On the simulation of polynomial NARMAX models

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

Abstract

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.
LanguageEnglish
Title of host publication2018 IEEE Conference on Decision and Control (CDC)
Place of PublicationPIscataway
PublisherInstitute of Electrical and Electronics Engineers
Pages1445-1450
Number of pages6
ISBN (Electronic)978-1-5386-1395-5
ISBN (Print)978-1-5386-1396-2
DOIs
StatePublished - 2018
Event57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States
Duration: 17 Dec 201819 Dec 2018
Conference number: 57

Conference

Conference57th IEEE Conference on Decision and Control, CDC 2018
Abbreviated titleCDC 2018
CountryUnited States
CityMiami
Period17/12/1819/12/18

Fingerprint

Stochastic models
Statistical Models
Identification (control systems)
Polynomials

Cite this

Khandelwal, D., Schoukens, M., & Toth, R. (2018). On the simulation of polynomial NARMAX models. In 2018 IEEE Conference on Decision and Control (CDC) (pp. 1445-1450). PIscataway: Institute of Electrical and Electronics Engineers. 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, 2018. pp. 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, PIscataway, pp. 1445-1450, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 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, 2018. p. 1445-1450.

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-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. 2018. p. 1445-1450. Available from, DOI: 10.1109/CDC.2018.8619372