Because of their high automation efficiency and precision control, EMSs have been widely used in automotive and aerospace applications in recent years. FD for BLDCM RBs is especially important as a key component powering these systems. However, current diagnostic methods suffer from low accuracy due to noise interference. To suppress noise and improve fault feature extraction capabilities, this study uses a WTD method to recover multiscale feature parameters from BC waveforms. Before applying WTD to suppress noise in BLDCM RB current signals, it is essential to understand BC and its vector and algebraic reconstruction processes. The process is illustrated in Figure 1 (Sulistyo et al., 2025; Zangana and Mustafa, 2024).

In Figure 1a, the BC is supplied by two independent alternating current (AC) power sources, namely, Phase 1 and Phase 2. Phase 1 and 2 share the same frequency but have a phase difference (PD) of 90°, causing their peaks to alternate in time and thus forming a BC. Equation 1 can be used to express the BC. I = u + λ v (1)

In Equation 1, I represents the magnitude of the BC in complex form. u denotes the magnitude of BC 1, with a phase angle of 0°. v denotes the magnitude of BC 2, with a phase angle of 90°. λ denotes the imaginary unit. To simplify the analysis and calculation of AC circuits, the magnitude and phase of BCs are typically represented by vectors in the complex plane, as shown in Equation 2. V e c t o r = u 2 + v 2 + arctan u / v λ (2)

In Equation 2, u 2 + v 2 represents the vector magnitude. ⁡ arctan u / v denotes the phase angle. V e c t o r indicates the vector representation. Combining Figure 1a with Equation 2 reveals that under normal conditions, the PD between the two AC currents is 90°. If a circuit fault occurs, both the PD and current magnitude will change. Therefore, by reconstructing the current signal parameters, the fault characteristics of the data can be highlighted. Current signal parameter reconstruction not only involves changes in the magnitude of current 1 and current 2 through addition, subtraction, and multiplication operations, but also includes calculating the phase angle changes of current 1 and current 2 to diagnose faults in RBs. Figure 1b provides an illustration of the procedure. First, the BC is vectorized, and its amplitude and phase angle are calculated. Subsequently, vector representation and algebraic reconstruction are performed. Finally, prominent features are obtained to diagnose faults through algorithms. To enhance the quality of algebraic reconstruction, this study combines relevant literature and employs a WTD method for algebraic reconstruction of the BC signal from BLDCM RBs. The WTD method is a signal processing technique based on wavelet transform (WT). It is extensively used in domains like audio processing and EMS monitoring, where it uses threshold processing to isolate noise from the actual signal. Figure 1 depicts the WTD procedure.

In Figure 2, the WTD process begins by inputting the original noisy signal and performing WTs at multiple scales. During the multiscale WT, an appropriate wavelet basis function (WBF) pair is adopted to decompose the noisy original signal (OS), yielding the quantity of decomposition levels (DLs). Next, the threshold and function for wavelet threshold processing are chosen and determined. Subsequently, reconstruction is performed via the inverse WT. Finally, the denoised current signal is obtained. The WT process can be expressed by Equation 3. y t = ∑ j = 1 J ∑ k 2 j − 1 d j , k φ j , k t + ∑ k = 1 N − 1 ω k φ J , k t (3)

In Equation 3, j denotes the scale, k denotes the frequency. d j , k represents the wavelet coefficient with scale j and frequency k . φ J , k t denotes the WBF. y t represents the OS. ω k denotes the high-frequency noise coefficient. J is the quantity of scales in the wavelet decomposition. N is the quantity of samples in the high-frequency component obtained from the WT. Threshold processing d j , k ′ is shown in Equation 4. d j , k ′ = d j , k , d j , k > a j 0 , d j , k ≤ a j (4)

In Equation 4, a j represents the threshold. To ensure effective noise suppression, the study combines relevant literature and multiple experiments to ultimately determine the WBF as Db8 and the DL as 4. Therefore, the study employs the WTD method to suppress noise and fuse multiscale features in the BC signal of the BLDCM RB. The preprocessing and multiscale feature fusion of the current signal are illustrated in Figure 3.

Figure 3a illustrates the preprocessing steps for the current signal. First, noise suppression is achieved using a four-level wavelet decomposition with a WTD method to extract the signal’s approximate information curve. Subsequently, algebraic operations are performed on the signal to obtain four types of current signal features. Finally, the signal undergoes normalization using the maximum-minimum normalization method to yield the final current signal vector representation. This method is expressed by Equation 5. x n o r = 2 * x − x min x max − x min − 1 (5)

In Equation 5, x min and x max represent the lowest and highest values, respectively. x n o r denotes the normalized value. x is the original data value. Thus, after normalization via the WTD method, the current signal undergoes multiscale feature fusion. Figure 3b illustrates the multiscale feature fusion process for the current signal. First, the current signal is converted into a vector representation, and its magnitude is extracted. Next, wavelet denoising is applied to reduce noise interference. Specifically, algebraic reconstruction methods, including addition, subtraction, multiplication, and angle calculations, are employed to extract and fuse current signal features across four scales. Ultimately, a neural network receives these processed feature vectors for additional examination and diagnosis.

