Flow-driven spectral chaos (FSC) method for long-time integration of second-order stochastic dynamical systems
Flow-driven spectral chaos (FSC) method for long-time integration of second-order stochastic dynamical systems
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DOI：
10.1016/j.cam.2021.113674
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发表时间：
2021-05
期刊：
影响因子：
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通讯作者：
Hugo Esquivel;A. Prakash;G. Lin
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文献类型：
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作者：
Hugo Esquivel;A. Prakash;G. Lin
几十年来，基于谱方法的不确定性量化技术已经被证明在计算上比蒙特卡罗方法更有效地处理各种问题，特别是在概率空间的维度相对较低的情况下。依赖于时间的广义多项式混沌(TD-GPC)就是这样一种技术，它使用演化的正交基来更好地表示解空间在时间上的随机部分。本文提出了一种新的数值方法，它利用丰富的随机流图的概念来跟踪解空间的随机部分在时间上的演化。与TD-GPC相比，流驱动随机混沌(FSC)方法的计算成本低一个数量级。这种计算成本的提高是因为，与大多数现有方法不同，跟踪解空间的随机部分所需的基向量的数量不依赖于概率空间的维度。文中给出了四个具有代表性的数值算例，以展示FSC方法在结构随机动力学背景下求解二阶随机动力系统长时间积分的性能。
For decades, uncertainty quantification techniques based on the spectral approach have been demonstrated to be computationally more efficient than the Monte Carlo method for a wide variety of problems, particularly when the dimensionality of the probability space is relatively low. The time-dependent generalized polynomial chaos (TD-gPC) is one such technique that uses an evolving orthogonal basis to better represent the stochastic part of the solution space in time. In this paper, we present a new numerical method that uses the concept ofenriched stochastic flow mapsto track the evolution of the stochastic part of the solution space in time. The computational cost of this proposed flow-driven stochastic chaos (FSC) method is an order of magnitude lower than TD-gPC for comparable solution accuracy. This gain in computational cost is realized because, unlike most existing methods, the number of basis vectors required to track the stochastic part of the solution space does not depend upon the dimensionality of the probability space. Four representative numerical examples are presented to demonstrate the performance of the FSC method for long-time integration of second-order stochastic dynamical systems in the context of stochastic dynamics of structures.