DOI QR코드

DOI QR Code

A generalized adaptive variational mode decomposition method for nonstationary signals with mode overlapped components

  • Liu, Jing-Liang (College of Transportation and Civil Engineering, Fujian Agriculture and Forestry University) ;
  • Qiu, Fu-Lian (College of Transportation and Civil Engineering, Fujian Agriculture and Forestry University) ;
  • Lin, Zhi-Ping (Fujian Expressway Group Co., LTD) ;
  • Li, Yu-Zu (College of Transportation and Civil Engineering, Fujian Agriculture and Forestry University) ;
  • Liao, Fei-Yu (College of Transportation and Civil Engineering, Fujian Agriculture and Forestry University)
  • Received : 2021.04.30
  • Accepted : 2022.04.28
  • Published : 2022.07.25

Abstract

Engineering structures in operation essentially belong to time-varying or nonlinear structures and the resultant response signals are usually non-stationary. For such time-varying structures, it is of great importance to extract time-dependent dynamic parameters from non-stationary response signals, which benefits structural health monitoring, safety assessment and vibration control. However, various traditional signal processing methods are unable to extract the embedded meaningful information. As a newly developed technique, variational mode decomposition (VMD) shows its superiority on signal decomposition, however, it still suffers two main problems. The foremost problem is that the number of modal components is required to be defined in advance. Another problem needs to be addressed is that VMD cannot effectively separate non-stationary signals composed of closely spaced or overlapped modes. As such, a new method named generalized adaptive variational modal decomposition (GAVMD) is proposed. In this new method, the number of component signals is adaptively estimated by an index of mean frequency, while the generalized demodulation algorithm is introduced to yield a generalized VMD that can decompose mode overlapped signals successfully. After that, synchrosqueezing wavelet transform (SWT) is applied to extract instantaneous frequencies (IFs) of the decomposed mono-component signals. To verify the validity and accuracy of the proposed method, three numerical examples and a steel cable with time-varying tension force are investigated. The results demonstrate that the proposed GAVMD method can decompose the multi-component signal with overlapped modes well and its combination with SWT enables a successful IF extraction of each individual component.

Keywords

Acknowledgement

This study is sponsored by the National Natural Science Foundation of China (NSFC) under Grants No. 51608122, China Postdoctoral Science Foundation under Grants No. 2018M632561, the Natural Science Foundation of the Fujian Province under Grants No. 2020J01581 and the Special fund for science and technology innovation of Fujian Agriculture and Forestry University under Grants No. CXZX2020112A.

