Broken Bar Fault Detection and Diagnosis Techniques for Induction Motors and Drives: State of the Art

Motors are the higher energy-conversion devices that consume around 40% of the global electrical generated energy. Induction motors are the most popular motor type due to their reliability, robustness, and low cost. Therefore, both condition monitoring and fault diagnosis of induction motor faults have motivated considerable research efforts. In this paper, a comprehensive review of the recent techniques proposed in the literature for broken bar faults detection and diagnosis is presented. This paper mainly investigates the fault detection methods in line-fed and inverter-fed motors proposed after 2015 and published in most relevant journals and conferences. The introduced review has deeply discussed the main features of the reported methods and compared them in many different aspects. Finally, the study has highlighted the main issues and the gaps that require more attention from researchers in this field.


I. INTRODUCTION
Induction motors (IMs) are the most widespread electric motor type across a broad range of industries involving oil and gas, cement, petrochemicals, electric traction, etc., due to their robustness and low cost. In addition, this type of motor accounts for about 85% of the industrial sector's energy consumption [1]. Therefore, an effective fault detection and diagnosis (FDD) system becomes an inevitable requirement for the industry to avoid catastrophic unplanned shutdowns, minimize maintenance costs and reduce downtime.
Failures of IMs can be originated from faults in the stator, the rotor, the motor mechanical system including bearing and shaft, or external sources [2], [3]. Many surveys were conducted to estimate the percentage of failures related to each motor component. It was found that these percentages varied with motor size, application type, manufacturing standard,. . . etc. For example, medium voltage motors are more vulnerable to broken bar and end ring faults than small motors [2].
The associate editor coordinating the review of this manuscript and approving it for publication was Gerard-Andre Capolino. Rotor faults comprise both end ring and broken bar faults (BBFs). Examples of BBFs are shown in Fig. 1 and Fig. 2. These types of faults are mainly caused by one or a combination of the following reasons [4], [5], [6]: -Dynamic stresses due to pulsating torques, concentrated centrifugal forces, and shaft torsional oscillation. -Thermal stresses those caused by hot spots, overloads, sparking due to imperfect fabrication of the rotor, heavy and frequent starting, and plugging transients. -Mechanical stresses caused by loose laminations, etc. -Environmental stresses due to the contamination by chemicals. -Magnetic stresses because of unbalanced electromagnetic forces. Once a full BBF is introduced, the bar current that would flow in the broken bar transfers to the adjacent bars causing more thermal and magnetic stresses on these bars [7], [8], [9]. In addition, the backward magnetic field increases due to rotor circuit asymmetry which is reflected in the stator current harmonic content and other motor quantities [10]. Thus, the BBF reduces motor efficiency and reliability [3]. Also, the BBF causes the vibration of the shaft that may lead to bearing and rotor eccentricity faults [11]. As a consequence of these extra stresses, the adjacent bars and bearing become more susceptible to faults, the motor may not be able to develop the required torque, and eventually, a complete motor failure may occur [8], [9], [12], [13]. A sudden motor failure may cause severe consequences such as unplanned shutdown, loss of production, financial losses,. . . etc [3], [14]. Therefore, the early detection and diagnosis of BBFs become crucial to the modern industry.
A case of a complete rotor failure of a 380 kW, 6.6 kV motor is illustrated in Fig. 2. The rotor of this motor has 58 bars, 20 of them are damaged, so it could not deliver the required torque to drive the load which accounts for a complete rotor failure (based on the angle of the photo taken, only four broken bars are shown in Fig. 2). In the last two decades, many review papers have attempted to analyze different FDD techniques of IMs and drives' faults in the literature such as [15], [16], [17], [18], [19], and [20]. However [15], [16], [19], and [20] provided broad reviews of FDD techniques of motor-drive systems including several electric machine types, faults types (BBF, stator faults, eccentricity, . . .), and power electronics were provided. They discussed a limited number of researches related to BBF, perhaps due to the wideness of the review scope and the paper length limitations. Lastly, these references did not discuss methods proposed after 2015. Similarly, a comprehensive survey of FDD methods for the four major IM faults: broken bar faults, stator inter-turn faults, eccentricity faults, and bearing faults was provided in [17]. In this article, different FDD methods before 2016 were introduced and compared in several aspects. In contrast, and in an attempt to give more concern to IMs broken bar faults taking into account the paper length limitation, a more detailed review of detection and diagnosis methods before 2017 is achieved with mathematical representation in [18]. However, some significant points were not extensively reviewed concerning the detection of BBFs in inverter-fed IMs, diagnosis of non-adjacent BBFs in IMs, and also flux-based detection techniques. Additionally, the authors of [21] and [22] pro- vided an overall comprehensive review of FFD for different devices and systems such as engines, motors, batteries,. . . etc. These two studies have proposed main frameworks for FDD techniques classification. A comparison with these seminal state-of-the-art papers is introduced in Table. 1.
So, this work is dedicated to filling the time gap between recent research studies and the latest available review articles and to help researchers to realize the current trends in this field (as shown in Table. 1). Also, the paper discusses the main BBF detection methods categories and considers the most common BBF signatures in the literature compared to other state-of-art and review papers. To enrich our review, integrate with previous works, and avoid duplications, most of the papers covered in this review were published after 2015 and more emphasis is placed on some highlighted points such as: • Detection and diagnosis of BBFs in inverter-fed IMs. • Classifying detection methods, including recent methods, into main groups and subgroups as demonstrated in Fig. 3 to help readers to comprehend the development of those methods.
• Holding extensive comparisons between different methods to show their merits and drawbacks.
• Assessing the usage of the data-driven approach in the detection and diagnosis of BBFs. The rest of the paper is organized as follows: an overview of the nature of the BBF fault and the challenges that accompanied BBFs diagnosis are presented in Section II, and the VOLUME 10, 2022 effect of BBF on motor variables is presented in Section III. Model-based methods are fully discussed in Section IV. Signal processing-based methods are reviewed comprehensively in Section V. Data-driven based methods are discussed in Section VI. Finally, the conclusions are drawn in Section VII in addition to some suggested future works.

II. MODELING OF BBF AND DIAGNOSIS CHALLENGES
In this section, the nature of the BBF and the diagnosis challenges will be discussed.

A. MODELING OF BBF
The broken bar fault is considered a type of asymmetry in the IM rotor circuit. This asymmetry results in increasing the backward magnetic field that already exists due to the inherent asymmetry of the rotor circuit [7], [12], [17]. The rotor's inherent asymmetry originates from the imperfection of the rotor casting, non-sinusoidal distribution of the rotor bars, etc. [7], [12], [23]. The increased backward field due to the fault deforms the motor magnetic flux density spatial  distribution by creating undesirable highly saturated regions around the broken bar [7], [24].
A full broken bar can be modeled in the equivalent circuit by a virtual current source [7], [17]. The magnitude of this current source is equal to that of the current that would flow in the broken bar in the healthy case [7]. The current generated from this current source passes through the rotor bars adjacent to the broken bars besides their original current, causing more stress to these bars. This increase in the adjacent bars currents is because of the cancelation of the armature reaction created by the broken bar in the healthy condition [7], [13]. So, if the BBF is not diagnosed and cured early, the severity of the fault increases, and accordingly the rotor is susceptible to complete failure [12], [13].
It is worth mentioning that the partial broken bar can be represented as a less severe case of a full broken bar where a portion of the bar current can still flow because the connection is not fully broken as in the case of BBF [7].

