Joint approximate diagonalization technique for modal identification of the Donghai Bridge

Abstract

The second-order blind identification (SOBI) and its variants have been extensively explored for output-only modal identification of civil structures under varied excitations. At the core of these methods is the matrix joint approximate diagonalization (JAD) technique, while their efficiency and accuracy are largely determined by how the target-matrices for JAD are constructed from multi-channel structural responses. This study first formulates the JAD framework for structural identification, where different techniques in formulating the target-matrices are summarized and mathematical tools to conduct JAD are also presented. Then two novel ways stemming from conventional identification methods are presented as alternatives to construct the target-matrices for ambient identification, to maintain a low-order formulation and even avoiding the formation of covariance matrix. Subsequently, in view of the large number of candidate target-matrices which are analytically usable, a guiding principle is proposed for selecting reliable target-matrices, where the closeness of the eigenvectors of the target-matrices are compared beforehand, therefore eliminating of distorted target-matrices and also improving the efficiency of the subsequent JAD. The proposed techniques are applied to modal identification of the Donghai Bridge from monitoring data and the proposed JAD-based methods are compared in this context. The results suggest the effectiveness of the proposed techniques and also provide a performance evaluation of these methods.

References

[1.] Alvin KF, Robertson AN, Reich GW, Park KC. Structural system identification: from reality to models. Comput Struct, 2003, 81(12): 1149-1176

[2.] Peeters B, Ventura CE. Comparative study of modal analysis techniques for bridge dynamic characteristics. Mech Syst Signal Process, 2003, 17(5): 965-988

[3.] Lu S, Yan L, He X, Guo H. Identification of modal parameters of long-span bridges under various wind velocities. Adv Bridg Eng, 2022, 3(1): 26

[4.] Mostafa N, Maio DD, Loendersloot R, Tinga T. Railway bridge damage detection based on extraction of instantaneous frequency by wavelet synchrosqueezed transform. Adv Bridg Eng, 2022, 3(1): 12

[5.] Fan Z, Tang X, Chen Y, Ren Y, Deng C, Wang Z, Peng Y, Shi C, Huang Q. Review of anomaly detection in large span bridges: available methods, recent advancements and future trends. Adv Bridg Eng, 2024, 5(1): 2

[6.] Antoni J. Blind separation of vibration components: Principles and demonstrations. Mech Syst Signal Process, 2005, 19(6): 1166-1180

[7.] Kerschen G, Poncelet F, Golinval JC. Physical interpretation of independent component analysis in structural dynamics. Mech Syst Signal Process, 2007, 21(4): 1561-1575

[8.] Zhou W, Chelidze D. Blind source separation based vibration mode identification. Mech Syst Signal Process, 2007, 21(8): 3072-3087

[9.] Poncelet F, Kerschen G, Golinval JC, Verhelst D. Output-only modal analysis using blind source separation techniques. Mech Syst Signal Process, 2007, 21(6): 2335-2358

[10.] Hyvärinen A, Karhunen J, Oja E. Independent component analysis, 2001, New York, J. Wiley

[11.] Stone JV. Independent component analysis: a tutorial introduction, 2004, Cambridge, Massachusetts, MIT Press

[12.] Cole HA Jr. On-the-line analysis of random vibrations. AIAA/ASME 9th Structures, Structural Dynamics and Materials Conference, 1968, Reston, American Institute of Aeronautics and Astronautics (AIAA) 68-288

[13.] Ibrahim SR. Random decrement technique for modal identification of structures. J Spacecr Rocket, 1977, 14(11): 696-700

[14.] James GH, Carne TG, Lauffer JP (1993) The natural excitation technique (NExT) for modal parameter extraction from operating wind turbines. Technical Report SAND92-1666, UC-261, Sandia National Laboratories

[15.] Juang JN, Pappa RS. An eigensystem realization algorithm for modal parameter identification and model reduction. J Guid Control Dyn, 1985, 8(5): 620-627

[16.] Juang JN. Applied System Identification, 1994, Englewood Cliffs, N.J., Prentice Hall

[17.] Overschee PV, Moor BD (1996) Subspace Identification for Linear Systems - Theory, Implementation, Applications. Kluwer Academic Publishers, Norwell, MA, USA

[18.] Belouchrani A, Abed-Meraim K, Cardoso JF, Moulines E. A blind source separation technique using second-order statistics. IEEE Trans Signal Process, 1997, 45(2): 434-444

