Stochastic model order reduction in randomly parametered linear dynamical systems

Abstract 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.

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