A framework for blind modal identification using joint approximate diagonalization

McNeill, Scot; Zimmerman, D. C.

doi:10.1016/j.ymssp.2008.01.010

Cited by 150 publications

(125 citation statements)

References 11 publications

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“…One recent and elegant solution consists of viewing the modal expansion of a set of structural responses as a mixture of modal coordinates -the "source signals" -where the mode shapes fill the columns of a mixing matrix. Then, under quite mild assumptions concerning only the mutual independence of the sources, it is possible to identify all constituents of the mixture up to an arbitrary scaling of the mode shapes [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. In turn, standard single-degreeof-freedom techniques can be applied on the separated modal coordinates to identify the global modal parameters.…”

Section: Introductionmentioning

confidence: 99%

“…The current state-ofthe-art in the context of operational modal analysis is rooted on the so-called Second-Order Blind Identification (SOBI) algorithm, which has proven extremely robust: its principle consists in separating sources -i.e. modal coordinates -which are least mutually correlated at several time-lags [4,[6][7][8][9]20]. This was shown to work surprisingly well, even though the assumption of mutual decorrelation of modes is not truly fulfilled as soon as the system is non-conservative (i.e.…”

Section: Introductionmentioning

confidence: 99%

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Least action criteria for blind separation of structural modes

Antoni

Chauhan

Monnier

et al. 2013

Mechanics & Industry

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-It was recently shown that blind source separation (BSS), as originally developed in the signal processing community, can be used in operational modal analysis to separate the responses of a structure into its individual modal contributions. This, in turn, allows the application of simple single-of-degreefreedom techniques to identify the modal parameters of interest. Several publications have recently attempted to give a posteriori physical interpretations to BSS -as initially developed in telecommunication signal processing -when applied to the field of structural dynamics. This paper proposes to follow the route the other way round. It shows that several separation criteria purposely dedicated to operational modal analysis can be deduced from general physical considerations. Three such examples are introduced, based on very different properties that uniquely characterise a structural mode. The first criterion, coined the "principle of shortest envelope", conjectures that the envelope of a modal response has, among all possible envelopes, the shortest length. That such a principle leads to the governing differential equation of a single-degree-of-freedom oscillator is proved from calculus of variation. The second criterion, coined the "principle of minimum spectral variance", conjectures that the frequency spectrum of a structural mode is maximally concentrated around its central frequency. Finally, the third criterion, coined the "principle of least spectral complexity", states that a structural mode has the lowest possible entropy in the frequency domain. All three criteria can be expressed in terms of a mixing matrix whose columns contain the unknown mode shapes. The recovery of the latter is then trivially achieved by minimising the criteria. Extensive simulations show that the proposed criteria lead to figures of merit very similar to those of the state-of-the-art, while at the same time providing physical insight that other algorithms issued form the signal processing community may dramatically lack. Key words:Operational modal analysis / blind source separation / least action principle / calculus of variation / structural dynamics Résumé -Principes de moindre action pour la séparation aveugle de modes. Des recherches récentes ont montré que certaines méthodes de séparation aveugle de sources, initialement développées pour les signaux de télécommunication, permettent de décomposer les réponses vibratoires d'une structure en ses différentes contributions modales. L'avantage qui s'ensuit pour l'analyse modale opérationnelle est une identification immédiate des paramètres modaux par application des techniques traditionnelles dédiées aux systèmesà un degré de liberté, et ceci sans connaissance des forces excitatrices appliquéesà la structure. L'approche est dite (( aveugle )), car elle ne nécessite aucune connaissance préalable des paramètres structuraux. Plusieurs publications ont récemment tenté de donner a posteriori une interprétation physique aux méthodes de séparation aveugle de sources, lors...

