Separation and identification of structural modes in largely underdetermined scenarios using frequency banding

Abstract In recent years, blind source separation (BSS) has gained significant interest in the context of operational modal analysis, as a non-parametric alternative to the identification of mechanical structures from output-only measurements. One persisting limitation of most BSS methods, however, is to they cannot identify more active modes than the number of simultaneously measured outputs. The aim of this work is to propose a solution to the largely underdetermined case – where many more modes are to be identified than the number of available measurements -- by dividing the frequency axis in subbands, such that each band provides an (over)determined problem where BSS can be applied separately. The approach comes with the proposal of a new second-order BSS that operates directly in the frequency domain and takes as an input the cross-spectral matrix of the data. A data augmentation technique is also devised to artificially increase the dimension of the measurements in severely undetermined scenarios. Finally, an identification algorithm is introduced that estimates the modal parameters of the separated structural modes. A remarkable aspect of these algorithms is that they are all based on the unified use of multi-filters designed in the frequency domain, yet with different frequency bandwidths. Another particularity of the present paper is to demonstrate the validity of the proposed approach on several benchmark databases with various degrees of difficulty including complex modes, high modal overlap, singular modes, and the presence of engine harmonics. In all cases, the proposed methodology was efficient and, above all, easy to deal with even in largely undetermined cases.

[1]  Satish Nagarajaiah,et al.  Structural damage identification via a combination of blind feature extraction and sparse representation classification , 2014 .

[2]  Jan Swevers,et al.  A subspace algorithm for the identification of discrete time frequency domain power spectra , 1997, Autom..

[3]  J. Juang Applied system identification , 1994 .

[4]  Richard A. Harshman,et al.  Foundations of the PARAFAC procedure: Models and conditions for an "explanatory" multi-model factor analysis , 1970 .

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

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

[7]  Yannick Deville,et al.  A time-frequency blind signal separation method applicable to underdetermined mixtures of dependent sources , 2005, Signal Process..

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

[9]  Barak A. Pearlmutter,et al.  Blind Source Separation by Sparse Decomposition in a Signal Dictionary , 2001, Neural Computation.

[10]  Jérôme Antoni,et al.  A review of output-only structural mode identification literature employing blind source separation methods , 2017 .

[11]  Jérôme Antoni,et al.  Interpretation and generalization of complexity pursuit for the blind separation of modal contributions , 2017 .

[12]  Jérôme Antoni,et al.  Second Order Blind Source Separation techniques (SO-BSS) and their relation to Stochastic Subspace Identification (SSI) algorithm , 2011 .

[13]  Mohammad Ali Ghannad,et al.  Blind identification of soil–structure systems , 2013 .

[14]  Jie Guo,et al.  Sparse Component Analysis Using Time-Frequency Representations for Operational Modal Analysis , 2015, Sensors.

[15]  Jie Guo,et al.  Output-only modal identification based on hierarchical Hough transform , 2016 .

[16]  Andrzej Cichocki,et al.  Adaptive Blind Signal and Image Processing - Learning Algorithms and Applications , 2002 .

[17]  Barak A. Pearlmutter,et al.  Blind source separation by sparse decomposition , 2000, SPIE Defense + Commercial Sensing.

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

[19]  J. Chang,et al.  Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition , 1970 .

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

[21]  Tohru Katayama,et al.  Subspace Methods for System Identification , 2005 .

[22]  Kai Yang,et al.  Estimation of modal parameters using the sparse component analysis based underdetermined blind source separation , 2014 .

[23]  Yongchao Yang,et al.  Output-only modal identification by compressed sensing: Non-uniform low-rate random sampling , 2015 .

[24]  Sriram Narasimhan,et al.  Ambient modal identification of structures equipped with tuned mass dampers using parallel factor blind source separation , 2014 .

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

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

[27]  Abdeldjalil Aïssa-El-Bey,et al.  Underdetermined Blind Separation of Nondisjoint Sources in the Time-Frequency Domain , 2007, IEEE Transactions on Signal Processing.

[28]  Edwin Reynders,et al.  System Identification Methods for (Operational) Modal Analysis: Review and Comparison , 2012 .

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

[30]  Budhaditya Hazra,et al.  Decentralized modal identification of structures using parallel factor decomposition and sparse blind source separation , 2013 .

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

[32]  Yehoshua Y. Zeevi,et al.  A Multiscale Framework For Blind Separation of Linearly Mixed Signals , 2003, J. Mach. Learn. Res..

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

[34]  Gaëtan Kerschen,et al.  Experimental modal analysis using blind source separation techniques , 2006 .