Induction motor’s rotor slot variation measurement using logistic regression

Rotor slots in induction motor expand due to thermal imbalance and create magnetic stress. Magnetic stress is a force that develops on the laminated surface of the rotor due to the curving or stretching magnetic flux. Traditional motor fault detection methods never measure magnetic stress on the rotor; a significant problem frequently arises in the motor. Magnetic stress is proportional to slot size variations in the rotor. High slot size variations on the laminated surface of the rotor lead to more curving and stretching magnetic flux and damage the rotor and stator, reducing their efficiency and induce harmonics. In this paper, the Average rotor Slot Size Variation (ASSV) in the rotor is predicted during the running condition of the motor through logistic regression. Logistic regression predicts ASSV by multimodal sensor signal sub-band energy values and measures rotor slot sizes from microscope images. Multimodal sensor signal is obtained from various sensors, such as vibration, temperature, current and Giant Magneto Resistance (GMR). Signal sub-band energy is obtained from Over complete Rational-Dilation Wavelet Transform (ORaDWT). From experimental results, ASSV is more than 75% from standard size, damaging the rotor and stator. The accuracy of ASSV prediction is about 92%.


Introduction
Motor works based on magnetic interlinking between stator and rotor. The stator comprises a cylindrical frame in the outer region, magnetic path, and electrical winding with insulation. It consists of lamination and slots; lamination is fabricated with high-grade alloy steels. Lamination in the stator reduces eddy current and heating. The stator coils are excited when the motor is powered. In a 3-phase induction motor, three sets of coils are inside the stator lamination with 120°of separation. The rotor always keeps rotating coaxially with the stator, when the motor is connected to the power supply. Figure 1 shows magnetic field line flow in squirrel cage motor and magnetic stress [1].
In the squirrel cage induction motor, the rotor is in a squirrel cage structure. The squirrel cage rotor interacts with magnetic fields in the stator and leads to torque formation. In the squirrel cage motor, bars in the rotor are designed based on speed-torque requirement. In the three-phase induction motor, the rotor is the most important component and experiences high thermal [2] and magnetic stress due to inrush current, overload, Transient, High voltage and current, low voltage due to single phasing and current. This stress leads to rotor stress [3].
During high-speed running condition motor, the centrifugal force and thermal stress are increased on the rotor surface. Permanent magnet motor has high compressive strength (800Mpa), and is brittle [4]. The stress in the rotor is calculated by numerical and analytical methods. The analytic method of rotor stress measurements [5][6][7] has a major drawback, i.e. assuming the rotor is in rotational symmetry. In [6,8] the displacement method was adapted for rotor stress calculation. Some analytical methods include axial stress [9] for rotor stress calculation and never consider edging effect and geometry discontinuity. Rotor stress calculation is more complicated due to non-linear factors and complicated structure. Moreover stress is not measured by temperature [10] during over speed and low speed concerning magnet tangential and radial stress. However, rotor sleeve thickness and rotor outer diameter are calculated with traditional designs [3]. The magnetic force on the rotor slot increases due to the double power frequency current [11]. This force leads to leakage magnetic flux in rotor slots [11][12][13][14][15] and moves towards the bottom of slots.
Significant stresses in the rotor are thermal, magnetic, and mechanical. These stresses need to be monitored and should be at a tolerant level for the long run of motor, without failures. The failures in an induction motor are stator, rotor, and bearing fault. The bearing and stator fault reduces through regular maintenance. Rotor faults can be prevented from regular monitoring of thermal and magnetic stresses in the motor during running conditions [16]. Rotor faults reduce by admitting a tolerant level of thermal and magnetic stresses on the motor [17]. These stresses cause a significant fault in the rotor system and simultaneously damage the stator. The thermal stress in the rotor of the squirrel cage induction motor arises due to frequent starting of the motor, vibration from the improper fixation of shaft and rotor, high starting current, negative sequencing current, uneven current circulation, rotor bowing and hot spots in the rotor. Moreover, rotor sparking arises because of thermal stress and damages the stator [18]. Furthermore, magnetic stress leads to rotor failures such as rotor bar bend, fatigue failure, heavy noise, and more vibration. Magnetic stress forms because of leakage flux from rotor slots' size variation and generates dynamic force proportional to the square of rotor current, which vibrates the rotor bar [19]. High vibration in the rotor leads to misalignment between shaft and bearing. Rotor vibration makes the rotor in an unbalanced position and may even hit the stator and causes damage.
Thermal and magnetic stresses are the major reasons for rotor and stator faults [18]. Thermal stress can be identified through visual interpretation of rotor and stator [19][20][21]. Rotor and stator under abnormal thermal stress exhibit melted regions on rotor-laminated surfaces. The rotor shows thermal stress through hot spots in its outer surface, melted paint, melted air passage, and bowing in rotor laminations [21,22]. Moreover, magnetic stress inside a motor is detected at the initial stage. Magnetic stress in the rotor is monitored for healthy running conditions and reduced harmonics. However, magnetic stress-based failure identification is very difficult in squirrel cage induction motors. Physical evidence for magnetic stress is the rub spot on the rotor. Magnetic stress leads to rubbing spots because of contact between the rotor and stator [23,24]. When magnetic stress does not create any physical contact between the rotor and stator, the identification of magnetic stress becomes very challenge. Magnetic stress is due to high current, overload, transient, high voltage and current, low voltage and current and thermal imbalance between the rotor and lamination leading to sparking. The high sparking period in the motor reduces its lifetime by damaging the rotor bar and end rings. Magnetic stress is due to curving, and stretching magnetic flux lines from rotor slots' size variation vibrates rotor bar and misaligns rotor position radially. Magnetic stress is due to leakage flux from rotor slot, pulls rotor from the centre and creates more vibration [25]. Magnetic stress rotates the rotor in different axes, leads to shaft bend, and damages the stator. Table 1 shows different sensor locations in the motor for rotor fault detection. However, existing rotor fault detection methods never addressed magnetic stress. The induction motor performance is investigated due to the end ring faults [26]. Deep learning-based motor fault detection can provide reliable solutions for industries [27]. The sliding mode observer technique detects rotor current faults. This method proves fast response and better stability than the existing method [28]. By the threephase current intersection signals, the induction motor rotor fault is diagnosed for high-and low-load motor operations [29]. A convolution neural network with batch normalization detects the bearing and broken rotor bars fault in squirrel cage induction motors [30].

