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http://dx.doi.org/10.12989/sss.2020.25.2.123

Modal parameter identification with compressed samples by sparse decomposition using the free vibration function as dictionary  

Kang, Jie (School of Civil and Environmental Engineering, Harbin Institute of Technology at Shenzhen, University Town)
Duan, Zhongdong (School of Civil and Environmental Engineering, Harbin Institute of Technology at Shenzhen, University Town)
Publication Information
Smart Structures and Systems / v.25, no.2, 2020 , pp. 123-133 More about this Journal
Abstract
Compressive sensing (CS) is a newly developed data acquisition and processing technique that takes advantage of the sparse structure in signals. Normally signals in their primitive space or format are reconstructed from their compressed measurements for further treatments, such as modal analysis for vibration data. This approach causes problems such as leakage, loss of fidelity, etc., and the computation of reconstruction itself is costly as well. Therefore, it is appealing to directly work on the compressed data without prior reconstruction of the original data. In this paper, a direct approach for modal analysis of damped systems is proposed by decomposing the compressed measurements with an appropriate dictionary. The damped free vibration function is adopted to form atoms in the dictionary for the following sparse decomposition. Compared with the normally used Fourier bases, the damped free vibration function spans a space with both the frequency and damping as the control variables. In order to efficiently search the enormous two-dimension dictionary with frequency and damping as variables, a two-step strategy is implemented combined with the Orthogonal Matching Pursuit (OMP) to determine the optimal atom in the dictionary, which greatly reduces the computation of the sparse decomposition. The performance of the proposed method is demonstrated by a numerical and an experimental example, and advantages of the method are revealed by comparison with another such kind method using POD technique.
Keywords
compressive sensing; sparse decomposition; redundant dictionary; orthogonal matching pursuit; modal parameter identification;
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1 Zhuo, P., Yuan, M. and Wakin, M. (2018), "A random demodulation architecture for sub-sampling acoustic emission signals in structural health monitoring", J. Sound Vib., 431, 390-404. https://doi.org/10.1016/j.jsv.2018.06.021   DOI
2 Wang, Y. and Hao, H. (2015), "Damage identification scheme based on compressive sensing", J. Comput. Civ. Eng., 29(2), 04014037. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000324   DOI
3 Zhang, C.D. and Xu, Y.L. (2016), "Comparative studies on damage identification with Tikhonov regularization and sparse regularization", Struct. Control Heal. Monit., 23(3), 560-579. https://doi.org/10.1002/stc.1785   DOI
4 Zhou, S., Bao, Y. and Li, H. (2013), "Structural damage identification based on substructure sensitivity and l1 sparse regularization", SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring, San Diego, CA, USA, March.
5 Zhou, X., Xia. Y. and Weng, S. (2015), "L1 regularization approach to structural damage detection using frequency data", Struct. Heal. Monit., 14(6), 571-582. https://doi.org/10.1177/1475921715604386   DOI
6 Bao, Y., Shi, Z., Wang, X. and Li, H. (2017), "Compressive sensing of wireless sensors based on group sparse optimization for structural health monitoring", Struct. Heal. Monit., 17(4), 823-836. https://doi.org/10.1177/1475921717721457   DOI
7 Bajwa, W., Haupt, J., Sayeed, A. and Nowak, R. (2006), "Compressive wireless sensing", Proceedings of the Fifth International Conference on Information Processing in Sensor Networks, Nashville, TN, USA, April.
8 Bao, Y., Beck, J.L. and Li, H. (2011), "Compressive sampling for accelerometer signals in structural health monitoring", Struct. Heal. Monit., 10(3), 235-246. https://doi.org/10.1177/1475921710373287   DOI
9 Bao, Y., Li, H., Sun, X., Yu, Y. and Ou, J. (2013), "Compressive sampling based data loss recovery for wireless sensor networks used in civil structural health monitoring", Struct. Heal. Monit., 12(1), 78-95. https://doi.org/10.1177/1475921712462936   DOI
10 Candes, E.J. (2006), "Compressive Sensing", Proceedings of the international congress of mathematicians, Madrid, Spain, August.
11 Candes, E.J., Romberg, J. and Tao, T. (2006), "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information", IEEE Trans. Inf. Theory., 52(2), 489-509. https://doi.org/10.1109/TIT.2005.862083   DOI
12 Eldar, Y. and Kutyniok, G. (2012), Compressed Sensing:Theory and Applications, Cambridge University Press, New York, NY, USA.
13 Cho, S., Jo, H., Jang, S., Park, J., Jung, H.J., Yun, C.B., Spencer, B.F. and Seo, J.W. (2010), "Structural health monitoring of a cable-stayed bridge using wireless smart sensor technology: Data analyses", Smart Struct. Syst., Int. J., 6(5-6), 461-480. https://doi.org/10.12989/sss.2010.6.5_6.461   DOI
14 Donoho, D.L. (2006), "Compressed sensing", IEEE Trans. Inf. Theory., 52(4), 1289-1306. https://doi.org/10.1109/TIT.2006.871582   DOI
15 Duan, Z. and Kang, J. (2014), "Compressed sensing techniques for arbitrary frequency-sparse signals in structural health monitoring", SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring, San Diego, CA, USA, March.
