# Decomposition of the symptom observation matrix and grey forecasting in vibration condition monitoring of machines

International Journal of Applied Mathematics and Computer Science (2008)

- Volume: 18, Issue: 4, page 569-579
- ISSN: 1641-876X

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topCzesław Cempel. "Decomposition of the symptom observation matrix and grey forecasting in vibration condition monitoring of machines." International Journal of Applied Mathematics and Computer Science 18.4 (2008): 569-579. <http://eudml.org/doc/207909>.

@article{CzesławCempel2008,

abstract = {With the tools of modern metrology we can measure almost all variables in the phenomenon field of a working machine, and many of the measured quantities can be symptoms of machine conditions. On this basis, we can form a symptom observation matrix (SOM) intended for condition monitoring and wear trend (fault) identification. On the other hand, we know that contemporary complex machines may have many modes of failure, called faults. The paper presents a method of the extraction of the information about faults from the symptom observation matrix by means of singular value decomposition (SVD), in the form of generalized fault symptoms. As the readings of the symptoms can be unstable, the moving average of the SOM is applied with success. An attempt to assess the diagnostic contribution of a primary symptom is made, and also an approach to assess the symptom limit value and to connect the SVD methodology with neural nets is considered. Finally, a condition forecasting problem is discussed and an application of grey system theory (GST) to symptom prognosis is presented. These possibilities are illustrated by processing data taken directly from the machine vibration condition monitoring area.},

author = {Czesław Cempel},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {machine wear; multidimensional observation; vibration; SVD decomposition; fault space; observation space; symptom limit value; forecasting; grey system theory},

language = {eng},

number = {4},

pages = {569-579},

title = {Decomposition of the symptom observation matrix and grey forecasting in vibration condition monitoring of machines},

url = {http://eudml.org/doc/207909},

volume = {18},

year = {2008},

}

TY - JOUR

AU - Czesław Cempel

TI - Decomposition of the symptom observation matrix and grey forecasting in vibration condition monitoring of machines

JO - International Journal of Applied Mathematics and Computer Science

PY - 2008

VL - 18

IS - 4

SP - 569

EP - 579

AB - With the tools of modern metrology we can measure almost all variables in the phenomenon field of a working machine, and many of the measured quantities can be symptoms of machine conditions. On this basis, we can form a symptom observation matrix (SOM) intended for condition monitoring and wear trend (fault) identification. On the other hand, we know that contemporary complex machines may have many modes of failure, called faults. The paper presents a method of the extraction of the information about faults from the symptom observation matrix by means of singular value decomposition (SVD), in the form of generalized fault symptoms. As the readings of the symptoms can be unstable, the moving average of the SOM is applied with success. An attempt to assess the diagnostic contribution of a primary symptom is made, and also an approach to assess the symptom limit value and to connect the SVD methodology with neural nets is considered. Finally, a condition forecasting problem is discussed and an application of grey system theory (GST) to symptom prognosis is presented. These possibilities are illustrated by processing data taken directly from the machine vibration condition monitoring area.

LA - eng

KW - machine wear; multidimensional observation; vibration; SVD decomposition; fault space; observation space; symptom limit value; forecasting; grey system theory

