Bearing Fault Diagnosis in Electric Motors: A Structured Review of Recent Methods and Engineering Trends

Abstract

Rolling bearings are among the most failure-prone critical components in electric motors, and their operational conditions have a direct impact on the safety and reliability of motor systems. Owing to weak incipient fault characteristics, complex operating conditions, and diverse signal manifestations, bearing fault diagnosis has become a key research focus in the field of motor condition monitoring. This paper presents a structured review of representative recent methods for electric motor bearing fault diagnosis, with particular emphasis on vibration signals and motor current signals. From the perspectives of physical interpretability, signal representation, and data-driven learning, bearing fault diagnosis approaches based on fault mechanism modeling, feature extraction, and artificial intelligence (AI) are structurally organized and compared. In addition, data augmentation techniques and meta-learning methods for small-sample scenarios, as well as transfer learning (TL) methods for variable operating conditions and virtual-to-real transfer scenarios, are summarized. Through a comparative analysis of different technical routes, the key challenges and emerging trends in bearing fault diagnosis under complex operating conditions and practical engineering scenarios are identified, providing an engineering-oriented reference for method selection and future research.

1. Introduction

Electric motors are essential power equipment in modern industrial systems and are extensively employed in manufacturing, energy systems, transportation, and other industrial sectors. Their operational reliability is directly associated with system safety, equipment service life, and overall economic performance. Rolling bearings are among the most failure-prone and critical components in motor systems, and their operating condition directly affects the safety and reliability of the overall system operation. A typical rolling bearing consists of an inner race, an outer race, rolling elements, and a cage, as shown in Figure 1. Due to the complex contact interfaces and harsh operating conditions, bearing faults often exhibit weak incipient features, strong concealment, and progressive deterioration. Previous engineering statistics and fault analysis studies have shown that bearing-related faults are among the most common failure types in electric motors [1,2]. If such faults are not detected and diagnosed in time, they may induce secondary failures and even lead to severe system-level accidents. Therefore, accurate and reliable bearing fault detection and diagnosis are essential for maintaining the safe operation of electric motors and related industrial equipment [3,4].

To monitor bearing operating conditions and extract fault-related information, a variety of sensing signals have been investigated, including vibration [5], acoustic emission [6], current [7], rotational speed [8], and other auxiliary signals. Among these sensing modalities, vibration and motor current signals have been studied most extensively because they provide rich fault-related information and are well suited to engineering monitoring. Vibration signals directly reflect impact responses and modulation effects caused by localized defects and therefore remain one of the primary information sources for bearing fault diagnosis [5]. By contrast, current-based diagnosis is non-intrusive, easy to deploy, and compatible with online monitoring, which makes it particularly suitable for practical motor systems [7]. With the continuous development of sensing technology, signal processing, and computational methods, bearing fault diagnosis has gradually evolved from traditional signal analysis toward more integrated and intelligent diagnostic frameworks.

From the perspective of diagnostic strategy, existing studies on motor bearing fault diagnosis can generally be categorized into three major routes: fault-mechanism-based methods, feature-extraction-based methods, and AI-based methods. Fault-mechanism-based methods focus on the physical formation and propagation mechanisms of bearing defects and attempt to reveal how localized faults are reflected in vibration responses or current sideband components [9,10]. Feature-extraction-based methods aim to characterize fault-sensitive information in the time, frequency, or time-frequency domains and combine these features with conventional classifiers for diagnosis [11]. AI-based methods, especially machine learning (ML) and deep learning (DL), further enhance diagnostic performance by learning discriminative representations directly from measured data [12,13]. These three technical routes differ considerably in physical interpretability, data dependence, implementation complexity, and robustness under varying operating conditions.

In recent years, with the rapid development of intelligent diagnosis, increasing attention has been paid to the application of DL methods in bearing fault diagnosis because of their powerful nonlinear feature learning capability and end-to-end modeling advantages [14]. However, practical engineering applications still face several persistent challenges, including limited fault samples, class imbalance, varying operating conditions, and discrepancies between laboratory and industrial data distributions [15]. This data scarcity issue is not merely a matter of sample quantity but is also closely related to the characteristics of the public datasets on which diagnostic methods are commonly validated [16]. Although benchmark datasets such as CWRU, Paderborn, IMS, and PRONOSTIA have greatly promoted methodological development, their laboratory-based acquisition settings, limited operating-condition coverage, and frequently reused evaluation protocols may lead to overly optimistic estimates of generalization performance and do not fully reflect the diversity of real industrial scenarios [17,18]. In addition, purely data-driven methods often lack explicit physical constraints, which may weaken interpretability and reduce generalization ability under cross-domain conditions. To address the above issues, especially limited sample availability and distribution shifts across operating scenarios, data augmentation, meta-learning, and TL have gradually become important research directions. Data augmentation enriches the training set under small-sample and imbalanced conditions, meta-learning facilitates rapid adaptation to new fault categories or working conditions with only a few labeled samples, and TL improves knowledge reuse and model adaptability across varying operating conditions and between virtual and real scenarios [19].

Although existing reviews have examined bearing fault diagnosis from the perspectives of vibration analysis, current signature analysis, and intelligent diagnosis, an integrated review focused specifically on electric motor rolling bearings is still lacking. In particular, the relationships among fault mechanism modeling, feature extraction, AI-based diagnosis, data augmentation, and TL have not yet been sufficiently discussed within a unified engineering-oriented framework. To explicitly demonstrate the incremental value and distinctive advantages of this paper,

Table 1. Comparison between the present structured review and recent related review papers.

Reference	Year	Primary Focus	Signal Modality	Mechanism-Data Fusion	Engineering Constraints
[12]	2023	DL and TL	Vibration mainly	Purely data-driven	TL focused
[13]	2023	AI and DL for rotating machinery	Vibration mainly	Purely data-driven	Standard conditions assumed
[15]	2022	Small and imbalanced data diagnosis	Various	Purely data-driven	Small and imbalanced data focused
[16]	2024	Limitations of DL	Vibration mainly	Conceptual discussion	Data distribution shift discussed
[20]	2023	Motor current signature analysis	Current exclusively	Mechanism analysis focused	Ideal conditions assumed
This review	2026	Integrated physical-data engineering framework	Vibration and Current	Deep mechanism-data fusion	Cross-domain and few-shot adaptation

provides a critical comparison with recent high-impact review articles. As illustrated, while previous works have made significant contributions, they typically exhibit clear boundaries—either isolating specific signal modalities or decoupling data-driven models from physical constraints. This paper bridges these gaps by proposing a structured, closed-loop framework.

The reviewed literature was identified through database searching and subsequent screening, including duplicate removal, title and abstract review, and full-text assessment, as illustrated in Figure 2. Consistent with the purpose of this structured review, the final literature set comprises representative studies organized by methodological themes rather than by exhaustive PRISMA-style inclusion. This review focuses on the synergy of vibration and stator current signals, localized defects of the inner race, outer race, and rolling elements, as well as practical engineering scenarios involving small samples, varying operating conditions, and virtual-to-real transfer. Accordingly, Section 2 discusses fault-mechanism-based diagnosis methods from the perspectives of vibration-signal-based and motor-current-signal-based modeling. Section 3 summarizes feature-extraction-based diagnosis methods. Section 4 reviews AI-based diagnosis methods. Section 5 discusses representative methods for bearing fault diagnosis under small-sample conditions, including data augmentation and meta-learning strategies. Section 6 further reviews TL methods for varying operating scenarios and virtual-to-real transfer settings. Finally, the major challenges and future research directions are summarized.

2. Bearing Fault Diagnosis Based on Fault Mechanism Models

2.1. Vibration-Signal-Based Bearing Fault Mechanism Models

Localized damage in a rolling bearing alters its internal contact state, load distribution, and dynamic response. These changes appear in vibration signals as periodic impacts and modulation components with clear physical meaning. Vibration-based diagnosis uses the relationship between these dynamic changes and their signal manifestations to identify fault type, location, and progression. Because of their strong physical interpretability and engineering relevance, such methods remain fundamental to bearing fault diagnosis.

2.1.1. Vibration Mechanisms and Characteristic Frequency Theory of Bearing Faults

Under normal operating conditions, continuous contact is maintained between the rolling elements and the inner and outer raceways, and the vibration response of a rolling bearing system is primarily dominated by the rotational frequency and its associated low-order harmonics. When localized defects develop on the surfaces of the inner race, outer race, or rolling elements, the contact behavior of the rolling elements during passage through the defect region transitions from continuous rolling to a nonstationary process characterized by intermittent contact and rapid recovery [21], thereby fundamentally altering the excitation mechanism of the bearing system.

From a contact mechanics perspective, the presence of localized defects leads to instantaneous unloading as the rolling elements enter the defect region, followed by a rapid restoration of contact stiffness upon recontact with the intact raceway. This process results in abrupt temporal variations in contact force and generates impact-type excitations [22]. Such impact excitations inherently exhibit broadband characteristics, with their spectral distributions jointly determined by defect geometry, contact stiffness nonlinearity, and load conditions. Due to structural constraints, these excitations are mainly manifested as a superposition of high-frequency decaying vibrations and low-frequency repetitive components in bearing systems. Accordingly, the resulting spectral structure can be described as structural resonance bands acting as carriers that are modulated by the impact repetition rate [23].

Focusing on the repetitive nature of impact excitations, their relationships with bearing geometric parameters can be analyzed from a kinematic perspective. For outer-race defects, the defect location remains fixed with respect to the load zone, and an impact is generated each time a rolling element passes through the defect region. Consequently, the impact repetition rate is determined by the relative motion between the rolling elements and the outer race [24]. In the case of inner-race defects, because the inner race rotates with the shaft, the defect location continuously varies relative to the load zone, leading to rotational-frequency modulation of the impact excitation superimposed on its fundamental repetition rate [25]. Defects on the rolling elements involve the coupling between rolling element spin and orbital motions, and the corresponding impact repetition rate reflects the combined kinematic behavior of the rolling elements within the raceways. These kinematic distinctions constitute the physical basis for the different characteristic frequency expressions associated with inner-race, outer-race, and rolling-element faults.

Based on the above fault mechanism analysis, the characteristic frequencies corresponding to inner-race, outer-race, and rolling-element defects are widely adopted in engineering practice as key indicators for bearing fault identification. The standard expressions of these characteristic frequencies can be written as [26]:

$$f_{\mathrm{o}}={\displaystyle \frac{Z}{2}}{f}_{\mathrm{r}}\left(1-{\displaystyle \frac{D_{\mathrm{b}}}{D_{\mathrm{c}}}}\cos \beta \right)$$

(1)

$$f_{\mathrm{i}}={\displaystyle \frac{Z}{2}}{f}_{\mathrm{r}}\left(1+{\displaystyle \frac{D_{\mathrm{b}}}{D_{\mathrm{c}}}}\cos \beta \right)$$

(2)

$$f_{\mathrm{b}}={\displaystyle \frac{D_{\mathrm{c}}}{2D_{\mathrm{b}}}}{f}_{\mathrm{r}}\left(1-{\left({\displaystyle \frac{D_{\mathrm{b}}}{D_{\mathrm{c}}}}\cos \beta \right)}^2\right)$$

(3)

where f_o denotes the characteristic frequency of outer race faults, f_i denotes the characteristic frequency of inner race faults, and f_b denotes the characteristic frequency of rolling element faults. Z represents the number of rolling elements, D_b is the diameter of the rolling element, D_c is the diameter of the rolling element pitch circle, β is the contact angle, and f_r is the rotational frequency of the shaft.

