A Novel Technique for Rotor Bar Failure Detection in Single-Cage Induction Motor Using FEM and MATLAB/SIMULINK

In this article, a new fault detection technique is proposed for squirrel cage induction motor SCIM based on detection of rotor bar failure. This type of fault detection is commonly carried out, while motor continues to work at a steady-state regime. Recently, several methods have been presented for rotor bar failure detection based on evaluation of the start-up transient current. The proposed method here is capable of fault detection immediately after bar breakage, where a threephase SCIM is modelled in finite element method FEM using Maxwell2D software. Broken rotor bars are then modelled by the corresponding outer rotor impedance obtained by GA, thereby presenting an analogue model extracted from FEM to be simulated in a flexible environment such as MATLAB/SIMULINK. To improve the failure recognition, the stator current signal was analysed using discrete wavelet transform DWT .


Introduction
Induction motors IMs play an important role in many industrial processes.Hence, IM failures should be detected at early stages before they become catastrophic and lead to shutdowns and enhanced maintenance costs.Condition monitoring is desirable for increasing machinery availability, reducing consequential damage, and improving operational efficiency 1-3 .IM faults may occur in three main parts of the machine; stator, rotor, and bearings.Rotor bars are commonly broken in squirrel cage induction motor SCIM due to several causes 4, 5 , including 1 thermal stress, 2 magnetic stress, 3 residual stresses from manufacturing, 4 dynamic stress from shaft torques, 5 mechanical stress owed to bearing failure, and 6 environmental stresses such as moisture.
In terms of condition monitoring, fault detection in SCIM is studied in two categories; steady-state condition and during start-up transient condition.For many years, researchers have focused on fault detection methods which are based on steady state such as FFT.Recently, following progress in signal processing, methods based on study of the startup transient current have attracted attention.Traditional methods for monitoring the rotor conditions are based on frequency domain analysis of stator currents 6, 7 , mechanical vibrations 8 , fluxes on search coils 9 , and rotor speed 10 in steady state.Motor current signature analysis MCSA is used by many researchers due to its availability and simplicity.The broken bars induce some harmonic components with special frequencies in stator currents sideband frequencies , as below where s is the slip and f is the supply frequency.Bar breakage occurs when the difference between the amplitude of fundamental frequency and the left sideband component is less than 50 dB 11 .The frequency analysis such as FFT, STFFT and recently multiple signal classification MUSIC and zoom-MUSIC are appropriate techniques to detect the sideband frequencies in stator current spectrum 12 .DWT is used by 18 who has suggested that "the frequency of the left sideband varies within a wide range during the start-up process and its amplitude reaches values that are several times higher than those in a stationary regime, and this is true for any load condition."The evolution of some frequencies allows the diagnosis and identification of broken rotor bars in IM during the startup transient.According to the frequency of sideband harmonic i.e., f L 1 − 2s f , when the motor is switched on s 1 , the left sideband component is equal to supply frequency.However, f L becomes 0 Hz when slip is reached half its value, and when the speed increases, the slip drops and f L almost reaches again the supply frequency 18 .This approach needs a minimum start-up time to avoid the electromagnetic transient which occurs immediately after start-up and masks the left sideband component 19 .
An efficient condition monitoring system should be able to detect and use measurements taken immediately after fault occurs.This is because detection of potentially catastrophic faults in incipient stages prevents large power and production losses and also reduces maintenance costs.In this study, a fault detection system in SCIM is developed by assuming that a bar is suddenly broken, while SCIM operates in a steady state.Providing that the fault is not diagnosed at its early stages, fault will propagate towards the adjacent bars, causing local hot spots and interbar currents to appear leading to further damage to the magnetic circuit.Diagnosis of the fault in the incipient steps is the key solution to control and protect the SCIM.The developed diagnosis system here detects broken rotor bars immediately after breakage at rated value condition.However, the study of broken bars immediately after breakage cannot take place in reality, due to lack of access to the rotor during the operation of SCIM.

