Mathematical Model and Regression Analysis of Acoustic Emission Signals Generated by Partial Discharges

Daria Wotzka

doi:doi:10.11648/j.acm.20140305.15

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Mathematical Model and Regression Analysis of Acoustic Emission Signals Generated by Partial Discharges

Daria Wotzka

Published in Applied and Computational Mathematics (Volume 3, Issue 5)

Received: 10 September 2014 Accepted: 19 September 2014 Published: 30 September 2014

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Abstract

An improved mathematical model describing acoustic emission (AE) signals generated by different types of partial discharges (PD) that occur in electric power transformer insulation system is presented in the paper. AE signals are analyzed within the AE method as applied for power transformer failure detection due to occurrence of PD. There are several types of basic defects, which are characterized by different types of PD. The mathematical model presented here is crucial for numerical analyses and simulations, where it acts as the function describing the acoustic source in an acoustic model of power transformer insulation system. The regression procedure was performed based on empirical AE signals, registered in a laboratory experiment. The AE signals are described by a mathematical model being a multi-parameter function, which involve both the time domain and the frequency domain. Goodness of the model was evaluated based on analysis of 480 data samples in the time, frequency and time-frequency domains. Also coherence between the registered and modeled signals was calculated. It was stated that the improved model fits very well to the real data, although, due to high level of noise embodied in signals registered in experiments, the coherence values remain low. Moreover, analyses of the estimated data were performed and some example results are presented in this paper. Based on the achieved outcomes a collection of parameter values was prepared for each of the eight considered PD basic types. One can simple use it now in a numerical model for simulation of AE signal source generated by specified type of PD, what corresponds to a particular power transformer insulation system failure. Furthermore, the regression procedure presented in this paper can be easily transferred to any other types of AE sources including processes of compression, tension and cracking.

Published in	Applied and Computational Mathematics (Volume 3, Issue 5)
DOI	10.11648/j.acm.20140305.15
Page(s)	225-230
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Modeling, Regression Analysis, Acoustic Emission, Partial Discharges

References

[1]	S. Borucki, “Diagnosis of technical condition of power transformers based on the analysis of vibroacoustic signals measured in transient operating conditions”, IEEE Trans. Pow. Del. Vol. 27, pp. 2012, 670–676. DOI: 10.11000009/TPWRD.2012.2185955
[2]	L. E. Lundgaard, “Partial discharge - part XIV: Acoustic PD detection – practical application”. IEEE El. Insul. Mag., Vol. 8, No. 5, 1992, pp. 34–43.DOI: 10.1109/57.156943
[3]	P. Frącz, “Influence estimation of the voltage value on the measurement results for the optical radiation generated by partial discharges on bushing isolator”, Acta Phys. Pol. A, Vol. 120, 2011, pp. 604-607,
[4]	A. Cichoń, P. Frącz, D. Zmarzły, “Characteristic of acoustic signals generated by operation of on load tap changers”, Acta Phys. Pol. A, Vol. 120, 2011, pp. 585-589.
[5]	J. Gubio-Serrano, M.V. Rojas-Moreno, J. Posada, J.M. Martinez-Tarifa, G. Robles, J.A. Garcia-Souto, „Electro-acoustic detection, identification and location of PD sources in oil-paper insulation systems”, IEEE trans. Dielectr. Electr. Insul., Vol. 19, No. 5, 2012, pp. 1569-1578, DOI: 10.1109/TDEI.2012.6311502
[6]	M. Pompili, R. Bartnikas, “On PD measurement in dielectric liquids”, IEEE Trans. Dielectr. Electr. Insul, Vol. 19, No. 5, 2012, pp. 1476-1481. DOI: 10.1109/TDEI.2012.6311489
[7]	M. Shibata, “A theoretical evaluation of AE signals - the rise time effect of dynamic forces”. Mat. Eval., Vol. 42, No. 1, 1984, pp. 107–115.
[8]	L. Bolin, “A model for estimating the signal from an acoustic emission source”. Ultrason., Vol. 17, No. 2, 1979, pp. 67–70.
[9]	T. Boczar, D. Zmarzły, “The application of correlation analysis to acoustic emission pulses generated by partial discharges”, Mat. Eval., Vol. 62, No. 9, 2004, pp. 935-942.
[10]	T. Boczar, D. Zmarzły, “Multiresolution analysis of the AE pulses generated by PD”, INSIGHT, Vol. 45, No. 7, 2003, pp. 488-492.
[11]	T. Boczar, A. Cichoń, S. Borucki “Diagnostic expert system of transformer insulation systems using the acoustic emission method”, IEEE Trans. Dielectr. Electr. Insul., Vol. 21, No. 2, 2014, pp. 854–865. DOI 10.1109/TDEI.2013.004126
[12]	S. Rudd, S.D.J. Mcarthur, M.D. Judd, “A generic knowledge-based approach to the analysis of PD data”, IEEE Trans. Dielectr. Electr. Insul., Vol. 17, No. 1, 2010, pp. 149 – 156. DOI: 10.1109/TDEI.2010.5412013
[13]	K.X. Lai, B.T. Phung, T.R. Blackburn, “Application of data mining on PD part I: predictive modelling classification”, IEEE Trans. Dielectr. Electr. Insul., Vol. 17, No. 3, 2010, pp. 846–854. DOI: 10.1109/TDEI.2010.5492258
[14]	T. Pinpart, M.D. Judd, “Differentiating between PD sources using envelope comparison of ultra-high-frequency signals”, IET Science, Measurement & Technology, Vol. 4 , No. 5, 2010, pp. 256–267. DOI: 10.1049/IET-SMT.2009.0064
[15]	A. Cichoń, S. Borucki, D. Wotzka, “Modeling of acoustic emission signals generated in on load tap changer” Acta Phys. Pol. A, Vol. 125, No. 6, 2014, pp.1396-1399. DOI: 10.12693/APhyspolA.125.1396
[16]	D. Wotzka, A. Cichoń, T. Boczar, “Modeling and experimental verification of ultrasound transmission in electro insulation oil”, Arch. Acoust., Vol. 37, No. 1, 2012, pp. 19-22, DOI: 10.2478/v10168-012-0003-x.

