Wavelet-Based Analysis of MCSA for Fault Detection in Electrical Machine

Early detection of irregularity in electrical machines is important because of their diversity of use in different fields. A proper fault detection scheme helps to stop the propagation of failure or limits its escalation to severe degrees, and thus it prevents unscheduled down‐ times that cause loss of production and financial income. Among different modes of fail‐ ures that may occur in the electrical machines, the rotor-related faults are around 20%. Successful detection of any failure in electrical machines is achieved by using a suitable condition monitoring followed by accurate signal processing techniques to extract the fault features. This article aims to present the extraction of features appearing in current signals using wavelet analysis when there is a rotor fault of eccentricity and broken rotor bar. In this respect, a brief explanation on rotor failures and different methods of condition moni‐ toring with the purpose of rotor fault detection is provided. Then, motor current signature analysis, the fault-related features appeared in the current spectrum and wavelet trans‐ form analyses of the signal to extract these features are explained. Finally, two case studies involving the wavelet analysis of the current signal for the detection of rotor eccentricity and broken rotor bar are presented. This case study proposes a feature extraction system for broken rotor bar detection using wavelet packet coefficients of the stator current. It is shown that in a faulty case, the amplitude in specific side bands increases and dominant features of signals can be extracted for fault diagnostics. The results of this study indicate that the energy, kurtosis and RMS value of WPD coefficients are the appropriate features for detecting broken rotor bar in particular bands.


Introduction
Electrical machines are widely used for many industrial processes and play a non-substitutable role in a variety of industries [1][2]. In spite of their reliability and robustness, electrical machines are still prone to failures due to the exposure to a wide diversity of strict conditions and environments, incorrect operations, or even manufacturing defects [3]. These faults, gradual deterioration, and failures can lead to motor interruption, if left undetected, and their resulting unplanned downtime is very expensive. Early detection of irregularity in electrical machines with proper fault diagnosis schemes will help prevent high-cost failures, thereby decreasing the cost of maintenance and preventing unscheduled downtimes. However, stopping the propagation of the fault limits its escalation to severe degrees, which results in loss of production and financial income.
The fault identification schemes are basically based on data collection of electrical machines followed by signal processing. The condition of an electrical machine is examined from data that are acquired through sensors and supportive equipment methods. By using a suitable signal processing technique, each fault can be then detected via a specific feature present in the measured signal of a faulty motor when compared to a fault-free one. Hitherto, a number of data acquisition techniques, which display a certain parameter of the electrical machine, have been established. Essentially, the efficiency of a data acquisition method is characterized by its accuracy, cost, and importantly its capability to quantify the fault. On the contrary, condition monitoring based on data acquisition techniques requires the user to have adequate knowledge and proficiency to differentiate a normal operating condition from a potential failure state. The key step, but a difficult task, in the fault detection of electrical machines is to extract the fault-related features from the acquired signal and identify the condition of motor. Fault-related features are parameters derived from the acquired data that specify the existence of failure in device. The current signal of electrical machine is non-linear and non-stationary with strong noise interference; hence, the energy of early signal is too low to extract faultrelated features in time domain [4]. Advanced signal processing methods based on analysis of time-frequency domain have been proposed as effective approaches for fault detection in electrical machines [5].
The focus of this chapter is on the extraction of features present in the current spectrum of electrical machine when one of two important rotor faults, eccentricity and broken rotor bar, exists. To extract features from the current spectrum in the presence of these faults, an advanced signal processing method, wavelet packet analysis, is used. In this regard, the fundamentals related to the detection of these two faults using wavelet packet analysis of current signal are explained in the following sections.

