A hybrid spectral and metamodeling approach for the stochastic finite element analysis of structural dynamic systems
A hybrid spectral and metamodeling approach for the stochastic finite element analysis of structural dynamic systems
复制标题
DOI：
10.1016/j.cma.2013.11.013
复制
发表时间：
2014-03
影响因子：
7.2
通讯作者：
A. Kundu;F. DiazDelaO;S. Adhikari;M. Friswell
中科院分区：
文献类型：
--
作者：
A. Kundu;F. DiazDelaO;S. Adhikari;M. Friswell
本文提出了一种随机参数化结构动力系统不确定性传播和响应统计估计的新方法。随机有限元系统的频域响应是解决在随机采样的设计点的输入随机空间与无限级数展开使用预处理随机Krylov基。系统响应表示在结构系统的特征向量空间中，用输入随机变量的有限阶有理函数加权，称为谱函数。谱函数的阶数越高，随机系统响应的近似阶数就越精确。然而，这种提高的准确性是以计算成本为代价的。通过使用贝叶斯元模型可以降低此成本。将该方法用于分析具有随机弹性参数的波纹板的随机振动响应。与建议的混合方法得到的结果进行比较，直接蒙特卡罗模拟，已被视为基准解决方案。
A novel approach for uncertainty propagation and response statistics estimation of randomly parametrized structural dynamic systems is developed in this paper. The frequency domain response of a stochastic finite element system is resolved at randomly sampled design points in the input stochastic space with an infinite series expansion using preconditioned stochastic Krylov bases. The system response is expressed in the eigenvector space of the structural system weighted with finite order rational functions of the input random variables, termed spectral functions. The higher the order of the spectral functions, the more accurate is the order of approximation of the stochastic system response. However, this increased accuracy comes at a computational cost. This cost is mitigated by using a Bayesian metamodel. The proposed approach is used to the analyze the stochastic vibration response of a corrugated panel with random elastic parameters. The results obtained with the proposed hybrid approach are compared with direct Monte Carlo simulations, which have been considered as the benchmark solution.