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

Abstract

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.

Structural health monitoring with non-linear sensor measurements robust to unknown non-stationary input forcing

“…A major goal of this paper is to design an SHM approach robust to the unknown input S g k without assuming or estimating its statistical properties. This study thus neither reconstructs the unknown input S g k as in [12,26,27,29,38], nor estimates its statistics as in [15,34].…”

“…With a similar objective, [12] proposed a dual filtering approach in which the structural parameters, as augmented states, are jointly estimated with the response states conditioned on an estimate for the input force. Instead of an explicit reconstruction of the input forces, [34] estimated the input force model through the parameters of a Gaussian process within a Bayesian framework.…”

“…Recently, for LTV systems with known system matrices, instead of estimating the input time histories [12,29,38], or its statistics [34], [43] developed a robust and stable linear state estimator unaffected by unknown inputs. This unknown input rejection approach is used in Kalman filter environment with linear measurements.…”

Bayesian Joint Input-State Estimation for Nonlinear Systems

“…One of the most useful aspects of this approach is that the whole system remains a linear Gaussian state-space model which can be solved with the Kalman filter and RTS smoother to recover the filtering and smoothing distributions exactly. It is this form of the model that has been exploited previously in structural dynamics [5,6,10].…”

“…Ding et al [9] present an approach based on an unscented Kalman filter. In recent work, Rogers et al [10] showed how the Gaussian process latent force framework could be used to solve this problem in a Bayesian manner with minimal user input.…”