DOI QR코드

DOI QR Code

Modal parameter estimation of civil structures based on improved variational mode decomposition

  • Zhi, Lun-hai (College of Civil Engineering, Hefei University of Technology) ;
  • Hu, Feng (College of Civil Engineering, Hefei University of Technology) ;
  • Zhao, Chunfeng (College of Civil Engineering, Hefei University of Technology) ;
  • Wang, Jingfeng (College of Civil Engineering, Hefei University of Technology)
  • Received : 2020.08.13
  • Accepted : 2021.07.15
  • Published : 2021.09.25

Abstract

This paper proposes an improved variational mode decomposition (IVMD) algorithm for structural modal parameter estimation based on non-stationary responses. In this improved VMD, the mean envelope entropy (MEE) and particle swarm optimization (PSO) are first employed to determine the optimal decomposition parameters for the subsequent VMD analysis. Then the VMD algorithm is used to decompose the non-stationary data into a number of intrinsic mode functions (IMFs). After obtaining the IMFs based on the IVMD, structural modal parameters such as natural frequencies and damping ratios of civil structures can be determined by using Natural Excitation Technique (NExT) and Direct Interpolating approach (DI). The feasibility and accuracy of the proposed procedure are evaluated by both numerical and full-scale examples. The natural frequencies and damping ratios are successfully identified from the vibration responses with high noise and non-stationary characteristics. The results of this study illustrate that the proposed procedure provides a powerful approach to identify the modal parameters of civil structures using non-stationary responses.

Keywords

Acknowledgement

The work described in this paper was fully supported by grants from the National Natural Science Foundation of China (51478371 and 51978230), the Fundamental Research Funds for the Central Universities (PA2019GDZC0094 and PA2021KCPY0031) and the Natural Science Foundation of Anhui Province (2108085J29). The financial support is gratefully acknowledged.