SCIM Analysis Using Finite Element Method
An effective diagnosis method requires an accurate and reliable SCIM model capable of revealing accurately the behaviour of the machine.Within the last few decades, FE method FEM has proved itself as an accurate and inexpensive technique for SCIM analysis by modelling material properties, nonlinearity, and complex structures of the machine such as rotating parts 20, 21 .In this regard, FE simulation has provided a powerful tool as well as a good benchmark to study faulty machine behaviours, by comparing the available monitoring techniques and signal processing methods devised for this purpose.However, despite FEM capability for accurate modelling of SCIM through the well-known Maxwell's equations, it requires an extensive computational time due to the involved geometrical complexities of machine parts.Principles of symmetry are employed wherever possible on machine parts to reduce the computation time.However, in the case of broken bars, this cannot be carried out due to asymmetric magnetic fields imposed by the fault.Therefore, to ensure the correct magnetic field distribution, the whole machine cross-section should be analysed.SCIM specifications required for this study are presented in Table 1. Figure 2 shows the whole cross-section of the simulated SCIM in the Maxwell2D 22, 23 , supplied by a symmetrical three-phase sinusoidal source with the stator windings in each of the three phases having identical turn number N 180 .Various sections of the machine are divided into small parts by mesh nodes as illustrated in Figure 3 for rotor bars, air gap, and stator slots.The FE program Maxwell2D is used here to evaluate the influence of the broken rotor bar BRB fault on motor performance and generate virtual data in an accurate and cheap manner.

Broken Rotor Bars Modelling
Proper modelling of broken bars is needed for accurate and reliable diagnosis.In this context, resistance of the broken bar is assumed to be as large as possible in the FEM, considering the fact that in reality there is an interbar current among bars, leading to increased Joule losses in the adjacent bars.Furthermore, distribution of flux lines around the broken bars is changed.increment resistance corresponding to the broken bars to be considered in the external rotor circuit is computed as follow 25 : where, n is the number of contiguous broken bars, N is rotor bar number, N s is turn number of stator phase winding, and R b is the rotor bar resistance.However, ΔR inc alone is not accurate enough, and since computation of the broken bar resistance and inductance ΔL inc is inherently a complicated process for which in general there is no reliable formula, genetic algorithm GA has been employed in this new method to obtain both inductance and resistance of the failed bars simultaneously as far as possible.The method for finding fault impedance is described in the next section.

Genetic Algorithm and Proposed Objective Function
GA is a global optimization and search technique motivated by the process of genetics and natural selection.In GA, a set of chromosomes population is led to evolve in a biased manner toward the fittest chromosomes based on special rules 26, 27 .The flowchart of the GA used in this work is presented in Figure 5.The goal is to search for an optimal solution while finding faulty broken bar impedance resistance and inductance and minimizing the objective function.To begin the GA process, an initial population size of 100 is randomly selected in the interval 0, 0.  FEM is also used and the mutation rate of 20% is selected.The objective function is then defined as follow: Objective Function where speed Max is the output speed in FEM using MAXWELL software, speed Mat is the output speed by MATLAB, and N is the total number of samples.Figure 6 shows a schematic diagram of the proposed method for finding the fault impedance.As illustrated in Figures 7 and 8, using the simulating setup for modelling validation in both healthy and faulty conditions, an analogous model is created in MATLAB/SIMULINK for both healthy and faulty cases, where faulty impedance is obtained by GA and the value of the resistance and inductance for one broken bar at rated condition is

Discrete Wavelet Transform
The excellent characteristic of the wavelet theory is that its frequency spectrum varies in time, which makes it suitable for analysing the nonstationary signals 28, 29 .Time evolution of the frequency components from the stator current signal depends on this specific phenomenon.
For instance, evolution of the left sideband frequency, during the start-up for the case of rotor asymmetry, evolves in a particular way; when the machine is switched on, it is equal to the supply frequency.Later, when the slip equals 0.5, it reaches 0 Hz and increases again close to the supply frequency, once the steady-state regime is achieved 18 .The discrete wavelet transform DWT decomposed the sampled signal x n as: where ϕ n denotes the scaling function, ψ n is the mother wavelet, and ϕ i 0 ,j n 2 i 0 /2 ϕ 2 i 0 n − j is the scaling function at a scale of s 2 i 0 shifted by j.Also, ψ i,j n 2 i/2 ψ 2 i n − j is the mother wavelet at a scale of s 2 i shifted by j, a i 0 ,j are the approximation coefficients at a scale of s 2 i 0 , and similarly d i,j are the detail coefficients at a scale of s 2 i 30 .As shown in Figure 9, the frequency range of the approximation signal a n , is in the interval 0, 2 − n 1 f s , and the detail d j contains the components whose frequencies belong to the interval 2 − j 1 f s , 2 −j f s , where f s is the sampling frequency.To decrease the overlap between bands, a high-order wavelet Daubechies 44 is used in this study to analyse the stator current signal immediately after bar breakage.DWT is able to locate accurately the frequencies and their exact time locations.Therefore, it can detect unforseen transient changes that might occur in any steady state due to its time-frequency decomposition.

