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

TL;DR

This paper introduces the state space Kriging (S2K) model, a sparse surrogate for efficiently emulating complex nonlinear dynamical systems under stochastic excitation, using minimal training data.

Contribution

The paper proposes a novel S2K model that combines state space representation with sparse Kriging, and introduces a tailored training design for improved robustness.

Findings

S2K accurately predicts complex systems with limited training data.

The model outperforms existing surrogates in stochastic dynamical system emulation.

Validation on benchmarks confirms its robustness and efficiency.

Abstract

We present a new surrogate model for emulating the behavior of complex nonlinear dynamical systems with external stochastic excitation. The model represents 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 observed time histories of the state vector and its derivative with respect to time. 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 validate the performance of the S2K model with various benchmarks. The results show that S2K yields accurate prediction of complex nonlinear dynamical systems under stochastic excitation with only a few training time histories of state vector.