Time-dependent uncertainty quantification analysis of complex dynamical systems

This paper presents a novel computational method, accompanied by robust numerical algorithms, for time-dependent uncertainty quantification (UQ) analysis of complex dynamical systems.The method involves a stochastic adaptation of the nonlinear auto regressive with exogenous input (NARX) model to accurately capture the underlying dynamical system behavior, a polynomial dimensional decomposition (PDD) of random coefficients generated by NARX, and a new integration between NARX and PDD, establishing the PDD-NARX approximation.The PDD-NARX method proposed is distinguished from conventional deterministic system identification tools by accounting for uncertainties arising both from the dynamic system properties (e.g., mass, stiffness, damping) and from the external forces (e.g., amplitude and frequency content of excitation time series).In addition, PDD, owing to its hierarchical, dimensionwise expansion, is capable of handling high-dimensional UQ problems better than many existing methods, including polynomial chaos expansion.Numerical results demonstrate that low-order PDD-NARX approximations not only provide accurate and computationally efficient estimates of the probabilistic characteristics of simple dynamical systems, but also underscore the method's effectiveness in addressing industrial-scale complex problems, as evidenced by the probabilistic vehicle dynamic analysis of a pick-up truck traversing road bumps.