Acoustic-Based Fault Diagnosis of Commutator Motor

Abstract

In the paper, the author presents acoustic-based fault diagnosis of a commutator motor (CM). Five states of the commutator motor were considered: healthy commutator motor, commutator motor with broken rotor coil, commutator motor with shorted stator coils, commutator motor with broken tooth on sprocket, commutator motor with damaged gear train. A method of feature extraction MSAF-15-MULTIEXPANDED-8-GROUPS (Method of Selection of Amplitudes of Frequency Multiexpanded 8 Groups) was described and implemented. Classification methods, such as nearest neighbour (NN), nearest mean (NM), self-organizing map (SOM), backpropagation neural network (BNN) were used for acoustic analysis of the commutator motor. The paper provides results of acoustic analysis of the commutator motor. The results had a good recognition rate. The results of acoustic analysis were in the range of 88.4–94.6%. The NM classifier and the MSAF-15-MULTIEXPANDED-8-GROUPS provided TE_RCM = 94.6%.

1. Introduction

Fault diagnosis of electrical rotating motors has been extensively investigated since the 20th century, and can increase the reliability and safety of electrical rotating motors. Condition monitoring of electrical motors are very important for industry, reducing loss due to unforeseen faults and damage. Unforeseen faults and damage of electrical rotating motors lead to the loss of production and income. Unfortunately, stator and rotor are the most important components in electrical rotating motors. Stator and rotor faults appear very often. Stators and rotors of electrical rotating motors must be monitored. Condition monitoring guarantees safe operation of machines and prevents unforeseen breakdowns. Acoustic signals contain a lot of diagnostic information, and can be used for detection of faults. Therefore, acoustic signals and signal processing methods should be deeply studied for proper recognition. Scientists developed many diagnostic methods of fault diagnosis. They are used for various types of machines and faults. Faults of electrical rotating motors (stator faults, rotor faults, broken rotor bar, ring cracking, bearing failures, rotor shaft failure, air-gap irregularities, broken teeth on sprocket) can be diagnosed by vibration [1,2,3,4,5,6,7,8,9,10,11,12] and acoustic signals [13,14,15,16,17,18,19,20,21,22]. Electric current analysis [23,24,25,26,27,28,29,30,31] and thermal analysis [32,33,34] are mostly used for limited faults, such as stator faults, rotor faults, and bearing failures. Acoustic signals are difficult to process, because they are very noisy (for example, several operating motors generate many acoustic signals). The advantage of acoustic-based fault diagnosis is non-invasive measurement (for example, we can measure an acoustic signal two meters from the machine). Vibration-based fault diagnosis is similar, but we have to put our measuring device close to the machine. Vibration signals are less noisy than acoustic signals.

The paper presents acoustic-based fault diagnosis of the commutator motor (CM). Five states of the commutator motor (CM) were considered: CM with shorted stator coils (Figure 1a and Figure 2a), CM with broken rotor coil (Figure 1b and Figure 2b), healthy CM (Figure 1c), CM with broken tooth on sprocket (Figure 3), CM with damaged gear train (Figure 4).

The described approach consists of methods of signal processing, such as amplitude normalization, FFT, the MSAF-15-MULTIEXPANDED-8-GROUPS, nearest neighbour (NN), or nearest mean (NM) or SOM (self-organizing map) or BNN (backpropagation neural network). The paper provided the results of acoustic analysis of the CM.

2. Acoustic-Based Fault Diagnosis Technique of the Commutator Motor

Acoustic-based fault diagnosis technique was based on pattern recognition. It used a pre-processing step, feature extraction step, and classification step. A block diagram of acoustic-based fault diagnosis technique was shown in Figure 5.

Acoustic signals were measured using ZALMAN ZM-MIC1 microphone. The following steps of signal processing were used: recording of acoustic signal of the CM, split of soundtrack into smaller data files, amplitude normalization, FFT, the MSAF-15-MULTIEXPANDED-8-GROUPS, NN classifier or NM classifier or SOM or BNN. Recording of the acoustic signal of the CM was carried out using digital voice recorder (format: WAVE, number of channel-1, sampling frequency-44,100 Hz). There was also possibility to record acoustic signals using a capacity microphone with a computer (Figure 6 and Figure 7). Next, splitting the soundtrack into smaller data files was carried out. The obtained data files (1 second samples) were processed by amplitude normalization, windowing (window size of 32,768), FFT, and the MSAF-15-MULTIEXPANDED-8-GROUPS. The MSAF-15-MULTIEXPANDED-8-GROUPS selected 1–15 frequency components, forming feature vectors consisting of 1–15 frequency components. Computed feature vectors were used for pattern creation and testing. Methods such as NN, NM, SOM, and BNN were used for data classification.