A. Inference from literature survey
Researchers identify rotor faults, such as rotor bar misalignment, unbalanced rotor, and rotor induction measured through various sensors such as current, voltage, flux sensor and visual inspection. However, the rotor experiences high thermal stress and magnetic stress on its laminated surface. Thermal stress is measured through temperature measurement. However, magnetic stress over rotor lamination needs to be measured. The magnetic stress forms due to the magnetic flux line curving and stretching between rotor and stator. The curving and stretching magnetic flux lines result from rotor slot size variation at the surface of rotor lamination. Rotor slot variation measurement needs to be done during the running condition of the motor. Magnetic stress over rotor lamination is the major root cause for all rotor faults.

B. Problem statement
Now and then, rotor faults, such as bar fault, unbalanced rotor fault, rotor surface damage, are detected in induction motor by various sensors, such as current, vibration, GMR and voltage. Sensor signals are analysed based on threshold levels of voltage, signal spectrum, or current signature analysis for rotor fault detection. Moreover, researchers concentrate more on stator and bearing faults detection. However, the rotor is the major source for all faults in the motor, such as bearing, shaft, and stator. Moreover, thermal and magnetic stresses in the rotor are the root cause for all types of rotor faults. Magnetic stress from rotor slot variations must be monitored to avoid destructive sparking, leakage flux and rotor damages. Measuring magnetic stress in the rotor is still a challenging task. For monitoring and measuring magnetic stress, rotor slot size variation during the running condition of the motor need to be measured. The major problem in magnetic stress measurement would be the identification of the appropriate location of the sensor for acquiring curving and stretching magnetic flux lines.