[19.] Nagarajaiah S, Yang Y. Modeling and harnessing sparse and low-rank data structure: a new paradigm for structural dynamics, identification, damage detection, and health monitoring. Struct Control Health Monit, 2017, 24(1): e1851

[20.] Yang Y, Nagarajaiah S. Time-frequency blind source separation using independent component analysis for output-only modal identification of highly damped structures. J Struct Eng, 2012, 139(10): 1780-1793

[21.] Yang Y, Nagarajaiah S. Blind identification of damage in time-varying system using independent component analysis with wavelet transform. Mech Syst Signal Process, 2014, 47(1–2): 3-20

[22.] Cardoso JF, Souloumiac A. Jacobi angles for simultaneous diagonalization. SIAM J Mat Anal Appl, 1996, 17(1): 161-164

[23.] Chabriel G, Kleinsteuber M, Moreau E, Shen H, Tichavsky P, Yeredor A. Joint matrices decompositions and blind source separation: A survey of methods, identification, and applications. IEEE Signal Process Mag, 2014, 31(3): 34-43

[24.] Hazra B, Roffel A, Narasimhan S, Pandey M. Modified cross-correlation method for the blind identification of structures. J Eng Mech, 2010, 136(7): 889-897

[25.] Cardoso JF. High-order contrasts for independent component analysis. Neural Comput, 1999, 11(1): 157-192

[26.] Tanaka A, Imai H, Miyakoshi M (2007) Selection of correlation matrices for second-order-statistics-based blind source separation. In: 2007 IEEE/SP 14th Workshop on Statistical Signal Processing. IEEE, Madison, WI, USA, pp 109–113

[27.] Hazra B, Narasimhan S. Wavelet-based blind identification of the UCLA Factor building using ambient and earthquake responses. Smart Mater Struct, 2010, 19(2): 025005

[28.] Hazra B, Sadhu A, Roffel A, Paquet P, Narasimhan S. Underdetermined blind identification of structures by using the modified cross-correlation method. J Eng Mech, 2012, 138(4): 327-337

[29.] Sadhu A, Hazra B, Narasimhan S. Blind identification of earthquake-excited structures. Smart Mater Struct, 2012, 21(4): 045019

[30.] Cheng L, Zheng D. The identification of a dam’s modal parameters under random support excitation based on the Hankel matrix joint approximate diagonalization technique. Mech Syst Signal Process, 2014, 42(1–2): 42-57

[31.] Zhou GD, Yi TH, Li WJ, Zhong JW, Zhang GH. Standardization construction and development trend of bridge health monitoring systems in china. Adv Bridg Eng, 2020, 1: 1-18

[32.] Zhang GQ, Wang B, Li J, Xu YL. The application of deep learning in bridge health monitoring: a literature review. Adv Bridg Eng, 2022, 3(1): 22

[33.] Kim J, Lynch JP. Experimental analysis of vehicle-bridge interaction using a wireless monitoring system and a two-stage system identification technique. Mech Syst Signal Process, 2012, 28: 3-19

[34.] Brewick PT, Smyth AW. On the application of blind source separation for damping estimation of bridges under traffic loading. J Sound Vib, 2014, 333(26): 7333-7351

[35.] Tong L, Soon V, Huang Y, Liu R (1990) AMUSE: a new blind identification algorithm. In: Proc. IEEE Int. Symp. Circuits and Systems. IEEE, New York, pp 1784–1787

[36.] Parra L, Sajda P. Blind source separation via generalized eigenvalue decomposition. J Mach Learn Res, 2004, 4(7–8): 1261-1269

[37.] Tome AM. The generalized eigendecomposition approach to the blind source separation problem. Digit Signal Process, 2006, 16(3): 288-302

[38.] Stone JV. Blind source separation using temporal predictability. Neural Comput, 2001, 13(7): 1559-1574

[39.] Khosravy M, Asharif M, Yamashita K. A theoretical discussion on the foundation of Stone’s blind source separation. Signal Image Video Process, 2011, 5(3): 379-388

[40.] Yang Y, Nagarajaiah S. Blind modal identification of output-only structures in time-domain based on complexity pursuit. Earthq Eng Struct Dyn, 2013, 42(13): 1885-1905

[41.] Huang C, Nagarajaiah S. Output-only structural health monitoring for deepwater risers: Experimental study of wavelet modified SOBI and distributed force index algorithm. Int J Struct Stab Dyn, 2014, 14(05): 1440010

