Online Adaptive Continuous Wavelet Transform and Fuzzy Logic Based High Precision Fault Detection of Broken Rotor Bars for IM

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1 Science Research 206; 4(6): htt:// doi: 0.648/j.sr ISSN: (Print); ISSN: (Online) Online Adative Continuous Wavelet Transform and Fuzzy ogic Based High Precision Fault Detection of Broken Rotor Bars for IM Ali Saghafinia, S. Hr. Kaboli 2 Deartment of Electrical Engineering, Majlesi Branch, Islamic Azad University, Majlesi, Iran 2 UM Power Energy Dedicated Advanced Centre (UMPEDAC), Wisma R&D, University of Malaya (UM), Jalan Pantai Baharu, Kuala umur, Malaysia address: Saghafi_Ali@yahoo.com (A. Saghafinia), kaboli0004@gmail.com (S. Hr. Kaboli) To cite this article: Ali Saghafinia, S. Hr. Kaboli. Online Adative Continuous Wavelet Transform and Fuzzy ogic Based High Precision Fault Detection of Broken Rotor Bars for IM. Science Research. Vol. 4, No. 6, 206, doi: 0.648/j.sr Received: November 24, 206; Acceted: January 6, 207; Published: February 7, 207 Abstract: This aer resents an intelligent fault detection based on adative continuous wavelet transform of broken rotor bars for Induction Motor (IM). Broken rotor bars, bearing decay, eccentricity, as motor faults aears as different frequencies in the stator current signals. The stator current and seed signals at deferent oeration conditions obtained from the winding function are analysed through the adative continuous wavelet transform (CWT) to detect the amlitudes and frequency comonents corresonding to different broken bar fault and load conditions. The adative coefficients of CWT based on the harmonics amlitude, are alied to train a fuzzy logic controller (FC) in simulation. Then, detection of the fault condition are done based on the adative CWT and trained FC in both simulation and real-time. The exerimental results are confirmed the simulation results and show the effectiveness of the roosed method to detect the motor fault conditions accurately. Keywords: Adative Continuous Wavelet Transform, Fault Detection, Squirrel Cage Induction Motor, Fuzzy ogic Controller, Broken Rotor Bars. Introduction Over the years, Induction motors (IM s) have some advantages features such as low cost, simle and robust construction and almost maintenance free. That is why, they are oular industry []. IMs suffer from different broken bar fault conditions due to the motor work continuously. Diagnosis of broken bars for IM has been investigated for a long time. Traditionally, fast Fourier transform (FFT) method is alicable to detect fault detection urose, widely [2-3]. However, in the case of load variation and seed changes, FFT of the rotor fault detection does not satisfy the aroriate accuracy, as the sli frequency varies with these variations [4, 5]. In addition, fault detection with FFT it is not able to evaluate the frequency detection on-line during transient state. Some works are focused on the broken rotor bar detection of IM using discrete wavelet transform (DWT) [6] and wavelet ackage decomosition (WPD) [7]. A few works has been reorted on continuous wavelet transform (CWT) for fault detection of IM [4]. However, in [4] authors resented a single hase stator current signal, which is not enough to detect the motor faults, accurately and the CWT was not adative in nature. Over the ast two decades, artificial intelligent algorithms have been utilized for motor drives, fault detection, rocess control [8-7]. In order to fuzzy fault detection considering the advantage of CWT, this aer resents an accurate fault detection through adative CWT and fuzzy logic controller (FC). The roosed fault detection method is checked in both simulation and exeriment at different oeration conditions. The results show the effectiveness of the online broken rotor bars fault detection of IM. The sueriority of this method to the conventional FFT method is also verified by the results. 2. Control Techniques The control techniques to train the FC and detect the fault for IM with broken rotor bars are shown in Figure and

