Vibration-Based Fault Diagnosis of Commutator Motor

+is paper presents a study on vibration-based fault diagnosis techniques of a commutator motor (CM). Proposed techniques used vibration signals and signal processing methods. +e authors analysed recognition efficiency for 3 states of the CM: healthy CM, CM with broken tooth on sprocket, CM with broken rotor coil. Feature extraction methods called MSAF-RATIO-50-SFC (method of selection of amplitudes of frequencies ratio 50 second frequency coefficient), MSAF-RATIO-50-SFC-EXPANDED were implemented and used for an analysis. Feature vectors were obtained using MSAF-RATIO-50-SFC, MSAF-RATIO-50-SFCEXPANDED, and sum of RSoV. Classification methods such as nearest mean (NM) classifier, linear discriminant analysis (LDA), and backpropagation neural network (BNN) were used for the analysis. A total efficiency of recognition was in the range of 79.16%–93.75% (TV). +e proposed methods have practical application in industries.


Introduction
Commutator motors are essential for various industries.
ey are used for application of automobile motors such as electric generators, wiper motor, window lifting motor, vehicle starters, seat incliner, fuel pump, side view mirror, and air-conditioning.Commutator motors are also used for power tools applications, for example, drilling machine motor, circular saw motor, and hammer tool motor.ey are used for home appliances such as washing machine motor, motor of vacuum cleaner, motor of printer, and hair dryer motor.
Unexpected failures of motors generate unexpected stops.It causes losses of production time and money.To avoid failures, engineers developed online condition monitoring of motors.Condition monitoring helps engineers to take diagnostic decision on the basis of measured signals.Fault diagnosis techniques can detect faults and provide diagnostic information about the motor.It also allows us to use the motor for a longer time.Vibrations signals depend on states of the commutator motor.Each fault is associated with vibration signals. is correlation between states of the motor and characteristic frequencies is essential for fault diagnosis.e main task for fault diagnosis based on vibration analysis is to find the best method for proper condition monitoring.
Condition monitoring of electric motors was developed for measurement and analysis of diagnostic signals such as acoustic [1,2], thermal [3,4], electric current [5][6][7], and vibration [8][9][10][11][12][13].Each type of signal has advantages and disadvantages.Measurements of acoustic signal and thermal signal are noninvasive.Acoustic and thermal signals can be measured without touching the motor.e disadvantage of mentioned diagnostic signals is difficult processing.A methodology based on the analysis of acoustic signals for faults of the induction motor was presented [1].e presented technique used the complete ensemble empirical mode decomposition.Delgado-Arredondo et al. analysed the following faults: bearing defects, mechanical unbalance, and two broken rotor bars [1].e proposed approach could be used to identify mentioned faults in the industry.Another approach based on acoustic analysis was developed by Islam et al. [2].In [2], the authors proposed a diagnostic method of induction motors using Gabor filtering and MCSVMs.Average classification accuracy of the diagnostic method was equal to 99.80%.
e thermal imaging camera is highly priced.Moreover, it takes time to diagnose temperature of the motor.It is also limited for electrical faults.However, industrial use of technique-based thermal imaging gained a noticeable attention [3].Inter-turn faults and cooling system faults were analysed in [3].e analysis was conducted for induction motors.Singh and Naikan proposed an algorithm using infrared thermography for diagnosis of induction motors.
e authors developed two thermal profiles indicators.Developed profiles indicators were used for analysis of thermal distributions [3].
Several industrial examples for thermal analysis of electrical motors operating in a petrochemical plant were presented.e results showed that thermal imaging can be useful for transmission system faults, cooling system faults, defective connections, stator faults, and bearing failures [4].
Current monitoring is low-cost and reliable method of fault diagnosis.Motor current signature analysis (MCSA) is often used for current analysis.Usually MCSA provides good results [1,5,6].Singh and Naikan [5] proposed a method using MUSIC analysis (MSC-MUSIC).e proposed method was analysed for broken rotor bar and half broken rotor bar faults of the induction motor.Surprisingly, MCSA was found to be ineffective to recognize half broken rotor bar fault properly [5].In [6], the authors studied MCSA and ZSC (zero sequence current) methods for 4 induction motors.Antonino-Daviu et al. analysed the following states: healthy, broken bar, two nonadjacent broken bars, and two adjacent broken bars.e authors proved the usefulness of the ZSC method for detection of broken rotor bars.However, they noticed that MCSA had some problems to detect analysed faults [6].Bazan et al. [7] described a current analysis for fault diagnosis of three-phase induction using ANN.Classification accuracy 99% was obtained for analysed cases [7].