2.1.2. Vibration Response Modeling Based on Dynamic Mechanism Models

Building upon the vibration mechanisms and characteristic frequency theory of bearing faults, dynamic-mechanism-based modeling approaches have been developed to further characterize the vibration responses of rolling bearings under practical operating conditions. These approaches describe the interaction processes among internal bearing components from a mechanical perspective. By formulating the equations of motion for systems consisting of rolling elements, inner and outer races, and the cage, such models can directly capture the formation mechanisms of vibration responses and their evolution with respect to structural parameters and operating conditions, thereby providing a fundamental theoretical basis for understanding rolling bearing vibration behavior.

In recent years, rolling bearing dynamic modeling has evolved from simplified representations toward multi-degree-of-freedom and strongly nonlinear models. Lumped-parameter approaches and multibody dynamics theory are commonly employed, in which bearing components are treated as motion units with mass and degrees of freedom. By incorporating Hertzian contact nonlinearity, damping, and inertial effects, these models are capable of directly generating time-domain vibration responses.

To translate these physical phenomena into a tractable mathematical framework, the vibration behavior of the bearing system is typically governed by a set of second-order nonlinear differential equations. Taking the inner race and its connected rotor as an example, the general equation of motion can be formulated as:

$$M_r{\ddot{X}}_r+C_r{\dot{X}}_r+K_r{X}_r=F_e(t)-{\displaystyle \sum _{j=1}^Z{F}_{cj}}({\dot{\theta }}_j,t)$$

(4)

where M_r, C_r, and K_r denote the mass, damping, and stiffness matrices, respectively; X_r is the displacement vector; F_e(t) represents the external load; and F_cj(θ_j, t) is the nonlinear contact force generated by the j-th rolling element [27].

The core of this dynamic model lies in the formulation of the restoring force F_cj, which bridges the macroscopic vibration responses to the microscopic localized defects. Based on nonlinear Hertzian contact theory, this force is expressed as:

$$F_{cj}({\theta }_j,t)=K_h{[{\delta }_j({\theta }_j,t)]}_{+}^n$$

(5)

where K_h is the Hertzian contact stiffness coefficient, n is the load-deflection exponent, and the bracket [·]₊ ensures the force is zero if the rolling element loses contact with the raceway. When a localized defect is present, the total elastic deformation δ_j(θ_j, t) is modified by a time-varying defect depth function H_d(θ_j, t):

$${\delta }_j({\theta }_j,t)=X_r\cos {\theta }_j+Y_r\sin {\theta }_j-c_r-H_d({\theta }_j,t)$$

(6)

where θ_j is the instantaneous angular position of the j-th rolling element, and c_r is the radial clearance. The term H_d becomes non-zero only when a rolling element enters the spall region, leading to an instantaneous drop in the contact deformation and a sudden unloading of the force. This abrupt physical disruption mathematically triggers the high-frequency structural resonances and low-frequency modulations characterizing the macroscopic vibration signals [28].

The spatial topology of such a mass-spring-damper system, which embodies these governing equations, can be visually represented through a structural schematic. Figure 3 presents a typical configuration of this multi-degree-of-freedom dynamic model for rolling bearings. Compared to simplified low-degree-of-freedom models, this spatial representation explicitly captures the complex coupling between radial and angular motions, offering superior fidelity for analyzing high-speed dynamic behaviors. Based on such modeling frameworks, multi-degree-of-freedom dynamic models have been widely applied to investigate vibration responses under localized defects, variations in structural parameters, and complex loading conditions [29].

With continued research efforts, the degrees of freedom in bearing dynamic models have progressively expanded from early radial or planar representations to spatial dynamic models that simultaneously account for radial, axial, and angular motions, enabling a more realistic description of internal load transmission and motion constraints within bearings [31]. On this basis, high-speed operation-related factors, including centrifugal forces, gyroscopic effects, and cage dynamics, have been incorporated, allowing these models to remain applicable under high-speed and heavy-load conditions [32]. Moreover, modeling approaches that consider rolling element slip and structural flexibility have attracted increasing attention, as they enable the characterization of vibration modulation effects induced by complex structural coupling.

To address system parameter variations arising from periodic changes in internal load distribution, time-varying parameter modeling has been widely adopted in recent years. Studies have shown that the time-varying stiffness caused by rolling elements entering and leaving the load zone is a major source of internal excitation in bearing vibration. This stiffness variation depends strongly on rotational speed, load, and defect geometry, and it substantially affects both vibration amplitude and spectral characteristics [33]. By incorporating time-varying stiffness, dynamic models can explain modulation phenomena and nonstationary features in vibration responses from a physics-based perspective, without relying on empirical excitation assumptions.

Furthermore, rolling bearing dynamic modeling has gradually extended toward system-level coupling. By integrating bearing models with rotors, shafting systems, or support structures, rotor–bearing system dynamic models can be established to investigate the influence of localized bearing defects, lubrication conditions, and structural nonlinearities on overall system vibration responses and stability [9]. Some studies have further incorporated elastohydrodynamic lubrication effects or structural flexibility models to improve the physical consistency of dynamic models in practical engineering applications [34].

With the increasing availability of computational resources, high-fidelity numerical modeling approaches have been widely adopted for investigating the vibration responses of rolling bearings. Finite element methods enable detailed representation of bearing geometries, material properties, and complex contact behaviors, making them particularly suitable for analyzing the effects of local structural variations on vibration responses. In comparison, explicit dynamic algorithms offer distinct advantages in handling strongly nonlinear contact interactions and transient impact phenomena, and are therefore well suited for simulating transient vibration processes under complex operating conditions. These high-fidelity models are capable of directly generating high-quality time-domain vibration responses, thereby providing a reliable physical foundation for subsequent vibration feature analysis and model validation [35]. Representative vibration signals obtained from such simulations are illustrated in Figure 4. As shown in the frequency spectra, these algorithms can distinctly isolate characteristic fault frequencies from baseline structural noise, visually confirming their modeling superiority. However, this superiority is primarily reflected in mechanism reproduction rather than direct diagnostic deployability. In practical applications, the high computational cost and dependence on accurately specified structural parameters often limit their use to offline analysis, simulation-assisted interpretation, or model validation.

Overall, vibration response modeling based on dynamic mechanism models has evolved from low-degree-of-freedom representations with simplified assumptions toward multi-degree-of-freedom, strongly nonlinear, and high-fidelity numerical models. Although the increasing model complexity substantially improves the ability to capture realistic operating conditions, it also leads to challenges such as parameter identification difficulty and high computational cost. Consequently, achieving an appropriate balance between physical fidelity, model simplification, and computational efficiency remains an important and ongoing research direction in rolling bearing dynamic vibration modeling.

2.2. Current-Signal-Based Bearing Fault Mechanism Models

When localized damage occurs in rolling bearings, it not only alters the mechanical operating state of the bearing system but also perturbs the internal electromagnetic processes of the motor through electromechanical coupling mechanisms, thereby introducing fault-related modulation characteristics into stator current signals. Specifically, bearing-fault-induced rotor vibration and eccentricity variations give rise to periodic disturbances in the air-gap magnetic field and electromagnetic parameters, resulting in modulation components in the current signals that are closely related to bearing geometric parameters and operating conditions. Current-signal-based bearing fault analysis approaches aim to identify and characterize bearing fault features by analyzing the mapping mechanisms of these mechanical disturbances within the electromagnetic system. Owing to their nonintrusive nature, adaptability to complex operating conditions, and seamless integration with motor drive systems, such approaches offer distinctive advantages for bearing fault diagnosis.

2.2.1. Electromagnetic Modulation Mechanisms and Current Characteristic Frequency Expressions of Bearing Faults

During motor operation, mechanical disturbances caused by local bearing defects interact with the electromagnetic system through the air-gap magnetic field and time-varying electromagnetic parameters, leading to deviations of stator currents from their ideal steady-state behavior. From a physical standpoint, these disturbances primarily manifest as periodic modulation of the air-gap permeance and magnetic flux distribution, which in turn introduces additional frequency components associated with bearing faults into the current spectrum. Based on such electromagnetic modulation phenomena, extensive studies have progressively established the correspondence between bearing faults and current characteristic frequencies, forming an analytical framework centered on modulation theory.

Early investigations mainly interpreted this modulation mechanism from the perspective of air-gap permeance variations induced by radial displacement disturbances. It was demonstrated that periodic mechanical vibrations caused by local bearing defects can induce small radial displacements of the rotor, thereby modulating the air-gap magnetic field distribution and giving rise to sideband components related to bearing fault characteristic frequencies in the stator current spectrum [36].

To mathematically describe this electromagnetic modulation mechanism, consider the radial rotor displacement e(t) caused by a bearing fault. This displacement can be modeled as

$$e(t)=e_0\cos ({\omega }_{v}t)$$

(7)

where e₀ is the fault-induced displacement amplitude and ω_v is the vibration angular frequency. This mechanical vibration directly modulates the effective air-gap length g(θ, t), which can be expressed as:

$$g(\theta ,t)=g_0-e(t)\cos (\theta -\phi )$$

(8)

where g₀ is the uniform air-gap length under healthy conditions, θ is the spatial angle, and φ is the initial phase angle. Consequently, the air-gap permeance Λ(θ, t) is inversely proportional to g(θ, t) and can be approximated using a Taylor series expansion as:

$$\mathsf{\Lambda }(\theta ,t)\approx {\displaystyle \frac{{\mu }_0}{g_0}}\left(1+{\displaystyle \frac{e_0}{g_0}}\cos ({\omega }_{v}t)\cos (\theta -\phi )\right)$$

(9)

where μ₀ is the permeability of free space. Based on this time-varying permeance, we can explicitly demonstrate the electromechanical coupling process. Let the fundamental magnetomotive force be expressed as

$$F(\theta ,t)=F_m\cos (p\theta -{\omega }_{s}t)$$

(10)

where F_m is the fundamental magnetomotive force amplitude, p is the number of pole pairs, and ω_s is the fundamental supply angular frequency [37]. The resulting magnetic flux density B(θ, t) is the product of the fundamental magnetomotive force F(θ, t) and the permeance Λ(θ, t):

$$B(\theta ,t)=F(\theta ,t)\mathsf{\Lambda }(\theta ,t)\approx F_m\cos (p\theta -{\omega }_{s}t){\displaystyle \frac{{\mu }_0}{g_0}}\left[1+{\displaystyle \frac{e_0}{g_0}}\cos ({\omega }_{v}t)\cos (\theta -\varphi )\right]$$

(11)

By expanding this product using trigonometric identities, the magnetic flux density comprises a fundamental component and a modulation component. The critical modulation term involves the multiplication of the time-varying functions cos(ω_st) and cos(ω_vt), which can be mathematically decomposed as:

$$\cos ({\omega }_{s}t)\cos ({\omega }_{v}t)={\displaystyle \frac{1}{2}}[\cos (({\omega }_s+{\omega }_v)t)+\cos (({\omega }_s-{\omega }_v)t)]$$

(12)

This expansion rigorously proves that the interaction between the fundamental magnetomotive force and the fault-induced permeance variation directly introduces additional spatial-temporal harmonics. Consequently, sideband frequencies at ω_s ± ω_v are explicitly generated in the magnetic flux linkage. According to Faraday’s law of induction, these flux variations induce corresponding electromotive forces, ultimately leading to current spectrum distortion and the emergence of characteristic sideband harmonics in the stator current signals [38]. Building upon this foundation, subsequent studies developed analytical models that simultaneously account for radial and torsional coupling effects, providing a coherent explanation of the relationship between bearing fault vibration characteristic frequencies and current sideband components [39].