B. CHALLENGES OF BBFs DIAGNOSIS
The types and modes of supply represent a major challenge for many fault detection and diagnosis methods. Therefore, in the next few lines, we will discuss different types of IM supply. These supply types can be classified into two main groups [7], [17]: In the first type, the IM is energized by a constantfrequency sinusoidal voltage supply whereas, in the second type, the supply voltage fundamental frequency can be varied, and the voltage supplied to the IM is rich in harmonics [7], [17], [25], where these additional harmonics may mask the fault-related harmonics [25].
Also, in inverter-fed mode, many motor's mechanical and electrical variables are subject to continuous changes, while the variation in line-fed mode is mainly dependable on loading level [12]. Accordingly, the process of fault detection and diagnosis in inverter-fed mode represents a more sophisticated challenge.
Generally, the BBFs diagnosis challenges were discussed separately in several reported papers in the literature, however, these challenges will be briefly offered in the following points to provide a complete review of FDD. -The source of false diagnosis of BBFs can be classified into false positive and false negative sources as indicated in Fig. 4. Despite the high efficiency of many detection methods proposed in the literature, their accuracies may deteriorate under many motor designs, fault locations, and operating conditions [26], [27], 28]. -Related to motor design, the axial rotor air ducts are the most common cause of false detection of broken bars. Such ducts, which are used mainly for cooling, produce frequencies in the stator current spectrum similar to those induced in the case of BBFs [26], [27]. -A closed rotor slot is another obstacle related to motor design that undermines the performance of many fault detection methods [29]. -Besides, the non-adjacent broken bar is a typical fault location that is commonly misdiagnosed [30], [31]. -Also, a fault in the outer cage of a double cage motor can be hardly detected [28], [32]. -Erroneous speed estimation can lead to misdiagnosis for methods that require speed measurement. -At the same time, the operating conditions and the mechanical load characteristics that negatively affect the FFD methods' accuracy include: -Low-frequency load oscillations [33], [34].

III. SIGNATURES OF BBF
Even though all motor variables are affected by BBF, some variables are more fault-sensitive [12]. These effects result in the appearance of certain patterns in the temporal evolution VOLUME 10, 2022 of the signal, in its spectrum or its spectrogram. These patterns are widely known in the literature as fault signatures. Moreover, the measurement of some motor variables is more straightforward than others [12], [37]. In other words, the measurement requirements vary from simple non-invasive sensors with simple sampling techniques like current and voltage sensors to invasive sensors with especially sampling techniques like air-gap flux sensors [12]. Although air-gap flux sensors are the most reliable and fault-sensitive sensor types, current sensors are the most common to detect this fault due to their availability and ease of installation [12], [18], [38]. Therefore, there are two main trends: -Increasing the reliability of the non-invasive methods through the development of post-processing techniques. -Development of new non-invasive sensors that can measure more fault-sensitive motor variables. An example of the first trend is the application of the dragon transform to a motor current signal to detect broken bar faults in an inverter-fed motor [38]. On the other hand, the usage of stray flux sensors represents the other trend [10].
Other fault signatures such as torque signatures do not attract researchers due to their low sensitivity and complexity [12].
In this paper current, voltage, flux, vibration, and acoustic signatures will be investigated.

A. BBF CURRENT SIGNATURE
As discussed in Section II.A, the BBF induces a backward magnetic field whose frequency equals sf s and rotates in a reverse direction to the motor main flux, where s describes the motor slip and f s is the supply frequency [7], [12]. This backward magnetic field finally develops a current component whose frequency equals (1 − 2s)f s [7], [12]. The new current component generates torque and speed ripples that generate another current component whose frequency equals (1 + 2s)f s [7]. The (1 + 2s)f s current component produces another (1−4s)f s component and the sequence continues [7]. More details and mathematical interpretation can found in [7] and [12]. Therefore, the characteristic frequencies of BBF f bbf in the stator current are: The fault-related harmonics can be recognized in the sideband around the supply frequency. The most significant faultrelated harmonics for BBF detection in the literature are the first-order ones where k = 1 in equation (1). The sideband at (1 − 2s)f s is called left sideband harmonic (LSH) whereas, the sideband at (1 + 2s)f s is called right sideband harmonic (RSH). The magnitude and frequency of the LSH and RSH mainly depend on loading conditions, motor slip, load inertia, and the location of broken bars [39]. The effects of loading level and fault severity on the LSH and RSH in the motor current spectrum are shown in Fig. 5. Therefore, the detection of BBF under light and zero loading level using standard spectrum analysis methods would be impossible as the fundamental current component (FC) masks sideband harmonics at low slip as described by equation (1). Based on Equation (1) and if we only consider the firstorder sideband then, the stator current (I a ) can be expressed by: where I , I l and I r are the r.m.s of the FC, LSH, and RSH current components respectively. Whereas, α, α l and α r are the phase angles of the FC, LSH, and RSH current components respectively. According to equation (2), the BBF induces periodic fluctuations into the stator current envelope in the time domain as shown in Fig. 6. Actually, as the fault severity increases, the amplitude of fluctuations increases [7].
In contrary to steady-state, the BBF detection under transient conditions is less sensitive to loading level and hence is more capable to detect such fault under zero loading conditions [13]. However, the BBF detection under transient conditions is influenced by load inertia since the inertia directly affects the starting time [13].
Nevertheless, the detection and diagnosis of BBF in inverter-fed induction motors are undisputed and more sophisticated in both steady-state and transient conditions since the high-frequency switching of the inverter produces several undesirable harmonics in the motor current and air gap flux [36].
In addition, the motor speed is no more dependable on the slip so, the BBF-related attributes are significantly different from those in line-fed cases [40]. The control strategies of the inverter have a great influence on sideband harmonics' magnitude and energy [36], [38]. The closed-loop control strategies such as field-oriented control system (FOC) and direct torque control (DTC) slightly increase the amplitudes of (1 − 2ks)f s [41], [42]. Whereas, the open-loop control strategies such as constant voltage/frequency (CV/F) significantly increase the main sideband frequencies [41].
As shown in Fig. 7, the LSH in line-fed mode has a unique V pattern in the time-frequency domain during motor starting that facilitates the detection of BBF. On the other hand, both the LSH and RSH are strictly close to the fundamental current component (FC) in the case of starting an inverter-fed motor. Consequently, the detection of BBF under these conditions is complicated.
Also, the BBF induces other frequency components around winding harmonics as expressed in [35]: where p is the number of pole pairs and k is an integer. This criterion was analyzed in steady-state and time-varying conditions in many papers to detect BBF such as in [43] and [44] when the diagnosis based on conventional harmonics LSH and RSH is not conclusive. The BBF occurrence increases the magnitude of many high-frequency components such as (5 − 4s)f s and (7 − 6s)f s [45]. These high-frequency current components are generated from the interaction of the spatial harmonics with the asymmetry due to broken bars. As discussed in Section II.B, low-frequency load oscillations can induce frequencies in the stator current spectrum similar to that produced from the BBF [33], [34]. Many papers discussed this problem such as [34], [46], [47], [48], [49], and proposed different methods that can discern BBFs from load oscillations. These methods will be discussed later.