Vibration analysis is an effective and immediate fault diagnosis technique.Vibration signals are also acquired with low noise level (from environment or other machines).Vibration analysis is used for detection of mechanical and electrical faults such as rotor, stator faults, bearings, misalignment, and faults of gear transmission systems [1,3,8].A review about fault diagnosis methods for gear transmission systems using vibration analysis was presented [8].It described following methodologies: methods based on ICA, order tracking, sparse decomposition, EMD, and wavelet [8].
e CMFE (composite multiscale fuzzy entropy) and ESVM (ensemble support vector machines) were used for detection of rolling bearing faults [9].Zheng et al. analysed the influence of parameters of the CMFE.
e CMFE was employed to extract features of the vibration signals.Next, ESVM was used as a classifier.e proposed approach was applied to experimental data analysis.It indicated that the approach was effective for detection of different faults of rolling bearings [9].Duan et al. [10] described the development of condition monitoring of rolling bearings using vibration analysis, acoustic analysis, oil analysis, temperature analysis, and ultrasonic analysis.e authors indicated that multisensors information fusion is the trend of development [10].Zurita-Millan et al. [11] proposed a vibration signal prognosis methodology of the electromechanical system (kinematic chain).e proposed methodology was based on neurofuzzy modeling using the patterns of the vibrations signal.
ey proved that the RMS method is a proper feature for vibration analysis.ey obtained the results with an error lower than 2%, but they did not analyse other sources of information, such as temperature and stator current [11].Lu et al. described vibration-based condition monitoring of motor bearings [12].A wireless sensor networks were used for motor bearings.e wireless sensor network prototype was developed.ey proved that the sampled data length of the proposed approach result in a decrease of over 80%.e proposed approach can be useful for machinery installed in remote areas, for example, wind farms [12].In [13], the authors conducted vibration analysis for the detection of motor damages.ey analysed bearing currents.Analyses of bearing faults are useful for industrial users of inverted-fed motors.ey proved that time-frequency analysis of vibration signal is useful source of information.
In proposed research, the authors developed vibrationbased fault diagnosis of the commutator motor (CM).Vibration signals of the CM (healthy CM, CM with broken tooth on sprocket, and CM with broken rotor coil) were not analysed in the literature, so the authors decided to conduct such analyses.e authors analysed recognition efficiency of the vibration signal for 3 states of the CM: healthy CM (Figure 1), CM with broken tooth on sprocket (Figure 2), and CM with broken rotor coil (Figure 3).e feature extraction methods called MSAF-RATIO-50-SFC (Method of Selection of Amplitudes of Frequencies Ratio 50 Second Frequency Coefficient), MSAF-RATIO-50-SFC-EXPANDED were implemented and used for the analysis.Feature vectors were obtained using MSAF-RATIO-50-SFC, MSAF-RATIO-50-SFC-EXPANDED, and sum of RSoV.Classification methods such as nearest mean (NM) classifier, Linear discirminant analysis (LDA), and backpropagation neural network (BNN) were used for the analysis.
e proposed techniques have practical application in industries.e analysed total efficiency of recognition was in the range of 79.16%-93.75% (T V -see Section 3).Low cost of the measuring device and low cost of the computer are the advantages of vibration-based fault diagnosis.It is also noninvasive technique of fault diagnosis.e acquired results are similar to other proposed techniques of fault diagnosis [1,11].In the paper, original methods of feature extraction-MSAF-RATIO-50-SFC and MSAF-RATIO-50-SFC-EXPANDED were used for vibration signals.It was proved that the proposed technique can be used for diagnosis of the CM.It was also proved that states of the motor such as healthy CM, CM with broken tooth on sprocket, and CM with broken rotor coil can be diagnosed using proposed techniques.

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Proposed Vibration Fault Diagnosis Techniques
e authors proposed 9 vibration diagnosis techniques (Figure 4).Techniques were based on signal processing methods and the step of acquisition of the vibration signal.
e step of acquisition used a measuring device.e USB data logger Voltcraft DL-131G (sampling frequency 20 Hz, 3-axis recording) was used for the step of acquisition.Next computer software (Voltsoft Client) was used to download recorded data from the USB data logger.ere are many types of acceleration USB data loggers and software.ere were many possibilities of the step of acquisition of vibration signal.e first step of signal processing was split of measured vibration data.Vibration data were split into 5-second samples.Each 5-second sample had 100 values.e next step was feature extraction.Feature extraction was carried out using three different methods: MSAF-RATIO-50-SFC, MSAF-RATIO-50-SFC-EXPANDED, and sum of RSoV.Classification of computed vectors was the last step of vibration signal processing.Classification was carried out using pattern creation and testing.It was carried out using three different methods: NM classifier, LDA, and BNN.

