On the application of Gaussian process latent force models for joint input-state-parameter estimation : With a view to Bayesian operational identification

The problem of identifying dynamic structural systems is of key interest to modern engineering practice and is often a first step in an analysis chain, such as validation of computer models or structural health monitoring. While this topic has been well covered for tests conducted in a laboratory setting, identification of full-scale structures in place remains challenging. Additionally, during in service assessment, it is often not possible to measure the loading that a given structure is subjected to; this could be due to practical limitations or cost. Current solutions to this problem revolve around assumptions regarding the nature of the load a structure is subject to; almost exclusively this is assumed to be a white Gaussian noise. However, in many cases this assumption is insufficient and can lead to biased results in system identification. This current work presents a model which attempts the system identification task (in terms of the parametric estimation) in conjunction with estimation of the inputs to the system and the latent states --- the displacements and velocities of the system. Within this paper, a Bayesian framework is presented for rigorous uncertainty quantification over both the system parameters and the unknown input signal. A Gaussian process latent force model allows a flexible Bayesian prior to be placed over the unknown forcing signal, which in conjunction with the state-space representation, allows fully Bayesian inference over the complete dynamic system and the unknown inputs.