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Sound based induction motor fault diagnosis using Kohonen self-organizing map
Mechanical Systems and Signal Processing 46 (2014) 45–58
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Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/ymssp
Sound based induction motor fault diagnosis using Kohonen self-organizing map Emin Germen, Murat Başaran n, Mehmet Fidan Department of Electrical and Electronics Engineering, Anadolu University, Eskisehir, Turkey
a r t i c l e i n f o
abstract
Article history: Received 30 January 2013 Received in revised form 19 June 2013 Accepted 2 December 2013 Available online 31 January 2014
The induction motors, which have simple structures and design, are the essential elements of the industry. Their long-lasting utilization in critical processes possibly causes unavoidable mechanical and electrical defects that can deteriorate the production. The early diagnosis of the defects in induction motors is crucial in order to avoid interruption of manufacturing. In this work, the mechanical and the electrical faults which can be observed frequently on the induction motors are classified by means of analysis of the acoustic data of squirrel cage induction motors recorded by using several microphones simultaneously since the true nature of propagation of sound around the running motor provides specific clues about the types of the faults. In order to reveal the traces of the faults, multiple microphones are placed in a hemispherical shape around the motor. Correlation and wavelet-based analyses are applied for extracting necessary features from the recorded data. The features obtained from same types of motors with different kind of faults are used for the classification using the Self-Organizing Maps method. As it is described in this paper, highly motivating results are obtained both on the separation of healthy motor and faulty one and on the classification of fault types. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Induction motors Fault detection Kohonen SOM Acoustic signal processing
1. Introduction Due to their simple construction, cost effectiveness and easy maintenance, the squirrel cage induction motors are the most preferable electrical motors in the industry. In order not to interrupt the industrial processes caused by unexpected failures of induction motors, preventive maintenance strategies are essential. Early diagnostics of incipient faults in induction motors are important to ensure safe operation and help to recognize and fix the problems with low costs and time. Significant amount of research have been focused on the methods for the early detection of the mechanical and electrical faults in induction motors [1]. Among all the methods in literature, motor current signature analysis (MCSA) is one of the most popular ones, which provides an effective way to detect incipient faults. MCSA mainly focuses on the analysis of the current data that is supplied from the ac network to the induction motor with time–frequency analysis techniques like Fast Fourier Transform (FFT), Short Time Fourier Transform (STFT), Wavelet Transform or Wavelet Packet Transform [2]. However there is a bottleneck to apply this technique to induction motors in their working environment since in most cases obtaining data is a cumbersome process because of the additional circuitry like isolators or data acquisition cards and interface that should be added between the supply and the test motors. Also it may not be possible to detach load from motor and run motor under no load condition. In order to get rid of disadvantages of current based techniques like MCSA, the acoustic and
n
Corresponding author. E-mail addresses: [email protected] (E. Germen), [email protected] (M. Başaran), [email protected] (M. Fidan).
0888-3270/$ - see front matter & 2014 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ymssp.2013.12.002
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vibrational methods are getting popular since those approaches do not require detaching motors from their working environment. Fault diagnosis methods based on vibration analysis have been applied for many years using the methods such as Fourier and Wavelet Transforms, and have shown significant success especially on detecting faulty bearing detection [3]. Vibration signal can be obtained via a contact device such as accelerometer; however in some special cases it may be problematic. For example the surface of the test motor may be irregular and the device could not be located properly on the test motors. Also the surface may be greasy or slippery due to the hard operating conditions like high temperature and humidity [4]. On the other hand, sound based fault diagnosis of motors offers a great advantage that solves many of these problems since it offers a contactless solution to obtain data. Only external microphones located around the operating motor are enough to record the information. Unlike vibration-based analysis, there is a very limited literature on fault diagnosis of induction motors, which are based on techniques of sound analysis. In Ref. [5] stator current, vibration and acoustic methods are compared and very detailed results for different types of faults in different load conditions have been introduced. It is worth to note that in this work, the acoustic methods are quite effective in order to capture the signatures of bearing faults. Previous work on acoustic analysis of induction motors also has promising results. In Ref. [6], compressor motor faults were successfully identified inside a semi-anechoic chamber environment. In Ref. [7] the effects of localization of multiple microphones have been scrutinized and their effects on results have been investigated. It is worth to mention the work [8], where a detailed sound based approach has been applied in order to make fault detection in high-speed motors. There, the vacuum cleaner motor experiments have been carried out in echo-free silent environment that provide significant results on detection of faults. However the real life applications in industry always introduce ambient noise. In this work, the acoustic data are collected from the same type of five different induction motors located in an environment with ambient noise, where four of them have specific incipient mechanical or electrical faults, via five microphones surrounding the test rig. These data can be analyzed like current or vibration data and can possibly contain many fault related information for diagnosis. Therefore this paper aims to scrutinize the suitable information hidden in acoustic data, which can distinguish the healthy motor from the faulty ones, and classify the fault types. Here the first strategy, features are obtained directly by calculating the cross correlation coefficients of the sound data recorded by the microphone pairs. For each experimental trial, 10 different correlation coefficients are calculated for each motor using 5 different microphones. In the second strategy, additional features are extracted by using 2D wavelet decomposition of the grayscale images, which are obtained by converting one-dimensional sound data, which are recorded by each separate microphone, to 2D grayscale images. As it has been described in Ref. [9], the 2D representation has many advantages over the regular one-dimensional data since it provides many additional information and possible usage of image processing tools. These two dimensional images are expected to show different type of textures and in former works for texture analysis, basically wavelet based methods were used [10–21]. These wavelet based texture analysis methods are applied on different kind of research areas including classification of tomography images [10,11], fingerprint classification [12], analysis of SAR images [13], power quality analysis from 2D represented power quality event data [14,15] and fault analysis of rotating machinery by using data obtained from infrared thermography [16]. The detection of faulty motor is a classification problem. Here it is reasonable to use neural network techniques, especially Kohonen Self-Organizing Map (SOM), in order to discriminate a faulty motor from a healthy one [22]. The idea behind the SOM is finding a projection of multi-dimensional vector space into two-dimensional lattices. While scattering the input vectors to the two-dimensional lattice, SOM also provides information about the possible similarities and resemblances of input vectors and it presents a visual representation of possible clusters in data set. In order to get the benefits of SOM, the feature vectors, which are used to identify the nature of the fault, should have to be designated in proper fashion. This paper also focuses on definition of those feature vectors obtained from acoustic data, which are used in SOM. This article continues with Section 2, which contains the explanation of motor fault types and detailed information of the experimental setup constructed by induction motors and microphones. Afterwards in Section 3, the features obtained from the sound data of the healthy and faulty motors to classify the fault types are expressed. Furthermore, Self-Organizing Maps (SOMs) and Learning Vector Quantization (LVQ) methods applied on the obtained features to classify the fault types are explained and the classification results are presented in details, in Section 4. Finally Section 5 concludes the paper. 2. Fault types and experimental setup In this work, five induction motors are used in order to obtain the acoustic data. Motors are driven directly from AC network. A 3-phase, 25 kVA, Δ-Υ connected isolation transformer is located between laboratory setup and the network where the motors are supplied with the output of this transformer. Test motors are 3-phase and 2-pole squirrel cage induction motors rated at 2.2 kW and 380-V line to line. Some commonly encountered mechanical and electrical faults are created synthetically on four of these motors. One of these identical motors is left untouched in order to get the healthy motor data. The faults are chosen and created such that those are the most encountered incipient faults in industry. The broken rotor bar fault is realized by drilling holes to 3 bars respectively over 18 bars as illustrated in left side of Fig. 1. This type of faults cause a rise in magnitude at adjacent side band frequency components of the motor current located symmetrically around the main frequency which the stator coils are supplied by Ref. [5]. However, monitoring the increase in magnitude at the predicted sideband frequencies alone may mislead the classification since different types of faults may have same frequency components. Also when the amount of slip
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Fig. 1. Creation of the broken rotor fault by drilling holes to rotor bars and creation of short-circuited stator winding fault.
Table 1 Table of faulty motors in experimental setup. Motor #
Fault type
Motor Motor Motor Motor Motor
Healthy motor Bearing fault (misalignment) Bearing fault (ball defect) Broken rotor bars (3 over 18) Short circuit in stator winding
1 2 3 4 5
is small, these sidebands come close to the fundamental frequency and it becomes difficult to grasp them by inspecting the spectral information due the dominancy of the fundamental component. Bearing damages are other common mechanical faults in induction motors. Due to improper lubrication, corrosion and contamination, the bearing surfaces and balls inside the inner and outer races may lose their perfection. Those types of faults cause abnormal noise and vibration during operation. Although the operation of the motor is not affected seriously, these incipient faults may deteriorate fast. In literature, there are significant amount of work that focus on the effects of the different bearing related faults to the frequency spectrum of the motor current [1,2]. Only considering current as fault diagnostic criteria it is not possible to track the acoustical traces of faults due to the noise and vibration, where these types of fault may seriously lead to ineffective classification. In the test bed, the bearings of two test motors are replaced with defective ball bearings of the motors that had been used for many hours in industry. One of these two used bearings has problem with alignment and the other bearing has ball defect complication. The last fault type, short-circuited stator winding problem, which is artificially created as in right side of Fig. 1, is implemented in another motor with pealing the insulation of two adjacent coils for a few millimeters and soldering them together. Table 1 below shows the fault types of the setup. In industry, induction motors are mostly driven directly from ac network with constant voltage and frequency under different loads. In this work, in order to test the motors under different load conditions, induction motors are coupled with a single-phase permanent magnet synchronous generator connected to an adjustable resistive load bank. The resistor values on load banks are adjusted to six different values such that the motors are driven by 3.6, 4.1, 4.7, 4.9, 5 and 5.4 A stator current. During the experiments, the motors start to operate without any load and after a minute, when the motor reaches to the steady state, the resistor values have been adjusted to load the motors consecutively to the levels given above. At each current level approximately 30 s of sound data are collected via a full transparent analog amplifier and through 5 microphones which are located around the test rig which can be seen in Fig. 2. One of these microphones is located approximately more than half a meter above the center of the test rig. Other remaining 4 microphones are set to construct the edges of a square, which surrounds the test rig and located at a little lower height compared to the microphone at the center. The locations of the microphones are very important when constructing the cross correlation between them. This settlement of microphone array produces a virtual hemisphere that covers all the experimental setup and can be seen in Fig. 3. The experiments are deliberately carried out in a noisy environment on purpose and the ambient sound pressure level (SPL) is recorded as 53.2 dB in average. The microphones that are used during the experiments are directional and cardioid type condenser ones. The microphones are connected to an analog amplifier and approximately 30 s of sound data are collected for 5 motors under 6 different loading conditions. The sound data are digitized with a sampling frequency of 44.1 kHz, which gives us digitized files containing approximately 1 million samples for each microphone. These procedures are repeated 3 times for each test motor by dissembling the motor from the test bed and reattaching it, in order to simulate different types of working conditions. In this way, different cases corresponding to differently aligned test bed possibilities are handled. Since the test rig has mechanical parts like screws and bolts, which fixes the motor to the skeleton, each different attempt of connection has its own mechanical characteristics. The aim of differentiating the faults in multi-experiments is, certifying the method.