C. Contributions
Destructive sparking and vibration in the motor result from magnetic stresses, such as curving and stretching magnetic flux lines. High Magnetic stress in the rotor leads to the variable radial position of the rotor during running conditions of the motor, and hits the stator [18]. Radially rotating rotor generates more leakage flux from the laminated surface of rotor and rotor slots [20] and develops excessive centrifugal forces. To avoid magnetic stress in the rotor, ASSV is predicted during running conditions of the motor. In this paper, magnetic stress is measured through Average rotor Slot Size Variation (ASSV), since magnetic stress is proportional to rotor slot size variation. For ASSV measurement, various sensors are used, such as temperature, current, vibration and GMR sensors. LM335 temperature sensor measures rotor temperature, the motor current signature is analysed through a toroidal sensor (Model no. SCT013). The vibration of the rotor is measured through the ADXL335 sensor, which measures free, forced, and dampen vibrations in the rotor due to magnetic stress. AA002-02 GMR sensor measures magnetic field strength over 3 CM distance with a minimum sensitivity of 0.45 mV/V-Oe. Curving and stretching (CS) flux from the rotor due to variation in rotor slot size is measured by the GMR sensor. The GMR sensor is fixed in the front side of the motor, and it collects CS flux magnetic lines. The GMR sensor is fixed very close to the rotor side of drain in the motor. The vibration sensor is kept at the end bearing gap and acquires rotor unbalancing vibration due to magnetic stress. Similarly, to measure high- and low-input current, the current sensor is fixed to the input power supply. Thermal stress is measured through a temperature sensor located at the drain, close to the rotor. The GMR sensor is fixed in between the rotor and stator air gap, as in Figure 2.

II. Materials and methods
The induction motor consists of air ducts for various applications, such as cooling, rotor weight reduction and reduced metal. Axial duct creates magnetic reluctance asymmetrically as the path for flux, whereas the shaft provides an alternate path for magnetic flux. Flux path varies according to the magnetic field and air ducts; such variations lead to magnetic reluctance in the motor and influence magnetizing current. Magnetizing flux affects the frequency of flux, leads to vibration, and varies the current spectrum. Magnetic flux overlaps with stray and leakage flux, which arise due to rotor damage or air gap eccentricity. Furthermore, frequent starting of the motor and high current during underload conditions leads to high heat and magnetic stress on rotor bars. Subsequently rotor slot sizes varys and generate CS flux due to thermal and magnetic stress. Heat over the rotor bars expands the rotor slot. High current in the rotor expands bars and makes a variation in the resistance value of lamination of rotor and rotor slots size. An uneven thermal and magnetic stress on the rotor bar leads to a change in magnetic reluctance in the rotor slots and leads to sparking. Such sparking in motor for a period damages rotor bar such as crack, broken bar and rub the spot. However, the sparking period decides the nature of sparking, such as defective or nondefective. Furthermore, the major reason for the fault in the rotor is due to magnetic and thermal stresses. Thermal stress causes heat in the rotor during running conditions and leads to uneven expansion of rotor slots. An uneven expansion of rotor slots creates CS flux in the rotor. CS flux due to the uneven expansion of rotor slot leads to the low air gap and form magnetic flux density with harmonic content. To study slot size variations in the rotor due to thermal imbalance needs multimodal sensors signals. Acquired signals' statistical parameter helps detect motor faults, such as destructive sparking various radially positioned rotor-running conditions and analyse the oscillatory behaviour of CS flux. Flux signal due to rotor slot size variation is studied through the appropriate location of GMR sensor in motor. The location for the GMR sensor is the air gap region near the rotor, identified after studying the oscillatory behaviour of CS flux from induced rotor slots such as 3 and 9 mm. CS flux travel inside the rotor due to the property of flux linkages and such flux can be collected from the material contact region of the motor, i.e. shaft region of the motor. CS flux travels between slots in the rotor, parallel to the entire rotor surface. CS flux moves out in the air gap due to uneven expansion of the rotor slot. Therefore, the optimum solution for placing the GMR sensor is fixed near the shaft region because the CS flux travels to both ends of the rotor. From GMR sensor signal analysis, the maximum of CS flux is obtained from the front end of the motor, i.e. on the drain. For ASSV prediction, sensor signals collected from different locations, such as vibration sensor, are kept in a non-drive end shield, GMR, temperature sensors at the drain region of the motor, and high current in motor measures through the current sensor. Figure 3 shows a methodology diagram for predicting ASSV, through which CS flux is monitored and measured.
Sensor signals are acquired through a 3-Dimensional Digital acquisition board. Figure 3 shows rotor slots images from microscope Smars ® HD 1920 × 1080P USB Digital Microscope camera. A microscope camera is used for measuring slot variations before and after induced faults in the motor. The various induced faults in the motor are different load conditions, variable input currents, and voltages, different radial positions of the rotor and manually created slots such as 3 and 9 mm.

