A latent restoring force approach to nonlinear system identification

Rogers, Timothy J.; Friis, Tobias

doi:10.1016/j.ymssp.2022.109426

Cited by 14 publications

(6 citation statements)

References 28 publications

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“…The identification of this nonlinear term, including its most plausible function form and parameters, is essential for the implementation of an accurate forward model of the system able to predict its response to any input forces. If a set of noisy measurements of the system’s response to a known driving force is available, the nonlinear force can be identified by applying the GPLFM in the formulation proposed by Rogers and Friis (2022). In this case, the latent force model is formulated by modeling the nonlinear function as a zero-mean GP in time with a stationary kernel : The performances of this nonlinear system identification method are strictly dependent on the ability of GPs of reconstructing the nonlinear force.…”

Section: Mathematical Formulation Of the Switching Gaussian Process L...mentioning

confidence: 99%

“…Several different approaches may be used for fitting; for instance, the parameters of an existing friction model can be estimated by minimizing the least squared error, or a black-box approach, such as a neural network or a further GP, can be considered. For instance, in Rogers and Friis (2022), where a standard GPLFM is used for the identification of a Duffing oscillator, the nonlinear term is characterized by using a Bayesian Information Criterion to establish the most likely polynomial order of the nonlinear force–displacement relationship. Here, it has been chosen to fit the nonlinear force–velocity estimates inferred by the switching GPLFM ( ) with the steady-state Dieterich-Ruina’s law introduced in Equation (20a).…”

Section: Numerical Case-study: a Dry-friction Oscillatormentioning

confidence: 99%

“…This approach also requires to provide a prior distribution for these parameters, which is usually specified based on engineering and physical knowledge. Nonetheless, as highlighted by Rogers and Friis (2022), the presence of a latent nonlinear force can introduce a bias in the parameter estimation. For instance, the presence of a Duffing-type nonlinearity is likely to lead to incorrect linear stiffness estimates.…”

Section: Numerical Case-study: a Dry-friction Oscillatormentioning

confidence: 99%

“…Further applications of the GPLFM to joint input-state identification can be found in recent experimental studies (Bilbao et al, 2022; Petersen et al, 2022; Zou et al, 2023, 2022b). Finally, in Rogers and Friis (2022), the GPLFM is applied to the nonlinear identification of mechanical systems with a known driving force. In the case of a SDOF Duffing oscillator, the joint estimation of system parameters, latent states and nonlinear restoring force was performed by modelling the latter as a GP latent force.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, a switching (GPLFM) is proposed to identify a discontinuous nonlinear force and the latent states of an SDOF mechanical system excited by a known driving force. This method is based on the introduction of the switching GPLFM framework (Hartikainen and Särkkä, 2012) in the latent nonlinear restoring force model (Rogers and Friis, 2022), which enables: (i) the use of different GPs to model the nonlinear forces acting under different motion regimes (e.g., during sliding and sticking responses of a dry friction oscillator); (ii) the use of resetting models for generating discontinuities in the latent nonlinear force. Moreover, an approach is developed for estimating the uncertain physical parameters of the system, i.e., mass, viscous damping, and stiffness, from the identified latent states and discontinuous nonlinear force.…”

Section: Introductionmentioning

confidence: 99%

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A switching Gaussian process latent force model for the identification of mechanical systems with a discontinuous nonlinearity

Marino

Cicirello

2023

DCE

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An approach for the identification of discontinuous and nonsmooth nonlinear forces, as those generated by frictional contacts, in mechanical systems that can be approximated by a single-degree-of-freedom model is presented. To handle the sharp variations and multiple motion regimes introduced by these nonlinearities in the dynamic response, the partially known physics-based model and noisy measurements of the system’s response to a known input force are combined within a switching Gaussian process latent force model (GPLFM). In this grey-box framework, multiple Gaussian processes are used to model the unknown nonlinear force across different motion regimes and a resetting model enables the generation of discontinuities. The states of the system, nonlinear force, and regime transitions are inferred by using filtering and smoothing techniques for switching linear dynamical systems. The proposed switching GPLFM is applied to a simulated dry friction oscillator and an experimental setup consisting of a single-storey frame with a brass-to-steel contact. Excellent results are obtained in terms of the identified nonlinear and discontinuous friction force for varying: (i) normal load amplitudes in the contact; (ii) measurement noise levels, and (iii) number of samples in the datasets. Moreover, the identified states, friction force, and sequence of motion regimes are used for evaluating: (1) uncertain system parameters; (2) the friction force–velocity relationship, and (3) the static friction force. The correct identification of the discontinuous nonlinear force and the quantification of any remaining uncertainty in its prediction enable the implementation of an accurate forward model able to predict the system’s response to different input forces.

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