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Least action criteria for blind separation of structural modes

Antoni

Chauhan

Monnier

et al. 2013

Mechanics & Industry

View full text Add to dashboard Cite

show abstract

“…It has been recently established [32][33][34][35][36][37][38][39][40][41] that there is a one-to-one mapping between the modal superposition model and the linear mixture model of the blind source separation (BSS), which can perform output-only modal identification efficiently. Among a family of BSS techniques that are suited for output-only modal identification, the complexity pursuit (CP) algorithm [36] was shown to be efficient and able to identify closely-spaced and highly-damped modes with little expert supervision and parameter adjustments; it is therefore adopted in this study.…”

Section: Blind Mode Separation Of Principal Componentsmentioning

confidence: 99%

Spatiotemporal video-domain high-fidelity simulation and realistic visualization of full-field dynamic responses of structures by a combination of high-spatial-resolution modal model and video motion manipulations

Yang

Dorn

Mancini

et al. 2018

Struct Control Health Monit

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SummaryStructures with complex geometries, material properties, and boundary conditions exhibit spatially local dynamic behaviors. A high-spatial-resolution model of the structure is thus required for high-fidelity analysis, assessment, and prediction of the dynamic phenomena of the structure. The traditional approach is to build a highly refined finite element computer model for simulating and analyzing the structural dynamic phenomena based on detailed knowledge and explicit modeling of the structural physics such as geometries, materials properties, and boundary conditions. These physics information of the structure may not be available or accurately modeled in many cases, however. In addition, the simulation on the high-spatial-resolution structural model, with a massive number of degrees of freedom and system parameters, is computationally demanding. This study, on a proof-of-principle basis, proposes a novel alternative approach for spatiotemporal video-domain high-fidelity simulation and realistic visualization of full-field structural dynamics by an innovative combination of the fundamentals of structural dynamic modeling and the advanced video motion manipulation techniques.Specifically, a low-modal-dimensional yet high-spatial (pixel)-resolution (as many spatial points as the pixel number on the structure in the video frame) modal model is established in the spatiotemporal video domain with full-field modal parameters first estimated from line-of-sight video measurements of the operating structure. Then in order to simulate new dynamic response of the structure subject to a new force, the force is projected onto each modal domain, and the modal response is computed by solving each individual single-degree-of-freedom system in the modal domain. The simulated modal responses are then synthesized by the full-field mode shapes using modal superposition to obtain the simulated full-field structural dynamic response. Finally, the simulated structural dynamic response is embedded into the original video, replacing the original motion of the video, thus generating a new photo-realistic, physically accurate video that enables a --

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“…Data augmentation via windowing and Hilbert transforms have been shown to improve estimated modal responses [26]. Variants of the SOBI method have been developed in order to enhance the results for the identification of earthquake-excited structures [27], underdetermined structural cases [28], and cases with narrow band excitation [29].…”

Section: Introductionmentioning

confidence: 99%

Increasing the efficiency and efficacy of second-order blind identification (SOBI) methods

Brewick

Smyth

2016

Struct. Control Health Monit.

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SUMMARYThis paper proposes a new technique to increase the efficiency and effectiveness of second-order blind identification (SOBI) methods by reducing the number of time-lagged covariance matrices required to produce highly accurate mixing matrix estimates. The technique is based on randomly selecting the time-lagged covariance matrices as opposed to choosing them sequentially, which takes advantage of a property of independence with regard to the selection of time-lagged covariance matrices, while simultaneously reducing the correlation between selected covariance matrices. The proposed randomized approach is first applied to undamped and damped sinusoids to demonstrate its effectiveness. The randomized method is then applied to a three-degree-of-freedom linear structure subjected to random excitation. Finally, the proposed method is incorporated into a modified version of the SOBI method and applied to perform identification of the UCLA Factor building from recorded earthquake responses. In each case, the performance of the randomized approach is compared with the traditional sequential selection of time-lagged covariance matrices, and the randomized approach consistently demonstrates superior performance both in terms of accuracy and efficiency. Additionally, the proposed randomized SOBI approach was easily inserted into the modified SOBI method demonstrating its malleability for SOBI variants and other blind source separation methods.

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A framework for blind modal identification using joint approximate diagonalization

Cited by 150 publications

References 11 publications

Least action criteria for blind separation of structural modes

Least action criteria for blind separation of structural modes

Spatiotemporal video-domain high-fidelity simulation and realistic visualization of full-field dynamic responses of structures by a combination of high-spatial-resolution modal model and video motion manipulations

Increasing the efficiency and efficacy of second-order blind identification (SOBI) methods

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