Uncertainty quantification of nonlinear stochastic dynamic problem using a Kriging-NARX surrogate model
Résumé
Uncertainty quantification of nonlinear stochastic dynamic problem is always a challenging task due to the complexity of the systems. In this paper, a hybrid surrogate modelling approach is proposed for the uncertainty quantification of nonlinear stochastic dynamical systems in the time domain. The proposed hybrid surrogate model is constructed using a nonlinear system identification tool, the Nonlinear AutoRegressive with eXogenous (NARX) input model, and the Kriging approach for uncertainty propagation. Further, to increase the computational efficiency, least angle regression (LARS) is utilized in the hybrid framework. The method is applied on a nonlinear stochastic dynamic oscillator to check its applicability. The time dependent mean and standard deviation are predicted using the proposed approach, and all the results are compared with the Monte Carlo simulation (MCS) results. A high-level accuracy is noticed using the proposed approach as compared to other state-of-the-art methods. This accuracy is achieved using a very limited number of model evaluations which is suggesting the efficiency of the proposed approach. Moreover, an excellent accuracy and efficiency is achieved using the proposed approach in predicting the probability density function (PDF) at several time instances for the nonlinear stochastic dynamic oscillator.