FAULT DIAGNOSTICS OF ACOUSTIC SIGNALS OF LOADED SYNCHRONOUS MOTOR USING SMOFS-25-EXPANDED AND SELECTED CLASSIFIERS

Original scientific paper A system of fault diagnostics of loaded synchronous motor was proposed. Proposed system was based on acoustic signals of loaded synchronous motor. A new method of feature extraction SMOFS-25-EXPANDED (shorted method of frequencies selection-25-Expanded) was proposed. Presented method was analysed for 3 classifiers: LDA (Linear Discriminant Analysis), NN (Nearest Neighbour), SOM (Self-organizing Map). Analysis was carried out for real incipient states of loaded synchronous motor. Acoustic signals generated by motor were used in analysis. The following states of motor were analysed: healthy motor, motor with shorted stator coil, motor with shorted stator coil and broken coil, motor with shorted stator coil and two broken coils. These states are caused by natural degradation of rotating synchronous motor. The results of recognition were good. Proposed method of acoustic signal recognition can be used to protect loaded synchronous motors.


Introduction
One of the types of AC motors is synchronous motor.The synchronous motors behave as constant speed motor.They are independent of load condition.The synchronous motors can be used for: line shafts, blowers, compressors, reciprocating pumps, centrifugal pumps and paper mills.At the end of transmission lines, these types of motors are used to regulate the voltage.Moreover synchronous motors are used with variable frequency drive system, by that meaning that wide range of speeds can be obtained in metallurgy industry [1].
The performance of the synchronous motor depends on the structure of electric circuit.Moreover it depends on the type of material and its treatment [2÷5].
To diagnose electric motor many methods were proposed in the literature.Some of them are based on recognition of electric, vibro-acoustic, thermal signals [6÷27].Most of them are based on electric signals, because these signals are not disturbed so much as acoustic signals [1,8,10,56].The methods based on acoustic signals are not known in the literature.Moreover these methods are non-invasive and inexpensive.Microphone and computer cost about 300 $.
The system of detection of predefined incipient faults is employed as a tool to protect the synchronous motors (Fig. 1).The most important profit of the system is that the probable fault of the synchronous motor can be predicted [25].Moreover incipient faults of motor may cause production and operation shutdowns.These shutdowns may cause waste of money, production time, resources and employee time.summarized in Section 4 along with the plan of future researches.

Presented method of recognition of acoustic signal of rotating synchronous motor
The presented method of recognition is showed in Fig. 2

Recording of acoustic signal
Capacitor microphone and a notebook computer are used to record acoustic signal of loaded synchronous motor [28].This soundtrack has the following parameters: mono, 44100 Hz, 16-bit depth, WAVE PCM.

Pre-processing
Pre-processing of acoustic signal consists of 3 steps: splitting recorded soundtrack into 5-seconds samples, normalization of the amplitude, calculation of FFT [8].Hamming window with the length of 32.768 is used to calculate 16.384 elements of FFT spectrum (32.768/44.100=0,743,duration of 1 window equals 0,743 s).

Shorted method of frequencies selection-25-Expanded
In the literature many feature extraction methods are described.In this subsection, author proposes method of feature extraction of loaded synchronous motor -SMOFS-25-EXPANDED.Presented method uses differences between amplitudes of frequencies of states of the loaded synchronous motor.Healthy where TOS -threshold of selection of amplitudes of frequencies (formula 1), ||AFS 1 | − |AFS 2 || -the difference of amplitudes of frequencies for states 1 and 2 of the motor, AFS 1 -amplitude of frequency of state 1 of the motor, AFS 2 -amplitude of frequency of state 2 of the motor.5. TOS is calculated according to the following formulas (2) and ( 3): If the parameter NF is greater than This parameter defines how many common frequencies are selected.For example, when TE is equal to 0,665, then 2 of 3 frequencies are required ((2/3) > 0,665) to make decision about common frequencies (see example above).In the mentioned example 110, 220, 340 Hz are selected for TE = 0,665.If parameter TE is equal to 0,668 ((2/3) < 0,668), none of frequencies will be selected.7. Select these amplitudes of selected frequencies and form feature vector.
A block diagram of the shorted method of frequencies selection-25-Expanded is showed in Fig. 3.

Linear discriminant analysis
Classification is the last step of signal processing.This step is described as supervised learning techniques.Classifier predicts the class of a new unlabelled observation (test sample).Classification methods are developed in the literature [29 ÷ 57].Many of them can be used for recognition of acoustic signals.A Linear Discriminant Analysis classifier (LDA) analyses data.Assume we have a set of D-dimensional samples x 1 , x 2 , x 3 ,..., x N , N 1 of which belongs to class w 1 , and N 2 to class w 2 .We want to obtain a scalar y by projecting the samples x onto a line y=w T x.Next we select the line that maximizes the separability of the scalars.A measure of separation is defined as the mean.The mean vector of each class in x-space and y-space is expressed by (4): LDA method maximizes the difference between the means.Next it is normalized by a measure of the withinclass scatter.The scatter is defined as: .) ( The within-class scatter is defined as ( 6): LDA maximizes the criterion function J(w) expressed by: .) ( Euclidean distance was used for the Nearest Neighbour classifier [11,29].

