Mechanical fault diagnosis of induction motor using Hilbert pattern

2013 IEEE 1st International Conference on Condition Assessment Techniques in Electrical Systems

Mechanical Fault Diagnosis of Induction Motor using Hilbert Pattern Pratyay Konar and Dr. Paramita Chattopadhyay* Department of Electrical Engineering, Bengal Engineering and Science University, Shibpur, Howrah, India [email protected], [email protected] Abstract— This paper deals with mechanical fault diagnosis in three-phase induction motor from radial vibration measurement. The Hilbert pattern of the 50 Hz mono-component signal extracted from the steady state vibration signature is analyzed and found to contain useful information needed for diagnosing different mechanicals faults. Since Hilbert transform can only be applied to a mono-component signal, Kaiser windowed FIR band pass filter is used to extract the monocomponent signal. Complex analytic signal is generated by using the mono-component signal as the real part and it’s Hilbert Transform as the imaginary part. The concept of Hilbert transform for extraction of the instantaneous amplitude and frequency is utilized to extract important fault information from the non-stationary vibration signal and found to be quite efficient. This method does not require the analysis of fault frequency components which are slip dependent. Finally, an automatic diagnosis algorithm is attempted using SVM. The proposed method is almost independent of loading condition of the motor and has consistent performance even in presence of high level of noise. Keywords— Induction Motor, Condition Monitoring, Hilbert Transform, Hilbert Pattern, Support Vector Machine (SVMs)

I.

INTRODUCTION

Induction Motors (IM) are extensively used in industries because of its simple structure, reliability, ruggedness, cost effective design and ease of control [1]. However, induction motors are subjected to mechanical stresses caused by overloads and abrupt load changes, which can produce bearing faults, rotor bar breakage and rotor unbalance [2]. ‘Mechanical’ problems affect the induction motor magnetic circuit, by causing variations in the air-gap. According to literature mechanical faults leads to discontinuities in the magnetic forces of attraction giving rise to vibration and also causes variation in motor torque. Vibration problems in induction motors can be extremely frustrating and may lead to greatly reduced reliability. It is imperative, in all operations and manufacturing processes that down time is avoided or minimized. If a problem does occur, the source of the problem must be quickly identified and corrected. With proper knowledge and diagnostic procedures, it is normally possible to quickly pinpoint the cause of the vibration [3]. Motor torque is produced where balanced forces exist on either side of the rotor. Vibration results whenever the forces of attraction are not balanced [2]. Thus, an unbalanced force results in vibrations with amplitude and/or phase modulations. Modulation diagnosis requires a tool for extracting the

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instantaneous phase and amplitude [4-9]. This can be done by associating a complex signal to the real measured one. The complex signal instantaneous phase and amplitude are expected to carry, respectively, information about the phase and amplitude modulations. The complex signal is classically obtained through the Hilbert transform. Complex signals are valuable, because they offer an opportunity to calculate instantaneous energy, amplitude and frequency. That is why complex signals are dubbed ‘analytic signals’. The signal can be analyzed sample-wise instead of frame-wise, and sometimes such fast access to analysis is very useful. In the process of vibration analysis, the first of these tasks is called fault detection and the second one is fault diagnosis. Fault detection is associated with detection of occurrence of fault. Fault diagnosis is often associated with detection of the type of fault which can be used to identify the root cause of vibration. Fault diagnosis helps to determine the cause, severity and corrective action [10]. When a vibration problem occur due to a fault, finding all the possible causes for the particular identified fault frequency of vibration needs good systematic and analytical approach [3]. To detect the presence of faults in an induction motor diagnostic methods are classically based on frequency analysis. However, many different problems either electrical or mechanical in nature can cause vibration at the same or similar frequencies like the 1x RPM component and for a 2pole induction motor, 2 X line frequency and 2 X RPM are very close especially on light load [2]. Thus, all too often erroneous conclusions may be reached as a consequence of not understanding the root cause of the vibration. This may result in trying to fix an incorrectly diagnosed problem, spending a significant amount of time and money in the process [3]. Thus, identification of the root cause of vibration becomes an elusive as well as challenging task. Another way to detect the presence of an abnormality is to compare the amplitude of the fault signatory components with a reference threshold [11]. Wavelet Transform (WT) and Hilbert transform (HT) [12-14] have been extensively used to analyze both vibration and current signals to diagnose the faults of Induction Motor. Hilbert Transform and HilbertHuang Transform (HHT) have become more popular because of their better time-frequency resolution [15,16]. The Hilbert transform is useful in calculating instantaneous attributes of a time series, especially the amplitude and frequency [17]. The instantaneous phase which reflects the way in which the local phase angle varies linearly over a single cycle can also be found [6]. Thus, the complex analytic signal obtained by

