Variational mode decomposition based modal parameter identification in civil engineering

Abstract

An out-put only modal parameter identification method based on variational mode decomposition (VMD) is developed for civil structure identifications. The recently developed VMD technique is utilized to decompose the free decay response (FDR) of a structure into to modal responses. A novel procedure is developed to calculate the instantaneous modal frequencies and instantaneous modal damping ratios. The proposed identification method can straightforwardly extract the mode shape vectors using the modal responses extracted from the FDRs at all available sensors on the structure. A series of numerical and experimental case studies are conducted to demonstrate the efficiency and highlight the superiority of the proposed method in modal parameter identification using both free vibration and ambient vibration data. The results of the present method are compared with those of the empirical mode decomposition-based method, and the superiorities of the present method are verified. The proposed method is proved to be efficient and accurate in modal parameter identification for both linear and nonlinear civil structures, including structures with closely spaced modes, sudden modal parameter variation, and amplitude-dependent modal parameters, etc.

Keywords

modal parameter identification / variational mode decomposition / civil structure / nonlinear system / closely spaced modes

References

[1] Nanthakumar S S, Lahmer T, Zhuang X, Zi G, Rabczuk T. Detection of material interfaces using a regularized level set method in piezoelectric structures. Inverse Problems in Science and Engineering, 2016, 24(1): 153–176

[2] Nanthakumar S S, Valizadeh N, Park H S, Rabczuk T. Surface effects on shape and topology optimization of nanostructures. Computational Mechanics, 2015, 56(1): 97–112

[3] Xia P Q, Brownjohn J M. Bridge structural condition assessment using systematically validated finite-element model. Journal of Bridge Engineering, 2004, 9(5): 418–423

[4] Chang K C, Kim C W. Modal-parameter identification and vibration-based damage detection of a damaged steel truss bridge. Engineering Structures, 2016, 122: 156–173

[5] Shahdin A, Mezeix L, Bouvet C, Morlier J, Gourinat Y. Monitoring the effects of impact damages on modal parameters in carbon fiber entangled sandwich beams. Engineering Structures, 2009, 31(12): 2833–2841

[6] Zhang M J, Xu F Y, Ying X Y. Experimental investigations on the nonlinear torsional flutter of a bridge deck. Journal of Bridge Engineering, 2017, 22(8): 04017048

[7] Xue K, Igarashi A, Kachi T. Optimal sensor placement for active control of floor vibration considering spillover effect associated with modal filtering. Engineering Structures, 2018, 165: 198–209

[8] Yang S, Allen M S. Output-only modal analysis using continuous-scan laser Doppler vibrometry and application to a 20 kW wind turbine. Mechanical Systems and Signal Processing, 2012, 31: 228–245

[9] Bagheri A, Ozbulut O E, Harris D K. Structural system identification based on variational mode decomposition. Journal of Sound and Vibration, 2018, 417: 182–197

[10] Bendat J S, Piersol A G. Engineering Applications of Correlation and Spectral Analysis. New York: John Wiley & Sons, 1993

[11] Brincker R, Zhang L, Andersen P. Modal identification of output-only systems using frequency domain decomposition. Smart Materials and Structures, 2001, 10(3): 441–445

[12] Jacobsen N J, Andersen P, Brincker R. Using enhanced frequency domain decomposition as a robust technique to harmonic excitation in operational modal analysis. In: Proceedings of the International rational Modal Analysis Conference, 2006. Leuven: 2006, 18–20

[13] Zhang L, Wang Y, Tamura T. A frequency-spatial domain decomposition (FSDD) method for operational modal analysis. Mechanical Systems and Signal Processing, 2010, 24(5): 1227–1239

[14] Ibrahim S R. Random decrement technique for modal identification of structures. Journal of Spacecraft and Rockets, 1977, 14(11): 696–700

[15] Juang J N, Pappa R S. An eigensystem realization algorithm for modal parameters identification and model reduction. Journal of Guidance, Control, and Dynamics, 1985, 8(5): 620–627

[16] Gautier P E, Gontier C, Smail M. Robustness of an ARMA identification method for modal analysis of mechanical systems in the presence of noise. Journal of Sound and Vibration, 1995, 179(2): 227–242

[17] Peeters B, De Roeck G. Stochastic system identification for operational modal analysis: A review. Journal of Dynamic Systems, Measurement, and Control, 2001, 123(4): 659–667

[18] Berkooz G, Holmes P, Lumley J L. The proper orthogonal decomposition in the analysis of turbulent flows. Annual Review of Fluid Mechanics, 1993, 25(1): 539–575

[19] Vu-Bac N, Lahmer T, Zhuang X, Nguyen-Thoi T, Rabczuk T. A software framework for probabilistic sensitivity analysis for computationally expensive models. Advances in Engineering Software, 2016, 100: 19–31

[20] Hamdia K M, Ghasemi H, Zhuang X, Alajlan N, Rabczuk T. Sensitivity and uncertainty analysis for flexoelectric nanostructures. Comput Method Appl Me, 2018, 337: 95–109

[21] Hamdia K M, Silani M, Zhuang X, He P, Rabczuk T. Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions. International Journal of Fracture, 2017, 206(2): 215–227

[22] Kijewski T, Kareem A. Wavelet transforms for system identification in civil engineering. Comput-Aided Civ Inf, 2003, 18(5): 339– 355

