Fault Diagnosis Method of Permanent Magnet Synchronous Motor Demagnetization and Eccentricity Based on Branch Current

Abstract

Since permanent magnets and rotors are core components of electric vehicle drive motors, accurate diagnosis of demagnetization and eccentricity faults is crucial for ensuring the safe operation of electric vehicles. Currently, intelligent diagnostic methods based on three-phase current signals have been widely adopted due to their advantages of easy acquisition, low cost, and non-invasiveness. However, in practical applications, the fault characteristics in current signals are relatively weak, leading to diagnostic performance that falls short of expected standards. To address this issue and improve diagnostic accuracy, this paper proposes a novel diagnostic method. First, branch current is utilized as the data source for diagnosis to enhance the fault characteristics of the diagnostic signal. Next, a dual-modal feature extraction module is constructed, employing Variational Mode Decomposition (VMD) and Fast Fourier Transform (FFT) to concatenate the input branch current along the feature dimension in both the time and frequency domains, achieving nonlinear coupling of time–frequency features. Finally, to further improve diagnostic accuracy, a cascaded convolutional neural network based on dilated convolutional layers and multi-scale convolutional layers is designed as the diagnostic model. Experimental results show that the method proposed in this paper achieves a diagnostic accuracy of 98.6%, with a misjudgment rate of only about 2% and no overlapping feature results. Compared with existing methods, the method proposed in this paper can extract higher-quality fault features, has better diagnostic accuracy, a lower misjudgment rate, and more excellent feature separation ability, demonstrating great potential in intelligent fault diagnosis and maintenance of electric vehicles.

1. Introduction

Permanent magnet synchronous motors (PMSMs) are widely used in sustainable wind power generation, new energy vehicles, and rail transportation due to their advantages of simple excitation, compact structure, and high power density [1]. However, the actual operating environments of motors are often complex and harsh. During operation, motors are not only highly susceptible to external environmental disturbances such as mechanical vibration, humidity, and high temperatures but also prone to various internal faults caused by overload operation, inevitable aging of coil insulation, and other inherent issues [2,3]. Therefore, timely diagnosis of motor faults is crucial for maintaining normal operation and ensuring operational safety [4]. Eccentricity faults and partial demagnetization faults are primary types of rotor-related failures [5]. Eccentricity faults induce vibration and Unbalanced Magnetic Force (UMF), which degrade machine performance, accelerate operational deterioration, and shorten the motor’s lifespan [6]. Specifically, eccentricity faults significantly increase bearing wear. The UMF can also act on the stator core and expose stator windings to unnecessary and potentially harmful vibrations. If the eccentricity is severe, the resulting UMF may cause physical contact between the stator and rotor, leading to damage in both components [7]. This will prevent the motor from operating normally. For a motor with local demagnetization, a higher stator current is required to generate the same amount of electromagnetic torque, which leads to severe thermal insulation stress and significantly reduces its expected lifespan [8]. In addition, local demagnetization increases the amplitude of higher force harmonic components, resulting in vibrations and acoustic noise radiating from the machine. It also alters the attractive force between the rotor and the stator, leading to changes in the trajectory of the machine shaft [9]. Moreover, although the mechanisms behind the local demagnetization fault of the permanent magnet and the rotor eccentricity fault are different, once these two types of faults occur, the fault characteristics exhibited by the permanent magnet motor are similar. They will generate comparable electrical and mechanical signal fault characteristics. For the fault diagnosis of a single fault type, it is impossible to accurately diagnose the actual fault, and misdiagnosis is likely to occur [10]. Therefore, conducting multi-fault diagnosis for these two types of faults and promptly and accurately diagnosing whether the motor has an eccentricity fault or a local demagnetization fault is of great significance for maintaining the normal operation of the motor, prolonging its service life, and reducing a series of hazards caused by the faults in a timely manner.

At present, the methods of fault diagnosis for PMSM can be mainly divided into three categories: the analytical model method, signal analysis and processing method, and artificial intelligence method [11]. The current research mainly focuses on the method based on signal analysis and processing, that is, by collecting the signals such as current, voltage, vibration and noise generated during the operation of the motor, and using specific signal processing technology to extract fault features, so as to realize motor fault diagnosis. Motor current characteristic analysis (MCSA) and motor voltage analysis are the most common online methods for single fault detection because they do not require any additional connections or hardware [12]. They are implemented by applying spectral or time–frequency analysis techniques (such as FFT, short-time Fourier transform, or D/CWT) to stator current or voltage signals.

Under the rapid development of big data and artificial intelligence, data-driven machine learning methods have gained widespread application [13]. Recent studies indicate that demagnetization and eccentricity faults can induce magnetic field asymmetry, generating specific sideband harmonics in motor currents, torque, and vibrations [14]. Researchers have proposed methods such as Fast Fourier Transform (FFT) combined with one-class Support Vector Machines (SVMs) to classify demagnetization faults [15]. Similarly, diagnostic approaches based on Continuous Wavelet Transform (CWT) and angular domain order tracking have been explored [16]. However, since the sideband harmonics caused by demagnetization and eccentricity exhibit similar characteristics, these conventional methods struggle to effectively distinguish between the two fault types [17].This limitation highlights the need for advanced feature extraction techniques and hybrid models capable of isolating subtle differences in harmonic patterns or integrating multi-domain information (e.g., time–frequency–energy features) to enhance fault discriminability. The research in the literature [18] shows that the demagnetization and eccentricity fault of permanent magnets can be detected by capturing the influence of phase commutation angle parameter change on stator winding current. The authors in [19] propose a diagnosis strategy based on magnetic flux harmonic characteristics by analyzing the mapping relationship between the spatio-temporal distribution characteristics of stator tooth flux and fault types. However, it should be noted that the intrusive detection method adopted in this scheme will change the motor body structure, and the feature extraction process is susceptible to interference, resulting in insufficient robustness. Based on the existing studies, it can be seen that there is no effective feature separation mechanism for the accurate identification of permanent magnet demagnetization and air gap eccentricity fault. It is worth noting that the current mainstream diagnostic methods generally choose three-phase stator current as the analysis carrier, which is mainly due to its strong testability and because there is no need to add special sensors. However, in the symmetric winding topology, the inherent balance of the three-phase current will cause the fault harmonics to cancel each other, resulting in the fault sensitive frequency band signal-to-noise ratio reduction, which has become a key technical bottleneck limiting the improvement of diagnostic accuracy. Reference [20] points out that for permanent magnet motors with a slot–pole ratio of 3/2 or its integer multiples, due to the symmetry of the topology and winding structure, many fault characteristics of the faulty motor cancel each other out in each branch of the phase current. In this case, the fault characteristics will disappear in the phase current signals of the faulty motor but exist in a certain branch current. Therefore, the branch current has the potential to be used as a source for diagnosing motor demagnetization and eccentricity faults.