As research progressed, it became evident that analyses based on ideal motor assumptions are insufficient to fully explain fault-related features observed in current spectra under complex operating conditions. Consequently, non-ideal factors such as inherent eccentricity, slotting effects, and magnetic saturation have been incorporated to extend electromagnetic modulation models. Studies based on magnetic field modulation theory have revealed a strong coupling between bearing faults and rotor slot harmonics, indicating that current characteristic frequencies are governed not only by bearing geometric parameters but also by motor structural characteristics [40]. Further investigations into slotting effects have shown that additional sideband components may emerge around the fundamental frequency and its harmonics [41].

From an analytical modeling perspective, equivalent magnetic circuit approaches have been employed to develop motor models that account for nonlinear air-gap permeance and magnetic saturation, enabling derivation of analytical expressions for fault-related frequency components in stator currents under bearing fault conditions [42]. Moreover, by jointly considering inherent eccentricity and magnetic saturation, improved winding-function-based multi-loop analytical models incorporating local bearing defects have been established, theoretically elucidating the characteristic frequency differences exhibited by different bearing fault types in stator current spectra [43].

The review of these studies indicates that, despite differences in modeling assumptions and analytical derivation methods, the resulting current characteristic frequencies can generally be interpreted as modulation products between the power supply fundamental frequency and its associated harmonics and the bearing fault characteristic frequencies. Although the mathematical forms of characteristic frequency expressions corresponding to different bearing fault types are largely consistent, variations exist in terms of whether rotational frequency, cage frequency, and structural harmonics are incorporated.

Table 2. Summary of components related to bearing fault in the stator current spectrum.

Fault Type	[36]	[39]	[40]	[41]	[42]	[43]
Outer Race Fault	$f_{\mathrm{c}}\pm n{f}_{\mathrm{o}}$	$f_{\mathrm{c}}\pm n{f}_{\mathrm{o}}$	$f_{\mathrm{c}}\pm q{f}_{\mathrm{r}}\pm n{f}_{\mathrm{o}}$	$f_{\mathrm{c}}\pm \left(mR\pm s\right)f_{\mathrm{r}}\pm n{f}_{\mathrm{o}}$	$f_{\mathrm{c}}\pm n{f}_{\mathrm{o}}$	$f_{\mathrm{c}}+i{f}_{\mathrm{c}}\pm n{f}_{\mathrm{o}}\pm r{f}_{\mathrm{r}}$
			$f_{\mathrm{rsh}}\pm n{f}_{\mathrm{o}}$
Inner Race Fault	$f_{\mathrm{c}}\pm n{f}_{\mathrm{i}}$	$f_{\mathrm{c}}\pm f_{\mathrm{r}}\pm n{f}_{\mathrm{i}}$	—	—	$k{f}_{\mathrm{c}}\pm j{f}_{\mathrm{r}}\pm n{f}_{\mathrm{i}}$	$f_{\mathrm{c}}+i{f}_{\mathrm{c}}\pm n{f}_{\mathrm{i}}\pm r{f}_{\mathrm{r}}$
Rolling Element Fault	$f_{\mathrm{c}}\pm n{f}_{\mathrm{b}}$	$f_{\mathrm{c}}\pm f_{\mathrm{cage}}\pm n{f}_{\mathrm{b}}$	—	—	$f_{\mathrm{c}}\pm j{f}_{\mathrm{cage}}\pm n{f}_{\mathrm{b}}$	$f_{\mathrm{c}}+i{f}_{\mathrm{c}}\pm c{f}_{\mathrm{cage}}\pm n{f}_{\mathrm{b}}\pm r{f}_{\mathrm{r}}$

k, q = 0, 1; i = 0, 2; n, m, j, s = 1, 2, 3, …; r, c = 0, 1, 2, ….

summarizes representative expressions of bearing-fault-related current characteristic frequencies reported in the literature. In Table 2, f_c denotes the stator current fundamental frequency, f_rsh denotes rotor slot harmonics, f_cage denotes the cage rotational frequency, R represents the number of rotor slots, and k, q, i, n, m, j, s, r, c denote harmonic orders.

2.2.2. Motor Current Response Modeling Based on Electromagnetic Modulation Mechanisms

Building upon the aforementioned electromagnetic modulation mechanisms of bearing faults, research on motor current response modeling has increasingly focused on mapping air-gap nonuniformities and rotor disturbances into stator current responses through computationally Magnetic Equivalent Circuit models (MEC). Most existing studies take the time-varying behavior of electromagnetic parameters as the core and achieve mechanism-consistent current response modeling by constructing appropriate machine electromagnetic models. In recent years, a widely adopted approach has been to introduce time-varying inductance or mutual inductance parameters into equivalent circuit models or dq-frame representations, such that periodic electromagnetic parameter variations are directly embedded in the current equations. Owing to their simple structure and high computational efficiency, these models are well suited for rapid analysis under varying rotational speeds and load conditions, and have been employed to generate stator current responses containing bearing-related disturbance features [2]. Nevertheless, because the time-varying characteristics of electromagnetic parameters are typically derived under simplified assumptions, such models have inherent limitations in capturing spatial effects and accurately reproducing fault-feature amplitudes. Consequently, they are more suitable for interpreting the frequency composition of modulation-related components than for precise amplitude prediction. This distinction is important in diagnosis, as amplitude-sensitive indicators are generally more vulnerable to modeling bias than those relying primarily on frequency location.

To enhance the physical consistency of current response modeling, Modified Winding Function Method (MWFM) has been increasingly adopted. By explicitly incorporating stator and rotor winding distributions together with air-gap nonuniformity into inductance parameter calculations, and coupling them with multi-loop circuit models, electromagnetic parameters can be dynamically updated during simulation. This enables a more realistic representation of current response characteristics. Compared with the foregoing equivalent-circuit and dq-based formulations, this framework provides a more explicit description of how winding distribution and air-gap nonuniformity affect the current response to fault-induced electromagnetic modulation. Models developed under this framework are able to generate response components that are consistent, at the physical-mechanism level, with experimentally observed current spectral features, and have been successfully applied to quantitative analysis of the effects of bearing-related disturbances on stator currents [10,44]. Representative simulation results are illustrated in Figure 5. The figure visually confirms the presence of fault-induced sidebands around the fundamental frequency, validating the superiority of winding-function-based multi-loop models in capturing complex electromagnetic modulations. Building upon this foundation, additional non-ideal factors, including slotting effects and magnetic saturation, have been incorporated into electromagnetic parameter modeling. By revising air-gap permeance formulations or inductance calculation methods, the applicability of these models under practical operating conditions has been significantly improved, leading to better agreement between simulated current response amplitudes and experimental observations [45].

As research has extended from single-machine models to system-level analysis, electromagnetic models have increasingly been coupled with rotor and bearing dynamic models, giving rise to integrated electromechanical modeling frameworks. In such frameworks, variations in electromagnetic parameters and mechanical system states are jointly updated through shared variables, enabling the relationship between current responses and overall system dynamics to be described within a unified modeling structure. Existing studies have demonstrated that incorporating unbalanced magnetic pull and explicitly accounting for electromagnetic-mechanical interactions can provide a more comprehensive characterization of motor current response characteristics [46]. This makes such models particularly useful when the current response is strongly affected by the dynamic interaction between bearing motion and the electromagnetic field.

For current-response studies requiring higher electromagnetic fidelity, the Finite Element Method (FEM) has also been introduced in a limited number of works. By numerically solving Maxwell’s equations on spatial meshes, it can represent slot geometry, winding distribution, and localized magnetic saturation in greater detail [47]. In principle, this makes it useful for examining how rotor eccentricity or air-gap perturbations distort current waveforms and sideband structures. However, because transient nonlinear FEM modeling is expensive in both model construction and computation, its use in current-based bearing fault studies remains relatively limited. In most cases, it serves mainly as a supplementary tool for mechanism verification or reference-data generation rather than a routine modeling approach for current response analysis [48].

Overall, current response modeling based on electromagnetic modulation has developed from simplified parameter-varying formulations toward physically richer winding-function and electromechanical coupled models. In comparison, simplified equivalent-circuit and dq-based models are advantageous for rapid interpretation of modulation-related frequency components, whereas MWFM-based and coupled models provide better physical consistency in describing the transfer from bearing-induced disturbance to stator current response. FEM can offer additional high-fidelity electromagnetic insight, but in current-based bearing fault studies it is used more often for supplementary verification than for routine modeling.

2.3. Bearing Fault Diagnosis Methods Based on Mechanism Models

Following the mechanism analysis and response modeling of vibration signals and motor current signals presented in the preceding sections, increasing attention has been devoted to incorporating the physical priors embedded in dynamic and electromagnetic models into the fault diagnosis process, with the aim of improving diagnostic reliability and interpretability under complex operating conditions. In recent years, mechanism-model-based bearing fault diagnosis approaches have evolved from conventional signal-driven paradigms toward integrated diagnostic frameworks that combine digital twins, physics-constrained learning, and mechanism-driven transfer strategies.

A representative research direction involves the construction of bearing system digital twins based on dynamic or electromagnetic models, where model-generated virtual responses are used to assist fault diagnosis. In such approaches, mechanism models are employed to generate or augment fault samples, while parameter calibration and model updating are performed to enhance the consistency between virtual and physical systems, thereby mitigating issues related to fault data scarcity and class imbalance in real-world applications. Existing studies have demonstrated the effectiveness of digital-twin-based approaches in improving diagnostic stability under imbalanced sample conditions [49]. However, their benefit depends strongly on whether the virtual model can remain sufficiently consistent with the evolving physical system. Without continuous parameter updating or uncertainty control, digital twins may reduce data scarcity while introducing model-induced bias into diagnosis.

Another class of approaches focuses on directly embedding mechanism models into the training process of diagnostic models, where physical consistency constraints are employed to guide feature learning and decision-making. In recent years, physics-informed neural networks and their extended variants have been increasingly applied to bearing fault diagnosis. By incorporating dynamic or electromagnetic constraints into network architectures or loss functions, these models enforce compliance with physical laws while maintaining data fitting capability. Existing studies have demonstrated that introducing physics-based residuals as constraint terms in deep neural networks can significantly enhance the interpretability and stability of diagnostic results [50].

With the growing availability of motor current signals in industrial environments, multi-source mechanism-based diagnostic approaches that integrate dynamic and electromagnetic models have received increasing attention. Some studies have developed multi-source physics-constrained networks that fuse vibration and current signals within a unified physical prior framework, thereby enhancing the comprehensive characterization of bearing faults [51]. A representative architecture of such approaches is illustrated in Figure 6. The flowchart maps how physical mechanisms are explicitly embedded into the convolutional layers, explaining the advantage of using physical priors to constrain network weights rather than relying solely on data-driven extractions. In addition, engineering-oriented diagnostic frameworks based on motor current signals have demonstrated the practical feasibility of current-based bearing fault diagnosis under electromagnetic model constraints in real-world applications [52].

Overall, mechanism-model-based bearing fault diagnosis approaches are evolving toward an integrated technical paradigm supported by digital twins, centered on physics-constrained learning, and complemented by multi-source fusion and mechanism-driven transfer strategies. The physical consistency provided by dynamic and electromagnetic models plays a critical role in ensuring reliable fault diagnosis under complex operating conditions. Future research should further focus on online model updating and uncertainty quantification, as well as the adaptive integration of multi-source physical priors within unified diagnostic frameworks.

3. Bearing Fault Diagnosis Based on Fault Feature Extraction

While mechanism-based models provide physical insights into how bearing faults affect vibration and current signals, practical diagnosis often relies on extracting discriminative information directly from measured data. Therefore, feature extraction techniques are widely used to convert these signal responses into quantitative descriptors for subsequent fault identification.