Method of Selection of Amplitudes of Frequencies Ratio 50 Second Frequency Coefficient.
e MSAF-RATIO-50-SFC was based on FFT (fast Fourier transform) coefficients.e method computes features from the frequency spectrum.It can be noticed that the vibration signal was dependent on type of fault, type of machine, rotation speed, and size of machine.
Steps of the MSAF-RATIO-50-SFC were as follows: (1) Computation of FFT spectra of analysed vibration signals.
(2) Computation of differences (difference of frequency coefficient (DFC)) between computed FFT spectra of analysed states.(3) Computation of a ratio RS for analysed differences.
e ratio RS was defined as where SDFC max is the second maximal amplitude of analysed difference of the FFT spectrum and DFC n is the amplitude of analysed difference with index n.If RS � 50% for MSAF-RATIO-50-SFC, then amplitude greater than 50% of second maximal amplitude is analysed.(4) Selection of frequency coefficients for ratio RS � 50%.
(5) Selection of common frequency coefficients for all computed differences.(6) Form a feature vector.
A flow diagram of the MSAF-RATIO-50-SFC is shown (Figure 5).e authors analysed vibration signals for 3 states of the CM: healthy CM, denoted as hcm; CM with broken tooth on sprocket, denoted as btos; CM with broken rotor coil, denoted as brc.Differences (DFC) between computed FFT spectra of analysed states are depicted in Figures 6-8.
e MSAF-RATIO-50-SFC computed following (five) common frequencies: 0.2, 5.6, 7.2, 7.8, 8 Hz. e computed frequency components were used for the feature vector.Next computed feature vectors were used for the classification step.

Method of Selection of Amplitudes of Frequencies Ratio 50 Second Frequency Coefficient EXPANDED.
e MSAF-RATIO-50-SFC-EXPANDED is similar to the MSAF-RATIO-50-SFC.It used several training sets to compute common frequency components.Steps of the MSAF-RATIO-50-SFC-EXPANDED were following: (1) Computation of FFT spectra of analysed vibration signals.
(2) Computation of differences (difference of frequency Coefficient (DFC)) between computed FFTspectra of analysed states.(3) Computation of the ratio RS for analysed differences.
e ratio RS was defined as follows: where SDFC max is the second maximal amplitude of analysed difference of the FFT spectrum and DFC n is the amplitude of analysed difference with index n.If RS � 50% for MSAF-RATIO-50-SFC, then amplitude greater than 50% of second maximal amplitude is analysed.(4) Selection of frequency coefficients for ratio RS � 50%.
(5) Selection of parameter R-EXPANDED � (number of required common frequencies)/(number of all selected frequencies).e parameter R-EXPANDED was used to find the final number of common frequencies.Let us consider following example R-EXPANDED � 0.999, in that case 3 of 3 frequencies are required ((3/3 > 0.999)).If R-EXPANDED � 0.6, the method required 2 of 3 frequencies ((2/3) > 0.6) to select specific frequency component.( 6) Selection of common frequency coefficients for all computed differences using parameter R-EXPANDED.Shock and Vibration 3 (7) Form a feature vector.

Feature Extraction Based on Sum of RSoV.
Feature extraction based on sum of RSoV 1-element feature vectors.First, acceleration USB data logger measured: X, Y, and Z values and a resultant sum of vectors (RSoV).e resultant sum of vectors was expressed using the following formula: where |X|, |Y|, and |Z| are the lengths of X, Y, and Z vectors.Measured five-second samples of vibration data had 100 values of RSoV.e measured values of RSoV were used to compute sum of RSoV.It was defined using the following formula: where RSoV i is the resultant sum of vector with index i.e authors presented 36 (1-element) feature vectors of vibration data consisting of sum of RSoV.It was presented in Table 1.
e computed values of feature vectors (sum of RSoV) are in the range 288.53-315 (m/s 2 ) for healthy CM, 298.08-349.67 (m/s 2 ) for CM with broken rotor coil, and 891.13-947.04(m/s 2 ) for CM with broken tooth on sprocket.A problem of computed feature vectors was noticed.Feature vectors of healthy CM were similar to feature vectors of CM with broken rotor coil.e difficulty of classification is observed if the training sets of features are close to each other.