After performing multiscale feature fusion on the current signals of RBs in EMSs using BLDCM through WTD, a hybrid FD method combining CBAM, residual networks, and ST encoders is studied and designed. The channel attention module (CAM) and the spatial attention module (SAM) make up the lightweight attention mechanism (AM) module known as CBAM. Global average pooling (GAP) and global max pooling (GMP) are used by the CAM to obtain global information for every channel. A multilayer perceptron (MLP) is then used to create CA weights. The CAM is expressed by Equation 6. M c F = δ M L P A v g p o o l F + M L P [ M a x p o o l F (6)

In Equation 6, F means the input feature map. A v g p o o l F and M a x p o o l F mean GAP and max pooling. M L P displays the MLP. δ denotes the S i g m o i d activation function (AF). M c F denotes the output processed by the CAM. The SAM first obtains weights for each channel through the output of the CAM. Equation 7 illustrates how these weights are subsequently transformed into SA weights by using GAP and GMP. M s F = δ f 7 * 7 A v g p o o l F ;   M a x p o o l F (7)

In Equation 7, M s F means the output processed by the SAM. The study incorporates the CBAM module into a residual neural network to take advantage of the AM’s benefits and its strong feature learning power in an attempt to further enhance the model’s feature representation capability and DA. Figure 4 displays the network architecture following the integration of the residual neural network and CBAM.

In Figure 4, BN denotes batch normalization, Conv represents the convolutional layer (CL), and FC signifies the fully connected layer (FCL). The notation 1@40 × 64 indicates that the number 1 before the @ denotes the number of input channels, while the number after the @ represents the input dimensions. In Module 1, the CL, the BN layer, and the first execution of AF P R e L U all yield an output dimension of 38 × 62, with the CL employing 8 convolutional kernels (CKs). The output dimensions for the second execution are both 36 × 60, with 16 CKs in the CL. Both the CA and SA layers have an output size of 36 × 60, with kernel sizes of 1 × 1 and 7 × 7 respectively, and 16 and 1 kernels respectively. The max pooling layer and residual blocks both have an output size of 18 × 30, with kernel sizes of 2 × 2 and 3 × 3 respectively, and 16 kernels each. In Module 2, the initial execution sets the output dimensions of the CL, BN layer, and PReLU output layer to 16 × 28, with 24 CKs in the CL. The subsequent execution sets all output dimensions to 14 × 26, with 32 CKs in the CL. Both the CA and SA outputs maintain a dimension of 14 × 26, with unchanged kernel size, employing 32 and 1 CKs respectively. The maximum pooling layer and residual blocks both employ 32 CKs, with an output size of 7 × 13. The FCL in Module 3 has an output size of 800. This architecture extracts input features by utilizing Conv and BN, PReLU, pooling layers, and residual blocks. CBAM is employed to enhance feature channels and SA. After multi-layer processing, classification is performed via FC layers to output the final results. Due to the multiscale nature of fault features, the DA of models incorporating CBAM still falls short of requirements. In light of this, the study introduces the encoder module of the ST to improve DA. Figure 5 illustrates an illustration of the ST model’s encoder module.

Figure 5 illustrates the processing flow of the ST model’s encoder module. First, the input data is segmented into 160 blocks, each containing a specific number of features. Next, the processed blocks are embedded into the model. This includes positional embeddings and fault type embeddings. Positional embeddings represent the sequential relationships among each block. Fault type embeddings capture the structure and categories of different fault data. Subsequently, the data enters the encoder. The encoder normalizes the input data through layer normalization to stabilize and accelerate the training process. It utilizes multi-head attention (MHA) to capture different features within the input data. Simultaneously, it employs a multi-layer perceptron for further data processing, adding residual connections between each sub-layer to prevent gradient explosion. Subsequently, it outputs the fault features and categories learned from the data. Finally, the features and AF A are classified through a FCL to output the fault category. Among these, MHA serves as a crucial component of the ST model’s encoder module. MHA excels at capturing complex dependencies between different positions, enabling the ST model to perform exceptionally well when processing long sequence data. The operation of MHA proceeds as follows: First, the input matrix X ∈ R n × d is transformed. Among them, d denotes the input feature dimension, and n represents the sequence length. Through linear transformation (LT), the query Q , key K , and V are obtained, as shown in Equation 8. Q i = X W i Q K i = X W i K V i = X V i V (8)

