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

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

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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 22nd International Congress on Acoustics
EditorsFederico Miyara, Ernesto Accolti , Vivian Pasch , Nilda Vechiatti
Place of PublicationBuenos Aires
PublisherAsociación de Acústicos Argentinos
Number of pages11
ISBN (Print)9781510831735
Publication statusPublished - Sept 2016
EventInternational Congress on Acoustics - Buenos Aires, Argentina
Duration: 5 Sept 20169 Sept 2016
Conference number: 22


ConferenceInternational Congress on Acoustics
CityBuenos Aires


  • System identification
  • Hilbert transform
  • Complex modes
  • SOBI


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