基于多项式混沌展开和KL散度的随机有限元模型修正

STOCHASTIC FINITE ELEMENT MODEL UPDATING BASED ON POLYNOMIAL CHAOTIC EXPANSION AND KL DIVERGENCE

考虑结构参数不确定性对响应的影响以及当前随机模型修正计算量大的问题,提出一种基于多项式混沌展开和KL散度的随机有限元模型修正方法。首先构建Kriging模型代替有限元模型分析,然后基于概率配点法和回归分析构建多项式混沌展开模型,建立起不确定性结构参数与响应之间的函数关系,快速估算响应的均值和标准差。最后以最小化KL散度为目标,同时对结构参数的均值和标准差进行修正。以三维桁架为例,对弹性模量和密度的均值和标准差进行修正,以此验证所提方法的可行性。结果表明:所提方法具有较高的修正精度和效率。

Considering the influence of structural parameter uncertainty on response and the problem of large calculation of stochastic model updating, a stochastic finite element model updating method based on polynomial chaotic expansion and KL divergence is proposed. Firstly, Kriging model is constructed instead of finite element model analysis, then polynomial chaotic expansion model is constructed based on probabilistic collocation method and regression analysis, and the functional relationship between uncertain structural parameters and response is established to quickly estimate the mean value and standard deviation of response. Finally, the mean value and standard deviation of structural parameters are modified to minimize KL divergence. Taking three-dimensional truss as an example, the mean value and standard deviation of elastic modulus and density are modified to verify the feasibility of the proposed method. The results show that the proposed method has high updating accuracy and efficiency.