2 Science Research 206; 4(6): Figure 2, resectively. The IM is first modelled by using the modified winding function method (WFM), under various load and relative failure conditions with considering the saturation effects [8]. The CWT rocesses the obtained stator current and seed signals with high resolution to obtain the amlitudes and frequencies corresonding to different broken bar fault and load conditions. The correction factors for the CWT are calculated based on the frequency of the current signal, which is discussed later. Based on the amlitudes and frequencies corresonding to the fault conditions first the FC is trained offline in simulation. Then, detection of the motor fault in real-time are done using the adative CWT and trained FC. A. WFM Based Modelling and Simulation of IM First the IM is modelled as accurately using WFM to identify the fault [9]. In this theory, a function called round function is obtained based on an initial angle on the stator erihery and the angle of rotor osition for all the coils with the same current. After calculating the round function for various windings, winding function should be then calculated for each winding. To do so, the related mean round function is subtracted from the main round function in one eriod. The self and mutual inductances of stator and rotor windings can be obtained based on the winding and the round functions. By using electrical and mechanical machine equations [20], all required electrical and mechanical motor characteristics are simulated using Matlab rogramming. Based on the aforementioned theory, the IM is modelled by using the modified WFM (the readers are referred to [20] for more details about the IM equations and model). Figure. Overall control algorithm to train the FC in simulation. Figure 2. Overall control scheme to detect the motor fault. B. Continuous Wavelet Transform (CWT) Continuous wavelet coefficients of an arbitrary function x(t) are calculated from the integration of the basic wavelet function between (-,+ ). According to the definition, wavelet coefficients are calculated as below. ψ ψ( t) a, b ψa, b C ( a, b) = x(). t () t dt =< x(), t () t > () where, Ψ a,b is the basic functions of the wavelet transform that is obtained from the main wavelet: ψ ab, () ( t b t = a ψ a ) (2) where, a and b are the scale and dislacement factors resectively. Ψ (t) is the Wavelet function which can be calculated from the following conditional equations: C ψ + + Ψ( ω) = dω < ω ψ() t dt = 0, ψ() t = where, Ψ ( ω) is the Fourier transform of Ψ ( ω). Alication of the Gaussian continuous wavelet function increases the accuracy of harmonic calculation significantly. The mathematical function of main Gaussian wavelet is written as follows: 2 (3)

3 59 Ali Saghafinia and S. Hr. Kaboli: Online Adative Continuous Wavelet Transform and Fuzzy ogic Based High Precision Fault Detection of Broken Rotor Bars for IM ψ() t = ex( jω t 0.5 t ) (4) g where,ω is the fundamental frequency of Gaussian wavelet function. C. Frequency Calculation of Harmonics Substituting the Gaussian wavelet function equation (4) in equation (), yield, where, C ψ( t) g t t 2 ( a, b) = t b 2 f0 x().ex(0.5( t ) ).ex( j2 π( )( t b)) dt a a t = at, t = at, t t = T In the above equation, T is wavelet function time. Considering (5), the harmonics frequency is obtained as, f f (5) = (6) a where, f 0 in the fundamental frequency of the wavelet function. In this aer, the scale factor a will be maximized at the lowest detected frequency (f ) and it will be minimized at the highest detected frequency (f H ). Thus, the following equation is obtained: a max = Ts f f T = f = (7) 0 0, amin fh where, T s is the signal rocessing time. Using (6), (7) scale factor can be obtained as, a scale f. Ts = (8) f. T where, f is the frequency, which is suosed to be detected. D. Amlitude and Phase Calculation of Harmonics Correction factors have a critical role in the accuracy of harmonic amlitude calculation. The amount and number of these coefficients deend on the detected bandwidth frequency. In fact, the accuracy of the harmonic calculation by using CWT deends on the estimated coefficients for the desired frequency bandwidth. th Considering (5), amlitude and hase of N harmonic are obtained as following equation. A n C n (a) n.c ψ(t) ((a) n) = (9) T Im( Cψ( t) ( a) n) θn = arctan Re( Cψ( t) ( a ) n ) th where, C n is correction factors of N harmonic. E. Adation of Correction factors (0) To calculate the correction factors in a secified frequency bandwidth, a sinusoidal single-frequency signal with desired frequency of the correction factors with unity amlitude is considered as the inut signal. The largest values of the calculated wavelet coefficients show the owerful corresonding frequency in the signal. Since the inut is a single frequency signal with unity amlitude, relacing one as the value of the harmonic amlitude in (9) leads to the desired frequency correction factor. So, the correction factor for a frequency f A is obtained as below. C f A T = () ( a). C (( a) ) f ψ( t) f A The linear interolation method is then used to calculate correction factors in the bandwidth frequency and for some frequencies in the form of integer or rational numbers in between two frequencies, deending on the desired accuracy. The obtained factors are used to correct the fault frequency amlitudes in different broken bar fault and load conditions. Correction factors deend on the resolution of scale factor, dislacement factor, minimum and maximum detected frequencies and samling frequency. These arameters are calculated by using trial and error method. The deendency of the correction factors on those arameters can be eliminated by selecting the aroriate frequency bandwidth to detect the fault recisely. However, the sensitivity of correction factors is different for each arameter. F. Calculation of Fault Frequencies The frequency comonents of the fault can be exressed as, A fb = fe ( ± 2 s ) (2) Where e f main frequency and s is sli coefficient. Considering the stator current sectrum which obtained from the roosed adative CWT, the frequencies and amlitudes corresonding to different broken bar fault conditions are calculated accurately using the following stes: ste: Calculate the fault frequencies from the equation (2) (fb). ste2: Calculate the maximum and the minimum seed in steady state to obtain the frequency variation domain f = maximum frequency minimum frequency. Ste3: Search for the maximum frequency amlitude in interval (fb- f, fb+ f) for uer and lower side fault frequencies from the stator current sectrum. Ste5: Search the corresonding frequencies to maximum amlitudes of the stator current sectrum. Ste6: Save the amlitudes and frequencies of the last 2stes. Ste7: If the ossibilities for all different broken bar fault and load conditions are considered go to sto, if not go to Ste. In the above stes, the sli frequency is calculated accurately in different broken bar fault and load conditions which concluded the aroriate accuracy of fault detection frequency.