3.1. Vibration-Signal-Based Bearing Fault Feature Extraction Methods

Vibration signals can directly capture the periodic impact responses induced by localized bearing defects during operation and are therefore widely employed in bearing fault feature extraction studies [3,26]. When localized damage occurs on the inner race, outer race, or rolling elements, defect-induced excitations periodically trigger structural resonances under load, giving rise to impact components with pronounced modulation characteristics in vibration signals. Consequently, the primary objective of vibration-based feature extraction is to suppress structural noise and transmission path effects while enhancing impact-related information associated with bearing characteristic frequencies.

In early research, vibration feature extraction mainly relied on time-domain statistical indicators and frequency-domain spectral features, such as root mean square, kurtosis, and characteristic frequency amplitudes [53]. While these features are effective under steady operating conditions and in mid-to-late fault stages, they often suffer from limited stability during the early stages of weak faults, where impact amplitudes are small and easily masked by broadband noise or structural resonances. To overcome these limitations, subsequent studies have increasingly focused on signal processing techniques centered on adaptive frequency-band selection and impact enhancement.

Spectral kurtosis quantifies the impulsiveness of signals across different frequency bands, enabling adaptive identification of fault-sensitive frequency regions, and has been widely applied in vibration-based feature extraction. For instance, spectral kurtosis has been used to determine optimal demodulation bands in combination with envelope analysis to extract bearing characteristic frequencies, thereby improving the detectability of weak fault-induced impacts [54]. Nevertheless, although these methods perform well under steady-state conditions, their frequency-band selection may still be affected by energy dispersion in nonstationary operating scenarios.

To address the nonstationary nature of vibration signals, time–frequency analysis methods have been widely employed to characterize the temporal evolution of bearing fault impact responses. The short-time Fourier transform (STFT) performs localized spectral analysis using a sliding time window, enabling a joint time–frequency representation, and has been applied to the time-varying detection of bearing fault features [55]. However, its fixed window length results in an inherent trade-off between time and frequency resolution. To mitigate this limitation, wavelet transform (WT) and wavelet packet decomposition introduce multi-scale analysis concepts, allowing transient impacts and high-frequency components to be more effectively represented across different scales, and have been widely applied to bearing fault feature extraction under complex background conditions [56]. Nevertheless, conventional time–frequency analysis methods remain susceptible to energy dispersion and frequency smearing when processing multicomponent vibration signals.

In recent years, high-resolution time–frequency analysis techniques have been increasingly adopted to further enhance the concentration of transient impact components. By redistributing time–frequency energy, synchrosqueezing-based methods enable fault-related frequency components to be more sharply localized in the time–frequency plane, thereby improving the identifiability of bearing fault features under variable-speed operating conditions [57], as illustrated in Figure 7. By comparing the subfigures, it is evident that synchrosqueezing and synchroextracting transforms significantly sharpen the time-frequency ridges compared to the blurred STFT result, providing visual proof of their superior resolution for nonstationary signals. Similarly, time–frequency reassignment methods improve the clarity of time–frequency representations for multicomponent vibration signals by correcting energy localization and have demonstrated strong potential under complex operating conditions [58].

In addition to time–frequency analysis, signal decomposition techniques have attracted considerable attention in vibration-based feature extraction. Complete ensemble empirical mode decomposition (CEEMD) introduces adaptive noise into the original signal to decompose vibration signals into a set of intrinsic mode functions, enabling fault-related impact components to be effectively separated from background interference [59]. By contrast, variational mode decomposition (VMD), which incorporates bandwidth constraint mechanisms, demonstrates improved performance in suppressing mode mixing and enhancing noise robustness [60]. In practical applications, decomposition-based methods are often combined with demodulation or statistical indicators to construct sensitive vibration features for weak bearing faults.

To further evaluate the engineering applicability of these feature extraction techniques,

Table 3. Critical comparison of signal processing techniques for bearing fault feature extraction under engineering constraints.

Method	Robustness to Heavy Noise	Suitability for Non-Stationary Conditions	Hyperparameter Sensitivity	Computational Complexity	Best Engineering Application Scenario
STFT [55]	Low	Low	Low	Low	Stationary conditions with late-stage severe faults
WT [56]	Moderate	Moderate	High	Moderate	Moderate speed variations with transient impacts
CEEMD [59]	Moderate	High	Moderate	High	Offline analysis of strongly non-stationary signals
VMD [60]	High	Moderate	Very High	Moderate	Noisy environments with narrowband modulations
SST/SET/SSET [57,58]	Low	Excellent	Moderate	Very High	High SNR environments with drastic speed variations

presents a critical comparison across four key dimensions: noise robustness, non-stationary adaptability, hyperparameter sensitivity, and computational complexity. As summarized, traditional time–frequency analysis methods (STFT, WT) suffer from inherent resolution trade-offs, limiting their effectiveness for early weak faults. Adaptive decomposition algorithms (CEEMD, VMD) improve noise resistance but introduce high computational overhead and parameter dependency. While high-resolution transforms (SST, SET, SSET) excel in localizing non-stationary signals, their reassignment rules are vulnerable to strong background noise. Consequently, the optimal selection must be tailored to specific operational constraints.

Overall, while vibration-based feature extraction methods offer high fault sensitivity and physical interpretability, the critical comparison in Table 3 reveals a clear trade-off between diagnostic resolution and engineering deployability. The performance of these techniques remains inherently constrained by sensor placement, structural resonances, and the high sensitivity to prior parameter selection. Consequently, bridging the gap between sophisticated signal processing and robust, parameter-free feature representation under complex, non-stationary operating conditions remains a primary challenge for future industrial implementation.

3.2. Current-Signal-Based Bearing Fault Feature Extraction Methods

Compared with vibration signals, stator current signals offer distinct engineering advantages, including nonintrusive measurement, ease of acquisition, and suitability for online monitoring, and have therefore received sustained attention in motor bearing fault diagnosis research. Bearing faults induce slight rotor vibrations and air-gap magnetic flux density distortions, which result in amplitude and phase modulation of stator currents and give rise to sideband structures associated with bearing characteristic frequencies in the current spectrum [36]. Nevertheless, because the amplitudes of the current fundamental component and its harmonics are significantly larger than those of fault-related components, bearing fault signatures in current signals are typically weak, rendering feature extraction particularly challenging.

Early stator current feature extraction methods primarily relied on spectral analysis [20], in which bearing faults were identified by detecting sideband components around the fundamental frequency and its harmonics. To mitigate the masking effect of dominant fundamental components on weak fault signatures, several studies proposed modeling healthy current components using linear prediction or adaptive notch filtering and extracting bearing-fault-related information from residual signals [61]. In addition, harmonic attenuation strategies have been employed in current-signal-based bearing fault diagnosis to suppress the supply fundamental and its harmonics, thereby enhancing weak fault-related components before subsequent feature extraction and classification [62]. As illustrated in Figure 8, extracting the mode via variational mode extraction makes the weak fault frequencies and their sideband harmonics more distinct compared to analyzing the residual envelope spectrum alone. However, such approaches are generally sensitive to operating condition variations and tend to experience performance degradation under fluctuating load or speed conditions.

To further enhance bearing-fault-related modulation features, demodulation-based approaches have been widely adopted in stator current feature extraction. By extracting instantaneous amplitude or phase variations using the Hilbert transform, modulation information induced by bearing faults can be effectively separated from the dominant fundamental component, allowing bearing characteristic frequencies to be directly revealed in the spectrum of the demodulated signals [63]. In three-phase motor systems, transforming stator currents into rotating reference frames using Park transformation helps suppress fundamental frequency components, thereby making fault-related features more concentrated in the transformed domain [2]. However, these methods remain effective only when fault-induced modulation is sufficiently stronger than inverter-induced distortion or supply-related fluctuations. Once the electromagnetic background becomes dominant, demodulation may amplify non-fault modulation together with useful fault information.

To address feature frequency drift caused by speed variations under nonstationary operating conditions, time-frequency analysis techniques have been introduced for stator current signal processing, enabling time-varying tracking of bearing fault features across different operating regimes [64]. In recent studies, frequency-domain energy distributions and entropy-based indicators have also been employed to quantify stator current features and characterize the occurrence and progression of bearing faults, among which frequency-domain entropy features have demonstrated favorable stability under varying load conditions [65]. These developments indicate that current-signal-based feature extraction is gradually evolving from simple sideband observation toward more robust representations under variable operating conditions.

Overall, stator-current-based bearing fault feature extraction methods offer considerable practical value for engineering applications. However, their performance remains sensitive to operating conditions, motor structures, and power supply characteristics. Since the extracted features are expected to reflect the electromagnetic modulation mechanisms and current characteristic frequency structures discussed in Section 2, enhancing the detection capability for early-stage weak faults while preserving the advantages of nonintrusive measurement remains an important and open research challenge.

4. AI-Based Bearing Fault Diagnosis Methods

The feature extraction methods discussed in Section 3 provide structured representations of fault-related information. However, traditional diagnostic frameworks based on handcrafted features may struggle to capture complex nonlinear relationships under varying operating conditions. To address this issue, AI-based methods have been increasingly applied to bearing fault diagnosis.

4.1. Machine-Learning-Based Bearing Fault Diagnosis Methods

ML approaches to bearing fault diagnosis typically follow a three-stage pipeline consisting of feature construction, feature selection or dimensionality reduction, and classification or regression. Since the principles of signal feature extraction have been discussed in Section 3, this section focuses on how these features are organized and utilized within ML-based diagnostic frameworks. Compared with DL models, ML methods generally require relatively smaller datasets and lower computational resources, while their model structures and parameters are easier to interpret and control. Consequently, they remain practical solutions for many engineering applications. In studies involving vibration and current signals, research has gradually evolved from simple statistical indicators toward more comprehensive feature representations derived from the signal analysis techniques discussed in Section 3, with increasing attention to classifier robustness and generalization under varying operating conditions.

With respect to feature construction, conventional time-domain, frequency-domain, and time–frequency-domain features remain fundamental to bearing fault diagnosis. Nevertheless, recent studies have increasingly emphasized feature fusion strategies to enhance the complementary representation of fault-related information. For example, multi-source feature fusion has been applied to fault pattern recognition, yielding more robust diagnostic performance under varying operating conditions [66], as illustrated in Figure 9. The diagram highlights how fusing time-frequency domain features with low-dimensional spatial mapping systematically reduces redundancy and enhances classifier accuracy compared to single-domain feature extraction. Furthermore, as excessive feature dimensionality can introduce redundancy and increase the risk of overfitting, growing attention has been directed toward feature selection and feature subset optimization. By integrating feature fusion with feature selection, diagnostic accuracy can be preserved while effectively reducing feature dimensionality and model training complexity [67]. To address the class imbalance problem that is prevalent in industrial applications, where normal-condition samples are abundant while fault samples are relatively scarce, existing studies typically adopt coordinated strategies at both the data and algorithm levels. For example, resampling techniques have been integrated with multiclass least squares support vector machines (SVMs) to alleviate classification bias and improve the recognition performance of minority fault classes [68]. Yet, the same process may also make the resulting model more dependent on the statistical properties of a specific dataset. If feature subsets are optimized on a narrow experimental distribution, their apparent effectiveness may not translate well across different machines or operating regimes.

