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Tracking and Removing Modulated Harmonic Components with Spectral Kurtosis and Kalman Filters

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Book cover Topics in Modal Analysis, Volume 7

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Abstract

This work describes an automatic method for removing modulated sinusoidal components in signals. The method consists in using the Optimized Spectral Kurtosis for initializing Series of Extended Kalman Filters. The first section is an introduction to vibration applications with Kalman Filters and modulated sinusoids. The detection process with OSK is described in the second section. The third section concerns the tracking algorithm with SEKF for amplitude and frequency modulated sinusoidal components. The last section deals with the complete process illustrated with an experimental application on a rotating machine.

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Abbreviations

ARMA:

Auto Regressive – Moving Average

DOF:

Degree Of Freedom

EKF:

Extended Kalman Filter

SEKF:

Series of Extended Kalman Filters

OMA:

Operational Modal Analysis

OSK:

Optimized Spectral Kurtosis

PBF:

Pass Band Filter

PSD:

Power Spectral Density

References

  1. Dion J-L, Tawfiq I, Chevallier G (2012) Sinusoidal component detection: Optimized Spectral Kurtosis for operational modal analysis. Mech Syst Signal Process 26:24–33

    Google Scholar 

  2. Kalman RE (1960) A new approach to linear filtering and prediction problems. Trans Am Soc Mech Eng Ser D – J Basic Eng 82:35–45

    Google Scholar 

  3. Seibold S, Weinert K (1996) A time domain method for the localization of cracks in rotors. J Sound Vib 195:57–73

    Google Scholar 

  4. Wang Z, Yan W, Shao Y (2009) Three-step method for stiffness identification of inter-story shearing structures under ambient excitation. Tsinghua Sci Technol 14:69–74

    Google Scholar 

  5. Ma C-K, Lin D-C, Chang J-M (1999) Estimation of forces generated by a machine mounted upon isolators under operating conditions. J Frankl Inst 336:875–892

    Google Scholar 

  6. Ma C-K, Ho C-C (2004) An inverse method for the estimation of input forces acting on non-linear structural systems. J Sound Vib 275:953–971

    Google Scholar 

  7. Zhan YM, Jardine AKS (2005) Adaptive autoregressive modeling of non-stationary vibration signals under distinct gear states. Part 1: modeling. J Sound Vib 286:429–450

    Google Scholar 

  8. Zhan Y, Mechefske CK (2007) Robust detection of gearbox deterioration using compromised autoregressive modeling and Kolmogorov–Smirnov test statistic. Part I: compromised autoregressive modeling with the aid of hypothesis tests and simulation analysis. Mech Syst Signal Process 21:1953–1982

    Google Scholar 

  9. Zhan Y, Mechefske CK (2007) Robust detection of gearbox deterioration using compromised autoregressive modeling and Kolmogorov–Smirnov test statistic. Part II: experiment and application. Mech Syst Signal Process 21:1983–2011

    Google Scholar 

  10. Shao Y, Mechefske CK (2009) Gearbox vibration monitoring using extended Kalman filters and hypothesis tests. J Sound Vib 325:629–648

    Google Scholar 

  11. Wang G, Luo Z, Qin X, Leng Y, Wang T (2008) Fault identification and classification of rolling element bearing based on time-varying autoregressive spectrum. Mech Syst Signal Process 22:934–947

    Google Scholar 

  12. Al-Zaharnah IT (2006) Suppressing vibrations of machining processes in both feed and radial directions using an optimal control strategy: the case of interrupted cutting. J Mater Process Technol 172:305–310

    Google Scholar 

  13. Dong X-J, Meng G, Peng J-C (2006) Vibration control of piezoelectric smart structures based on system identification technique: numerical simulation and experimental study. J Sound Vib 297:680–693

    Google Scholar 

  14. Marzbanrad J, Ahmadi G, Zohoor H, Hojjat Y (2004) Stochastic optimal preview control of a vehicle suspension. J Sound Vib 275:973–990

    Google Scholar 

  15. Yoshimura T, Edokoro K, Ananthanarayana N (1993) An active suspension model For rail/vehicle systems with preview and stochastic optimal control. J Sound Vib 166:507–519

    Google Scholar 

  16. Bai M, Huang J, Hong M, Su F (2005) Fault diagnosis of rotating machinery using an intelligent order tracking system. J Sound Vib 280: 699–718

    Google Scholar 

  17. Blough JR (2003) Development and analysis of time variant discrete Fourier transform order tracking. Mech Syst Signal Process 17:1185–1199

    Google Scholar 

  18. Guo Y, Tan KK (2009) Order-crossing removal in Gabor order tracking by independent component analysis. J Sound Vib 325:471–488