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2013 IEEE 1st International Conference on Condition Assessment Techniques in Electrical Systems Hilbert transform seems to contain very useful information. Interestingly, several different patterns can be obtained from this complex co-efficient which comprises of real and imaginary parts [18]. But the Hilbert Transform can only produce physically meaningful results only for ‘monocomponent’ signals [19]. Therefore, to make the Hilbert Transform applicable, the key is the ability to decompose a signal into some individual mono-component signals. Thus, a filter will be required to extract the mono-component signal from the vibration signal.

The signal g(t) and its Hilbert transform gˆ (t ) together form an analytic signal [6, 11] given by:

Keeping the above viewpoints in mind, an attempt is made to extract the fundamental component from the radial vibration signature with the help of a filter and analyze the mono-component signal so obtained by Hilbert Transform Pattern visualization method to detect the mechanical faults. However, the motor condition monitoring science is moving toward an automated computerized scheme, trying to remove human experts from the condition monitoring process. The proposed investigation aims to develop an automatic multiclass fault diagnosis of induction motor using Hilbert Pattern and SVM.

A(t )  cos ( 0 t )  sin ( 0 t )  1 gˆ (t )  (t )  arctan  0 t  g (t )

II.

HILBERT TRANSFORM

Physicist Arthur E. Kennelly and the scientist Charles P. Steinmetz introduced the complex notation of harmonic wave forms in electrical engineering, that is: 

e jt  cos(t )  j sin(t ) 

A. Analytic signals in the time domain The Hilbert transform of g(t) is the convolution of g(t) with the signal 1/πt. It is the response to g(t) of a linear timeinvariant filter (called a Hilbert transformer) having impulse response 1/πt. The Hilbert transform H[g(t)] is often denoted as gˆ (t ) and can emphasize the local properties of g(t). The Hilbert transform H[g(t)] is defined as: 

H [ g (t )]  gˆ (t )  g (t ) *





The instantaneous amplitude A(t) and instantaneous phase φ (t) are given by:

A(t )  g 2 (t )  gˆ (t ) 2 (t )



2













2

The analytic signal A[g(t)] is calculated using different methods. One of these methods uses the Fourier transform. Indeed, the Fourier Transform of the signal gˆ (t ) is given by the following equation [11]:  A[ g (t )]F  G( f )  j  j sgn( f )G( f )  1  sgn( f )G( f )  where, the function G ( f ) represents the Fourier transform of g(t) and sgn( f ) the sign function, with (1+ sgn( f )) given by:



Later on, in the beginning of the 20th century, the German scientist David Hilbert (1862-1943) showed that the function sin(ωt) is the Hilbert transform of cos(ωt). This gave us the ±π/2 phase-shift operator which is a basic property of the Hilbert transform [20]. A real function g(t) and its Hilbert transform gˆ (t ) are related to each other in such a way that they together create a so called strong analytic signal. The strong analytic signal can be written with amplitude and a phase where the derivative of the phase can be identified as the instantaneous frequency. A function and its Hilbert transform are orthogonal. The Hilbert transform defined in the time domain is a convolution between the Hilbert transformer 1/(πt) and a function g(t).