Linear Discriminant Analysis (LDA).
e authors used the LDA as a second method of data classification.Ronald 4

Shock and Vibration
Aylmer Fisher developed the LDA in 1936.Implementation of the LDA classi er was little time-consuming.e LDA also classi ed data for multiclass problems.It was used for many classi cation problems such as fault diagnosis [16][17][18], face recognition [25], and identi cation of cancer samples [26].e LDA used the concept of searching for a linear combination of variables.It computed the score function.
Next, it estimated the linear coe cients that maximize the score.Next, unknown test feature vector was classi ed.
Vector was projected onto the maximally separating direction (smaller subspace).
e steps of the LDA are presented in Figure 10.e LDA classi er was described more precisely in following articles [16-18, 25, 26].Shock and Vibration 5

Nearest Mean (NM).
e nearest mean classi er used training average feature vector and test feature vector for data classi cation.Training average feature vector a was denoted as follows: where a is training average feature vector, f is training feature vector, n is the number of training feature vectors, and f k is the value of training average feature vector with k index (k 5 for MSAF-RATIO-50-SFC, k 3 for MSAF-RATIO-50-SFC-EXPANDED, and k 1 for sum of RSoV).e NM classi er computed distance between the training average feature vector and test vector.It used distance function such as Manhattan distance or Euclidean distance.e authors used Manhattan distance: where d(t − a) distance, unknown test vector t [t 1 , . . ., t i ], and training average feature vector a [a 1 , . . ., a i ].
e classi er made decision about the class using the computed nearest distance.e NM classi er was described more precisely in following articles [27,28].

Backpropagation Neural Network.
e neural network based on the backpropagation method was the common supervised classi cation method.It used training and test sets of feature vectors.In the literatures [29][30][31][32], neural networks were used for fault diagnosis [29,30], controlling a temperature eld [31], prediction of speech quality [32], and classi cation of emotion recognition [33].e authors used three-layer backpropagation neural network for data classi cation (input layer, hidden layer, and output layer).It was typical structure of the backpropagation neural network.
e authors used following backpropagation neural network (Figure 11).e input layer had 1, 3, or 5 neurons depending on feature extraction method.e hidden layer had 20 neurons.
e output layer of BNN had 3 neurons.e values of output neurons were 001, healthy CM, 010, CM with broken tooth on sprocket, and 100, CM with broken rotor coil.

Results and Discussion
Vibration signals of the CM were measured in a at.e authors conducted analysis for 3 states of the CM: healthy CM (Figure 1), CM with broken tooth on sprocket (Figure 2), and CM with broken rotor coil (Figure 3).Parameters of the CM were Q 1.84 kg, P 500 W, S 3000 rpm, V 230 V, and f 50 Hz, where Q is the weight of the CM motor, P is the power of the CM motor, S is the rotor speed of the CM motor, V is the supply voltage of the CM motor, and f is the frequency of the CM motor.
Vibration signals were measured from 1 CM (healthy CM, CM with broken rotor coil, or CM with broken tooth on sprocket).e authors used 9 training samples and 48 test samples of vibration signals (each sample has 5 seconds of vibration signal-100 measured values) for the analysis.Proposed fault diagnosis techniques (Figure 4) were used for signal processing of vibration signals.e evaluation of analysis of vibration signals was carried out using recognition e ciency of vibration signal E V .e value of E V was expressed as follows: where N recognized is the number of test samples recognized for speci c class, N all is the number of all test samples for speci c class, and E V is the recognition e ciency of vibration signal for speci c class.e total e ciency of vibration signal recognition was denoted as T V follows: where E V1 is the E V of the healthy CM, E V2 is the E V of the CM with broken rotor coil, E V3 is the E V of the CM with broken tooth on sprocket, and T V is the total E V of analysed states of the CM. e results are shown in Tables 2-10.In Table 2, the authors presented the results of recognition of vibration signals.e sum of RSoV (1 analysed feature) and the NM classi er were used.
In Table 3, the authors presented the results of recognition of vibration signals.

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In Table 4, the authors presented the results of recognition of vibration signals.
In Table 5, the authors presented the results of recognition of vibration signals.e sum of RSoV (1 analysed feature) and the LDA classi er were used.
In Table 6, the authors presented the results of recognition of vibration signals.
In Table 7, the authors presented the results of recognition of vibration signals.
In Table 8, the authors presented the results of recognition of vibration signals.e sum of RSoV (1 analysed feature) and the backpropagation neural network were used.

