State Space Kriging model for emulating complex nonlinear dynamical systems under stochastic excitation

Surrogate modeling can drastically reduce the computational efforts when evaluating complex nonlinear dynamical systems subjected to stochastic excitation. However, existing surrogate modeling techniques suffer from the “curse of dimensionality” when emulating complex nonlinear systems due to the discretization of the stochastic excitation. In this work, we present a new surrogate model framework for efficient performance assessment of complex nonlinear dynamical systems with external stochastic excitations. Instead of learning the high-dimensional map from the stochastic excitation to model the response quantity of interest, we propose to learn the system dynamics in state space form, through a sparse Kriging model. The resulting surrogate model is termed state space Kriging (S2K) model. Sparsity in the Kriging model is achieved by selecting an informative training subset from the whole observed training time histories. We propose a tailored technique for designing the training time histories of state vector and its derivative, aimed at enhancing the robustness of the S2K prediction. We compare the performance of S2K model to the NARX (auto-regressive with exogenous input) model with various benchmarks. The results show that S2K outperforms the NARX model up to several orders of magnitude in accuracy. It yields an accurate prediction of complex nonlinear dynamical systems under stochastic excitation with only a few training time histories. This work paves the way for broader application of state space surrogate modeling for emulating stochastic dynamical systems in various scenarios that require the rapid evaluation of response trajectories of systems subject to stochastic excitations.