2.1. Method of Selection of Amplitudes of Frequency Multiexpanded 8 Groups

The Method of Selection of Amplitudes of Frequency Multiexpanded 8 Groups (MSAF-15-MULTIEXPANDED-8-GROUPS) depended on differences of spectra of acoustic signals. Differences of spectra of acoustic signals depended on generated acoustic signals of the CM. Generated acoustic signals depended on type of the motor, motor size, rotor speed, and analysed faults of the motor. The author analysed 5 states of the CM (healthy CM, CM with broken rotor coil, CM with shorted stator coils, CM with broken tooth on sprocket, and CM with damaged gear train). Steps of the MSAF-15-MULTIEXPANDED-8-GROUPS were listed below:

• Compute frequency spectra of acoustic signals of commutator motors (the author used 6 one-second samples for state A, 6 one-second samples for state B, 6 one-second samples for state C, 6 one-second samples for state D). Computed frequency spectrum of state A (healthy CM) was described as vector of 16,384 elements hcm = [hcm₁, hcm₂, ..., hcm₁₆₃₈₄]. Computed frequency spectrum of state B (CM with broken rotor coil) was denoted as vector of 16,384 elements cmbrc = [cmbrc₁, cmbrc₂, ..., cmbrc₁₆₃₈₄]. Computed frequency spectrum of state C (CM with shorted stator coils) was expressed as vector of 16,384 elements cmssc = [cmssc₁, cmssc₂, ..., cmssc₁₆₃₈₄]. Computed frequency spectrum of state D (CM with broken tooth on sprocket) was expressed as vector of 16384 elements cmbts = [cmbts₁, cmbts₂, ..., cmbts₁₆₃₈₄]. Computed frequency spectrum of state E (CM with damaged gear train) was expressed as vector of 16,384 elements cmdgt = [cmdgt₁, cmdgt₂, ..., cmdgt₁₆₃₈₄].
• Compute differences of computed frequency spectra of states A, B, C, D, E: hcm − cmbrc, hcm − cmssc, cmbrc − cmssc, cmbts − hcm, cmbts − cmbrc, cmbts − cmssc, cmdgt − hcm, cmdgt − cmbrc, cmdgt − cmssc, cmdgt − cmbts.
• Compute absolute values: |hcm − cmbrc|, |hcm − cmssc|, |cmbrc − cmssc|, |cmbts − hcm|, |cmbts − cmbrc|, |cmbts − cmssc|, |cmdgt − hcm|, |cmdgt − cmbrc|, |cmdgt − cmssc|, |cmdgt − cmbts|.
• Select 15 maximum differences of computed frequency spectra of states A, B, C, D, E: max₁(|hcm − cmbrc|), max₂(|hcm − cmbrc|), …, max₁₅(|hcm − cmbrc|), max₁(|hcm − cmssc|), max₂(|hcm − cmssc|), …, max₁₅(|hcm − cmssc|), max₁(|cmbrc − cmssc|), max₂(|cmbrc − cmssc|), …, max₁₅(|cmbrc − cmssc|), max₁(|cmbts − hcm|), max₂(|cmbts − hcm|), …, max₁₅(|cmbts − hcm|), max₁(|cmbts − cmbrc|), max₂(|cmbts − cmbrc|), …, max₁₅(|cmbts − cmbrc|), max₁(|cmbts − cmssc|), max₂(|cmbts − cmssc|), …, max₁₅(|cmbts − cmssc|), max₁(|cmdgt − hcm|), max₂(|cmdgt − hcm|), …, max₁₅(|cmdgt − hcm|), max₁(|cmdgt − cmbrc|), max₂(|cmdgt − cmbrc|), …, max₁₅(|cmdgt − cmbrc|), max₁(|cmdgt − cmssc|), max₂(|cmdgt − cmssc|), …, max₁₅(|cmdgt − cmssc|), max₁(|cmdgt − cmbts|), max₂(|cmdgt − cmbts|), …, max₁₅(|cmdgt − cmbts|). The result of feature extraction method MSAF-15 is the vector consisted of 1–15 frequency components. Let us see following example using the MSAF-15. There are 5 states of the CM: A, B, C, D, E. Five frequency spectra of acoustic signals of the CM ((FS-A), (FS-B), (FS-C), (FS-D), (FS-E)-frequency spectra of states A, B, C, D, E) were computed. The MSAF-15 computed frequency components 100, 160, 200, 260, 300 Hz for difference |(FS-A) − (FS-B)|. The MSAF-15 computed frequency components 120, 160, 210, 260, 310 Hz for difference |(FS-A) − (FS-C)|. The MSAF-15 computed frequency components 120, 170, 220, 230, 310 Hz for difference |(FS-B) − (FS-C)|. The MSAF-15 computed frequency components 400, 410, 420, 430, 440 Hz for difference |(FS-D) − (FS-A)|. The MSAF-15 computed frequency components 405, 415, 425, 435, 445 Hz for difference |(FS-D) − (FS-B)|. The MSAF-15 computed frequency components 410, 415, 420, 425, 430 Hz for difference |(FS-D) − (FS-C)|. The MSAF-15 computed frequency components 500, 505, 510 Hz for difference |(FS-E) − (FS-A)|. The MSAF-15 computed frequency components 515, 520, 525 Hz