Decomposition of vibration signals into deterministic and nondeterministic components and its capabilities of fault detection and identification

Tomasz Barszcz

International Journal of Applied Mathematics and Computer Science (2009)

  • Volume: 19, Issue: 2, page 327-335
  • ISSN: 1641-876X

Abstract

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The paper investigates the possibility of decomposing vibration signals into deterministic and nondeterministic parts, based on the Wold theorem. A short description of the theory of adaptive filters is presented. When an adaptive filter uses the delayed version of the input signal as the reference signal, it is possible to divide the signal into a deterministic (gear and shaft related) part and a nondeterministic (noise and rolling bearings) part. The idea of the self-adaptive filter (in the literature referred to as SANC or ALE) is presented and its most important features are discussed. The flowchart of the Matlab-based SANC algorithm is also presented. In practice, bearing fault signals are in fact nondeterministic components, due to a little jitter in their fundamental period. This phenomenon is illustrated using a simple example. The paper proposes a simulation of a signal containing deterministic and nondeterministic components. The self-adaptive filter is then applied - first to the simulated data. Next, the filter is applied to a real vibration signal from a wind turbine with an outer race fault. The necessity of resampling the real signal is discussed. The signal from an actual source has a more complex structure and contains a significant noise component, which requires additional demodulation of the decomposed signal. For both types of signals the proposed SANC filter shows a very good ability to decompose the signal.

How to cite

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Tomasz Barszcz. "Decomposition of vibration signals into deterministic and nondeterministic components and its capabilities of fault detection and identification." International Journal of Applied Mathematics and Computer Science 19.2 (2009): 327-335. <http://eudml.org/doc/207939>.

@article{TomaszBarszcz2009,
abstract = {The paper investigates the possibility of decomposing vibration signals into deterministic and nondeterministic parts, based on the Wold theorem. A short description of the theory of adaptive filters is presented. When an adaptive filter uses the delayed version of the input signal as the reference signal, it is possible to divide the signal into a deterministic (gear and shaft related) part and a nondeterministic (noise and rolling bearings) part. The idea of the self-adaptive filter (in the literature referred to as SANC or ALE) is presented and its most important features are discussed. The flowchart of the Matlab-based SANC algorithm is also presented. In practice, bearing fault signals are in fact nondeterministic components, due to a little jitter in their fundamental period. This phenomenon is illustrated using a simple example. The paper proposes a simulation of a signal containing deterministic and nondeterministic components. The self-adaptive filter is then applied - first to the simulated data. Next, the filter is applied to a real vibration signal from a wind turbine with an outer race fault. The necessity of resampling the real signal is discussed. The signal from an actual source has a more complex structure and contains a significant noise component, which requires additional demodulation of the decomposed signal. For both types of signals the proposed SANC filter shows a very good ability to decompose the signal.},
author = {Tomasz Barszcz},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {decomposition; vibration; deterministic component; nondeterministic component; rolling bearing},
language = {eng},
number = {2},
pages = {327-335},
title = {Decomposition of vibration signals into deterministic and nondeterministic components and its capabilities of fault detection and identification},
url = {http://eudml.org/doc/207939},
volume = {19},
year = {2009},
}

TY - JOUR
AU - Tomasz Barszcz
TI - Decomposition of vibration signals into deterministic and nondeterministic components and its capabilities of fault detection and identification
JO - International Journal of Applied Mathematics and Computer Science
PY - 2009
VL - 19
IS - 2
SP - 327
EP - 335
AB - The paper investigates the possibility of decomposing vibration signals into deterministic and nondeterministic parts, based on the Wold theorem. A short description of the theory of adaptive filters is presented. When an adaptive filter uses the delayed version of the input signal as the reference signal, it is possible to divide the signal into a deterministic (gear and shaft related) part and a nondeterministic (noise and rolling bearings) part. The idea of the self-adaptive filter (in the literature referred to as SANC or ALE) is presented and its most important features are discussed. The flowchart of the Matlab-based SANC algorithm is also presented. In practice, bearing fault signals are in fact nondeterministic components, due to a little jitter in their fundamental period. This phenomenon is illustrated using a simple example. The paper proposes a simulation of a signal containing deterministic and nondeterministic components. The self-adaptive filter is then applied - first to the simulated data. Next, the filter is applied to a real vibration signal from a wind turbine with an outer race fault. The necessity of resampling the real signal is discussed. The signal from an actual source has a more complex structure and contains a significant noise component, which requires additional demodulation of the decomposed signal. For both types of signals the proposed SANC filter shows a very good ability to decompose the signal.
LA - eng
KW - decomposition; vibration; deterministic component; nondeterministic component; rolling bearing
UR - http://eudml.org/doc/207939
ER -

References

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  1. Antoni, J. and Randall, R.B. (2004). Unsupervised noise cancellation for vibration signals: Part I-Evaluation of adaptive algorithms, Mechanical Systems and Signal Processing 18(1): 89-101. 
  2. Barszcz, T. (2004). Proposal of new method for mechanical vibration measurement, Metrology and Measurement Systems 11(4): 409-421. 
  3. Chaturvedi, G.K. and Thomas, D.W. (1981). Adaptive noise cancelling and condition monitoring, Journal of Sound and Vibration 76(3): 391-405. 
  4. Haykin, S. (1996). Adaptive Filter Theory, Prentice-Hall, Upper Saddle River, NJ. Zbl0723.93070
  5. Ho, D. and Randall, R.B. (2000). Optimisation of bearing diagnostic techniques using simulated and actual bearing faults, Mechanical Systems and Signal Processing 14(5): 763-788. 
  6. Lee, S.K. and White, P.R. (1998). The enhancement of impulsive noise and vibration signals for fault detection in rotating and reciprocating machinery, Journal of Sound and Vibration 217(3): 485-505. 
  7. Shao, Y. and Nezu, K. (2005). Design of mixture de-noising for detecting faulty bearing signals, Journal of Sound and Vibration 282(4): 899-917. 
  8. Shynk, J.J. (1992). Frequency-domain and multirate adaptive filtering, IEEE Signal Processing Magazine 9(1): 14-37. 
  9. The MathWorks (2006). Filter Design Toolbox, Matlab documentation, Mathworks V4.2 /R2008a/. 
  10. Widrow, B., Glover, J. R., McCool, J. M., Kaunitz, J., Williams, C. S., Hearn, R. H., Zeidler, J. R., Dong, E. and Goodlin, R. C. (1975). Adaptive noise cancelling: Principles and applications, Proceedings of the IEEE 63(12): 1692-1716. 
  11. Zeidler, J., Satorius, E., Chabries, D. and Wexler, H. (1978). Adaptive enhancement of multiple sinusoids in uncorrelated noise, IEEE Transactions on Acoustics, Speech, and Signal Processing 26(3): 240-254. Zbl0415.93039
  12. Zieliński, T.P. (2007). Digital Signal Processing. From Theory to Applications, WKŁ, Warsaw, (in Polish). 
  13. Żółtowski, B. and Cempel, C. (Eds.) (2004). Engineering of Machinery Diagnostics, PTDT ITE PIB Radom, Warsaw/Bydgoszcz/Radom, (in Polish). 

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