Extraction method for signal effective component based on extreme-point symmetric mode decomposition and Kullback–Leibler divergence

  • Yong Zhu
  • Shengnan TangEmail author
  • Lingxiao Quan
  • Wanlu Jiang
  • Ling ZhouEmail author
Technical Paper


Data processing is widely used to extract effective component from original signal, which is essential in mechanical condition monitoring and fault diagnosis. In order to solve the invalid component and non-stationary feature in the measured signal, the extraction method for effective signal component is proposed based on extreme-point symmetric mode decomposition (ESMD) and Kullback–Leibler (K–L) divergence. This method fully integrates the characteristics of ESMD in self-adaptive decomposition and the advantages of K–L divergence in measuring the distance between different signals. The effective and invalid components of non-stationary signal are automatically separated by ESMD, and the effective components are further identified through K–L divergence calculation. Some analyses of simulated data and experimental data were investigated. And the effect of the proposed method in effective component extraction was emphatically explored. Research results indicate that the proposed method can adaptively acquire effective signal components with higher accuracy. Moreover, compared with the classic method, it is more efficient in the extraction of effective components from complex signal. In addition, this research solves the interference problem of invalid signals and accurately reconstructs the desired useful signal.


Mechanical signal Effective component extraction Extreme-point symmetric mode decomposition Kullback–Leibler divergence 



This work is supported by National Natural Science Foundation of China (51805214, 51875498, 51609106) and Natural Science Foundation of Hebei Province (E2018203339). The authors would also like to thank the reviewers for their valuable suggestions and comments.