A. Data acquisition system (DAQ) for multimodal sensor signal acquisition
USB data acquisition system consists of a Digital Class-B amplifier. USB data acquisition has four analogue channels and a data controller. The data controller collects signals from sensors, buffers data in the controller, and transfers them to the personal computer. The buffer in the Data acquisition system holds 984-bit samples and 512-984-bit length in size, based on the number of samples per packet. The analogue channels acquire signals up to 1200 samples per second with 300 scans per second for high-speed acquisition. The analogue channels are of 12-bit resolution. The supply voltage of DAQ is +3.6V. DAQ acquired signals sent to MATLAB software for analysis.

B. Experimental procedure for magnetic stress analysis in rotor slots
Thermal and magnetic stress are analysed through signals acquired from various sensors. Sensor signals are acquired from the motor at different input parameters such as current ranging from 1.5 to 5 A, voltage ranging from 180 to 450 V, motor speed ranging from 1400 to 1500 rpm, and load is varied from 0 to 17 kg. During running conditions of the motor, CS flux is created through induced faults such as transient fault, over and under load, variable input current and voltage. Sensor signals, such as temperature, GMR, current and vibrations, are acquired through a USB-3D-DAQ card and MATLAB Data acquisition toolbox. After each and every induced fault, signals from sensors are acquired and the rotor is removed immediately, for acquiring images of rotor slots through a Smars ® HD 1920 × 1080P USB Digital Microscope camera. The rotor slot image is used for measuring slots variation after every induced fault in the motor through pixel measurements. The pixel-based length measurements of rotor slots helps identify average slot variations after every induced fault. For example, induced transient fault is created by frequent disconnection of voltage through fast ON and OFF switching for continuous 5-10 min and the rotor gets the maximum of high current during every switching. After every switching period, CS flux-based stress is seen through the increase in amplitude, temperature and current signal, and the rotor is removed from the motor within 180-240 s for acquiring microscopic images. In a similar method, 2500 signals from each sensor are acquired, and their respective rotor slot images are acquired for measuring Average rotor Slot Size Variations. These signals acquired through a 3-Dimensional data acquisition system are pre-processed with a Non-Decimated Discrete Stationary Wavelet Transform filter.

C. NDSWT scaling filter for white and unscaled noises
The DAQ acquired sensor signals are white and unscaled noise. White noise arises due to uncorrelation in successive samples during the acquisition of magnetic, vibration and current signals. In acquired signals all frequency components are in a similar bandwidth. The white noise in signals is in the form of random signals with similar intensity, variable frequencies, and with constant power spectral density. The white noises in the vibration signals are sequential with time and flat spectrum. The unscaled noises are spatially correlated with arbitrary correlation. The unscaled noises are added in signals according to sensor location in the motor. For example, the GMR sensor located in the rotor region acquires stator leakage flux. To avoid unscaled noises, the optimum location of sensors in the motor plays a vital role. In the proposed ASSV prediction, white and unscaled noises are filtered through the NDSWT. The NDSWT fills the gap created during the decimation process of the discrete wavelet transform through shift-invariant property and redundant frequency information is obtained from signals. The NDSWT identifies te stationary and nonstationary signals collected from sensors. The NDSWT   is based on the sensitivity of choice in the starting point for a time series, i.e. Shift-invariant. The sensitivity is due to downsampling of the signal at each stage. Figure 4 shows GMR sensors signal with white noise and unscaled noise during overload conditions. The acquired signals from the motor are pre-processed for reducing white and unscaled noises, which arise during signal acquisition. The sensor signals are pre-processed through traditional algorithms such as Discrete Wavelet Transform (DWT). Figure 5 shows GMR sensor signals filtered with DWT. Figure 6 shows NDSWT filtered GMR signal. Table 2 shows the performance of various filtering algorithms such as DWT and FFT to reduce white and unscaled noises. From statistical analysis, the NDSWT filter performs better for GMR, vibration and current sensor signals, whereas the DWT performs better for temperature signals due to less white noise.
White and unscaled noises are very high in GMR and Vibration sensor signals. Higher white noise variation in GMR and Current sensor signals need NDSWT filtering. The NDSWT is more suitable for filtering all sensor signals. NDSWT filtered signal is given as input to the ORaDWT algorithm for energy band analysis.