4 Science Research 206; 4(6): Design of Secific Fuzzy ogic Controller As shown in Figure, the inuts to the FC are low side frequencies (f ), high-side frequencies (f h ) and their amlitude (A ),(A h ) and the outut is the number of broken rotor bars. The structure of the FC is shown in Figure 3. The outut of the FC can be exressed mathematically as a function f( x ) as follows: f( x) = M N y = i= M N = i= ( µ ( x)) A i µ ( xi) Ai i (3) where, y and µ ( ) are initializing value and degree of A x i i each membershi function, x i resectively. Figure 3. The FC structure. The membershi functions of inuts include f, f h and their amlitude (A ), (A h ), is shown in Figure 4. Interval of these membershi functions and their fuzzy sets are shown in (4)- (7), resectively. min = min( f ) 2 max = max( f ) delta = min = min( f ) 2 H max = max( f ) + 2 H delta = min = min( A ) max = max( A ) delta = min = min( A ) H max = max( A ) H delta = (4) (5) (6) (7) where, the min and max values are determined from all the values obtained from CWT analysis. Outut membershi functions are selected by trial and error as shown in Figure 5. Also, outut of fuzzy system which is the number of broken bars varies from 0 to 0 and is defined as below. [ ] (8) Fuzzy rules are generally in the form of if-then which i th rule is written as below. ( R): if f is A and f is B and A is C i i H i i and A is D then Y is E H i i (9) TABE ists fuzzy rules based look-u table resulted from CWT analysis. There are total 48 rules which are generated based on simulation tests with known data. 0.8 Degree of Membershi minmum Delta maximum Frequency or amlitude of inut Figure 4. Inut membershi function for the FC.

5 6 Ali Saghafinia and S. Hr. Kaboli: Online Adative Continuous Wavelet Transform and Fuzzy ogic Based High Precision Fault Detection of Broken Rotor Bars for IM 0.8 Degree of Membershi Number of broken bars Figure 5. Outut membershi function for the FC. 4. Training Algorithm for FC Fuzzy logic controller (FC) is trained based on the outut of the adative CWT as shown in Figure 2. In the training rocess the triangular membershi functions is changed to Gaussian functions to obtain the otimum outut based on gradient steeest descent training method. The objective of training the FC membershi functions is to determine the function f( x ) so that the error between desired f( x 0) and actual outut y 0 is minimized. f( x) = In (20), is M N xi x i 2 y ex( ( ) ) = i= σi M N xi x i 2 ex( ( ) ) = i= σi y, e x i, and (20) [ ( 2 0 ) = f x y0 ] (2) 2 σ i are initializing value and in (2) th outut error. To achieve this goal these stes are e needed: Ste: Identifying fuzzy rules and initializing values x i, y, and σ i. Ste2: Oututs calculation based on the inuts of fuzzy th model in q inut ste as shown in (22)-(24). Table. Rule based matrix for the flc. Rule Number A i B i C i D i E i Rule Number A i B i C i D i E i