B. BBF VOLTAGE SIGNATURE
As discussed before, the BBF gives rise to asymmetrical rotor flux distribution. So, after disconnecting the main supply, the induced voltage in the motor stator winding reflects the rotor flux distortion [18]. Mainly the spectrum analysis of the induced voltage shows BBF-related components that can be used for fault detection and diagnosis [18]. The major drawback of this fault signature is that disconnection of the motor from the supply is required, which is not applicable in industrial applications. Besides, other faults such as stator winding faults induce fluctuations in the stator-induced voltage also [12].
Another BBF voltage signature is investigated in the literature to overcome the source disconnection requirement and provide continuous motor monitoring. It depends on measuring and analysis of the motor-neutral voltage that reveals fault-related information [50], [51]. The difficulty of measuring neutral voltage ranges from a simple connection in a star-connected winding motor to more advanced connections in the case of inverter-fed motors [51], [52]. In delta-connected winding motors, an alternative to the neutral voltage called stator circular current is used for fault detection and diagnosis [51]. However, the neutral-voltage signature provides one of the most accurate, robust, and reliable fault-related information for line-fed and inverter-fed motors [18].
In contrast to the effect of open and closed-loop control strategies on the current signature, the control strategies VOLUME 10, 2022 have less effect on the voltage signature especially on zero-sequence voltage components [52].

C. BBF FLUX SIGNATURE
The motor air-gap flux is the coupling between the stator circuit and the rotor circuit, so any fault in the stator or the rotor appears in the air-gab flux. Hence, it is one of the most accurate and reliable motor fault-related signatures [28]. The BBF does not represent an exception to this rule; this fault increases the magnitude of flux density components whose frequencies depend on sf s [53].
The variation of motor flux distribution due to BBF during starting is displayed in Fig. 8. The air-gap flux is measured using one search coil or more embedded in the air gap so, it is an invasive technique [28], [54]. Essentially, the induced voltage on the search coil is measured and analyzed to extract the fault signature. This fault signature can be used for fault detection in steady-state and starting conditions under linefed and inverter-fed supply modes [12], [28]. This fault signature is immune from low-frequency load oscillations and unbalanced voltage supply [53].
To keep the advantages we got from air gap magnetic flux usage and avoid the invasive requirements for measuring air-gap flux, the motor stray flux is recently used in the literature. A coil or more is installed outside the motor in an axial or radial direction to capture the stray flux [10]. The BBF increases the magnitude of flux components in the axial direction whose frequencies equal sf s and 3sf s [28], [55]. It raises the magnitude of flux components in the radial direction whose frequencies equal (5 − 4s) f s , (5 − 6s) f s , (7 − 6s) f s , (7 − 8s) f s [28], [55]. Then, the coil's induced voltage is analyzed to detect BBF [10], [28]. However, stray flux monitoring can provide nearly the same advantages as air-gap flux, the magnitude of the external stray flux is very low and depends on motor frame material [53], [56]. Moreover, a high-frequency resolution is required to distinguish the fault-related frequencies in the spectrum [53], [56]. Furthermore, the captured signal is susceptible to interference from other sources since the external search coil acts as a low-frequency antenna [53].
It is worth mentioning that the inverter control strategies have a considerable impact on the detectability of BBFs using stray flux. Generally, the inverter generates additional noise that may hide the fault-related frequency, especially at low slip [57]. Moreover, the compensation effect of the closed-loop control strategies suppresses some fault-related frequencies which makes the detection of such faults more challenging.

D. VIBRATION AND ACOUSTIC SIGNATURES
The vibration analysis is widely used for machines' health conditions monitoring. The vibration is generally produced by electrical, mechanical, and magnetic forces [18]. Based on the fact that the BBF results in unbalanced magnetic force conditions in addition to speed fluctuations [58], [59]. Therefore, vibration analysis can be used to detect such faults. The vibration can be measured using different types of vibration sensors placed in axial or radial directions [58].
The spectrum analysis of vibration signals is usually used for fault detection purposes [58]. The BBF produces sideband harmonics around the rotational frequency [58], [59]. However, the detection methods based on vibration analysis were found experimentally to be more sensitive to bearing faults than BBF [58]. It is worth mentioning that the amplitude of the sideband harmonics depends on motor speed more than loading conditions [18], [58]. The inverter control strategies -especially closed-loop control such as FOC-have minor effects on the vibration signature [60]. However, the detection of BBF using vibration signature may require more advanced signal processing tools under low load operation conditions and variable loading conditions [60].
On the other side, the acoustics-based methods are very attractive to researchers for machine fault diagnosis as they contain less noise and interference within the frequency band of interest [18], [58]. In addition, they are noninvasive techniques as the acoustic signatures are captured by using a set of microphones [58], [61]. The BBF appears in the frequency spectrum as sideband harmonics around the driving frequency [58]. Unfortunately, the acoustic spectra cannot demonstrate explicit differences between healthy and BBF cases. Consequently, the acoustics-based methods are considered the least sensitive methods to BBFs [58].

E. CONCLUSION AND DISCUSSION ON BBF SIGNATURES
In a conclusion to this section, the BBF causes variations in all motor quantities with different degrees. These variations are reflected in motor measures such as current, voltage, flux, vibration, and acoustics, known as fault signatures. Table 2 illustrates the frequencies of interest for BBF detection and diagnosis for different signatures.
The BBF signatures can be measured using invasive or non-invasive techniques and require different conditions. In Table 3, a comparison between different BBF signatures was held to illustrate the differences between these signatures.
The sensitivity of different signatures to BBF is divergent. For example, the sensitivity of the air-gap flux signature to the BBF is superior to that of other signatures, but measuring this quantity requires an invasive technique [12], [28], [54]. On the other hand, the current signature analysis is the most common technique in the literature for BBF due to its non-invasive nature and simplicity.