D. Over complete rational-dilation wavelet transforms (ORaDWT)
The acquired signals from motor, such as current, vibration and flux signals, are piecewise smooth that need effective transform for analysis. The various transforms such as DWT, RaDWT, Dyadic perform less due to low-frequency resolution, i.e. low Q-factor. The oscillatory behaviour of CS flux signal from the GMR sensor is analysed through Over complete Rational-Dilation Wavelet Transforms (ORaDWT). ORaDWT applies over completeness through increased sampling rate in frequency and time with a high range of redundancy factors. ORaDWT performs based on nondyadic dilations flexible range of Q-factors and obtains redundancy factors. The proposed ASSV prediction uses ORaDWT for all acquired sensor signals. In the ORaDWT algorithm, frequency bands are represented in numbers, after passing through bandpass filters and interlaced to form subband signals. Furthermore, the frequency domain approach is through polynomial matrix factorization. ORaDWT performs better than dyadic transform due to high Q-factor and improves resolution for shot time-periodic k oscillatory signals.
Let us consider The output of the filter bank is given by Equation (7): H(ω) represents low-pass filter, and G(ω) represents high-pass filter. Figure 7 shows Rational-Dilation wavelet transforms sampling, and Figure 8 shows the ORaDWT sampling method. The p/q is the dilation factor, which is a rational number.
The NDSWT pre-processed vibration signal is given as an input signal to ORaDWT and RaDWT. Figures 9 and 11 show the percentage of energy subbands. Figures 10 and 12 show the reconstruction of the signal from ORaDWT and RaDWT. From simulated results, ORaDWT performs better than RaDWT due to more sub-band energy levels. Energy band values of ORaDWT are used for measuring rotor slot size variation.

III. Results and discussion
Rotor slot size variations due to high current, high voltage and frequent starting of the motor are experimented. The CS flux is generated due to Rotor slot size variations. Flux due to rotor slot size variation is detected through a multimodal sensor located at end shield and drain of the motor. To predict rotor slot size variation, energy band amplitude values from ORaDWT and rotor size variation measured from microscope camera values are correlated through logistic regression for prediction. An experimental result proves that all motor-induced faults vary the rotor slot sizes. The rotor slot size variations lead to harmonics and damage the stator. Further section discusses rotor size variations due to high current, variable conditions, non-radial position of the rotor and induced rotor slot variations more elaborately.

A. Rotor slot variations during high current and variable load conditions
The rotor slot variations during high current and variable load conditions are analysed through current, temperature, GMR, vibration sensors signals and microscope camera images of the rotor. To find rotor slot variations the motor is fed with the current of 1.       These pulses interfere in motors that are used for the experimental analysis. Figure 14 shows energy band variation of GMR sensor signals during low speed. Figure 15 shows a microscopic image of the rotor slot taken from the Smars ® HD 1920 × 1080P USB digital microscope camera. After every induced fault, the rotor in motor is removed and microscopic images obtained to measure the average slot variation in the rotor. The rotor image is obtained within 240 s and sometimes below the 240 s, so the maximum temperature in the rotor is maintained. Average rotor Slot Size Variations are measured through pixel measurements between gaps in slots in Figure 15. Furthermore,   rotor slot size variation is analysed through the nonradial position of the rotor in the motor during running conditions.

