Predicting Nonlinear Structural Dynamic Response of ODE Systems Using Constrained Gaussian Process Regression

Identification and characterization of a nonlinear structural dynamic system often involve inferring unknown parameters from experimental data. Compared to its linear counterparts, nonlinear systems include additional parameters related to the restoring force, making identifiability more challenging. In this chapter, we propose to augment linear structural dynamic models with empirically inferred state-dependent parameters to predict the responses of nonlinear structural dynamic models. Specifically, we represent the state-dependent parameter by a constrained Gaussian process regression (cGP). In addition to computational efficiencies, the use of cGP to constrain the model from uncertainty by incorporating prior knowledge is intended to enhance extrapolation performance. To demonstrate the feasibility and effectiveness of the proposed approach, we focus on a simple ordinary differential equations (ODEs) case study and impose the monotonicity constraint on a state-dependent parameter to highlight the impact of prior knowledge on predictive performance.