Rotor faults
From the investigations on different failure modes in electrical machines, the rotor-related faults are around 20% of failures may happen in the motor [6]. The rotor is exposed to different types of stresses that seriously affect its normal condition and subsequently create faults in it. Bonnett and Soukup explained the stresses that motors are subjected to and their unfavourable causes [7]. Failures in rotor are classified into eccentricity of rotor, crack and/or breakage of rotor cage bars, and crack and/or breakage of end rings and rotor bow [8]. These irregularities bring specific secondary failures that cause serious faults in electrical machines. Moreover, these types of faults may not show any symptoms during early stage until propagating to the next step and leading to the sudden collapse [9][10][11]. In recent years, rotor faults have been increasingly studied for developing advanced techniques that permit online early detection and diagnosis of motor faults to avoid any negative consequences of unexpected shutdowns, but this area still needs more research because of the complexity of the motor during the runtime. In this section, a brief description of different rotor faults is provided.

Rotor eccentricity
In a fault-free machine, the rotor is centre aligned in the stator bore that results in uniform air gap between the stator and rotor. In fault-free electrical machines, the rotation centre of the rotor is the same as the geometric centre of the stator bore. As a result, the rotor symmetrical axis (C r ), stator symmetrical axis (C s ), and rotor rotational axis (C g ) coincide with each other, and thus the magnetic forces are balanced in opposite directions. Rotor eccentricity, displacement of the rotor from its centred position in the stator bore, generates an asymmetric air gap between the stator and rotor [12]. The rotor eccentricity also produces unbalanced magnetic pull (UMP), which is a radial magnetic force on the rotor shaft. The UMP also pulls away the rotor from the stator bore centre, thus causing excessive stress on the electrical machine [13,14]. Eccentricity commonly presents in rotating electrical machines, and the maximum permissible level of eccentricity is defined, which is 5 or 10% of the air-gap length [15]. If eccentricity exceeds the permissible level, it will increasingly damage the winding, stator core and rotor core in the motor due to rubbing of the stator with the rotor [12,14]. Three different types of eccentricity occur in an electrical machine: static eccentricity, dynamic eccentricity, and mix eccentricity. As an example, static eccentricity is explained next.
Static eccentricity in electrical machines occurs when the rotor symmetrical axis is concentric with the rotor rotational axis; however, they are dislocated with respect to the stator symmetrical axis; hence, the position of minimum radial air-gap length is fixed. In this state, the mutual inductances across the stator and rotor as well as the self-and mutual inductances among the rotor phases are related to the angular position of the rotor [16]. The implication of static eccentricity fault in motor is depicted in Figure 1.
Static eccentricity can be due to numerous motives such as elliptical stator core, wrong placement of the rotor or stator at the setup or subsequent of maintenance, incorrect bearing positioning, bearing deterioration, shaft deflection, housing imperfection, end-shield misalignment, excessive tolerance, and rotor weight or pressure of interlocking ribbon [17][18][19]. Static eccentricity leads to second failures which cause drastic harm to the rotor, stator core and windings. The radial forces in the static eccentricity condition produce a steady UMP in the radial route across the motor because the reluctance of the magnetic flux path decreases with the transmission of flux on the side of tiny air gap [20]. Albeit, the winding current induces more magnetic flux that causes a stronger pull and leads to the expansion of the air gap on the opposite side where the reluctance increases, thereby decreasing the flux and magnetic side pull. Therefore, the UMP compels the rotor to move toward the area of the narrowest air-gap length. During abrasion, the stator core subsequently generates abnormal vibration and severely damages the rotor, windings and the stator [7]. Consequently, the static eccentricity causes acoustic noise, premature failure in the bearing, rotor deflection and bent rotor shaft.
where C s C g → is the vector of static transfer which is invariant for rotor angular positions and g is the uniform air-gap length.