B. Rotor slot variations due to non-radial positions of the rotor
The non-radial position of the rotor in the motor is induced through bending shaft and loose fit of bearing. The shaft bending is done between 3°and 5°, whereas the acceptable bending of the shaft is about 0.04°. The bending for a higher degree in the shaft has more thermal stress in the rotor due to improper fixation of shaft and rotor. Due to the improper fixation of the rotor and frequent starting of the motor leads to high currents and uneven current circulations in rotor slots. The uneven CS flux is due to current circulation and detection through GMR sensor signals. Simultaneously, the vibration sensor signal shows variation in amplitude. During high starting current, vibration amplitude is high of about 3.5 V. The shaft bend leads to an amplitude voltage of 2.5 V from the vibration sensor. Furthermore, the signal pattern of the GMR sensor shows random variations due to the bend shaft. GMR signal is acquired from different locations of the motor such as stator side, and stator winding side, the random signals in GMR sensor signal are less when the GMR sensor is placed between the gap of the rotor and stator slots, show high random signal variations due to high CS flux. Figure 15 shows a microscopic image of the rotor slot captured 5 hr of continuous running of the motor with a shaft bend.
The frequent starting of the motor increases the vibration in the motor. Furthermore, improper fixation of shaft and rotor, high starting currents and high current increases slot size in the rotor. The CS increases due to rotor slot size variation and generates a dynamic force proportional to the square of rotor current, which vibrates the rotor. The high vibration in the rotor due to flux from varying rotor slot sizes leads to misalignment between shaft and bearing. The rotor vibration makes rotor in unbalanced position and causes damage in the rotor. Furthermore, motor under frequent start and high current under load condition leads to heat, damages the rotor slots and is seen through microscope images as in Figures 16 and 17. Subsequently, rotor slots size variations generate CS flux due to thermal stress on the motor. In the next section, CS flux over slots is analysed by induced rotor slots.

C. Induced rotor slot variations for magnetic stress analysis
To study the effect of variations in rotor slots, the rotor in the motor is induced with two slots in irregular directions, as shown in Figures 18 and 19. CS flux is analysed through an induced rotor slot of 3 mm and measured through a microscope image. Figure 19 shows an induced rotor slot of 9 mm. Initially, a 3 mm induced rotor slot is kept in the motor and tested in different conditions such as overload, overcurrent, load, and no load. Sensor signals are analysed for energy bands. GMR and temperature signals show a big difference in amplitude and slight changes in vibration. The energy band for the GMR sensor signal is shown in Figures 18  and 19 for 3-and 9 mm-induced slots, respectively.
Furthermore, the rotor with 9 mm-induced slots tested under different load conditions and their corresponding signals and sub-band energy levels are analysed for CS flux behaviour. GMR energy band signals for 9 mm slot show more bands (8) as shown in Figure 19. Moreover, the percentage of sub-band energy of the signal is high for 3 mm-induced slot as in Figure 18. The energy band variations show more CS flux as slot size increases. CS flux signals increase bands numbers for the higher size of induced slots. Table 3 shows different induced faults and corresponding values of rotor slot size variation energy band. The identification of stress due to CS flux needs a multimodal sensor. In Table 3, the energy band signal amplitude values are shown for respective induced faults. Table 3 shows the faults and their respective sensors value required for measuring CS flux stress in the motor, and these sensor values need to be acquired at the same time and duration. However, thermal stress in the rotor region is identified through a temperature sensor, CS flux stress over rotor surface needs GMR, current and vibration signals. During rotor slot size