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In Table 9, the authors presented the results of recognition of vibration signals.
In Table 10, the authors presented the results of recognition of vibration signals.e MSAF-RATIO-50-SFC-EXPANDED (3 analysed features) and the backpropagation neural network were used.
e obtained results of analysed classifiers were in the range of 75%-100% (T V was in the range of 79.16%-93.75%).Surprisingly, the sum of RSoV was the best feature for recognition of analysed states of the CM motor.It had T V � 93.75% for the NM classifier.e MSAF-RATIO-50-SFC and the MSAF-RATIO-50-SFC-EXPANDED had a bit lower total efficiency (T V ).
e authors compared the obtained results with other literature references.e acquired results were similar to other proposed techniques of vibration analysis [11,20,[34][35][36][37].In [11], results with an error lower than 2% were obtained.However, they [11] analysed bearing failure, 1/2-broken rotor bar, and 1 broken rotor bar of the induction motor.
e article [34] presented a vibrationbased method for detection of bearing faults of the induction motor.Vibration signals were analysed using the FFT.
e classification method was based on the SVM.Detection probability was in the range of 0.96-1 [34].Another technique based on vibration signals was also used for diagnosis of the induction motor [35].
e proposed technique used the Shannon entropy.
e K-means clustering method was used for classification.Recognition rate was 100% for healthy motor, half broken rotor bar, one broken rotor bar, and two broken rotor bars [35].Learning features of vibration signals of the induction motor were analysed in the literature [36].Deep Belief Network was used for the classification.Classification rate was in the range of 85.6-95.8%[36].Gangsar and Tiwari [37] presented vibration-based analysis for fault prediction of the induction motor.e MSVM (multiclass support vector machine) was used.It had average recognition rate in the range of 75-90%.In [20], the authors also analysed vibration signals of the induction motor.e analysis was conducted using DWT and 3 classifiers: SVM, k-NN, and MLP. e best results were obtained for the SVM (classification rate in the range of 98.8%-100%).

Conclusions
In this study, fault diagnostic techniques of the CM were developed.
e developed techniques analysed vibration signals.e total efficiency of vibration signal recognition was analysed for 3 states of the CM: healthy CM, CM with broken tooth on sprocket, CM with broken rotor coil.Feature extraction methods MSAF-RATIO-50-SFC and MSAF-RATIO-50-SFC-EXPANDED were implemented and used for fault diagnosis.Feature vectors were obtained using MSAF-RATIO-50-SFC, MSAF-RATIO-50-SFC-EXPANDED, and sum of RSoV.Classification methods such as NM, LDA, and BNN were used for the analysis.e analysed total efficiency was in the range of 79.16%-93.75% (T V ). e best feature for recognition was the sum of RSoV of analysed states of the CM motor.It had T V � 93.75% for the NM classifier.
Low cost of the measuring device (about 120$) and low cost of the computer (about 270$) are advantages of vibrationbased fault diagnosis.It is also noninvasive technique of fault diagnosis.Other faults such as bearing faults, rotor, and stator faults can be also diagnosed by analysis of vibration signals.
Future research will focus on development of new fault diagnosis techniques based on acoustic, vibration, and thermal signals.
e authors will also analyse motors for different rotor speeds.New types of motors and faults will be analysed.e proposed techniques will be used for industries.

Table 2 :
e results of recognition of vibration signals-the sum of RSoV and the NM classi er were used.

Table 3 :
e results of recognition of vibration signals-the MSAF-RATIO-50-SFC and the NM classi er were used.

Table 4 :
e results of recognition of vibration signals-the MSAF-RATIO-50-SFC-EXPANDED and the NM classi er were used.

Table 5 :
e results of recognition of vibration signals-the sum of RSoV and the LDA classi er were used.

Table 6 :
e results of recognition of vibration signals-the MSAF-RATIO-50-SFC and the LDA classifier were used.

Table 7 :
e results of recognition of vibration signals-the MSAF-RATIO-50-SFC-EXPANDED and the LDA classifier were used.

Table 8 :
e results of recognition of vibration signals-the sum of RSoV and the backpropagation neural network were used.

Table 9 :
e results of recognition of vibration signals-the MSAF-RATIO-50-SFC and the backpropagation neural network were used.

Table 10 :
e results of recognition of vibration signals-the MSAF-RATIO-50-SFC-EXPANDED and the backpropagation neural network were used.