A Soft Sensor for Measuring the Wear of an Induction Motor Bearing by the Park’s Vector Components of Current and Voltage

This paper presents a methodology for creating a soft sensor for predicting the bearing wear of electrical machines. The technique is based on a combination of Park vector methods and a classifier based on an artificial neural network (ANN-classifier). Experiments are carried out in laboratory conditions on an asynchronous motor of AIR132M4 brand. For the experiment, the inner rings of the bearing are artificially degraded. The filtered and processed data obtained from the installation are passed through the ANN-classifier. A method of providing the data into the classifier is shown. The result is a convergence of 99% and an accuracy of 98% on the test data.


Introduction
Today's trend in industrial companies is to improve automation systems in all areas of operation [1,2]. This is primarily due to the digitalization of production [3]. The power supply industry is no exception. Automated electric drives are getting to become a major part of any industry, and their efficiency defines the growth and development strategy for companies [4,5]. The digital transformation of the energy sector is rapidly bringing new solutions to the market [6,7]. This development goes hand in hand with an uncontrolled increase in computing and instrumentation capacity. Current sensors and measurement principles for key process parameters are lagging far behind. However, sensor developments are much slower than necessary to keep up with the trend towards digitalization. The electricity supply area is no exception. There are a number of parameters that have to be measured, but for a number of reasons that is still not possible. The same trend can be seen in monitoring and maintenance systems for electrical machines. This in turn prevents the development of evaluation maps drive conditions for different process equipment topologies [8,9].
The induction motor is the key link and the most susceptible to wear and tear. An analysis of company data [10][11][12] identifies a segment of frequently occurring faults and research related to them, of which bearing defects are to be highlighted. Bearing failure leads to deviations in the mating components due to the multi-component nature of electrical machines. Untimely detection leads to accelerated wear and gradual degradation of coupled mechanical (couplings, reducers, etc.) and electrical (stator and rotor windings) parts of machines. It is of scientific interest to search for software and hardware solutions ensuring detection of bearing faults at the minimum stages of development with a minimum number of sensors.
In this context, the development of a soft sensor is an urgent task. It enables real-time measurements of various parameters that can subsequently be used to diagnose and assess where i max -maximum amplitude value of phase current, A; ω-power angular frequency, rad/s; t-time, s. In a coordinate system-dq, the generalized vector of I S current is written as (5) and is valid for (1)- (4).
These mathematical transformations are shown in a vector diagram, Figure 1. According to Equation (5), the generalized vector in the complex plane will describe a trajectory-the hodograph. The distortion of the real current vector trajectory with respect to the reference one is observed.
If the asynchronous motor is defective in terms of stator, rotor or mechanical damage, the hodograph of the generalized current vector changes relative to the reference. If one of the stator phases is damaged, the hodograph degenerates into an ellipse. The proportional change in ellipticity and width of the Park's vector hodograph corresponds to the defect level [21]. Disturbance in the rotor causes the hodograph to degenerate into a complex shape [22]. Damage to the mechanical part of the motor gives rise to circular distortions and variations in the width of the described hodograph [20]. The study of complex trajectories According to Equation (5), the generalized vector in the complex plane will describe a trajectory-the hodograph. The distortion of the real current vector trajectory with respect to the reference one is observed.
If the asynchronous motor is defective in terms of stator, rotor or mechanical damage, the hodograph of the generalized current vector changes relative to the reference. If one of the stator phases is damaged, the hodograph degenerates into an ellipse. The proportional change in ellipticity and width of the Park's vector hodograph corresponds to the defect level [21]. Disturbance in the rotor causes the hodograph to degenerate into a complex shape [22]. Damage to the mechanical part of the motor gives rise to circular distortions and variations in the width of the described hodograph [20]. The study of complex trajectories makes it possible to determine the types and intensity of the influence of defects on the rotor speed and torque on the motor shaft in a comprehensive manner.
In this paper, a neural network classifier is used to identify changes in the Park vector, which allows for estimating changes in the state of the Park vector and signals the onset of a defect in a timely manner.
However, in order to use such a classifier, it needs to be adapted to process the data coming in the real-time mode [31,32]. Figure 2 shows the algorithm used in developing the ANN-classifier [33].
A brief list of actions, according to this algorithm, is as follows: supply values equal to one given time period to the input of the model; obtain values for the Park vector; generate a matrix of values for the input to the classifier; obtain the result. The basic idea, in this case, is the idea of the special formation of the input vector for the ANN-classifier. As such a vector is taken as a vector showing how many times the data vector falls into one or another abstraction region of the Park vectors' hodograph. In total, the hodograph was divided into 100 abstraction zones from minus 1 to 1 with a step of 0.2 (10 segments on the imaginary and real axis). Thus an array of size (100 × 1) is fed to the input of the ANNclassifier, where the value of each element of the array is the number of points falling into a given abstract zone.
In order to train and test the neural network, the data captured during the experiment were divided into groups. A total of 600,000 values were captured during the experiment. Ten percent was used for training. The rest of the data were used for testing. The im- In this paper, a neural network classifier is used to identify changes in the Park vector, which allows for estimating changes in the state of the Park vector and signals the onset of a defect in a timely manner.
However, in order to use such a classifier, it needs to be adapted to process the data coming in the real-time mode [31,32]. Figure 2 shows the algorithm used in developing the ANN-classifier [33].
A brief list of actions, according to this algorithm, is as follows: supply values equal to one given time period to the input of the model; obtain values for the Park vector; generate a matrix of values for the input to the classifier; obtain the result. The basic idea, in this case, is the idea of the special formation of the input vector for the ANN-classifier. As such a vector is taken as a vector showing how many times the data vector falls into one or another abstraction region of the Park vectors' hodograph. In total, the hodograph was divided into 100 abstraction zones from minus 1 to 1 with a step of 0.2 (10 segments on the imaginary and real axis). Thus an array of size (100 × 1) is fed to the input of the ANN-classifier, where the value of each element of the array is the number of points falling into a given abstract zone.
In order to train and test the neural network, the data captured during the experiment were divided into groups. A total of 600,000 values were captured during the experiment. Ten percent was used for training. The rest of the data were used for testing. The important point in training and testing the data was to keep the right sequence. For the network to work correctly, an unbroken vector of data was required for the 1st period of operation. The data were therefore pre-divided into these periods with certain labels. portant point in training and testing the data was to keep the right sequence. For the network to work correctly, an unbroken vector of data was required for the 1st period of operation. The data were therefore pre-divided into these periods with certain labels.