At present, the frequency domain analysis is generally used as the main method of feature extraction in the research of permanent magnet synchronous motor fault diagnosis, but the signal time domain information has not been fully paid attention to. However, the extraction of fault features in the time domain is equally important, because it can effectively retain the fault features involved in the process of signal change [21]. The time domain parameter can retain the fault information in the process of signal change more completely, which gives it a unique advantage in the field of fault diagnosis. Therefore, the in-depth study of time domain features provides a new research direction for the construction of a multi-dimensional fault feature system. In the field of fault diagnosis, some scholars have carried out research on time-domain feature analysis, such as analyzing the characteristic factors of signals.

In reference [22], a fault diagnosis method based on back electromotive force (EMF) was proposed, combining FFT spectrum analysis and Support Vector Machine (SVM) for fault classification. This method effectively identifies faults such as rotor eccentricity and permanent magnet demagnetization. However, its diagnostic performance is greatly affected by the changes in load and rotational speed, and its diagnostic accuracy is only about 89–93%. In reference [23], a method based on motor terminal voltage signals was proposed, also using SVM for fault differentiation. However, this method exhibits limited robustness under complex operating conditions, making accurate diagnosis challenging. In reference [24], a fault diagnosis model based on the KNN-Bayesian method was proposed, utilizing current and voltage signals as fault feature sources. Although it demonstrates high accuracy in multi-label classification tasks, the KNN method requires a large dataset and the effectiveness of feature extraction significantly impacts diagnostic accuracy. To simplify the feature extraction process, reference [25] introduced Convolutional Neural Networks (CNNs) for fault classification, directly extracting fault features from raw signals. However, the performance of this method relies on large-scale annotated datasets and high computational resources. Additionally, reference [26] optimized fault feature extraction by using wavelet transform to extract the energy entropy of characteristic frequency bands, but the accuracy of wavelet transform directly affects the fault classification results. In reference [27], a method was proposed for diagnosing rotor demagnetization and eccentricity faults in interior permanent magnet synchronous motors (IPMSMs) based on ResNet. This method has achieved a good diagnostic rate of approximately 98%. However, it only takes into account IPMSMs (interior permanent magnet synchronous motors) and does not consider PMSMs (permanent magnet synchronous motors), which are the most commonly used in practice. At the same time, there is a lack of research on the influence of frequency-domain characteristics. In reference [28], a bearing fault diagnosis method based on multi-scale feature fusion and transfer adversarial learning was proposed. This method captures multi-level fault features, significantly improving diagnostic accuracy, while demonstrating strong generalization capabilities to adapt to diagnostic requirements under different operating conditions. In reference [29], a method for enhanced feature extraction considering frequency-domain and time-domain characteristics has been proposed. It has achieved a fault diagnosis rate of approximately 99% in bearing fault diagnosis. However, it utilizes multi-source data, increasing the consumption of computational resources. Moreover, both reference [28] and reference [29] focus on bearing fault diagnosis and have not been applied to the diagnosis of demagnetization and eccentricity faults in motors. When discussing the fault diagnosis methods based on machine learning as described above, existing research typically employs the following typical parameter ranges: for SVM, the bandwidth parameter of the Radial Basis Function (RBF) kernel ranges from 0.01 to 1, and the penalty factor ranges from 1 to 100. In a CNN, the size of the convolutional kernel is usually between 3 and 7, and the number of channels is 256.

In response to the above issues, this paper proposes a method for diagnosing demagnetization and eccentricity faults in permanent magnet synchronous motors based on branch current. The method proposed in this study has achieved a diagnostic accuracy rate of 98.6%, with only about a 2% misjudgment rate and results without overlapping features. The specific innovations are as follows:

• In view of the problem of weak fault characteristics in three-phase currents, this paper uses branch current instead of three-phase current as the diagnostic source to enhance fault harmonics.
• Regarding the issue of insufficient fault feature extraction, this paper constructs a dual-mode feature extraction module that combines time-domain Variational Mode Decomposition (VMD) and frequency-domain Fast Fourier Transform (FFT). This is used to enhance the time-domain and frequency-domain details of fault features and can separate overlapping fault features.
• To address the problem of insufficient fault diagnosis accuracy, this paper designs a multi-scale convolutional attention neural network architecture to capture local details and global periodic patterns in fault signals.

The rest of this paper is organized as follows. Section 2 presents the derivation of fault features based on branch current. Section 3 introduces the construction of the simulation-based dataset. Section 4 provides the detailed descriptions of the two major modules of the diagnostic method. Section 5 conducts experimental studies based on the dataset to verify the performance of the proposed method. Finally, conclusions are drawn.

2. Theoretical Analysis of Demagnetization Fault and Eccentric Fault of Permanent Magnet Synchronous Motor

In this section, the fault characteristics of eccentricity faults and demagnetization faults in the branches are analyzed, and a finite element model is established. This provides a theoretical basis for the subsequent selection of branch current as the source of fault features and the method of extracting the frequency-domain features of the branch current.

When the motor is healthy, the back electromotive force E(t) generated by the permanent magnet in the stator winding is as follows:

$$E(t)=-{\displaystyle \frac{\mathrm{d}{\psi }_{\mathrm{s}}}{\mathrm{d}t}}$$

(1)

$${\psi }_{\mathrm{s}}({\theta }_{\mathrm{r}})=\pi rl{\displaystyle \sum _{n=1}^{\infty }{N}_{\mathrm{n}}{B}_{\mathrm{n}}}\cos (n{\theta }_{\mathrm{r}})$$

(2)

In the formula, r is the air gap radius; ψ_s is a function related to the position of rotor angle θ_r; Specifically, as shown in Formula (2), l is the axial length of the motor; N_n is a function amplitude of the stator winding distribution of reference angle θ_s, and its value is determined by the physical design of the winding and the surface of the single-slot winding. At a constant speed, θ_r = ω_rt, where ω_r is the mechanical angular velocity, and the back electromotive force E(t) can be further expressed as follows:

$$E(t)=\pi rl{\omega }_{\mathrm{r}}{\displaystyle \sum _{n=1}^{\infty }n{N}_{\mathrm{n}}{B}_{\mathrm{n}}\cos ({\omega }_{\mathrm{r}}t)}$$

(3)

It can be observed that when a motor experiences a fault, both the back electromotive force and the magnetic flux density of the motor are affected.

