Decoupling static nonlinearities in a parallel Wiener-Hammerstein system: a first-order approach

Philippe Dreesen; Maarten Schoukens; Koen Tiels; Johan Schoukens

doi:10.1109/I2MTC.2015.7151404

Decoupling static nonlinearities in a parallel Wiener-Hammerstein system: a first-order approach

Philippe Dreesen
, Maarten Schoukens
, Koen Tiels
, Johan Schoukens

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

11 Citations (Scopus)

Abstract

We present a method to decompose a static MIMO (multiple-input-multiple-output) nonlinearity into a set of SISO (single-input-single-output) polynomials acting on internal variables that are related to the inputs and outputs of the MIMO nonlinearity by linear transformations. The method is inspired on the small-signal analysis of nonlinear circuits and proceeds by collecting first-order information of the MIMO function into a set of Jacobian matrices. A simultaneous diagonalization of the set of Jacobian matrices is computed using a tensor decomposition, providing the required linear transformations, after which also the coefficients of the internal SISO polynomials can be computed. The method is validated on measurements of a parallel two-branch Wiener-Hammerstein identification setup.

Original language	English
Title of host publication	I²MTC 2015 IEEE International Instrumentation and Measurement Technology Conference : proceedings : The "Measurable" of Tomorrow : Providing a Better Perspective on Complex Systems : Palazzo dei Congresi, May 11-14, 2015, Pisa Italy
Editors	A. Ferrero
Place of Publication	Piscataway
Publisher	Institute of Electrical and Electronics Engineers
Number of pages	6
ISBN (Electronic)	9781479961446
ISBN (Print)	9781479961139
DOIs	https://doi.org/10.1109/I2MTC.2015.7151404
Publication status	Published - 1 Jan 2015
Externally published	Yes
Event	2015 IEEE International Instrumentation and Measurement Technology Conference, I2MTC 2015 - Palazzo dei Congressi, Pisa, Italy Duration: 11 May 2015 → 14 May 2015

Conference

Conference	2015 IEEE International Instrumentation and Measurement Technology Conference, I2MTC 2015
Abbreviated title	I2MTC 2015
Country/Territory	Italy
City	Pisa
Period	11/05/15 → 14/05/15

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10.1109/I2MTC.2015.7151404

Cite this

Dreesen, P., Schoukens, M., Tiels, K., & Schoukens, J. (2015). Decoupling static nonlinearities in a parallel Wiener-Hammerstein system: a first-order approach. In A. Ferrero (Ed.), I²MTC 2015 IEEE International Instrumentation and Measurement Technology Conference : proceedings : The "Measurable" of Tomorrow : Providing a Better Perspective on Complex Systems : Palazzo dei Congresi, May 11-14, 2015, Pisa Italy Article 7151404 Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/I2MTC.2015.7151404

Dreesen, Philippe ; Schoukens, Maarten ; Tiels, Koen et al. / Decoupling static nonlinearities in a parallel Wiener-Hammerstein system : a first-order approach. I²MTC 2015 IEEE International Instrumentation and Measurement Technology Conference : proceedings : The "Measurable" of Tomorrow : Providing a Better Perspective on Complex Systems : Palazzo dei Congresi, May 11-14, 2015, Pisa Italy . editor / A. Ferrero. Piscataway : Institute of Electrical and Electronics Engineers, 2015.

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abstract = "We present a method to decompose a static MIMO (multiple-input-multiple-output) nonlinearity into a set of SISO (single-input-single-output) polynomials acting on internal variables that are related to the inputs and outputs of the MIMO nonlinearity by linear transformations. The method is inspired on the small-signal analysis of nonlinear circuits and proceeds by collecting first-order information of the MIMO function into a set of Jacobian matrices. A simultaneous diagonalization of the set of Jacobian matrices is computed using a tensor decomposition, providing the required linear transformations, after which also the coefficients of the internal SISO polynomials can be computed. The method is validated on measurements of a parallel two-branch Wiener-Hammerstein identification setup.",

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Dreesen, P, Schoukens, M , Tiels, K & Schoukens, J 2015, Decoupling static nonlinearities in a parallel Wiener-Hammerstein system: a first-order approach. in A Ferrero (ed.), I²MTC 2015 IEEE International Instrumentation and Measurement Technology Conference : proceedings : The "Measurable" of Tomorrow : Providing a Better Perspective on Complex Systems : Palazzo dei Congresi, May 11-14, 2015, Pisa Italy ., 7151404, Institute of Electrical and Electronics Engineers, Piscataway, 2015 IEEE International Instrumentation and Measurement Technology Conference, I2MTC 2015, Pisa, Italy, 11/05/15. https://doi.org/10.1109/I2MTC.2015.7151404

Decoupling static nonlinearities in a parallel Wiener-Hammerstein system: a first-order approach. / Dreesen, Philippe; Schoukens, Maarten ; Tiels, Koen et al.
I²MTC 2015 IEEE International Instrumentation and Measurement Technology Conference : proceedings : The "Measurable" of Tomorrow : Providing a Better Perspective on Complex Systems : Palazzo dei Congresi, May 11-14, 2015, Pisa Italy . ed. / A. Ferrero. Piscataway: Institute of Electrical and Electronics Engineers, 2015. 7151404.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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T2 - 2015 IEEE International Instrumentation and Measurement Technology Conference, I2MTC 2015

AU - Dreesen, Philippe

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AU - Tiels, Koen

AU - Schoukens, Johan

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N2 - We present a method to decompose a static MIMO (multiple-input-multiple-output) nonlinearity into a set of SISO (single-input-single-output) polynomials acting on internal variables that are related to the inputs and outputs of the MIMO nonlinearity by linear transformations. The method is inspired on the small-signal analysis of nonlinear circuits and proceeds by collecting first-order information of the MIMO function into a set of Jacobian matrices. A simultaneous diagonalization of the set of Jacobian matrices is computed using a tensor decomposition, providing the required linear transformations, after which also the coefficients of the internal SISO polynomials can be computed. The method is validated on measurements of a parallel two-branch Wiener-Hammerstein identification setup.

AB - We present a method to decompose a static MIMO (multiple-input-multiple-output) nonlinearity into a set of SISO (single-input-single-output) polynomials acting on internal variables that are related to the inputs and outputs of the MIMO nonlinearity by linear transformations. The method is inspired on the small-signal analysis of nonlinear circuits and proceeds by collecting first-order information of the MIMO function into a set of Jacobian matrices. A simultaneous diagonalization of the set of Jacobian matrices is computed using a tensor decomposition, providing the required linear transformations, after which also the coefficients of the internal SISO polynomials can be computed. The method is validated on measurements of a parallel two-branch Wiener-Hammerstein identification setup.

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Dreesen P, Schoukens M , Tiels K, Schoukens J. Decoupling static nonlinearities in a parallel Wiener-Hammerstein system: a first-order approach. In Ferrero A, editor, I²MTC 2015 IEEE International Instrumentation and Measurement Technology Conference : proceedings : The "Measurable" of Tomorrow : Providing a Better Perspective on Complex Systems : Palazzo dei Congresi, May 11-14, 2015, Pisa Italy . Piscataway: Institute of Electrical and Electronics Engineers. 2015. 7151404 doi: 10.1109/I2MTC.2015.7151404

Decoupling static nonlinearities in a parallel Wiener-Hammerstein system: a first-order approach

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