Adaptive Dimensional Decomposition Based On Orthogonal Polynomial And Its Application

In stochastic system analysis,"Curse of Dimensionality" is a difficult problem in computing.The dimension-reduction approximation is one of the solutions to solve the problem.However,the existing Dimension-reduction method still irrational model selection and Inefficient.As two difficult problems in stochastic systems,reliability analysis and composite random vibration analysis are also faced with the problem of " Curse of Dimensionality".The existing methods are still complicated and inefficient.Therefore,this paper develops an Adaptive dimensional decomposition based on orthogonal polynomial,and all kinds of reliability and the composite random vibration are analyzed.(1)Adaptive dimension-reduction approximation method based on orthogonal polynomials.The accuracy of the dimensionality reduction approach is influenced by the composition of the response function,and the response functions usually need to be iterated to ensure the accuracy of the calculation.The iteration results in the low efficiency of the calculation and even the result is not convergent.In this paper,firstly,according to the different probability information of random variables,it is divided into multiple sub vectors and converted into appropriate reference vectors,and the corresponding orthogonal polynomials are selected for each reference variable to fit the component function.Then the nonlinear degree method of the single variable function is derived,thus the orthogonal polynomial order is directly determined.No need to be iterated;the cross term judgment theorem is introduced,so that the non existent component functions need not be fitted.Based on this perfect adaptive orthogonal polynomial approximation method,the feasibility and efficiency accuracy of this method are verified by an example.(2)Reliability analysis based on orthogonal polynomial reduction dimension approximation.The existing response surface method involves high dimensional problems with low aging rate,especially for the reliability and dynamic reliability of structural systems.In this paper,the proposed method is used to solve the reliability degree of the component,the reliability of the system and the reliability of the power.The reliability of the component is solved by the response surface method based on the adaptive orthogonal polynomial reduction approximation.After the explicit expression is obtained,the reliability index is calculated by Monte Carlo method.The system reliability of the failure mode and the dynamic reliability of the dynamic load are solved by using the equivalent extreme value event to get a single function function,and then the adaptive orthogonal polynomial approximation method is used to fit it,and the reliability is finally obtained by the Monte Carlo method.Finally,the accuracy and efficiency of this method in various reliability problems are verified by various examples.(3)Analysis and study of composite random vibration method.Compound random vibration is one of the difficult problems in stochastic analysis.Because of its double randomness,it will be more difficult to solve it when the system parameters are of high dimension.In this paper,the complex random vibration problem is converted into a statistical moment estimation problem of general random vibration analysis by means of conditional system derivation.Then,the explicit expression of the response of the composite random system is obtained by introducing the virtual excitation method and the time domain explicit analysis method in the analysis of the general random vibration.In the solution,the adaptive orthogonal polynomial approximation method and the point estimation method are introduced,and the efficient method of complex random vibration analysis is obtained.Finally,the feasibility and efficiency of the proposed method are verified by an example.Finally,the main conclusions and innovations of this paper are briefly summarized,and the next research is prospected and discussed.