Experiments
The object of the research is an asynchronous motor with the parameters given in Table 1. It is powered from a 50 Hz mains supply in a continuous duty mode S1 and a constant shaft load. The appearance and wiring diagram of the AM is shown in Figure 3. A similar motor in generator mode gives a constant load.

Experiments
The object of the research is an asynchronous motor with the parameters given in Table 1. It is powered from a 50 Hz mains supply in a continuous duty mode S1 and a constant shaft load. The appearance and wiring diagram of the AM is shown in Figure 3. A similar motor in generator mode gives a constant load.   The impact of bearing failure has the most intense distortion of the magnetic field in the air gap, as shown in Figure 4, as well as in [34]. This type of defect has an increased rate of development, resulting in rapid degradation of the mechanical and associated electrical parts of the motor [35].   The impact of bearing failure has the most intense distortion of the magnetic field in the air gap, as shown in Figure 4, as well as in [34]. This type of defect has an increased rate of development, resulting in rapid degradation of the mechanical and associated electrical parts of the motor [35].  The impact of bearing failure has the most intense distortion of the magnetic fie the air gap, as shown in Figure 4, as well as in [34]. This type of defect has an incre rate of development, resulting in rapid degradation of the mechanical and associated trical parts of the motor [35].   According to the motor datasheet, the motor AIR132M4 is fitted with deep groove ball bearings series-6208 with the following technical data (Figure 4 and Table 2). According to Figure 4, bearing 6208 has the following dimensions, Table 2.
The procedure for the experiment is to artificially degrade the inner rings of the bearing as a number of friction-induced degradation shells in the deep-groove ball bearing. The degradation shells are shown in Figure 5.
Sensors 2021, 21,7900 According to the motor datasheet, the motor AIR132M4 is fitted with deep ball bearings series-6208 with the following technical data (Figure 4 and Table 2) According to Figure 4, bearing 6208 has the following dimensions, Table 2.
The procedure for the experiment is to artificially degrade the inner rings of t ing as a number of friction-induced degradation shells in the deep-groove ball The degradation shells are shown in Figure 5.   The experiment was carried out on four states of the machine:

1.
Reference motor operation without load at idle speed 2.
Motor operation in reference condition at rated load 3.
Motor operation with one shell in the inner ring of the bearing 4.
Motor operation with three shells in the inner bearing ring Tests in cases 3 and 4 were carried out at nominal load.          Study [30] on the spectral analysis of the current consumption of an electric motor highlights the characteristic frequencies by which the presence of a defect can be determined (6). The initial stage of bearing wear is the occurrence of contact parts with rolling elements, namely balls, on the inner or outer ring.