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Fig. 2. Laboratory setup.
Fig. 3. The settlement of the microphones over the test motor.
3. Feature extraction In this work, feature extraction from sound data are realized by using two different methods. First one is calculating the cross correlation of the sound data recorded from microphone pairs. It is always expected that, the mechanical and the electrical faults cause irregular rotor spin. According to these irregularities and effects of the faults to the proper working conditions, the amplitude of fundamental frequency and its related sideband artifacts show variations according to the placements of microphones [7]. Just because of those, it is worth to note that, the characteristic of recorded sound differs in each microphone. Therefore, according to its distance to certain parts of the motor. The interrelation between channels of the semispherical microphone array installed over the motor is also changed due to these discrepancies on the sound. In addition, different types of faults are supposed to cause different types of channel interrelationship. For the purpose of classifying different motor faults, cross-correlation coefficients between channels are used as one of the features set. In order to calculate the cross-correlation coefficients, Pearson product-moment correlation coefficient method, defined in Eq.1, is used [23]. N1
∑ ½ðxi ðnÞ xi Þðxj ðnÞ xj Þ n¼0 r xi xj ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi N 1 N 1 ∑ ðxj ðnÞ xj Þ2 ∑ ðxi ðnÞ xi Þ2 n¼0
n¼0
ð1Þ
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In Eq. (1), subscripts i and j denote different microphones, and xi and xj are their corresponding data array. Here N is the number of samples in these arrays, which is taken as 800,000 in this work. Since 5 channels are used, the number of total couple combinations among 5 microphones is 10, 10 correlation coefficients are calculated. Therefore first 10 features of the feature set are obtained from these cross correlation coefficients. While forming the remaining items in the feature set, the second method is an indirect one, which uses 2D grayscale images obtained from sound data. The 2D image representation of one dimensional data are getting popular recently in pattern recognition and signal processing and also has great potential in detecting power quality related events [14,15]. During the conversion process of 1D acoustic data to 2D grayscale image, the amplitude of each sound data samples are normalized between 0 and 255, which becomes the pixel intensity range for grayscale. When an unloaded induction machine is driven directly from ac network, it rotates very close but a bit slower than the synchronous speed. Under different loading conditions, the rotation speed of the motor will decrease slowly with the increase of the stator current. Also the fault type may affect the rotation speed. For these reasons, determination of the exact real rotor frequency is a cumbersome process and has a vital importance for constructing 2D images from sound data. The widths of the images are determined due to the length of a complete period of the power signal. Since the sampling frequency is 44.1 kHz, and motor fundamental frequency is 50 Hz, for each complete cycle, 882 samples are necessary. However in practice, the fundamental frequency fluctuates and in general it is slightly less than 50 Hz. In these kinds of situations, it is necessary to use more samples than 882. In order to construct the 2D grayscale image with non-overlapping period segments, determination of the sample size of a complete period is crucial. Here this problematic issue has been solved by analyzing the autocorrelation peaks, which naturally indicates the oscillation cycle. The autocorrelation sequences of the sound data of Motors 1–5 under 3.6 A recorded by microphone 1 are plotted in Fig. 4. The cycle values at different loading conditions are also calculated in the same manner. The results for sample sizes of a single period at each loading conditions for each motor are given in Table 2. During obtaining 2D images of one dimensional data process, the first element of normalized data is assigned as the first pixel value, which is the top-left corner of the image. The succeeding elements are assigned to the right of first pixel until
0.5
Motor1
N: 900 R: 0.6572
0 −0.5
0
500
1000
1500
2000
2500
3000
3500
4000
4500
1500
2000
2500
3000
3500
4000
4500
1500
2000
2500
3000
3500
4000
4500
1500
2000
2500
3000
3500
4000
4500
1500
2000
2500
3000
3500
4000
4500
0.5
Autocorrelation (R)
Motor2
N: 905 R: 0.4331
0 −0.5
0
500
1000
0.5
Motor3
N: 901 R: 0.2384
0
−0.5
0
500
N: 903 R: 0.7548
0.5
Motor4
0 −0.5
0
500
0.5
Motor5
1000
1000 N: 901 R: 0.6867
0 −0.5
0
500
1000
Distance in Number of Samples (N) Fig. 4. The autocorrelation sequences of sound data of Motor1 to Motor5 under 3.6 A recorded by microphone 1.
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Table 2 Period values of the sound data collected from motors running under different loads.
M1 M2 M3 M4 M5
3.6 A
4.1 A
4.7 A
4.9 A
5.0 A
5.4 A
900 905 901 903 901
906 910 907 910 906
912 914 908 912 913
914 917 916 919 914
916 918 919 922 915
919 921 923 926 920
Motor1
Motor2
Motor3
Motor4
Motor5 Fig. 5. 2D Image representation of sound data recorded from first microphone over Motor 1–Motor 5 under 3.6 A.
E. Germen et al. / Mechanical Systems and Signal Processing 46 (2014) 45–58
Energy Image
Horizontal Image
Vertical Image
Diagonal Image
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Fig. 6. Sub-band images obtained by wavelet decomposition of the 2D image representation of Motor 1 given in left top of Fig. 5.
the elements corresponding to are rendered to form one row. After the assignment of the last pixel in the first row, the same procedure is carried out for the next row and this process is repeated until the image using all data samples is obtained. The ultimate image representations of the data recorded under 3.6 A by the first microphone over Motor 1 to Motor 5 are shown in Fig. 5. The 2D image extraction process is carried out for every separate 5 microphones for 5 test motors under 6 different loads for 3 different trials. Therefore, image database consists of 450 grayscale square shaped images, whose widths are ranging from 900 to 926 according to their corresponding autocorrelation values. In order to extract second group of features, single level 2D discrete wavelet transformation (DWT) is applied to these images. The discrete wavelet transformation is the projection of a discrete signal onto two subspaces called the approximation space and the detail space. By iteratively applying DWT to the approximation, a series of detail spaces can be achieved. The projection process is accomplished by discrete-time sub-band decomposition of input signals using low-pass and highpass filtering operations followed by down-sampling operation. For a N N 2D square shaped image, first the low-pass and high-pass filters and the down-sampling by 2 operations are applied along rows. The outputs of this stage are two subimages, L and H, which are sized N N=2. Secondly, the same procedure is applied to the columns of these new obtained images L and H. The outputs of the second stage are 4 square-shaped grayscale images sized N=2 N=2. These two stages correspond to one-level discrete wavelet transform of the image and the output images (denoted as LL, LH, HL and HH) are called the energy, horizontal, vertical and the diagonal sub-images, respectively. The energy image (LL), which is also called the approximation image, resembles the original image. On the other hand, remaining images contain detail textures. Clearly, those textures have some close relationship with the traces of motor failures. The wavelet decomposition of Motor 1 image shown in the left top of Fig. 5 can be demonstrated as in Fig. 6. Fig. 7 consists of zoomed vertical images of the 5 different motor types recorded by microphone 1. In wavelet decomposition, the selection of the wavelet type may also affect the process. In this work, various types of wavelet filters such as coiflet, morlet and several types of filters from Daubechies family are used in the experiments. Nevertheless, db2, which is also called as Haar filter, happened to show the necessary success compared to other wavelets. Since this filter is fairly simple, for the minimum computational cost, it is chosen in the filtering process of the decomposition in the rest of the work. In the equations below, mother wavelet ψðtÞ and the scaling function ϕðtÞ of Haar
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Motor1
Motor2
Motor3
Motor4
Motor5 Fig. 7. Zoomed vertical images obtained by wavelet decomposition of the 2D image representations of Motor 1–Motor 5 under 3.6 A.
