On the application of Gaussian process latent force models for Bayesian identification of the Duffing system

Throughout the past 50 years, researchers have been developing methods for identification of systems that are behaving nonlinearly due to the more frequent occurrence of nonlinearity in the mechanical and structural dynamics. The paper presents a novel and modern approach to the problem of nonlinear system identification by combining a physical system model and a technique from machine learning in a Bayesian framework. A state-space model is employed to represent the underlying linear system together with a latent force model to constitute the nonlinear forces, which is modelled by a Gaussian process. The Bayesian identification of the system is enabled by the use of the Kalman filter and inference is performed using the Markov-Chain Monte-Carlo method. This gives posterior distributions over the system parameters and produces a prediction of the nonlinear forces. The method is demonstrated on a simulation of the Duffing equation, based on which it is concluded that it shows to be a promising method for identification of nonlinear systems.