A[ g (t )]  g (t )  jgˆ (t )  a(t ).e j (t ) 



 III.

2  1  sgn( f )  1  0 

for f  0 for f  0   for f  0

SIMULATION OF FAULTS AND DATA AQUISITION

Machinery Fault Simulator (MFS) was used for simulating various types of induction motor faults. The MFS was initially fitted with a healthy motor and thereafter faulty motors of same specification were used for the fault simulation [21]. The vibration data corresponding to a particular motor condition were collected using an accelerometer probe mounted in the radial direction. The data was recorded at a sampling frequency of 5120 Hz under five different loading (given with the help of brake-clutch mechanism and belt pulley system) and stored using a computer with four-channel data acquisition system (DAQ) [21]. The supply frequency was set to 50 Hz. The collection was done for a healthy motor and faulty motors with four different mechanical faults under the same running conditions. Motor with bowed rotor, unbalanced rotor, broken rotor bar and faulted bearing were considered. The time domain frame vibration signal obtained from the healthy motor and faulty motor with faulted bearing are shown in Fig. 1(a) and (b).

1 g ( ) 1 g ( ) d   d  

t t











Thus, if the real signal is given by: g (t )  cos(0 t ) its Hilbert transform is given by: gˆ (t )  sin(0 t )

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2013 IEEE 1st International Conference on Condition Assessment Techniques in Electrical Systems Healthy_4 (Full Load) 1 0.8 0.6 0.4 0.2 0 0

0.02 0.04 0.06 0.08

0.1

0.12 0.14 0.16

(a)

FaultedBearing_4 (Full Load) 1 0.8 0.6 0.4

Fig. 2. The schematic representation of pattern extraction using Hilbert Transform

0.2 0 0

0.02 0.04 0.06 0.08

0.1

0.12 0.14 0.16

(b) Fig. 1. (a) Time domain signal of Healthy motor (b) Time domain signal of motor with Faulty Bearing

IV.

FAULT DETECTION BASED ON HILBERT PATTERN

For successful application of Hilbert Transform [22], it is necessary to have a mono-component signal. To obtain the mono-component signal Kaiser windowed FIR band pass filter [22] was designed for the fundamental frequency component (50 Hz) with a pass band of ±5 Hz. The vibration signal was passed through this filter and finally the mono-component signal was obtained. Hilbert transform was applied to the mono-component signal. The analytic signal obtained has real and imaginary part. Thus, the Hilbert pattern is just the trajectory of the analytic signal in the complex plane. The schematic representation of pattern extraction using Hilbert Transform is shown in Fig 2. The pattern obtained for different faults at full load (brake-4) using Hilbert Transform are shown in Fig 3. And the Hilbert patterns obtained for faulty motors at two different loading are shown in Fig 4.

Fig. 3. The Patterns obtained for different faulty motor using Hilbert Transform

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2013 IEEE 1st International Conference on Condition Assessment Techniques in Electrical Systems brake positions ‘0’-‘2’-‘4’ were used for training. Test set data was prepared from all the five brake positions ‘0’-‘1’-‘2’-‘3’‘4’ and used for validating the SVM model generalization ability. Another three sets of data were prepared from the original raw data by adding different levels of noise having Signal-to Noise Ratio (SNR) 20 dB, 15 dB and 10dB. This data with different noise level was used to test the performance of the SVM model in presence of noise. The classification performance of the SVM model is presented in TABLE-I. TABLE-I. PATTERN CLASSIFICATION PERFORMANCE OF SVM No Noise Noise Noise Overall Noise 20dB 15dB 10dB Healthy

100 %

80 %

80 %

80 %

85 %

100 %

100 %

100 %

80 %

95 %

100 %

100 %

100 %

100 %

100 %

100 %

100 %

100 %

100 %

100 %

100 %

100 %

100 %

100 %

100 %

100 %

96 %

96 %

92 %

96 %

Bowed Rotor Broken Rotor Unbalanced Rotor Faulted Bearing Overall

The Hilbert Pattern of the healthy motor being almost similar to that of the faulted bearing, the healthy pattern data were misclassified as Faulted Bearing in presence of noise. Similarly, the Bowed Rotor fault is misclassified as Broken Rotor Bar in presence of very high level of noise. Fig. 4. The Hilbert Patterns obtained for faulty motors at two different loading

V.

