Term and variable selection for non-linear system identification

A novel modelling scheme that can be used to estimate and track time-varying properties of nonstationary signals is investigated. This scheme is based on a class of time-varying AutoRegressive with an eXogenous input (ARX) models where the associated time-varying parameters are represented by multi-wavelet basis functions. The orthogonal least square (OLS) algorithm is then applied to refine the model parameter estimates of the time-varying ARX model. The main features of the multi-wavelet approach is that it enables smooth trends to be tracked but also to capture sharp changes in the time-varying process parameters. Simulation studies and applications to real EEG data show that the proposed algorithm can provide important transient information on the inherent dynamics of nonstationary processes.

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“…Detailed discussions -6 -of the procedure of the forward OLS can be found in [23], [28]- [31]. The TV coefficients   i at and   n bt in Eq.…”

Section: Model Identification and Parameter Estimationmentioning

confidence: 99%

Time-varying model identification for time–frequency feature extraction from EEG data

Wei

Billings

et al. 2011

Journal of Neuroscience Methods

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“…Various methods exist for the selection of suitable variables relating to the polynomial and dynamic order. A standard method is based on the identification of linear models of the system [42] and the approach used here is based on this method. The required dynamic orders can therefore be inferred by comparison of linear models, i.e.…”

Section: Identification and Analysis Proceduresmentioning

confidence: 99%

Control-focused, nonlinear and time-varying modelling of dielectric elastomer actuators with frequency response analysis

Jacobs

Wilson

Assaf

et al. 2015

Smart Mater. Struct.

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ReuseUnless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version -refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher's website. TakedownIf you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. Control September 2014Abstract. Current models of dielectric elastomer actuators (DEAs) are mostly constrained to first principal descriptions that are not well suited to the application of control design due to their computational complexity. In this work we describe an integrated framework for the identification of control focused, data driven and time-varying DEA models that allow advanced analysis of nonlinear system dynamics in the frequency-domain. Experimentally generated input-output data (voltagedisplacement) was used to identify control-focused, nonlinear and time-varying dynamic models of a set of film-type DEAs. The model description used was the nonlinear autoregressive with exogenous input (NARX) structure. Frequency response analysis of the DEA dynamics was performed using generalised frequency response functions (GFRFs), providing insight and a comparison into the time-varying dynamics across a set of DEA actuators. The results demonstrated that models identified within the presented framework provide a compact and accurate description of the system dynamics. The frequency response analysis revealed variation in the time-varying dynamic behaviour of DEAs fabricated to the same specifications. These results suggest that the modelling and analysis framework presented here is a potentially useful tool for future work in guiding DEA actuator design and fabrication for application domains such as soft robotics.

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“…Qualitatively in the RSM the third order multiple, that is, the  3 5 component is weak, but there is no specific measurement of the weakness. For quantitative analysis, a useful measurement provided by the OLS procedure (Billings, et al, 1988;Wei and Billings, 2004) called Error-Reduction-Ratio(ERR), which indicates, in terms of energy, the contribution of each regressor in the LS estimation, can be adopted here. In our case the ERR gives the percentage contribution of each harmonic in the LS estimation in (18), plotted in Figure 7.…”

Section: Cubic Nonlinear Oscillationmentioning

confidence: 99%

A new frequency domain representation and analysis for subharmonic oscillation

Billings

2012

Nonlinear Dyn

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MonographAbstract: For a weakly nonlinear oscillator, the frequency domain Volterra kernels, often called the generalised frequency response functions, can provide accurate analysis of the response in terms of amplitudes and frequencies, in a transparent algebraic way. However a Volterra series representation based analysis will become void for nonlinear oscillators that exhibit subharmonics, and the problem of finding a solution in this situation has been mainly treated by the traditional analytical approximation methods. In this paper a novel method is developed, by extending the frequency domain Volterra representation to the subharmonic situation, to allow the advantages and the benefits associated with the traditional generalised frequency response functions to be applied to severely nonlinear systems that exhibit subharmonic behaviour.

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Term and variable selection for non-linear system identification

Cited by 141 publications

References 28 publications

Time-varying model identification for time–frequency feature extraction from EEG data

Time-varying model identification for time–frequency feature extraction from EEG data

Control-focused, nonlinear and time-varying modelling of dielectric elastomer actuators with frequency response analysis

A new frequency domain representation and analysis for subharmonic oscillation

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