Diagnosis of Induction Motor Rotor Fault through ...

Advances in Applied and Pure Mathematics

Diagnosis of Induction Motor Rotor Fault through Discrete Wavelet Transform Applied to Residual Current NABIL NGOTE, SAID GUEDIRA, Electromechanical Engineering Department Ecole Nationale de l’Industrie Minérale BP 753, Agdal, Rabat MOROCCO [email protected] [email protected] MOHAMED CHERKAOUI Electrical Engineering Department Ecole Mohammadia d’Ingénieurs BP 765, Agdal, Rabat MOROCCO [email protected] MOHAMMED OUASSAID Industrial Engineering Department Ecole Nationale des Sciences Appliquées Safi MOROCCO [email protected]

Abstract: - Induction motors are critical components in industrial processes since their failure usually lead to an unexpected interruption at the industrial plant. The condition monitoring of the induction motors have been a challenging topic for many electrical machine researchers. Indeed, the effectiveness of the fault diagnosis and prognosis techniques depends very much on the quality of the fault features selection. However, in inductionmotor drives, rotor defects are the most complex in terms of detection since they interact with the supply frequency within a restricted band around this frequency, especially in the no-loaded case. To overcome this drawback, this paper deals with an efficient and new method to diagnose the induction-motor rotor fault based on the application of the Discrete Wavelet Transform (DWT) to the residual current, obtained by subtraction between stator current and its Time Synchronous Averaging (TSA). Simulation and experimental results are presented in order to show the effectiveness of the proposed method. The obtained results are largely satisfactory, indicating a promising industrial application of the hybrid DWT-TSA approach.

Key-Words: - Condition monitoring, Diagnosis, Discrete Wavelet Transform (DWT), Induction motor, Motor Current Signature Analysis (MCSA), Rotor fault, Time Synchronous Averaging (TSA) and heavy loads, internal faults can sometimes occur, and the well-functioning of these machines is, consequently, affected [1]. Therefore, an effective incipient fault detection technique would be very beneficial for the induction machine condition monitoring, since it would reduce the maintenance and downtime expenses [2]-[3]. In this regard, there has been research in order to provide new monitoring techniques for induction motors based on analyzing pulsations in speed,

1 Introduction The electrical drives using induction motors are very common within industrial applications due to their rugged configuration, low cost, versatility, reasonably small size and capability to operate with an easily available power supply. However, due to the fact that these motors are operating in difficult working environments, with many factors that degrade their performance such as: dust, temperature level, humidity, continuous operation

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performed on the test bench are presented. Finally, conclusions are mentioned in Section 5.

airgap flux, axial flux, and vibration [4]-[7] and the motor condition is examined from the signals acquired through the sensors. However, the drawback of these methods is that they require direct access to the machine in order to place transducers for the monitoring. To overcome this disadvantage, most recent research has been directed toward electrical monitoring of the motor, in particular, on inspecting the stator current, since this signal presents the main advantage of being measurable, even with no direct access to the machine [8]. The Discrete Wavelet Transform (DWT) was used with different approaches for the diagnosis of anomalies in induction machine. More intensive research efforts have been focused on the use of approximation and detail signals for extracting the contribution of fault frequency components in case of rotor faults [9]-[12]. Most of the reported contributions are based on wavelet analysis of the currents during start-up or load variation for diagnosis purposes. In this context, the frequency components are spread in a wide bandwidth as slip and speed vary considerably. The situation is more complicated under rotor faults due to the proximity of the fault components to the fundamental one, especially in the no-load motor. To alleviate this drawback, a method exploiting the cyclostationarity of electrical signals (voltage and current) will be developed, for the motor condition monitoring [13]. Indeed, in the case of the cyclostationary signal, each period (or cycle) is considered as the same random process realization. Therefore, if these cycles are superposed, the overall average can be calculated: this average is also called Time Synchronous Average [14]. Nowadays, very little work has been done to exploit the electrical-signal cyclostationary characteristics [13]. In this paper, a new approach which uses the cyclostationarity of the electrical signals, in order to determine the TSA of the stator current, will be presented. Then, the residual current will be determined by subtraction between the stator current and its TSA. Finally, the DWT will be performed to residual current in order to diagnose the inductionmotor rotor fault, even in the non-loaded case. The main novelty of this article stems from the introduction of the notion of “hybrid TSA – DWT approach” in order to diagnose induction-motor drive faults. The rest of this paper is organized as follows. The Wavelet analysis theory is developed in Section 2. Section 3 is devoted to present the TSA method. Then, in Section 4, the experimental results

