Uncertainty Bounds on Higher-Order FRFs from Gaussian Process NARX Models

One of the most versatile and powerful algorithms for the identification of nonlinear dynamical systems is the NARMAX (Nonlinear Auto-regressive Moving Average with eXogenous inputs) approach. The model represents the current output of a system by a nonlinear regression on past inputs and outputs and can also incorporate a nonlinear noise model in the most general case. In recent papers, one of the authors introduced a NARX (no noise model) formulation based on Gaussian Process (GP) regression and derived the corresponding expressions for Higher-order Frequency Response Functions (HFRFs). This paper extends the theory for the GP-NARX framework by providing a means of converting the GP prediction bounds in the time domain into bounds on the HFRFs. The approach is demonstrated on the Duffing oscillator.