2.1. Characteristics of Branch Current in Motor Eccentric Fault

Rotating self-eccentricity refers to the uneven distribution of the air gap length between the rotor and the stator of the motor in the circumference.

In this paper, the influence of rotor eccentricity on induced electromotive force is analyzed for dynamic eccentricity fault. As shown in Figure 1, when the rotation center of the rotor coincides with the center of the stator but deviates from the center of the rotor, the air gap length changes periodically with the rotation of the rotor on the circumference. The change in air gap length will lead to the change in air gap permeability of the motor, which will lead to the change in air gap flux of the motor.

When the PMSM has dynamic eccentricity, the air gap length at any mechanical angle will change with the rotor motion, as shown in Figure 2:

The air gap length after eccentricity δ is expressed as follows:

$$\delta (\phi ,t)={\delta }_h(1-{\displaystyle \frac{e}{{\delta }_h}}\cos (w_{r}t-\phi ))$$

(4)

In the formula, δ_h is the length of the radial air gap when the motor is normal and e represents the eccentricity distance, indicating the eccentricity of the rotor relative to the stator. Its unit is consistent with that of the air gap length, and in this paper, it is expressed in mm. At this time, the air gap length can be expressed as follows:

$$\Lambda (\phi ,t)={\displaystyle \frac{1}{\delta ({\phi }_r,t)}}={\displaystyle \frac{1}{{\delta }_h(1-\epsilon \cos (w_{r}t-\phi ))}}={\displaystyle \frac{1}{{\delta }_h}}\left(\begin{array}{l}1+\epsilon \cos (w_{r}t-\phi )\\ -{\displaystyle \frac{\epsilon \cos {(w_{r}t-\phi )}^2}{2}}\\ +{\displaystyle \frac{\epsilon \cos {(w_{r}t-\phi )}^3}{6}}\\ +\cdots \end{array}\right)$$

(5)

In the formula, ε represents the degree of eccentricity, ε = e/δ_h; when the cosine function is less than 1, the third term in the formula can be ignored. The air gap permeability can also be expressed as follows:

$$\Lambda (\phi ,t)={\displaystyle \frac{1}{{\delta }_h}}(1+\epsilon \cos ({\displaystyle \frac{w_r}{p}}t-\phi ))$$

(6)

In the formula, w_s = pw_r, w_s is the electromechanical angular velocity, and p is the number of poles of the permanent magnet motor. According to Ampere’s law, the air gap flux density B_a of the motor stator can be defined as follows:

$$B_a(\phi ,t)=\Lambda (\phi ,t){\displaystyle \int {\mu }_0{j}_s(\phi ,t)}d\phi$$

(7)

$$j_s(\phi ,t)=j_0\sin (w_{s}t-p\phi )$$

(8)

In the formula, μ₀ represents the vacuum permeability, j_s represents the current density on the inner surface of the stator, and j₀ represents the peak current density. Bringing forms (6) and (8) into form (7), we can obtain the following:

$$B_{\mathrm{a}}(\phi ,t)={\displaystyle \frac{{\mu }_0{j}_0}{{\delta }_{\mathrm{h}}p}}\cos (w_{\mathrm{s}}t-\phi )+{\displaystyle \frac{{\mu }_0{j}_0\epsilon }{2{\delta }_{\mathrm{h}}p}}\cos ((1\pm {\displaystyle \frac{1}{p}})w_{\mathrm{s}}t-(p\pm 1)\phi )$$

(9)

At the same time, the neglected part of Formula (5) is considered, and the influence of motor winding structure and load is considered. The air-gap flux density B_a of the stator can be expressed as follows:

$$B_{\mathrm{a}}(\phi ,t)={\displaystyle \frac{{\mu }_0{j}_0}{{\delta }_{\mathrm{h}}p}}\cos (w_{\mathrm{s}}t-\phi )+{\displaystyle \frac{{\mu }_0{j}_0\epsilon }{2{\delta }_{\mathrm{h}}p}}\cos ((1\pm {\displaystyle \frac{2n-1}{p}})w_{\mathrm{s}}t-(p\pm 1)\phi )$$

(10)

Formula (10) represents the change in the air gap magnetic flux density B_a of the stator after the hotel and the dynamic eccentricity fault, and n represents the positive integer. On the main magnetic circuit of the motor, the air gap flux is connected with the stator surface flux. Considering the existence of stator reluctance, there will be a voltage drop. The magnetic flux density B_s on the stator surface after fault can be estimated as follows:

$$B_{\mathrm{s}}(\phi ,t)=\eta B_{\mathrm{a}}(\phi ,t)$$

(11)

In the formula, η is used to mathematically specify the change in the magnetic flux density Bs of the stator surface relative to the magnetic flux density B_a of the stator air gap, which is usually in the range of [0, 1]. Substituting Formula (11) into Formula (9), it can be concluded that the magnetic flux density B_s of the stator surface after the dynamic eccentricity fault of the motor is as follows:

$$B_{\mathrm{a}}(\phi ,t)=\eta {\displaystyle \frac{{\mu }_0{j}_0}{{\delta }_{\mathrm{h}}p}}\cos (w_{\mathrm{s}}t-\phi )+\eta {\displaystyle \frac{{\mu }_0{j}_0\epsilon }{2{\delta }_{\mathrm{h}}p}}\cos ((1\pm {\displaystyle \frac{2n-1}{p}})w_{\mathrm{s}}t-(p\pm 1)\phi )$$

(12)

Formula (12) shows that after the eccentric fault of the motor, the harmonic component of (1 ± (2n − 1)/p) will appear in B_s. The change in B_s will cause these harmonic components to appear in the back electromotive force of the motor. Therefore, there will be fault harmonics of specific frequencies in various electrical signals of the motor with eccentric fault. The frequency of these fault harmonics is expressed as follows:

$$f_{\mathrm{ec}}^k=(1\pm {\displaystyle \frac{(2n-1)k}{p}})f_{\mathrm{s}}$$

(13)