Rotor bar breakage
The breakage of rotor bars is one of the important failures in the rotor cage of electrical machines. During the operation of electrical machines, rotor bars may be broken partially or completely. The main reasons for bar breakage include electrical, mechanical, and environmental stresses during the operation of electrical machines and/or improper design of rotor geometry. Once a bar breaks, the stress increases and deteriorates the condition of the neighbouring bars progressively. Such a destructive process can be prevented, if any crack in the bar is detected early [21]. Typical causes of rotor bar breakage are referred as follows [22]: high thermal and mechanical stresses, direct online starting duty cycles for which the rotor cage was not well designed to endure against the stresses, imperfections in design and fabrication process of the rotor cage bars. Any failure in rotor bars itself causes unbalanced currents and torque pulsation and, therefore, decreases the average torque [23].
The rotor bars are short-circuited on both sides of the rotor by end rings. Depending on the type of squirrel cage in the motor, the source of failures in the end ring differs, in die-cast aluminium rotors caused by porosity of casting and in fabricated rotor cages caused by poor end-ring joints during manufacturing. Once the preliminary failure occurs, localized heat may extend to the rotor cage excessively. Therefore, the fault propagation is continued by multiple start-ups similar to load variations, which create high centrifugal forces. Accordingly, end-ring faults cause a drastic increase in the current and speed fluctuation [21].

Rotor bow
Any irregular thermal variation (heating or cooling) and unfavourable thermal distribution of the rotor during operation of electrical machines may bow the rotor [24]. The bow created in the rotor prevents sufficient alignment in the motor and generally produces a preload on the bearings. Bend locations in the rotor cause major failures in other parts of the motor [25]. The bow in the rotor is classified as local and extended [24]. When an asymmetrical heating is confined to a part of the rotor, a local bow is generated. For example, rotor-to-stator rubbing can generate a local asymmetric thermal distribution, which causes the local bow. When an asymmetrical heating extends along the rotor, an extended bow is generated. Long-lasting gravity effects on off-line machines generate rotor bow classified as an extended bow, when unsuitable rotor straightening turning system is not used [24]. Since the rotor is limited by two bearings, extended bow commonly causes a shaft bow [24].

Condition monitoring techniques for rotor fault detection
Condition monitoring programme which can predict a failure in electrical machines has received considerable attention for many years [2,8]. Successful detection of any failure in electrical machines is achieved by using suitable condition monitoring. When a failure occurs, some machine parameters are exposed to changes that depend upon the fault degree. Any irregularity in the rotor of electrical machines presents with variation distributed in the rotor currents. The feedback of these currents to the air-gap field produces specific signatures of fault in the spectrum of speed, torque, current, and power. Reliable condition monitoring techniques depend on the best understanding of the mechanical and electrical characteristics of the electrical machines in both fault-free and faulty situations. Researchers have used different condition monitoring techniques that can be categorized as follows [8]:

Motor current signature analysis
The drowned current signal by an electrical machine contains a single component. Any magnetic or mechanical asymmetries in the machine generate other frequency components in the stator current spectrum. These frequency components are diverse according to each specific fault in the machine.
Motor current signature analysis (MCSA) analyses the stator current signal to identify the presence of any failure in electrical machines. This analysis method has been introduced as an effective way for monitoring electrical machines for many years [8]. From all these methods suggested in the literature, MCSA is a forerunner because of its advantages [10,13,[26][27][28]: • Online monitoring characteristics • Remote monitoring ability • Non-invasive feature • Inexpensive equipment and easy measurement • Different fault detection capability (such as broken rotor bars, air-gap eccentricity, stator faults, etc.) • Early-stage fault detection • Highly sensitive

• Selective
When a failure is generated in the electrical machine, depending on the severity of this fault, some of the machine parameters change. For instance, the current spectrum of an ideal electrical machine contains a single component corresponding to the supply frequency. Any asymmetry in electrical machine causes other components to appear in a spectrum of stator current. When a rotor bar breaks, current does not flow through it, and hence no magnetic flux is created around the breakage bar. Therefore, there is no non-zero backward rotating field that rotates at the slip frequency speed with respect to the rotor. This asymmetry in the magnetic field of rotor induces harmonics in stator windings, which are superimposed on it. These superimposed harmonics appear at frequency spectrums as described in where f BRB is the harmonic component due to broken rotor bar, S is the slip, f S is the fundamental frequency, and k = 1, 2,... [29].
Any asymmetry caused by static eccentricity produced other components that appear in the spectrum of stator current. The characteristic frequency component associated with static eccentricity is located according to Eq. (3) [16]: where f static is the harmonic component due to static eccentricity in line start permanent magnet synchronous motor (LSPMSM), m is an odd integer value, p is the number of pole pair, and f is the line frequency.