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2 Discrete Wavelet Transform (DWT) During many years, Fourier Transform has been used for signal processing, since it is suitable for the study of a wide range of signals. The Fourier analysis consists in decomposing a signal into sine waves with different frequencies. Similarly, a wavelet analysis is the decomposition of a signal into shifted and scaled versions of a function called the ‘mother wavelet’. The Discrete Wavelet Transform consists in sampling the scaling and shifted parameters. This leads to high-frequency resolution at low frequencies and high-time resolution for higher frequencies. DWT decomposes a signal by passing it successively through high-pass and low-pass filters into its approximate and detailed versions using Multi-Resolution Analysis (MRA), and this is called the Mallat Algorithm as shown in Fig. 1. [15]. The original signal is denoted by s(t), with a sampling rate of f samples/sec. The low-pass filter is denoted by LPF while the high-pass filter is denoted by HPF. The first level of decomposition coefficients are a1 and d1, where a1 is the approximate version of the original signal and d1 is the detailed version of the original signal. Further decomposition of a1 gives a2 and d2 and so on. At each level, the HPF produces the detail coefficients (dj), while the LPF produces the approximation coefficients (aj). Finally, the signal s(t) can be approximated using the DWT by [15]: s (t ) =

∑α i

n n i φ i (t ) +

n

∑∑ β ψ j

i

j =1

i

j i

(t )

(1)

= a n + d n + ..... + d 1

where αin, βij are respectively, the scaling and the wavelet coefficients, φn(t), ψj(t) are respectively the scaling function at level n and the wavelet function at level j, n is the decomposition level, an is the approximation signal at level n and dj is the detail signal at level j. [16]. If ƒ (samples/sec) is the sampling rate used for capturing s(t), the detail dj contains the information concerning the signal components whose frequencies are included in the interval [f/2j+1, f/2j]. The approximation signal an includes the low frequency components of the signal, belonging to the interval [0, f/2n+1].

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HPF

2

d1 [f/4 – f/2]

Signal s(t) 2

HPF

Sampling rate f LPF

d2 [f/8 – f/4]

2

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2

dn [f/2n+1 – f/2n]

LPF

2

an [0 – f/2n+1]

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Fig. 1 Mallat Algorithm

3 Time Synchronous Averaging (TSA)

By applying a similar approach, the stator current can be decomposed as follows:

The asynchronous motor operating process and the electric supply fluctuations cause the non-stationary behavior of the stator current signal. However, there has been very little work [13] exploiting the electrical-signal cyclostationary characteristics to identify the faults which occur in an asynchronous-motor drive. The idea is to extend the application of these signal-processing tools to the case of electrical signals. In this work, the firstorder cyclostationarity of stator current and voltage will be largely exploited. Furthermore, a rotor fault can be detected by highlighting a stator-current amplitude or phase modulation. However, the modulated-signal weak frequency band makes it too difficult to detect modulation. An alternative to overcome this difficulty is proposed by MacFadden [14]: the Time Synchronous Averaging (TSA) method. It’s a way to reshape the signal before its processing. The T-period TSA of a signal s(t) is defined as follows: s (t )

T

1 K → +∞ K

= lim

I s (t ) = I sh (t ) + I smec (t ) + n(t )

where Ish(t), Ismec(t) and n(t) are respectively the harmonic stator-current harmonic component, the mechanical-structure-related stator current and the noise. In fact, the asynchronous motor monitoring consists of supervising the signal harmonic part. So, harmonic frequency (50Hz) which is related to electrical phenomena and mechanical-structurerelated frequency must be separated. For this purpose, the TSA method will be applied to the stator current. The Th-period TSA of stator current is done by the following relation, as established in (3) and (4): I s (t )

K −1

∑

s (t + k ⋅ T )

s (t )

T1

= s1 (t )