IV. MODEL-BASED-METHODS FOR BBF DETECTION AND DIAGNOSIS
As illustrated in Fig. 3, this section is dedicated to discussing the conceptual basis of the model-based approaches. Generally, in model-based approaches, the IM is modeled to simulate its real behavior. A schematic diagram of the observer-based failure detection is displayed in Fig. 9. The observer or the state estimator can use the process inputs to estimate measurement variables [62]. The residual between the measured values and the estimated ones is used to identify the error [62]. There are three main approaches to these methods: • Resistance estimation-based methods, • Other parameter estimation-based methods, • Digital twin-based methods. The conceptual basis of the first approach is to use a state estimator to estimate the rotor resistance and compare it to a known value of rotor resistance for error detection. The deviation of the estimated resistance from a known value is used as an error severity indicator.
In contrast, the second approach estimates the parameter rather than the rotor resistance and compares it to the known value of the parameter. In this case, the severity of the error is assessed using these parameters. In general, this approach is suitable for mixed and simultaneous fault identification.
Finally, the digital twin technology offers a very promising tool for detecting BBF. This is because the technology can automatically estimate engine parameters and behavior based on online data.

A. RESISTANCE ESTIMATION-BASED METHODS
The problem of BBF detection for a sensorless vectorcontrolled induction motor drive was discussed in [66]. The used technique of control was based on the FOC in which the BBF effect in the speed is compensated. In this paper, the extended Kalman filter (EKF) was used to estimate the speed of a sensorless vector control induction motor. In addition, EKF is applied to estimate in real-time the equivalent rotor resistance of the reduced multi-winding model of IM in healthy and faulty conditions under both transient and steadystate operation.
The estimated rotor resistance was proposed as a fault indicator. In addition, the spectrum analysis of stator current and quadratic current using fast Fourier transform was introduced for further confirmation of fault occurrence. The proposed method was validated experimentally as well as the results showed a good performance. Despite the effectiveness of the proposed method, 3-ph current and 3-ph voltage measurements besides motor parameters were required. Furthermore, EKF suffers from linearization error as well as the computational burden is high [67]. A comparative study between Unscented Kalman Filter (UKF) and EKF was introduced in [68] as promising methods to estimate the equivalent rotor resistance of the motor model. The two methods were tested using computer simulations under the same conditions. The test results illustrated that UKF had a better performance than EKF regarding computational burden, complexity, and mathematical stability. However, UKF may not converge in high-dimensional systems [67].
Later, Square-Root Transformed Cubature Quadrature Kalman Filter (SR-TCQKF) was proposed in [67] to overcome the EKF shortcomings, provide more accurate results, and ensure mathematical stability. The SR-TCQKF can accurately estimate the equivalent rotor resistance of the IM model. The change in the estimated rotor resistance from the reference value was utilized as a BBF fault indicator. This method was validated using a line-fed induction motor testbed under low loading conditions. The test results demonstrated that the proposed method precisely detected the BBF. Nevertheless, 3-ph current and 3-ph voltage measurements besides motor parameters were required.

B. OTHER PARAMETERS ESTIMATION-BASED METHODS
In [69], a model based on Park's model for BBF and stator inter-turn faults was developed for IMs. The faulty parameters were estimated using this model and sequential electrical data samples with the help of the output error technique to indicate fault level, while the other motor model parameters did not change. This method was validated using a set of experiments. Although this method showed very good accuracy and was suitable for inverter-fed IMs with FOC algorithms, 3-ph current, 3-ph voltage, and speed measurements besides motor parameters were required. These requirements may be not available in a real case. Furthermore, the model-based approach was applied in [62] to detect incipient BBF and inter-turn faults. The dynamic nonlinear unknown input observer (DNUIO) was presented to overcome motor nonlinearity problems and load variations effects. The DNUIO was used to predict the rotor equivalent resistance of a highly nonlinear model of IM. This method was verified using simulations to illustrate its effectiveness and asymptotic stability. However, 3-ph current, flux, and speed measurements besides motor parameters were required.
On the other hand, an analytical model that can represent IM with stator inter-turn faults and BBFs occurring simultaneously or alone was presented in [70]. The proposed method can detect motor faults in real-time by utilizing the pendulous oscillation phenomenon of the magnetic field with the aid of particle swarm optimization. The experimental validation of the proposed method using a line-fed induction motor illustrated that the method is immune to load variations, voltage unbalance, and voltage distortion. Contrary, the proposed method is susceptible to false classification. Like the previous method, 3-ph current and 3-ph voltage measurements were required.

C. DIGITAL TWIN-BASED METHODS
Another trending technology is called digital twin (DT), which is the creating and sustaining of a digital representation of physical objects and supporting their performance through digital simulation and optimization tools that are continuously fed with real-time and updated data [71].
Normally, the digital twin architecture typically consists of five main components; the physical entity in the real world, the virtual entity, the services entity, the data, and the connections [71], [72]. The virtual entity simulates the physical object from different approaches and provides multi-functions for the digital twin such as fault identification, optimization, simulation, and control strategies [72]. The data drives the complete system and updates the digital model. The service entity acts as a platform with a variety of services. Also, it reacts to requests from both physical and virtual entities [72]. The DT automatically measures and estimates motor parameters and quantities based on online data, which generally makes it a very efficient tool for detecting motor faults [72]. On the other hand, the DT faces many challenges such as developing comprehensive multi-physical modeling with a suitable calculation burden for online simulation, worthless complexity, expensive technology, etc. [72], [73].
The DT term was used in the field of broken bar fault detection only in [74], but in a way represents a misconception of definitions in [71] and [72]. In [74], a 3-D finite element model was introduced to simulate a 5-hp motor. The stator current obtained by the simulation was used to test artificial neural networks (ANN) accuracy to classify BBF.

D. DISCUSSION ON MODEL-BASED METHODS FOR BBF DETECTION AND DIAGNOSIS
To conduct some comparative analysis between different methods introduced in the literature, some abbreviations are used as defined in Table. 4. Accordingly, a detailed comparison among different model-based methods is illustrated in Table. 5.
It can be concluded that the model-based methods require a relatively large number of sensors and a detailed knowledge of motor models and parameters compared to other BBF detection methods. Also, a precise selection of the observer's type is essential for rigorous results in both resistance estimation and other parameter estimation-based methods. Furthermore, the rotor temperature estimation accuracy is largely dependent on the identification accuracy. However, most of these methods can provide accurate results under zero in addition to low loading conditions, unbalanced voltage supply, mixed faults, and closed-loop inverter fed modes which represent a stumbling block for most of the other methods.
The digital twin-based methods represent a trending technology for efficient monitoring and accurate fault detection and diagnosis of IMs. However, it may not be the best solution for monitoring small motors due to the cost of implementation and complexity. Nowadays, developing a multi-physical model for the IM with a compromised computational burden and accuracy for online simulations takes researchers' attention.

V. SIGNAL PROCESSING-BASED METHODS FOR BBF DETECTION AND DIAGNOSIS
The concept of these methods is to use a variety of different techniques to extract the fault-related features from the measured signals. These features can be extracted from the time, frequency, or time-frequency domain.