wavelet can be seen. 8 > <1 ψðtÞ ¼ 1 > : 0 ϕðtÞ ¼
1 0
9 0 r t o 1=2 > = 1=2 rt o 1 otherwise
0 rt o 1 otherwise
> ;
ð2Þ
ð3Þ
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After one level 2D wavelet transformation process, 6 different features are extracted from these 4 sub-band images. First and second features are the root mean square energies of the vertical and diagonal images. Remaining features are obtained by calculating the row correlations of the horizontal image and the column correlations of the vertical, diagonal and energy images. In this work, the correlations between two adjacent rows or columns are calculated over the sub-images and the mean of these calculated values are taken as the feature. The detailed analysis of the images obtained by Wavelet decomposition unveils the fact that the most distinguishable information is captured in their columns mostly, instead of rows. The main cause of this situation emerges from the fact that, rows approximately consisted of one period of the sound data. Therefore there are no distinguishable differences between rows. However according to this periodicity situation, the column information contains the possible distinguishable characteristics of the artifacts caused by faults and focusing of this data would be more informative. Here it is important to note that, both in vertical and diagonal images, the textures conceal the signatures of faults, because the column information is mostly contained by vertical and diagonal images. For the calculation of column correlation Eq. (4) is used, which is the mean of the cross-correlation coefficients among neighbor columns within the image. In Eq. (4), N and M denote number of columns and rows respectively. 0
N2
N2
∑ r Ið⋯;jÞIð⋯;j þ 1Þ
j¼0
∑ ðIði;jÞ Ið⋯;jÞÞ
1
∑ ðIði;j þ 1Þ Ið⋯;j þ 1ÞÞ
i ¼ 0
¼
N1
B C ∑ ðIði;jÞ Ið⋯;jÞÞðIði;j þ 1Þ Ið⋯;j þ 1ÞÞ C j ¼ 0 ∑ B ffiC Bsffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi C j¼0@ A M1 M1 2 2
N2 B
r column ¼
i ¼ 0
N1
ð4Þ
On the other hand, rows of the 2D representation of the sound data also carry necessary information for classification because of changes in the duration of one period of the sound. These periodicity changes cause some inconsistent shifting effects, which can only be analyzed with relationship between neighbor columns of the horizontal image. For the row correlation Eq. (5) is used, which is the mean of the cross-correlation coefficients among neighbor rows within the image. In Eq. (5), N and M denote number of columns and rows respectively. 0
1 N1 B C ∑ ðIði;jÞ Iði;⋯ÞÞðIði þ 1;jÞ Iði þ 1;⋯ÞÞ M 2 B C j ¼ 0 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi s ∑ B C B C i¼0 @ A N1 N1 2 2
N2
∑ r Iði;⋯ÞIði þ 1;⋯Þ
r row ¼
i¼0
M1
∑ ðIði;jÞ Iði;⋯ÞÞ
¼
j ¼ 0
∑ ðIði þ 1;jÞ Iði þ 1;⋯ÞÞ
j ¼ 0
M 1
ð5Þ
Row correlation that we calculate for the horizontal image has the similar meaning with autocorrelation value Rxx ðNÞ for the one-dimensional signal. N is the period of one-dimensional signal, which is also the width of the two-dimensional image upon which we apply wavelet decomposition. This naturally corresponds to an autoregressive model, AR-1 with a correlation coefficient, ρ, and a fixed time-lag of N: x½n ¼ ρN x½n N þ ε½n
ð6Þ
where ε½n is the model error. Column correlation that we calculate for the vertical image has the similar meaning with autocorrelation value Rxx ð1Þ for the one-dimensional signal. This time, the model corresponds to the simple AR-1 with a different correlation coefficient and a simple time-lag of 1: x½n ¼ ρ1 x½n 1 þε½n
ð7Þ
The reason of calculating row correlation and column correlation of the horizontal and vertical wavelet components of the 2D image, instead of calculating AR(1) parameters directly from 1D signal, is the strengthened information about Rxx ðNÞ and Rxx ð1Þ by the wavelet decomposition that also corresponds to horizontal and vertical textures in the 2D image representation of the 1D signal. Horizontal textures are more distinct in horizontal component than the original 2D image representation because of filtering effects of vertical textures. The same case is also valid for vertical textures in vertical component because of filtering effects of horizontal textures. Although the energy image is expected to lack texture information, experiments show that one level of wavelet decomposition is inadequate for strict extraction of the detail information from the 2D representation. That means energy image has still some detail information, which is beneficial for the analysis of the texture and in parallel with classification of the fault type. For the purpose of obtaining the necessary information contained by energy image, column correlation is calculated also for energy image, instead of applying second level wavelet decomposition. All these 40 features obtained from both cross correlations of sound data recorded by different microphones and wavelet decomposition of the 2D images constructed from 1D sound data of each microphone are listed in Table 3. Also, the flow diagram of the entire feature extraction and classification process is given below in Fig. 8.
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Table 3 Feature numbers and their explanation. Cross-correlation features #1: #2: #3: #4: #5:
Wavelet decomposition features #6: r χ 2 χ 4 #7: r χ 2 χ 5 #8: r χ 3 χ 4 #9: r χ 3 χ 5 #10: r χ 4 χ 5
rχ1 χ2 rχ1 χ3 rχ1 χ4 rχ1 χ5 rχ2 χ3
#11, #17, #23, #29, #35: RMS energy of vertical images from microphones 1 to 5 #12, #18, #24, #30, #36: RMS energy of diagonal images from microphones 1 to 5 #13, #19, #25, #31, #37: column correlation of vertical images from microphones 1 to 5 #14, #20, #26, #32, #38: column correlation of diagonal images from microphones 1 to 5 #15, #21, #27, #33, #39: row correlation of horizontal images from microphones 1 to 5 #16, #22, #28, #34, #40: column correlation of energy images from microphones 1 to 5
4. SOM and results The objective of this section is to describe classification of healthy and defective motors using neural networks and to figure out the identification of types of the faults. As it has been denoted in Section 1, SOM is a well-known and popular method to organize the input feature vectors. Since SOM algorithm can be considered as a vector quantization variant, in order to improve the quality of the quantization, the class boundaries should have to be well adjusted. Here the supervised Learning Vector Quantization (LVQ) algorithm is a suitable one to adjust boundaries. Although there are separate algorithms in the literature on LVQ, the LVQ3 algorithm has been used in this paper [24]. 4.1. SOM and LVQ as classifier SOM provides a very attractive and powerful method based on Hebbian type neural network for the classification problems. The main outcome of the SOM is the possibility of tracing the resemblance and the discrepancies of input data. SOM projects the input data vector Λ A ℝn which is taken from a sample space of size p to the m many codebook vectors of M A ℝn which are organized in planar fashion where p»m. The result after training SOM is a lattice of neurons representing the possible clusters. During the training phase, SOM is organized in an unsupervised manner according to the formula: M i ðkÞ ¼ M i ðk 1Þ þ ðαðkÞ U βði; c; kÞ U½ΛðkÞ M i ðk 1ÞÞ
8i
1 ri r m
ð8Þ
where αðkÞ is the learning rate and βði; c; kÞ is the neighborhood parameter which change during the adaptation phase. The c parameter denotes the index of the Best Matching Neuron, which depends on c ¼ arg min jjΛðkÞ M i ðkÞjj
ð9Þ
i
After the training process, the codebook vectors organized in planar lattice structure and for each input vector, the closest codebook vectors represent the possible cluster. Here in order to delineate the classification regions, and the region of clusters, a supervised method Learning Vector Quantization 3 (LVQ3) algorithm has been used [22]. This algorithm can be expressed as M i ðk þ1Þ ¼ M i ðkÞ ðξðkÞ U ½ΛðkÞ M i ðkÞÞ M j ðk þ1Þ ¼ M j ðkÞ þ ðξðkÞ U ½ΛðkÞ M j ðkÞÞ
ð10Þ
where Mi and Mj are the two closest codebook vectors for ΛðkÞ, and both ΛðkÞ and Mj belongs to the same class however Mi is not. Here also it is necessary that Mi, Mj ΛðkÞ and have to be in the window as
d1 d2 1 window ð11Þ min 4 s where ; 1 þ window d2 d1 where d1 and d2 are the distances between the closest codebook vector M i and the input data ΛðkÞ and second closest codebook vector Mj and ΛðkÞ respectively. In the algorithm if Mi and Mj are in the same class then the adaptation scheme will be as M i ðk þ1Þ ¼ M i ðkÞ þ ðη U ξðkÞ U½ΛðkÞ M i ðkÞÞ M j ðk þ 1Þ ¼ Mj ðkÞ þ ðη UξðkÞ U ½ΛðkÞ Mj ðkÞÞ
ð12Þ
where ξðkÞ and η are learning rate parameters. 4.2. Classification using SOM þLVQ3 and fault detection In this work three different experiments have been carried out and, for each experiment, data are collected from five different motors in six different load conditions. While doing those experiments, the same motors are decupled from the generator load, and their fixing locations and recoupled. Every experiment produces data with different acoustic nature and sound pressure levels because of the inconsistencies of the fixation using manual screwing and bolting. This has been done
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on purpose, because the main aim is trying to focus on to the identification the possible traces of faults independent from the trials. Otherwise, there is always a danger of tracking the discrepancies due to experimental variations. The environmental Sound Pressure Level of the experiments was about 53.2 dB, which shows a moderate noise platform. Here the materials around the rig are designed such that the reflections and refractions have no effect on the experimental results. Table 4 below shows the Sound Pressure Level (SPL) from three different experiments recorded under different load conditions for each motor type.
Fig. 8. Flow diagram of the sound-based fault diagnosis process.
