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 of \emph{enriched stochastic flow maps} to 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, and consequently the computational cost associated with the solution of the resulting system of equations, 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.

翻译：几十年来,基于光谱方法的不确定性量化技术被证明比蒙特卡洛方法在一系列广泛问题上的计算效率更高,特别是当概率空间的维度相对较低时。基于时间的通用多元混杂(TD-gPC)是一种技术,它使用一个不断演变的正方位基础,以更好地代表解决办法空间的随机部分。在本文件中,我们提出了一个新的数字方法,使用mph{enried schochatical 流图的概念来跟踪解决办法空间的随机部分的演变过程。这一拟议流动驱动的随机混乱(FSC)方法的计算成本比TD-gPC的可比较溶性准确性要低一个数量级。计算成本的提高是因为与大多数现有方法不同,跟踪解决办法空间的随机部分所需的基础矢量数量,以及由此产生的方程式的解决方案的计算成本,并不取决于空间概率空间的第二个层面。四个具有代表性的方位化性能模型展示了FS-sti结构的概率。