A Local Gaussian Process Regression Approach to Frequency Response Function Estimation

TL;DR

This paper introduces a novel local Gaussian process regression method for frequency response function estimation, effectively addressing model order selection and lightly damped system identification with improved accuracy and robustness.

Contribution

The paper proposes LGPR, a new kernel-based local method that embeds prior knowledge to enhance FRF estimation, outperforming existing methods in accuracy and robustness.

Findings

LGPR achieves superior estimation accuracy compared to existing local methods.

LGPR demonstrates increased robustness to sample size and noise levels.

Numerical simulations validate the effectiveness of LGPR in practical scenarios.

Abstract

Frequency response function (FRF) estimation is a classical subject in system identification. In the past two decades, there have been remarkable advances in developing local methods for this subject, e.g., the local polynomial method, local rational method, and iterative local rational method. The recent concentrations for local methods are two issues: the model order selection and the identification of lightly damped systems. To address these two issues, we propose a new local method called local Gaussian process regression (LGPR). We show that the frequency response function locally is either analytic or resonant, and this prior knowledge can be embedded into a kernel-based regularized estimate through a dot-product kernel plus a resonance kernel induced by a second-order resonant system. The LGPR provides a new route to tackle the aforementioned issues. In the numerical simulations, the LGPR shows the best FRF estimation accuracy compared with the existing local methods, and moreover, the LGPR is more robust with respect to sample size and noise level.