Simulation Result
Simulation of SCIM for rotor bar failure detection was carried out to validate the proposed method.Figure 10 shows the schematic for detection of broken rotor bars in SCIM, shortly after bar breakage in MATLAB/SIMULINK.As can be seen, the broken bar failure is modelled by connecting impedance to the rotor end.To model the bar failure quickly after breakage, an ideal switch is used in the outer circuit of the rotor.Figure 11 shows the simulation result of the current curve of an ideal switch used for modelling bar failure during SCIM operation without having a significant effect on the motor performance.It is assumed that a bar is broken two seconds after the motor has reached steady-state operation.
Considering the advantages offered by DWT, in signal processing, it was used for stator current signal of the studied SCIM as depicted in Figure 12, in which healthy and broken bars conditions could be distinguished.Upon the occurrence of a fault, the variations in the DWT coefficients become higher than what they were prior to this incident.The seventh approximation, a 7 , corresponding to the low-frequency components below 60 Hz , shows a meaningful variation following the fault.The peak variations after fault occurs are clearly seen in the sixth detail signal d 6 which corresponds to the frequency range between 78 Hz to 156 Hz and other detail signals.Much higher variations, representing the high-frequency content of the current signal, can be seen in details one to five d 1 -d 5 which cover the frequency range between 156 to 5000 Hz. Figure 12 shows how the harmonics appear in the wavelet coefficients after broken rotor bar fault.

Conclusion
Fault detection in incipient stages is important for control and protection of the SCIM.This paper aims to develop a diagnosis system of bar failure immediately after its breakage.By using FEM, GA, and MATLAB, an accurate model is simulated for fast fault detection using DWT to the stator current.Wavelet decomposition shows the meaningful variations in details numbered 1-5 and an approximation at level 7 referred to as a 7 , which correspond to the faulty bandwidth frequencies.Simulated start-up current DWT for full-load machine indicates that the breakage in one bar can be diagnosed correctly in its incipient stages.The simulation results indicate that the proposed technique is able to simulate accurately bar failure immediately after bar breakage.

Figure 1
shows how STFFT is able to diagnose the broken bars in a full-load IM.The main drawbacks to STFFT 13 include 1 load dependence of the approach and 2 false diagnosis caused by ball bearing faults and voltage/load fluctuations.Many researchers have tried to improve the diagnosis by introducing a new criterion 14 or using such higher-frequency components as fault indicators which are not affected by load 15 .In the last few years, start-up transient current has been studied considering the progress made in signal processing techniques.Burnett et al. 16 and Watson and Paterson 17 have shown the superiority of the wavelet decomposition over other signal processing techniques for analysing the nonstationary signals.Discrete wavelet transform

Figure 1 :
Figure 1: Frequency spectrum of stator current for rotor broken bar case in full load.

Figure 5 :
Figure 5: Flowchart of a GA for finding the impedance.

Figure 6 :Figure 7 :
Figure 6: Structure of the proposed technique in this work.

Figure 8 :
Figure 8: Comparison of Maxwell2D and MATLAB curves in motor with one broken bar full-load operation .

Figure 9 :
Figure 9: Frequency range of details and approximations in DWT.

Figure 12 :
Figure 12: Wavelet decomposition of stator current signal for one broken rotor bar at rated condition.

Table 1 :
Characteristics of the studied induction motor.
1 .The faulty resistance and inductance that should be optimized is being fitted as chromosome.Hence, MATLAB/SIMULINK is executed for all chromosomes to obtain the speed curve in the faulty condition, and each chromosome's worth is assessed by the objective function.It has to be pointed out that, for more accuracy and close relationship between real and simulated case,