Results & Discussion
where f rm -rotor speed; n-number of balls in the bearing; β-contact angle; D pit -diameter of the circumference of the ball centres; D ball -ball diameter. Compared to spectrum analysis (FFT) [36], where part of the information is lost due to the use of low and high-pass filters and is in the noise region (−75-80 dB), it is almost impossible to detect the initial stages of the defect. The occurrence of a defect (in our case a bearing defect) in the hodograph can be detected earlier as a distortion in its trajectory ( Figure 10), which the spectrum does not provide. The expected calculated bearing fault frequencies according to (6) and Table 2 at cos β = 1 are f rb = 175 Hz, 256 Hz. By analyzing the hodographs and spectra (Figures 10-15) changes in the current hodograph ( Figure 10) are observed as the defect degree changes. However, it is difficult to isolate the peaks of the frequency components of the spectrum, which is an advantage of the generalized current vector method. However, due to the visual identification of faults in the trajectory distortion hodograph, it is not possible to construct a fault-level estimation system. A visual assessment of the hodographs in Figures 6-9 makes it possible to assert that the Park vector changes its state depending on the cases under consideration. The additional evidence for the expediency of using Park's vector is shown below.
Study [30] on the spectral analysis of the current consumption of an electric motor highlights the characteristic frequencies by which the presence of a defect can be determined (6). The initial stage of bearing wear is the occurrence of contact parts with rolling elements, namely balls, on the inner or outer ring.
where frm-rotor speed; n-number of balls in the bearing; β-contact angle; Dpit-diameter of the circumference of the ball centres; Dball-ball diameter. Compared to spectrum analysis (FFT) [36], where part of the information is lost due to the use of low and high-pass filters and is in the noise region (−75-80 dB), it is almost impossible to detect the initial stages of the defect. The occurrence of a defect (in our case a bearing defect) in the hodograph can be detected earlier as a distortion in its trajectory ( Figure 10), which the spectrum does not provide. The expected calculated bearing fault frequencies according to (6) and Table 2 at cosβ =1 are frb = 175 Hz, 256 Hz. By analyzing the hodographs and spectra (Figures 10-15) changes in the current hodograph ( Figure 10) are observed as the defect degree changes. However, it is difficult to isolate the peaks of the frequency components of the spectrum, which is an advantage of the generalized current vector method. However, due to the visual identification of faults in the trajectory distortion hodograph, it is not possible to construct a fault-level estimation system.            Further analysis of the method has highlighted a number of advantages. The first is that only two current sensors (Hall-effect compensated current sensors) are required to detect faults, as shown in Figure 16. The third phase current is determined indirectly [37][38][39].  Further analysis of the method has highlighted a number of advantages. The first is that only two current sensors (Hall-effect compensated current sensors) are required to detect faults, as shown in Figure 16. The third phase current is determined indirectly [37][38][39]. Further analysis of the method has highlighted a number of advantages. The first is that only two current sensors (Hall-effect compensated current sensors) are required to detect faults, as shown in Figure 16. The third phase current is determined indirectly [37][38][39]. The second is achieved by a synchronous recording of the phase voltage currents (uA, uB, uC), which eliminates the influence of mains distortion. Distortions due to mains quality [40] have to be mutually excluded in the analysis from the asynchronous motor hodograph, (Figure 17).  The second is achieved by a synchronous recording of the phase voltage currents (uA, uB, uC), which eliminates the influence of mains distortion. Distortions due to mains quality [40] have to be mutually excluded in the analysis from the asynchronous motor hodograph, (Figure 17). The second is achieved by a synchronous recording of the phase voltage currents (uA, uB, uC), which eliminates the influence of mains distortion. Distortions due to mains quality [40] have to be mutually excluded in the analysis from the asynchronous motor hodograph, (Figure 17).  The information value of the hodograph is quite high, but in addition to the trajectories already obtained and their changes to which certain stages and types of both individual and complex defects correspond [41]. Figure 18 shows the results of training the ANN-classifier. The classifier was trained using three methods: Decision Tree [42], Support Vector Machine [43] and K-nearest neighbors [44]. The information value of the hodograph is quite high, but in addition to the trajectories already obtained and their changes to which certain stages and types of both individual and complex defects correspond [41]. Figure 18 shows the results of training the ANN-classifier. The classifier was trained using three methods: Decision Tree [42], Support Vector Machine [43] and K-nearest neighbors [44]. As can be seen in the Figure, the best was K-nearest neighbors, with an accuracy of 99.9%. This is a good result. Figure 19. shows the result as a confusion matrix. Testing the ANN-classifier algorithm on real data gave significant results as well. The accuracy was 98%. The excessively high accuracy of the results is due to the idealized conditions of the experiment. Under real-life conditions, the machine can be subject to several types of defects [45]. It may operate under disturbing conditions and at different modes. This paper has shown the validity of the proposed methodology, however, for real objects it may not give such high results. However, the authors believe that in order to As can be seen in the Figure, the best was K-nearest neighbors, with an accuracy of 99.9%. This is a good result. Figure 19 shows the result as a confusion matrix. The information value of the hodograph is quite high, but in addition to the trajectories already obtained and their changes to which certain stages and types of both individual and complex defects correspond [41]. Figure 18 shows the results of training the ANN-classifier. The classifier was trained using three methods: Decision Tree [42], Support Vector Machine [43] and K-nearest neighbors [44]. As can be seen in the Figure, the best was K-nearest neighbors, with an accuracy of 99.9%. This is a good result. Figure 19. shows the result as a confusion matrix. Testing the ANN-classifier algorithm on real data gave significant results as well. The accuracy was 98%. The excessively high accuracy of the results is due to the idealized conditions of the experiment. Under real-life conditions, the machine can be subject to several types of defects [45]. It may operate under disturbing conditions and at different modes. This paper has shown the validity of the proposed methodology, however, for real objects it may not give such high results. However, the authors believe that in order to Testing the ANN-classifier algorithm on real data gave significant results as well. The accuracy was 98%. The excessively high accuracy of the results is due to the idealized conditions of the experiment. Under real-life conditions, the machine can be subject to several types of defects [45]. It may operate under disturbing conditions and at different modes. This paper has shown the validity of the proposed methodology, however, for real objects it may not give such high results. However, the authors believe that in order to make it applicable to real objects it is necessary to break the Park hodograph into smaller abstract zones. This would solve the problem of possible overlapping distortions of Park's vector.

