A Latent Restoring Force Approach to Nonlinear System Identification

• URL: http://arxiv.org/abs/2109.10681v1
• Date: Wed, 22 Sep 2021 12:21:16 GMT
• Title: A Latent Restoring Force Approach to Nonlinear System Identification
• Authors: Timothy J. Rogers and Tobias Friis
• Abstract summary: This work suggests an approach based on Bayesian filtering to extract and identify the contribution of an unknown nonlinear term in the system. The approach is demonstrated to be effective in both a simulated case study and on an experimental benchmark dataset.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Identification of nonlinear dynamic systems remains a significant challenge across engineering. This work suggests an approach based on Bayesian filtering to extract and identify the contribution of an unknown nonlinear term in the system which can be seen as an alternative viewpoint on restoring force surface type approaches. To achieve this identification, the contribution which is the nonlinear restoring force is modelled, initially, as a Gaussian process in time. That Gaussian process is converted into a state-space model and combined with the linear dynamic component of the system. Then, by inference of the filtering and smoothing distributions, the internal states of the system and the nonlinear restoring force can be extracted. In possession of these states a nonlinear model can be constructed. The approach is demonstrated to be effective in both a simulated case study and on an experimental benchmark dataset.

Related papers

• Bayesian Spline Learning for Equation Discovery of Nonlinear Dynamics with Quantified Uncertainty [8.815974147041048]
  We develop a novel framework to identify parsimonious governing equations of nonlinear (spatiotemporal) dynamics from sparse, noisy data with quantified uncertainty. The proposed algorithm is evaluated on multiple nonlinear dynamical systems governed by canonical ordinary and partial differential equations.
  arXiv  Detail & Related papers  (2022-10-14T20:37:36Z)
• Learning Reduced Nonlinear State-Space Models: an Output-Error Based Canonical Approach [8.029702645528412]
  We investigate the effectiveness of deep learning in the modeling of dynamic systems with nonlinear behavior. We show its ability to identify three different nonlinear systems. The performances are evaluated in terms of open-loop prediction on test data generated in simulation as well as a real world data-set of unmanned aerial vehicle flight measurements.
  arXiv  Detail & Related papers  (2022-04-19T06:33:23Z)
• A Priori Denoising Strategies for Sparse Identification of Nonlinear Dynamical Systems: A Comparative Study [68.8204255655161]
  We investigate and compare the performance of several local and global smoothing techniques to a priori denoise the state measurements. We show that, in general, global methods, which use the entire measurement data set, outperform local methods, which employ a neighboring data subset around a local point.
  arXiv  Detail & Related papers  (2022-01-29T23:31:25Z)
• Structure-Preserving Learning Using Gaussian Processes and Variational Integrators [62.31425348954686]
  We propose the combination of a variational integrator for the nominal dynamics of a mechanical system and learning residual dynamics with Gaussian process regression. We extend our approach to systems with known kinematic constraints and provide formal bounds on the prediction uncertainty.
  arXiv  Detail & Related papers  (2021-12-10T11:09:29Z)
• Exact solutions of interacting dissipative systems via weak symmetries [77.34726150561087]
  We analytically diagonalize the Liouvillian of a class Markovian dissipative systems with arbitrary strong interactions or nonlinearity. This enables an exact description of the full dynamics and dissipative spectrum. Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.
  arXiv  Detail & Related papers  (2021-09-27T17:45:42Z)
• Dynamical symmetry breaking through AI: The dimer self-trapping transition [0.0]
  We use a physics motivated machine learning model that is shown to be able to capture the original dynamic self-trapping transition. Exploitation of this result in the case of the non-degenerate nonlinear dimer gives additional information on the more general dynamics.
  arXiv  Detail & Related papers  (2021-09-20T15:31:35Z)
• Learning Nonlinear Waves in Plasmon-induced Transparency [0.0]
  We consider a recurrent neural network (RNN) approach to predict the complex propagation of nonlinear solitons in plasmon-induced transparency metamaterial systems. We prove the prominent agreement of results in simulation and prediction by long short-term memory (LSTM) artificial neural networks.
  arXiv  Detail & Related papers  (2021-07-31T21:21:44Z)
• Linear embedding of nonlinear dynamical systems and prospects for efficient quantum algorithms [74.17312533172291]
  We describe a method for mapping any finite nonlinear dynamical system to an infinite linear dynamical system (embedding) We then explore an approach for approximating the resulting infinite linear system with finite linear systems (truncation)
  arXiv  Detail & Related papers  (2020-12-12T00:01:10Z)
• Identification of Probability weighted ARX models with arbitrary domains [75.91002178647165]
  PieceWise Affine models guarantees universal approximation, local linearity and equivalence to other classes of hybrid system. In this work, we focus on the identification of PieceWise Auto Regressive with eXogenous input models with arbitrary regions (NPWARX) The architecture is conceived following the Mixture of Expert concept, developed within the machine learning field.
  arXiv  Detail & Related papers  (2020-09-29T12:50:33Z)
• Active Learning for Nonlinear System Identification with Guarantees [102.43355665393067]
  We study a class of nonlinear dynamical systems whose state transitions depend linearly on a known feature embedding of state-action pairs. We propose an active learning approach that achieves this by repeating three steps: trajectory planning, trajectory tracking, and re-estimation of the system from all available data. We show that our method estimates nonlinear dynamical systems at a parametric rate, similar to the statistical rate of standard linear regression.
  arXiv  Detail & Related papers  (2020-06-18T04:54:11Z)
• Bayesian differential programming for robust systems identification under uncertainty [14.169588600819546]
  This paper presents a machine learning framework for Bayesian systems identification from noisy, sparse and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in differentiable programming to propagate gradient information through ordinary differential equation solvers. The use of sparsity-promoting priors enables the discovery of interpretable and parsimonious representations for the underlying latent dynamics.
  arXiv  Detail & Related papers  (2020-04-15T00:51:14Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.