T2

= s 2 (t )

k =0

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Th

= lim

K → +∞

1 K

K −1

∑I k =0

s

(t + k ⋅ Th ) = I s

h

(t )

(5)

where Th=1/fs is the harmonic period and fs =50Hz is the harmonic frequency corresponding to supply frequency. The subtraction between the stator current and its TSA gives the residual current where only mechanical-related frequencies remain, as shown in (6):

(2)

The TSA method consists of averaging s(t)-signal shifted versions of a whole number of T periods. This method allows the separation between the excitation sources and, consequently, fault identification. Indeed, consider a signal s(t) sum of T1-period signal s1(t), T2-period signal s2(t) and noise. The application of the TSA method to s(t), at respectively T1 and T2 period allows the separation between s1(t) and s2(t). In fact, we can prove that: s (t )

(4)

I res (t ) = I s − I s

Th

(6)

It’s a very interesting property that will allow conditioning a mechanical-structure-related indicator monitoring an eventual rotor fault.

(3)

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4 Presentation of the Experiment Is

0 -10

4.1 Experimental Setup

5

a10

The testing ground used includes an industrial threephase wound rotor asynchronous motor of 400V, 6.2A, 50Hz, 3kW, 1385rpm. The sampling rate taken is 25.6 kHz, so the number of samples per average cycle of 50 Hz is 512 (25600/50 = 512). The rotor fault has been carried out by adding an extra 40mΩ resistance on one of the rotor phases. The stator current and voltage signals are acquired using a data acquisition system and the velocity is measured with an optical tachometer. The DWT is carried out decomposing the stator current signal into 10 levels, each one of them having its own detailed coefficients and a determined range of frequencies, as shown in Table II. The DWT is done using the MATLAB Wavelet Toolbox, where the wavelet Daubechies 5 (db5) with 10 decomposition levels is selected [17].

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d8

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Fig. 2. High-level wavelet signals results from the DWT signal analysis of experimental stator current in healthy case Experimental Results - Defective case

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12800 – 6400 6400 – 3200 3200 – 1600 1600 – 800 800 – 400 400 – 200 200 – 100 100 – 50 50 – 25 25 – 12.5 12.5 – 0

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Frequency Range (Hz)

0

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Frequency Bands at Different Decomposition Levels

0 -10

Fig. 3. High-level wavelet signals results from the DWT signal analysis of experimental stator current in faulty case

The comparison between the plots of DWT in the healthy and faulty case does not allow us to detect easily the rotor fault. The 9th detail-level plot shows a little difference between the two cases, but this difference is too small to be significant. So, the idea is to apply the DWT to the residual current Ires. Fig. 4 and Fig. 5 show the experimental residual-current signal (Ires) and the upper-level signals a10, d10, d9 and d8, for the healthy and faulty cases respectively.

4.2 Experimental Results The DWT of the stator current Is is applied in first. Fig. 2 and Fig. 3 show the experimental statorcurrent signal (Is) and the upper-level signals a10, d10, d9 and d8, for the healthy and faulty cases respectively.

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0.2

0 -2

Table 1

Detail d1 Detail d2 Detail d3 Detail d4 Detail d5 Detail d6 Detail d7 Detail d8 Detail d9 Detail d10 Approximate a10

0

0 -5

2

Decomposition Level

Experimental Results - Healthy case

10

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Ires

using (9) up to level 10, for the healthy and defective cases and the results are given in Table 2 (Total Energy).

Experimental Results - Healthy case

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Table 2 Total Energies at Different Decomposition Levels Ej (Joules) Ej (Joules) Level Healthy Case Faulty Case d1 10 10 d2 0 0 d3 10 10 d4 30 30 d5 290 300 d6 2760 2800 d7 2350 2420 d8 5.740e+5 5.837e+5 d9 1.263e+5 1.308e+5 d10 224 227

0 -0.2 1

d9

0 -1

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d8

0 -0.5

Fig. 4. High-level wavelet signals results from the DWT signal analysis of experimental residual current in healthy case Experimental Results - Defective case

Ires

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The corresponding graphs are shown in Fig.6 below.