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Table 4 SPL of three experiments of dataset. Load levels 3.6 A
4.1 A
4.7 A
4.9 A
5A
5.4 A
Environment SPL: 53.2 dB Motor 1 Exp1 73.8 Exp2 74.9 Exp3 73.8
76.5 76.1 73.8
78.5 74.6 73.8
78.5 75.1 73.8
78.5 76 73.8
79.4 75.4 72.6
dB dB dB
Motor 2 Exp1 Exp2 Exp3
86.2 83.7 83.2
84.5 83.7 83.2
84.2 83.2 83.4
84.3 84.2 83.7
84.2 83.2 83.2
84.2 82 82
dB dB dB
Motor 3 Exp1 Exp2 Exp3
84.6 83.2 83.2
83.7 83.2 83.7
83.3 83.2 83.4
83.2 83.2 83.4
83.2 83.2 83.8
83.2 83.2 83.2
dB dB dB
Motor 4 Exp1 Exp2 Exp3
75 76 75
76.1 74.5 74.5
77.1 75 74.1
77.1 75 74.1
78.1 75.4 74.2
77.1 74.5 73.8
dB dB dB
Motor 5 Exp1 Exp2 Exp3
75.4 74.1 74.8
74.7 73.8 74.4
74.5 74.1 74.8
74.6 74.4 74.4
74.1 73.8 73.8
74.1 74.2 74.7
dB dB dB
Fig. 9. 5 10 Dimension SOM map is trained with Exp1 and Exp3 data set.
In order to train a 5 10 dimension SOM, the feature vectors obtained from two different experiment sets Exp1 and Exp3 are used. Prior to training, the input vectors are normalized. After training phase, the resultant map in Fig. 9 has been obtained. Naturally, the SOM results depend on the nature of the feature vectors. In this work the vectors are composed of both cross correlation values of time domain data and the image-related correlations as explained in Section 3. The motor number labels, which can be seen on the map, are the corresponding localizations of the training motor data on the map. The vicinity in two-dimensional map shows the possible close relationship of the input feature vectors. In other words, if two feature vectors from two different experiments are mapped to neurons which are close to each other in the lattice, it is possible to deduce that there is somehow a resemblance between those motors. Conversely, the increase in the space between the neurons indicates the differences of the features obtained from the motors. By scrutinizing Fig. 10, Motors 2 and 3 data have been localized at the left of the healthy motor and the other faults are settled at the right of the healthy one. It is not surprising that Motors 2 and 3 faults have some close relationship with each other and the SOM map has a consistent result with this relationship. In order to test the results, the experiment set Exp2 data are directly applied to the trained map and the following results have been obtained. Test1–Test5 labels are the test data for Motor1–Motor5. Clearly, the test data localization is highly consistent with the trained data at a first glance. In the figure below, the number in parentheses designates the number of
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Fig. 10. Localization of test data from Experiment 2 on 5 10 dimension SOM map. Table 5 Classification results of test data without applying LVQ algorithm.
Motor Motor Motor Motor Motor
1 2 3 4 5
Motor 1
Motor 2
Motor 3
Motor 4
Motor 5
Correct classification %
6 0 0 1 0
0 6 0 0 0
0 0 6 0 0
0 0 0 5 0
0 0 0 0 6
100 100 100 83 100
Table 6 Classification results of test data after applying LVQ algorithm.
Motor Motor Motor Motor Motor
1 2 3 4 5
Motor 1
Motor 2
Motor 3
Motor 4
Motor 5
Correct classification %
6 0 0 0 0
0 6 0 0 0
0 0 6 0 0
0 0 0 6 0
0 0 0 0 6
100 100 100 100 100
hits for the relevant motor. For example “Test 3 (5)” means that this neuron has five hit values for the test data of Motor 3, similarly “Test 5(2)” designates the same neuron has been hit 2 times with the test data of Motor 5. As it can be seen in Table 5, the probability of correct classification for the healthy motor is 100%. This table demonstrates the results without applying LVQ algorithm. After applying LVQ3 algorithm, the results show that there is an improvement in the classification percentage as shown in Table 6. The results obtained from the training and test sets indicate 100% correct classifications. Both the cross correlation of time series data and 2D images obtained for each microphone with different load conditions provide these amazing results. The success of the classification is directly related with the proper combinations of the features obtained from different microphones. If the methods explained in Section 3 are applied separately, a substantial degradation in the percentage of success is observed. The image processing techniques contribute an important value for pattern recognition in motor faults. Here it is always worth to note that, the traces of each fault are always hidden in data and it is necessary to scrutinize and conceive a proper method in order to unveil them.
5. Conclusions The stator current and the vibrational analyses techniques are quite sensitive to electrical and mechanical faults, whereas the acoustical approaches are sensitive to the interference of the environmental noises. In this work, a test bed containing 5 different microphones settled on the motor in hemispherical shape is constructed. Consequently, a valuable data set for the possible faults is constructed. Each type of fault, which investigated in this paper, has its own acoustical shapes. The cross correlation coefficients of the microphones give acoustic clues about the type of the noise produced by faulty motors. In this work, it is observed that the steady-state signatures of the relations of data of different microphones reveal the traces of possible faults. By proper feature set, SOM and LVQ is an efficient method in order to discriminate motor faults. It must be noted that the methods proposed in this paper not only evaluate the possible differences between faulty and
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healthy motors, but also provide the definition of the fault type such as bearing faults, short circuit in stator, or broken rotor bars. In this work also it is concluded that, the same kind of faults such as bearing damages caused by misalignment or defective balls are identified in close regions in the map. This is quite an exciting result, since the similarities between the faults can be tracked and a pre-defined maintenance program can be developed for preventive maintenance strategies. References [1] S. Nandi, H.A. Toliyat, X. Li, Condition monitoring and fault diagnosis of electrical motors – a review, IEEE Trans. Energy Convers. 20 (2005) 719–729. [2] M.E.H. Benbouzid, A review of induction motors signature analysis as a medium for faults detection, IEEE Trans. Power Electron. 14 (2000) 984–993. [3] H. Ocak, K.A. Loparo, Estimation of the running speed and bearing defect frequencies of an induction motor from vibration data, Mech. Syst. Signal Process. 18 (2004) 515–533. [4] W. Lu, W. Jiang, H. Wu, J. Hou, A fault diagnosis scheme of rolling element bearing based on near-field acoustic holography and gray level co-occurrence matrix, J. Sound Vib. 331 (2012) 3663–3674. [5] W. Li, C.K. Mechefske, Detection of induction motor faults: a comparison of stator current, vibration and acoustic methods, J. Vib. Control 12 (2006) 165–188. [6] A. Kaya, E. Germen, U. Unlu, S. Toprak, Fault Classification in Hermetic Compressors Using Self-Organizing Map, International Compressor Engineering Conference at Purdue, July 14–17, 2008, Paper 1243. [7] E. Germen, A. Kaya, U. Unlu, Effects of sound radiation direction in faulty hermetic compressors. In: Proceedings of the International Compressor Engineering Conference at Purdue, July 12–15, 2010, Paper 2015. [8] U. Benko, J. Petrovic, D. Juricic, C.J. Tavcar, C.J. Rejec, A. Stefanovska, Fault diagnosis of a vacuum cleaner motor by means of sound analysis, J. Sound Vib. 276 (2004) 781–806. [9] V.T. Do, U.P. Chong, Signal model-based fault detection and diagnosis for induction motors using features of vibration signal in two-dimension domain, J. Mech. Eng. 57 (2011) 655–666. [10] L. Semler, L. Dettori, J. Furst, Wavelet-based texture classification of tissues in computed tomography. In: 18th IEEE Symposium on Computer-Based Medical Systems Proceedings, 2005, pp. 265–270. [11] L. Dettori, L. Semler, A comparison of wavelet, ridgelet, and curvelet-based texture classification algorithms in computed tomography, Comput. Biol. Med. 37 (2007) 486–498. [12] C. Hsieh, E. Lai, Y. Wang, An effective algorithm for fingerprint image enhancement based on wavelet transform, Pattern Recognit. 36 (2003) 303–312. [13] S. Fukuda, H. Hirosawa, A wavelet-based texture feature set applied to classification of multifrequency polarimetric SAR images, IEEE Trans. Geosci. Remote Sens. 37 (1999) 2282–2286. [14] D.G. Ece, O.N. Gerek, Power quality event detection using joint 2-D-wavelet subspaces, IEEE Trans. Instrum. Meas. 53 (2004) 1040–1046. [15] O.N. Gerek, D.G. Ece, 2-D analysis and compression of power-quality event data, IEEE Trans. Power Deliv. 19 (2004) 791–798. [16] A.M.D. Younus, B. Yang, Intelligent fault diagnosis of rotating machinery using infrared thermal image, Expert Syst. Appl. 39 (2012) 2082–2091. [17] T. Chang, C.-C.J. Kuo, Texture analysis and classification with tree-structured wavelet transform, IEEE Trans. Image Process. 2 (1993) 429–441. [18] A. Laine, J. Fan, Texture classification by wavelet packet signatures, IEEE Trans. Pattern Anal. Mach. Intell. 15 (1993) 1186–1191. [19] M. Unser, Texture classification and segmentation using wavelet frames, IEEE Trans. Image Process. 4 (1995) 1549–1560. [20] N. Sebe, M.S. Lew, Wavelet based texture classification. In: 15th International Conference on Pattern Recognition Proceedings, vol. 3, 2000, pp. 947–950. [21] S. Arivazhagan, L. Ganesan, Texture classification using wavelet transform, Pattern Recognit. Lett. 24 (2003) 1513–1521. [22] T. Kohonen, Self-Organizing Maps, Springer-Verlag, Berlin, 1995. [23] J.L. Rodgers, W.A. Nicewander, Thirteen ways to look at the correlation coefficient, Am. Stat. 42 (1988) 59–66. [24] T. Kohonen, The self organizing map, Proc. IEEE 78 (1990) 1464–1480.