A. TIME-DOMAIN-BASED METHODS FOR BBF DETECTION AND DIAGNOSIS
In this subsection, FDD methods that are based on processing data obtained from the measured signals in the time domain are presented.
A straightforward algorithm to automatically detect BBFs even at the incipient phase under starting conditions was proposed in [75]. Firstly, the starting current signal was filtered and segmented before being processed. In the processing stage, the segmented current was compared with a set of reference current signals that represent healthy and different fault conditions. This algorithm can efficiently diagnose the BBF however, reference current signals were required.
A method based on the spectral analysis of the air gap flux measured by a hall effect sensor embedded between two stator slots was proposed in [76] to diagnose BBF in IMs running at very low slips. In this method, multiple statistical features were extracted from the time domain and frequency domain of the air-gap flux to be fed to different artificial intelligence classifiers for BBF detection and classification. However, an invasive technique was used to measure the air gap flux and large data was used to train the classifier. In contrast, in [77], the information entropy analysis of the current waveform at either starting or steady-state was utilized as an index for BBFs. Although the low complexity and the high efficiency of the proposed method under starting and steady-state, several trials were required to determine the thresholds in a process similar to the training process.
The investigation of vibration and current monitoring for effective mechanical and electrical fault prediction in IMs was introduced in [78]. Three statistical features extracted from current and/or vibration in the time domain were employed in [78] in conjunction with a multiclass support vector machine to detect BBFs in addition to different electrical and mechanical faults. The proposed scheme was validated experimentally. The test results showed that a high accuracy could be achieved using the current signal only. Another objective of this paper was to hold a comparison between vibration signal and current signal as a media for detecting different electrical and mechanical faults. It was found that the vibration signal and current signal provided information-rich media for detecting mechanical and electrical faults respectively however, both signals were required for efficient detection of combined mechanical and electrical faults.
On the other hand, an invasive method was presented in [79] that was based on a differential measurement of the air-gap magnetic field captured by two series search coils installed on the stator tooth. The resultant induced voltage at the series coils terminals was employed as a fault indicator.  Later in [80], a method is introduced that could effectively discriminate both BBF and eccentricity fault and then estimate the severity of each fault. In this method, the air-gap flux density was acquired using 36 flux sensors installed in the air gap. The analysis of the air-gap flux density in both time and space was the base of BBF detection and diagnosis in that study.
Furthermore, the homogeneity of one phase stator current during the starting was suggested in [81] to be used for early detection of BBF with a relatively low computational burden. The proposed method was experimentally validated as an online tool that can detect and classify BBFs even in the early stages. This method could achieve a high accuracy reaching 99.7%, however, a considerable amount of data was required to define acceptance and rejection regions. Although the proposed method successfully diagnosed faults of different levels of severity up to two broken bars, we think that diagnosing faults of higher severity will be challenging for this method. As with the increase of the fault severity over two broken bars, the density function of the homogeneity in the case of fault resembles that in the healthy cases.
The orthogonal Component Decomposition technique (OCD) was utilized to efficiently detect BBF in both line-fed and inverter-fed modes in [82]. It was found that the decomposition products of currents and voltages are rich in fault-related data in both the two operation modes. The proposed technique is supported by support vector machines to detect and classify faults with accuracy that reached 100% and 98.76% in the case of line-fed and inverter-fed modes respectively.
The differential measurement of the air-gap magnetic field was employed again in [53] to detect BBF even under load torque oscillations, unbalanced voltage source, and nonadjacent BBF. The time-domain analysis of the differential induced voltage at two search coils per phase was introduced as a fault indicator.
The chaos theory-based method was proposed in [83] as a prospective solution to detect and classify BBF under low slip conditions and variable loading conditions with the minimum window length. The analysis of only one chaotic variable called density of maxima could efficiently indicate BBF occurrence.
A Histogram of Oriented Gradients (HOG), a widely used image-processing tool, is used in [33] to detect the BBF of an IM running at low slip conditions without the need for slip measurement. The HOG extracted features were fed to a multilayer perceptron neural network and Bayesian classifier for fault detection and classification. The proposed method was validated under no-load conditions and in the existence of oscillatory loads.
Finally, a detailed comparison among different timedomain-based fault detection methods introduced in the literature is presented in Table. 6.

B. FREQUENCY-DOMAIN-BASED METHODS FOR BBF DETECTION AND DIAGNOSIS
In these methods, various signal processing techniques are applied to extract fault-related features from the signals in the frequency domain.

1) FAST FOURIER TRANSFORM-BASED METHODS
In these methods, the frequency spectrum of several quantities such as current, magnetic flux, power, etc. is used for fault detection. This frequency spectrum is calculated primarily using fast Fourier transform (FFT).
Motor current spectrum analysis using FFT is one of the most common and early techniques used to detect BBFs. However, the FFT is valid only for steady-state operation. Also, it suffers from several limitations like spectral leakage and low-frequency resolution. Therefore, different solutions were presented in the literature to overcome these limitations. In [84], to overcome the problem of detecting BBF in large IMs running at very low slip, the resultant magnetic flux density was analyzed instead of the current using FFT to avoid the high-frequency resolution requirement in the case of current spectrum analysis under low-slip operation, however, a special arrangement was required for the installation of the flux sensor. Furthermore, the air-gap and radial leakage flux were analyzed by FFT in [85], where the attenuation of the f r sidebands component was used as a fault indicator. The aim of the proposed method was to overcome motor-currentsignature analysis (MCSA) drawbacks and to discriminate BBF from other fault and load defects. In [34], the magnitude of certain frequencies in the frequency spectrum of the stray flux that was calculated using FFT was used to detect BBFs. In [86], the frequency spectrum that was obtained by FFT was processed using the independent component analysis (ICA) to extract FFT-ICA features for fault detection and diagnosis in an inverter-fed motor. A similar approach to detect BBFs in a line-fed motor was introduced in [87], where the ICA was supported by artificial neural networks (ANN). Furthermore, the frequency spectrum obtained by FFT was fed to an intelligent multi-agent system for BBFs detection and diagnosis as presented in [88].
In another attempt to overcome the detection BBF in IMs working at very low slip, such as large machines with a very small rated slip or unloaded IMs in off-line tests, an enhanced discrete Fourier transform (DFT) based on zero-padding of the sampled stator current was used in [89] to minimize original FFT spectral leakage. Moreover, DFT with a sliding window and its related sidelobes leakage phenomenon was utilized to detect and diagnose BBFs in [90]. In [59], the FFT followed by the orthogonal matching pursuit algorithm was applied to analyze the vibration signal for BBF detection. In [91], an efficient index to detect BBF under variable loading and different inertia conditions was proposed through the monitoring of the LSH and RSH phase angle variation. Also, another index was proposed to estimate fault severity.
In [46], [47], and [48], the fast Fourier transform was applied to the stator current in the d-q frame to provide a robust basis to discern broken bar from mechanical oscillations. In [46], the magnitude of some frequency components in the active and reactive current spectrum was utilized as a fault indicator. A more advanced fault indicator based on the variation of the magnitude and phase angle of the active and reactive current spectrum was proposed in [47]. Later in [48], it was proved that the d-component of the current is immune from load oscillations and suggested to use of its spectrum as a fault indicator. However, these methods provided efficient methods to detect BBFs under the presence of load oscillations, the three-phase current measurements were required in [46] and three-phase current and voltage measurements were required in [47]. On the other hand, a method was introduced in [34] to avoid the false alarm of BBF and discriminate the BBF from eccentricity fault and load oscillations. In this method, the frequency spectrum of the stray flux collected using a flux sensor was proposed to overcome this problem. In [49], it was proved that the 5 th sideband harmonics of the rotor speed in stray or air gab flux are immune to this problem and some other causes of misdiagnosis. But the rotor speed measurement is still a requirement for these methods.
The frequency analysis of the instantaneous power was used for BBFs detection. The BBF-related frequency components are shifted from (1 ± 2ks)f s in the current spectrum to 2ksf s in the instantaneous power spectrum far from the fundamental frequency component. Moreover, the results of this method were confirmed in [92]. In addition, it was proved in [92] that the frequency analysis of the instantaneous active and reactive power and their derived signalsthe power factor and its phase angle could provide a robust base for differentiating BBF and eccentricity faults from load oscillations.