In Equation 8, W i Q , W i K , and V i V represent the weight matrices for the i th head. Next, the attention score A t t e n t i o n i Q i , K i , V i for the i th head is computed as shown in Equation 9. A t t e n t i o n i Q i , K i , V i = S o f m a x Q i K i T d k V i (9)

In Equation 9, d k is the scaling factor. Then, all heads are concatenated as shown in Equation 10. Concat A t t e n t i o n 1 , A t t e n t i o n 2 , … , A t t e n t i o n h = A t t e n t i o n 1 , A t t e n t i o n 2 , … , A t t e n t i o n h (10)

In Equation 10, h means the number of heads. Finally, a LT yields the final MHA output M u l t i H e a d Q , K , V , as expressed in Equation 11. M u l t i H e a d Q , K , V = C o n c a t A t t e n t i o n 1 , A t t e n t i o n 2 , … , A t t e n t i o n h W o (11)

In Equation 11, W o represents the weight matrix. Furthermore, the study uses a cross-loss entropy function, as indicated by Equation 12, to improve the accuracy of the model. C E L x = 1 N ∑ j − y j * l o g p j + 1 − y * ⁡ log 1 − p j C E L y = − 1 N ∑ j ∑ c = 1 M y i c ⁡ log p i c (12)

In Equation 12, C E L x and C E L y represent the cross-entropy losses for input feature x and output feature y . N means the total quantity of samples. M means the total quantity of classes. p j means the probability that a sample is positive. y i c means the true label (TL) of the c th class in the j th sample. p i c means the probability that the j th sample belongs to the c th category. y j represents the TL of the j th sample. Ultimately, based on the above, this study constructs a BLDCM bearing FD method incorporating multiscale features and noise suppression. This method is illustrated in Figure 6.

Figure 6 illustrates the process of this method. First, the BC signal is reconstructed to obtain comprehensive signal features. Next, preprocessing is performed using WTD, followed by further extraction of multiscale features through algebraic reconstruction methods such as addition, multiplication, subtraction, and phase angle. These multiscale features undergo feature fusion via the CBAM and residual network modules, as well as the encoder of the ST model. Finally, the fused features undergo merging and concatenation before being processed through a FCL to output the BLDCM bearing FD results for the EMS.

After establishing the BLDCM RB FD method for EMSs based on noise suppression and multiscale analysis, a comparative analysis of its performance is conducted. The comparison algorithms are convolutional neural network-long short-term memory (CNN-LSTM), variational mode decomposition-genetic algorithm-support vector machine (VMD-GA-SVM), and variational mode decomposition-continuous WT-convolutional neural network (VMD-CWT-CNN). Model parameter settings employs stochastic gradient descent as the optimizer with a learning rate of 0.001 and momentum of 0.9. The ST features 4 attention heads, a window size of 5, 5 classification heads, 5 input channels, and an input feature dimension of 160. The cross-entropy loss function is utilized. The parameter settings for CBAM and the residual module follow consistent methodologies. Data is sourced from the PU dataset at the University of Paderborn, Germany. The current signal in the PU dataset is a BC, a type of AC consisting of two sinusoidal currents that are 90° out of phase with each other. This is consistent with the BC signal of the rolling bearing proposed in the research. A total of 3,478 data points are selected, with current signals acquired over 4 s at a sampling frequency of 64 kHz. With 300 training iterations, the dataset consists of an 80% training set and a 20% test set. Accuracy, recall, and F1 score are evaluation metrics. Table 1 provides specifics on the experimental setup.

The study initially compares the accuracy and recall rates (RRs) of each approach in the previously specified context. The experimental results are displayed in Figure 7.

In Figure 7a, the suggested FD method achieves the highest accuracy of 98.97%. The accuracy of CNN-LSTM is 90.89%, VMD-GA-SVM is 88.26%, and VMD-CWT-CNN is 85.23%. In Figure 7b, the RRs of the proposed FD method, CNN-LSTM, VMD-GA-SVM, and VMD-CWT-CNN are 98.69%, 93.12%, 89.34%, and 89.15%. The suggested FD approach outperforms the others in terms of RR. The results presented above indicate that the recommended FD technique has the best accuracy and recall. The comparison of loss values and running times (RTs) among the methods is shown in Figure 8.

In Figure 8a, the suggested FD method achieves the earliest convergence in the loss curve, with a loss value of 0.74, significantly lower than the 4.76 of CNN-LSTM, 8.27 of VMD-GA-SVM, and 10.62 of VMD-CWT-CNN. In Figure 8b, the average RTs for the proposed FD method, CNN-LSTM, VMD-GA-SVM, and VMD-CWT-CNN are 2.38s, 3.16s, 3.98s, and 4.48s, respectively. Among these, the proposed method exhibits the shortest average RT. In summary, from the perspectives of loss values and average RT, the proposed FD method outperforms the comparison methods. Figure 9 displays each method’s mean square error (MSE) and root mean square error (RMSE) outcomes.