  1. 1.
    Zhu Y, Jiang WL, Kong XD (2017) Adaptive extraction method for trend term of machinery signal based on extreme-point symmetric mode decomposition. J Mech Sci Technol 31(2):493–500CrossRefGoogle Scholar
  2. 2.
    Long Y, Xie QM, Zhong MS, Lu L, Li XH (2012) Research on trend removing methods in preprocessing analysis of blasting vibration monitoring signals. Eng Mech 29(10):63–68Google Scholar
  3. 3.
    Wu ZC, Wang CY, Ren AJ (2013) Optimal selection of wavelet base functions for eliminating signal trend based on wavelet analysis. Trans Beijing Inst Technol 33(8):811–814zbMATHGoogle Scholar
  4. 4.
    Liu TY, Jiang Q, Li Y, Xu ZD (2018) A review of rotating machinery fault signal processing and diagnosis methods. China Energy Environ Prot 40(1):163–166Google Scholar
  5. 5.
    Huang NE, Shen Z, Long SR et al (1998) The empirical mode decomposition and the hilbert spectrum for nonlinear and non-stationary time series analysis. Proc R Soc A: Math Phys Eng Sci 454(1971):903–995MathSciNetCrossRefGoogle Scholar
  6. 6.
    Lei YG, Lin J, He ZJ, Zuo MJ (2013) A review on empirical mode decomposition in fault diagnosis of rotating machinery. Mech Syst Signal Process 35(1–2):108–126CrossRefGoogle Scholar
  7. 7.
    Zhang F, Fu J, Fan YL, Zhou XJ (2017) Main shaft run-out research of hydraulic generator unit in load rejection process based on empirical mode decomposition. J Drainage Irrig Mach Eng 35(10):863–868Google Scholar
  8. 8.
    Kong Q, Song Q, Hai Y, Gong R, Liu J, Shao X (2018) Denoising signals for photoacoustic imaging in frequency domain based on empirical mode decomposition. Optik 160:402–414CrossRefGoogle Scholar
  9. 9.
    Sharma R, Vignolo L, Schlotthauer G, Colominas MA, Rufiner HL, Prasanna SRM (2017) Empirical mode decomposition for adaptive am-fm analysis of speech: a review. Speech Commun 88:39–64CrossRefGoogle Scholar
  10. 10.
    Liang B, Wang TQ (2013) Method of vibration signal trend extraction based on HHT. Electronic Meas Technol 36(2):119–122Google Scholar
  11. 11.
    Jia R, Ma FQ, Wu H, Luo X, Ma X (2018) Coupling fault feature extraction method based on bivariate empirical mode decomposition and full spectrum for rotating machinery. Math Probl Eng 2:1–10Google Scholar
  12. 12.
    Yuan J, He Z, Ni J, Brzezinski AJ, Zi Y (2018) Ensemble noise-reconstructed empirical mode decomposition for mechanical fault detection. J Vib Acoust 135(2):021011CrossRefGoogle Scholar
  13. 13.
    Wang JL, Li ZJ (2013) Extreme-point symmetric mode decomposition method for data analysis. Adv Adapt Data Anal 5(3):1350015MathSciNetCrossRefGoogle Scholar
  14. 14.
    Li HF, Wang JL, Li ZJ (2013) Application of ESMD method to air-sea flux investigation. Int J Geosci 4(5):8–11CrossRefGoogle Scholar
  15. 15.
    Lin Q, Wu Z, Singh VP, Sadeghi SHR, He H, Lu G (2017) Correlation between hydrological drought, climatic factors, reservoir operation, and vegetation cover in the xijiang basin, south china. J Hydrol 549:512–524CrossRefGoogle Scholar
  16. 16.
    Yang WA, Zhou W, Liao W, Guo Y (2015) Identification and quantification of concurrent control chart patterns using extreme-point symmetric mode decomposition and extreme learning machines. Neurocomputing 147(1):260–270CrossRefGoogle Scholar
  17. 17.
    Tian X, Li Y, Zhou H, Li X, Chen L, Zhang X (2016) Electrocardiogram signal denoising using extreme-point symmetric mode decomposition and nonlocal means. Sensors 16(10):1584CrossRefGoogle Scholar
  18. 18.
    Liu X, Tang Y, Lu Z, Huang H, Tong X, Ma J (2018) ESMD-based stability analysis in the progressive collapse of a building model: a case study of a reinforced concrete frame-shear wall model. Measurement 120:34–42CrossRefGoogle Scholar
  19. 19.
    Hu C, Lin H, Li Z, He B, Liu G (2018) Kullback–Leibler divergence based distributed cubature kalman filter and its application in cooperative space object tracking. Entropy 20(2):116CrossRefGoogle Scholar
  20. 20.
    Han ZH, Zhu XX, Li WH (2012) A false component identification method of EMD based on Kullback–Leibler divergence. Proc CSEE 32(11):112–117Google Scholar
  21. 21.
    Wang B, Jiang Q, Yan X (2014) Fault detection and identification using a Kullback–Leibler divergence based multi-block principal component analysis and bayesian inference. Korean J Chem Eng 31(6):930–943CrossRefGoogle Scholar
  22. 22.
    Xie L, Zeng J, Kruger U, Wang X, Geluk J (2015) Fault detection in dynamic systems using the Kullback–Leibler divergence. Control Eng Pract 43:39–48CrossRefGoogle Scholar
  23. 23.
    Youssef A, Delpha C, Diallo D (2015) An optimal fault detection threshold for early detection using Kullback–Leibler Divergence for unknown distribution data. Sig Process 120:266–279CrossRefGoogle Scholar
  24. 24.
    Aggoune L, Chetouani Y, Raïssi T (2016) Fault detection in the distillation column process using Kullback Leibler divergence. ISA Trans 63:394–400CrossRefGoogle Scholar
  25. 25.
    Delpha C, Diallo D, Youssef A (2017) Kullback–Leibler divergence for fault estimation and isolation: application to Gamma distributed data. Mech Syst Signal Process 93:118–135CrossRefGoogle Scholar
  26. 26.
    Chen H, Jiang B, Lu N (2018) An improved incipient fault detection method based on Kullback–Leibler divergence. ISA Trans 79:127–136CrossRefGoogle Scholar
  27. 27.
    Youssef A, Delpha C, Diallo D (2016) An optimal fault detection threshold for early detection using Kullback–Leibler divergence for unknown distribution data. Sig Process 120:266–279CrossRefGoogle Scholar
  28. 28.
    Heda KE, Louani D (2018) Optimal bandwidth selection in kernel density estimation for continuous time dependent processes. Stat Probab Lett 138:9–19MathSciNetCrossRefGoogle Scholar
  29. 29.
    Raitoharju M, Ángel F, García-Fernández Piché R (2017) Kullback–Leibler divergence approach to partitioned update kalman filter. Sig Process 130:289–298CrossRefGoogle Scholar
  30. 30.
    Chai Y, Tao S, Mao W, Zhang K, Zhu Z (2018) Online incipient fault diagnosis based on Kullback–Leibler divergence and recursive principle component analysis. Can J Chem Eng 96(2):426–433CrossRefGoogle Scholar
  31. 31.
    Wen GR, Li Y, Liao YH, He Q (2013) Faulty rotor system vibration acceleration signal integration method based on precise information reconstruction. J Mech Eng 49(8):1–9CrossRefGoogle Scholar
  32. 32.
    Zhu Y, Jiang WL, Kong XD, Zheng Z, Hu HS (2015) An accurate integral method for vibration signal based on feature information extraction. Shock Vib 2015:962793Google Scholar
  33. 33.
    Xue ZH, Cao X, Wang TZ (2018) Vibration test and analysis on the centrifugal pump. J Drainage Irrig Mach Eng 36(6):472–477Google Scholar
  34. 34.
    Ren Y, Zhang K (2018) Integrated condition monitoring and fault diagnosis technology for wind turbine drive-train. J Drainage Irrig Mach Eng 36(7):613–616Google Scholar
  35. 35.
    He NC, Tan MG, Liu HL, Huang X, Wu XF (2018) Test and analysis on pressure pulsation and hydraulic performance of saddle zone in axial flow pump. J Drainage Irrig Mach Eng 36(2):118–123Google Scholar
  36. 36.
    Zhong WY, Zhu RS, Wang XL, Lu YG, Liu Y, Kang JJ (2018) Mechanical properties of nuclear reactor coolant pump impeller based on bidirectional fluid structure interaction. J Drainage Irrig Mach Eng 36(6):485–493Google Scholar
  37. 37.
    Wang C, Shi W, Wang X, Jiang X, Yang Y, Li W, Zhou L (2017) Optimal design of multistage centrifugal pump based on the combined energy loss model and computational fluid dynamics. Appl Energy 187:10–26CrossRefGoogle Scholar
  38. 38.
    Wang C, Chen X, Qiu N, Zhu Y, Shi W (2018) Numerical and experimental study on the pressure fluctuation, vibration, and noise of multistage pump with radial diffuser. J Braz Soc Mech Sci Eng 40(10):481CrossRefGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Research Center of Fluid Machinery Engineering and TechnologyJiangsu UniversityZhenjiangChina
  2. 2.Hebei Provincial Key Laboratory of Heavy Machinery Fluid Power Transmission and ControlYanshan UniversityQinhuangdaoChina

Personalised recommendations