for difference |(FS-E) − (FS-B)|. The MSAF-15 computed frequency components 530, 540, 550 Hz for difference |(FS-E) − (FS-C)|. The MSAF-15 computed frequency components 560, 570, 580 Hz for difference |(FS-E) − (FS-D)|. None of common frequency components were selected for the presented example. The MSAF-15-MULTIEXPANDED-GROUPS extends the MSAF-15 method. A parameter called TCoF-TS (Threshold of common frequency components-training sets) was used. This parameter was defined as: TCoF-TS = (number of required common frequency components of analysed training sets)/(number of analysed differences).
• Set the parameter TCoF-TS. This parameter affects the number of common frequency components. Let us consider following example using the MSAF-15-MULTIEXPANDED. Four training sets of acoustic training samples are given: (A1, B1, C1, D1, E1), (A2, B2, C2, D2, E2), (A3, B3, C3, D3, E3), (A4, B4, C4, D4, E4), where A1, A2, A3, A4—denoted 4 acoustic training samples of state A; B1, B2, B3, B4—denoted 4 acoustic training samples of state B; C1, C2, C3, C4—denoted 4 acoustic training samples of state C; D1, D2, D3, D4—denoted 4 acoustic training samples of state D; E1, E2, E3, E4—denoted 4 acoustic training samples of state E. The MSAF-15-MULTIEXPANDED computed frequency components (FS-A1, FS-B1, FS-C1, FS-D1, FS-E1), (FS-A2, FS-B2, FS-C2, FS-D2, FS-E2), (FS-A3, FS-B3, FS-C3, FS-D3, FS-E3), (FS-A4, FS-B4, FS-C4, FS-D4, FS-E4), where FS-A1, FS-A2, FS-A3, FS-A4—denoted 4 frequency spectra of state A, FS-B1, FS-B2, FS-B3, FS-B4—denoted 4 frequency spectra of state B, FS-C1, FS-C2, FS-C3, FS-C4—denoted 4 frequency spectra of state C, FS-D1, FS-D2, FS-D3, FS-D4—denoted 4 frequency spectra of state D, FS-E1, FS-E2, FS-E3, FS-E4—denoted 4 frequency spectra of state E. Next, 40 differences between frequency spectra are computed: |(FS-A1) − (FS-B1)|, |(FS-A1) − (FS-C1)|, |(FS-B1) − (FS-C1)|, |(FS-D1) − (FS-A1)|, |(FS-D1) − (FS-B1)|, |(FS-D1) − (FS-C1)|, |(FS-E1) − (FS-A1)|, |(FS-E1) − (FS-B1)|, |(FS-E1) − (FS-C1)|, |(FS-E1) − (FS-D1)|, ... , |(FS-A4) − (FS-B4)|, |(FS-A4) − (FS-C4)|, |(FS-B4) − (FS-C4)|, |(FS-D4) − (FS-A4)|, |(FS-D4) − (FS-B4)|, |(FS-D4) − (FS-C4)|, |(FS-E4) − (FS-A4)|, |(FS-E4) − (FS-B4)|, |(FS-E4) − (FS-C4)|, |(FS-E4) − (FS-D4)|. Let us consider following example. If we set TCoF-TS = 4/40 = 0.1, then the MSAF-15-MULTIEXPANDED selects frequency components found 4 times for 40 differences. If we set TCoF-TS = 6/40 = 0.15, then the MSAF-15-MULTIEXPANDED selects frequency components found 6 times for 40 differences. The MSAF-15-MULTIEXPANDED found frequency component 160 Hz-6 times, frequency component 210 Hz-4 times. The MSAF-15-MULTIEXPANDED selects 160, 210 Hz (if TCoF-TS = 4/40 = 0.1). The MSAF-15-MULTIEXPANDED selects 160 Hz (if TCoF-TS = 6/40 = 0.15). The MSAF-15-MULTIEXPANDED selects none of frequency components (if TCoF-TS = 8/40 = 0.2). The parameter TCoF-TS depends on analysed signal.
• Select groups of common frequency components. The MSAF-15-MULTIEXPANDED-8-GROUPS used 8 groups. Each group of common frequency components consists of the best frequency components for recognition. Let us analyse following example. There are 4 states of the CM: A, B, C, D (for 5 states it will be similarly). The MSAF-15-MULTIEXPANDED-8-GROUPS found: frequency component 210 Hz (4 times), frequency component 160 Hz (6 times), frequency component 400 Hz (7 times). The frequency component 210 Hz is good for recognition of |(FS-A) − (FS-B)|, |(FS-A) − (FS-C)|, |(FS-B) − (FS-C)|. The frequency component 160 Hz is good for recognition of |(FS-D) − (FS-A)|, |(FS-D) − (FS-B)|, |(FS-D) − (FS-C)|. The frequency component 400 Hz is good for recognition of |(FS-A) − (FS-B)|. Essential frequency components are 210 Hz and 160 Hz. The frequency component 400 Hz is not good for analysis. The essential frequency components 160 Hz and 210 Hz form 1 group of essential frequency components.
• Use 1–8 computed groups.
• Form a feature vector.

