods are verified by several examples.(3)The efficient adaptive orthogonal polynomial dimension-reduction model.In order to improve the efficiency of the existing adaptive orthogonal polynomial dimension-reduction model,this paper first introduces the Kriging approximation method of the bivariate component function proposed in the previous chapter into the calculation of the expansion coefficient of the orthogonal polynomial,and then introducing the active dimension judgment criterion into the dimension-reduction model to retain the important variables and reduce the number of bivariate component functions.Finally,the efficiency and accuracy of the proposed methods are verified by several examples.Finally,the main conclusions and innovations of this paper are briefly summarized,and the next research is prospected and discussed.