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Total Energy - Experimental Results

x 10

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Fig. 5. High-level wavelet signals results from the DWT signal analysis of experimental residual current in faulty case

j

(n )

2

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6 7 5 Wavelet's Detail Level

8

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10

From this experiment, it is observed that the total energy consumption in faulty case is the same as in healthy case, since the two curves are combined, as shown in Fig. 6. It is also noted that the 8th level-total-energy value is the highest. This can be explained by the predominance of the fundamental component (50 Hz) at this level, since the frequency range associated to this level is 100 to 50Hz, as shown in Table 1. Therefore, the diagnosis of rotor fault by this method is impossible: the total energy cannot be considered as a sensitive indicator of rotor fault. To overcome the above inconvenience, the same procedure will be followed for the residual current, obtained by subtraction between the stator current and its TSA. Detail energy of residual current signal is calculated

(7)

n =1

where j is the level of detail, dj is the detail signal at level j and N is the total number of samples in the signal. In this paper, the observation time is of 2 seconds, so N = 512000 (N = 2 s x 25.6 kHz). Detail energy of stator current signal is calculated

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Fig. 6. Total energy corresponding to stator current in healthy and faulty cases

To show the effectiveness of the proposed approach, the signal will be conditioned in order to develop an induction-motor diagnosing indicator. For this purpose, the energy concentrated in each detail level of wavelet decomposition will be calculated, for both the healthy and defective cases. The detail energy at level j is given by:

∑d

2

0

4.3 Discussion

N

3

1

The difference between the 8th and 9th detail-level plots of residual current, in healthy and defective cases, is very clear. So, the DWT applied to residual current allows the detection of rotor fault.

Ej =

4

394


for the healthy and defective cases and the results are given in Table 3 (Residual Energy).

distinction between the healthy and defective cases.

Table 3 Residual Energies at Different Decomposition Levels Ej (Joules) Ej (Joules) Level Healthy Case Faulty Case d1 7.302 9.500 d2 3.183 4.900 d3 8.075 12.60 d4 26.82 36.10 d5 157.8 162.7 d6 410.0 412.9 d7 64.09 74.20 d8 104.7 1008 d9 430.3 5771 d10 49.36 67.70

4 Conclusion In this paper, a new approach combining the TSA method and Discrete Wavelet Transform of stator current in order to diagnose the induction-motor rotor fault at no-load is presented. The proposed method has two major advantages. First, it is a method which is based on the analysis of the “current” signal. It can therefore be applied even to the inaccessible engines (such as the engines immersed in the motor-driven pump groups), unlike the methods based on the analysis of the accelerometer signal, where a direct access to the engine is necessary to be able to place the sensors. Besides, the approach is relatively simple: the monitoring of the DWT of residual current makes it possible to clearly detect the defective case. In fact, with a no-load engine, where the fault is hardest to detect, the residual energy plot shows a significant difference between the healthy and faulty cases.

The corresponding graphs are shown in Fig.7. Residual Energy - Experimental Results

6000

Healthy case Defective case

Residual Signal's Energy (J)

5000

4000

3000

Appendix: Test Bench Photos

2000

1000

0

1

2

3

4

5 6 7 Wavelet's Detail Level

8

9

10

Fig. 7. Residual energy (corresponding to residual current) in healthy and faulty cases

From this experiment, it is observed that the residual energy consumption in faulty case is greater than in healthy case, especially at the 9th and 8th detail levels. Indeed, the frequencies components induced by the rotor fault are given by the following relations [18]: f defect = (1 ± 2 s ) ⋅ f s

References: [1] A.H. Bonnett, G.C. Soukup, “Cause and analysis of stator and rotor failures in threephase squirrel-cage induction motors,” IEEE Transactions on Industry Applications, vol. 28, pp. 921–937, 1992. [2] S. Nandi, H.A. Toliyat, X. Li, “Condition monitoring and fault diagnosis of electrical motors - a review,” IEEE Transactions on Energy Conversion, vol. 20, pp. 719-729, 2005. [3] W.T. Thomson, D. Rankin, “Case histories of rotor winding fault diagnosis in induction motors,” in Proc. 1987 International Conference on Condition Monitoring, pp. 798819. [4] B. G. Gaydon, “An instrument to detect induction motor rotor circuit defects by speed fluctuation measurements,” in Proc. 1979