The f_s in the formula represents the power frequency of the motor. In addition to the fundamental harmonic f_ec, dynamic eccentricity introduces higher-order harmonics due to spatial modulation between rotor slots and pole pairs. For a PMSM with Q slots and p poles, the k-th order spatial harmonic modulates the eccentricity-induced frequency components. The research of this paper mainly focuses on the case where k = 1. The back electromotive force E_ec(t) after the eccentric fault is expressed as follows:

$$E_{\mathrm{ec}}(t)=\pi rl{\omega }_{\mathrm{r}}\left\{\left.\begin{array}{l}{\displaystyle \sum _{n=1}^{\infty }n{N}_{\mathrm{n}}\eta }{\displaystyle \frac{{\mu }_0{j}_0}{{\delta }_{\mathrm{h}}p}}\cos (w_{\mathrm{s}}t-\phi )\\ +{\displaystyle \sum _{n=1}^{\infty }n{N}_{\mathrm{n}}\eta }{\displaystyle \frac{{\mu }_0{j}_0}{{\delta }_{\mathrm{h}}p}}\cos ((1\pm {\displaystyle \frac{2n-1}{p}})\\ w_{\mathrm{s}}t-(p\pm 1)\phi )\end{array}\right\}\right.$$

(14)

In the Formula (14), n represents the harmonic order. Specifically, when an eccentricity fault occurs, the back electromotive force of the motor exhibits corresponding fault components. Since the voltage and current of an AC permanent magnet motor are triangular periodic functions, the back electromotive force is also a triangular periodic function. When a rotor fault occurs, the fault components appearing in the back electromotive force cause the current to exhibit specific fault components as well.

2.2. Characteristics of Branch Current in Motor Demagnetization Fault

In healthy motors, the back electromotive force changes periodically with time. When the demagnetization fault occurs, the demagnetized permanent magnet causes the magnetic flux density to change, which in turn affects the back electromotive force. When the demagnetized permanent magnet acts on a stator slot, the back electromotive force in the slot decreases. When other healthy permanent magnets act on the stator slot, the back electromotive force remains unchanged. This uneven distribution of back electromotive force will lead to the distortion of back electromotive force and current in the stator slot of the motor. The back electromotive force E_{de_slot} in the stator slot of the demagnetization fault motor can be expressed as follows:

$$E_{\mathrm{de\_slot}}=V_{\mathrm{slot}}(1-{\displaystyle \frac{K_{\mathrm{de}}}{2p}})\cos (2\pi f_{\mathrm{e}}t)-K_{\mathrm{de}}{V}_{\mathrm{slot}}{\displaystyle \sum _{n=1}^{\infty }\frac{1}{n\pi }}\sin ({\displaystyle \frac{\pi n}{2p}})\cos (2\pi f_{\mathrm{e}}t(1\pm {\displaystyle \frac{n}{p}}))$$

(15)

In the formula, V_slot is the back electromotive force amplitude generated by the normal motor in the stator slot; k_de represents the demagnetization degree of a single permanent magnet; p is the number of poles of the motor; and f_e is the fundamental frequency of the motor.

According to the principle of back electromotive force superposition, when the motor is healthy, the back electromotive force E_{de_b} of the branch should be the superposition of the back electromotive force of each stator slot on the branch, which is as follows:

$$E_{\mathrm{de\_b}}=2G{k}_{\mathrm{N}1}{E}_{\mathrm{de\_slot}}$$

(16)

$$G=\left\{\begin{array}{l}{\displaystyle \frac{p}{a}}q \mathrm{single-layer} \mathrm{winding}\\ 2{\displaystyle \frac{p}{a}}q \mathrm{double-layer} \mathrm{winding}\end{array}\right.$$

(17)

In the formula, k_N1 is the motor winding coefficient; G is the winding coefficient, which can be expressed as above. q is the number of slots per pole per phase, q = Q/2mp, Q is the number of motor slots, and a is the number of motor branches.

In the integer slot motor, the branch winding is symmetrically distributed in the mechanical circle. When a permanent magnet in the motor demagnetizes, taking the motor with two parallel branches as an example, the back electromotive force of each branch in the fault motor can be expressed as follows:

The back electromotive force E_{de_b1} on the first branch is

$$E_{\mathrm{de\_b}1}=2G{K}_{\mathrm{N}1}{V}_{\mathrm{slot}}(1-{\displaystyle \frac{K_{\mathrm{de}}}{2p}})\cos (2\pi f_{\mathrm{e}}t)-2K_{\mathrm{de}}G{K}_{\mathrm{N}1}{V}_{\mathrm{slot}}{\displaystyle \sum _{n=1}^{\infty }\frac{1}{n\pi }}\sin ({\displaystyle \frac{\pi n}{2p}})\cos (2\pi f_{\mathrm{e}}t(1\pm {\displaystyle \frac{n}{p}}))$$

(18)

The back electromotive force E_{de_b2} on the second branch is

$$E_{\mathrm{de\_b}2}=2G{K}_{\mathrm{N}1}{V}_{\mathrm{slot}}(1-{\displaystyle \frac{K_{\mathrm{de}}}{2p}})\cos (2\pi f_{\mathrm{e}}t)-2K_{\mathrm{de}}G{K}_{\mathrm{N}1}{V}_{\mathrm{slot}}{\displaystyle \sum _{n=1}^{\infty }\frac{1}{n\pi }}\sin ({\displaystyle \frac{\pi n}{2p}})\cos (2\pi f_{\mathrm{e}}t(1\pm {\displaystyle \frac{n}{p}})-\pi )$$

(19)

According to the superposition theorem, the opposite electromotive force of the motor is

$$E_{\mathrm{Th}}=2G{K}_{\mathrm{N}1}{V}_{\mathrm{slot}}(1-{\displaystyle \frac{K_{\mathrm{de}}}{2p}})\cos (2\pi f_{\mathrm{e}}t)$$

(20)

From the derivation, it is evident that when partial demagnetization occurs in the motor, some fault harmonics in the stator phase current of a PMSM with a slot–pole ratio of 3/2 or its integer multiples are canceled out, making it difficult to use the three-phase stator current for diagnosing partial demagnetization faults. However, the branch current is not affected by the motor winding structure. In the case of partial demagnetization, the branch current exhibits fractional-order current harmonics, and its time-domain information contains fault location details of the partially demagnetized magnetic poles. This makes the branch current suitable for demagnetization fault localization.

2.3. Finite Element Model of PMSM Based on Maxwell

This paper focuses on an 8-pole 48-slot surface-mounted permanent magnet synchronous motor (PMSM) as the research subject. A simulation model is established to compare and analyze the stator current and branch current under three fault conditions, verifying the effectiveness of branch current in distinguishing faults compared to traditional fault signal characteristics. The main parameters of the simulated motor are listed in

Table 1. Parameters for 8-pole 48-slot motor.

Parameter	Value	Parameter	Value
Axial length (mm)	125	Stator inner diameter (mm)	105
Rotor outer diameter (mm)	100	Air gap length (mm)	0.5
Number of slots	48	Number of poles	8
Number of phases	3	Number of Parallel Branches (a)	2
Permanent magnet material	NdFe35	Number of winding turns (N)	54

, and the finite element model is illustrated in Figure 3.