The author presented the MSAF-15-MULTIEXPANDED-8-GROUPS in Figure 8.

The author used 30 one-second training samples for proper pattern creation process. The author used 6 training sets (30 one-second samples). Computed absolute values of differences: |hcm − cmbrc|, |hcm − cmssc|, |cmbrc − cmssc|, |cmbts − hcm|, |cmbts − cmbrc|, |cmbts − cmssc|, |cmdgt − hcm|, |cmdgt − cmbrc|, |cmdgt − cmssc|, |cmdgt − cmbts| were depicted in Figure 9, Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17 and Figure 18 (rotor speed-3000 rpm, training set 6).

The MSAF-15-MULTIEXPANDED-8-GROUPS found 28 essential frequency components: 48, 50, 79, 81, 97, 101, 128, 157, 159, 1469, 1471, 1672, 1926, 1927, 1934, 1935, 1939, 1942, 1953, 1957, 1958, 1961, 1978, 2038, 2039, 2042, 2059, 2547 Hz for TCoF-TS = 0.125 (3/18 = 0.125). Computed essential frequency components were presented in

Table 1. Computed essential frequency components for vector hcm (healthy CM).

Value of Feature
0.006776	0.011506	0.003938	0.006896
0.003093	0.007896	0.005020	0.006722
0.009599	0.006721	0.034127	0.041374
0.006398	0.001086	0.006096	0.002857
0.004421	0.002796	0.005071	0.005120
0.006776	0.011506	0.003938	0.006896
0.003093	0.007896	0.005020	0.006722

,

Table 2. Computed essential frequency components for vector cmbrc (CM with broken rotor coil).

Value of Feature
0.005696	0.009528	0.026896	0.004757
0.005556	0.010468	0.026023	0.012042
0.003759	0.009350	0.006706	0.007029
0.005175	0.006020	0.013454	0.003632
0.008541	0.000666	0.005728	0.005724
0.005696	0.009528	0.026896	0.004757
0.005556	0.010468	0.026023	0.012042

,

Table 3. Computed essential frequency components for vector cmssc (CM with shorted stator coils).