References

  1. Ai, T.J. and Kachitvichyanukul, V. (2009), "A particle swarm optimization for the vehicle routing problem with simultaneous pickup and delivery", Comput. Oper. Res., 36(5), 1693-1702. https://doi.org/10.1016/j.cor.2008.04.003.
  2. Ardakani, A.J., Ardakani, F.F. and Hosseinian, S.H. (2008), "A novel approach for optimal chiller loading using particle swarm optimization", Energy Build., 40(12), 2177-2187. https://doi.org/10.1016/j.enbuild.2008.06.010.
  3. Bagheri, A., Ozbulut, O.E. and Harris, D.K. (2018), "Structural system identification based on variational mode decomposition", J. Sound Vib., 417, 182-197. https://doi.org/10.1016/j.jsv.2017.12.014.
  4. Bendat, J.S. and Piersol, A.G. (2010), Random Data: Analysis and Measurement Procedures, 4th Edition, John Wiley & Sons, New York, USA.
  5. Bossea, A., Taskerb, F. and Fisherc, S. (1998), "Real-time modal parameter estimation using subspace methods: Applications", Mech. Syst. Signal Pr., 12(6), 809-823. https://doi.org/10.1006/mssp.1998.0162.
  6. Chen, J., Xu, Y.L. and Zhang, R.C. (2004), "Modal parameter identification of Tsing Ma suspension bridge under Typhoon Victor: EMD-HT method", J. Wind Eng. Indus. Aerodyn., 92, 805-827. https://doi.org/10.1016/j.jweia.2004.04.003.
  7. Dragomiretskiy, K. and Zosso, D. (2014), "Variational Mode Decomposition", IEEE Tran. Signal Pr., 62(3), 531-544. https://doi.org/10.1109/TSP.2013.2288675.
  8. Elegbede, C. (2005), "Structural reliability assessment based on particles swarm optimization", Struct. Saf., 27, 171-186. https://doi.org/10.1016/j.strusafe.2004.10.003.
  9. Farrar, C.R. and James III, G.H. (1997), "System identification from ambient vibration measurements on a bridge", J. Sound Vib., 205(1), 1-18. https://doi.org/10.1006/jsvi.1997.0977.
  10. Gilles, J. (2013), "Empirical wavelet transform", IEEE Tran. Signal Pr., 61(16), 3999-4010. https://doi.org/10.1109/TSP.2013.2265222.
  11. Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, H.H., Zheng, Q., Yen, N.C., Tung, C.C. and Liu, H.H. (1998), "The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis", Proc. Roy. Soc. London, Ser. A: Math. Phys. Eng. Sci., 454, 903-995. https://doi.org/10.1098/rspa.1998.0193.
  12. Ibrahim, S.R. (1977), "Random decrement technique for modal identification of structures", J. Spacecraf. Rocket., 14(11), 696-700. https://doi.org/10.2514/3.57251.
  13. Jacobsen, N.J., Andersen, P. and Brincker, R. (2006), "Using enhanced frequency domain decomposition as a robust technique to harmonic excitation in operational modal analysis", Proceedings of ISMA2006: International Conference on Noise & Vibration Engineering, Leuven, Belgium.
  14. Kennedy, J. and Eberhart, R.C. (1995), "Particle swarm optimization", Proceedings of the IEEE International Conference on Neural Networks, 1942-1948. https://doi.org/10.1109/ICNN.1995.488968.
  15. Lahmiri, S. (2015), "Comparing variational and empirical mode decomposition in forecasting day-ahead energy prices", IEEE Syst. J., 11(3), 1907-1910. https://doi.org/10.1109/JSYST.2015.2487339.
  16. Li, F.H., Li, R., Tian, L.L., Chen, L. and Liu, J. (2019), "Data-driven time-frequency analysis method based on variational mode decomposition and its application to gear fault diagnosis in variable working conditions", Mech. Syst. Signal Pr., 116, 462-479. https://doi.org/10.1016/j.ymssp.2018.06.055.
  17. Li, Q.S. and Wu, J.R. (2007), "Time-frequency analysis of typhoon effects on a 79-storey tall building", J. Wind Eng. Indus. Aerodyn., 95(12), 1648-1666. https://doi.org/10.1016/j.jweia.2007.02.030.
  18. Li, Q.S., Fang, J.Q., Jeary, A.P. and Wong, C.K. (1998), "Full scale measurement of wind effects on tall buildings", J. Wind Eng. Indus. Aerodyn., 74-76, 741-750. https://doi.org/10.1016/S0167-6105(98)00067-1.
  19. Li, Q.S., Zhi, L.H., Tuan, A.Y., Kao, S.H., Su, S.C. and Wu, C.F. (2011), "Dynamic behavior of Taipei 101 Tower: field measurement and numerical analysis", J. Struct. Eng., ASCE, 137(1), 143-155. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000264.
  20. Li, Q.S., Zhi, L.H., Yi, J., To, A. and Xie, J.M. (2014a), "Monitoring of typhoon effects on a super-tall building in Hong Kong", Struct. Control Hlth. Monit., 21(6), 926-949. https://doi.org/10.1002/stc.1622.
  21. Li, Y., Cheng, G., Liu, C. and Chen, X.H. (2018), "Study on planetary gear fault diagnosis based on variational mode decomposition and deep neural networks", Measure., 130, 94-104. https://doi.org/10.1016/j.measurement.2018.08.002.