Self-organizing map
A self-organizing map (SOM) is a method that uses unsupervised learning to create a map on a twodimensional (training step).The location of points on the two-dimensional map shows the similarity between the considered points.This method is motivated by the observation of the operation of the biological brain.The SOM contains two steps: training and identification (mapping).Training samples are used to build the map.Test samples are used in identification step.The SOM consists of nodes.Nodes have weight vectors, which may be initialized randomly (similar to artificial neural network).Weight vectors are of the same dimension as the training vectors.To implement the SOM author uses Matlab Neural network toolbox [29].More about the SOM and its learning algorithm can be found in the literature [40,41].

Analysis of acoustic signals of loaded synchronous motor
Analysed loaded synchronous motor is presented in Fig. 1.Considered motor was loaded by the resistance R LO = 1 Ω.All acoustic signals were recorded for rotor speed of 1500 rpm.This speed was also constant for fault states.Broken coils and short circuit were located in the stator circuit of the analysed motor (Fig. 10 where: TEoR -the total efficiency of recognition of acoustic signal, EoR 1 -the efficiency of recognition of acoustic signal of healthy loaded synchronous motor, EoR 2 -the efficiency of recognition of acoustic signal of loaded synchronous motor with shorted stator coil (B1-B2), EoR 3 -the efficiency of recognition of acoustic signal of loaded synchronous motor with shorted stator coil (B1-B2) and broken coil (C2-C3), EoR 4 -the efficiency of recognition of acoustic signal of loaded synchronous motor with shorted stator coil (B1-B2) and two broken coils (C2-C3, E2-E3).The results of recognition of acoustic signals of loaded synchronous motor were presented in Tabs. 2 ÷ 4. The analysed efficiency of recognition of acoustic signal (EoR) was in the range of 92 ÷ 100 % (Tab.2).The total efficiency of recognition of acoustic signal (TEoR) was equal to 98 % for SMOFS-25-EXPANDED and LDA.

Conclusions
The feature extraction method called SMOFS-25-EXPANDED was presented in this paper.This method was applied to diagnostics of loaded synchronous motor.The proposed approach used acoustic signals produced by 4 analysed states of machine.Classifiers such as LDA, NN, SOM were analysed.The best results were obtained for parameter TE = 0,65, SMOFS-25-EXPANDED and NN classifier TEoR (total efficiency of recognition of acoustic signal) = 99 %.
Proposed approach is inexpensive, non-invasive and can be used to protect loaded synchronous motors.It can find application in other diagnostic methods related to other types of electric motors, engines and equipment consisting of rotating electric motors.In the future it can be also used with other fault detection methods based on electric and thermal signals.In this way more reliable methods of fault detection will be used in the industry.

Figure 1
Figure 1 Analyzed loaded synchronous motor (right side) and system of fault diagnostics (left side)This paper describes a new method of diagnostics of the loaded synchronous motor.The paper is organized in 4 sections.Section 1 describes applications of rotating synchronous motors and method of diagnostics of electrical motors.Presented method of recognition of acoustic signal of rotating synchronous motor is developed in Section 2. The new method of feature extraction SMOFS-25-EXPANDED is also presented in Section 2. Analysis of acoustic signal of loaded synchronous motor is described in Section 3. The paper is . It has 6 steps of processing.Step 1 is the recording of acoustic signal of loaded synchronous motor.Capacitor microphone and a notebook computer are used to record acoustic signal.Various microphones can be used in this step.Step 2 is splitting the recorded soundtrack into small samples.Step 3 is normalization of the amplitude of the obtained small samples.Step 4 is calculation of FFT spectrum.Step 5 is calculation of SMOFS-25-EXPANDED algorithm.Step 6 consists of 2 substeps -Steps 6a, 6b.Step 6a is calculation of patterns (training samples).Step 6b is calculation of results (test samples).

Figure 2
Figure 2 Presented method of recognition of acoustic signal of rotating synchronous motor using FFT, SMOFS-25-EXPANDED, NN, LDA and SOM

Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9
Figure 4 The difference between FFT spectra of acoustic signal of healthy state of loaded synchronous motor and acoustic signal of loaded synchronous motor with shorted stator coil (|h-ss|) and the obtained threshold by SMOFS-25-EXPANDED

2 )
the training examples from the same class are projected close to each other.Moreover the obtained means are as farther apart as it is possible.More information about LDA classifier is available in the literature [8, 29, 38, 53].2.5 Nearest neighbour A nearest neighbour classifier is a technique for classification of different classes.The categorization of a new test sample is determined by the labels of the most similar already existing training sample.The NN classifier can be improved by distance functions such as: Manhattan, Euclidean, Minkowski, Jaccard distance.The NN classifier is the following: 1) For each sample S in the test set calculate the distance (S, G) between S and every sample G in the training set, Neighbourhood contains the 1 neighbour in the training set closest to S, 3) On the basis of neighbourhood, select class for sample S [39].

Table 1
Selection of common frequencies of 4 states of loaded synchronous motor depending on parameter TE and training sets

Table 2
Results of recognition of acoustic signal of loaded synchronous motor using SMOFS-25-EXPANDED and LDA

Table 3
Results of recognition of acoustic signal of loaded synchronous motor using SMOFS-25-EXPANDED and NN

Table 4
Results of recognition of acoustic signal of loaded synchronous motor using SMOFS-25-EXPANDED and SOM