Value of Feature
0.002803	0.002988	0.008468	0.004678
0.004008	0.002770	0.001949	0.006048
0.021171	0.004456	0.005253	0.002312
0.005484	0.005549	0.003781	0.004390
0.005037	0.000740	0.008683	0.004213
0.002803	0.002988	0.008468	0.004678
0.004008	0.002770	0.001949	0.006048

,

Table 4. Computed essential frequency components for vector cmbts (CM with broken tooth on sprocket).

Value of Feature
0.007080	0.007388	0.006834	0.001410
0.006244	0.007172	0.003946	0.005266
0.002335	0.002029	0.004501	0.007593
0.020768	0.016296	0.016799	0.018125
0.003584	0.011559	0.007451	0.003169
0.007080	0.007388	0.006834	0.001410
0.006244	0.007172	0.003946	0.005266

and

Table 5. Computed essential frequency components for vector cmdgt (CM with damaged gear train).

Value of Feature
0.002066	0.002245	0.001124	0.000820
0.000845	0.000655	0.002080	0.001540
0.002178	0.001563	0.000810	0.001933
0.002259	0.001234	0.002635	0.003116
0.002729	0.006634	0.000739	0.004000
0.051576	0.012309	0.007059	0.015156
0.019388	0.008816	0.028623	0.016604

(Figure 19, Figure 20, Figure 21, Figure 22 and Figure 23).

Found essential frequency components were classified by the NN classifier [35,36], NM classifier, SOM [37], BNN [38,39,40,41,42,43,44]. There was possibility to use another classifier such as naive Bayes, support vector machine [45,46,47], linear discriminant analysis [48], fuzzy classifiers [49,50], and fuzzy c-means clustering [51]. The results of recognition depended on number of found essential frequency components and selected classification method.

2.2. Nearest Neighbour Classifier

A classification step can be achieved by the nearest neighbour (NN) classifier. This method of classification is well-known. It is used in economics, telecommunication, pattern recognition, fault diagnosis, and image recognition. The NN classifier can classify data (linearly separable and non-linearly separable) with high recognition rate. The NN is simple to implement, and it requires a few training feature vectors for proper classification. It uses labels for classification of test feature vectors. The classifier uses metric distance to compare two vectors (training and test feature vectors). There are many distance metrics to compare training and test vector. Distance metrics such as Euclidean, Manhattan, and Minkowski had similar results. In this paper, the classification step was carried out using Manhattan distance (1):

$$d(\mathbf{x}\mathbf{-}\mathbf{cmbrc})={\displaystyle \sum _{i=1}^1\left|(x_i-cmbr{c}_i)\right|}$$

(1)

where d(x-cmbrc)—computed distance, unknown test feature vector x = [x₃₆, x₃₇, x₅₉, x₆₀, x₇₂, x₇₅, x₉₅, x₁₁₇, x₁₁₈, x₁₀₉₂, x₁₀₉₄, x₁₂₄₃, x₁₄₃₂, x₁₄₃₃, x₁₄₃₈, x₁₄₃₉, x₁₄₄₂, x₁₄₄₄, x₁₄₅₂, x₁₄₅₅, x₁₄₅₆, x₁₄₅₈, x₁₄₇₁, x₁₅₁₅, x₁₅₁₆, x₁₅₁₈, x₁₅₃₁, x₁₈₉₄] and training feature vector cmbrc = [cmbrc₃₆, cmbrc₃₇, cmbrc₅₉, cmbrc₆₀, cmbrc₇₂, cmbrc₇₅, cmbrc₉₅, cmbrc₁₁₇, cmbrc₁₁₈, cmbrc₁₀₉₂, cmbrc₁₀₉₄, cmbrc₁₂₄₃, cmbrc₁₄₃₂, cmbrc₁₄₃₃, cmbrc₁₄₃₈, cmbrc₁₄₃₉, cmbrc₁₄₄₂, cmbrc₁₄₄₄, cmbrc₁₄₅₂, cmbrc₁₄₅₅, cmbrc₁₄₅₆, cmbrc₁₄₅₈, cmbrc₁₄₇₁, cmbrc₁₅₁₅, cmbrc₁₅₁₆, cmbrc₁₅₁₈, cmbrc₁₅₃₁, cmbrc₁₈₉₄]. The result of classification was depended on the nearest distance d(). Description of the NN classifier is available in following articles [35,36].

