Least action criteria for blind separation of structural modes

Abstract

-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...

A frequency domain blind identification method for operational modal analysis using a limited number of sensors

“…However, in this case, the eigenvalues of the right part of equation ( 11) are the squares of the natural frequencies. The minimization of the cost function minimizes the variance of the spectra of the sources, which is similar to the minimum spectrum variance criterion (Antoni et al, 2014). The smooth orthogonal decomposition (Zhou and Chelidze, 2008) (SOD)-based modal analysis approach is also similar to this approach.…”

“…To verify the theoretical findings, FSOBI is used to identify modal parameters from the experimental data (Antoni et al, 2014), and the results are compared with those from the SOBI method. The structure is a scale model of a wind turbine blade shown in Figure 11(a).…”

Comparison of Different Independent Component Analysis Algorithms for Output-Only Modal Analysis

“…Abazarsa et al [9] adopted a second-order blind identification (SOBI) technique to nonclassically damped systems. Antoni et al [10] showed that several separation criteria purposely dedicated to operational modal analysis (OMA) can be deduced from general physical considerations. Sadhu et al [11][12][13] took use of multirank parallel factor decomposition, time-series analysis-based BSS, and a decentralized BSS algorithm for ambient modal identification.…”

“…Furthermore, independent component analysis (ICA) combined with wavelet transform has been used to identify damage for time-varying systems [24]. Therefore, the study of output-only modal analysis based on ICA is of great significance [7][8][9][10][11][12][13].…”

“…10, and 12, the order of identified modal parameters is different from the order of those calculated by FEA, and the reason is that ICA algorithms are with three uncertainties, with all the modal shapes normalized which are shown inFigures 4, 6, 8, 10, and 12. (4) FromFigures 3-12, by comparing the modal shapes and natural frequencies as shown inTables 3FFT of the 6th independent component…”