On using the Hilbert transform for blind identification of systems with complex modes

José Antunes, Philippe Piteau, Xavier Delaune, Laurent Borsoi, Vincent Debut

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Downloads (Pure)

Abstract

The modal identification of dynamical systems under operational conditions, when subjected to wide-band unmeasured excitations, is today a viable alternative to more traditional modal identification approaches based on processing sets of measured FRFs or impulse responses.
Among current techniques for performing operational modal identification, the so-called blind identification methods are the subject of considerable investigation. In particular, the SOBI (Second-Order Blind Identification) method was found to be quite efficient. SOBI was originally developed for systems with normal modes. To address systems with complex modes, various extension approaches have been proposed, in particular: (a) Using a first-order state-space
formulation for the system dynamics; (b) Building complex analytic signals from the measured responses using the Hilbert transform. In this paper we further explore the latter option, which is conceptually interesting while preserving the model order and size. Focus is on applicability of the SOBI technique for extracting the modal responses from analytic signals built from a set of
vibratory responses. Aspects of the theoretical formulation for complex SOBI using the Hilbert transform are clarified and a convenient computational procedure for obtaining the complex cross-correlation response matrix is developed. We show that the correlation matrix of the analytic responses can be computed through a straightforward Hilbert transform of the standard
real correlation matrix typically obtained from measurements. Then, based on numerical simulations of a physical multi-modal system subjected to distribute random excitation, we assert the quality of the identified modal matrix and modal responses extracted using both the standard and the complex SOBI techniques. To perform such analysis, a simple and feasible physical device is proposed, which enables controlled levels of the modeshapes complexity, without introducing significant modal damping even for strongly complex modes.
Original languageEnglish
Title of host publicationProceedings of the International Congress on Acoustics
Place of PublicationBuenos Aires
Number of pages11
Publication statusPublished - Sep 2016
EventInternational Congress on Acoustics - Buenos Aires, Argentina
Duration: 5 Sep 20169 Sep 2016
Conference number: 22

Conference

ConferenceInternational Congress on Acoustics
CountryArgentina
CityBuenos Aires
Period5/09/169/09/16

Fingerprint

Dynamical systems
Impulse response
Damping
Computer simulation
Processing

Keywords

  • System identification
  • Hilbert transform
  • Complex modes
  • SOBI

Cite this

Antunes, J., Piteau, P., Delaune, X., Borsoi, L., & Debut, V. (2016). On using the Hilbert transform for blind identification of systems with complex modes. In Proceedings of the International Congress on Acoustics Buenos Aires.
Antunes, José ; Piteau, Philippe ; Delaune, Xavier ; Borsoi, Laurent ; Debut, Vincent. / On using the Hilbert transform for blind identification of systems with complex modes. Proceedings of the International Congress on Acoustics. Buenos Aires, 2016.
@inproceedings{3d5a612752b84c20a2f09d001b22629c,
title = "On using the Hilbert transform for blind identification of systems with complex modes",
abstract = "The modal identification of dynamical systems under operational conditions, when subjected to wide-band unmeasured excitations, is today a viable alternative to more traditional modal identification approaches based on processing sets of measured FRFs or impulse responses.Among current techniques for performing operational modal identification, the so-called blind identification methods are the subject of considerable investigation. In particular, the SOBI (Second-Order Blind Identification) method was found to be quite efficient. SOBI was originally developed for systems with normal modes. To address systems with complex modes, various extension approaches have been proposed, in particular: (a) Using a first-order state-spaceformulation for the system dynamics; (b) Building complex analytic signals from the measured responses using the Hilbert transform. In this paper we further explore the latter option, which is conceptually interesting while preserving the model order and size. Focus is on applicability of the SOBI technique for extracting the modal responses from analytic signals built from a set ofvibratory responses. Aspects of the theoretical formulation for complex SOBI using the Hilbert transform are clarified and a convenient computational procedure for obtaining the complex cross-correlation response matrix is developed. We show that the correlation matrix of the analytic responses can be computed through a straightforward Hilbert transform of the standardreal correlation matrix typically obtained from measurements. Then, based on numerical simulations of a physical multi-modal system subjected to distribute random excitation, we assert the quality of the identified modal matrix and modal responses extracted using both the standard and the complex SOBI techniques. To perform such analysis, a simple and feasible physical device is proposed, which enables controlled levels of the modeshapes complexity, without introducing significant modal damping even for strongly complex modes.",
keywords = "System identification, Hilbert transform, Complex modes, SOBI",
author = "Jos{\'e} Antunes and Philippe Piteau and Xavier Delaune and Laurent Borsoi and Vincent Debut",
note = "info:eu-repo/grantAgreement/FCT/5876/147236/PT# UID/EAT/00472/2013",
year = "2016",
month = "9",
language = "English",
booktitle = "Proceedings of the International Congress on Acoustics",

}

Antunes, J, Piteau, P, Delaune, X, Borsoi, L & Debut, V 2016, On using the Hilbert transform for blind identification of systems with complex modes. in Proceedings of the International Congress on Acoustics. Buenos Aires, International Congress on Acoustics, Buenos Aires, Argentina, 5/09/16.