16 Feng, C., Valaee, S. and Tan, Z. (2009), "Localization of wireless sensors using compressive sensing for manifold learning", Proceedings of the 2009 IEEE International Symposium on Workload Characterization, Austin, TX, USA, October.
17 Fornasier, M. and Rauhut, H. (2011), Handbook of mathematical methods in imaging, Springer Science & Business Media, New York, NY, USA.
18 Ganesan, V., Das, T., Rahnavard, N. and Kauffman, J.L. (2017), "Vibration-based monitoring and diagnostics using compressive sensing", J. Sound Vib., 394, 612-630. https://doi.org/10.1177/1475921712462936   DOI
19 Huang, Y., Beck, J.L., Wu, S. and Li, H. (2016), "Bayesian compressive sensing for approximately sparse signals and application to structural health monitoring signals for data loss recovery", Probabilistic Eng. Mech., 46, 62-79. https://doi.org/10.1016/j.probengmech.2016.08.001   DOI
20 Hou, R., Xia. Y, Bao, Y. and Zhou, X. (2018), "Selection of regularization parameter for l1-regularized damage detection", J. Sound Vib., 423, 141-160. https://doi.org/10.1016/j.jsv.2018.02.064   DOI
21 Lynch, J.P., Law, K.H., Kiremidjian, A.S., Kenny, T. and Carryer, E. (2002), "A wireless modular monitoring system for civil structures", Proceedings of the 20th International Modal Analysis Conference, Los Angeles, CA, USA, February.
22 Ling, Q. and Tian, Z. (2010), "Decentralized sparse signal recovery for compressive sleeping wireless sensor networks", IEEE Trans. Signal Process., 58(7), 3816-3827. https://doi.org/10.1109/TSP.2010.2047721   DOI
23 Liu, E. and Temlyakov, V.N. (2012), "The orthogonal super greedy algorithm and applications in compressed sensing", IEEE Trans. Inf. Theory., 58(4), 2040-2047. https://doi.org/10.1109/TIT.2011.2177632   DOI
24 Lynch, J.P. (2007), "An overview of wireless structural health monitoring for civil structures", Philos. Trans. A. Math. Phys. Eng., 365(1851), 345-372. https://doi.org/10.1098/rsta.2006.1932
25 Lynch, J.P., Sundararajan, A., Law, K.H., Kiremidjian, A.S. and Carryer, E. (2003), "Power-efficient data management for a wireless structural monitoring system", Proceedings of the 4th International Workshop on Structural Health Monitoring, Stanford University, USA, September.
26 Mascarenas, D., Cattaneo, A., Theiler, J. and Farrar, C. (2013), "Compressed sensing techniques for detecting damage in structures", Struct. Heal. Monit., 12(4), 325-338. https://doi.org/10.1177/1475921713486164   DOI
27 Park, J.Y., Wakin, M.B. and Gilbert, A.C. (2015), "Sampling considerations for modal analysis with damping", Proceedings of Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2015, Vol. 9435, San Diego, CA, USA, March.
28 O'Connor, S.M., Lynch, J.P. and Gilbert, A.C. (2014), "Compressed sensing embedded in an operational wireless sensor network to achieve energy efficiency in long-term monitoring applications", Smart Mater. Struct., 23(8), 085014. https://doi.org/10.1088/0964-1726/23/8/085014   DOI
29 Pan, C.D., Yu. L., Liu, H.L. and Luo, W.F. (2018), "Moving force identification based on redundant concatenated dictionary and weighted l1-norm regularization", Mech. Syst. Signal Progress., 98, 32-49. https://doi.org/10.1016/j.ymssp.2017.04.032   DOI
30 Park, J.Y., Wakin, M.B. and Gilbert, A.C. (2014), "Modal analysis with compressive measurements", IEEE Trans. Signal Process., 62(7), 1655-1670. https://doi.org/10.1109/TSP.2014.2302736   DOI
31 Rauhut, H., Schnass, K. and Vandergheynst, P. (2008), "Compressed sensing and redundant dictionaries", IEEE Trans. Inf. Theory., 54(5), 2210-2219. https://doi.org/10.1109/TIT.2008.920190   DOI
32 Spencer, B.F., Park, J.W., Mechitov, K.A., Jo, H. and Agha, G. (2017), "Next Generation Wireless Smart Sensors Toward Sustainable Civil Infrastructure", Procedia Eng., 171, 5-13.   DOI
33 Wei, F. and Qiao, P. (2011), "Vibration-based damage identification methods: a review and comparative study", Struct. Heal. Monit., 10(1), 83-111. https://doi.org/10.1177/1475921710365419   DOI
34 Xu, N., Rangwala, S. and Chintalapudi, K.K. (2004), "A wireless sensor network for structural monitoring", Proceedings of the 2nd International Conference on Embedded Networked Sensor Systems, MD, USA, November.