PATTERN CLASSIFICATION USING SVM

In recent years, Support Vector Machines (SVMs) have been found to be remarkably effective in many real-world applications. Detailed information about SVM theory can be found in [23,24]. SVMs have been successfully applied in various classification and pattern recognition tasks. In the area of fault diagnostics they have been used as a classifier effectively [24]. But in the area of pattern classification for condition monitoring it is not widely studied. The SVM model was obtained for pattern classification with cost c = 10 and gamma g = 0.8. Apart from taking all the real and imaginary part of the analytic signal as attributes, the RMS value and the data range for both real and imaginary part was also taken into account. Thus, in total five attributes were taken as input to the SVM model. The data range is essential to distinguish the bowed rotor fault from the broken rotor bar fault and the RMS value of the analytic signal helps to diagnose the motor with faulted bearing effectively. VI.

RESULTS AND ANALYSIS

VII. CONCLUSIONS The Hilbert pattern of the 50 Hz mono-component obtained from the radial vibration signature of the induction motor was found to contain information suitable enough to efficiently diagnosis different types of mechanical faults. Only analysis of the fundamental component was required without the need to analyze the fault frequency components which are slip dependent. Each type of fault was found to have unique patterns with different inner and outer diameter. The monocomponent signal was successfully extracted with the help of Kaiser windowed FIR band pass filter without the need to go for Hilbert–Haung mono-component signal extraction model, “Intrinsic Mode Function (IMF)” proposed by Hilbert –Haung [19]. The automatic pattern classification yielded satisfactory results which can be effectively used to diagnose different mechanical fault. ACKNOWLEDGMENT The authors are thankful to Council of Scientific and Industrial Research (CSIR) for their support for continuation of this project. The authors are also thankful to AICTE and TEQIP-I (BESU, Shibpur unit), Govt. of India for their financial support toward the project.

Total 2048 data was taken to represent one pattern. The pattern data obtained from three loading conditions denoted by

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2013 IEEE 1st International Conference on Condition Assessment Techniques in Electrical Systems REFERENCES [1]

A.H. Bonnett, G.C. Soukup, “Cause and analysis of stator and rotor failures in three-phase squirrel-cage induction motors”, IEEE Transactions on Industry Applications, 1992, vol. 28 (4), pp. 921-937. [2] G. H. Bate Bate, “Application notes: Vibration diagnostics for industrial Electric Motor-Drives”, Brüel and Kjaer [3] W. R Finley, M. M. Hodowanec,W. G. Holter, “An analytical approach to solving motor vibration problems”, IEEE Transactions on Industry Applications, vol.36 (5), pp. 1467-1480. [4] S. A. McInerny and Y. Dai, “Basic vibration signal processing for bearing fault detection”, IEEE Transactions on Education, 2003, vol. 46(1), pp. 149–156. [5] J. R. Stack , R. G. Harley, T. G.Habetler , “An amplitude Modulation detector for fault diagnosis in rolling element bearings”, IEEE Transactions on Industrial Electronics, 2004, vol. 15 (5), pp. 1097-1102. [6] M.E.K. Oumaamar, H. Razi, A. Rezzoug, A. Khezzar, “Line Current Analysis for Bearing fault Detection In Induction Motors Using Hilbert Transform Phase”, International Aegean Conference on Electrical Machines and Power Electronics and 2011 Electromotion Joint Conference (ACEMP), pp. 288 – 293. [7] G. Didier, E. Ternisien, O. Caspary, and H. Razik, A New Approach to Detect Broken Rotor Bars in Induction Machines by Current Spectrum Analysis, Mechanical Systems and Signal Processing, 2007, vol. 21 (2), pp. 1127-1142. [8] B. Trajin, M. Chabert, J. Regnier, J. Faucher, “Hilbert versus Concordia transform for three-phase machine stator current time-frequency monitoring”, Mechanical Systems and Signal Processing, 2009, vol. 23, pp. 2648–2657. [9] Y. Amirat, V. Choqueuse, and M.E.H Benbouzid, “Wind Turbines Condition Monitoring and Fault Diagnosis Using Generator Current Amplitude Demodulation”, IEEE International Energy Conference and Exhibition (EnergyCon), 2010, pp. 310-315. [10] M. Tsypkin, “Induction motor condition monitoring: Vibration analysis technique - A practical implementation”, 2011 IEEE International Electric Machines & Drives Conference (IEMDC), pp. 406 -411. [11] A. Medoued, A. Lebaroud and D. Sayad, “Application of Hilbert transform to fault detection in electric machines”, Advances in Difference Equations: Recent Trends on Applied Mathematics And Modeling, 2013, pp. 1-7.