6 Science Research 206; 4(6): o ( X ; Y ), =,2,... q = 0,,2,... (22) Z n xoi xi ( q) 2 = ex[ ( ) ] (23) i= σi ( q) M M a ( ),, ( 0) (24) b = = a = y q Z b = Z f x = e y ( q + ) = y ( q) α q, =,2,..., M y (25) e f a = ( f( xo) yo). = [ f( x0) yo] a y y b (26) e xi ( q + ) = xi ( q) α q (27) x i th Ste3: Parameters correction in q ste (identifying arameters value in ste q + ) as shown in (25-29) e f Z = [ f( x0) y0].. i Z xi x (28) e σi ( q + ) = σi ( q) α q = σ σ f x0 y0 oi i i ( q) α [ y ( q) f( x0)]. Z. 3 b σi ( ) 2[ x x ( q)] i =,2,.., n, =,2,..., M i 2 (29) Ste4: Returning to second ste and relacing q with q + to decrease f( x0) y0 value to ε or reaching to determined error. Ste5: Returning to second ste and relacing with + to calculate arameters of new inuts for inut-outut air( X0 ; y0 ) Ste6: Relacing with = and reeating stes 4 and 5 to obtain the better fuzzy model outut Simulation Results First, a samle comarison of the roosed adative CWT and FC based analysis with the conventional FFT based analysis is done based on distorted signal with main frequency equal to 50Hz. Amlitudes and hases of harmonic frequencies were chosen arbitrarily. The comarative results are shown in TABE 2. From TABE 2, it is found that the amlitude, frequency, and esecially hase accuracy of the harmonics in the roosed method is more accurate than FFT method [2]. Table 2. Comarison of the roosed CWT and conventional FFT methods. Frequency (Hz) Amlitude (A) Phase (degree) true values FFT The adative CWT true values FFT The adative CWT true values FFT The adative CWT The erformance of the roosed CWT and FC based fault detection method is tested in simulation at different load and broken bar fault conditions. The motor arameters used for simulation is shown in TABE 3. Table 3. Test motor secifiactions. Motor Secifications Parameters Value Parameters Value P R 4 kw V V f 50 Hz Pole Paris 2 N R 380 rm R s.4 Ω s Ω R R.4 Ω R Ω m 0.7 Ω J 0.05 Kg.m 2 F Kg.m 2 /s The motor with more than five broken bars is not required to be discussed, because in this case the motor fault and maloeration is obvious. That is why; various simulated conditions only include healthy status, one broken bar, two broken bars with 7 ermutation, three broken bars with 8 ermutation, four broken bars with 3 ermutation and five broken bars with ermutation, which in total of 5 ermutation. Some samle results are resented below. Figure 6 shows simulation of stator current and motor seed for both healthy and faulty motor with two broken bars. The winding function theory is used to calculate the stator current and seed. It is hard to distinguish between healthy and faulty motors when there are only two broken rotor bars. Figure 7 illustrates the frequency sectrum of the stator current for healthy and faulty motor with five broken bars at full load while stator current for each condition with 600 Hz samling frequency and selective bandwidth frequency from 20 to 300 Hz is rocessed with CWT and frequency sectrum is obtained in each condition using trial and error

7 63 Ali Saghafinia and S. Hr. Kaboli: Online Adative Continuous Wavelet Transform and Fuzzy ogic Based High Precision Fault Detection of Broken Rotor Bars for IM method. As seen in Figure 7 (a), the frequency comonents around the main frequency cannot be seen aarently. But, the frequencies with the very low amlitudes can be found around the main frequency according to the mentioned stes in section ІІ-F. From Figure 7 (b), the low and high side frequencies can be clearly seen around the main frequency which obtained from the mentioned stes in section ІІ-F. From Figure 7 (b), it can also be seen that the rated sli frequency is increased due to faulty motor with five broken bars based on equation 2 (s=3%) as comared to the healthy motor based on TABE 3 (s=8%). Figure 6. Motor seed and current resonses for both healthy and faulty motors with two broken bars based on modified WFM method. Figure 7. Stator current sectrum for healthy (a) and faulty motor with five broken bars (b) at full load for the roosed adative CWT method. Figure 8 comares the harmonic amlitudes at low and high frequencies from healthy condition to five broken bars of the simulated motor for the roosed adative CWT. Figure 9 and Figure 0 show comarison between FFT and the roosed adative CWT for low side amlitudes and their frequency, resectively from healthy condition to five broken bars. It is seen clearly from Figs. 8, 9 that the harmonic amlitudes are increasing with the increased number of rotor broken bars. It is also seen from Figure 8 that the low side amlitudes are always higher than the high side amlitudes due to the currents asymmetry, which is risen by increasing the number broken bars [25]. From Figure 9, it is also seen that the harmonic amlitudes obtained from both FFT and the roosed adative CWT analysis are not same due to the

