On the simulation of polynomial NARMAX models

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

Uittreksel

In this paper, we show that the common approach for simulation non-linear stochastic models, commonly used in system identification, via setting the noise contributions to zero results in a biased response. We also demonstrate that to achieve unbiased simulation of finite order NARMAX models, in general, we require infinite order simulation models. The main contributions of the paper are two-fold. Firstly, an alternate representation of polynomial NARMAX models, based on Hermite polynomials, is proposed. The proposed representation provides a convenient way to translate a polynomial NARMAX model to a corresponding simulation model by simply setting certain terms to zero. This translation is exact when the simulation model can be written as an NFIR model. Secondly, a parameterized approximation method is proposed to curtail infinite order simulation models to a finite order. The proposed approximation can be viewed as a trade-off between the conventional approach of setting noise contributions to zero and the approach of incorporating the bias introduced by higher-order moments of the noise distribution. Simulation studies are provided to illustrate the utility of the proposed representation and approximation method.
TaalEngels
Titel2018 IEEE Conference on Decision and Control (CDC)
Plaats van productiePIscataway
UitgeverijInstitute of Electrical and Electronics Engineers (IEEE)
Pagina's1445-1450
Aantal pagina's6
ISBN van elektronische versie978-1-5386-1395-5
ISBN van geprinte versie978-1-5386-1396-2
DOI's
StatusGepubliceerd - 2018
Evenement57th IEEE Conference on Decision and Control, CDC 2018 - Miami, Verenigde Staten van Amerika
Duur: 17 dec 201819 dec 2018
Congresnummer: 57

Congres

Congres57th IEEE Conference on Decision and Control, CDC 2018
Verkorte titelCDC 2018
LandVerenigde Staten van Amerika
StadMiami
Periode17/12/1819/12/18

Vingerafdruk

Stochastic models
Statistical Models
Identification (control systems)
Polynomials

Citeer dit

Khandelwal, D., Schoukens, M., & Toth, R. (2018). On the simulation of polynomial NARMAX models. In 2018 IEEE Conference on Decision and Control (CDC) (blz. 1445-1450). PIscataway: Institute of Electrical and Electronics Engineers (IEEE). DOI: 10.1109/CDC.2018.8619372
Khandelwal, D. ; Schoukens, M. ; Toth, R./ On the simulation of polynomial NARMAX models. 2018 IEEE Conference on Decision and Control (CDC) . PIscataway : Institute of Electrical and Electronics Engineers (IEEE), 2018. blz. 1445-1450
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Khandelwal, D, Schoukens, M & Toth, R 2018, On the simulation of polynomial NARMAX models. in 2018 IEEE Conference on Decision and Control (CDC) . Institute of Electrical and Electronics Engineers (IEEE), PIscataway, blz. 1445-1450, Miami, Verenigde Staten van Amerika, 17/12/18. DOI: 10.1109/CDC.2018.8619372

On the simulation of polynomial NARMAX models. / Khandelwal, D.; Schoukens, M.; Toth, R.

2018 IEEE Conference on Decision and Control (CDC) . PIscataway : Institute of Electrical and Electronics Engineers (IEEE), 2018. blz. 1445-1450.

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

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AB - In this paper, we show that the common approach for simulation non-linear stochastic models, commonly used in system identification, via setting the noise contributions to zero results in a biased response. We also demonstrate that to achieve unbiased simulation of finite order NARMAX models, in general, we require infinite order simulation models. The main contributions of the paper are two-fold. Firstly, an alternate representation of polynomial NARMAX models, based on Hermite polynomials, is proposed. The proposed representation provides a convenient way to translate a polynomial NARMAX model to a corresponding simulation model by simply setting certain terms to zero. This translation is exact when the simulation model can be written as an NFIR model. Secondly, a parameterized approximation method is proposed to curtail infinite order simulation models to a finite order. The proposed approximation can be viewed as a trade-off between the conventional approach of setting noise contributions to zero and the approach of incorporating the bias introduced by higher-order moments of the noise distribution. Simulation studies are provided to illustrate the utility of the proposed representation and approximation method.

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Khandelwal D, Schoukens M, Toth R. On the simulation of polynomial NARMAX models. In 2018 IEEE Conference on Decision and Control (CDC) . PIscataway: Institute of Electrical and Electronics Engineers (IEEE). 2018. blz. 1445-1450. Beschikbaar vanaf, DOI: 10.1109/CDC.2018.8619372