Efficient importance analysis methods for structures with distribution parameter uncertainty based on cubature formula

分布参数不确定性重要性分析的高效求积公式法

School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China

Received: 5 March 2022

Abstract

The importance analysis of a structural system with distribution parameter uncertainty can identify key parameters that significantly affect its output performance, thus providing importance guidance for its design and optimization. However, the traditional importance analysis method requires the three-loop Monte Carlo sampling to estimate the importance measurement index of a distribution parameter with such output characteristic values as mean and variance, whose computational cost is too large. To solve this problem, two efficient cubature formula methods based on the surrogate sampling probability density function (SSPDF) for the importance analysis of distribution parameters are proposed: ①the double-loop cubature formula based on the surrogate sampling probability density function (S-DLCF); ②the single-loop cubature formula based on the surrogate sampling probability density function (S-SLCF). The two methods use cubature formulas to efficiently compute the nested mean and variance in the importance measurement index of a distribution parameter, thus solving the problem that the computational effort of propagating parameter uncertainty to output characteristic values depends on parameter dimensionality because of SSPDF. The S-DLCF makes full use of the efficiency and accuracy of the cubature formula to estimate output statistical moments; the S-SLCF simplifies the integral to calculate output moments by expanding the dimensionality of the distribution parameter. The numerical and engineering examples verify the efficiency and accuracy of the two methods for the importance analysis of distribution parameters.

摘要

参数重要性分析能够识别对输出性能有重要影响的关键参数, 从而为结构系统的优化和设计提供指导。对于具有分布参数不确定性的结构系统, 传统方法求解分布参数对输出特征值(如均值和方差)的重要性测度指标需要3层抽样, 此过程计算量巨大。针对这一问题, 提出了2种基于代理抽样概率密度函数(SSPDF)的分布参数不确定性重要性分析的高效求积公式方法: 基于代理抽样概率密度函数的双层求积公式方法(S-DLCF)和基于代理抽样概率密度函数的单层求积公式方法(S-SLCF)。所提方法利用求积公式有效地提高了分布参数重要性测度指标中嵌套的期望和方差算子求解效率, 并通过代理抽样概率密度函数解除了参数不确定性向输出特征值传递过程中计算量依赖于参数维度的问题。S-DLCF充分利用了求积公式在求解输出统计矩时的高效性和准确性, 而S-SLCF通过扩展分布参数的维数来减少输出统计矩计算过程中的积分层数。数值算例和工程算例验证了2种新算法在参数重要性分析中的效率和精度。