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## Ingeniare. Revista chilena de ingeniería

*versión On-line* ISSN 0718-3305

### Ingeniare. Rev. chil. ing. v.18 n.2 Arica ago. 2010

#### http://dx.doi.org/10.4067/S0718-33052010000200002

Ingeniare. Revista chilena de ingeniería, vol. 18 Nº 2, 2010, pp. 158-164

**ARTÍCULOS**

**APPLICATIONS OF WAVELETS IN INDUCTION MACHINE FAULT DETECTION**

**Erick Schmitt ^{1} , Peter Idowu^{1} , Aldo Morales^{1} **

^{1} Electrical Engineering Program, Penn State Harrisburg, 777 West Harrisburg Pike,

**RESUMEN**

Este trabajo presenta un nuevo algoritmo basado en wavelets para la detección de fallas en máquinas de inducción de tres fases. Este nuevo método utiliza la desviación estándar de los coeficientes wavelet, que se obtiene de la descomposición de n-niveles de cada fase, para identificar fallas en el voltaje en una fase o fallas en la resistencia del estator en máquinas de inducción. El algoritmo propuesto puede funcionar independiente de la frecuencia de operación, tipo de falla y condiciones de carga. Los resultados muestran que este algoritmo tiene una mejor respuesta de detección que las técnicas basadas en la transformada de Fourier.

**Palabras clave:** Wavelets, detección de fallas, máquinas de inducción, transformada rápida de Fourier, detección temprana.

*ABSTRACT *

*This paper presents a new wavelet-based algorithm for three-phase induction machine fault detection. This new method uses the standard deviation of wavelet coefficients, obtained from n-level decomposition of each phase voltage and current, to identify single-phasing faults or unbalanced stator resistance faults in induction machines. The proposed algorithm can operate independent of the operational frequency, fault type and loading conditions. Results show that this algorithm has better detection response than the Fourier transform-based techniques.*

**Keywords**: *Wavelets, fault detection, induction machines, fast Fourier transform, early detection. *

**INTRODUCTION**

This paper presents a novel induction motor fault detection system that does not require a large amount of data such as in the Fourier analysis techniques. The method uses wavelet analysis to classify winding related motor problems such as open winding and winding resistance. Specifically standard deviation of wavelets coefficients were used for this purpose. After extensive simulations, it was determined that the reverse biorthogonal wavelet is the best one to extract features for our fault-detection algorithm. Note that in this algorithm, machine's characteristic frequencies do not have to be known in advance as in [2]. This algorithm also uses voltage and current information; unlike in [3] that use only armature current. In addition, in [3], the performance of the reverse biorthogonal wavelet was not investigated. Furthermore, the reduction of memory requirements allow the implementation of this system with lower cost hardware and permit the algorithm to be run in near real-time.

**OVERVIEW OF THE WAVELET TRANSFORM TECHNIQUE**

Fourier analysis techniques provide significant information on frequency components of signals under study, but offer no information regarding where a particular frequency was located in the time axis. In contrast, wavelet transforms offers time-frequency information of signals under study, thereby making wavelet transform methods more comprehensive than Fourier transforms in signal analysis.

_{ } ) and its scaling function (given as ) describe a family of functions which are required to satisfy a number of criteria [7,8]. It must have a zero mean denoted as in (1).

(1) |

_{ } must have a square norm of one as denoted in (2).

(2) |

(3) |

The use of these wavelet functions provides a robust method of analyzing non-stationary signals to provide both frequency and time information. In practice, wavelet coefficients are obtained by a filter bank approach, with a low-pass filter and its complementary high-pass filter.

**APPLICATION OF WAVELETS IN INDUCTION MACHINE FAULT DIAGNOSIS**

*details'* and '*approximate'* parts as shown in the simplified block diagram of Figure 1. The '*approximation'* signal can be further decomposed into a new set of '*approximation'* and '*details'* signals and continue until *n* decomposition levels are obtained.

Figure 1. First level decomposition.

*details'* signal contains high frequency information whereas the approximate part contains signal data with the low frequency components. Computing this decomposition to *n* levels results in those higher detail parts being removed, thereby reducing the overall frequency characteristics of the resulting data. This implies that lower levels of decomposition provide detail data that contains the highest frequency components. For the induction machine signature analysis, the higher frequency wavelet components represent system noise or harmonics due to the input power inverter. Therefore decomposition levels higher than one are of interest in the technique presented in this paper.

*n-*level wavelet decomposition through a variety of strategies, including filter banks and classification algorithms [8]. In this study a statistical analysis of the wavelet '*detail*s' coefficients is used as the basis for fault detection. From the mean or standard deviation of the wavelet coefficients it could be inferred that the average magnitude of frequency components are present in the signal under analysis.

*n*-level detail coefficients are analyzed then each level represents the spatial information for a small range of frequencies. This allows the analysis of the frequency differences and their time location in the signal under analysis. In this paper, the standard deviation of the wavelets coefficients is used to identify frequency anomalies in a given time range in the input data set. The detection algorithm is discussed in details in the next section of this paper.

