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Frontiers of Structural and Civil Engineering

ISSN 2095-2430

ISSN 2095-2449(Online)

CN 10-1023/X

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2018 Impact Factor: 1.272

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Front. Struct. Civ. Eng.    2019, Vol. 13 Issue (5) : 1082-1094    https://doi.org/10.1007/s11709-019-0537-3
RESEARCH ARTICLE
Variational mode decomposition based modal parameter identification in civil engineering
Mingjie ZHANG, Fuyou XU()
School of Civil Engineering, Dalian University of Technology, Dalian 116024, China
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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     
Corresponding Author(s): Fuyou XU   
Just Accepted Date: 05 May 2019   Online First Date: 06 June 2019    Issue Date: 11 September 2019
 Cite this article:   
Mingjie ZHANG,Fuyou XU. Variational mode decomposition based modal parameter identification in civil engineering[J]. Front. Struct. Civ. Eng., 2019, 13(5): 1082-1094.
 URL:  
https://academic.hep.com.cn/fsce/EN/10.1007/s11709-019-0537-3
https://academic.hep.com.cn/fsce/EN/Y2019/V13/I5/1082
Fig.1  FDR of a 3-DOF system and amplitude spectra
Fig.2  Modal responses of a 3-DOF system and instantaneous amplitudes
Fig.3  EMD results for FDR of a 3-DOF system. (a) IMF1 and IMF2; (b) IMF3–IMF8
Fig.4  Modal frequencies of a 3-DOF system
Fig.5  Modal damping ratios of a 3-DOF system
mode mean[f(t)] mean[x(t)]
1st DOF 2nd DOF 3rd DOF 1st DOF 2nd DOF 3rd DOF
1 0.567 0.567 0.568 0.010 0.010 0.010
2 1.006 unavailable 1.006 0.010 unavailable 0.010
3 1.095 1.094 1.095 0.010 0.010 0.010
Tab.1  Mean values of modal frequencies and modal damping ratios of a 3-DOF system
SNR (dB) mean[f(t)] mean[x(t)]
Mode 1 Mode 2 Mode 3 Mode 1 Mode 2 Mode 3
40 0.567 1.006 1.095 0.010 0.010 0.010
30 0.567 1.006 1.095 0.011 0.010 0.010
20 0.570 1.009 1.097 0.012 0.010 0.010
10 0.572 1.010 1.099 0.012 0.011 0.011
Tab.2  Mean values of modal frequencies and modal damping ratios of a 3-DOF system for different SNRs
Fig.6  Modal responses for Mode 1 of a 3-DOF system and instantaneous amplitudes
Fig.7  Amplitude ratios of modal responses for Mode 1
Mode Mode shape vector
identified theoretical
1 [1.00, 2.73, 1.00]T [1.00, 2.73, 1.00]T
2 [1.00, 0.00, - 1.00]T [1.00, 0.00, - 1.00]T
3 [1.00, - 0.72, 1.00]T [1.00, - 0.73, 1.00]T
Tab.3  Mode shape vectors a 3-DOF system
Fig.8  FDR of a 2-DOF system and amplitude spectra
Fig.9  Modal responses of a 2-DOF system
Fig.10  EMD results for FDR of a 2-DOF system. (a) IMF1 and IMF2; (b) IMF3 ~ IMF6
Fig.11  Modal frequencies of a 2-DOF system
Fig.12  Modal damping ratios of a 2-DOF system
Fig.13  Schematic diagram of a spring-suspended flat plate system
Fig.14  FDR of a SDOF system and amplitude spectra
Fig.15  Modal response of a SDOF system and amplitude spectra
Fig.16  Modal frequencies of a SDOF system
Fig.17  Modal damping ratios of a SDOF system
Fig.18  Comparison between extracted and calculated modal responses
Fig.19  Ambient vibration response of a 3-DOF system
Fig.20  Reconstructed FDR of a 3-DOF system and its amplitude spectra
Fig.21  Modal responses of a 3-DOF system extracted from ambient vibration and instantaneous amplitudes
Fig.22  Modal frequencies of a 3-DOF system extracted from ambient vibration
Fig.23  Modal damping ratios of a 3-DOF system extracted from ambient vibration
Mode mean[f(t)] mean[x(t)]
1st DOF 2nd DOF 3rd DOF 1st DOF 2nd DOF 3rd DOF
1 0.567 0.567 0.566 0.010 0.010 0.010
2 1.006 unavailable 1.005 0.010 unavailable 0.010
3 1.094 1.093 1.097 0.010 0.010 0.010
Tab.4  Mean values of modal frequencies and modal damping ratios of a 3-DOF system extracted from ambient vibrations
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[1] JI Xiaodong, QIAN Jiaru, XU Longhe. Experimental study of modal parameter identification in a simulated ambient-excited structure[J]. Front. Struct. Civ. Eng., 2007, 1(3): 281-285.
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