To validate the accuracy of the finite element model, this study compares the simulation results with the magnetic field distribution and current harmonic characteristics of an 8-pole 48-slot permanent magnet synchronous motor reported in reference [20]. Under healthy conditions, the simulated no-load back electromotive force (EMF) amplitude is 175 V, as shown in Figure 4 (the theoretical calculation value is 180 V, with an error < 2.8%). Furthermore, when rotor faults are present, the characteristic frequencies detected in the simulation results deviate by less than 1.5% from the experimental data reported in reference [20]. These comparisons confirm the high consistency between the simulation model and theoretical/experimental results, demonstrating the reliability of the finite element model.

A comparative analysis of the stator current and branch current in the time and frequency domains was conducted for three motor conditions: healthy, 50% single-pole demagnetization, and 10% dynamic eccentricity, as shown in Figure 5 and Figure 6.

The results show that while the amplitude of the phase current changes under eccentricity and demagnetization faults, the waveforms of these two faults are too similar to distinguish through analysis. However, when the motor experiences faults, the branch current not only exhibits amplitude changes but also shows distinct fault harmonics for each fault type. Therefore, using branch current for fault identification is more straightforward than relying on three-phase stator current.

3. Dataset Construction

3.1. Signal Preprocessing

The finite element simulation software Ansys Maxwell is widely used in motor simulation. Based on the PMSM model constructed in Section 2.3, six motor conditions are established: healthy, 10% dynamic eccentricity, 20% dynamic eccentricity, 25% single-pole demagnetization, 50% single-pole demagnetization, and 75% single-pole demagnetization; the specific operating conditions and their detailed information are presented in

Table 2. Acquisition condition table.

No.	Speed (rpm/min)	Load Torque (N·m)
0	500	4
1	500	8
2	1000	5
3	1000	10
4	1500	8
5	1500	12

below. The collection experiment ensured that these working conditions were all under closed-loop control. All data were uniformly collected under all conditions. The specific division of the dataset is given below.

In this paper, data collection was carried out in a constant-temperature environment with the ambient temperature maintained at 25 °C. Data on branch current and three-phase current amplitude under six different operating conditions were collected in total. The specific operating conditions and their detailed information are shown in the following table. To ensure the accuracy and representativeness of the data, the data collection for each operating condition followed the same standardized procedure. The sampling rate for data collection was set at 10 kHz (constant across all operating conditions), meaning that 10,000 signal points were collected per second. Each data collection lasted for 10 s, so each collection included 100,000 signal points. To enhance data reliability and statistical significance, each condition is measured 10 times, yielding a total of 1,000,000 signal points per condition. Each fault category (healthy, 10%/20% dynamic eccentricity, 25%/50%/75% single-pole demagnetization) contains 1,000,000 samples, totaling 6,000,000 samples. The dataset was divided into training, validation, and test sets in a 7:2:1 ratio. Specifically, the total dataset size is 6,000,000, with 4,200,000 samples (70%) for training, 1,200,000 samples (20%) for validation, and 600,000 samples (10%) for testing. To ensure class balance, each fault category was proportionally allocated: healthy (1,000,000 samples), dynamic eccentricity (2,000,000 samples), and single-pole demagnetization (3,000,000 samples). To evaluate the model’s generalization capability, five-fold cross-validation was applied on the training set. In each fold, the training set was randomly split into five mutually exclusive subsets. Four subsets (80% of the data) were used for training, and the remaining subset (20%) for validation. This process was repeated five times, and the average accuracy was recorded. The final model performance was evaluated on the independent test set (600,000 samples). This dataset forms the basis of the analysis in this study.

3.2. Ablation Experiment

To validate the effectiveness of branch current compared to three-phase current in fault diagnosis, this section conducts an ablation experiment for analysis. The training set is used to train a convolutional neural network (CNN) model with identical parameters, which incorporates basic structures such as convolutional layers and batch normalization (BN) layers. It contains three convolutional layers in total. The sizes of the convolutional kernels are all 3, the strides are 2, 2, and 3, respectively, and the number of output channels is 16, 64, and 128, respectively. The specific model structure is shown in Figure 7 below:

Specifically, the number of iterations for each experiment is set to 50 to ensure the convergence and stability of the model. The test set is further divided into three subsets, Test Set A, Test Set B, and Test Set C, each equally split in a 1:1:1 ratio. Each test subset is subjected to three experiments to evaluate the model’s performance and robustness across different data subsets.

The primary evaluation metric used in this experiment is the average diagnostic accuracy, aiming to comprehensively assess the model’s overall performance in fault diagnosis tasks.

$$Accuracy={\displaystyle \frac{TP+FN}{TP+FP+FN+TN}}\times 100\%$$

(21)

where TP, FN, FN, and FP denote the numbers of true-positive samples, true-negative samples, false-negative samples, and false-positive samples, respectively.

The primary evaluation metric used in this experiment is the average diagnostic accuracy, aiming to comprehensively assess the model’s overall performance in fault diagnosis tasks. All experimental results are visualized in Figure 8 to intuitively demonstrate the performance differences in the model under various conditions. From the comparison, it can be observed that the diagnostic accuracy using branch current as the input signal is approximately 1% higher than that using three-phase current. This result indicates that branch current can provide more distinct and discriminative fault features in diagnosing motor demagnetization and eccentricity faults. Compared to three-phase current, branch current more effectively expresses fault information. Therefore, as a diagnostic signal, branch current demonstrates superior diagnostic capabilities in this study, particularly in diagnosing demagnetization and eccentricity faults, showcasing greater potential and application value.

4. Diagnostic Method

Due to the relatively weak fault characteristics contained in the three-phase current signals, which are insufficient to meet the requirements of high-precision fault diagnosis, this paper proposes a fault diagnosis method that utilizes branch current as the diagnostic signal source. However, existing intelligent diagnosis models still fail to fully exploit and extract the critical fault features from these signal sources. To address this, the paper further proposes a diagnostic model designed to enhance the expression of fault features, thereby improving the extraction of fault characteristics and enhancing diagnostic accuracy. The specific structure is illustrated in Figure 9 below.

The fault diagnosis model proposed in this paper employs a dual-branch parallel feature extraction architecture, aiming to integrate deep features from both the time and frequency domains to achieve high-precision classification of current signals. The model consists of the following core modules: a dual-modal feature extraction module, a multi-scale dilated convolutional attention module, and a classifier. The detailed structure and working principles of each module are elaborated in this section.