On using the Hilbert transform for blind identification of systems with complex modes. / Antunes, José; Piteau, Philippe; Delaune, Xavier; Borsoi, Laurent; Debut, Vincent.

Proceedings of the International Congress on Acoustics. Buenos Aires, 2016.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

TY - GEN

T1 - On using the Hilbert transform for blind identification of systems with complex modes

AU - Antunes, José

AU - Piteau, Philippe

AU - Delaune, Xavier

AU - Borsoi, Laurent

AU - Debut, Vincent

N1 - info:eu-repo/grantAgreement/FCT/5876/147236/PT# UID/EAT/00472/2013

PY - 2016/9

Y1 - 2016/9

N2 - The modal identification of dynamical systems under operational conditions, when subjected to wide-band unmeasured excitations, is today a viable alternative to more traditional modal identification approaches based on processing sets of measured FRFs or impulse responses.Among current techniques for performing operational modal identification, the so-called blind identification methods are the subject of considerable investigation. In particular, the SOBI (Second-Order Blind Identification) method was found to be quite efficient. SOBI was originally developed for systems with normal modes. To address systems with complex modes, various extension approaches have been proposed, in particular: (a) Using a first-order state-spaceformulation for the system dynamics; (b) Building complex analytic signals from the measured responses using the Hilbert transform. In this paper we further explore the latter option, which is conceptually interesting while preserving the model order and size. Focus is on applicability of the SOBI technique for extracting the modal responses from analytic signals built from a set ofvibratory responses. Aspects of the theoretical formulation for complex SOBI using the Hilbert transform are clarified and a convenient computational procedure for obtaining the complex cross-correlation response matrix is developed. We show that the correlation matrix of the analytic responses can be computed through a straightforward Hilbert transform of the standardreal correlation matrix typically obtained from measurements. Then, based on numerical simulations of a physical multi-modal system subjected to distribute random excitation, we assert the quality of the identified modal matrix and modal responses extracted using both the standard and the complex SOBI techniques. To perform such analysis, a simple and feasible physical device is proposed, which enables controlled levels of the modeshapes complexity, without introducing significant modal damping even for strongly complex modes.

AB - The modal identification of dynamical systems under operational conditions, when subjected to wide-band unmeasured excitations, is today a viable alternative to more traditional modal identification approaches based on processing sets of measured FRFs or impulse responses.Among current techniques for performing operational modal identification, the so-called blind identification methods are the subject of considerable investigation. In particular, the SOBI (Second-Order Blind Identification) method was found to be quite efficient. SOBI was originally developed for systems with normal modes. To address systems with complex modes, various extension approaches have been proposed, in particular: (a) Using a first-order state-spaceformulation for the system dynamics; (b) Building complex analytic signals from the measured responses using the Hilbert transform. In this paper we further explore the latter option, which is conceptually interesting while preserving the model order and size. Focus is on applicability of the SOBI technique for extracting the modal responses from analytic signals built from a set ofvibratory responses. Aspects of the theoretical formulation for complex SOBI using the Hilbert transform are clarified and a convenient computational procedure for obtaining the complex cross-correlation response matrix is developed. We show that the correlation matrix of the analytic responses can be computed through a straightforward Hilbert transform of the standardreal correlation matrix typically obtained from measurements. Then, based on numerical simulations of a physical multi-modal system subjected to distribute random excitation, we assert the quality of the identified modal matrix and modal responses extracted using both the standard and the complex SOBI techniques. To perform such analysis, a simple and feasible physical device is proposed, which enables controlled levels of the modeshapes complexity, without introducing significant modal damping even for strongly complex modes.

KW - System identification

KW - Hilbert transform

KW - Complex modes

KW - SOBI

M3 - Conference contribution

BT - Proceedings of the International Congress on Acoustics

CY - Buenos Aires

ER -

Antunes J, Piteau P, Delaune X, Borsoi L, Debut V. On using the Hilbert transform for blind identification of systems with complex modes. In Proceedings of the International Congress on Acoustics. Buenos Aires. 2016