Contents lists available at ScienceDirect
Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/ymssp
Sound based induction motor fault diagnosis using Kohonen self-organizing map Emin Germen, Murat Başaran n, Mehmet Fidan Department of Electrical and Electronics Engineering, Anadolu University, Eskisehir, Turkey
a r t i c l e i n f o
abstract
Article history: Received 30 January 2013 Received in revised form 19 June 2013 Accepted 2 December 2013 Available online 31 January 2014
The induction motors, which have simple structures and design, are the essential elements of the industry. Their long-lasting utilization in critical processes possibly causes unavoidable mechanical and electrical defects that can deteriorate the production. The early diagnosis of the defects in induction motors is crucial in order to avoid interruption of manufacturing. In this work, the mechanical and the electrical faults which can be observed frequently on the induction motors are classified by means of analysis of the acoustic data of squirrel cage induction motors recorded by using several microphones simultaneously since the true nature of propagation of sound around the running motor provides specific clues about the types of the faults. In order to reveal the traces of the faults, multiple microphones are placed in a hemispherical shape around the motor. Correlation and wavelet-based analyses are applied for extracting necessary features from the recorded data. The features obtained from same types of motors with different kind of faults are used for the classification using the Self-Organizing Maps method. As it is described in this paper, highly motivating results are obtained both on the separation of healthy motor and faulty one and on the classification of fault types. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Induction motors Fault detection Kohonen SOM Acoustic signal processing
1. Introduction Due to their simple construction, cost effectiveness and easy maintenance, the squirrel cage induction motors are the most preferable electrical motors in the industry. In order not to interrupt the industrial processes caused by unexpected failures of induction motors, preventive maintenance strategies are essential. Early diagnostics of incipient faults in induction motors are important to ensure safe operation and help to recognize and fix the problems with low costs and time. Significant amount of research have been focused on the methods for the early detection of the mechanical and electrical faults in induction motors [1]. Among all the methods in literature, motor current signature analysis (MCSA) is one of the most popular ones, which provides an effective way to detect incipient faults. MCSA mainly focuses on the analysis of the current data that is supplied from the ac network to the induction motor with time–frequency analysis techniques like Fast Fourier Transform (FFT), Short Time Fourier Transform (STFT), Wavelet Transform or Wavelet Packet Transform [2]. However there is a bottleneck to apply this technique to induction motors in their working environment since in most cases obtaining data is a cumbersome process because of the additional circuitry like isolators or data acquisition cards and interface that should be added between the supply and the test motors. Also it may not be possible to detach load from motor and run motor under no load condition. In order to get rid of disadvantages of current based techniques like MCSA, the acoustic and
n
Corresponding author. E-mail addresses: [email protected] (E. Germen), [email protected] (M. Başaran), [email protected] (M. Fidan).
0888-3270/$ - see front matter & 2014 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ymssp.2013.12.002
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vibrational methods are getting popular since those approaches do not require detaching motors from their working environment. Fault diagnosis methods based on vibration analysis have been applied for many years using the methods such as Fourier and Wavelet Transforms, and have shown significant success especially on detecting faulty bearing detection [3]. Vibration signal can be obtained via a contact device such as accelerometer; however in some special cases it may be problematic. For example the surface of the test motor may be irregular and the device could not be located properly on the test motors. Also the surface may be greasy or slippery due to the hard operating conditions like high temperature and humidity [4]. On the other hand, sound based fault diagnosis of motors offers a great advantage that solves many of these problems since it offers a contactless solution to obtain data. Only external microphones located around the operating motor are enough to record the information. Unlike vibration-based analysis, there is a very limited literature on fault diagnosis of induction motors, which are based on techniques of sound analysis. In Ref. [5] stator current, vibration and acoustic methods are compared and very detailed results for different types of faults in different load conditions have been introduced. It is worth to note that in this work, the acoustic methods are quite effective in order to capture the signatures of bearing faults. Previous work on acoustic analysis of induction motors also has promising results. In Ref. [6], compressor motor faults were successfully identified inside a semi-anechoic chamber environment. In Ref. [7] the effects of localization of multiple microphones have been scrutinized and their effects on results have been investigated. It is worth to mention the work [8], where a detailed sound based approach has been applied in order to make fault detection in high-speed motors. There, the vacuum cleaner motor experiments have been carried out in echo-free silent environment that provide significant results on detection of faults. However the real life applications in industry always introduce ambient noise. In this work, the acoustic data are collected from the same type of five different induction motors located in an environment with ambient noise, where four of them have specific incipient mechanical or electrical faults, via five microphones surrounding the test rig. These data can be analyzed like current or vibration data and can possibly contain many fault related information for diagnosis. Therefore this paper aims to scrutinize the suitable information hidden in acoustic data, which can distinguish the healthy motor from the faulty ones, and classify the fault types. Here the first strategy, features are obtained directly by calculating the cross correlation coefficients of the sound data recorded by the microphone pairs. For each experimental trial, 10 different correlation coefficients are calculated for each motor using 5 different microphones. In the second strategy, additional features are extracted by using 2D wavelet decomposition of the grayscale images, which are obtained by converting one-dimensional sound data, which are recorded by each separate microphone, to 2D grayscale images. As it has been described in Ref. [9], the 2D representation has many advantages over the regular one-dimensional data since it provides many additional information and possible usage of image processing tools. These two dimensional images are expected to show different type of textures and in former works for texture analysis, basically wavelet based methods were used [10–21]. These wavelet based texture analysis methods are applied on different kind of research areas including classification of tomography images [10,11], fingerprint classification [12], analysis of SAR images [13], power quality analysis from 2D represented power quality event data [14,15] and fault analysis of rotating machinery by using data obtained from infrared thermography [16]. The detection of faulty motor is a classification problem. Here it is reasonable to use neural network techniques, especially Kohonen Self-Organizing Map (SOM), in order to discriminate a faulty motor from a healthy one [22]. The idea behind the SOM is finding a projection of multi-dimensional vector space into two-dimensional lattices. While scattering the input vectors to the two-dimensional lattice, SOM also provides information about the possible similarities and resemblances of input vectors and it presents a visual representation of possible clusters in data set. In order to get the benefits of SOM, the feature vectors, which are used to identify the nature of the fault, should have to be designated in proper fashion. This paper also focuses on definition of those feature vectors obtained from acoustic data, which are used in SOM. This article continues with Section 2, which contains the explanation of motor fault types and detailed information of the experimental setup constructed by induction motors and microphones. Afterwards in Section 3, the features obtained from the sound data of the healthy and faulty motors to classify the fault types are expressed. Furthermore, Self-Organizing Maps (SOMs) and Learning Vector Quantization (LVQ) methods applied on the obtained features to classify the fault types are explained and the classification results are presented in details, in Section 4. Finally Section 5 concludes the paper. 2. Fault types and experimental setup In this work, five induction motors are used in order to obtain the acoustic data. Motors are driven directly from AC network. A 3-phase, 25 kVA, Δ-Υ connected isolation transformer is located between laboratory setup and the network where the motors are supplied with the output of this transformer. Test motors are 3-phase and 2-pole squirrel cage induction motors rated at 2.2 kW and 380-V line to line. Some commonly encountered mechanical and electrical faults are created synthetically on four of these motors. One of these identical motors is left untouched in order to get the healthy motor data. The faults are chosen and created such that those are the most encountered incipient faults in industry. The broken rotor bar fault is realized by drilling holes to 3 bars respectively over 18 bars as illustrated in left side of Fig. 1. This type of faults cause a rise in magnitude at adjacent side band frequency components of the motor current located symmetrically around the main frequency which the stator coils are supplied by Ref. [5]. However, monitoring the increase in magnitude at the predicted sideband frequencies alone may mislead the classification since different types of faults may have same frequency components. Also when the amount of slip
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Fig. 1. Creation of the broken rotor fault by drilling holes to rotor bars and creation of short-circuited stator winding fault.
Table 1 Table of faulty motors in experimental setup. Motor #
Fault type
Motor Motor Motor Motor Motor
Healthy motor Bearing fault (misalignment) Bearing fault (ball defect) Broken rotor bars (3 over 18) Short circuit in stator winding
1 2 3 4 5
is small, these sidebands come close to the fundamental frequency and it becomes difficult to grasp them by inspecting the spectral information due the dominancy of the fundamental component. Bearing damages are other common mechanical faults in induction motors. Due to improper lubrication, corrosion and contamination, the bearing surfaces and balls inside the inner and outer races may lose their perfection. Those types of faults cause abnormal noise and vibration during operation. Although the operation of the motor is not affected seriously, these incipient faults may deteriorate fast. In literature, there are significant amount of work that focus on the effects of the different bearing related faults to the frequency spectrum of the motor current [1,2]. Only considering current as fault diagnostic criteria it is not possible to track the acoustical traces of faults due to the noise and vibration, where these types of fault may seriously lead to ineffective classification. In the test bed, the bearings of two test motors are replaced with defective ball bearings of the motors that had been used for many hours in industry. One of these two used bearings has problem with alignment and the other bearing has ball defect complication. The last fault type, short-circuited stator winding problem, which is artificially created as in right side of Fig. 1, is implemented in another motor with pealing the insulation of two adjacent coils for a few millimeters and soldering them together. Table 1 below shows the fault types of the setup. In industry, induction motors are mostly driven directly from ac network with constant voltage and frequency under different loads. In this work, in order to test the motors under different load conditions, induction motors are coupled with a single-phase permanent magnet synchronous generator connected to an adjustable resistive load bank. The resistor values on load banks are adjusted to six different values such that the motors are driven by 3.6, 4.1, 4.7, 4.9, 5 and 5.4 A stator current. During the experiments, the motors start to operate without any load and after a minute, when the motor reaches to the steady state, the resistor values have been adjusted to load the motors consecutively to the levels given above. At each current level approximately 30 s of sound data are collected via a full transparent analog amplifier and through 5 microphones which are located around the test rig which can be seen in Fig. 2. One of these microphones is located approximately more than half a meter above the center of the test rig. Other remaining 4 microphones are set to construct the edges of a square, which surrounds the test rig and located at a little lower height compared to the microphone at the center. The locations of the microphones are very important when constructing the cross correlation between them. This settlement of microphone array produces a virtual hemisphere that covers all the experimental setup and can be seen in Fig. 3. The experiments are deliberately carried out in a noisy environment on purpose and the ambient sound pressure level (SPL) is recorded as 53.2 dB in average. The microphones that are used during the experiments are directional and cardioid type condenser ones. The microphones are connected to an analog amplifier and approximately 30 s of sound data are collected for 5 motors under 6 different loading conditions. The sound data are digitized with a sampling frequency of 44.1 kHz, which gives us digitized files containing approximately 1 million samples for each microphone. These procedures are repeated 3 times for each test motor by dissembling the motor from the test bed and reattaching it, in order to simulate different types of working conditions. In this way, different cases corresponding to differently aligned test bed possibilities are handled. Since the test rig has mechanical parts like screws and bolts, which fixes the motor to the skeleton, each different attempt of connection has its own mechanical characteristics. The aim of differentiating the faults in multi-experiments is, certifying the method.
