Global Sensitivity Analysis On Dynamic Polynomialchaos Expansion Method

Partial least squares regression method can well consider the correlation between variables.The integrity of modeling is strong.The general method usually reduces the problem of multi-dependent variable-to-variable regression to a simple superposition of multiple single-dependent variable regression problems.Partial least squares regression will make up for this defect,avoid calculation redundancy,and give full play to the advantages of polynomial chaos expansion method.In the field of global sensitivity analysis,this paper integrates nonlinear partial least squares regression ideas and multi-dependent variable models into the existing partial least squares-polynomial chaos expansion agent model method.The rationality and efficiency of the method are verified through static and dynamic examples.The research content of this paper mainly includes the following three points:(1)For the single dependent variable model,the quadratic internal relationship in the nonlinear partial least squares idea is integrated into the linear partial least squarespolynomial chaos expansion agent model method to obtain the nonlinear partial least squares-polynomial chaos expansion agent model method.The results of the calculation example show that,given the same number of known sample points,the global sensitivity index obtained by this method is closer to the reference solution obtained by Monte Carlo simulation than the linear agent model method.It shows that the single dependent variable nonlinear partial least squares-polynomial chaos expansion agent model method has higher accuracy.(2)For the multi-dependent variable model,the multi-dependent variable expansion based on the linear partial least squares-polynomial chaos expansion agent model method can effectively analyze the static multi-dependent variable problem.The result of the calculation example shows that under the condition that the number of sample points is consistent,the calculation accuracy of the multi-dependent variable agent model method for the global sensitivity of one of the dependent variables is not lower than that of the single dependent variable agent model method.And based on the multi-output weighted global sensitivity analysis concepts and methods established in this paper,the multi-dependent variable agent model method can calculate the effect index of a single input variable (34)on the overall output response Y.Therefore,it is possible to quantitatively examine the overall importance of the input variables to all output responses.But for the nonlinear dynamic problem,the calculation result of this method is not accurate.(3)For the multi-dependent variable model,the nonlinear partial least square regression idea and the multi-dependent variable model are simultaneously integrated into the existing partial least squares-polynomial chaos expansion agent model method,and the multi-dependent variable nonlinear partial least squares is established.The results of the calculation example show that the method can make full use of the information of the known sample points in the static and dynamic problems with multiple dependent variables.In the case of a small number of known samples,it is still possible to identify the random variables with important influence more accurately.Especially when the output variable and the input variable have a curvilinear relationship,the multi-dependent variable nonlinear model reduces the number of independent variables in the polynomial chaos expansion from the source to increase the modeling speed and reduce the calculation cost.