Scan-Net: few-shot diagnosis of hydropower auxiliary bearings via Siamese mutual learning

3.1.1. Overall framework

The proposed Siamese Cross-Attention Network (Scan-Net) is designed to address the challenge of fault diagnosis for auxiliary equipment (e.g., governor oil pumps) under few-shot conditions. As illustrated in Fig. 2, the framework employs a dual-stream Siamese architecture that processes vibration signals from the Drive End (DE) and Fan End (FE) independently. Three design choices distinguish this method from prior work: (1) dual-sensor features interact through bidirectional cross-attention rather than post-hoc concatenation; (2) two branches are jointly regularized by a symmetric KL consistency loss rather than trained independently; (3) the method is validated across 10-shot learning, cross-load transfer, and a field pilot, rather than reporting accuracy on a standard split alone. The overall process consists of three key stages:

1) Multi-scale time-frequency feature encoding: First, MSWT transforms one-dimensional vibration signals into two-dimensional RGB images containing rich time-frequency details. Subsequently, through a ResNet-18 backbone network integrated with Convolutional Block Attention Module (CBAM), deep feature representations with channel and spatial sensitivity are extracted from DE and FE branches.

2) Siamese cross-attention fusion: Unlike traditional feature concatenation, we design a cross-attention module that enables dual-branch features to interact in latent space. This module allows the DE branch to dynamically retrieve complementary information from the FE branch (and vice versa), generating enhanced feature vectors that fuse advantages from both sources.

3) Mutual learning and consistency constraints: Beyond the main classification task, we introduce auxiliary classifiers for each branch and constrain consistency of prediction distributions between two branches through KL divergence. This mutual learning mechanism forces the model to extract inherent consistency between dual views in the absence of labels, significantly improving robustness in few-shot scenarios.

Fig. 2Overall framework of Scan-Net. The dual-branch Siamese backbone (ResNet-18+CBAM) extracts features from DE and FE sensors with shared weights. Cross-attention fusion enables bidirectional feature interaction (red dashed lines). KL divergence consistency loss (purple dashed lines) aligns branch predictions PDE and PFE. Main classifier CMain and auxiliary classifiers CDE, CFE are jointly optimized via LTotal

3.1.2. Dual-branch feature extraction

Input Representation: Multi-Scale Synchrosqueezed Wavelet Transform (MSWT). Raw vibration signals are often submerged in strong background noise, and fault features exhibit non-stationarity. To fully preserve transient impact components and suppress noise, we adopt Multi-Scale Synchrosqueezed Wavelet Transform (MSWT) [16] as a signal preprocessing method. MSWT significantly improves time-frequency resolution by redistributing energy in the time-frequency plane.

For signal $x\left(t\right)$, its Continuous Wavelet Transform (CWT) [17] is defined as:

where $\psi \left(t\right)$ is the mother wavelet, $a$ is the scale parameter, $b$ is the time shift.

Synchrosqueezed Transform (SWT) sharpens time-frequency representation by reassigning wavelet coefficients to instantaneous frequency positions:

where ${\omega }_k(a_k,b)$ is the instantaneous frequency estimate.

To capture multi-frequency-band fault features of auxiliary bearings under complex operating conditions (such as high-frequency inner race impacts, mid-frequency outer race periodic components, low-frequency rolling element modulations), we perform transformations at three complementary frequency scales ($s_1=$ 0.5, $s_2=$ 1.0, $s_3=$ 2.0) and map the resulting time-frequency coefficients to three channels of an RGB image:

This multi-scale representation not only preserves high-frequency impacts of inner race faults but also captures mid-to-low-frequency modulation features of outer race and rolling element faults, providing physically meaningful input representation for deep networks.

Backbone Network: CBAM-Enhanced ResNet-18. Given ResNet-18’s [18] excellent performance in feature extraction, we adopt it as the backbone architecture of the Siamese network. To further enhance the model’s sensitivity to key fault features, we embed the Convolutional Block Attention Module (CBAM) [19] after each residual block. CBAM includes two sub-modules: Channel Attention and Spatial Attention.

Channel attention module is computed as:

Spatial attention module is computed as:

where $F$ is the input feature, $F^{\mathrm{\text{'}}}$ is the channel-refined feature, $\sigma$ is the sigmoid activation function, $f^{7\times 7}$ is the convolution operation.

1) Channel attention: Adaptively recalibrates channel weights, emphasizing key frequency bands containing fault pulses while suppressing noise bands.

2) Spatial attention: Focuses on fault impact regions in time-frequency maps, ignoring background regions.

3) Advantages of Siamese Architecture: The two branches share network structure and weight parameters, i.e., ${\theta }_{DE}={\theta }_{FE}$. This design has three advantages: (1) Parameter efficiency: Compared to two independent networks, parameters are reduced by approximately 50 %, lowering overfitting risk; (2) Implicit regularization: Weight sharing forces the model to learn universal fault feature representations insensitive to sensor position, improving cross-sensor generalization; (3) Symmetry guarantee: Symmetric dual-branch design ensures fairness of subsequent mutual learning mechanisms, avoiding dominance by one branch.