  22. Li, Y., Zhang, J.W. and Li, Q.S. (2014b), "Experimental investigation of characteristics of torsional wind loads on rectangular tall buildings", Struct. Eng. Mech., 49(1), 129-145. https://doi.org/10.12989/sem.2014.49.1.129.
  23. Liu, W., Cao, S. and Chen, Y. (2016), "Applications of variational mode decomposition in seismic time-frequency analysis", Geophys., 81(5), 365-378. https://doi.org/10.1190/geo2015-0489.1.
  24. Lv, Z., Tang, B., Zhou, Y. and Zhou, C. (2016), "A novel method for mechanical fault diagnosis based on variational mode decomposition and multikernel support vector machine", Shock Vib., 2016, 1-11. https://doi.org/10.1155/2016/3196465.
  25. Ni, P.H., Li, J., Hao, H., Xia, Y., Wang, X.Y., Lee, J.M. and Jung, K.H. (2018), "Time-varying system identification using variational mode decomposition", Struct. Control Hlth. Monit., 25(6), e2175. https://doi.org/10.1002/stc.2175.
  26. Nuttall, A.H. and Bedrosian, E. (1996), "On the quadrature approximation to the Hilbert transform of modulated signals", Proc. IEEE, 54(10), 1458-1459. https://doi.org/10.1109/PROC.1966.5138.
  27. Rato, R.T., Ortigueira, M.D. and Batista, A.G. (2008), "On the HHT, its problems, and some solutions", Mech. Syst. Signal Pr., 22(6), 1374-1394. https://doi.org/10.1016/j.ymssp.2007.11.028.
  28. Shi, Z.Y. and Law, S.S. (2007), "Identification of linear time-varying dynamical systems using Hilbert transform and empirical mode decomposition method", J. Appl. Mech., 74(2), 223-230. https://doi.org/10.1115/1.2188538.
  29. Soyoz, S. and Feng, M.Q. (2009), "Long-term monitoring and identification of bridge structural parameters", Comput. Aid. Civil Infrastr. Eng., 24(2), 82-92. https://doi.org/10.1111/j.1467-8667.2008.00572.x.
  30. Sun, J., Xiao, Q., Wen, J. and Wang, F. (2014), "Natural gas pipeline small leakage feature extraction and recognition based on LMD envelope spectrum entropy and SVM", Measure., 55, 434-443. https://doi.org/10.1016/j.measurement.2014.05.012.
  31. Sweeney, K.T., McLoone, S.F. and Ward, T.E. (2013), "The use of ensemble empirical mode decomposition with canonical correlation analysis as a novel artifact removal technique", IEEE Tran. Biomed. Eng., 60(1), 97-105. https://doi.org/10.1109/TBME.2012.2225427.
  32. Wang, J.L. and Li, Z.J. (2013), "Extreme-point symmetric mode decomposition method for data analysis", Adv. Adapt. Data Anal., 5(3), 1137-1137. https://doi.org/10.1142/S1793536913500155.
  33. Wang, Y.X., Markert, R., Xiang, J.W. and Zheng, W.G. (2015), "Research on variational mode decomposition and its application in detecting rub-impact fault of the rotor system", Mech. Syst. Signal Pr., 60-61, 243-251. https://doi.org/10.1016/j.ymssp.2015.02.020.
  34. Wu, Z. and Huang, N.E. (2009), "Ensemble empirical mode decomposition: A noise-assisted data analysis method", Adv. Adapt. Data Anal., 1(1), 1-41. https://doi.org/10.1142/S1793536909000047.
  35. Yan, X. and Jia, M. (2019), "Application of csa-vmd and optimal scale morphological slice bispectrum in enhancing outer race fault detection of rolling element bearings", Mech. Syst. Signal Pr., 122, 56-86. https://doi.org/10.1016/j.ymssp.2018.12.022.
  36. Yan, X., Jia, M. and Xiang, L. (2016), "Compound fault diagnosis of rotating machinery based on ovmd and a 1.5-dimension envelope spectrum", Measure. Sci. Technol., 27(7), 075002. https://doi.org/10.1088/0957-0233/27/7/075002.
  37. Yang, J.N., Lei, Y., Pan, S.W. and Huang, N. (2003a), "System identification of linear structures based on Hilbert-Huang spectral analysis, Part 1: normal models", Earthq. Eng. Struct. Dyn., 32(9), 1443-1467. https://doi.org/10.1002/eqe.287.
  38. Yang, J.N., Lei, Y., Pan, S.W. and Huang, N. (2003b), "System identification of linear structures based on Hilbert-Huang spectral analysis, Part 2: complex models", Earthq. Eng. Struct. Dyn., 32(10), 1533-1554. https://doi.org/10.1002/eqe.288.
  39. Zhang, G., Liu, H.C., Zhang, J.B., Yan, Y., Zhang, L., Wu, C., Hua, X. and Wang Y.Q. (2019), "Wind power prediction based on variational mode decomposition multi-frequency combinations", J. Mod. Power Syst. Clean Energy, 7(2), 281-288. https://doi.org/10.1007/s40565-018-0471-8.
  40. Zhang, M.J. and Xu, F.Y. (2019), "Variational mode decomposition based modal parameter identification in civil engineering", Front. Struct. Civil Eng., 13(5), 1082-1094. https://doi.org/10.1007/s11709-019-0537-3.