A Kriging–NARX Model for Uncertainty Quantification of Nonlinear Stochastic Dynamical Systems in Time Domain
Publication: Journal of Engineering Mechanics
Volume 146, Issue 7
Abstract
A novel approach, referred to as sparse Kriging–NARX (KNARX), is proposed for the uncertainty quantification of nonlinear stochastic dynamical systems. It combines the nonlinear autoregressive with exogenous (NARX) input model with the high fidelity surrogate model Kriging. The sparsity in the proposed approach is introduced in the NARX model by reducing the number of polynomial bases using the least-angle regression (LARS) algorithm. Sparse KNARX captures the nonlinearity of a problem by the NARX model, whereas the uncertain parameters are propagated using the Kriging surrogate model, and LARS makes the model efficient. The accuracy and the efficiency of the sparse KNARX was measured through uncertainty quantification applied to three nonlinear stochastic dynamical systems. The time-dependent mean and standard deviation were predicted for all the numerical examples. Instantaneous stochastic response characteristics and maximum absolute response were also predicted. All the results were compared with the full scale Monte Carlo simulation (MCS) results and a mean error was calculated for all the numerical problems to measure the accuracy. All the results had excellent agreement with the MCS results at a very limited computational cost. The efficiency of the sparse KNARX also was measured by the CPU time and the required number of surrogate model evaluations. In all instances, sparse KNARX outperformed other state-of-the-art methods, which justifies the applicability of this model for nonlinear stochastic dynamical systems.
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Data Availability Statement
Some or all data, models, or code generated or used during the study are available from the corresponding author by request, including theNARX model, and the NARX polynomial basis functions.
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Published In
Journal of Engineering Mechanics
Volume 146 • Issue 7 • July 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Jul 9, 2019
Accepted: Jan 17, 2020
Published online: Apr 29, 2020
Published in print: Jul 1, 2020
Discussion open until: Sep 29, 2020
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