Under strong background noise and pronounced nonstationary conditions, the stability of feature extraction plays a critical role in determining the reliability of subsequent classification boundaries. To this end, a line of research has introduced adaptive signal decomposition and optimization mechanisms to extract more discriminative intrinsic feature components. For example, swarm-intelligence-based signal decomposition methods have been demonstrated to improve feature separability across multi-operating-condition datasets and enhance robustness to noise interference and operating condition variations [69]. With respect to classifier design, SVMs remain among the most widely adopted techniques for rolling bearing fault diagnosis. Recent research has increasingly focused on the automated optimization of kernel functions and hyperparameters. For instance, Bayesian optimization has been employed to tune hybrid-kernel SVM parameters, thereby improving generalization performance while preserving engineering interpretability and controllability [70].

Beyond fault type classification, ML-based health state assessment and degradation stage identification have emerged as important research directions. In contrast to end-to-end classification approaches, these studies emphasize extracting health indicators (HI) from raw signals to characterize degradation evolution, followed by state identification through anomaly detection, clustering, or discriminative techniques. For example, isolation forest models have been applied to bearing health state modeling, enabling effective condition characterization even in the absence of complete fault labels [71]. Meanwhile, feature selection strategies have evolved from single-algorithm approaches toward multi-algorithm comparison and ensemble selection schemes to improve the stability and interpretability of selected feature sets. When combined with SVM-based classifiers, such frameworks constitute engineering-feasible feature-engineering-based diagnostic solutions.

Under composite fault scenarios and strongly nonstationary signal conditions, increasing attention has been directed toward more targeted signal representation methods and complexity-based metrics. For instance, the combination of adaptive cyclic singular spectrum analysis and Rényi entropy has been shown to enhance the characterization of modulation components associated with composite faults, thereby improving diagnostic robustness [72]. With respect to visualization and dimensionality reduction of high-dimensional features, supervised manifold mapping techniques continue to attract considerable interest. By constructing refined composite multiscale complexity features and integrating supervised manifold dimensionality reduction with SVM classifiers, feature redundancy can be effectively reduced while preserving critical discriminative information, leading to improved overall model stability [73].

In online monitoring and early warning applications, achieving an appropriate balance among sensitivity, smoothness, and monotonicity is particularly critical when constructing health indicators. Related studies have proposed health indicator construction methods that combine multiple envelope spectrum features with cumulative sum concepts, enabling more sensitive detection of state variations at early stages of degradation [74]. A schematic illustration of this approach is shown in Figure 10. Through this cumulative transformation, weak degradation-related fluctuations can be progressively enhanced rather than masked by instantaneous noise, which makes the method particularly suitable for online monitoring scenarios requiring both early sensitivity and trend consistency. In addition, robust feature extraction strategies based on feature matrix construction and structured decomposition have also been explored. For example, health state identification methods that exploit gradient information of feature matrices in combination with multi-directional and multi-scale decomposition techniques can significantly enhance resistance to noise interference and rotational speed fluctuations [75].

In motor systems, stator current signals offer notable advantages, including non-intrusive acquisition and ease of measurement, and have therefore been increasingly employed in bearing fault diagnosis through the combination of current-based feature extraction and ML classifiers. For application scenarios such as electric vehicle drive systems, current signal feature construction methods integrated with classification strategies have demonstrated effective bearing fault identification, highlighting the practical potential of current-based approaches in engineering applications [76]. Meanwhile, adaptive signal decomposition techniques remain important tools for fault feature enhancement. For example, improved empirical Fourier decomposition methods based on optimized spectral segmentation strategies can yield more robust feature representations, providing cleaner inputs for subsequent ML-based classification [77].

Overall, ML approaches exhibit high engineering feasibility in industrial scenarios characterized by limited sample availability, constrained computational resources, or requirements for rapid deployment. These methods typically rely on handcrafted feature extraction and selection mechanisms combined with classifiers such as SVMs and k-nearest neighbors, enabling effective representation of bearing operating states while maintaining a balance between diagnostic accuracy and model interpretability. However, their performance is inherently limited by the completeness and adaptability of manually designed features, making it challenging to fully capture high-order nonlinear characteristics under complex operating conditions. This limitation has motivated increasing interest in DL approaches centered on end-to-end feature learning, with the objective of improving model adaptability in the presence of complex operating conditions and multi-source disturbances.

4.2. Deep-Learning-Based Bearing Fault Diagnosis Methods

DL enables end-to-end representation learning and reduces reliance on handcrafted features, which makes it well suited to complex operating conditions, noisy environments, and cross-domain transfer scenarios [12]. Compared with traditional ML methods, deep models can automatically extract multi-scale discriminative patterns from raw vibration signals or current waveforms. Their generalization ability and diagnostic reliability can be further improved through TL, self-supervised learning, contrastive learning, and uncertainty modeling. In recent years, Transformers and their variants, benefiting from self-attention mechanisms for modeling long-range dependencies, have been increasingly applied to bearing fault diagnosis tasks, with a representative architecture shown in Figure 11. By organizing local signal patterns into a sequence before global interaction, the model can reweight informative components in a more context-aware manner, which is advantageous when fault signatures are dispersed across nonstationary signal segments. Studies have demonstrated that models combining time–frequency representations with self-attention mechanisms can more effectively focus on critical fault patterns under complex background conditions, thereby improving overall diagnostic performance [78]. Furthermore, Transformer architectures specifically tailored to rolling bearing diagnosis have shown strong competitiveness in multi-class fault recognition and cross-operating-condition generalization through task-oriented structural optimization [79]. Nevertheless, stronger representation capacity also increases the risk that models learn dataset-specific texture cues rather than fault-essential structures. This risk becomes more pronounced when training data are limited or collected from highly consistent laboratory settings.

When labeled data are unavailable or only limited samples are available under target operating conditions, self-supervised pretraining and contrastive learning provide effective pathways for learning general representations prior to diagnostic tasks. Studies have demonstrated that diagnostic frameworks based on self-supervised and contrastive learning can acquire more discriminative feature representations under unlabeled or weakly labeled conditions, thereby improving the detectability of the early-stage faults as well as cross-condition generalization capability [80]. In cross-condition domain adaptation scenarios, contrastive learning also plays a pivotal role. By learning transferable discriminative features between source and target domains, domain-adaptive networks are able to maintain high recognition stability even under significant operating condition discrepancies [81].

In motor bearing fault diagnosis, the application of DL to stator current signals has gradually shifted from direct end-to-end classification toward representation enhancement targeting weak fault-related components. Since fault modulation components in current signals are often masked by the fundamental frequency and its harmonics, many studies introduce noise suppression and re-representation steps consistent with physical mechanisms prior to deep network modeling, thereby reducing reliance on empirical strategies such as increasing network depth. For example, fractional-order wavelet denoising has been applied to stator current signals prior to deep network input to enhance the separability of fault-related modulation components. By exploiting the symmetry-breaking characteristics of three-phase currents induced by bearing damage, multi-phase current signals can be treated as multi-source inputs and processed using Multi-branch Convolutional Neural Networks (CNN) architectures for feature extraction and temporal modeling, followed by information fusion for classification [82]. Furthermore, channel attention mechanisms and periodic feature extraction modules have been introduced to adaptively enhance weak fault responses and emphasize periodic modulation patterns in current signals, thereby improving the ability of deep networks to focus on subtle fault signatures [83].

For multi-source diagnosis, recent studies have increasingly emphasized information complementarity within deep networks rather than simple feature concatenation. For instance, deep ensemble networks for multi-sensor information fusion have been proposed, in which weighted fusion suppresses strong noise interference and attention mechanisms combined with topology learning modules are used to uncover discriminative structures in fused signals, leading to improved diagnostic stability under complex noise environments [84]. As DL models progressively advance toward trustworthy engineering deployment, interpretability and diagnostic reliability have emerged as evaluation criteria on par with recognition accuracy. Accordingly, research efforts have shifted from solely enhancing discriminative performance toward explicitly characterizing diagnostic confidence and risk controllability. For instance, probabilistic modeling and uncertainty decomposition frameworks have been developed for manufacturing systems, allowing models to exhibit more conservative confidence responses when confronted with out-of-distribution samples, thereby improving the usability and auditability of diagnostic decisions [85].

Another important research direction focuses on embedding physical priors or relational structures into deep architectures to mitigate the uncontrollable risks associated with black-box models. Physics-informed DL frameworks incorporate system-mechanism-related constraints into the learning process, enabling models to learn representations that are more consistent with fault mechanisms and thus improving interpretability [50,86]. Meanwhile, graph learning approaches have been employed to capture the global correlation structure of bearing signals. For example, graph structures constructed via Granger causality analysis have been combined with graph neural network inference to provide traceable support for correlation analysis, causal modeling, and diagnostic decision-making [87]. Other studies have attempted to construct graph structures from feature maps extracted by conventional CNN and use them as inputs to graph neural networks. By leveraging graph aggregation mechanisms to capture global relational information among nodes, these approaches enhance diagnostic performance and global relationship modeling capability under different operating conditions [88]. The corresponding methodological architecture is illustrated in Figure 12. By introducing domain adaptation after relational structure construction, the transferred features remain anchored to inter-sample dependencies rather than being aligned as isolated feature vectors, which is beneficial for preserving discriminative structure under varying operating conditions.

To systematically synthesize the diverse methodologies discussed above and provide a clear quantitative perspective,

Table 4. Quantitative Summary of Representative DL-based Diagnosis Methods.

Reference	Method	Signal Modality	Dataset Used	Reported Accuracy	Key Contribution
[78]	Time-Frequency Transformer	Time-Frequency Representation	SEU and ABLT-1A bearing dataset	99.94% (SEU), 99.94% (ABLT-1A)	Novel Time–Frequency Representation Tokenizer
[79]	Diagnosisformer	Frequency domain signals	CWRU dataset and Self-built test rig	99.84% (CWRU), 99.85% (Self)	Parallel Feature Fusion
[80]	Self-supervised Pretraining with Contrastive Learning	Vibration signals	FEMTO-ST and ABLT-1A datasets	>97.5%	Self-supervised Pretraining
[82]	Fractional Wavelet Denoising + CNN	Stator currents	Self-built induction motor test rig	97.02%	Positive Unlabeled Learning
[84]	Multi-sensor information fusion deep ensemble learning network	Multi-sensor vibration signals	SLIET bearing dataset	98.83%	Multi-sensor Weighted Fusion
[86]	GNN with Granger Causality Test	Time and frequency-domain features	CWRU and Paderborn datasets	100% (CWRU), 96.51% (Paderborn)	Causal Graph Modeling

presents a structured summary of these representative DL-based diagnostic models.

As indicated by this summary, DL-based bearing fault diagnosis has evolved from single-signal end-to-end classification toward a paradigm centered on representation enhancement, multi-source information fusion, and trustworthy diagnosis. Rather than simply chasing near-perfect accuracies—which often approach saturation on standard public benchmarks like CWRU—recent advanced architectures decisively shift toward resolving complex industrial bottlenecks. For current-signal-based diagnosis, research has primarily focused on noise suppression and weak-feature enhancement, while joint vibration–current diagnosis has increasingly emphasized fusion strategies and lightweight network architectures. From the perspective of interpretability and reliability, recent studies have also introduced uncertainty quantification, physics-informed constraints, and relational modeling to improve diagnostic credibility.

Despite these advances, DL methods still face several practical limitations in real industrial applications. Most deep models rely heavily on large labeled datasets, which are often difficult and costly to obtain in practical environments. As a result, data augmentation techniques have been widely applied to mitigate the challenges posed by small and imbalanced datasets. Furthermore, meta-learning strategies have emerged to enable rapid adaptation to new fault categories or varying operating conditions with only a few labeled samples. In addition, deep models are sensitive to distribution shifts caused by varying operating conditions, which may lead to performance degradation when models trained under laboratory conditions are deployed in industrial scenarios. Their computational complexity and limited interpretability may further restrict large-scale deployment in resource-constrained monitoring systems. These challenges, to some extent, hinder the long-term stable operation and widespread industrial adoption of DL-based diagnostic systems.