[42.] Hazra B, Sadhu A, Roffel AJ, Narasimhan S. Hybrid time-frequency blind source separation towards ambient system identification of structures. Comput-Aided Civ Infrastruct Eng, 2012, 27(5): 314-332

[43.] Huang NE, Shen Z, Long SR, Wu MC, Shih HH, Zheng Q, Yen NC, Tung CC, Liu HH. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc R Soc Lond Ser A Math Phys Eng Sci, 1998, 454(1971): 903-995

[44.] Sadhu A, Hazra B, Narasimhan S. Decentralized modal identification of structures using parallel factor decomposition and sparse blind source separation. Mech Syst Signal Process, 2013, 41(1–2): 396-419

[45.] Ghahari SF, Abazarsa F, Ghannad MA, Taciroglu E. Response-only modal identification of structures using strong motion data. Earthq Eng Struct Dyn, 2013, 42(8): 1221-1242

[46.] McNeill SI, Zimmerman DC. A framework for blind modal identification using joint approximate diagonalization. Mech Syst Signal Process, 2008, 22(7): 1526-1548

[47.] Li XL, Adali T, Anderson M. Joint blind source separation by generalized joint diagonalization of cumulant matrices. Signal Process, 2011, 91(10): 2314-2322

[48.] Antoni J, Chauhan S. A study and extension of second-order blind source separation to operational modal analysis. J Sound Vib, 2013, 332(4): 1079-1106

[49.] Sadhu A, Goldack A, Narasimhan S (2014) Ambient modal identification using multi-rank parallel factor decomposition. Struct Control Health Monit 22(4):595–614

[50.] Hyvärinen A (2013) Independent component analysis: recent advances. Phil Trans R Soc A Math Phys Eng Sci 371(1984):20110534.

[51.] Bhowmik B. Advancements in online modal identification: A recursive simultaneous diagonalization comprehensive framework for real-time applications. Eng Struct, 2024, 305: 117770

[52.] He X, Moaveni B, Conte J, Elgamal A, Masri S. System identification of Alfred Zampa Memorial Bridge using dynamic field test data. J Struct Eng, 2009, 135(1): 54-66

[53.] Vandiver JK, Dunwoody AB, Campbell RB, Cook MF. A mathematical basis for the random decrement vibration signature analysis technique. J Mech Des, 1982, 104(2): 307-313

[54.] Brincker R, Krenk S, Jensen JL. Estimation of correlation functions by the random decrement technique. 9th International Modal Analysis Conference, 1991, Bethel, Society for Experimental Mechanics (SEM) 610-615

[55.] Spanos PD, Zeldin BA. Generalized random decrement method for analysis of vibration data. J Vib Acoust, 1998, 120(3): 806-813

[56.] Belouchrani A, Cichocki A. Robust whitening procedure in blind source separation context. Electron Lett, 2000, 36(24): 2050-2051

[57.] Sun L, Dan D, Zhang Q, Yue Q (2005) Conceptual design and key issues of structural health monitoring system for Donghai bridges. In: Proceedings of the 2nd International Structural Health Monitoring and Intelligent Infrastructure, International Society for Structural Health Monitoring of Intelligent Infrastructure (ISHMII). Taylor & Francis Ltd, Shenzhen, China, pp 255–264

[58.] Sun L, Dan D, Sun Z, Yule Q. Health monitoring system for a cross-sea bridge in Shanghai. IABSE Symp Rep, 2006, 92(28): 9-16

[59.] Sun L, Zhou Y. Analysis on modal frequency variation of a cable-stayed bridge based on monitoring data. IABSE Symp Rep, 2013, 99(26): 417-424

[60.] Daubechies I, et al.. Ten lectures on wavelets, 1992, Philadelphia, SIAM 61

[61.] Yuen KV, Katafygiotis LS. Modal decomposition using multi-channel response measurements. Probabilistic Eng Mech, 2014, 37: 60-73

[62.] Siringoringo DM, Fujino Y. System identification of suspension bridge from ambient vibration response. Eng Struct, 2008, 30(2): 462-477

[63.] Allemang RJ, Brown DL (1982) A correlation coefficient for modal vector analysis. In: Proceedings of the 1st international modal analysis conference, vol 1. SEM, Orlando, pp 110–116

Funding

Open Fund of State Key Lab for Disaster Reduction in Civil Engineering(SLDRCE13-MB-01)