3.1.3. Siamese cross-attention fusion

Traditional feature fusion methods, such as concatenation or weighted summation, often overlook the semantic correlations between features from different sensors. To address this limitation, we propose a deep fusion strategy based on Cross-Attention. This mechanism enables the model to dynamically “query” features from one sensor using the features from the other, achieving selective information aggregation that exploits the complementary nature of the data.

Let ${\mathbf{f}}_{DE}$, ${\mathbf{f}}_{FE}\in {\mathbb{R}}^d$ be feature vectors extracted from DE and FE branches respectively. In practice, the attention is computed after reshaping features into multi-head subspaces; for clarity, we present the single-head formulation below. To capture complementary relationships between different sensor features, we design a bidirectional cross-attention mechanism. Query, Key, and Value vectors are generated through linear projection:

Using Scaled Dot-Product Attention to compute bidirectional cross features. Taking the DE branch aggregating FE information as an example, the generated cross feature ${\mathbf{f}}_{DE\leftarrow FE}$ is computed as:

Similarly, the FE branch aggregating DE information feature ${\mathbf{f}}_{FE\leftarrow DE}$ is:

To preserve original branch features and fuse cross information, we introduce Residual Connection and Layer Normalization, then concatenate the two enhanced feature vectors and generate the final fused feature ${\mathbf{f}}_{fused}$ through a fully connected layer:

This bidirectional fusion mechanism ensures the model considers both sensor views when making decisions. For example, when the DE sensor is severely interfered by noise, the model can automatically assign higher attention to FE features.

3.1.4. Mutual Learning and optimization objective

To mitigate the impact of label scarcity in few-shot scenarios, we introduce a Mutual Learning mechanism. This mechanism serves as a powerful regularization technique. The core idea is to utilize the consistency of dual-branch predictions as a supervisory signal, so that the model can extract structural information from unlabeled data, thereby reducing the reliance on annotated samples.

The overall loss function ${\mathcal{L}}_{total}$ consists of three parts: main task classification loss, branch auxiliary classification loss, and consistency constraint loss:

where $\gamma$ and $\beta$ are hyperparameters balancing each loss weight.

1) Classification Loss: We adopt standard Cross-Entropy Loss as the classification objective. For a given sample and its true label $y$, and model predicted probability distribution $P$, the loss is defined as:

Therefore, main task loss ${\mathcal{L}}_{main}={\mathcal{L}}_{CE}(y,P_{Main})$, auxiliary branch losses ${\mathcal{L}}_{DE}={\mathcal{L}}_{CE}(y,P_{DE})$ and ${\mathcal{L}}_{FE}={\mathcal{L}}_{CE}(y,P_{FE})$. This forces each branch and fusion module to possess accurate discriminative capability.

2) Consistency Loss ${\mathcal{L}}_{consist}$ (Core of Mutual Learning): We require prediction probability distributions $P_{DE}$ and $P_{FE}$ of two branches on the same sample to be as close as possible. We adopt symmetrized bidirectional KL divergence (Kullback-Leibler Divergence) as the metric:

where $D_{KL}\left(P\right|\left|Q\right)=\sum P\left(x\right)\mathrm{l}\mathrm{o}\mathrm{g}\frac{P\left(x\right)}{Q\left(x\right)}$.

Theoretical Advantages of KL Divergence Consistency Constraint: This mechanism draws on Deep Mutual Learning (DML) [15] ideas but adapts them for dual-sensor diagnosis scenarios. Its advantages are reflected in three levels:

1) Self-supervised regularization: In few-shot scenarios, label signals are sparse and prone to overfitting. KL divergence constraints provide additional soft supervision signals – two branches must reach “consensus” on the same fault. This constraint does not rely on additional labeling but effectively narrows the hypothesis space, preventing the model from memorizing noise.

2) Knowledge complementarity: DE and FE sensors are at different bearing positions, each potentially capturing complementary fault information (e.g., DE sensitive to inner race faults, FE sensitive to outer race faults). Through KL divergence minimization, two branches “teach” each other during training, with high-confidence predictions from one branch influencing the other, achieving knowledge transfer.

3) Robustness improvement: When one sensor is interfered by noise, consistency constraints force the interfered branch’s predictions to align with the clean branch, suppressing noise propagation. Ablation experiments (Table 2) show that removing consistency loss reduces 10-shot accuracy by 4.4 %, indicating the importance of this mechanism in few-shot scenarios.

The KL divergence consistency loss encourages predictive agreement between the two branches, acting as a regularizer that extracts shared structure from dual-view data and improves the model’s generalization boundary.

