Model validity tests for non-linear signal processing applications

Billings, S.A.; Tao, Qingchang

doi:10.1080/00207179108934155

Cited by 40 publications

(12 citation statements)

References 10 publications

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“…More advanced indicators, based on higher order correlations of the residuals have therefore been applied. [6][7][8][9] The main idea behind the approach developed in this paper is the consideration that, if the reconstruction of the magnetic fields was perfect and the noise additive, the residuals should simply consist of noise. Therefore, in the case of additive white noise, the residuals should present the statistical distribution typical of this noise.…”

Section: The Problem Of Consistently Weighting Different Measurementsmentioning

confidence: 99%

Improved equilibrium reconstructions by advanced statistical weighting of the internal magnetic measurements

Murari

Gelfusa

Peluso

et al. 2014

Review of Scientific Instruments

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In a Tokamak the configuration of the magnetic fields remains the key element to improve performance and to maximise the scientific exploitation of the device. On the other hand, the quality of the reconstructed fields depends crucially on the measurements available. Traditionally in the least square minimisation phase of the algorithms, used to obtain the magnetic field topology, all the diagnostics are given the same weights, a part from a corrective factor taking into account the error bars. This assumption unduly penalises complex diagnostics, such as polarimetry, which have a limited number of highly significant measurements. A completely new method to choose the weights, to be given to the internal measurements of the magnetic fields for improved equilibrium reconstructions, is presented in this paper. The approach is based on various statistical indicators applied to the residuals, the difference between the actual measurements and their estimates from the reconstructed equilibrium. The potential of the method is exemplified using the measurements of the Faraday rotation derived from JET polarimeter. The results indicate quite clearly that the weights have to be determined carefully, since the inappropriate choice can have significant repercussions on the quality of the magnetic reconstruction both in the edge and in the core. These results confirm the limitations of the assumption that all the diagnostics have to be given the same weight, irrespective of the number of measurements they provide and the region of the plasma they probe.

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Section: The Problem Of Consistently Weighting Different Measurementsmentioning

confidence: 99%

Improved equilibrium reconstructions by advanced statistical weighting of the internal magnetic measurements

Murari

Gelfusa

Peluso

et al. 2014

Review of Scientific Instruments

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“…To check whether an identified model is adequate to provide a sufficient description for a given data set, the validity of the model can be tested using the following tests (Billings and Tao 1991) "" ðÞ ¼ ðÞ, 8…”

Section: A Procedures To Implement the Multiresolution Wavelet Modelmentioning

confidence: 99%

Long term prediction of non-linear time series using multiresolution wavelet models

Wei

Billings

2006

International Journal of Control

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“…Consequently, additional boundary conditions need to be specified for model (6). Three kinds of boundary conditions are most commonly used, Dirichlet (fixed), Neumann (zero flux) and Toroidal (periodic) boundary conditions.…”

Section: Autonomous Cellular Neural Networkmentioning

confidence: 99%

“…The sampling time of the identification data from the CNN patterns which are continuously evolving over a discrete lattice needs to be appropriately determined to ensure the regression matrix is well defined. In this section, a correlation function based method [4] [6] [22] will be used to select an appropriate sampling procedure. Compared with other methods which are mostly based on information theoretical tools, the correlation method is quite simple and robust to noise.…”

Section: The Selection Of the Sampling Interval For The Identificatiomentioning

confidence: 99%

The Identification of Coupled Map Lattice Models for Autonomous Cellular Neural Network Patterns

Pan

Billings

Zhao

2008

Int. J. Bifurcation Chaos

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Monograph:Pan, Y., Billings, S.A. and Zhao, Y. (2007) The identification of coupled map lattice models for autonomous cellular neural network patterns. Research Report. ACSE Research Report no. 949 . Automatic Control and Systems Engineering, University of Sheffield eprints@whiterose.ac.uk https://eprints.whiterose.ac.uk/ Reuse Unless 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. Sheffield University, Sheffield, S1 3JD, UK March, 2007Abstract The identification problem for spatiotemporal patterns which are generated by autonomous Cellular Neural Networks (CNN) is investigated in this paper. The application of traditional identification algorithms to these special spatiotemporal systems can produce poor models due to the inherent piecewise nonlinear structure of CNN. To solve this problem, a new type of Coupled Map Lattice model with output constraints and corresponding identification algorithms are proposed in the present study. Numerical examples show that the identified CML models have good prediction capabilities even over the long term and the main dynamics of the original patterns appears to be well represented.

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Model validity tests for non-linear signal processing applications

Cited by 40 publications

References 10 publications

Improved equilibrium reconstructions by advanced statistical weighting of the internal magnetic measurements

Improved equilibrium reconstructions by advanced statistical weighting of the internal magnetic measurements

Long term prediction of non-linear time series using multiresolution wavelet models

The Identification of Coupled Map Lattice Models for Autonomous Cellular Neural Network Patterns

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