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Fig. 2. Laboratory setup.
Fig. 3. The settlement of the microphones over the test motor.
3. Feature extraction In this work, feature extraction from sound data are realized by using two different methods. First one is calculating the cross correlation of the sound data recorded from microphone pairs. It is always expected that, the mechanical and the electrical faults cause irregular rotor spin. According to these irregularities and effects of the faults to the proper working conditions, the amplitude of fundamental frequency and its related sideband artifacts show variations according to the placements of microphones [7]. Just because of those, it is worth to note that, the characteristic of recorded sound differs in each microphone. Therefore, according to its distance to certain parts of the motor. The interrelation between channels of the semispherical microphone array installed over the motor is also changed due to these discrepancies on the sound. In addition, different types of faults are supposed to cause different types of channel interrelationship. For the purpose of classifying different motor faults, cross-correlation coefficients between channels are used as one of the features set. In order to calculate the cross-correlation coefficients, Pearson product-moment correlation coefficient method, defined in Eq.1, is used [23]. N1
∑ ½ðxi ðnÞ xi Þðxj ðnÞ xj Þ n¼0 r xi xj ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi N 1 N 1 ∑ ðxj ðnÞ xj Þ2 ∑ ðxi ðnÞ xi Þ2 n¼0
n¼0
ð1Þ
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49
In Eq. (1), subscripts i and j denote different microphones, and xi and xj are their corresponding data array. Here N is the number of samples in these arrays, which is taken as 800,000 in this work. Since 5 channels are used, the number of total couple combinations among 5 microphones is 10, 10 correlation coefficients are calculated. Therefore first 10 features of the feature set are obtained from these cross correlation coefficients. While forming the remaining items in the feature set, the second method is an indirect one, which uses 2D grayscale images obtained from sound data. The 2D image representation of one dimensional data are getting popular recently in pattern recognition and signal processing and also has great potential in detecting power quality related events [14,15]. During the conversion process of 1D acoustic data to 2D grayscale image, the amplitude of each sound data samples are normalized between 0 and 255, which becomes the pixel intensity range for grayscale. When an unloaded induction machine is driven directly from ac network, it rotates very close but a bit slower than the synchronous speed. Under different loading conditions, the rotation speed of the motor will decrease slowly with the increase of the stator current. Also the fault type may affect the rotation speed. For these reasons, determination of the exact real rotor frequency is a cumbersome process and has a vital importance for constructing 2D images from sound data. The widths of the images are determined due to the length of a complete period of the power signal. Since the sampling frequency is 44.1 kHz, and motor fundamental frequency is 50 Hz, for each complete cycle, 882 samples are necessary. However in practice, the fundamental frequency fluctuates and in general it is slightly less than 50 Hz. In these kinds of situations, it is necessary to use more samples than 882. In order to construct the 2D grayscale image with non-overlapping period segments, determination of the sample size of a complete period is crucial. Here this problematic issue has been solved by analyzing the autocorrelation peaks, which naturally indicates the oscillation cycle. The autocorrelation sequences of the sound data of Motors 1–5 under 3.6 A recorded by microphone 1 are plotted in Fig. 4. The cycle values at different loading conditions are also calculated in the same manner. The results for sample sizes of a single period at each loading conditions for each motor are given in Table 2. During obtaining 2D images of one dimensional data process, the first element of normalized data is assigned as the first pixel value, which is the top-left corner of the image. The succeeding elements are assigned to the right of first pixel until
0.5
Motor1
N: 900 R: 0.6572
0 −0.5
0
500
1000
1500
2000
2500
3000
3500
4000
4500
1500
2000
2500
3000
3500
4000
4500
1500
2000
2500
3000
3500
4000
4500
1500
2000
2500
3000
3500
4000
4500
1500
2000
2500
3000
3500
4000
4500
0.5
Autocorrelation (R)
Motor2
N: 905 R: 0.4331
0 −0.5
0
500
1000
0.5
Motor3
N: 901 R: 0.2384
0
−0.5
0
500
N: 903 R: 0.7548
0.5
Motor4
0 −0.5
0
500
0.5
Motor5
1000
1000 N: 901 R: 0.6867
0 −0.5
0
500
1000
Distance in Number of Samples (N) Fig. 4. The autocorrelation sequences of sound data of Motor1 to Motor5 under 3.6 A recorded by microphone 1.
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Table 2 Period values of the sound data collected from motors running under different loads.
M1 M2 M3 M4 M5
3.6 A
4.1 A
4.7 A
4.9 A
5.0 A
5.4 A
900 905 901 903 901
906 910 907 910 906
912 914 908 912 913
914 917 916 919 914
916 918 919 922 915
919 921 923 926 920
Motor1
Motor2
Motor3
Motor4
Motor5 Fig. 5. 2D Image representation of sound data recorded from first microphone over Motor 1–Motor 5 under 3.6 A.
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Energy Image
Horizontal Image
Vertical Image
Diagonal Image
51
Fig. 6. Sub-band images obtained by wavelet decomposition of the 2D image representation of Motor 1 given in left top of Fig. 5.
the elements corresponding to are rendered to form one row. After the assignment of the last pixel in the first row, the same procedure is carried out for the next row and this process is repeated until the image using all data samples is obtained. The ultimate image representations of the data recorded under 3.6 A by the first microphone over Motor 1 to Motor 5 are shown in Fig. 5. The 2D image extraction process is carried out for every separate 5 microphones for 5 test motors under 6 different loads for 3 different trials. Therefore, image database consists of 450 grayscale square shaped images, whose widths are ranging from 900 to 926 according to their corresponding autocorrelation values. In order to extract second group of features, single level 2D discrete wavelet transformation (DWT) is applied to these images. The discrete wavelet transformation is the projection of a discrete signal onto two subspaces called the approximation space and the detail space. By iteratively applying DWT to the approximation, a series of detail spaces can be achieved. The projection process is accomplished by discrete-time sub-band decomposition of input signals using low-pass and highpass filtering operations followed by down-sampling operation. For a N N 2D square shaped image, first the low-pass and high-pass filters and the down-sampling by 2 operations are applied along rows. The outputs of this stage are two subimages, L and H, which are sized N N=2. Secondly, the same procedure is applied to the columns of these new obtained images L and H. The outputs of the second stage are 4 square-shaped grayscale images sized N=2 N=2. These two stages correspond to one-level discrete wavelet transform of the image and the output images (denoted as LL, LH, HL and HH) are called the energy, horizontal, vertical and the diagonal sub-images, respectively. The energy image (LL), which is also called the approximation image, resembles the original image. On the other hand, remaining images contain detail textures. Clearly, those textures have some close relationship with the traces of motor failures. The wavelet decomposition of Motor 1 image shown in the left top of Fig. 5 can be demonstrated as in Fig. 6. Fig. 7 consists of zoomed vertical images of the 5 different motor types recorded by microphone 1. In wavelet decomposition, the selection of the wavelet type may also affect the process. In this work, various types of wavelet filters such as coiflet, morlet and several types of filters from Daubechies family are used in the experiments. Nevertheless, db2, which is also called as Haar filter, happened to show the necessary success compared to other wavelets. Since this filter is fairly simple, for the minimum computational cost, it is chosen in the filtering process of the decomposition in the rest of the work. In the equations below, mother wavelet ψðtÞ and the scaling function ϕðtÞ of Haar
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Motor1
Motor2
Motor3
Motor4
Motor5 Fig. 7. Zoomed vertical images obtained by wavelet decomposition of the 2D image representations of Motor 1–Motor 5 under 3.6 A.
