A Regular Vine Selection Strategy Based Reliability Analysis Method Research For Structural Variables

In the stage of engineering machinery design and manufacturing,reliability analysis of construction machinery structure is indispensable and important to ensure that the equipment produced has proper functions and service life under the following actual operating conditions.At present,researchers have adopted many reliability analysis methods to analyze the reliability of various construction machinery structures,but most reliability analysis methods consider structural variables as independent and irrelevant.However,in the actual structural reliability analysis of Engineering machinery,ignoring the complex correlation between variables will greatly affect the solution accuracy of the final analysis results.In recent years,Copula function proposed by statistician Sklar,with its flexibility and adaptability in dealing with correlation problems,has been firstly applied to data analysis in financial field and then introduced by scholars to deal with reliability analysis of mechanical structure with complex correlation variables step by step.Copula function can decompose the joint probability distribution function of variables difficult to obtain in general into edge distribution function of each variable which is relatively easy to obtain for analysis,so that when dealing with practical engineering problems with universal non-linear characteristics,it can still better describe the correlation form between variables and obtain more accurate joint probability distribution function.However,the binary Copula function,which focuses on research and application,can not be used to solve the problem of correlation variables above two dimensions,which greatly hinders its application in the field of structural reliability analysis of construction machinery.In order to make the binary Copula function realize the treatment of correlation between variables of higher dimensions,scholars combine the Vine tree type based on graph theory with the Copula function,and a Regular Vine Copula mathematical model comes into being.Based on the tree configuration of Regular Vine,the model can transform the joint distribution function of higher dimension complex correlation variables to the edge distribution function of each variable through the Air-Copula module constructed by several binary Copula functions.Although the construction of Regular Vine Copula mathematical model realizes the treatment of binary Copula function to the correlation problems of variables above two dimensions;However,there are a large number of highdimensional Regular Vine tree types.At present,C-Vine and D-Vine are two types of Regular Vine tree types used to solve the reliability analysis of Engineering structures.This not only can not accurately describe the complex correlation between structural variables of actual construction machinery,but also greatly reduces the flexibility of Regular Vine Copula mathematical model in dealing with complex correlation problems.Therefore,two selection strategies based on Regular Vine tree type are proposed in this paper.By obtaining the most appropriate Regular Vine tree type through the correlation variables of different reliability analysis problems,the solution accuracy of engineering structure reliability problems with complex correlation variables can be significantly improved.Based on the reliability analysis method dealing with correlated variables,this paper discusses the selection strategy of the correlation between the Regular Vine tree adaptive variables in the Regular Vine Copula mathematical model,so as to improve the accuracy of the solution of the reliability analysis problem dealing with correlated variables.The specific research contents are as follows:(1)Considering that previous researchers mostly used c-Vine or d-Vine tree to construct Regular Vine Copula model for the analysis of structural reliability problems with correlated variables,this paper proposes an overall tree selection strategy based on Regular Vine.Firstly,based on the C-Vine and D-Vine tree types,a certain kind of Regular Vine tree types are selected and selected based on AIC information criterion,and then combined with the firstorder reliability method(FORM)for reliability analysis;Then,the obtained reliability analysis results are compared with the Monte Carlo simulation results.Through the comparison with the relative error of the Monte Carlo simulation results,the adaptability of the selected optimal Regular Vine tree to the correlation form between variables in the reliability problem is verified.At the same time,it also reflects that correctly dealing with the correlation problem of variables is of certain significance to improve the accuracy of reliability analysis results.(2)As the number of Regular Vine tree types increases significantly with the increase of dimension,it is still difficult to correctly describe the correlation between variables by expanding several Regular Vine tree types based on the original C-Vine and D-Vine tree types.This paper proposes a layer by layer selection strategy of Regular Vine tree type.Based on AIC criteria and following the definition of Regular Vine tree,the strategy selects the optimal edge combination of each layer from top to bottom,so as to deduce the configuration of each level tree and realize the overall construction of the optimal Regular Vine tree;Compared with the overall selection strategy of Regular Vine tree,the layer by layer selection strategy of Regular Vine tree can better construct the Regular Vine tree adapting to the correlation of variables,and improve the accuracy of subsequent reliability analysis results.(3)Considering the complexity of solving reliability analysis algorithm based on Regular Vine tree type selection strategy,this paper builds a software platform for Regular Vine overall tree type selection and reliability analysis based on Visual Basic programming language(VB),realizes one-key input of parameters and one-key generation of calculation results,significantly simplifies the process of using the algorithm,and improves the efficiency of using the reliability analysis algorithm.