2) ENVELOP SPECTRUM ANALYSIS-BASED METHODS
Another solution to discriminate the sideband harmonics from the fundamental current component was proposed in [93], [94], and [95]. This solution was based on applying the Hilbert transform (HT) to the sampled current to calculate the current analytical signal or the current envelope. The spectrum analysis of the analytical signal using FFT showed that the main sideband harmonic transferred to 2sf s . Furthermore, ANN was used in [94] and [95] to identify BBFs in inverter-fed motor and line-fed motor respectively. Also, [96] provided a solution for detecting BBF under light loading conditions with a relatively small number of samples. In this method, the analytic current signal (current envelope) obtained by a low-cost time-shift-based method was processed using multicoset sampling method at a very low sampling rate. On the other hand, HT was applied to starting current to get its envelope and the standard deviation of this envelope is utilized for fault detection and diagnosis in [97]. VOLUME 10, 2022

3) HIGH-FREQUENCY RESOLUTION-BASED METHODS
To overcome FFT spectral leakage drawbacks especially at low loading conditions and under mixed faults conditions, high-resolution frequency or frequency estimator techniques are used such as multiple signal classification (MUSIC) in [98] and estimation of signal parameters via rotational invariance techniques (ESPRIT) in [99] but, the high-frequency resolution comes at high computational burden. A proposed solution to decrease the computational burden of MUSIC through the use of frequency estimator and ZOOM technique was introduced in [100]. A model order estimation algorithm to improve frequency estimator efficiency and a fault severity criterion to estimate fault severity were proposed in [101]. The MUSIC technique was modified in [102] to detect incipient BBF in inverter-fed motors through the adjustment of three parameters based on load level and the power source. That is presented as a major limitation of this technique. The selection of the optimum values of these parameters is considered the major limitation of this technique.

4) FUNDAMENTAL FREQUENCY SUPPRESSION-BASED METHODS
In [103], the fundamental frequency component was removed from the current signal using interference suppression techniques. Then the maximum likelihood principle is utilized to estimate the fault-related frequencies followed by the fault severity estimation stage based on a generalized likelihood ratio test. An alternative technique to estimate fault-related components in motor operates at low slip with low acquisition time was presented in [104] based on frequency estimation using two cascaded Taylor-Kalman (TK) filters with a subsampling scheme. Later, an estimation technique called nonlinear least squares was applied to the current signal in [105] to estimate and highly attenuate the fundamental current component by suppressing only the frequency component instead of a frequency band like the previous methods. Hence, a clear spectrum that shows fault-related obliviously could be obtained. Moreover, a more simple technique that was based on spectral subtraction, moving average algorithm, and autocorrelation of the stray flux was introduced in [106].
The computational burden of a frequency-based method mainly depends on acquisition time and sampling frequency. So, the BBFs detection method that utilizes a lower sampling frequency without degrading method efficiency is introduced in [107]. This method showed that a low sampling frequency integrated with a notch filter could be efficiently applied with the discrete-time Fourier transform and autoregressive-based spectrum methods to detect BBFs.

5) EMPIRICAL MODE DECOMPOSITION-BASED METHODS
Empirical mode decomposition (EMD) was used as another tool to decompose the current signal into its intrinsic mode functions (IMFs) in [108]. The standard deviation of the samples and the time between successive zero crossings of two current IMFs were presented in [108] as fault indicators.
As the EMD has many limitations such as mode mixing problems, stopping criteria, and border effects, Complete Ensemble Empirical Mode Decomposition (CEEMD), a more advanced version of EMD, was presented in [109] to decompose acoustic sound and vibration signals to its IMFs. Then, the spectrum of some IMFs was estimated using the marginal frequency of the Gabor representation and introduced as a fault indicator.  Table. 7. The comparison covers the number and type of required sensors, tested state (either steady-state or transient), type of IM supply (either line-fed mode. or inverter-fed mode), the severity of tested BBFs, and loading conditions. It also shows the sampling frequency and training required and finally evaluates the achieved accuracy.

C. TIME-FREQUENCY DOMAIN-BASED METHODS FOR BBF DETECTION AND DIAGNOSIS
The conceptual basis of these methods is to use multiple signal processing techniques which are applied to monitor fault-related conditions in the time-frequency domain. Such techniques were introduced in the literature to identify the fault-related components under the transient conditions in the time-frequency (t − f ) plane.