Wavelet
Frequency domain analysis is not reliable for fault detection because some outside parameters can affect the location and amplitude of fault-related feature. This parameter can be classified as follows: first, the fault frequency components depend on the slip of the motor; second, the fault feature amplitude is load dependent; third, the frequencies of the fault components are affected by voltage fluctuations; and fourth, long sampling interval is needed for a highresolution frequency. Therefore, in general, frequency domain analyses are suitable for the steady-state situation. The problem involved in the analysis of non-stationary signals can be shunned by time-frequency analysis of the signal, which illustrates the signal in threedimensional axis as time, frequency, and amplitude. The most popular time-frequency representations include Wigner-Ville distribution, short-time Fourier transform, and wavelet transform.
Wavelet transform expresses a signal in oscillatory function series at different frequencies and time. Wavelet transform divides the original signal into time-scale space, where the dimension of windows at time and scale (frequency) is not rigid [30]. Therefore, in fault diagnostics domain, wavelet transform has been used to extract the dominant features from original signals [31]. Various types of wavelet transforms have been widely used in the condition monitoring of electrical machine. Among all these techniques, discrete wavelet transform and wavelet packet transform (WPT) are the most common ones, explained in the following.

The principle of discrete wavelet decomposition
Discrete wavelet transform is based on signal analyses using a minor set of scales and specific number of translations at each scale. Mallat (1989) introduced a practical version of discrete wavelet transform called wavelet multi-resolution analysis [32]. This algorithm is based on the fact that one signal is disintegrated into a series of minor waves belonging to a wavelet family.
A discrete signal f[t] could be decomposed as where ϕ is the scaling function (father wavelet) and ψ is the wavelet function (mother wavelet), A is the approximate coefficient and D is the detail coefficient.
The multi-resolution analysis commonly uses discrete dyadic wavelet, in which positions and scales are based on powers of two. In this approach, the scaling function is depicted by the following equation: that is, ϕ m0,n is the scaling function at a scale of 2 m0 shifted by n. Wavelet function is also defined that is, ψ m,n is the mother wavelet at a scale of 2 m shifted by n.
Generally, approximate coefficients A m0,n are obtained through the inner product of the original signal and the scaling function The approximate coefficients decomposed from a discretized signal can be expressed as In the dyadic approach, the approximation coefficients A m0,n are at a scale of 2 m0 . The filter, , is a low-pass filter. Similarly, the detail coefficients D m,n can be generally obtained through the inner product of the signal and the complex conjugate of the wavelet function: The detail coefficients decomposed from a discretized signal can be expressed as In the dyadic approach, D m,n are the detail coefficients at a scale of 2 m0 . The filter, h[n] is a high-pass filter.
The multi-resolution analysis utilizes discrete dyadic wavelet and extract approximations of the original signal at different levels of resolution. An approximation is a low-resolution representation of the original signal. The approximation at a resolution 2 −m can be split into an approximation at a coarser resolution 2 −m−1 and the detail. The detail represents the highfrequency contents of the signal. The approximations and details can be determined using lowand high-pass filters. In the multi-resolution analysis, the approximations are split successively, while the details are never analysed further. The decomposition process can be iterated, with successive approximations being decomposed in turn; hence one signal is broken down into many lower-resolution components. This process is called the wavelet decomposition tree as shown in Figure 3. It illustrates the dyadic wavelet decomposition algorithm regarding the coefficients of the transform at different levels according to the description by Polikar et al. (1998) [33].