5. Bearing Fault Diagnosis Under Small-Sample Conditions

Although AI-based methods have demonstrated promising diagnostic performance, their effectiveness often depends on sufficient labeled data. In practical industrial environments, however, fault samples are usually scarce and imbalanced. Data augmentation techniques, together with meta-learning strategies, have been developed to expand training datasets and improve model generalization and rapid adaptability under small-sample conditions.

5.1. Rule-Based Data Augmentation Methods

Under small-sample conditions, one of the most critical challenges in bearing fault diagnosis arises from class imbalance and insufficient data coverage, which tend to bias decision boundaries toward majority classes. To address this issue, traditional data augmentation approaches primarily operate at the data level by increasing the number of minority-class samples and expanding their local coverage through resampling and perturbation strategies, thereby improving the learnability of training distributions without modifying model architectures [15].

In practical bearing datasets, simple random oversampling is computationally efficient but often results in duplicated samples, which may exacerbate overfitting and lead to decision boundary contraction. To improve the diversity of synthesized samples, the synthetic minority over-sampling technique (SMOTE) and its variants have been widely adopted. These methods generate new samples via interpolation within minority-class neighborhoods and enhance effectiveness by prioritizing boundary or hard-to-classify samples. To further address intra-class structural variability and sparse minority-class distributions in bearing fault data, improved SMOTE approaches that incorporate boundary reinforcement and hybrid modeling have been proposed to enhance the rationality of synthesized sample distributions. When combined with attention-based convolutional networks, such approaches have demonstrated effective diagnosis performance on imbalanced bearing datasets [89]. However, interpolation-based augmentation does not create truly new fault mechanisms; it mainly densifies the existing local sample space. As a result, its benefit becomes limited when minority samples themselves do not adequately cover the real fault variability.

Under complex operating conditions, minority-class samples are not only scarce but also frequently contaminated by noise and affected by class overlap, which may cause conventional interpolation strategies to generate samples in misleading regions. To overcome this limitation, clustering- and weighting-based oversampling strategies have been introduced, in which minority-class samples are first clustered and sampling weights are assigned according to density or representativeness. This approach simultaneously alleviates inter-class and intra-class imbalance and has been shown to improve classifier stability on complex rolling bearing datasets [90]. Furthermore, for noise-imbalanced scenarios, noise-immune weighted oversampling techniques have been developed and integrated with classifiers to form diagnostic frameworks in which synthesized samples provide effective class compensation while mitigating the risk of noise propagation [91].

Beyond interpolation-based oversampling, signal-segment-based data augmentation has also demonstrated strong applicability in bearing fault diagnosis. The core idea of this approach is to modify local sample views through sliding-window segmentation, scale cropping, and recombination, thereby exposing learning models to richer morphological variations during feature extraction. For vibration signals, small-scale cropping and fusion strategies combined with multi-channel convolutional networks can increase the effective number of training samples and enhance multi-scale information coverage without relying on additional generative models, leading to improved convergence behavior and generalization performance under small-sample conditions [92]. The schematic diagram of the corresponding multi-scale clipping fusion augmentation strategy is shown in Figure 13. By recombining existing signal content across different scales, the augmentation process expands sample diversity while remaining closely tied to the original measurement structure, which helps avoid unrealistic pattern injection in small-sample scenarios. To mitigate the tendency of fault-related features to be overwhelmed by noise in small-sample scenarios, analytic-wavelet-based methods have also been introduced to construct controllable time-frequency augmentation views. By preserving the fidelity of fault-induced impulsive components, such approaches enhance the effectiveness of augmented samples and have been shown to facilitate cross-operating-condition generalization in bearing fault diagnosis tasks [93].

For current-signal-based bearing fault diagnosis, traditional data augmentation methods place particular emphasis on enhancing the separability of weak fault-related features. A representative approach exploits periodicity and synchronization characteristics to design resampling or shifting strategies, enabling original current sequences to form more stable periodic representations at the sample level. When combined with feature fusion modules, such strategies can improve classification robustness. For example, periodic resampling-based augmentation integrated with time–frequency channel attention mechanisms has been shown to enhance the distinguishability of bearing faults in the current domain without introducing additional sensors [94]. Similarly, frameworks that combine time-shift-based denoising of current sequences with CNN have demonstrated the effectiveness of augmentation and preprocessing in improving the learnability of weak fault features [95].

Beyond direct sample expansion, undersampling, cost-sensitive learning, and ensemble reweighting are frequently employed as complementary strategies to correct class imbalance at the training-objective level. For instance, resampling can be jointly optimized with classifier parameters, or discriminators can be used to assign higher weights to hard samples, thereby improving minority-class recall while suppressing false alarms [96]. In addition, some studies have integrated traditional augmentation with digital twin models or information transfer strategies to generate auxiliary samples or transferable features, thereby reducing the burden of real data acquisition and providing a bridge from rule-based augmentation to more advanced model-based or transfer-based solutions [97].

Overall, traditional data augmentation methods primarily rely on resampling and signal-segment construction. Their advantages lie in simplicity, strong controllability, and decoupling from diagnostic model architectures, making them suitable for rapidly improving the trainability of small-sample diagnostic tasks. However, their performance ceiling is often limited by insufficient information gain in synthesized samples and the potential amplification of noise and class overlap. In extremely data-scarce or strongly distribution-shifted scenarios, these approaches typically need to be combined with more advanced generative or transfer-based strategies.

5.2. Generative-Model-Based Data Augmentation Methods

When fault samples are extremely scarce or exhibit pronounced distribution discrepancies, conventional interpolation- and segment-based augmentation methods are often limited to expanding local neighborhoods and fail to introduce substantial new discriminative information. In contrast, generative data augmentation methods aim to learn the underlying fault data distribution and generate new samples that are highly consistent with real data in a controllable manner, thereby improving minority-class coverage over a broader feature space. In bearing fault diagnosis, widely adopted generative approaches include generative adversarial networks (GAN), variational autoencoders (VAE), and their hybrid architectures, with recent extensions toward diffusion models and combined generative–TL strategies [98].

GAN-based methods play a prominent role in bearing fault diagnosis due to their ability to approximate fault data distributions through adversarial training and generate synthetic samples with high diversity. To enhance training stability and mitigate mode collapse, many studies introduce conditional constraints, multiple discriminators, or feature-consistency losses, ensuring that generated samples simultaneously satisfy class separability and temporal structural consistency. For instance, dual-discriminator conditional adversarial generative networks have been employed for rolling bearing fault augmentation, improving the discriminative effectiveness of synthesized samples under imbalanced conditions [99]. In scenarios characterized by both class imbalance and limited sample availability, adversarial generation frameworks integrated with oversampling strategies have been proposed to enhance minority-class representations and stabilize downstream classifier training, thereby improving small-sample bearing fault recognition performance [100]. Furthermore, to address training instability and collapse risks associated with imbalanced data, generative models incorporating enhanced relative losses and gradient penalty mechanisms have been applied to rolling bearing diagnosis, resulting in improved generation quality and diagnostic accuracy [101]. With respect to the practical usability of generated samples, several studies impose deep feature constraints or discriminator feature alignment, enabling synthetic samples not only to follow similar data distributions but also to populate sparse regions near decision boundaries in feature space [102]. Even so, visually plausible or feature-aligned samples are not necessarily diagnostically reliable. If the generated samples fail to preserve physically meaningful impulsive or modulation patterns, they may improve classifier fitting while weakening real-data credibility.

VAE and their variants emphasize learning continuous generative mechanisms through latent variable modeling. Owing to their stable training behavior and improved interpretability, VAEs are particularly suitable for distribution smoothing and structured sample generation under small-sample conditions. For imbalanced bearing fault diagnosis, weighted adaptations of conditional VAEs have been proposed to enhance the consistency between generated samples and target data distributions while suppressing the negative transfer effects of low-quality synthetic samples on downstream classifiers [103]. Furthermore, hybrid frameworks that combine VAEs with adversarial learning, such as VAEGAN, have been developed. As illustrated in Figure 14, these models integrate the stability of latent-variable-based generation with the high fidelity of adversarial learning, making them well suited for unified data augmentation and diagnostic modeling in imbalanced bearing fault scenarios [104].

In recent years, diffusion models have increasingly been explored for fault diagnosis data augmentation owing to their favorable training stability and strong generative diversity. The key principle of diffusion-based augmentation is to generate high-quality samples through a progressive denoising process, while enabling controllable class-conditioned generation via conditional constraints or feature guidance. Diffusion-model-based augmentation methods have been applied to imbalanced rolling bearing datasets to enhance minority-class coverage and achieve a more favorable balance between diagnostic accuracy and generation quality [105]. In addition, bearing diagnosis frameworks centered on diffusion-based augmentation have been proposed to further improve the separability and robustness of synthesized samples, with their effectiveness validated through downstream classification performance [106].

Beyond standalone generation, generative techniques are sometimes combined with transfer-aware reweighting strategies to address distribution shifts arising from cross-operating-condition scenarios. For example, TrAdaBoost-based transfer reweighting leverages auxiliary-domain data together with a small amount of target-domain data for joint training, iteratively reducing the influence of irrelevant samples through adaptive weighting [107]. In addition, integrating digital twin models with generative autoencoders has been explored to provide interpretable augmented samples under imbalanced conditions, offering a promising direction for engineering-oriented deployment [108]. The corresponding structural framework is illustrated in Figure 15. By embedding the digital twin directly into the generative pathway, physical knowledge participates in sample formation rather than only in posterior validation, which strengthens the interpretability of the augmented results.

In application scenarios where both current and vibration signals are available, generative augmentation can further compensate for weak fault-related features. In the current domain, fault components are typically weak and highly entangled with dominant background components, requiring stronger conditional constraints or feature-guided generation to prevent noise-dominated samples. In contrast, vibration-domain augmentation places greater emphasis on faithfully reproducing impulsive responses and time–frequency textures. As a result, within unified augmentation frameworks, different constraint designs and evaluation criteria are often adopted for different signal modalities. Generative approaches that combine motor current signals with bearing fault diagnosis further reflect a growing trend toward enhancing fault separability through sample generation while reducing dependence on handcrafted features [109].

Overall, generative data augmentation methods are highly effective in scenarios with localized data scarcity or mild class imbalance, where they are capable of compensating minority-class distributions over a broader feature space and enhancing sample diversity. However, it is crucial to recognize the boundary conditions of their effectiveness: under extreme small-sample conditions combined with severe cross-domain shifts, pure data-driven augmentation often becomes ineffective or even detrimental. If the original minority samples lack the structural diversity to represent true fault mechanisms, generative models tend to amplify inherent noise and class overlap rather than capturing actual fault dynamics [98]. Consequently, their practical deployment is heavily constrained by challenges related to generation quality assessment, training stability, and negative transfer risk control. For bearing fault diagnosis involving both vibration and current signals, generative augmentation must be jointly designed with strict signal-structure constraints, physical plausibility checks, quality screening mechanisms, and domain adaptation strategies to ensure that augmentation gains can be reliably translated into diagnostic performance improvements.

