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

Operational modal analysis is an experimental modal analysis approach, which uses vibration data collected when the structure is under operating conditions. Amongst the methods for operational modal analysis, blind source separation–based methods have been shown to be efficient and powerful. The existing blind source separation modal identification methods, however, require the number of sensors to be at least equal to the number of modes in the frequency range of interest to avoid spatial aliasing. In this article, a frequency domain algorithm that overcomes this problem is proposed, which is based on the joint diagonalization of a set of weighted covariance matrices. In the proposed approach, the frequency range of interest is partitioned into several frequency ranges in which the number of active modes in each band is less than the number of sensors. Numerical simulations and an experimental example demonstrate the efficacy of the method.

[1]  Jérôme Antoni,et al.  Separation and identification of structural modes in largely underdetermined scenarios using frequency banding , 2018 .

[2]  Fabian J. Theis,et al.  Sparse component analysis and blind source separation of underdetermined mixtures , 2005, IEEE Transactions on Neural Networks.

[3]  Robert H. Halstead,et al.  Matrix Computations , 2011, Encyclopedia of Parallel Computing.

[4]  Jean-Claude Golinval,et al.  Physical interpretation of independent component analysis in structural dynamics , 2007 .

[5]  Kihong Shin,et al.  Fundamentals of Signal Processing for Sound and Vibration Engineers , 2008 .

[6]  D. C. Zimmerman,et al.  A framework for blind modal identification using joint approximate diagonalization , 2008 .

[7]  Yongchao Yang,et al.  Output-only modal identification with limited sensors using sparse component analysis , 2013 .

[8]  Rasmus Bro,et al.  Multi-way Analysis with Applications in the Chemical Sciences , 2004 .

[9]  David J. Ewins,et al.  Modal Testing: Theory, Practice, And Application , 2000 .

[10]  Yongchao Yang,et al.  Blind modal identification of output‐only structures in time‐domain based on complexity pursuit , 2013 .

[11]  Antoine Souloumiac,et al.  Jacobi Angles for Simultaneous Diagonalization , 1996, SIAM J. Matrix Anal. Appl..

[12]  Michael Zibulevsky,et al.  Underdetermined blind source separation using sparse representations , 2001, Signal Process..

[13]  Erkki Oja,et al.  Independent component approach to the analysis of EEG and MEG recordings , 2000, IEEE Transactions on Biomedical Engineering.

[14]  David E. Booth,et al.  Multi-Way Analysis: Applications in the Chemical Sciences , 2005, Technometrics.

[15]  Jérôme Antoni,et al.  Least action criteria for blind separation of structural modes , 2013 .

[16]  Wenliang Zhou,et al.  Generalized Eigenvalue Decomposition in Time Domain Modal Parameter Identification , 2008 .

[17]  Eric Moulines,et al.  A blind source separation technique using second-order statistics , 1997, IEEE Trans. Signal Process..

[18]  Tong Wang,et al.  A frequency–spatial domain decomposition (FSDD) method for operational modal analysis , 2010 .

[19]  T. Ens,et al.  Blind signal separation : statistical principles , 1998 .

[20]  Aouni A. Lakis,et al.  Independent component analysis as applied to vibration source separation and fault diagnosis , 2016 .

[21]  D. Chelidze,et al.  Blind source separation based vibration mode identification , 2007 .

[22]  G. Kerschen,et al.  Output-only modal analysis using blind source separation techniques , 2007 .

[23]  Brian Dykas,et al.  Blind source separation for vibration-based diagnostics of rotorcraft bearings , 2016 .

[24]  Pierre Comon,et al.  Independent component analysis, A new concept? , 1994, Signal Process..

[25]  D. Chakrabarti,et al.  A fast fixed - point algorithm for independent component analysis , 1997 .

[26]  Jérôme Antoni,et al.  An Alternating Least Squares (ALS) based Blind Source Separation Algorithm for Operational Modal Analysis , 2011 .

[27]  Jérôme Antoni,et al.  A study and extension of second-order blind source separation to operational modal analysis , 2013 .

[28]  M. Hulle.  Clustering approach to square and non-square blind source separation , 1999 .

[29]  Si McNeill,et al.  An analytic formulation for blind modal identification , 2012 .

[30]  Arndt Goldack,et al.  Ambient modal identification using multi‐rank parallel factor decomposition , 2015 .

[31]  Nikos D. Sidiropoulos,et al.  Blind Speech Separation Using Parafac Analysis and Integer Least Squares , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.