2.3. Nearest Mean Classifier

Similar to the NN classifier, the nearest mean (NM) classifier is also based on computed distance. It uses average feature vector instead of training feature vectors. Average feature vector afv is defined as (2)

$$\mathbf{afv}=\frac{1}{p}{\displaystyle \sum _{i=1}^p{y}_i}$$

(2)

where afv—average feature vector, p—number of essential frequency components, and y_i—value of essential frequency component with i index.

The nearest distance between test and average feature vector is computed. Next, the label occurring with specific average feature vector is the label for the test feature vector. The NM classifier can classify data with a high recognition rate. For the classification step, the author used Manhattan distance (1).

2.4. Self-Organizing Map

The self-organizing map was used for machine learning. The self-organizing map (SOM) is a clustering method. It does not use labels for classification of test feature vectors. The SOM is an unsupervised neural network. It is used for clustering data, meteorology and oceanography, project prioritization, selection, and failure analysis. For example, the SOM is used for meteorological applications such as climate change analysis, precipitation, snow, wind, air temperature, etc. The SOM analysis has been applied for computed feature vectors of acoustic signals. Similarity between feature vectors depends on the location of features on the two-dimensional map (nodes). The SOM uses training step and testing step. In the training step, weights of nodes are changed (at the beginning, values of weights are random). The author used the following self-organizing map (Figure 24). It was implemented in MATLAB. Description of the SOM is available in the following article [37].

2.5. Backpropagation Neural Network

Backpropagation neural network (BNN) was also used for machine learning. It is a supervised learning method. It is also a well-known method of data classification. It has been used for many applications, such as speaker recognition, image recognition, signal recognition, control, prediction, computer games, robots, etc. The applied backpropagation algorithm has been described in the literature [38,39,40,41,42,43,44]. The author implemented a backpropagation neural network (Figure 25).

Layers of BNN had following number of neurons: input layer—28, hidden layer—100, output layer—5. The values of output neurons were 10000—healthy CM, 01000—CM with shorted stator coils, 00100—CM with broken rotor coil, 00010—CM with broken tooth on sprocket, and 00001—CM with damaged gear train. More information about BNN can be found in following papers [38,39,40,41,42,43,44].

3. Results of Acoustic-Based Fault Diagnosis Technique of the Commutator Motor

Measurements of acoustic signals of commutator motors were conducted in the workshop. The author measured and analysed 5 states of the CM: healthy CM, CM with shorted stator coils (Figure 26a), CM with broken rotor coil (Figure 26b), CM with broken tooth on sprocket (Figure 27), and CM with damaged gear train (Figure 28). Analysed commutator motors had the following parameters: W_oM = 1.84 kg, P_oM = 500 W, RS_oM = 3000 rpm, V_oM = 230 V, f_oM = 50 Hz, where W_oM—weight of the motor, P_oM—rated power of the motor, RS_oM—rotor speed, V_oM—supply voltage of the motor, and f_oM—current frequency of the motor.

The author used 30 one-second training samples for proper pattern creation process. The author used 500 one-second test samples for proper testing process. Training and test samples of the CM were processed and analysed. The author used technique presented in Section 2 for proper fault diagnosis. Acoustic data of the CM were analysed using efficiency of recognition (E_RCM). It was defined as (3):

$$E_{RCM}=(N_{TSCMTP})/(N_{ATSCM})\cdot 100\%$$

(3)

where: E_RCM—efficiency of recognition of the CM for defined class, N_TSCMTP—number of test samples of the CM for defined class tested properly, N_ATSCM—number of all test samples of the CM for defined class.

Total efficiency of recognition of the CM (TE_RCM) was introduced to evaluate efficiency of recognition of all states of the CM. It was expressed as (4):

$$T{E}_{RCM}=(E_{RCM1}+E_{RCM2}+E_{RCM3}+E_{RCM4}+E_{RCM5})/5$$

(4)

where TE_RCM—total efficiency of recognition of the CM, E_RCM1—efficiency of recognition of the healthy CM, E_RCM2—efficiency of recognition of the CM with broken rotor coil, E_RCM3—efficiency of recognition of the CM with shorted stator coils, E_RCM4—efficiency of recognition of the CM with broken tooth on sprocket, and E_RCM5—efficiency of recognition of the CM with damaged gear train.

Acoustic signal analysis of the CM is presented in

Table 6. Acoustic signal analysis of the CM using the MSAF-15-MULTIEXPANDED-8-GROUPS and the NN.