[12] G. A. Jimenez , A. O. Munoz and M. A. Duarte-Mermoud, “Fault detection in induction motors using Hilbert and Wavelet transforms”, Electrical Engineering, 2007, vol. 89(3), pp. 205-220. [13] S. K. Ahamed, Diagnosis of Broken Rotor Bar Fault of Induction Motor through Envelope Analysis of Motor Startup Current using Hilbert and Wavelet Transform, Innovative Systems Design and Engineering, vol. 2 (4), 2011 pp. 163-176. [14] Z. Liu, X. Zhang, X. Yin, Z. Zhang, “Rotor cage fault diagnosis in induction motors based on spectral analysis of current Hilbert modulus”, IEEE Power Engineering Society General Meeting, 2004, Vol. 2, pp. 1500-1503. [15] Y. Ruqiang, R.X. Gao, “Hilbert–Huang Transform-Based Vibration Signal Analysis for Machine Health Monitoring”, IEEE Transactions on Instrumentation and Measurement, vol.55 (6), pp.2320-2329. [16] E. Akin, I. Aydin, M. Karakose, “FPGA based intelligent condition monitoring of induction motors: Detection, diagnosis, and prognosis”, 2011 IEEE International Conference on Industrial Technology (ICIT), pp. 373-378. [17] H. Luo, X. Fang, B. Ertas. “Hilbert Transform and Its Engineering Applications”, AIAA Journal, Vol. 47 (4), 2009, pp. 923-932. [18] X. Boqiang, L. Heming, S. Liling, Z. Zhenbo, “A Novel Approach to Detect Rotor Bar Breaking Fault of Induction Motors Based on Hilbert Transform and Graph Visualization Technique” , International Conference on Electrical Engineering, 2002, pp 975-978. [19] Huang, et al., “The empirical mode decomposition and the Hilbert spectrum for non-linear and non-stationary time series analysis”, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 1998, vol. 454(1971), pp 903-995. [20] P. Konar, S. Bhawal, M. Saha, J. Sil, P. Chattopadhyay, “Rough set based multi-class fault diagnosis of induction motor using Hilbert Transform”, 2012 International Conference on Communications, Devices and Intelligent Systems (CODIS), pp. 337-340. [21] Spectra Quest Inc. User's Manual, Machinery Fault Simulator, Spectra Quest Inc., USA, 2005. [22] Signal Processing Toolbox-User’s Guide, Available from: http://www.mathworks.com. [23] V. N. Vapnik, The Nature of Statistical Learning Theory, Information Science and Statistics , SpringerVerlag, New York, 2000. [24] P. Konar, P. Chattopadhyay, “Bearing fault detection of induction motor using wavelet and Support Vector Machines (SVMs)”, Applied Soft Computing, 2011, vol. 11(6), pp. 4203–421.

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