5.3. Meta-Learning-Based Few-Shot Diagnosis Methods

Although generative data augmentation can alleviate sample scarcity by expanding minority-class data and enhancing diversity, it may still fail when labeled samples are extremely limited or when fault types and operating conditions vary. Meta-learning addresses this limitation by extracting task-level transferable knowledge, enabling rapid adaptation with few labeled samples. This property is particularly valuable in small-sample industrial fault diagnosis scenarios, where the diversity of operating conditions and evolving fault types make conventional augmentation insufficient. Meta-learning methods are designed to capture common patterns across related tasks, providing the model with a prior that facilitates learning from only a handful of examples.

To achieve such rapid adaptation, optimization-based meta-learning frameworks, such as Model-Agnostic Meta-Learning (MAML), have been developed. These methods learn a generalizable initialization that can be quickly fine-tuned on new tasks. They allow the model to adapt to unseen fault categories or changing operating conditions with minimal labeled data, improving both generalization and adaptation speed [110]. For example, causal-Transformer-based meta-learning models integrate physical fault propagation priors into MAML, enhancing cross-condition fault classification and outperforming traditional adaptation approaches on multi-bearing datasets [111]. Despite these advantages, optimization-based methods require repeated gradient updates, increasing computational cost, and their performance may degrade when the distribution gap between meta-training and target tasks is large.

In addition to optimization-based strategies, metric-based meta-learning offers a more computationally efficient alternative. Metric-based meta-learning constructs discriminative embedding spaces and performs similarity-based classification. Elastic variants of prototypical networks adjust distance metrics to capture complex task-specific relationships, improving few-shot classification under unstable speeds or varying load conditions [112]. Prototype matching models meta-train embeddings across multiple tasks and then classify new samples based on similarity, achieving robust performance in few-shot and zero-shot scenarios [113]. However, they may fail to fully capture higher-order correlations in tasks with high heterogeneity or complex signal patterns, limiting their applicability in certain industrial scenarios.

To further enhance robustness and cross-condition generalization, researchers have explored hybrid meta-learning frameworks and multi-modal signal integration. Self-supervised meta-learning frameworks combining contrastive learning with meta-adaptation demonstrate strong representation learning even with few labeled samples, improving diagnostic accuracy in complex, noisy environments [114]. These approaches enhance robustness and cross-condition generalization but introduce additional network complexity and rely on high-quality multi-modal signals, which may not always be available in real industrial applications, especially in the presence of sensor noise or missing data.

Beyond hybrid and multi-modal methods, Bayesian meta-learning frameworks incorporate uncertainty estimation to further improve generalization. Bayesian meta-learning frameworks enhance performance under imbalanced and unseen sample conditions [115], allowing models to account for prediction uncertainty and provide reliable adaptation in industrial environments. Additional strategies include task scheduling, adaptive fine-tuning, and gradient prioritization, reducing negative transfer between tasks and improving meta-training efficiency. These methods, however, increase implementation complexity and require careful calibration of meta-training tasks and hyperparameters.

Overall, meta-learning establishes a task-level learning paradigm, capturing task commonalities and enabling rapid adaptation to new classes or conditions with minimal labeled data. By combining optimization-based, metric-based, hybrid, and Bayesian frameworks, meta-learning complements data augmentation and bridges the gap toward TL. These approaches provide a comprehensive toolkit for small-sample bearing fault diagnosis, supporting both cross-condition adaptability and robust performance under scarce label scenarios. Despite its advantages, meta-learning still faces challenges such as sensitivity to task distribution differences, high computational cost, and reliance on representative meta-training tasks. These limitations indicate that additional strategies are needed to further improve generalization and adaptability in highly variable industrial conditions.

6. Transfer-Learning-Based Bearing Fault Diagnosis Methods

In practical bearing fault diagnosis, small-sample limitations often interact with shifts in operating conditions, creating a compounded challenge: models trained under one set of conditions may not generalize well to new operating scenarios, even if augmented data or meta-learned representations are available. To mitigate such cross-domain performance degradation, TL has been applied to enable adaptation across varying working conditions as well as the transfer from virtual datasets to real industrial data.

6.1. TL Methods Under Varying Operating Conditions

In engineering applications of bearing fault diagnosis, changes in rotational speed and load alter excitation conditions, transmission paths, and modulation mechanisms simultaneously. As a result, pronounced distribution shifts often arise between source and target domains in terms of time-domain impact intervals, frequency-domain energy distributions, and time-frequency texture patterns. Consequently, discriminative boundaries learned under source operating conditions are often difficult to directly transfer to target conditions, resulting in feature mismatch and class overlap. To address this challenge, TL methods under varying operating conditions generally aim to learn operating-condition-invariant representations, achieving cross-condition generalization through the joint enforcement of distribution alignment and discriminative structure preservation.

From the perspective of distribution alignment, recent studies have increasingly adopted more powerful discrepancy measures to characterize cross-condition differences and enable end-to-end adaptation in unlabeled target-domain scenarios. By leveraging more stable alignment metrics, the adaptation process can remain well controlled under nonlinear speed variations and load disturbances, thereby alleviating the risk of insufficient alignment associated with simple statistical matching approaches [116]. However, as the gap between operating conditions increases, aligning marginal distributions alone may degrade class structures, compress inter-class margins, and even induce negative transfer. To mitigate this issue, structure-preserving constraints have been incorporated into domain alignment frameworks, ensuring that the adaptation process not only reduces domain discrepancy but also maintains fault class separability, rather than merely enforcing domain indistinguishability [117].

Regarding discriminative structure preservation, adversarial adaptation remains a widely adopted strategy due to its ability to learn domain-invariant features without requiring target-domain labels. Nevertheless, conventional adversarial alignment methods often suffer from insufficient intra-class alignment and inter-class boundary drift, particularly under strong noise, weak fault signatures, or highly heterogeneous operating conditions. To overcome these limitations, contrastive-constraint-based domain adaptation strategies have been proposed. By explicitly promoting intra-class compactness and inter-class separability, such approaches encourage the alignment process to focus on class geometric structures, thereby improving stability in cross-speed and cross-load transfer tasks [118]. However, reduced domain discrepancy does not necessarily imply preserved fault semantics. When operating-condition-related variations are incorrectly aligned as transferable fault information, negative transfer may still occur and compromise diagnostic reliability.

In practical engineering datasets, class imbalance and prior distribution shift are almost inevitable. On the one hand, certain fault categories may be sparsely represented in the source domain; on the other hand, the fault class proportions in the target domain may differ substantially from those observed during training. If uniform alignment weights are applied without considering these discrepancies, models tend to overfit majority classes while exhibiting degraded recognition performance for minority classes. To address this challenge, integrating imbalance modeling with domain adaptation—through class-prior correction, reweighting, or cost-sensitive learning mechanisms—has been shown to effectively suppress minority-class dilution and significantly enhance diagnostic robustness under the combined effects of varying operating conditions and imbalanced data distributions [119]. Moreover, under composite fault scenarios or strong interference backgrounds, the selection of transfer pathways may require dynamic adjustment. Exploiting correlation measures and alignment difficulty indicators to guide transfer strategies can reduce ineffective alignment and improve overall adaptation efficiency [120].

In more complex deployment scenarios, the target domain often comprises multiple operating-condition subdomains rather than a single homogeneous condition, such as alternating speed ranges, load levels, or operating stages. In such cases, aligning the target domain as a whole may obscure intra-domain heterogeneity and lead to overly averaged adaptation results. To overcome this limitation, multi-target domain adaptation approaches have been proposed, in which multiple target subdomains are jointly adapted based on shared representations. This enables models to maintain consistent performance across multiple operating points and is particularly suitable for systems with frequent operating-condition switching [121], as illustrated in Figure 16. By handling shared representation learning and subdomain-specific alignment simultaneously, the adaptation process can accommodate operating-state heterogeneity without collapsing all target variations into a single averaged transfer path. Furthermore, long-term operation of industrial equipment is typically accompanied by gradual operating-condition changes and the accumulation of data drift, rendering one-shot offline TL insufficient for sustained reliability. By integrating incremental TL with ensemble strategies, continuous model updating and dynamic fusion can mitigate catastrophic forgetting and provide effective support for long-term deployment [122].

Beyond alignment strategies, the effectiveness of TL under varying operating conditions is also highly dependent on the choice of representations. For nonstationary variable-speed signals, the combination of multi-scale time–frequency representations with finer-grained class-conditional constraints can strengthen the expression of weak fault-related features and mitigate errors dominated by operating condition variations, thereby improving cross-condition transferability [123]. Meanwhile, driven by data compliance and privacy isolation requirements, an increasing number of engineering scenarios restrict direct access to source-domain data and allow only pretrained source models to be shared. In such settings, source-free TL offers a practical solution by exploiting the implicit discriminative structures encoded in source models together with self-supervised information from the target domain for adaptive updating [124]. Its practicality is evident in privacy-sensitive scenarios, but the absence of source data also makes transfer errors harder to diagnose and correct. As a result, source-free adaptation usually requires stronger confidence control or pseudo-label screening to avoid reinforcing early misalignment.

Under label-scarce field conditions, TL under varying operating conditions is often tightly coupled with small-sample challenges. Excessively strong alignment may lead to negative transfer, whereas overly weak alignment may fail to adapt to target conditions. By incorporating sample difficulty modeling and representation regularization, limited target samples can more effectively constrain the alignment direction, thereby enhancing adaptation stability in few-shot cross-condition scenarios [125]. Moreover, for more general unseen operating conditions, domain adaptation approaches that emphasize cross-domain local structure preservation can reduce class boundary drift and improve generalization consistency [126]. When the source domain itself comprises multiple operating conditions or devices, different source domains contribute unequally to the target domain. Conditional distribution guidance and multi-source weighted transfer strategies can suppress redundant alignment and improve overall transfer efficiency [127].

To provide a concise quantitative comparison of the representative TL methods discussed above,

Table 5. Quantitative Summary of Representative TL Methods under Varying Operating Conditions.

Reference	Method	Target Scenario	Quantitative Result	Key Contribution
[116]	Domain Adaptation Method Based on Joint Sliced Wasserstein Distance	Cross-speed/cross-load transfer	94.48% (CWRU); 87.94% (JNU); 97.08% (MFPT); 79.04% (LZUT)	Conditional alignment
[118]	Domain Adaptation Network Based on Contrastive Learning	Variable working conditions	96.49% (simulator); 99.84% (CWRU)	Contrastive separation
[121]	Unsupervised Multiple-Target Domain Adaptation	Cross-speed transfer for compound fault diagnosis	90.88% (engineering cross-speed tasks)	Adversarial reinforcement
[124]	Source-Free Domain Adaptation Based on Label Reliability	Source-free cross-domain diagnosis	96.78% (PU); +6.52% over DANN; +2.47% over GPLUE	Reliable pseudo-labeling
[127]	Conditional Distribution-Guided Adversarial Transfer Learning Network with Multi-Source Domains	Multi-source transfer across different machines	92.64% (ablation-reported transfer tasks)	Source weighting

summarizes several typical strategies for bearing fault diagnosis under varying operating conditions in terms of target scenario, quantitative result, and key contribution.

As indicated by this summary, TL for bearing fault diagnosis under varying operating conditions has gradually evolved from discrepancy reduction alone toward more adaptive frameworks that integrate conditional alignment, contrastive discrimination, multi-target adaptation, source-free updating, and multi-source coordination. Although recent methods have reported strong quantitative performance on both benchmark datasets and engineering tasks, their evaluation settings still differ in datasets, transfer protocols, and definitions of operating-condition shifts. Therefore, the reported accuracy gains should be interpreted together with transfer scenario complexity, source-data accessibility, and robustness to realistic operating variations. Future research should further emphasize training stability, negative-transfer suppression, and coordinated utilization of heterogeneous multi-source information so as to support more reliable deployment in long-term and complex industrial environments.