D. Predication of Average rotor slot size variation through logistic regression
Multinomial logistic regression method is the extension of the Logistic regression method and is used for more than two classes of the dependent variable. The logistic regression method is a complement of linear regression for categorizig the target variable. For a dependent variable Y with two class and predictor variable X let g(x) = Pr(X = x) = 1-Pr(X = x), Logistic regression consists of a linear form for Logit with probability as in Equation (11): where the odds = Logit is a linear approximation and equal to the logarithm of the odds. β represent rate of increase or decrease in the S-shaped curve of g(x). Logistic regression extended to models with multiple predictor variables. Let μ represent the number of predictors for a binary variable Y as x1, x2 . . . xμ. The model for log-log odds is as in Equation (12): Logit[PrPr(T = 1)] = α + β1x1 + β2x2 + .+βμxμ (12) and h(x) is given as Equation (13): The βi,for 1 < i ≤n and 1 < j . n and i = j which represents the effect of xi on log-odds T = 1, controls the other xj, for example, exp (βi)is the multiplicative effect on odds of a one-unit which increases the xi, at a fixed level of other xj. If "n" independent observations with "n" predictor variables and target variable consist of q categories, to build the Logits in the multinomial, one of the categories considered as a base level and Logits functions constructed relative to base level. Let H j represents the multinomial probability of jth category, the relationship between this probability and the n-predictor variables, X1, X2 . . . Xμ, the multinomial logistic regression model is as in Equation (14): where j = 1,2, . . . .z-1 and i = 1,2, . . . n. Since all the H's adds to unity, this reduces to For j = 1,2, . . . z−1. The model parameters are determined by the multinomial linear method. Prediction of laminated slot variation size in the rotor is done through logistic regression: a supervised learning method. The prediction of the target value is obtained from probability. The logistic regression is classified as binary logistic regression and multinomial regression model. In binomial logistic regression, a variable is of two types: zero and one. Through such variables, the predication of success or failure is obtained. Multinomial logistic regression has more than three dependent variables. The prediction of Average rotor Slot Size Variations is done through multinomial logistic regression due to non-multi-collinearity in data, i.e. independent variables are independent of each other. Furthermore, energy band data are larger with no quantitative significance, sensor signal energy value data are in unordered types. From experimental analysis sensor signal energy values and measured values of rotor slot size obtained from microscopic images are used for ASSV prediction during running conditions of the motor. From Equation (16), slot average variations are predicted through Sub band Energy Amplitude Values (SEAV) of GMR, Vibration, Current, and Temperature. As given in Table 4 the experimental data prove that thermal stress creates magnetic variation. Furthermore, high current burns rotor lamination after attaining an extreme rotor slot size expansions. The extreme size of rotor slots size variation is seen through more energy bands, i.e more than seven energy bands from GMR sensor signals. Average rotor Slot Size Variation (ASSV) is as shown in Equation (16)  The predicted ASSV values of the new motor are depicted in Table 5. Table 5 shows ASSV five threephase induction motors under different running conditions, such as ideal, no-load, and loading conditions. For example, sample motor SM1 has 1.75 mm of rotor slot and during no-load condition, motor runs for 5 hr and rotor slot expands to 2.04 mm due to CS flux stress, whereas during load condition rotor slot expands to 3.25 mm after the continuous running of motor for 5 hr. The ASSV Equation (16) predicts rotor slot variation. If the rotor slot expands more than 75% of the original size, i.e. 3.25 mm slot expands to 5.68 mm size, the motor has more CS flux stress.

IV. Conclusion
The rotors are prone to high thermal and magnetic stress during running conditions due to inrush  , overload, over-current, frequent starting, transient fault, non-radial rotor, shaft bend, harmonics, and high speed. The magnetic stresses need to be monitored and should be in the tolerant level for the long run of the motor, without failures. In this paper, magnetic stress on rotor slot is analysed through various sensor signals, such as temperature, GMR, current and vibration. The appropriate locations of the sensor in motor, such as Non-drive end shield, drain, and terminal box, are identified through induced rotor slots such 9 and 3 mm energy band signal analysis. From acquired sensor signals, energy band values are obtained through band spectrum and identified through ORaDWT. Moreover, microscope images of rotor slots are used for measuring rotor slot sizes and verified with predicted ASSV for accuracy. The average slot expansion in the rotor leads to understanding magnetic stress over rotor slots. The ASSV is predicted during running conditions of the motor through logistic regression from sensor signal energy band values. The average expansion of rotor slot size exceeds more than 75% and needs maintenance. Maintenance improves the efficiency of the motor, maximum torque is maintained.
In the industrial environment, dismantling of stator and rotor during burnt or electrical smell is very frequent for mentioned motor duty cycles, such Continuous duty, Continuous duty with intermittent periodic loading, Continuous duty with starting and braking, and Continuous duty with periodic speed changes. The ASSV method measures slot variations, which are the major signs for all faults that arise in the motor during running states and prevent the faults at an earlier stage. In modern industries early motor faults detection increases production and minimizes the downtime. The proposed ASSV method avoids frequent dismantling for continuous duty cycle motor because of slot variation predictions. The proposed method performs less for the Short time duty, intermittent periodic duty, intermittent periodic duty with starting, intermittent periodic duty with starting and braking induction motors.
The proposed work can be extended with Nano coating over laminated sheets and can be monitored for CS flux through ASSV prediction values to evaluate the efficiency of the induction motor.