1) LINEAR T-F TRANSFORMS-BASED METHODS
In [110], the fractional Fourier transform was applied to the current signal after being filtered using wavelet transform (WT) to extend the capabilities of Fourier transform to deal with the whole range of the motor speed under transient conditions. Then, linear transforms were widely applied to the current, flux signals to evaluate the main side-band harmonics in the (t − f ) plane. Such transformers include short-time Fourier transform (STFT), WT, Stockwell transform (ST), adaptive slope transform (AST), and chirplet Transform (CT). The STFT utilizes a fixed time and frequency resolution window dependent on the Heisenberg uncertainty principle. i.e. the improvement of frequency resolution worsen time resolution and vice versa. The resolution of this window cannot be changed from one point to another which represents the major weakness of this transform. In the literature, the STFT was used to detect BBFs in the (t − f ) domain in [111] during start-up and counter-current braking respectively. In [112], STFT supported by Otsu segmentation was utilized to early detect and classify BRB faults in IMs under starting of linefed IMs is proposed. In addition, the STFT was applied to stray flux to detect BBFs in [24], [28], [55], and [113].
In contrast, the window width in the WT is variable and depends on the frequency of the analyzed signal. Therefore, this window provides a high-frequency resolution with a lower time resolution at low frequencies whereas; a low-frequency resolution with a higher time resolution at high frequencies can be obtained. In the literature, the continuous wavelet transform (CWT) was applied to the current signal in the starting to detect BBFs pattern in [114] and [115]. In [116], the STFT, CWT, and a multilabel classification framework were applied to detect BBFs in the starting of a line-fed motor. In addition, the synchro-squeezing transform that is based on CWT but with a higher t-f resolution is used to detect the same fault in [117]. The DWT that is discretized form of CWT was utilized in [27] to detect BBFs using the current signal. The energy eigenvalues of these frequency bands under steady-state condition were utilized as a fault indicator in [118] whereas, a fault indicator related to a certain frequency band under transient conditions were proposed in [27]. An outstanding performance method was applied in [119] to detect multiple motor faults online at early stages regardless of motor characteristics. In this method, a wavelet function and a multivariate control chart were applied to the current signal in the steady-state to detect and classify BBFs regardless of the supply mode. In contrast, the energy of sub-bands extracted from the acoustic signals using rational-dilation wavelet transform was presented as a useful fault indicator in [61].
Later, DWT is combined with Local Binary Pattern to extract features from the acoustic signal as presented in [120]. Neighborhood Component Analysis, Support Vector Machine, and K Nearest Neighborhood were utilized to select the most informative features and classify BBFs.
Furthermore, a multiple-windowed harmonic wavelet packet transform (WPT) as a modified version of the DWT was introduced in [121] to overcome the problem of continuous redefinition of the decomposition tree levels to deal VOLUME 10, 2022 with the variable frequency content in the case of inverterfed motors. In [11], WPT was applied to the vibration signal to detect BBF. However, WT has many limitations such as dependence on the mother wavelet and number decomposition levels [13].
Also, to automatically detect and diagnose early BBF under the variable loading and inertia conditions without the need for expert knowledge, a method that is based on ST was applied in [13]. The ST that have a variable window width with more control parameters for better resolution adjustment than WT. In such study, the window width control parameters were selected using an active-set optimization technique and the ST was applied to the current signal to detect and diagnose BBFs in a directly fed motor.
As the previous linear transforms, AST is subjected to trade-off between time and frequency resolution. Nevertheless, the AST has a major benefit over STFT and WT in that the window can be adjusted at every point in t-f plane. Consequently, the trajectory of the LSH and RSH can be represented efficiently. Actually, the AST was utilized in [25] and [122] to detect BBFs of a line-fed motor and inverter-fed motor respectively.
The chriplet transform (CT) shares the same feature with other linear transformers. On the other hand, CT does not follow the t-f trade-off rule like other linear transformers [25]. While the window of STFT for example has a definite length and width in the t-f plane, the window of CT provides only thickness and direction [25]. Therefore, the CT represents one of the most suitable linear transforms to monitor LSH and RSH in the case of BBFs in inverter-fed motors. It is worth mentioning that the CT is not suitable for analyzing signals that change their directions in the t-f plane abruptly. In [124], the CT was applied to the current signal of an inverter-fed IM operating at low slip conditions where the fault component frequencies are very close to the fundamental component in the t-f plane.
Based on the previous discussion, it can be deduced that the CT can efficiently monitor LSH and RSH in the case of the inverter-fed motor during starting whereas, AST can monitor these fault-related harmonics during steady-state. To overcome the shortcoming of AST and CT, the dragon transform (DT) was introduced in [38] and [125]. The DT employs a more advanced window, so it can efficiently represent the trajectories of the fault-related components during starting and steady-state in both line-fed and inverter-fed modes under sophisticated control algorithms.

2) QUADRATIC T-F DISTRIBUTION-BASED METHODS
In the literature, another type of t-f representation called quadratic t-f distribution is presented. In this type, a higher time and frequency resolution can be provided simultaneously. However, this type suffers from cross terms drawbacks when analyzing multicomponent signals. The Wigner-Ville Distribution (WVD) represents this type of t-f distribution. In [126] and [127], the WVD was applied to the starting current of a direct-fed motor and the steady state current of an inverter-fed motor in [128]. Also, another type of quadratic distribution, called Zhao-Atlas-Marks (ZAM) distribution, was applied to vibration signals to detect BBFs in [129]. To limit the cross terms that degrade the quality of WVD, a filtered current signal during starting of a direct-fed motor was used instead of the original signal as in [130].

3) HILBERT-HUANG TRANSFORM-BASED METHODS
Moreover, the Hilbert-Huang Transform (HHT) was introduced in the literature to detect the BBFs in both modes of supply. This transform is based on the decomposition of the analyzed signal to a number of IMFs using EMD to be more suitable to be processed using the HT [25]. The HT can accurately define the instantaneous frequency of each IMF and its amplitude. More advanced decomposition algorithms like the Ensemble Empirical Mode Decomposition (EEMD) and Variational Mode Decomposition (VMD) are introduced in the literature to overcome EMD problems (discussed before in Section V. B-6). The HHT was presented in [131] and [132] to detect BBFs in line-fed and inverter-fed modes under steady-state respectively, while, in [133] and [134], the HHT was applied to detect BBFs in the line-fed mode under transient conditions.

4) HIGH T-F RESOLUTION-BASED METHODS
In another attempt to improve the t-f resolution, the highresolution frequency method such as MUSIC was presented in the literature to detect BBFs, especially in the case of inverter-fed mode. In [135], the current signal was decomposed by CEEMD and the resulting IMFs were processed using MUSIC algorithm to detect BBFs in both steady-state and starting inverter-fed motors. In fact, this method and the method based on DT have an outstanding performance compared to other transforms, especially in inverter-fed mode. Later, a method based on MUSIC and non-uniform demodulation was applied in [136] on the current signal to detect BBFs in the inverter-fed mode under starting conditions. In [137], a non-uniform sampling technique and MUSIC were used to change the trajectories of LSH and RSH in the t-f plane in the case of starting an inverter-fed motor to be easily monitored. In addition, the MUSIC algorithm was applied to the zero-sequence current in [6] to detect such faults in linefed mode.  Table. 8.

5) COMPARISON OF T-F DOMAIN-BASED METHODS
Also to illustrate the difference in the resolution between some t-f transforms, some t-f representations are presented in Fig. 10, for the current signal of a real motor with one broken bar has the following characteristics: 400 V, 1.5 kW, 2-poles, 3.25 A, and 2860 rpm at full load.

D. DISCUSSION ON SIGNAL PROCESSING-BASED METHODS FOR BBF DETECTION AND DIAGNOSIS
As discussed before, the fault-related features are extracted in signal processing-based methods from the time, frequency, and time-frequency domains. Accordingly, some issues are summarized regarding the implementation of these methods as follows: • Statistical features are generally extracted from the signal in the time domain. Therefore, the computational burden of these features' processing is low compared to other signal processing-based methods. However, an artificial or statistical classifier is required for fault severity diagnosis and hence classifier training is required.
• In contrast, when the fault-related features are extracted from the frequency domain, the diagnosis of BBFs is based on monitoring the magnitude of fault-related frequency components mainly LSH and RSH. These frequencies are strictly close to the fundamental components, especially in case zero and low loading conditions. In addition, in the inverter-fed mode, harmonics of high levels are injected into the current that may flood fault-related frequencies. Therefore, the main contributions in this field can be concluded in: -Suppressing fundament components and harmonics for better monitoring of LSH and RSH, -Applying high-resolution methods to clearly show fault-related frequencies, -Monitoring frequencies in the current envelop or instantaneous power where the frequencies of interest are from fundamental components and monitoring frequency band rather than certain frequencies.
-Although, the frequency-based methods are the common BBFs detection method, they require more computational burden than time-based methods. In addition, a threshold determination for fault detection or a classifier may be required.
• In the time-frequency domain-based methods, the fault-related features are extracted from the t-f plane VOLUME 10, 2022 generally during starting conditions. The fault-related features appear as a unique pattern in the t-f plane in the case of line-fed mode and as two lines strictly close to the fundamental components. Therefore, the detection of BBFs in the case of inverter-fed modes is more challenging. Although the detection of BBFs is easier than the previous two approaches, the transformers used in these methods require more computational burden. In addition, expert knowledge is required for fault identification. The Persistence Spectrum may be a potential solution that we suggest to overcome the challenges associated with detecting fault-related components in inverter-fed modes with a suitable calculation burden [138], [139]. It is widely used to detect the hidden weak signals in other powerful signals.