The principle of wavelet packet decomposition
The wavelet packet transform is a direct expansion of discrete wavelet transform, where the details as well as approximation are split up. Therefore, this tree algorithm is a full binary tree that offers rich possibilities for signal processing and better signal representation in comparison to a discrete one.
A wavelet packet function has three naturally interpreted indices in time-frequency functions: where integers j, k, and i are called the scale, translation, and simulation parameters, respectively. Scaled filter h(n) and the wavelet filter g(n) are quadrature mirror filters associated with the scaling function Φ(t) and the wavelet function ψ(t) [32]. The conjugate mirror filters h and g with finite impulse responses (FIRs) of size k can define the fast binary wavelet packet decomposition (WPD) algorithm of the signal f(t): The wavelet packet component signals f j i (t) are produced by a combination of wavelet packet function ψ j,k n (t) as follows: where the wavelet packet coefficients C j,k i (t) are calculated by Provided the wavelet packet functions are orthogonal As data sets of wavelet packet coefficients increase in size, the energy principle is applied to current signals after WPT for fault location estimation [35].

A review of wavelet decomposition for fault detection
Different types of wavelet transform techniques have been widely used in algorithms designed for fault detection in electrical machines.   Table 1. Summary of published paper with the aim of using wavelet transform for broken rotor bar and eccentricity fault detection

Case study 1
The detection of static eccentricity in three-phase LSPMSM using motor current signature analysis is studied. A detailed description of experimental test rig used in this study and the method used for signal measurement and analysis is provided in the following.

Experimental set-up
The experimental test rig is shown in Figure 4. The tested motor for both fault-free and faulty (with static eccentricity) cases is a three-phase LSPMSM with the specification as mentioned in Table 2. The motor is directly fed by the grid power supply, while the stator windings are Y connected, and the current nominal value is 1.28 A. The LSPMSM is coupled to torque/speed sensor in order to measure the torque value in different operation conditions. On the other side, a mechanical load is provided by a DC-excited magnetic powder brake (MPB) coupled to torque/speed sensor. The specific load torque level could be furnished to the motor shaft by controlling the input dc voltage of MPB. This system is used to sample the stator current noninvasively when the motor is operated in the steady-state condition. Notably, only one phasecurrent signal is required to be recorded for the detection process in this study. The recorded signals are analysed by a computer-based signal processing program.

Method
The method proposed in this study for the creation of eccentricity fault in LSPMSM, by changing the original bearings of motor with a new set of bearing with larger inner diameter and smaller outer diameter, results in the creation of free space between the shaft and bearings and also between the bearings and the housing of end shields. Static eccentricity is created by fixing concentric inner rings between the new bearings and shaft on both ends of LSPMSM and non-concentric outer rings between the new bearings and housings of both end shields. The aforementioned strategy is used to create 33% and 50% static eccentricity in the motor discussed in the case study.
The current spectrum is stored with the sampling frequency ( f S ) of 5 kHz over a total sampling period of 6.5 s, which allows the analysis of the signals with a minimum frequency of 0.15 Hz. Daubechies-24 (db24) is used as the mother wavelet in discrete wavelet transform (DWT) analyses. Since the four-pole, three-phase LSPMSM is considered, the characteristic frequency component associated with static eccentricity is located at 25 Hz, according to Eq. (3) [16].
The number of decomposition levels (l d ) can be determined using Eq. (16) which is l d = 7 in this case.
The frequency bands of wavelet signals are summarized in Table 3. Energies of the detail coefficient E(D j ) are calculated using the following formulas [45]: where j = 1, 2, ..., l d and N l is the data length of the decomposition level.     and eccentric LSPMSM with 33% and 50% static eccentricity as shown in Figure 8. The energy variation of D 7 (index) for stator current signal using db24 is provided in Table 4.