Conclusions
In the course of the work, on the whole, it was possible to prove the consistency of the hypothesis. Machine defects can be estimated using a mathematical apparatus that allows the combination of Park's vector transformation and an ANN-classifier. Using this mathematical apparatus in the real-time mode with a certain periodicity allows us to work out the fully-fledged soft sensor for measuring a certain type of defect. However, the accuracy of the results obtained in the work may be reduced in conditions of real operation of electrical machines. The authors emphasize that the basic idea of the method when these conditions occur will not change. Only the components of this methodology will change, for example, the number of abstract zones in the division of the Park hodograph will increase.
The authors thus offer a method of determining the condition of a bearing in near real-time, or with a minimum decision time. The authors have shown that it is possible to tell just by one spin of the Park hodograph, i.e., by one period (0.02 s) that a bearing has developed a defect. This can be carried out by applying a special ANN-classifier, which in turn determines which of the predefined abstract zones the current Park vector values fall into. The division into such zones or quadrants is the basic tool for improving the accuracy of the soft sensor. The closer the bearing conditions are to ideal, the larger the abstract zones that are allocated. However, it must be remembered that the allocation of such zones is initially laid down and their extension is not possible during operation, i.e., on the go. Therefore, experiments under real-field conditions should be carried out beforehand to determine the necessary width of the considered abstract zones for the Park hodograph.

Funding:
The study was carried out at the expense of a subsidy for the fulfillment of the state task in the field of scientific activity for 2021 No. FSRW-2020-0014.

Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.