References

  1. Auger, F. and Flandrin, P. (1995), "Improving the readability of time-frequency and time-scale representations by the reassignment method", IEEE Trans. Sig. Pr., 43(5), 1068-1089. https://doi.org/10.1109/78.382394
  2. 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
  3. Cempel, C. and Tabaszewski, M. (2007), "Multidimensional condition monitoring of machines in non-stationary operation", Mech. Syst. Sig. Pr., 21(3), 1233-1241. https://doi.org/10.1016/j.ymssp.2006.04.001
  4. Chen, X.Y. and Cui, B.B. (2016), "Efficient modeling of fiber optic gyroscope drift using improved EEMD and extreme learning machine", Signal Process., 128, 1-7. https://doi.org/10.1016/j.sigpro.2016.03.016
  5. Chen, G.D. and Wang, Z.C. (2012), "A signal decomposition theorem with Hilbert transform and its application to narrowband time series with closely-spaced frequency components", Mech. Syst. Sig. Pr., 28, 258-279. https://doi.org/10.1016/j.ymssp.2011.02.002
  6. Chen, S.Q., Yang, Y., Dong, X.J., Xing, G.P., Peng, Z.K. and Zhang, W.M. (2019), "Warped variational mode decomposition with application to vibration signals of varying-speed rotating machineries", IEEE Trans. Instrum. Meas., 68(8), 2755-2767. https://doi.org/10.1109/TIM.2018.2869440
  7. Clausel, M., Oberlin, T. and Perrier, V. (2015), "The monogenic synchrosqueezed wavelet transform: A tool for the decomposition/demodulation of AM-FM images", Appl. Comput. Harmon. Anal., 39(3), 450-486. https://doi.org/10.1016/j.acha.2014.10.003
  8. Daubechies, I., Lu, J.F. and Wu, H.T. (2011), "Synchrosqueezed wavelet transforms: an empirical mode decomposition-like tool", Appl. Comput. Harmon. Anal., 30(2), 243-261. https://doi.org/10.1016/j.acha.2010.08.002
  9. Dragomiretskiy, K. and Zosso, D. (2014), "Variational mode decomposition", IEEE Trans. Sig. Pr., 62(3), 531-544. https://doi.org/10.1109/TSP.2013.2288675
  10. Feldman, M. (2006), "Time-varying vibration decomposition and analysis based on the Hilbert transform", J. Sound Vib., 295(3-5), 518-530. https://doi.org/10.1016/j.jsv.2005.12.058
  11. Feng, Z.P., Yu, X.N., Zhang, D. and Liang, M. (2020), "Generalized adaptive mode decomposition for nonstationary signal analysis of rotating machinery: Principle and applications", Mech. Syst. Sig. Pr., 136, 106530. https://doi.org/10.1016/j.ymssp.2019.106530
  12. Ferhatoglu, E., Cigeroglu, E. and Ozguven, H.N. (2018), "A new modal superposition method for nonlinear vibration analysis of structures using hybrid mode shapes", Mech. Syst. Sig. Pr., 107, 317-342. https://doi.org/10.1016/j.ymssp.2018.01.036
  13. Mohanty, Gupta, K.K. and Raju, K.S. (2014), "Bearing fault analysis using variational mode decomposition", Proceedings of the 9th International Conference on Industrial and Information Systems, Gwalior, India, December, pp. 1-6. https://doi.org/10.1109/ICIINFS.2014.7036617
  14. 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. Math. Phys. Eng. Sci., 454, 903-995. https://doi.org/10.1098/rspa.1998.0193
  15. Isham, M.F., Leong, M.S., Lim, M.H. and Ahmad, Z.A. (2018), "Variational mode decomposition: mode determination method for rotating machinery diagnosis", J. Vib., 20(7), 2604-2621. https://doi.org/10.21595/jve.2018.19479
  16. Lahmiri, S. (2014), "Comparative study of ECG signal denoising by wavelet thresholding in empirical and variational mode decomposition domains", Healthc. Technol. Lett., 1, 104-109. https://doi.org/10.1049/htl.2014.0073
  17. Le, T.H. and Caracoglia, L. (2015), "High-order, closely-spaced modal parameter estimation using wavelet analysis", Struct. Eng. Mech., Int. J., 56(3), 423-442. https://doi.org/10.12989/sem.2015.56.3.423
  18. Lee, J.H., Kim, J. and Kim, H.J. (2001), "Development of enhanced wigner-ville distribution function", Mech. Syst. Sig. Pr., 15(2), 367-398. https://doi.org/10.1006/mssp.2000.1365
  19. Li, C. and Liang, M. (2012), "A generalized synchrosqueezing transform for enhancing signal time-frequency representation", Signal Process., 92(9), 2264-2274. https://doi.org/10.1016/j.sigpro.2012.02.019
  20. Liu, J.L., Wang, Z.C., Ren, W.X. and Li, X.X. (2015), "Structural time-varying damage detection using synchrosqueezing wavelet transform", Smart Struct. Syst., Int. J., 15(1), 119-133. https://doi.org/10.12989/sss.2015.15.1.119
  21. Liu, J.L., Wei, X.J., Qiu, R.H., Zheng, J.Y., Zhu, Y.J. and Laory, I. (2018), "Instantaneous frequency extraction in time-varying structures using a maximum gradient method", Smart Struct. Syst., Int. J.., 22(3), 359-368. https://doi.org/10.12989/sss.2018.22.3.359
  22. Liu, J.L., Zheng, J.Y., Wei, X.J., Ren, W.X. and Laory, I. (2019), "A combined method for instantaneous frequency identification in low frequency structures", Eng. Struct., 194, 370-383. https://doi.org/10.1016/j.engstruct.2019.05.057
  23. Oberlin, T., Meignen, S. and Perrier, V. (2015), "Second-order synchrosqueezing transform or invertible reassignment? Towards ideal time-frequency representations", IEEE Trans. Sig. Pr., 63(5), 1335-1344. https://doi.org/10.1109/TSP.2015.2391077
  24. Olhede, S. and Walden, A.T. (2005), "A generalized demodulation approach to time-frequency projections for multicomponent signals", Proc. R. Soc. A., 461(2059), 2159-2179. https://doi.org/10.1098/rspa.2005.1455
  25. Poon, C.W. and Chang, C.C. (2007), "Identification of nonlinear elastic structures using empirical mode decomposition and nonlinear normal modes", Smart Struct. Syst., 3(4), 423-437. https://doi.org/10.12989/sss.2007.3.4.423
  26. Smith, J.S. (2005), "The local mean decomposition and its application to EEG perception data", J. R. Soc. Interface, 2, 443-454. https://doi.org/10.1098/rsif.2005.0058
  27. Thakur, G., Brevdo, E., Fuckar, N.S. and Wu, H.T. (2013), "The Synchrosqueezing algorithm for time-varying spectral analysis: Robustness properties and new paleoclimate applications", Signal Process., 93(5), 1079-1094. https://doi.org/10.1016/j.sigpro.2012.11.029
  28. Wang, C., Ren, W.X., Wang, Z.C. and Zhu, H.P. (2013), "Instantaneous frequency identification of time-varying structures by continuous wavelet transform", Eng. Struct., 52(9), 17-25. https://doi.org/10.1016/j.engstruct.2013.02.006
  29. Zhu, J., Wang, C., Hu, Z.Y., Kong, F.R. and Liu, X.C. (2015), "Adaptive variational mode decomposition based on artificial fish swarm algorithm for fault diagnosis of rolling bearings", J. Mech. Eng. Sci., 231(4), 635-654. https://doi.org/10.1177/0954406215623311