wavelet can be seen. 8 > <1 ψðtÞ ¼ 1 > : 0 ϕðtÞ ¼
1 0
9 0 r t o 1=2 > = 1=2 rt o 1 otherwise
0 rt o 1 otherwise
> ;
ð2Þ
ð3Þ
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53
After one level 2D wavelet transformation process, 6 different features are extracted from these 4 sub-band images. First and second features are the root mean square energies of the vertical and diagonal images. Remaining features are obtained by calculating the row correlations of the horizontal image and the column correlations of the vertical, diagonal and energy images. In this work, the correlations between two adjacent rows or columns are calculated over the sub-images and the mean of these calculated values are taken as the feature. The detailed analysis of the images obtained by Wavelet decomposition unveils the fact that the most distinguishable information is captured in their columns mostly, instead of rows. The main cause of this situation emerges from the fact that, rows approximately consisted of one period of the sound data. Therefore there are no distinguishable differences between rows. However according to this periodicity situation, the column information contains the possible distinguishable characteristics of the artifacts caused by faults and focusing of this data would be more informative. Here it is important to note that, both in vertical and diagonal images, the textures conceal the signatures of faults, because the column information is mostly contained by vertical and diagonal images. For the calculation of column correlation Eq. (4) is used, which is the mean of the cross-correlation coefficients among neighbor columns within the image. In Eq. (4), N and M denote number of columns and rows respectively. 0
N2
N2
∑ r Ið⋯;jÞIð⋯;j þ 1Þ
j¼0
∑ ðIði;jÞ Ið⋯;jÞÞ
1
∑ ðIði;j þ 1Þ Ið⋯;j þ 1ÞÞ
i ¼ 0
¼
N1
B C ∑ ðIði;jÞ Ið⋯;jÞÞðIði;j þ 1Þ Ið⋯;j þ 1ÞÞ C j ¼ 0 ∑ B ffiC Bsffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi C j¼0@ A M1 M1 2 2
N2 B
r column ¼
i ¼ 0
N1
ð4Þ
On the other hand, rows of the 2D representation of the sound data also carry necessary information for classification because of changes in the duration of one period of the sound. These periodicity changes cause some inconsistent shifting effects, which can only be analyzed with relationship between neighbor columns of the horizontal image. For the row correlation Eq. (5) is used, which is the mean of the cross-correlation coefficients among neighbor rows within the image. In Eq. (5), N and M denote number of columns and rows respectively. 0
1 N1 B C ∑ ðIði;jÞ Iði;⋯ÞÞðIði þ 1;jÞ Iði þ 1;⋯ÞÞ M 2 B C j ¼ 0 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi s ∑ B C B C i¼0 @ A N1 N1 2 2
N2
∑ r Iði;⋯ÞIði þ 1;⋯Þ
r row ¼
i¼0
M1
∑ ðIði;jÞ Iði;⋯ÞÞ
¼
j ¼ 0
∑ ðIði þ 1;jÞ Iði þ 1;⋯ÞÞ
j ¼ 0
M 1
ð5Þ
Row correlation that we calculate for the horizontal image has the similar meaning with autocorrelation value Rxx ðNÞ for the one-dimensional signal. N is the period of one-dimensional signal, which is also the width of the two-dimensional image upon which we apply wavelet decomposition. This naturally corresponds to an autoregressive model, AR-1 with a correlation coefficient, ρ, and a fixed time-lag of N: x½n ¼ ρN x½n N þ ε½n
ð6Þ
where ε½n is the model error. Column correlation that we calculate for the vertical image has the similar meaning with autocorrelation value Rxx ð1Þ for the one-dimensional signal. This time, the model corresponds to the simple AR-1 with a different correlation coefficient and a simple time-lag of 1: x½n ¼ ρ1 x½n 1 þε½n
ð7Þ
The reason of calculating row correlation and column correlation of the horizontal and vertical wavelet components of the 2D image, instead of calculating AR(1) parameters directly from 1D signal, is the strengthened information about Rxx ðNÞ and Rxx ð1Þ by the wavelet decomposition that also corresponds to horizontal and vertical textures in the 2D image representation of the 1D signal. Horizontal textures are more distinct in horizontal component than the original 2D image representation because of filtering effects of vertical textures. The same case is also valid for vertical textures in vertical component because of filtering effects of horizontal textures. Although the energy image is expected to lack texture information, experiments show that one level of wavelet decomposition is inadequate for strict extraction of the detail information from the 2D representation. That means energy image has still some detail information, which is beneficial for the analysis of the texture and in parallel with classification of the fault type. For the purpose of obtaining the necessary information contained by energy image, column correlation is calculated also for energy image, instead of applying second level wavelet decomposition. All these 40 features obtained from both cross correlations of sound data recorded by different microphones and wavelet decomposition of the 2D images constructed from 1D sound data of each microphone are listed in Table 3. Also, the flow diagram of the entire feature extraction and classification process is given below in Fig. 8.
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E. Germen et al. / Mechanical Systems and Signal Processing 46 (2014) 45–58
Table 3 Feature numbers and their explanation. Cross-correlation features #1: #2: #3: #4: #5:
Wavelet decomposition features #6: r χ 2 χ 4 #7: r χ 2 χ 5 #8: r χ 3 χ 4 #9: r χ 3 χ 5 #10: r χ 4 χ 5
rχ1 χ2 rχ1 χ3 rχ1 χ4 rχ1 χ5 rχ2 χ3
#11, #17, #23, #29, #35: RMS energy of vertical images from microphones 1 to 5 #12, #18, #24, #30, #36: RMS energy of diagonal images from microphones 1 to 5 #13, #19, #25, #31, #37: column correlation of vertical images from microphones 1 to 5 #14, #20, #26, #32, #38: column correlation of diagonal images from microphones 1 to 5 #15, #21, #27, #33, #39: row correlation of horizontal images from microphones 1 to 5 #16, #22, #28, #34, #40: column correlation of energy images from microphones 1 to 5
4. SOM and results The objective of this section is to describe classification of healthy and defective motors using neural networks and to figure out the identification of types of the faults. As it has been denoted in Section 1, SOM is a well-known and popular method to organize the input feature vectors. Since SOM algorithm can be considered as a vector quantization variant, in order to improve the quality of the quantization, the class boundaries should have to be well adjusted. Here the supervised Learning Vector Quantization (LVQ) algorithm is a suitable one to adjust boundaries. Although there are separate algorithms in the literature on LVQ, the LVQ3 algorithm has been used in this paper [24]. 4.1. SOM and LVQ as classifier SOM provides a very attractive and powerful method based on Hebbian type neural network for the classification problems. The main outcome of the SOM is the possibility of tracing the resemblance and the discrepancies of input data. SOM projects the input data vector Λ A ℝn which is taken from a sample space of size p to the m many codebook vectors of M A ℝn which are organized in planar fashion where p»m. The result after training SOM is a lattice of neurons representing the possible clusters. During the training phase, SOM is organized in an unsupervised manner according to the formula: M i ðkÞ ¼ M i ðk 1Þ þ ðαðkÞ U βði; c; kÞ U½ΛðkÞ M i ðk 1ÞÞ
8i
1 ri r m
ð8Þ
where αðkÞ is the learning rate and βði; c; kÞ is the neighborhood parameter which change during the adaptation phase. The c parameter denotes the index of the Best Matching Neuron, which depends on c ¼ arg min jjΛðkÞ M i ðkÞjj
ð9Þ
i
After the training process, the codebook vectors organized in planar lattice structure and for each input vector, the closest codebook vectors represent the possible cluster. Here in order to delineate the classification regions, and the region of clusters, a supervised method Learning Vector Quantization 3 (LVQ3) algorithm has been used [22]. This algorithm can be expressed as M i ðk þ1Þ ¼ M i ðkÞ ðξðkÞ U ½ΛðkÞ M i ðkÞÞ M j ðk þ1Þ ¼ M j ðkÞ þ ðξðkÞ U ½ΛðkÞ M j ðkÞÞ
ð10Þ
where Mi and Mj are the two closest codebook vectors for ΛðkÞ, and both ΛðkÞ and Mj belongs to the same class however Mi is not. Here also it is necessary that Mi, Mj ΛðkÞ and have to be in the window as
d1 d2 1 window ð11Þ min 4 s where ; 1 þ window d2 d1 where d1 and d2 are the distances between the closest codebook vector M i and the input data ΛðkÞ and second closest codebook vector Mj and ΛðkÞ respectively. In the algorithm if Mi and Mj are in the same class then the adaptation scheme will be as M i ðk þ1Þ ¼ M i ðkÞ þ ðη U ξðkÞ U½ΛðkÞ M i ðkÞÞ M j ðk þ 1Þ ¼ Mj ðkÞ þ ðη UξðkÞ U ½ΛðkÞ Mj ðkÞÞ
ð12Þ
where ξðkÞ and η are learning rate parameters. 4.2. Classification using SOM þLVQ3 and fault detection In this work three different experiments have been carried out and, for each experiment, data are collected from five different motors in six different load conditions. While doing those experiments, the same motors are decupled from the generator load, and their fixing locations and recoupled. Every experiment produces data with different acoustic nature and sound pressure levels because of the inconsistencies of the fixation using manual screwing and bolting. This has been done
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55
on purpose, because the main aim is trying to focus on to the identification the possible traces of faults independent from the trials. Otherwise, there is always a danger of tracking the discrepancies due to experimental variations. The environmental Sound Pressure Level of the experiments was about 53.2 dB, which shows a moderate noise platform. Here the materials around the rig are designed such that the reflections and refractions have no effect on the experimental results. Table 4 below shows the Sound Pressure Level (SPL) from three different experiments recorded under different load conditions for each motor type.
Fig. 8. Flow diagram of the sound-based fault diagnosis process.