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Daria Wotzka. (2014). Mathematical Model and Regression Analysis of Acoustic Emission Signals Generated by Partial Discharges. Applied and Computational Mathematics, 3(5), 225-230. https://doi.org/10.11648/j.acm.20140305.15

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Daria Wotzka. Mathematical Model and Regression Analysis of Acoustic Emission Signals Generated by Partial Discharges. Appl. Comput. Math. 2014, 3(5), 225-230. doi: 10.11648/j.acm.20140305.15

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Daria Wotzka. Mathematical Model and Regression Analysis of Acoustic Emission Signals Generated by Partial Discharges. Appl Comput Math. 2014;3(5):225-230. doi: 10.11648/j.acm.20140305.15

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@article{10.11648/j.acm.20140305.15,
  author = {Daria Wotzka},
  title = {Mathematical Model and Regression Analysis of Acoustic Emission Signals Generated by Partial Discharges},
  journal = {Applied and Computational Mathematics},
  volume = {3},
  number = {5},
  pages = {225-230},
  doi = {10.11648/j.acm.20140305.15},
  url = {https://doi.org/10.11648/j.acm.20140305.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140305.15},
  abstract = {An improved mathematical model describing acoustic emission (AE) signals generated by different types of partial discharges (PD) that occur in electric power transformer insulation system is presented in the paper. AE signals are analyzed within the AE method as applied for power transformer failure detection due to occurrence of PD. There are several types of basic defects, which are characterized by different types of PD. The mathematical model presented here is crucial for numerical analyses and simulations, where it acts as the function describing the acoustic source in an acoustic model of power transformer insulation system. The regression procedure was performed based on empirical AE signals, registered in a laboratory experiment. The AE signals are described by a mathematical model being a multi-parameter function, which involve both the time domain and the frequency domain. Goodness of the model was evaluated based on analysis of 480 data samples in the time, frequency and time-frequency domains. Also coherence between the registered and modeled signals was calculated. It was stated that the improved model fits very well to the real data, although, due to high level of noise embodied in signals registered in experiments, the coherence values remain low. Moreover, analyses of the estimated data were performed and some example results are presented in this paper. Based on the achieved outcomes a collection of parameter values was prepared for each of the eight considered PD basic types. One can simple use it now in a numerical model for simulation of AE signal source generated by specified type of PD, what corresponds to a particular power transformer insulation system failure. Furthermore, the regression procedure presented in this paper can be easily transferred to any other types of AE sources including processes of compression, tension and cracking.},
 year = {2014}
}