[23] Huang N E, Shen Z, Long S R, Wu M C, Shih H H, Zheng Q. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society of London, Series A, 1998, 454: 903–95

[24] Rilling G, Flandrin P, Goncalves P. On empirical mode decomposition and its algorithms. In: IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing, 2003, 8–11

[25] Yang J N, Lei Y, Pan S, Huang N. System identification of linear structures based on Hilbert-Huang spectral analysis. Part 1: normal modes. Earthquake Engineering & Structural Dynamics, 2003, 32(9): 1443–1467

[26] Yang J N, Lei Y, Pan S, Huang N. System identification of linear structures based on Hilbert-Huang spectral analysis. Part 2: Complex modes. Earthquake Engineering & Structural Dynamics, 2003, 32(10): 1533–1554

[27] Chen J, Xu Y L, Zhang R C. Modal parameter identification of Tsing Ma suspension bridge under Typhoon Victor: EMD-HT method. Journal of Wind Engineering and Industrial Aerodynamics, 2004, 92(10): 805–827

[28] Pines D, Salvino L. Structural health monitoring using empirical mode decomposition and the Hilbert phase. Journal of Sound and Vibration, 2006, 294(1–2): 97–124

[29] He X H, Hua X G, Chen Z Q, Huang F L. EMD-based random decrement technique for modal parameter identification of an existing railway bridge. Engineering Structures, 2011, 33(4): 1348–1356

[30] Shi Z Y, Law S S. Identification of linear time-varying dynamical systems using Hilbert transform and empirical mode decomposition method. Journal of Applied Mechanics, 2007, 74(2): 223–230

[31] Bao C, Hao H, Li Z X, Zhu X. Time-varying system identification using a newly improved HHT algorithm. Computers & Structures, 2009, 87(23–24): 1611–1623

[32] Peng Z K, Peter W T, Chu F L. An improved Hilbert–Huang transform and its application in vibration signal analysis. J Sound Vib 2005; 23; 286(1–2): 187–205

[33] Rilling G, Flandrin P. One or two frequencies? The empirical mode decomposition answers. IEEE Transactions on Signal Processing, 2008, 56(1): 85–95

[34] Dragomiretskiy K, Zosso D. Variational mode decomposition. IEEE Transactions on Signal Processing, 2014, 62(3): 531–544

[35] Xue Y J, Cao J X, Wang D X, Du H K, Yao Y. Application of the variational mode decomposition for seismic time-frequency analysis. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2016, 9(8): 3821–3831

[36] Poornachandran P, Athira S, Harikumar K. Recursive variational mode decomposition algorithm for real time power signal decomposition. Procedia Technology, 2015, 21: 540–546

[37] Upadhyay A, Pachori R B. Instantaneous voiced/non-voiced detection in speech signals based on variational mode decomposition. Journal Franklin I, 2015, 352(7): 2679–2707

[38] Wang Y, Markert R, Xiang J, Zheng W. Research on variational mode decomposition and its application in detecting rub-impact fault of the rotor system. Mechanical Systems and Signal Processing, 2015, 60–61: 243–251

[39] Zheng J D, Cheng J S, Yang Y. A new instantaneous frequency estimation approach-empirical envelope method. Journal of Vibration and Shock, 2012, 31(17): 86–90 (in Chinese)

[40] Hestenes M R. Multiplier and gradient methods. Journal of Optimization Theory and Applications, 1969, 4(5): 303–320

[41] Liu Y, Yang G, Li M, Yin H. Variational mode decomposition denoising combined the detrended fluctuation analysis. Signal Processing, 2016, 125: 349–364

[42] Clough R W, Penzien J. Dynamics of Structures. Berkeley: Computers & Structures Inc, 2003

[43] Bedrosian E A. Product theorem for Hilbert transforms. Proceedings of the IEEE, 1963, 51(5): 868–869

[44] Nuttall A H, Bedrosian E. On the quadrature approximation to the Hilbert transform of modulated signals. Proceedings of the IEEE, 1966, 54(10): 1458–1459

[45] Huang N E, Wu Z H, Long S R, Arnold K C, Chen X Y, Blank K. On instantaneous frequency. Advances in Adaptive Data Analysis, 2009, 1(2): 177–229

[46] Siringoringo D M, Fujino Y. System identification of suspension bridge from ambient vibration response. Engineering Structures, 2008, 30(2): 462–477

[47] Zhang M J, Xu F Y. Nonlinear vibration characteristics of bridge deck section models in still air. Journal of Bridge Engineering, 2018, 23(9): 04018059

[48] Staubli T. Calculation of the vibration of an elastically mounted cylinder using experimental data from forced oscillation. Journal of Fluids Engineering, 1983, 105(2): 225–229

[49] Knapp J, Altmann E, Niemann J, Werner K D. Measurement of shock events by means of strain gauges and accelerometers. Measurement, 1998, 24(2): 87–96

[50] Acar C, Shkel A M. Experimental evaluation and comparative analysis of commercial variable-capacitance MEMS accelerometers. Journal of Micromechanics and Microengineering, 2003, 13(5): 634–645

Acknowledgments

The research is jointly supported by the Fundamental Research Funds for the Central Universities (No. DUT17ZD228), National Program on Key Basic Research Project (973 Program, No. 2015CB057705), and National Natural Science Foundation of China (Grant No. 51478087), which are gratefully acknowledged.

RIGHTS & PERMISSIONS

2019 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature