多项式混沌
非线性系统
不确定度量化
有限元法
水准点(测量)
蒙特卡罗方法
维数之咒
降维
计算机科学
维数(图论)
应用数学
不确定性传播
数学优化
计算力学
还原(数学)
多项式的
算法
数学
结构工程
人工智能
工程类
机器学习
物理
数学分析
统计
量子力学
几何学
大地测量学
地理
纯数学
作者
Éder Domingos de Oliveira,Udo Nackenhorst
标识
DOI:10.1016/j.probengmech.2023.103556
摘要
Finite Element Simulations in solid mechanics are nowadays common practice in engineering. However, considering uncertainties based on this powerful method remains a challenging task, especially when nonlinearities and high stochastic dimensions have to be taken into account. Although Monte Carlo Simulation (MCS) is a robust method, the computational burden is high, especially when a nonlinear finite element analysis has to be performed behind each sample. To overcome this burden, several “model-order reduction” techniques have been discussed in the literature. Often, these studies are limited to quite smooth responses (linear or smooth nonlinear models and moderate stochastic dimensions). This paper presents systematic studies of the promising Sparse Polynomial Chaos Expansion (SPCE) method to investigate the capabilities and limitations of this approach using MCS as a benchmark. A nonlinear damage mechanics problem serves as a reference, which involves random fields of material properties. By this, a clear limitation of SPCE with respect to the stochastic dimensionality could be shown, where, as expected, the advantage over MCS disappears. As part of these investigations, options to optimize SPCE have been studied, such as different error measures and optimization algorithms. Furthermore, we have found that combining SPCEs with sensitivity analysis to reduce the stochastic dimension improves accuracy in many cases at low computational cost.
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