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Projection methods for stochastic dynamic systems: A frequency domain approach

机译：随机动态系统的投影方法：频域方法

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摘要

A collection of hybrid projection approaches are proposed for approximating the response of stochastic partial differential equations which describe structural dynamic systems. In this study, an optimal basis for the approximation of the response of a stochastically parametrised structural dynamic system has been computed from its generalised eigenmodes. By applying appropriate approximations in conjunction with a reduced set of modal basis functions, a collection of hybrid projection methods are obtained. These methods have been further improved by the implementation of a sample based Galerkin error minimisation approach. In total six methods are presented and compared for numerical accuracy and computational efficiency. Expressions for the lower order statistical moments of the hybrid projection methods have been derived and discussed. The proposed methods have been implemented to solve two numerical examples: the bending of a Euler-Bernoulli cantilever beam and the bending of a Kirchhoff-Love plate where both structures have stochastic elastic parameters. The response and accuracy of the proposed methods are subsequently discussed and compared with the benchmark solution obtained using an expensive Monte Carlo method. (C) 2018 Elsevier B.V. All rights reserved.
机译：提出了混合投影方法的集合，用于逼近描述结构动力系统的随机偏微分方程的响应。在这项研究中，已从其广义本征模计算出了随机参数化结构动力系统响应的最佳近似基础。通过将适当的近似值与一组简化的模态基础函数结合使用，可以获得混合投影方法的集合。通过实施基于样本的Galerkin误差最小化方法，这些方法得到了进一步的改进。总共提出并比较了六种方法的数值精度和计算效率。已经推导并讨论了混合投影方法的低阶统计矩的表达式。所提出的方法已经实现，可以解决两个数值示例：两个结构都具有随机弹性参数的Euler-Bernoulli悬臂梁的弯曲和Kirchhoff-Love板的弯曲。随后讨论了所提出方法的响应和准确性，并与使用昂贵的蒙特卡洛方法获得的基准解决方案进行了比较。 （C）2018 Elsevier B.V.保留所有权利。

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