Online system identification by sparse component analysis based on wavelet transform

Document Type : Research Article


1 Department of Civil Engineering, Islamic Azad University, Sanandaj, Iran

2 Department of Civil Engineering, University of Kurdistan, Sanandaj, Iran


Recently, online identification of structures, only based on the measured outputs during the vibration, has received much attention. One of the most powerful methods of offline system identification is the sparse component analysis (SCA) method which is a subset of blind source identification (BSI) methods. This method by transferring the dynamic responses from time domain to frequency one has led to the sparsity in the data and accordingly the modal parameters of the system are identified. In this research, a Wavelet Transform based Sparse Component Analysis (WT-SCA) method is suggested to identify the system. Then, using WT-SCA and a semi-active tuned mass damper (STMD), an algorithm is presented to achieve a smart structure. The results show that the WT-SCA is able to identify the system momentarily with an acceptable accuracy and also reduce the dynamic responses of a structure equipped with STMD.


Main Subjects

[1]S.W. Doebling, C.R. Farrar, M.B. Prime, D.W. Shevitz, Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: a literature review, Los Alamos National Lab., NM (United States), 1996.
[2]S.R. Ibrahim, Modal confidence factor in vibration testing, Journal of Spacecraft and Rockets, 15(5) (1978) 313-316.
[3]J.-N. Juang, R.S. Pappa, An eigensystem realization algorithm for modal parameter identification and model reduction, Journal of guidance, control, and dynamics, 8(5) (1985) 620-627.
[4]P. Georgiev, F. Theis, A. Cichocki, Sparse component analysis and blind source separation of underdetermined mixtures, IEEE transactions on neural networks, 16(4) (2005) 992-996.
[5]R. Gribonval, S. Lesage, A survey of sparse component analysis for blind source separation: principles, perspectives, and new challenges, in:  ESANN’06 proceedings-14th European Symposium on Artificial Neural Networks, d-side publi., 2006, pp. 323--330.
[6]F. Amini, Y. Hedayati, Underdetermined blind modal identification of structures by earthquake and ambient vibration measurements via sparse component analysis, Journal of Sound and Vibration, 366 (2016) 117-132.
[7]X.J. Yao, T.H. Yi, C. Qu, H.N. Li, Blind modal identification using limited sensors through modified sparse component analysis by time‐frequency method, Computer‐Aided Civil and Infrastructure Engineering, 33(9) (2018) 769.287
[8]K. Karami, F. Amini, Decreasing the damage in smart structures using integrated online DDA/ISMP and semiactive control, Smart Materials and Structures, 21(10) (2012) 105017.
[9]K. Karami, S. Akbarabadi, Developing a smart structure using integrated subspace‐based damage detection and semi-active control, Computer‐Aided Civil and Infrastructure Engineering, 31(11) (2016) 887-903.
[10]K. Karami, S. Nagarajaiah, F. Amini, Developing a smart structure using integrated DDA/ISMP and semi-active variable stiffness device, SMART STRUCTURES AND SYSTEMS, 18(5) (2016) 955-982.
[11]K. Karami, S. Manie, K. Ghafouri, S. Nagarajaiah, Nonlinear structural control using integrated DDA/ ISMP and semi-active tuned mass damper, Engineering Structures, 181 (2019) 589-604.
[12]N. Fisco, H. Adeli, Smart structures: part I—active and semi-active control, Scientia Iranica, 18(3) (2011) 275284.
[13]N. Fisco, H. Adeli, Smart structures: part II—hybrid control systems and control strategies, Scientia Iranica, 18(3) (2011) 285-295.
[14]M.G. Soto, H. Adeli, Tuned mass dampers, Archives of Computational Methods in Engineering, 20(4) (2013) 419-431.