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E. Germen et al. / Mechanical Systems and Signal Processing 46 (2014) 45–58
Table 4 SPL of three experiments of dataset. Load levels 3.6 A
4.1 A
4.7 A
4.9 A
5A
5.4 A
Environment SPL: 53.2 dB Motor 1 Exp1 73.8 Exp2 74.9 Exp3 73.8
76.5 76.1 73.8
78.5 74.6 73.8
78.5 75.1 73.8
78.5 76 73.8
79.4 75.4 72.6
dB dB dB
Motor 2 Exp1 Exp2 Exp3
86.2 83.7 83.2
84.5 83.7 83.2
84.2 83.2 83.4
84.3 84.2 83.7
84.2 83.2 83.2
84.2 82 82
dB dB dB
Motor 3 Exp1 Exp2 Exp3
84.6 83.2 83.2
83.7 83.2 83.7
83.3 83.2 83.4
83.2 83.2 83.4
83.2 83.2 83.8
83.2 83.2 83.2
dB dB dB
Motor 4 Exp1 Exp2 Exp3
75 76 75
76.1 74.5 74.5
77.1 75 74.1
77.1 75 74.1
78.1 75.4 74.2
77.1 74.5 73.8
dB dB dB
Motor 5 Exp1 Exp2 Exp3
75.4 74.1 74.8
74.7 73.8 74.4
74.5 74.1 74.8
74.6 74.4 74.4
74.1 73.8 73.8
74.1 74.2 74.7
dB dB dB
Fig. 9. 5 10 Dimension SOM map is trained with Exp1 and Exp3 data set.
In order to train a 5 10 dimension SOM, the feature vectors obtained from two different experiment sets Exp1 and Exp3 are used. Prior to training, the input vectors are normalized. After training phase, the resultant map in Fig. 9 has been obtained. Naturally, the SOM results depend on the nature of the feature vectors. In this work the vectors are composed of both cross correlation values of time domain data and the image-related correlations as explained in Section 3. The motor number labels, which can be seen on the map, are the corresponding localizations of the training motor data on the map. The vicinity in two-dimensional map shows the possible close relationship of the input feature vectors. In other words, if two feature vectors from two different experiments are mapped to neurons which are close to each other in the lattice, it is possible to deduce that there is somehow a resemblance between those motors. Conversely, the increase in the space between the neurons indicates the differences of the features obtained from the motors. By scrutinizing Fig. 10, Motors 2 and 3 data have been localized at the left of the healthy motor and the other faults are settled at the right of the healthy one. It is not surprising that Motors 2 and 3 faults have some close relationship with each other and the SOM map has a consistent result with this relationship. In order to test the results, the experiment set Exp2 data are directly applied to the trained map and the following results have been obtained. Test1–Test5 labels are the test data for Motor1–Motor5. Clearly, the test data localization is highly consistent with the trained data at a first glance. In the figure below, the number in parentheses designates the number of
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57
Fig. 10. Localization of test data from Experiment 2 on 5 10 dimension SOM map. Table 5 Classification results of test data without applying LVQ algorithm.
Motor Motor Motor Motor Motor
1 2 3 4 5
Motor 1
Motor 2
Motor 3
Motor 4
Motor 5
Correct classification %
6 0 0 1 0
0 6 0 0 0
0 0 6 0 0
0 0 0 5 0
0 0 0 0 6
100 100 100 83 100
Table 6 Classification results of test data after applying LVQ algorithm.
Motor Motor Motor Motor Motor
1 2 3 4 5
Motor 1
Motor 2
Motor 3
Motor 4
Motor 5
Correct classification %
6 0 0 0 0
0 6 0 0 0
0 0 6 0 0
0 0 0 6 0
0 0 0 0 6
100 100 100 100 100
hits for the relevant motor. For example “Test 3 (5)” means that this neuron has five hit values for the test data of Motor 3, similarly “Test 5(2)” designates the same neuron has been hit 2 times with the test data of Motor 5. As it can be seen in Table 5, the probability of correct classification for the healthy motor is 100%. This table demonstrates the results without applying LVQ algorithm. After applying LVQ3 algorithm, the results show that there is an improvement in the classification percentage as shown in Table 6. The results obtained from the training and test sets indicate 100% correct classifications. Both the cross correlation of time series data and 2D images obtained for each microphone with different load conditions provide these amazing results. The success of the classification is directly related with the proper combinations of the features obtained from different microphones. If the methods explained in Section 3 are applied separately, a substantial degradation in the percentage of success is observed. The image processing techniques contribute an important value for pattern recognition in motor faults. Here it is always worth to note that, the traces of each fault are always hidden in data and it is necessary to scrutinize and conceive a proper method in order to unveil them.
5. Conclusions The stator current and the vibrational analyses techniques are quite sensitive to electrical and mechanical faults, whereas the acoustical approaches are sensitive to the interference of the environmental noises. In this work, a test bed containing 5 different microphones settled on the motor in hemispherical shape is constructed. Consequently, a valuable data set for the possible faults is constructed. Each type of fault, which investigated in this paper, has its own acoustical shapes. The cross correlation coefficients of the microphones give acoustic clues about the type of the noise produced by faulty motors. In this work, it is observed that the steady-state signatures of the relations of data of different microphones reveal the traces of possible faults. By proper feature set, SOM and LVQ is an efficient method in order to discriminate motor faults. It must be noted that the methods proposed in this paper not only evaluate the possible differences between faulty and
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healthy motors, but also provide the definition of the fault type such as bearing faults, short circuit in stator, or broken rotor bars. In this work also it is concluded that, the same kind of faults such as bearing damages caused by misalignment or defective balls are identified in close regions in the map. This is quite an exciting result, since the similarities between the faults can be tracked and a pre-defined maintenance program can be developed for preventive maintenance strategies. References [1] S. Nandi, H.A. Toliyat, X. Li, Condition monitoring and fault diagnosis of electrical motors – a review, IEEE Trans. Energy Convers. 20 (2005) 719–729. [2] M.E.H. Benbouzid, A review of induction motors signature analysis as a medium for faults detection, IEEE Trans. Power Electron. 14 (2000) 984–993. [3] H. Ocak, K.A. Loparo, Estimation of the running speed and bearing defect frequencies of an induction motor from vibration data, Mech. Syst. Signal Process. 18 (2004) 515–533. [4] W. Lu, W. Jiang, H. Wu, J. Hou, A fault diagnosis scheme of rolling element bearing based on near-field acoustic holography and gray level co-occurrence matrix, J. Sound Vib. 331 (2012) 3663–3674. [5] W. Li, C.K. Mechefske, Detection of induction motor faults: a comparison of stator current, vibration and acoustic methods, J. Vib. Control 12 (2006) 165–188. [6] A. Kaya, E. Germen, U. Unlu, S. Toprak, Fault Classification in Hermetic Compressors Using Self-Organizing Map, International Compressor Engineering Conference at Purdue, July 14–17, 2008, Paper 1243. [7] E. Germen, A. Kaya, U. Unlu, Effects of sound radiation direction in faulty hermetic compressors. In: Proceedings of the International Compressor Engineering Conference at Purdue, July 12–15, 2010, Paper 2015. [8] U. Benko, J. Petrovic, D. Juricic, C.J. Tavcar, C.J. Rejec, A. Stefanovska, Fault diagnosis of a vacuum cleaner motor by means of sound analysis, J. Sound Vib. 276 (2004) 781–806. [9] V.T. Do, U.P. Chong, Signal model-based fault detection and diagnosis for induction motors using features of vibration signal in two-dimension domain, J. Mech. Eng. 57 (2011) 655–666. [10] L. Semler, L. Dettori, J. Furst, Wavelet-based texture classification of tissues in computed tomography. In: 18th IEEE Symposium on Computer-Based Medical Systems Proceedings, 2005, pp. 265–270. [11] L. Dettori, L. Semler, A comparison of wavelet, ridgelet, and curvelet-based texture classification algorithms in computed tomography, Comput. Biol. Med. 37 (2007) 486–498. [12] C. Hsieh, E. Lai, Y. Wang, An effective algorithm for fingerprint image enhancement based on wavelet transform, Pattern Recognit. 36 (2003) 303–312. [13] S. Fukuda, H. Hirosawa, A wavelet-based texture feature set applied to classification of multifrequency polarimetric SAR images, IEEE Trans. Geosci. Remote Sens. 37 (1999) 2282–2286. [14] D.G. Ece, O.N. Gerek, Power quality event detection using joint 2-D-wavelet subspaces, IEEE Trans. Instrum. Meas. 53 (2004) 1040–1046. [15] O.N. Gerek, D.G. Ece, 2-D analysis and compression of power-quality event data, IEEE Trans. Power Deliv. 19 (2004) 791–798. [16] A.M.D. Younus, B. Yang, Intelligent fault diagnosis of rotating machinery using infrared thermal image, Expert Syst. Appl. 39 (2012) 2082–2091. [17] T. Chang, C.-C.J. Kuo, Texture analysis and classification with tree-structured wavelet transform, IEEE Trans. Image Process. 2 (1993) 429–441. [18] A. Laine, J. Fan, Texture classification by wavelet packet signatures, IEEE Trans. Pattern Anal. Mach. Intell. 15 (1993) 1186–1191. [19] M. Unser, Texture classification and segmentation using wavelet frames, IEEE Trans. Image Process. 4 (1995) 1549–1560. [20] N. Sebe, M.S. Lew, Wavelet based texture classification. In: 15th International Conference on Pattern Recognition Proceedings, vol. 3, 2000, pp. 947–950. [21] S. Arivazhagan, L. Ganesan, Texture classification using wavelet transform, Pattern Recognit. Lett. 24 (2003) 1513–1521. [22] T. Kohonen, Self-Organizing Maps, Springer-Verlag, Berlin, 1995. [23] J.L. Rodgers, W.A. Nicewander, Thirteen ways to look at the correlation coefficient, Am. Stat. 42 (1988) 59–66. [24] T. Kohonen, The self organizing map, Proc. IEEE 78 (1990) 1464–1480.