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首页> 外文期刊>Applied Mathematical Modelling >Stochastic model order reduction in randomly parametered linear dynamical systems
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Stochastic model order reduction in randomly parametered linear dynamical systems

机译：随机参数线性动力系统中的随机模型阶数减少

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摘要

This study focuses on the development of reduced order models for stochastic analysis of complex large ordered linear dynamical systems with parametric uncertainties, with an aim to reduce the computational costs without compromising on the accuracy of the solution. Here, a twin approach to model order reduction is adopted. A reduction in the state space dimension is first achieved through system equivalent reduction expansion process which involves linear transformations that couple the effects of state space truncation in conjunction with normal mode approximations. These developments are subsequently extended to the stochastic case by projecting the uncertain parameters into the Hilbert subspace and obtaining a solution of the random eigenvalue problem using polynomial chaos expansion. Reduction in the stochastic dimension is achieved by retaining only the dominant stochastic modes in the basis space. The proposed developments enable building surrogate models for complex large ordered stochastically parametered dynamical systems which lead to accurate predictions at significantly reduced computational costs.
机译：这项研究的重点是用于对具有参数不确定性的复杂大阶线性动力学系统进行随机分析的降阶模型的开发，目的是在不影响求解精度的情况下减少计算成本。在此，采用了一种模型降阶的孪生方法。状态空间维数的减小首先通过系统等效缩减扩展过程实现，该过程包括线性变换，该变换将状态空间截断的影响与正常模式近似结合在一起。通过将不确定的参数投影到希尔伯特子空间中，并使用多项式混沌展开来获得随机特征值问题的解决方案，这些发展随后扩展到了随机情况。随机维度的减小是通过仅在基础空间中保留主要随机模式来实现的。拟议的发展使建立复杂的大型有序随机参数动力学系统的替代模型成为可能，从而以大大降低的计算成本实现了准确的预测。

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