4.1. Dual-Modal Feature Extraction Module

The basic structure of the dual-modal feature extraction module is illustrated in Figure 10 below:

As shown in Figure 8, the branch current signal is simultaneously fed into the time-domain and frequency-domain feature extraction branches, which process data in parallel. In the time-domain branch, the raw signal is decomposed by Variational Mode Decomposition (VMD) into 6 intrinsic mode functions (IMFs), stacked row-wise as a matrix M_VMD ∈ R^K×L. In the frequency-domain branch, the signal is windowed with a Hanning window, transformed via FFT, and truncated to the 25–150 Hz characteristic frequency band, then expanded into a matrix M_FFT ∈ R^M×L with the same length as M_VMD. The outputs of both branches are concatenated along the channel dimension to form a fused feature matrix M_combine ∈ R^(M+K)×L. Specifically, the branch current x(t) ∈ R^L is input into the dual-modal feature extraction module and simultaneously passed to the time-domain and frequency-domain branches. In the time-domain transformation branch, the original branch current signal x(t) is decomposed using Variational Mode Decomposition (VMD) to extract its time-domain features. The VMD can be expressed by the following formula:

$$\{u_1(t),u_2(t),\dots ,u_K(t)\}=VMD(x(t),K,\alpha )$$

(22)

where x(t) is the original branch current signal, K is the number of modes (in this paper, K = 6), α is the penalty factor (defined as 2000 in this paper), and u₁(t), u₂(t),…, u_K(t) are the K intrinsic mode functions (IMFs) obtained from the VMD. The selection of K and α is based on the following criteria: by analyzing the spectrum characteristics of motor fault signals, which are mainly distributed in the frequency band of 25–150 Hz. To avoid mode mixing, K is set to 6. The value of α is determined through grid search optimization, with a range of [500, 5000]. However, when α < 1000, the IMF bandwidth is too wide, resulting in frequency-domain aliasing; when α > 3000, the IMF is over-smoothed, losing time-domain details. Therefore, in this paper, α is set to 2000. Specifically, the method for decomposing the original branch current signal using VMD is as follows:

$$\left\{\begin{array}{l}{\displaystyle \sum _{k=1}^K{u}_k(t)=x(t)}\\ \underset{\left\{u_k\right\},\left\{w_k\right\}}{\min }\left\{{\displaystyle \sum _{k=1}^K{‖\partial t\left[\left(\delta (t)+\frac{j}{\pi t}\right)*uk(t)\right]e^{-jwkt}‖}_2^2}\right\}\end{array}\right.$$

(23)

In Formula (24), the upper part represents the constraint condition, while the lower part represents the objective function. Here, ∂(t) denotes the time derivative, indicating the local rate of change in the branch current, and δ(t) is the Dirac function, used to construct the analytical branch current. The symbol * represents the convolution operation. It can be observed that VMD adjusts the size of the IMF components through the objective function. To handle the constraint condition of the objective function, a quadratic penalty term α and a Lagrange multiplier λ(t) are introduced, transforming the VMD problem into an unconstrained optimization problem, as shown in the following equation:

$$\mathcal{L}(\{u_k\},\{w_k\},\lambda )=\alpha {\displaystyle \sum _{k=1}^K{‖\partial t\left[\left(\delta (t)+\frac{j}{\pi t}\right)*uk(t)\right]e^{-jwkt}‖}_2^2}+{‖x(t)-{\displaystyle \sum _{k=1}^K{u}_k(t)}‖}_2^2+〈\lambda (t),x(t)-{\displaystyle \sum _{k=1}^K{u}_k(t)}〉$$

(24)

By alternately updating u_k, w_k and λ until convergence, K IMF components u_k(t) can be obtained. Subsequently, these u_k(t) are arranged row-wise to form a two-dimensional matrix, expressed mathematically as

$$M_{VMD}=\left[\begin{array}{cccc}{u}_1(t_1)& u_1(t_2)& \cdots & u_1(t_L)\\ u_2(t_1)& u_2(t_2)& \cdots & u_2(t_L)\\ ⋮& ⋮& \ddots & ⋮\\ u_K(t_1)& u_K(t_2)& \cdots & u_K(t_L)\end{array}\right]$$

(25)

Here, M_VMD is a matrix of size K × L. In the frequency-domain transformation branch, a Hanning window w(t) is first applied to the original branch current signal x(t) to reduce spectral leakage:

$$\left\{\begin{array}{l}{x}_{win}(t)=x(t)\cdot w(t)\\ w(t)=0.5\left(1-\cos \left({\displaystyle \frac{2\pi t}{L}}\right)\right)\end{array}\right.$$

(26)

where L is the signal length, set to L = 3600 in this paper. Next, the Fast Fourier Transform is applied to x_win(t), calculated as follows:

$$x(f)={\displaystyle \sum _{n=0}^{N_{fft}-1}{x}_{win}(n)e^{-j2\pi fn/N_{fft}}}$$

(27)

where N_fft is the number of FFT points; while a longer N_fft can reduce the truncation effect and ensure the concentration of fault harmonic energy, it will also increase the consumption of computing resources. Considering the concentration of harmonic energy and the performance of computing resources in this paper, N_fft is set to 4096. The magnitude spectrum is then computed as follows:

$$A(f)=\left|x(f)\right|$$

(28)

Subsequently, the magnitude spectrum is truncated to the frequency band of interest. Based on the frequency-domain analysis in Section 2, the characteristic frequency bands for eccentricity and demagnetization faults are distributed within the range of [25, 150] Hz. The truncated result is expressed as follows:

$$M_{\mathrm{FFT}}={\left.A(f)\right|}_{f\in \left|f_{\min },f_{\max }\right|}$$

(29)

Next, the one-dimensional spectrum is expanded into a matrix aligned with the VMD time domain. First, it is necessary to check whether the length of the FFT matches the length of M_VMD, as shown in the following formula:

$$M_{\mathrm{FFT}}=M_{\mathrm{FFT}}\otimes 1_L$$

(30)

Here, the symbol ⊗ denotes the dot product between M_FFT and a column vector of length L. Specifically, M_FFT is a matrix of size M × L, where M is calculated as follows:

$$M={\displaystyle \frac{f_{\max }}{\Delta f}}-{\displaystyle \frac{f_{\min }}{\Delta f}}+1$$

(31)