(8)

where fs is the electrical supply frequency and s is the per unit slip, which value in this case is s = 2.2% (the speed value measured by the tachometer is 1467 rpm). So, the defect frequencies are 47.8 Hz and 52.2 Hz, and these values are respectively contained in the 9th (50 – 25 Hz) and 8th (100 – 50 Hz) detail levels. Therefore, the residual energy allows an easy

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[14] P.D. McFadden, “A Revised Model for the Extraction of Periodic Waveforms by Time Domain Averaging,” Mechanical Systems and Signal Processing, vol. 1, no. 1, pp. 83-95, Jan. 1987. [15] C. S. Burrus, Introduction to Wavelets and Wavelet Transforms. A Primer. Englewood Cliffs, NJ: Prentice-Hall, 1998. [16] M. Riera-Guasp, J.A. Antonino-Daviu, J.R. Folch, M.P. Molina Palomares, “The use of the wavelet approximation signal as a tool for the diagnosis of rotor bar failures,” IEEE Transactions on Industry Applications, vol. 44, no. 3, pp. 716-726, May-Jun. 2008. [17] C. Combastel, S. Lesecq, S. Petropol, S. Gentil, “Model-based and wavelet approaches to induction motor on-line fault detection,” Control Engineering Practice, vol. 10, no. 5, pp. 493-509, May 2002. [18] A. Bellini, F. Filippetti, G. Frabceschini, C. Tassoni, G.B. Kliman, “Quantitative Evaluation of Induction Motor Broken Bars by Means of Electrical Signature Analysis,” IEEE Transactions on Industry Applications, vol. 37, pp. 1248-1255, Sep.-Oct. 2001.

Electric Test and Measuring Instrumentation Conference, pp. 5–8. [5] S. C. Chang and R. Yacamini, “Experimental study of the vibrational behavior of machine stators,” in Proc. 1996 Electrical Power Applications, pp. 242–250. [6] C. J. Dister and R. Schiferl, “Using temperature, voltage, and/or speed measurements to improve trending of induction motors RMS currents in process control and diagnostics,” in Proc. 1998, Industry Applications Conference, pp. 312–318. [7] T. A. Lipo, K. C. Chang, “A new approach to flux and torque-sensing in induction machines,” IEEE Transactions on Industry Applications, vol. IA-12, pp. 142–148, May 1986. [8] M.E.H. Benbouzid, “A review of induction motors signature analysis as a medium for faults detection,” IEEE Transactions on Industrial Electronics, vol. 47, no. 5, pp. 984993, Oct. 2000. [9] A. Ordaz-Moreno, R.J. Romero-Troncoso, J.A. Vite-Frias, J.R. Rivera-Gillen, A. Garcia-Perez, “Automatic online diagnosis algorithm for broken-bar detection on induction motors based on discrete wavelet transform for FPGA implementation,” IEEE Transactions on Industrial Electronics, vol. 55, no. 5, pp. 13611368, May 2008. [10] M. Riera-Guasp, J.A. Antonino, J. RogerFolch, M.P. Molina, “The use of the wavelet approximation signal as a tool for the diagnosis and quantification of rotor bar failures,” IEEE Transactions on Industrial Applications, vol. 44, no. 3, pp. 716-726, 2008. [11] M. Riera-Guasp, J.A. Antonino-Daviu, M. Pineda-Sanchez, R. Puche-Panadero, J. PerezCruz, “A general approach for the transient detection of slip-dependent fault components based on the discrete wavelet transform,” IEEE Transactions on Industrial Electronics, vol. 55, no. 12, pp. 4167-4180, 2008. [12] S.H. Kia, H. Henao, G.-A. Capolino, “Diagnosis of broken-bar fault in induction machines using discrete wavelet transform without slip estimation,” IEEE Transactions on Industrial Applications, vol. 45, no. 4, pp. 1395-1404, 2009. [13] N. Ngote, S. Guedira, M. Ouassaid, M. Cherkaoui, M. Maaroufi, “On the Monitoring of Rotor Fault in Induction Machine by the use of the TSA Method Applied to Stator Current,” International Review of Electrical Engineering, vol.7, no. 4, pp. 4822-4828, Aug. 2012.

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