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TY - JOUR
T1 - Mathematical Model and Regression Analysis of Acoustic Emission Signals Generated by Partial Discharges
AU - Daria Wotzka
Y1 - 2014/09/30
PY - 2014
N1 - https://doi.org/10.11648/j.acm.20140305.15
DO - 10.11648/j.acm.20140305.15
T2 - Applied and Computational Mathematics
JF - Applied and Computational Mathematics
JO - Applied and Computational Mathematics
SP - 225
EP - 230
PB - Science Publishing Group
SN - 2328-5613
UR - https://doi.org/10.11648/j.acm.20140305.15
AB - An improved mathematical model describing acoustic emission (AE) signals generated by different types of partial discharges (PD) that occur in electric power transformer insulation system is presented in the paper. AE signals are analyzed within the AE method as applied for power transformer failure detection due to occurrence of PD. There are several types of basic defects, which are characterized by different types of PD. The mathematical model presented here is crucial for numerical analyses and simulations, where it acts as the function describing the acoustic source in an acoustic model of power transformer insulation system. The regression procedure was performed based on empirical AE signals, registered in a laboratory experiment. The AE signals are described by a mathematical model being a multi-parameter function, which involve both the time domain and the frequency domain. Goodness of the model was evaluated based on analysis of 480 data samples in the time, frequency and time-frequency domains. Also coherence between the registered and modeled signals was calculated. It was stated that the improved model fits very well to the real data, although, due to high level of noise embodied in signals registered in experiments, the coherence values remain low. Moreover, analyses of the estimated data were performed and some example results are presented in this paper. Based on the achieved outcomes a collection of parameter values was prepared for each of the eight considered PD basic types. One can simple use it now in a numerical model for simulation of AE signal source generated by specified type of PD, what corresponds to a particular power transformer insulation system failure. Furthermore, the regression procedure presented in this paper can be easily transferred to any other types of AE sources including processes of compression, tension and cracking.
VL - 3
IS - 5
ER -

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Daria Wotzka

Faculty of Electrical Engineering, Automatic Control and Informatics, Opole University of Technology, Opole, Poland

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Daria Wotzka. (2014). Mathematical Model and Regression Analysis of Acoustic Emission Signals Generated by Partial Discharges. Applied and Computational Mathematics, 3(5), 225-230. https://doi.org/10.11648/j.acm.20140305.15

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ACS Style

Daria Wotzka. Mathematical Model and Regression Analysis of Acoustic Emission Signals Generated by Partial Discharges. Appl. Comput. Math. 2014, 3(5), 225-230. doi: 10.11648/j.acm.20140305.15

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AMA Style

Daria Wotzka. Mathematical Model and Regression Analysis of Acoustic Emission Signals Generated by Partial Discharges. Appl Comput Math. 2014;3(5):225-230. doi: 10.11648/j.acm.20140305.15

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@article{10.11648/j.acm.20140305.15,
  author = {Daria Wotzka},
  title = {Mathematical Model and Regression Analysis of Acoustic Emission Signals Generated by Partial Discharges},
  journal = {Applied and Computational Mathematics},
  volume = {3},
  number = {5},
  pages = {225-230},
  doi = {10.11648/j.acm.20140305.15},
  url = {https://doi.org/10.11648/j.acm.20140305.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140305.15},
  abstract = {An improved mathematical model describing acoustic emission (AE) signals generated by different types of partial discharges (PD) that occur in electric power transformer insulation system is presented in the paper. AE signals are analyzed within the AE method as applied for power transformer failure detection due to occurrence of PD. There are several types of basic defects, which are characterized by different types of PD. The mathematical model presented here is crucial for numerical analyses and simulations, where it acts as the function describing the acoustic source in an acoustic model of power transformer insulation system. The regression procedure was performed based on empirical AE signals, registered in a laboratory experiment. The AE signals are described by a mathematical model being a multi-parameter function, which involve both the time domain and the frequency domain. Goodness of the model was evaluated based on analysis of 480 data samples in the time, frequency and time-frequency domains. Also coherence between the registered and modeled signals was calculated. It was stated that the improved model fits very well to the real data, although, due to high level of noise embodied in signals registered in experiments, the coherence values remain low. Moreover, analyses of the estimated data were performed and some example results are presented in this paper. Based on the achieved outcomes a collection of parameter values was prepared for each of the eight considered PD basic types. One can simple use it now in a numerical model for simulation of AE signal source generated by specified type of PD, what corresponds to a particular power transformer insulation system failure. Furthermore, the regression procedure presented in this paper can be easily transferred to any other types of AE sources including processes of compression, tension and cracking.},
 year = {2014}
}

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