In the above equation, f_max is the maximum truncation frequency (150 Hz), f_min is the minimum truncation frequency (25 Hz), and Δf is the frequency resolution, calculated as follows:

$$\Delta f={\displaystyle \frac{f_s}{N_{\mathrm{FFT}}}}$$

(32)

where f_s is the sampling frequency (10 kHz). When the length of M_FFT equals that of M_VMD, M_FFT remains unchanged. If the length of M_FFT exceeds that of M_VMD, the excess portion is truncated. If the length of M_FFT is less than that of M_VMD, it is padded with ones to match the length. The calculation formula for expanding M_FFT is as follows:

$$M_{\mathrm{FFT}}=\left[\begin{array}{cccc}A(f_{\min })& A(f_{\min })& \cdots & A(f_{\min })\\ A(f_{\min }+\Delta f)& A(f_{\min }+\Delta f)& \cdots & A(f_{\min }+\Delta f)\\ ⋮& ⋮& \ddots & ⋮\\ A(f_{\max })& A(f_{\max })& \cdots & A(f_{\max })\end{array}\right]$$

(33)

Finally, M_FFT and M_VMD are concatenated along the feature dimension to obtain the result of the dual-modal feature extraction module, M_combine, calculated as follows:

$$M_{\mathrm{combine}}=stack(M_{\mathrm{VMD}},M_{\mathrm{FFT}})=\left[\begin{array}{c}{M}_{\mathrm{VMD}}\\ M_{\mathrm{FFT}}\end{array}\right]$$

(34)

Here, M_combine is a matrix of size (K + M) × L. As the output of the dual-modal feature extraction module, each row of M_combine undergoes z-score normalization.

In the dual-mode feature extraction module, the parallel extraction design of time-domain and frequency-domain features is based on considerations of complementarity and independence. The complementarity is specifically manifested as follows: time-domain VMD is good at capturing the transient features of non-stationary signals (such as current distortion in demagnetization faults), while frequency-domain FFT can explicitly extract fault harmonic components (such as f_ec in eccentricity faults). The independence is reflected in the fact that there is no parameter sharing in the extraction process of the two-mode features, avoiding mutual interference and ensuring the integrity of fault information.

The normalized result is then fed into the multi-scale dilated convolutional attention module for further processing.

4.2. Multi-Scale Dilated Convolutional Attention Module

To capture both the local detailed features and long-range periodic patterns of the current signals, this paper proposes a multi-scale dilated convolutional attention module. The basic structure of this module is illustrated in Figure 11 below:

As shown in the figure, the multi-scale dilated convolutional attention module primarily consists of a multi-scale dilated convolutional feature extraction module and an SE channel attention module. The specific workflow will be elaborated in the following sections.

First, the multi-scale dilated convolutional feature extraction module is introduced, and its internal structure is shown in Figure 12:

Initially, M_combine enters the multi-scale dilated convolutional module, which comprises four parallel dilated convolutional branches, each covering features at different time scales. The specific parameters of each branch are shown in the figure, and the output of each branch is calculated as follows:

$$y_i=\mathrm{ReLU}\left(\mathrm{BN}\right(\mathrm{Conv}1\mathrm{D}(x,k_i,d_i)))$$

(35)

In the above equation, x represents the processed M_combine input data with a batch size of 32, and k_i and d_i denote the convolution kernel and dilation rate of the four parallel dilated convolutional branches, respectively. The kernel sizes (3, 5) and dilation rates (1, 2, 3) were selected through sensitivity analysis. Smaller kernels (e.g., 3) capture local waveform distortions caused by demagnetization, while larger kernels (e.g., 5) detect long-period harmonic patterns from eccentricity. Dilated convolutions expand the receptive field without increasing parameters, which is critical for retaining high-frequency fault details. The output channel number for each branch is 64.

The outputs of all branches are concatenated along the channel dimension, resulting in

$$F_{\mathrm{extract}}=\mathrm{Concat}(y_1,y_2,y_3,y_4)$$

(36)

In the above equation, y₁ represents the local detail features of the input feature M_combine, which are the local detail features of the branch current. Similarly, y₂ represents the medium-range features of the branch current, y₃ represents the relatively broader local pattern features of the branch current, and y₄ represents the long-range periodic features of the branch current. Concat stands for the concatenation operation. The output channels of each branch are all set to 64, and the final output result is F_extract with 256 channels. Next, F_extract is fed into the SE channel attention module for further processing. The specific structure of the SE channel attention module is shown in Figure 13.

To validate the rationality of the CNN hyperparameters proposed above, we conducted a sensitivity analysis on the validation set. The results are shown in

Table 3. Sensitivity experimental results.

Parameter	Values	Accuracy (%)
Kernel Sizes	[3, 5]	98.6
Kernel Sizes	[1, 1]	97.4
Kernel Sizes	[7, 7]	97.1
Dilation Rates	<3	98.6
Dilation Rates	>3	96.8
Output Channel	64	98.6
Output Channel	32	96.3
Output Channel	128	97.9

.

When the convolution kernel size was adjusted from [3, 5] to [1, 1] and [7, 7], the accuracy decreased by 1.2% and 1.5%, respectively, indicating that small kernels (e.g., 3) and large kernels (e.g., 5) are crucial for capturing the local waveform distortion caused by demagnetization and the long-period harmonics related to eccentricity. Similarly, when the dilation rate exceeded 3, feature overlap occurred in the model (with a 1.8% decrease in accuracy). The number of filters was also tested: reducing it to 32 led to underfitting (with an accuracy of 96.3%), and increasing it to 128 led to overfitting (with an accuracy of 97.9%, while it was 98.6% when there were 64 output channel).

As illustrated, F_extract first undergoes global average pooling to obtain channel statistics:

$$z_c={\displaystyle \frac{1}{L}}{\displaystyle \sum _{t=1}^L{F}_{\mathrm{extract}}^{(c,t)}}$$

(37)

Subsequently, the channel weights are learned through two fully connected layers:

$$s=\sigma (W_2\mathrm{ReLU}((W_{1}z)))$$

(38)

In the above equation, W₁ is the first fully connected layer, which reduces dimensionality with a compression ratio of 8, and W₂ is the second fully connected layer, which restores the dimensionality. The weights of the two fully connected layers are initialized with a random distribution, and the bias terms are initialized to zero. The input dimension of the first layer connected is the number of channels C, and the output dimension is C/8. σ represents the Sigmoid activation function. For the learned channel weights s, they are multiplied by Fextract to obtain the output of the SE channel attention module:

$$F_{\mathrm{se}}=s\cdot F_{\mathrm{extract}}$$

(39)

F_se will be fed into the classifier to obtain the final classification result. The specific structure of the classifier is shown in Figure 14.

As illustrated, the classifier consists of a global average pooling layer and a fully connected layer. Through the classifier, F_se can be mapped to the category space, thereby yielding the final diagnostic result.

