Physics-derived covariance functions for machine learning in structural dynamics⁎The authors would like to acknowledge the support of the EPSRC, particularly through grant reference number EP/S001565/1. Issue 7 (2021)

• Record Type: Journal Article
• Authors: Cross, Elizabeth J.; Rogers, Timothy J.
• Is Part Of: IFAC-PapersOnLine. Volume 54:Issue 7(2021)
• Page Start: 168
• Page End: 173
• Publication Date: 2021
• Subjects: Bayesian methods -- mechanical -- aerospace estimation -- grey-box modelling -- physics-informed machine learning -- time-series modelling -- stochastic systems; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2021.08.353
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: This paper attempts to bridge the gap between standard engineering practice and machine learning when modelling stochastic processes. For a number of physical processes of interest, derivation of the (auto)covariance is achievable. This paper suggests their use as priors in a standard Gaussian process regression as a means of enhancing predictive capability in situations where they are reflective of the process of interest. A covariance function of a linear oscillator under random load is derived and used in a regression context to predict the displacements of a vibratory system. A simulation case study is used to demonstrate the enhancement over a standard Gaussian process regression model.