Type of Acoustic Signal	ERCM [%]
Healthy CM	90
CM with broken rotor coil	87
CM with shorted stator coils	94
CM with broken tooth on sprocket	100
CM with damaged gear train	100
	TERCM [%]
	94.2

,

Table 7. Acoustic signal analysis of the CM using the MSAF-15-MULTIEXPANDED-8-GROUPS and the NM.

Type of Acoustic Signal	ERCM [%]
Healthy CM	89
CM with broken rotor coil	91
CM with shorted stator coils	93
CM with broken tooth on sprocket	100
CM with damaged gear train	100
	TERCM [%]
	94.6

,

Table 8. Acoustic signal analysis of the CM using the MSAF-15-MULTIEXPANDED-8-GROUPS and the SOM.

Type of Acoustic Signal	ERCM [%]
Healthy CM	87
CM with broken rotor coil	86
CM with shorted stator coils	81
CM with broken tooth on sprocket	90
CM with damaged gear train	98
	TERCM [%]
	88.4

and

Table 9. Acoustic signal analysis of the CM using the MSAF-15-MULTIEXPANDED-8-GROUPS and the BNN.

Type of Acoustic Signal	ERCM [%]
Healthy CM	85
CM with broken rotor coil	88
CM with shorted stator coils	82
CM with broken tooth on sprocket	91
CM with damaged gear train	99
	TERCM [%]
	89

. The acoustic signal analysis of the CM using the MSAF-15-MULTIEXPANDED-8-GROUPS and the NN are presented in Table 6 (28 analysed frequency components).

The acoustic signal analysis of the CM using the MSAF-15-MULTIEXPANDED-8-GROUPS and the NM are shown in Table 7 (28 analysed frequency components).

The acoustic signal analysis of the CM using the MSAF-15-MULTIEXPANDED-8-GROUPS and the SOM were presented in Table 8 (28 analysed frequency components).

The acoustic signal analysis of the CM using the MSAF-15-MULTIEXPANDED-8-GROUPS and the BNN were presented in Table 9 (28 analysed frequency components).

The method of feature extraction the MSAF-15-MULTIEXPANDED-8-GROUPS and selected classifiers provided high recognition rates (TE_RCM in the range of 88.4–94.6%). The MSAF-15-MULTIEXPANDED-8-GROUPS used 28 frequency components of the CM. The NN classifier and the MSAF-15-MULTIEXPANDED-8-GROUPS provided TE_RCM = 94.2%. The NM classifier and the MSAF-15-MULTIEXPANDED-8-GROUPS provided TE_RCM = 94.6%. The SOM (self-organizing map) and the MSAF-15-MULTIEXPANDED-8-GROUPS provided TE_RCM = 88.4%. The BNN and the MSAF-15-MULTIEXPANDED-8-GROUPS provided TE_RCM = 89%.

Self-organizing map and backpropagation neural network are trained. The training is different each time. The NN classifier and the NM classifier had the same results each time. Moreover, feature vectors had small differences between them. The NN classifier and the NM classifier were better for the recognition of close feature vectors.

4. Conclusions

The article presented acoustic-based fault diagnosis technique of the CM. Five states of the CM were considered: healthy CM, CM with broken rotor coil, CM with shorted stator coils, CM with broken tooth on sprocket, and CM with damaged gear train. The method of feature extraction MSAF-15-MULTIEXPANDED-8-GROUPS was described and implemented. Classifiers NN, NM, SOM, and BNN were used for acoustic analysis of the CM.

Analysed values of TE_RCM were in the range of 88.4–94.6%. The NM classifier and the MSAF-15-MULTIEXPANDED-8-GROUPS provided TE_RCM = 94.6%. The implementation of the proposed fault diagnosis technique had low cost. Laptop and microphones are available for $300. Other types of rotating electric motors (such as DC motors, synchronous motors, induction motors) can also be diagnosed using acoustic analysis.

The proposed acoustic-based fault diagnosis technique has its limitations. If the motor runs too quietly, it is difficult to use the mentioned technique and microphone. However, the presented acoustic-based fault diagnosis technique is appropriate for acoustic signals of rotating motor and other types of acoustic signals (for example acoustic signal of an engine). The proposed acoustic-based fault diagnosis technique can be extended to detect more complicated faults. Future research will focus on the analysis of new feature extraction methods, other types of faults, and other diagnostic signals, such as vibrations.