Conclusion
Discrete wavelet transform is employed to analyse the stator current signal of three-phase LSPMSM in order to propose an effective index for static eccentricity fault detection. The energy of detail signal (D 7 ) is introduced as eccentricity index. The achieved results confirm the productivity of the proposed method for the motor discussed in the case study.

Case study 2
The detection of broken rotor bar in three-phase squirrel cage induction motor using motor current signature analysis is studied. A detailed description of experimental test rig used in this study and the method used for signal measurement and analysis is explained in the following. Figure 9 illustrates the experimental test rig used in this study. Table 5 presents the parameters of the three-phase squirrel cage induction motor used for both fault-free and faulty motors. The faulty motor is with three broken rotor bars. The motor is directly fed by the grid power supply, while the stator windings are Y connected and the current nominal value is 2.2 A. In order to measure the torque and speed value of the squirrel cage induction motor in different operation conditions, a torque/speed sensor is coupled to it. A generator is used as a load and the specific load torque level can be furnished to the motor shaft by controlling the resistor connected to the generator. Recall that only one phase current signal is required to be recorded for the detection process in this study. The recorded signals are then analysed by a computerbased signal processing program.  Table 5. Specification of a three-phase squirrel cage induction motor

Method
The architecture of the proposed system for broken rotor bar detection is shown in Figure 10, and the procedure used in this study is as follows: First, to force a real bar breakage in the rotor, a hole is drilled artificially in it. The original stator current was recorded from a threephase induction motor. The stator current is sampled at 20 kHz lasting four seconds for both fault-free and faulty motors (three-rotor bar breakage) at 80% full load. The measured current signals are then decomposed using wavelet packet transform with two different purposes: One as a pre-processing of signal for FFT analysis and the frequency of ((1-2s)f S ) obtained is used as a fault feature for broken rotor bar detection. The other purpose of using WPT is for feature extraction, where some statistical features determined by wavelet packet coefficients are used for broken rotor bar detection. For both purposes, Daubechies-44 (db44) is applied as a mother wavelet in 12 levels of decomposition. To extract the fault-related feature, those nodes are taken that involve fault frequency (f BRB ). Figure 11 shows the process explained above, called the wavelet packet tree. In this work, the signal energy, root mean square (RMS), and kurtosis are obtained as selected features for the diagnosis of the broken rotor bar.

Results and discussion
In order to obtain the differences between fault-free and faulty conditions under 80% full-load conditions, WPD was used for the feature extraction. The WPD gives distinguishable signatures from stator current signal in a specific frequency band. After WPD of the current signal, two procedures for failure feature extraction using WPD are used ( Figure 10). One procedure includes using FFT for the determination of amplitude of fault frequency and the other includes the statistical analysis of coefficients extracted by WPD.
The amplitude of fault frequency in the current spectrum for fault-free motors and for motors with three broken bars achieved in the first procedure is presented in Table 6. The results indicate that the amplitude of harmonic components ((1-2s)f S ) in both nodes, presented in Table 6, increase the faulty condition. However, the degree of increase is not significant, and it cannot be used to differentiate the conditions. In the second procedure, three statistical parameters including RMS, kurtosis and energy are calculated using the statistical analysis of coefficients determined by WPD of current signal. Table 7 presents these statistical parameters in three different nodes [10,6], [11,13] and [12,26]. These parameters are compared to define the most appropriate frequency band that represents the frequency components from the broken rotor bar. According to

Conclusions
This case study proposes a feature extraction system for broken rotor bar detection using wavelet packet coefficients of the stator current. It is shown that in a faulty case, the amplitude in specific side bands increases and dominant features of signals can be extracted for fault diagnostics. The results of this study indicate that the energy, kurtosis and RMS value of WPD coefficients are the appropriate features for detecting broken rotor bar in particular bands.