    Google Scholar 

  19. Pan M-C, Chiu C-C (2006) Investigation on improved Gabor order tracking technique and its applications. J Sound Vib 295:810–826

    Google Scholar 

  20. Pan M-C, Liao S-W, Chiu C-C (2007) Improvement on Gabor order tracking and objective comparison with Vold–Kalman filtering order tracking. Mech Syst Signal Process 21:653–667

    Google Scholar 

  21. Vold H, Leuridan J (1993) High resolution order tracking at extreme slew rates, using Kalman tracking filters SAE Paper No. 931288

    Google Scholar 

  22. Vold H, Herlufsen H (1997) Multi axle order tracking with the Vold–Kalman tracking filter Sound Vib 31(5):30–34

    Google Scholar 

  23. Guo Y, Tan KK (2010) High efficient crossing-order decoupling in Vold–Kalman filtering order tracking based on independent component analysis. Mech Syst Signal Process 24:1756–1766

    Google Scholar 

  24. Pan M-C, Lin Y-F (2006a) Further exploration of Vold–Kalman-filtering order tracking with shaft-speed information–I: theoretical part, numerical implementation and parameter investigations. Mech Syst Signal Process 20:1134–1154

    Google Scholar 

  25. Pan M-C, Lin Y-F (2006b) Further exploration of Vold–Kalman-filtering order tracking with shaft-speed information–II: engineering applications. Mech Syst Signal Process 20:1410–1428

    Google Scholar 

  26. Pan M-C, Wu C-X (2007) Adaptive Vold–Kalman filtering order tracking. Mech Syst Signal Process 21:2957–2969

    Google Scholar 

  27. Wang KS, Heyns PS (2011a) An empirical re-sampling method on intrinsic mode function to deal with speed variation in machine fault diagnostics. Appl Soft Comput 11:5015–5027

    Google Scholar 

  28. Wang KS, Heyns PS (2011b) The combined use of order tracking techniques for enhanced Fourier analysis of order components. Mech Syst Signal Process 25:803–811

    Google Scholar 

  29. Wang KS, Heyns PS (2011c) Application of computed order tracking, Vold–Kalman filtering and EMD in rotating machine vibration. Mech Syst Signal Process 25:416–430

    Google Scholar 

  30. Pan M-C, Wu C-X (2010) Extended angular-velocity Vold–Kalman order tracking. J Dyn Syst Meas Control 132(3) doi:10.1115/1.4001326

    Google Scholar 

  31. Parks TW, Burrus CS (1987) Digital filter design. Wiley, New York. Chapter 7

    Google Scholar 

  32. Randall RB (2001) Cepstrum analysis. In: Ewins D, Rao SS, Braun S (eds) Encyclopedia of vibration. Elsevier, Oxford, pp 216–227

    Google Scholar 

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Author information

Authors and Affiliations

  1. Laboratoire d’Ingénierie des Systèmes Mécaniques et des Matériaux (LISMMA) – EA 2336, SUPMECA Paris 3, rue Fernand Hainaut, 93407, Saint Ouen, France

    Jean-Luc Dion, Gaël Chevallier & Hugo Festjens

  2. ONERA, Châtillon, France

    Cyrille Stephan

Authors
  1. Jean-Luc Dion
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  2. Cyrille Stephan
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  3. Gaël Chevallier
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  4. Hugo Festjens
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Corresponding author

Correspondence to Jean-Luc Dion .

Editor information

Editors and Affiliations

  1. University of Cincinnati, Cincinnati, 45221-0018, Ohio, USA

    Randall Allemang

  2. , The Enterprise Program, Michigan Technological University, Townsend Drive 1400, Houghton, 49931, Mississippi, USA

    James De Clerck

  3. , Dept. of Mechanical Engineering, University of Massachusetts Lowell, Riverside St. 197, Lowell, 01854, Massachusetts, USA

    Christopher Niezrecki

  4. & State University, Department of Mechanical Engineering, Virginia Polytechnic Institute, Randolph Hall 114 T, Blacksburg, 24060, Virginia, USA

    Alfred Wicks

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© 2014 The Society for Experimental Mechanics

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Dion, JL., Stephan, C., Chevallier, G., Festjens, H. (2014). Tracking and Removing Modulated Harmonic Components with Spectral Kurtosis and Kalman Filters. In: Allemang, R., De Clerck, J., Niezrecki, C., Wicks, A. (eds) Topics in Modal Analysis, Volume 7. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6585-0_20

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  • DOI: https://doi.org/10.1007/978-1-4614-6585-0_20

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-6584-3

  • Online ISBN: 978-1-4614-6585-0

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