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Time-dependent uncertainty quantification analysis of complex dynamical systems
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DOI：10.1016/j.probengmech.2025.103776.png)
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Abstract
En 中文
This paper introduces a novel computational methodology, supported by robust numerical algorithms, for performing time-dependent uncertainty quantification (UQ) analysis on complex dynamical systems. The proposed approach consists of three key components: (1) a new stochastic adaptation of the nonlinear autoregressive with exogenous input (NARX) model, utilizing dimension-wise tensor product expansion to effectively capture the behavior of dynamical systems, (2) a polynomial dimensional decomposition (PDD) technique to propagate uncertainty in input random variables to the NARX coefficients, and (3) a unique integration between NARX and PDD, resulting in the PDD-NARX approximation for time-dependent UQ analysis. The PDD-NARX method distinguishes itself from conventional deterministic system identification tools by considering uncertainties originating from both the system’s dynamic properties (e.g., mass, stiffness, and damping) and external forces (e.g., amplitude and frequency content of excitation time series). Unlike traditional methods, which rely on an intuitive selection of NARX basis functions, this approach employs dimensional decomposition and importance factors to systematically construct the NARX model function. Furthermore, PDD, due to its hierarchical, dimension-wise expansion, is better equipped to handle high-dimensional UQ problems than many existing methods, including the widely recognized polynomial chaos expansion. Numerical results demonstrate that low-order PDD-NARX approximations provide accurate and computationally efficient estimates of the probabilistic characteristics of simple dynamical systems. Moreover, the probabilistic vehicle dynamic analysis of a pick-up truck traversing road bumps underscores the effectiveness of the PDD-NARX method in addressing industrial-scale complex problems.
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