6.2. Virtual-to-Real TL Methods

Compared with TL under varying operating conditions, virtual-to-real transfer typically involves more complex and heterogeneous domain discrepancies. These discrepancies arise not only from statistical distribution shifts induced by operating condition variations, but also from the combined effects of simulation modeling errors, inconsistent boundary conditions, differences in sensing and data acquisition chains, and on-site noise contamination. Although virtual domains can generate low-cost datasets covering multiple fault types and operating conditions, their distributions often exhibit inherent structural deviations from those of real domains. Consequently, the central challenge of virtual-to-real transfer lies in constructing trustworthy virtual priors and reliably transferring transferable knowledge to real equipment through effective cross-domain alignment mechanisms.

To effectively address this challenge and ensure the reliability of these virtual priors, specific evaluation criteria for synthetic and virtual data quality must be strictly established before performing domain adaptation. First, physical plausibility checks are required to verify that the simulated kinematics and defect frequencies generated by digital twin models accurately match the real physical structural parameters, rather than merely fitting statistical distributions. Second, spectral and temporal constraints must be imposed on the generated signals. The virtual data should retain physically meaningful impulsive or modulation patterns, including resonance frequency bands and impact repetition rates, to prevent the model from learning spurious background textures. Finally, quantitative domain gap metrics, like Maximum Mean Discrepancy or Wasserstein distance, should be continuously monitored. These metrics help measure the discrepancy between the virtual and real domains, ensuring that the alignment process dynamically calibrates simulation biases without destroying the intrinsic fault feature topology [128,129].

Guided by these strict evaluation criteria, from a methodological standpoint, digital-twin-driven transfer frameworks provide an effective pathway to unify virtual-domain task construction, representation learning, and rapid real-domain adaptation, enabling models to fully exploit virtual data while achieving effective calibration under few-sample real-domain conditions [130]. Furthermore, introducing physical constraints or parameter inversion mechanisms into digital twin models can impose explicit restrictions on representation learning during transfer, thereby reducing reliance on noise or spurious correlations inherent in purely data-driven approaches and improving robustness under class imbalance and disturbance conditions [131]. When the virtual domain covers a wide operating range, contains redundant states, or exhibits label spaces that are not fully consistent with those of the real domain, partial domain adaptation strategies can be employed. By suppressing non-transferable components and emphasizing alignment within transferable subspaces, such approaches can effectively alleviate negative transfer in virtual-to-real scenarios [132].

Beyond digital twins, simulation data generated from dynamic or finite element models are also widely used as source domains for virtual-to-real transfer. Given the pronounced nonlinear discrepancies between simulated and real domains, alternating transfer and progressive correction mechanisms have been proposed to continuously refine decision boundaries during adaptation, enabling simulation knowledge to be smoothly transitioned to real domains [133], as illustrated in Figure 17. By feeding correction results back into the transfer loop, the adaptation is performed as an iterative refinement process rather than a fixed one-pass mapping, which is more suitable for the coexistence of simulation bias and real-world disturbances. To further address simulation-induced domain shifts, simulation-guided domain adaptation strategies have been explored, in which robust cross-domain features are learned to reduce dependence on labeled target-domain data while maintaining favorable generalization performance under cross-operating-condition and cross-load variations [134]. Building upon this idea, incorporating structural priors available in the simulation domain for subdomain-level matching can further reduce class confusion caused by global alignment, making such approaches particularly suitable for virtual-to-real scenarios characterized by data scarcity, weak fault signatures, and coupled multi-operating conditions [135].

To effectively minimize the aforementioned domain gap metrics, from an alignment perspective, multi-adversarial constraints weaken virtual–real discrepancies across multiple representation levels while preserving class structures, demonstrating enhanced stability in the presence of complex domain gaps [136]. Given that simulation errors are inherently uncertain and vary with operating conditions, a single alignment strategy is often insufficient to address diverse error patterns. More generalized simulation-domain adaptation approaches therefore introduce stronger domain generalization constraints, allowing models to maintain a certain level of transfer performance even when digital-twin inaccuracies are pronounced or simulation coverage is limited, thereby improving the fault tolerance of virtual-to-real transfer in engineering applications [137].

In diagnostic tasks spanning digital and physical spaces, constructing cross-space consistent representations and alignment mechanisms enables knowledge learned in digital environments to be more reliably transferred to physical equipment, thereby enhancing the reusability of virtual-to-real transfer methods [138]. Furthermore, joint paradigms that combine virtual-domain pretraining with few-sample real-domain fine-tuning and alignment can exploit the coverage advantages of virtual data while enabling rapid calibration to real operating conditions, thereby improving on-site adaptation efficiency [139].

Overall, virtual-to-real transfer has evolved from early simulation pretraining–real fine-tuning paradigms toward integrated frameworks that combine physical constraints, partial domain suppression, and multi-level alignment. Future research should focus on improving the credibility of virtual-domain modeling and uncertainty quantification, and on developing more robust, interpretable, and continuously adaptive cross-space transfer diagnostic systems capable of operating reliably under complex noise conditions and coupled multi-operating scenarios.

7. Discussion

7.1. Methodological Taxonomy: Mapping Scenarios to Solutions

To synthesize the diverse challenges and methodological solutions discussed in the preceding sections,

Table 6. Comparative analysis and taxonomy of motor bearing fault diagnosis methods.

Methodological Category	Targeted Scenarios	Data Requirement	Physical Interpretability	Computational Cost	Primary Limitations and Failure Modes
Mechanism Models	Fault mechanism analysis; Virtual data generation	Low	High	High	Learning spurious correlations; Dataset-specific overfitting; High computational complexity.
Feature Extraction	Weak faults under strong noise; Stationary operating conditions	Low	Moderate	Low to Moderate	Energy dispersion; Frequency smearing; Noise amplification; Sensor placement dependent.
Machine Learning	Limited computational resources; Manual feature dependency	Moderate	Moderate	Low	Classifier bias; Overfitting to narrow distributions; Limited non-linear adaptability.
Deep Learning	Complex nonlinear features; Multi-source data fusion	High	Low	High	Learning spurious correlations; Dataset-specific overfitting; High computational complexity.
Data Augmentation and Meta-Learning	Data scarcity; Class imbalance; Few-shot adaptation	Low to Moderate	Low	High	Unrealistic sample generation; Bounded by original sample diversity; Negative transfer across tasks.
Transfer Learning	Varying operating conditions; Virtual-to-real discrepancies	Moderate	Low to Moderate	High	Class boundary drift; Minority-class dilution; Alignment to simulation biases.

presents a comparative matrix and methodological taxonomy. This updated framework explicitly evaluates mechanism-based, feature-extraction-based, and AI-based diagnostic categories across critical engineering dimensions, including data requirements, physical interpretability, and computational cost. Furthermore, it maps these methods to their optimal targeted scenarios while highlighting their primary limitations and inherent failure modes. Recognizing these multi-dimensional trade-offs is essential, as applying these methods outside their effective scopes can easily lead to negative transfer, amplified noise, or severe overfitting, thereby compromising diagnostic trustworthiness.

From the standpoint of diagnostic trustworthiness, a meaningful comparison of diagnostic methods should not rely solely on accuracy reported under isolated experimental settings. Instead, greater attention should be paid to whether a method remains effective under practically relevant conditions such as data imbalance, domain shift, cross-device transfer, and constrained deployment resources. In this sense, Table 6 already provides a partial performance-oriented assessment by comparing existing approaches across multiple engineering dimensions rather than through accuracy alone. Although this analysis does not replace a dedicated reproducible benchmark, it offers a more structured view of the strengths, limitations, and practical applicability of different diagnostic routes.

7.2. Open Challenges and Future Research Trends

Building on the above comparative analysis and applicability boundaries of different methods, several open challenges and future directions can be further identified in motor bearing fault diagnosis.

A.

Long-term drift and cross-device generalization

Although many methods achieve high accuracy on laboratory datasets, their robustness under long-term operation and cross-device transfer remains insufficiently validated. In practical applications, changes in operating conditions, structural properties, sensor mounting, and equipment aging may continuously shift data distributions, causing significant performance degradation. Future research should therefore pay more attention to long-term drift modeling and cross-device generalization, rather than limiting evaluation to static train-test settings.

B.

Uncertainty quantification and trustworthy diagnosis

Most existing studies still focus on classification accuracy, while the reliability of diagnostic decisions is rarely assessed explicitly. However, in real maintenance scenarios, a diagnostic system should not only provide predictions but also indicate when the result is uncertain or potentially unreliable. Incorporating uncertainty quantification into bearing fault diagnosis is thus an important future direction, especially for weak faults, noisy conditions, and cross-domain applications.

C.

Real-time deployment under resource constraints

A clear gap remains between high-performing diagnostic models and the requirements of industrial deployment. Many advanced methods rely on complex preprocessing, large model sizes, or repeated adaptation procedures, which limits their practical use in embedded or online monitoring systems. Future work should therefore emphasize lightweight architectures, efficient inference, and robustness under latency, memory, and computational constraints.

D.

Standardized benchmarks and reproducible evaluation

Current studies are still heavily dependent on a limited number of public datasets and often use inconsistent experimental settings, making fair comparison difficult. In particular, issues such as class imbalance, domain shift, and TL are frequently discussed, but not evaluated under unified protocols. Building more standardized benchmark settings and encouraging reproducible reporting will be essential for obtaining more reliable and cumulative conclusions in future research.

8. Conclusions

This paper has presented a structured review of recent research on bearing fault diagnosis in electric motors, with emphasis on the coordinated development of fault-mechanism-based modeling, feature-extraction-based methods, and AI-based diagnosis frameworks. Around the two representative signal modalities, namely vibration signals and stator current signals, the reviewed studies were organized from the perspectives of physical interpretation, signal representation, and engineering applicability. In addition, recent advances in data augmentation, meta-learning, and TL were further discussed in connection with practical scenarios involving small samples, varying operating conditions, and virtual-to-real transfer.

From the reviewed literature, it can be seen that different diagnostic routes exhibit distinct strengths and limitations. Mechanism-based methods provide clear physical interpretability and are valuable for revealing the relationships between localized defects and signal responses, but their practical use is often constrained by modeling complexity and parameter dependence. Feature-extraction-based methods remain attractive in engineering practice because of their controllability and relatively low implementation cost, although their performance is sensitive to noise, nonstationarity, and prior parameter selection. AI-based methods, especially deep-learning-based approaches, have shown strong capability in nonlinear feature learning, multi-source information fusion, and cross-condition diagnosis, but their deployment in real applications still depends heavily on data quality, sample sufficiency, and model reliability.

To address the gap between laboratory studies and engineering deployment, increasing attention has been paid to diagnosis under data-scarce and cross-domain conditions. In this context, rule-based and generative data augmentation methods can improve the trainability of imbalanced datasets, while meta-learning provides a promising route for rapid adaptation under few-shot conditions. TL further extends diagnostic models to varying operating scenarios and virtual-to-real tasks, making it an important support for improving practical adaptability. At the same time, digital-twin-assisted diagnosis and physics-informed learning indicate a clear trend toward deeper integration of physical knowledge and data-driven intelligence.

Overall, bearing fault diagnosis in electric motors is evolving toward more physically consistent, data-efficient, and engineering-oriented intelligent frameworks. Future research should further strengthen robust diagnosis under complex operating conditions, improve cross-device and long-term generalization, and enhance uncertainty awareness and deployment feasibility. These directions are essential for promoting more reliable and practical bearing fault diagnosis systems in real industrial environments.