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

• Published in: Mechanical systems and signal processing Vol. 140; p. 106580
• Main Authors: Rogers, T.J., Worden, K., Cross, E.J.
• Format: Journal Article
• Language: English
• Published: Berlin Elsevier Ltd 01.06.2020; Elsevier BV
• Subjects: Bayesian; Bayesian analysis; Gaussian process; Identification; Latent force model; Operational modal analysis; Parameter estimation; Parameter identification; Random noise; Signal processing; State space models; Statistical inference; Structural health monitoring; System identification; Gaussian process; System identification; Bayesian; Operational modal analysis; Latent force model
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2019.106580

•An output only analysis of structural systems under non-Gaussian excitation is shown.•The GPLFM is shown for joint input-state-parameter identification for wave loading.•MCMC solutions of the model recover posterior distributions of parameters in the system.•The extension of the model for use in modal coordinates is discussed. 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.