UR - http://eudml.org/doc/207909

ER -

## References

top- Bartelmus W., Zimroz Z. and Batra H. (2003). Gearbox vibration signal preprocessing and input values choice for neural network training, Proceedings of the Conference on AI Methods, Gliwice, Poland.
- Cempel C. (1999). Innovative developments in systems condition monitoring, Keynote Lecture, Proceedings of the Conference on Damage Assessment DAMAS'99, Dublin, Ireland, pp. 172-188.
- Cempel C., Natke H.G. and Yao J.P.T. (2000). Symptom reliability and hazard for systems condition monitoring, Mechanical Systems and Signal Processing 14(3): 495-505.
- Cempel C. (2003). Multidimensional condition monitoring of mechanical systems in operation, Mechanical Systems and Signal Processing 17(6): 1291-1303.
- Cempel C. and Tabaszewski M. (2007). Multidimensional vibration condition monitoring of nonstationary systems in operation, Mechanical Systems and Signal Processing 21(3): 1233-1241.
- Cempel C., Krakowiak, M. (2006a). Influence of running stability and randomness of observation on the condition assessment in multidimensional machine diagnostics, Diagnostyka 40(4): 19-25 .
- Cempel C. and Tabaszewski M. (2006b). Averaging the symptoms in multidimensional condition monitoring for machines in nonstationary operation, Proceedings of the 13 International Congress on Sound and Vibration, Vienna, Austria, CD-ROM.
- Cempel C. (2004). Implementing multidimensional inference capability in vibration condition monitoring, Proceedings of the Conference on Acoustical and Vibratory Surveillance, Senlis, France.
- Cempel C. (2005). Multi fault vibrational diagnostics of critical machines, Zagadnienia Eksploatacji Maszyn 4(144): 133-142.
- Cempel C. (1991). Vibroacoustic Condition Monitoring, Ellis Horwood, London.
- Cempel C. (1987). Simple condition forecasting techniques in vibroacoustical diagnostics, Mechanical Systems and Signal Processing 1(1): 75-82. Zbl0673.62095
- Cempel C. (2008). Forecasting the global and partial system condition by means of multidimensional condition monitoring, Journal of Theoretical and Applied Mechanics 46(4): 777-797.
- Deng J.L. (1982). Control problems of grey systems, Systems and Control Letters 1(5): 288-294. Zbl0482.93003
- Deng J-L. (1989). Introduction to grey system theory, The Journal of Grey Systems 1(1): 1-24. Zbl0701.90057
- Dunham M.H. (2003). Data Mining-Introductory and Advanced Topics, Prentice Hall, Englewood Cliffs, NJ.
- Golub G.H., VanLoan C. F. (1983), Matrix Computation, North Oxford Academic, Oxford.
- Jasiński M. (2004). Empirical models in gearbox diagnostics, Ph.D. thesis, Warsaw University of Technology, (in Polish).
- Korbicz J., Koscielny J.M., Kowalczuk Z. and Cholewa W. (Eds.) (2004). Fault Diagnosis-Models, Artificial Intelligence, Applications, Springer Verlag, Berlin. Zbl1074.93004
- Kiełbasiński A. and Schwietlick H. (1992). Numeric Linear Algebra, WNT, Warsaw, (in Polish).
- Natke H. G. and Cempel C. (2002). The symptom observation matrix for monitoring and diagnosis, Journal of Sound and Vibration 248(4): 597-620.
- Natke H. G. and Cempel C. (1997). Model Aided Diagnosis of Mechanical Systems, Springer-Verlag, Berlin. Zbl1080.93589
- Pantopian N. H. and Larsen J. (1999). Unsupervised condition detection in large diesel engines, Proceedings of the IEEE Workshop on Neural Networks.
- Tabaszewski M. (2006). Forecasting of residual life of a fan mill by means of neural nets, Diagnostyka 3(39): 149-156, (in Polish).
- Tumer I.Y. and Huff E.M. (2002). Principal component analysis of tri-axial vibration data from helicopter transmission, Proceedings of 56th Meeting of the Society of Machine Failure Prevention Technology.
- Wen K.L. and Chang T. C. (2005). The research and development of completed GM(1,1) model toolbox using Matlab, International Journal of Computational Cognition 3(3): 42-48.
- Will T. (2005). Hanger matrix, two-thirds theorem, available at: http://www.uwlax.edu/faculty/will/svd/svd/index.html.
- Żółtowski B. and Cempel C. (Eds.) (2004). Engineering of Machine Diagnostics, ITE Press, Radom, p. 1308, (in Polish).
- Yao A.W.L. and Chi S.C. (2004). Analysis and design of a Taguchi-Grey based electricity demand predictor for energy management systems, Energy Conversion and Management 45: 1205-1217.

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