8 Science Research 206; 4(6): inaccuracy in FFT, which was shown earlier in TABE 2. With increasing the number of the rotor broken bars, the roduced torque by the rotor bars is decreased. Therefore, the motor seed is reduced which decreases the low side frequencies as shown in Figure 0 for both FFT and the roosed adative CWT methods. However in the healthy motor, unlike to the faulty motor, the seed variations are almost equal to zero and the value of the low side frequency does not follow these variations which can be clearly seen in Figure 0 for the roosed method. Furthermore it is clearly found out from Figure 0, the differences of the low side frequencies between the FFT and the roosed adative CWT methods are increasing with the increased number of the rotor broken bars. These differences are related to the seed variations which considered for calculating of the harmonic comonents in the roosed method. It is noteworthy that with increasing the number of the rotor broken bars, the seed variations are increased. Under the foretold scenario, the roosed method shows a high accuracy to calculate the harmonic comonents and it is more accurate than the conventional FFT. Figure 8. Comarison between high and low side amlitudes of the roosed adative CWT from healthy to five broken bars. Figure 9. Comarison of the low side amlitudes between FFT and the roosed adative CWT method from healthy condition to five broken bars.

9 65 Ali Saghafinia and S. Hr. Kaboli: Online Adative Continuous Wavelet Transform and Fuzzy ogic Based High Precision Fault Detection of Broken Rotor Bars for IM Figure 0. Comarison of the low side frequencies between FFT and the adative CWT roosed method from healthy condition to five broken bars. To show the erformance of the trained FC, the tested data including harmonic comonents of 3 broken bars (, 6, 7), 4 broken bars (, 8, 9, 0), and 5 broken bars (,, 2, 3, 4) at full load is used as inuts for the FC. TABE 4 shows Outut results of the trained FC for simulation tests of the roosed method. This Table confirm the roer erformance of the trained FC and adative CWT. It is found that the roosed trained FC can detect the fault accurately in simulation. Traditionally in FFT, the fault frequencies are calculated based on (2) and the constant sli, which is calculated based on average steady-state seed of the motor. However, the sli changes during fault condition as the motor seed changes. Therefore, the conventional FFT method rovides inaccurate result for fault frequencies. In this aer, the adative CWT method is used to calculate the accurate fault frequency based on the Stes mentioned in section ІІ-F. Finally, after finding the frequency range and side frequencies through sli calculation, actual high and low frequencies and the corresonding stator current amlitudes are obtained. 6. Exerimental Result In order to test the erformance of the roosed adative CWT and FC based fault detection method an exerimental setu is built for IM drive. The hardware schematic for the exerimental setu is shown in Figure. The tested motor has 26 stator bars and among them 5 bars were broken manually deending on the requirement, the broken bars can be fixed by welding. The samling frequency of 0 khz is used for the current signal. The load on the motor is adjusted with the Foco Brake in exeriment. Since adjusting load using the Foco Brake does not have enough accuracy, the load is exressed by the linguistic terms. For exerimental test, the very high load (VH) is considered for 90% to 00% of the full load current, high load (H) for 75% to 90%, medium load (M) for 50% to75%, low load () for 25% to 50%, and very low load (V) for 0% to 25%. It is noteworthy that the load is alied for the faulty motor so that the harmonic contents can easily be seen. Figure. Hardware schematic for exerimental tests of the roosed fault detection algorithm. Figure 2 and Figure 3 illustrate the exerimental frequency sectrum of the stator current for healthy and faulty motor with five broken bars at no load and very high load, resectively. It is clearly seen that there is no harmonic content for healthy condition. But for faulty motor there are low and high side harmonic contents in stator current. Figure 4 shows low and high side frequency amlitudes of the roosed method from healthy condition to five broken bars in exerimental test. It is found from Figure 4 that the low side amlitudes are higher than high side amlitudes in real time, which also validates the simulation results. Figure 5 shows low frequency amlitudes between simulation and exerimental results from healthy condition to five broken bars for the roosed method. It is found from