This chapter has provided a detailed introduction to the proposed diagnostic model and its working principles. To validate the superiority of the model, the next chapter will present experimental verification.

5. Experiment

To validate the effectiveness of the proposed diagnostic model, this chapter conducts ablation experiments on the dataset constructed in Section 3. All compared models were trained on the same dataset with 50 epochs and batch size 32. In addition to this, the learning rate is adjusted through the Adam optimizer (β₁ = 0.9, β₂ = 0.999), comparing four diagnostic models:

(a)

The ResNet model;

(b)

The multi-scale feature model;

(c)

The TFCAM model;

(d)

The multi-scale dilated convolutional attention model proposed in this paper.

The experimental parameters are consistent with those in the ablation experiments in Section 3.2. The specific experimental results are shown in the Figure 15:

From the figure, the diagnostic accuracies of Method a, Method b, Method c, and Method d are 94.9%, 96.8%, 97.5%, and 98.6%, respectively. Specifically, it can be observed that Method (a) achieves relatively good diagnostic performance, but its accuracy still falls short of meeting the requirements for practical applications. Methods (b), (c), and (d) all employ multi-scale feature extraction, resulting in higher accuracy compared to Method (a). This indicates that multi-scale feature extraction is an effective approach for feature extraction. Furthermore, both Methods (c) and (d) consider the influence of the frequency domain. Method (d) effectively truncates frequencies in the frequency domain using prior knowledge, enhances features in the time domain, and further strengthens feature representation by introducing dilated convolution and channel attention. As a result, Method (d) outperforms Method (c) in diagnostic performance.

To better observe the diagnostic rates and misclassification rates for each fault, this paper further analyzes the experimental results using a confusion matrix, as shown in Figure 16 below:

From the confusion matrix, it can be seen that Method (a) exhibits significant misclassification across all categories except for the “Nor” category, which has a misclassification rate of 0.01. Method (b) shows some improvement in misclassification, but the issues with misclassifying “De1” and “De2” remain unresolved. Method (c) demonstrates significant improvement, with a substantial reduction in misclassification; however, its average misclassification rate is still approximately 1.6%, which is inferior to Method (d). Method (d) achieves an average misclassification rate of about 0.8%, representing an improvement of approximately 0.8% over Method (c). This indicates that the proposed method in this paper can learn more valuable information from limited samples, significantly enhancing classification performance.

To further analyze the reasons for the superiority of Method (d), this paper employs the t-SNE method to visualize the feature clustering results, as shown in Figure 17.

From the clustering results, it can be observed that the six different categories are represented by distinct colors. Specifically, Method (a) exhibits significant overlap, primarily between Ec1 and Ec2. Method (b) shows some improvement in this regard, but there is still slight overlap between Ec1 and Ec2, Ec2 and De2, and De2 and De1, with relatively close distances between the features. Method (c) demonstrates slight improvements in both aspects, but overlapping points still exist between Ec1 and Ec2, and the distances between De1 and De2, as well as Ec1 and Ec2, remain relatively close. Method (d) performs the best, with clearly separated feature distances and no overlapping points. This indicates that the proposed method outperforms others in fault feature separation and is highly suitable for multi-class motor fault diagnosis tasks.

To evaluate the impact of noise, Gaussian white noise with signal-to-noise ratios (SNRs) of 20 dB, 10 dB, and 5 dB was added to the test set. As shown in

Table 4. Table of experimental results on the impact of noise.

Method	Clean	SNR = 20 dB	SNR = 10 dB	SNR = 5 dB
a	94.9%	91.6%	87.3%	76.1%
b	96.8%	94.2%	90.5%	83.6%
c	97.5%	95.9%	92.4%	87.6%
d	98.6%	97.1%	95.4%	92.3%

, the method proposed in this paper still maintains an accuracy of 97.1% at 20 dB SNR, outperforming Method a (91.6%), Method b (94.2%), and Method c (95.9%). Even under the strong noise of 5 dB, the accuracy is still higher than 92.3%. This is attributed to the fact that the dual-mode module suppresses high-frequency noise through FFT truncation (25–150 Hz), and the VMD can separate the transient components related to faults.

6. Summary

To address the limitations of three-phase current signals in the diagnosis of electrical faults in electric vehicle motors, this paper proposes a motor electrical fault diagnosis method based on branch current. First, the effectiveness of branch current in motor electrical fault diagnosis is analyzed using theoretical knowledge, and ablation experiments demonstrate that branch current outperforms three-phase current in motor electrical fault diagnosis. Therefore, this paper adopts branch current as the source data for fault diagnosis and establishes an experimental dataset through simulation experiments. Next, to tackle the issue of weak and indistinct fault features in nonlinear signals, a dual-modal feature extraction module is constructed for branch current. This module amplifies and focuses on fault features using Variational Mode Decomposition (VMD) and Fast Fourier Transform segmentation methods. Finally, a multi-scale dilated convolutional attention module is proposed. This module, built on multi-scale convolution, dilated convolution, and SE channel attention, aims to extract comprehensive and effective fault features from different dimensions using multi-scale and dilated convolutions. The SE channel attention mechanism is employed to allocate appropriate weights to these fault features. Experimental results validate the efficiency of the proposed method, which outperforms existing diagnostic approaches with a diagnostic accuracy of 98.6%.

However, in practical industrial settings, motors often suffer from compound faults. For example, eccentricity may accelerate bearing wear, while demagnetization increases thermal stress on windings, potentially leading to insulation degradation. Existing diagnostic methods predominantly target single faults, assuming mutual independence, a simplification that limits their real-world utility. The proposed dual-modal feature extraction and multi-scale attention mechanisms inherently support disentangling overlapping fault signatures, positioning this framework as a promising candidate for multi-fault scenarios. Future extensions will explicitly address simultaneous fault conditions (e.g., demagnetization + eccentric fault + insulation failures) to bridge this gap. At the same time, the current eccentricity model has not yet considered the actual model that is more inclined to multiple harmonics. Moreover, the current method only collects the fault data at a constant temperature. Therefore, on the one hand, future research will continue to focus on more practical eccentricity models, for example, developing multi-harmonic eccentricity models that include high-order spatial harmonics with k > 1 to reflect the slot–pole interactions in industrial motors and so on; on the other hand, the limitation of this study is that it only focuses on demagnetization and eccentricity faults. Although the methodology shows great potential for wide application, empirical verification for other types of faults remains to be completed. Future research will incorporate these faults to comprehensively evaluate the generalization ability of the framework. Additionally, future research can be extended to diagnostic methods under extreme temperatures.