Rogers, T.J., Worden, K. and Cross, E.J. (2020) Bayesian joint input-state estimation for nonlinear systems. Vibration, 3 (3). pp. 281-303.
Abstract
This work suggests a solution for joint input-state estimation for nonlinear systems. The task is to recover the internal states of a nonlinear oscillator, the displacement and velocity of the system, and the unmeasured external forces applied. To do this, a Gaussian process latent force model is developed for nonlinear systems. The model places a Gaussian process prior over the unknown input forces for the system, converts this into a state-space form and then augments the nonlinear system with these additional hidden states. To perform inference over this nonlinear state-space model a particle Gibbs approach is used combining a “Particle Gibbs with Ancestor Sampling” Markov kernel for the states and a Metropolis-Hastings update for the hyperparameters of the Gaussian process. This approach is shown to be effective in a numerical case study on a Duffing oscillator where the internal states and the unknown forcing are recovered, each with a normalised mean-squared error less than 0.5%. It is also shown how this Bayesian approach allows uncertainty quantification of the estimates of the states and inputs which can be invaluable in further engineering analyses.
Metadata
Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2020 The Authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). | ||||
Keywords: | bayesian; Gaussian process; latent force model; nonlinear; particle Gibbs; sequential monte carlo | ||||
Dates: |
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Institution: | The University of Sheffield | ||||
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Mechanical Engineering (Sheffield) | ||||
Funding Information: |
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Depositing User: | Symplectic Sheffield | ||||
Date Deposited: | 30 Sep 2020 13:24 | ||||
Last Modified: | 30 Sep 2020 15:53 | ||||
Status: | Published | ||||
Publisher: | MDPI AG | ||||
Refereed: | Yes | ||||
Identification Number: | https://doi.org/10.3390/vibration3030020 |