Identification of MIMO non-linear systems using a forward-regression orthogonal estimator

Billings, S.A.; Chen, S.; Korenberg, Michael J.

doi:10.1080/00207178908961377

Cited by 184 publications

(165 citation statements)

References 2 publications

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“…The standard NARMAX procedure of replacing the original set of monomials composed of these factors by an auxiliary set of orthogonal polynomials had been implemented. For each time period the ERR ratio have p 1/2 VB T sin 6 (/2)(t − 1) 31.32 VB s (t − 1) 12.76 n 1/6 V 4/3 B T sin 4 (/2)(t − 1) 10.30 p 1/2 VB T sin 4 (/2)(t − 1) 8.37 D st (t − 2) 7.23 been calculated for these auxiliary polynomials and afterwards recalculated for the original monomials, similar to the procedure described by Billings et al [1989]. The monomials identified by the NARMAX algorithm that correspond to the CF functions with highest NERR are given in Table 3.…”

Section: Results Of Err Based Data Analysismentioning

confidence: 99%

“…In the framework of the NARMAX approach the function F[…] is not searched for in an explicit form, but is decomposed in some complete basis (e.g., polynomial). The mathematical derivation of NARMAX takes into account both measurement noise and error resulting from incomplete knowledge of all inputs [Billings et al, 1989]. A simplified description of NARMAX is provided here for illustrative purposes and does not account for these factors.…”

Section: Introductionmentioning

confidence: 99%

“…[8] The relative contribution of the basis function w k into the evolution of F can be estimated as Billings et al [1989]:…”

Section: Introductionmentioning

confidence: 99%

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Data based quest for solar wind‐magnetosphere coupling function

Balikhin

Boynton

Billings

et al. 2010

Geophysical Research Letters

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[1] The NARMAX (Nonlinear Autoregressive Moving Average with eXogenous inputs) modeling based approach is used to identify the relations for Solar wind Magnetosphere Coupling Functions in order to identify the one with the best D st index forecasting abilities. It is argued that the Error Reduction Ratio which is a cornerstone concept in the NARMAX system identification methodology is more appropriate for such nonlinear system as the terrestrial magnetosphere than correlation function analysis which has often been used in the past. It is shown that the identified relationships for coupling functions are proportional to sin 2 À Á 6 , where is the clock angle, and not to sin 2 À Á 4 as was suggested in earlier studies. It is shown that the factor sin 2 À Á 6 appears naturally within the analytical model of Kan and Lee (1979)

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Section: Results Of Err Based Data Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Data based quest for solar wind‐magnetosphere coupling function

Balikhin

Boynton

Billings

et al. 2010

Geophysical Research Letters

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“…To overcome this problem, a search algorithm, called the forward regression algorithm (Billings et al, 1988;Swain & Billings, 1998), is used. A large ERR will indicate that an estimated variable is signi®cant and should be included in the ®nal model.…”

Section: Error-reduction Ratio Testmentioning

confidence: 99%

Modelling of small-angle X-ray scattering data using Hermite polynomials

et al. 2001

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A new algorithm, called the term‐selection algorithm (TSA), is derived to treat small‐angle X‐ray scattering (SAXS) data by fitting models to the scattering intensity using weighted Hermite polynomials. This algorithm exploits the orthogonal property of the Hermite polynomials and introduces an error‐reduction ratio test to select the correct model terms or to determine which polynomials are to be included in the model and to estimate the associated unknown coefficients. With no a priori information about particle sizes, it is possible to evaluate the real‐space distribution function as well as three‐ and one‐dimensional correlation functions directly from the models fitted to raw experimental data. The success of this algorithm depends on the choice of a scale factor and the accuracy of orthogonality of the Hermite polynomials over a finite range of SAXS data. An algorithm to select a weighted orthogonal term is therefore derived to overcome the disadvantages of the TSA. This algorithm combines the properties and advantages of both weighted and orthogonal least‐squares algorithms and is numerically more robust for the estimation of the parameters of the Hermite polynomial models. The weighting feature of the algorithm provides an additional degree of freedom to control the effects of noise and the orthogonal feature enables the reorthogonalization of the Hermite polynomials with respect to the weighting matrix. This considerably reduces the error in orthogonality of the Hermite polynomials. The performance of the algorithm has been demonstrated considering both simulated data and experimental data from SAXS measurements of dewaxed cotton fibre at different temperatures.

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“…The error reduction ratio (ERR) is another practical method to optimize the model structure. By selecting the most relevant regressor according to regressor quality in an orthogonal space [6,15,[23][24][25], the ERR has been successfully applied to experimental data. Finally, Aguirre and Letellier have presented a comprehensive review of modeling nonlinear dynamics and chaos [26].…”

Section: Introductionmentioning

confidence: 99%

Global modeling of complex data series using the term-ranking approach and its application to voice synthesis

2011

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A term-ranking approach is proposed to globally model the underlying dynamics of a chaotic series. The basic idea of this approach is to rank candidate bases before they are used to construct the global model. The ranked bases are involved in the global model one by one in a sequence from high to low until the best model is found. Simulations show that the model obtained by the term-ranking approach has a much longer prediction time, but fewer coefficients, than the widely used standard model. The proposed approach is also successfully applied to coding and synthesis of chaoslike voice data, showing promise for its use with truly noisy experimental data.

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Identification of MIMO non-linear systems using a forward-regression orthogonal estimator

Cited by 184 publications

References 2 publications

Data based quest for solar wind‐magnetosphere coupling function

Data based quest for solar wind‐magnetosphere coupling function

Modelling of small-angle X-ray scattering data using Hermite polynomials

Global modeling of complex data series using the term-ranking approach and its application to voice synthesis

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