[15]F. Sadek, B. Mohraz, A.W. Taylor, R.M. Chung, A method of estimating the parameters of tuned mass dampers for seismic applications, Earthquake Engineering & Structural Dynamics, 26(6) (1997) 617-635.
[16]N. Anh, N. Nguyen, Design of TMD for damped linear structures using the dual criterion of equivalent linearization method, International Journal of Mechanical Sciences, 77 (2013) 164-170.
[17]J.C. Miranda, Discussion of system intrinsic parameters of tuned mass dampers used for seismic response reduction, Structural Control and Health Monitoring, 23(2) (2016) .863-943
[18]N. Varadarajan, S. Nagarajaiah, Wind response control of building with variable stiffness tuned mass damper using empirical mode decomposition/Hilbert transform, Journal of engineering mechanics, 130(4) (2004) 451-458.
[19]P.Y. Lin, L.L. Chung, C.H. Loh, Semiactive Control of Building Structures with Semiactive Tuned Mass Damper, Computer-Aided Civil and Infrastructure Engineering, 20(1) (2005) 35-51.
[20]S. Nagarajaiah, N. Varadarajan, Short time Fourier transform algorithm for wind response control of buildings with variable stiffness TMD, Engineering Structures, 27(3) (2005) 431-441.
[21]S. Nagarajaiah, E. Sonmez, Structures with semiactive variable stiffness single/multiple tuned mass dampers, Journal of Structural Engineering, 133(1) (2007) 67-77.
[22]C. Sun, S. Nagarajaiah, Study on semi‐active tuned mass damper with variable damping and stiffness under seismic excitations, Structural Control and Health Monitoring, 21(6) (2014) 890-906.
[23]B. Hazra, S. Narasimhan, Wavelet-based blind identification of the UCLA Factor building using ambient and earthquake responses, Smart Materials and Structures, 19(2) (2009) 025005.
[24]U.P. Poudel, G. Fu, J. Ye, Wavelet transformation of mode shape difference function for structural damage location identification, Earthquake Engineering & Structural Dynamics, 36(8) (2007) 1089-1107.
[25]Y. Yang, S. Nagarajaiah, Output-only modal identification with limited sensors using sparse component analysis, Journal of Sound and Vibration, 332(19) (2013) 47414765.
[26]K. Yu, K. Yang, Y. Bai, Estimation of modal parameters using the sparse component analysis based underdetermined blind source separation, Mechanical Systems and Signal Processing, 45(2) (2014) 302-316.
[27]J.J. Thiagarajan, K.N. Ramamurthy, A. Spanias, Mixing matrix estimation using discriminative clustering for blind source separation, Digital Signal Processing, 23(1), 9-18.
[28]S. Ghahari, F. Abazarsa, M. Ghannad, M. Celebi, E. Taciroglu, Blind modal identification of structures from spatially sparse seismic response signals, Structural Control and Health Monitoring, 21(5) (2014) 649-674.
[29]J.C. Bezdek, R. Ehrlich, W. Full, FCM: The fuzzy c-means clustering algorithm, Computers & Geosciences, 10(2-3) (1984) 191-203.
[30]V.G. Reju, S.N. Koh, Y. Soon, An algorithm for mixing matrix estimation in instantaneous blind source separation, Signal Processing, 89(9) (2009) 1762-1773.
[31]D.L. Donoho, M. Elad, Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ1 minimization, Proceedings of the National Academy of Sciences, 100(5) (2003) 2197-2202.
[32]J.C. Asmussen, Modal analysis based on the random decrement technique: application to civil engineering structures, Instituttet for Bygningsteknik, Aalborg Universitet, 1997.
[33]S. Nagarajaiah, Structural vibration damper with continuously variable stiffness, in, Google Patents, 2000.
[34]S. Narasimhan, S. Nagarajaiah, A STFT semiactive controller for base isolated buildings with variable stiffness isolation systems, Engineering structures, 27(4) (2005) 514-523.
[35]M. Abe, T. Igusa, Semi-active dynamic vibration absorbers for controlling transient response, Journal of Sound and Vibration, 198(5) (1996) 547-569.