**PROPOSED ALGORITHM FOR FAULT DETECTION**

*n*-level wavelet decomposition, then the standard deviation of these coefficients is obtained.

To detect the fault type, the maximum and minimum SDWC values are compared between the three phases. The ratio of these values is then used to detect the fault type. The ratio of the SDWC between phase 1 (minimum) and phase 2 (maximum) is given by . For example, if a sample set in phase A contains the greatest SDWC and phase B contains the lowest SDWC at half of the value of phase A, then this would produce a SDWC ratio of . This value is used to test each data set to determine the presence of a winding fault. In the test cases presented in this paper, the optimal threshold values to determine the proper ratio for different faults were determined through experimentation. These ratio values will be denoted as , , and for the three signature types detected. That is, is the SDWC range for a decision of no fault, is the range for a winding resistance fault, and is the range for open winding diagnosis. The decision process is shown functionally in the flow chart of Figure 2.

^{®} was used for testing the proposed algorithm.

**EXPERIMENTAL RESULTS AND FAULT DETECTION**

^{®} to offer a convenient environment for users to run the detection algorithm and determine the fault type from test files generated following fault simulation. The GUI is shown in Figure 3.

*n*, the wavelet decomposition level, was ten, a value that will greatly magnify the frequency differences. This is considered a good choice because frequency differences for relatively low frequency systems such as the machines under study exist in lower bands. Decomposition coefficients at the lower levels simply compare electrical noise. The ranges used for , , and where chosen to be [0 - 0.1], [0.1 - 0.4], and [0.4 - 1] respectively. Sixty-three cases (each case was stored in an excel file) with 10,000 data points each were used for testing this detection algorithm. The data was obtained at Penn State Harrisburg's Energy Conversion Laboratory. The data was wavelet-decomposed and the standard deviation of the wavelet coefficients for each phase obtained. The wavelet coefficients for each phase is summarized and shown graphically in Figure 4.

Figure 4. Normalized Standard deviation of Wavelet coefficients for all 63 data samples.

Figure 5. Wavelet coefficients showing no winding fault (32 files out of 63). |

Figure 6. Wavelet coefficients showing winding resistance fault (24 files out of 63). |

Figure 7. Wavelet coefficients showing open winding fault (7 files out of 63). |

Figure 8. Relative ratio between phases of standard deviation of wavelet coefficients.

**COMPARIN WITH FOURIER TRANSFORM TECHNIQUES**

Figure 9. FFT of motor current with known fault condition.

**CONCLUSIONS**

**ACKNOWLEDGMENT**

Preliminary version of this paper was presented at the 2008 American Society for Engineering Education Conference, Pittsburgh, Pennsylvania, USA.

**REFERENCES**

[2] T. Chow and H. Shi. "Induction machine fault diagnostic analysis with wavelet technique". IEEE Transactions on Industrial Electronics. Vol. 51, Issue 3, pp. 558-565. June, 2004. [ Links ]

[3] W.G. Zanardelli, E.G. Strangas, H.K. Khalil and J.M. Miller. "Wavelet-based methods for the prognosis of mechanical and electrical failures in electric motors". Mechanical Systems and Signal Processing. Vol. 18, Issue 2, pp. 411-426. March, 2005. [ Links ]

[4] G.K. Singh, S. Kazzaz. "Vibration signal analysis using wavelet transform for isolation and identification of electrical faults in induction machine". Electric Power Systems Research. Vol. 68, Issue 2, pp. 119-136. February, 2004. [ Links ]

[5] E.A. Ebrahim and N. Hammad. "Fault analysis of current-controlled PWM-inverter fed induction-motor drives". Proceedings of the IEEE International Conference on Properties and Applications of Dielectric Materials. Vol. 3, pp. 1065-1070. 2003. [ Links ]

[6] M. Benbouzid and G. Kliman. "What stator current processing-based technique to use for induction motor rotor faults diagnosis?". IEEE Transactions on Energy Conversion. Vol. 18, Issue 2, pp. 238-244. June, 2003. [ Links ]

[7] G. Strang and T. Nguyen. "Wavelets and Filters Banks". Wellesley-Cambridge Press.

[8] M. Vetterli and J. Kovacevic. "Wavelets and Subband Coding". Prentice-Hall.

[9] Z. Zhengping, R. Zhen and H. Wenying. "A novel detection method of motor broken rotor bars based on wavelet ridge". IEEE Transactions on Energy Conversion. Vol. 18, Issue 3, pp. 417- 423. September, 2003. [ Links ]

[10] W.T. Thomson and M. Fenger. "Current signature analysis to detect induction motor faults". IEEE Industry Applications Magazine. Vol. 7, Issue 4, pp. 26-34. July/August, 2001. [ Links ]

[11] P. Idowu, J. Atiyeh, E. Schmitt and A. Morales. "MATLAB^{®} Tool for Introducing Basics of Induction Motor Signature (IMCS) Analysis". Accepted for publication. International Journal of Electrical Engineering Education. July 29, 2009. [ Links ]

*Received: December 3, 2009, Accepted: July 26, 2010.*