10 Science Research 206; 4(6): Figure 4 that the harmonic amlitudes in real-time is higher than simulation results. It is due to the welding of broken bars in several tests which increases the resistance of rotor bars more than its original value. The motor is tested for healthy,, 3, and 5 broken rotor bars at different load conditions. Table 5 shows the summary of exerimental test to diagnose the healthy or faulty condition of the motor at different load conditions. It is found from Table 5 that the roosed adative CWT and trained FC can detect the healthy condition or number of broken rotor bars for IM accurately in real-time. Table 4. Outut result of the trained FC for simulation test of the IM with broken rotor bars. The trained FC inut The trained FC diagnose Uer side amlitude Uer side frequency ower side amlitude ower side frequency Broken bar 3 broken bars ,6,7 4 broken bars ,8,9,0 5 broken bars ,,2,3,4 Figure 2. Stator current sectrum in healthy condition in no load for the exerimental test of roosed method. Figure 3. Stator current sectrum with five broken bars in very high load for the exerimental test of roosed method. Figure 4. ow and high side frequency amlitudes of the roosed model from healthy condition to five broken bars in exerimental test.

11 67 Ali Saghafinia and S. Hr. Kaboli: Online Adative Continuous Wavelet Transform and Fuzzy ogic Based High Precision Fault Detection of Broken Rotor Bars for IM Figure 5. Comarison of low side amlitudes between simulation and exerimental results from healthy condition to five broken bars for the roosed method. Inut to the FC Table 5. Outut result of the trained FC for analysed motor in exerimental test. Fuzzy system diagnose Uer side amlitude Uer side frequency ower side amlitude ower side frequency oad condition Healthy motor Very low load Healthy motor Medium load Healthy motor High load broken bar Very low load broken bar High load 3 broken bars High load 5 broken bars High load 5 broken bars Very high load 7. Conclusion An online adative continuous wavelet transform and fuzzy logic based high recision fault detection method for three hases IM has been resented in this work. Based on the motor current signature analysis at different broken bar fault and load conditions, the CWT generates the harmonic amlitudes and frequencies of the motor stator current. The coefficients of CWT are adated online based on the harmonics amlitude, which are the outut of CWT. Based on this information, first the FC is trained in simulation. Then, the trained FC detects faulty or healthy condition of the IM in real time. The results found that the roosed adative CWT based analysis is more accurate than the conventional FFT based analysis to detect the harmonic comonents of a signal and the roosed adative CWT and FC based fault detection method can detect the IM fault accurately. Therefore, this method could be a otential candidate for real-time fault detection. References [] S. S. Sebtahmadi, H. Pirasteh, S. H. Aghay Kaboli, A. Radan and S. Mekhilef, "A 2-Sector Sace Vector Switching Scheme for Performance Imrovement of Matrix-Converter- Based DTC of IM Drive," in IEEE Transactions on Power Electronics, vol. 30, no. 7, , July 205. [2] M. Riera-Guas, M. F. Cabanas, J. A. Antonino-Daviu, M. Pineda-Sanchez, and C. Garcia, "Influence of Nonconsecutive Bar Breakages in Motor Current Signature Analysis for the Diagnosis of Rotor Faults in Induction Motors," Energy Conversion, IEEE Transactions on, vol. 25, , 200. [3] K. S. Gaeid, H. W. Ping, M. K. Masood, and M. A. Saghafinia, "Induction motor fault tolerant control with wavelet indicator," in Transortation, Mechanical, and Electrical Engineering (TMEE), 20 International Conference on, 20, [4] P. Konar and P. Chattoadhyay, "Bearing Fault Detection of Induction Motor using Wavelet and Suort Vector Machines (SVM)," Alied Soft Comuting, 20.

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