Parameter Estimation by Optimization of Interpretable Hyperparameters with Physics-Informed Gaussian Processes

Abstract

In this work, the feasibility of a covariance-based parameter estimation approach utilising a physics-informed Gaussian process regression is considered and explored. There are a number of ways of incorporating physical assumptions or knowledge into a Gaussian process regression. One of the richest is through adapting the kernel to reflect some known behaviour of the system of interest. In some cases, it is possible to derive such covariance functions from stochastic differential equations, demonstrated for a singledegree- of-freedom (SDoF) oscillator in [1], where the result is a very flexible kernel that can be used in a variety of modelling situations. In this case, in aid of interpretability, the covariance function has hyperparameters that are the natural frequency and damping ratio of the SDoF system from which the covariance is derived. The current paper explores whether this model may feasibly be used for parameter estimation, and herein, an investigation into the SDoF kernel’s parameter estimation behaviour is conducted. This involves the visualisation of optimisation surfaces, exploration of what signal characteristics affect the estimates found, and finally, the proposal of a method to efficiently produce reliable parameter estimates. The estimates produced by this method show good agreement with the known system parameters over the range of systems tested, as well as good robustness to noise in the measured data.