VI. DATA-DRIVEN-BASED METHODS FOR BBF DETECTION AND DIAGNOSIS
In this approach, the data-driven methods are applied directly to the measured signals to detect and estimate the severity of the fault with high accuracy [140]. These methods, in contrast to the model-based methods and signal-processing-based methods, expert experience to select and extract fault features is not required. On the other hand, the data-driven-based methods do not provide the physical interpretation for fault detection and diagnosis [140]. In addition, a considerable amount of training data is required to achieve reasonable accuracy [22]. In an industrial environment, providing a large amount of data for training may be unavailable and require a high computational burden [22], [141]. The learning strategy of the data-driven methods can be classified as supervised and unsupervised [22]. In the unsupervised learning strategy, the knowledge base is extracted from the historical unlabeled data to simulate healthy system behavior, which is used to judge the real-time system behavior [22]. So, the unsupervised learning strategy depends on the AI to detect hidden patterns in the provided data without human aid. Whereas, in the supervised learning strategy the knowledge bases for both healthy and faulty conditions are extracted from labeled data that are used for system monitoring [22]. In the literature, an unsupervised learning technique was used in [142] to detect and diagnose BBFs where a deep neural network (DNN) was trained using features extracted by sparse auto-encoder from unlabeled data, and a dropout algorithm was utilized to avoid overfitting during the training stages. The deep-SincNet method supported with a convolutional neural network (CNN) represents another example of an unsupervised learning technique implemented in [143] to detect BBFs using the current signal with high accuracy for single and mixed faults in noisy environments. Whereas a supervised learning approach was utilized in [144], where an adaptive gradient optimizer-based deep convolutional neural network (ADG-dCNN) technique was introduced to automatically detect BBFs using multi-vibration sensors with minimum human intervention. Another data-driven approach that was based on Interpolated Kernel Density Estimator (IKDE) was utilized in [145] due to its superiority over other Kernel Density Estimators in terms of speed improvement and computational burden. Where the Naive Bayes Classifier (NBC) supported with Interpolated Kernel Density Estimate (IKDE) was presented to detect and classify BBFs using multi-vibration sensors. Furthermore, auto-encoder networks were used for BBF detection and diagnosis utilizing both labeled and unlabeled data. In [146], stacked auto-encoder networks were used to extract fault features from the current signal in the frequency domain using labeled data. This method could screen false alarms and detect interturn, BBFs, and bearing faults while reducing expertise demand. In [147], a Noisy Domain Adaptive marginal Stacking Denoising Auto-encoder (NDAmSDA) technique was employed to detect and classify BBFs based on an acoustic signal using an unsupervised learning approach. On the other hand, a method for early detection and classification of BBFs was proposed in [148] based on using 2-D CNN to classify t-f images obtained by applying STFT to starting current after removing the fundamental current component using a notch filter. A relatively similar approach was proposed in [149], but images were obtained by applying STFT to stray flux during starting. In [150], shallow and adaptive 1-D CNN was proposed to automatically extract features from the raw current signal and classify faults with high accuracy.
The main advantages of shallow CNN over deep CNN are suitability for real-time application, limited data required for training, and cost-effective implementation [150]. On the other hand, deep CNN and DNN have more advanced feature extraction and learning abilities [144]. However, DNN suffers from some drawbacks such as overfitting, high computational burden, and the selection of its parameters becomes challenging for complicated problems [144]. In contrast, deep CNN requires less computational burden than DNN as it utilizes fewer connections between layers than DNN resulting in less probability of overfitting [144]. In general, the deep models are more efficient in feature extraction and more suitable for BBF than shallow ones.
A comparison among different data-driven-based fault detection methods introduced in the literature is presented in Table. 9.
However, the data-driven approach can independently extract features from the row signals without the need for signal processing tools. This advantage comes at a high cost of computational burden and the amount of data required for training that may not be available in the industrial environment. Also, the data-driven-based methods do not provide any physical interpretation for fault detection and diagnosis [140]. On the other hand, the classical approach including model-based methods and signal processing-based methods provides a good physical interpretation and requires a relatively low amount of data. But, expert knowledge is required to build detailed models or manually extract fault features. In our point of view, hybrid techniques which are a combination between data-driven and classical approaches are the most promising techniques for BBF fault detection and diagnosis. As these techniques provide the main advantages of both approaches. Methods in [151], [152], and [153] are examples of this approach.

VII. CONCLUSION AND IDEAS FOR FUTURE WORK
In this paper, a comprehensive review of the most recent BBFs detection and diagnosis methods up-to-date are provided. The BBFs fault signatures on different motor variables are discussed. In addition, the fault detection and diagnosis methods are classified into: groups and sub-groups to be deeply described and evaluated. A comparison between different methods in the same group and sub-group is presented in a tabulated format for easy interpretation. Additionally, a comprehensive discussion of such methods is offered.
Although the development achieved in the field of BBFs detection and diagnosis, some issues that still require more attention from researchers can be summarized and highlighted in: • A complete and integrated system for different IM faults identification including broken bar, stator inter-turn, bearing, and eccentricity faults is still required.
• However, model-based methods are one of the most promising methods, the investigation of the performance of model-based methods in the case of the presence of false diagnosis sources such as low-frequency load oscillations and with a lesser number of sensors is still needed.
• The digital twin approach represents a trending technology in the field of monitoring and fault detection, however, a comprehensive application that can detect and diagnose different motor faults is still missing.
• Another alternative to fulfill the requirements is the datadriven-based methods but a relatively large amount of data is required. To overcome this drawback, transfer learning may be a promising solution.
• Regarding signal processing-based methods, the development of methods that provide high accuracy and require low sampling frequency, short acquisition time, and a low computational burden is needed.
• In the time-frequency-based methods, a wellexperienced operator is required to identify fault patterns from the t-f plane. So, a numerical indicator is required for easy fault detection. Also, the performance of these methods under short-start duration is needed to be more investigated.
• On the other hand, the papers that discuss end ring faults detection in the literature are still rare so; more research is required on this point.