In Figure 9a, the average MSE values for the proposed FD method, CNN-LSTM, VMD-GA-SVM, and VMD-CWT-CNN are 1.18, 2.46, 3.74, and 4.02, respectively. Among these, the proposed FD method exhibits the lowest average MSE. In Figure 9b, the proposed FD method reaches an average RMSE of 0.31, significantly lower than the 0.46 for CNN-LSTM, 0.63 for VMD-GA-SVM, and 0.87 for VMD-CWT-CNN. Among these, the proposed method exhibits the lowest average RMSE. In summary, in terms of both RMSE and MSE values, the recommended FD technique outperforms the reference approaches. To verify which module made the highest contribution to the model, the study conducts an ablation experiment on it. The experimental results are shown in Table 2.

In Table 2, with the removal of the model module, its F1 score and AUC value decrease rapidly. When the CBAM and ST modules are removed, the F1 score drops from 98.62% to 82.14%, and the AUC value drops from 0.986 to 0.836. Among them, when the ST module is removed, the decrease intervals of F1 score and AUC value are the largest. The above results indicate that the ST module plays a key role in the model.

After verifying the performance of the suggested FD method, a comparative analysis of its diagnostic effectiveness is carried out. A BLDCM RB from an automotive EMS is selected for FD. The data sources are divided into two parts. Some of the signal information comes from the actual collected signals stored when the BLDCM rolling bearing malfunctions and is repaired. These signals provide the original data under the fault state for the research. To further supplement the signal characteristics in the fault state. Another part of the data comes from the BLDCM that is under repair. During the signal acquisition process, current sensors are used to take measurements, and a low-pass filter is employed to remove high-frequency noise from the current signal while retaining useful information related to FD. Finally, the filtered signal is converted into a digital signal with a frequency of 64 kHz. Diagnosis is performed for four fault categories: normal state (A), inner ring fault (IRF) (B), outer ring fault (ORF) (C), and combined inner and outer ring faults (CIORF) (D). The diagnostic results for each method are shown in Figure 10.

In Figure 10a, the proposed FD method achieves DA rates of 99.4%, 98.9%, 98.8%, and 99.3% for normal state, IRF, ORF, and CIORF, respectively. These values surpass the 86.4%, 88.3%, 85.2%, and 90.4% achieved by the CNN-LSTM approach in Figure 10b. Moreover, it outperforms the VMD-GA-SVM method in Figure 10c (84.8%, 86.2%, 83.8%, 82.7%) and the VMD-CWT-CNN method in Figure 10d (85.7%, 83.7%, 83.6%, 89.7%). In conclusion, the suggested FD approach performs better on each of the four FD accuracy metrics. The comparison results for precision, area under the curve (AUC) values, and central processing unit (CPU) utilization among the various methods are presented in Table 3.

As shown in Table 3, the proposed diagnostic method achieves a precision rate of 99.68% and an AUC value of 0.986. These results are significantly higher than those of CNN-LSTM (90.08% and 0.874), VMD-GA-SVM (86.78% and 0.882), and VMD-CWT-CNN (89.23% and 0.903). The proposed diagnostic method exhibits the lowest CPU utilization at 42.14% among all approaches. These findings reveal that the suggested FD approach performs best in terms of CPU usage, accuracy, and AUC value. The Transformer + ResNet hybrid model proposed in the research shows better convergence speed and CPU occupancy rate compared with the more lightweight CNN-LSTM model. The causes of this phenomenon can be attributed to several key factors. First, this model adopts an efficient self-attention mechanism and residual connection. The self-attention mechanism allows the model to swiftly identify long-distance dependencies in the data, which is essential for comprehending intricate data patterns. Residual connections help alleviate the vanishing gradient problem, which is a common challenge in deep learning models, especially when dealing with deep networks. These architectural advantages jointly promote the improvement of the model’s efficiency during the training process. Second, an adaptive learning rate and a mixed-precision training strategy were adopted in the model training. The adaptive learning rate can be dynamically adjusted according to the training progress of the model, thus converging rapidly in the early stage of training and fine-tuning in the later stage of training to improve accuracy. Mixed-precision training combines single- and half-precision computations to reduce memory usage and computational requirements while maintaining model accuracy. This further accelerates convergence and optimizes CPU usage. In addition, the dataset has undergone excellent preprocessing to ensure the quality and diversity of the data. Good data preprocessing includes not only cleaning and normalization, but also feature selection and enhancement. This helps the model learn effective feature representations more quickly. High-quality data input is another key factor for the model to converge rapidly. These factors work together to make the model perform well in handling complex tasks.