3.2.1. Dataset

This study adopts the internationally recognized Case Western Reserve University (CWRU) bearing dataset [20] for algorithm validation. The dataset includes vibration signals of Normal, Inner Race Fault, Outer Race Fault, and Rolling Element Fault (collectively called 4-class classification) collected under different loads (0-3 hp). We follow standard data processing procedures, segmenting raw signals into 2048-point samples and dividing them 70 %/15 %/15 % for training/validation/testing. All samples are converted to 224×224 RGB time-frequency images through the aforementioned MSWT method.

To demonstrate the effectiveness of MSWT, Fig. 3 visualizes the signal processing results. As illustrated, the time-domain signals (Column a) for different fault types often show overlapping characteristics and are difficult to distinguish visually. In contrast, the MSWT time-frequency maps (Columns b and c) reveal distinct visual patterns: Normal samples exhibit low and uniform energy distribution; Inner Race faults show high-frequency periodic impulses; Outer Race faults display mid-frequency components; Ball faults present complex modulations. These discriminative signatures, consistent across both Drive End (DE) and Fan End (FE) sensors, enable effective classification.

3.2.2. Few-shot learning setup

To simulate the severe label-scarcity scenario encountered in industrial practice, we construct a strict 10-shot setting: for each fault category, only 10 labeled samples are randomly selected from the training split as the sole training data, with the remainder discarded. All few-shot results reported in this paper use this setting. Each experiment is repeated 10 times with different random seeds, and the average accuracy is reported to ensure stability and reliability.

3.2.3. Implementation details

All models are implemented in PyTorch framework and trained using a single NVIDIA RTX 3090 GPU. We adopt the Adam optimizer with an initial learning rate of 5×10^-5 and use cosine annealing strategy for learning rate scheduling. Training batch size is 16, trained for 100 epochs, and early stopping strategy (patience = 20) is adopted to prevent overfitting. In the composite loss function, auxiliary loss weight $\gamma$ is set to 0.15, consistency loss weight $\beta$ is set to 0.1 based on experimental tuning.

Fig. 3Visualization of signal processing results for different health states. The rows correspond to Normal, Ball Fault, Inner Race Fault, and Outer Race Fault conditions. Columns display: a) Time-domain vibration signals; b) MSWT time-frequency maps from Drive End (DE) sensor; c) MSWT time-frequency maps from Fan End (FE) sensor. The MSWT maps reveal distinct texture patterns and frequency energy distributions for each fault type, whereas time-domain signals are less discriminative

a) Time-domain signal

b) MSWT – drive end

c) MSWT – fan end

4.3.1. Contribution analysis of key components

Table 3 shows model performance after progressively removing each module.

1) Importance of MSWT (a vs b): Compared to directly using one-dimensional raw signals (Baseline), introducing MSWT time-frequency maps improves accuracy from 76.20 % to 89.50 % (+13.3 %). This result indicates that under extremely few samples, two-dimensional time-frequency textures provided by MSWT contain more distinguishable physical features than raw waveforms, reducing the learning difficulty for deep networks.

2) Gain from dual-sensor fusion (b vs c): Expanding from single sensor (DE end) to dual sensors (DE+FE) with simple feature concatenation (Concat) further improves accuracy by 3.9 %. This validates that information complementarity from different measurement points can effectively eliminate diagnostic blind spots inherent to single perspectives.

3) Critical role of cross-attention and mutual learning mechanisms (c/e vs f):

– Cross-attention mechanism (comparing c and f) brings an improvement (+3.1 %). This indicates that simple concatenation cannot fully exploit semantic correlations between sensors. Cross-Attention achieves deep feature interaction through Query-Key-Value mechanisms, allowing one branch to dynamically retrieve complementary information from the other.

– KL divergence consistency loss (comparing e and f) contributes 4.4 % performance improvement, the largest single contribution among all improvements. This finding confirms the effectiveness of the mutual learning mechanism. When lacking abundant label supervision, the constraint forces dual-branch prediction distribution alignment (i.e., $P_{DE}\approx P_{FE}$), providing powerful regularization that extracts inherent consistency structure in dual-view data and prevents the model from overfitting to noise.

– Fine-grained focus of CBAM (d vs f): Removing CBAM results in a slight performance decrease of 1.7 %. This indicates that channel and spatial attention mechanisms help locate key fault impact frequency bands in complex time-frequency maps. However, their contribution is relatively smaller than that of the mutual learning mechanism.

4.3.2. Visualization of learned representations

To provide deeper insights into the model’s internal workings, we visualize the learned attention patterns and feature evolution process.

Cross-Attention Weight Analysis. Fig. 6 visualizes the learned attention weights between DE and FE sensor features across different fault types. The heatmaps reveal several important patterns: (1) For Normal samples, attention weights are relatively balanced between sensors, indicating that both views contribute equally to the healthy state representation; (2) For Inner Race faults, higher attention is allocated to the DE sensor, which is physically closer to the inner race and thus captures stronger fault signatures; (3) For Outer Race faults, the attention distribution shifts toward the FE sensor, reflecting the different propagation paths of outer race vibrations; (4) For Rolling Element faults, the attention pattern shows dynamic interaction between both sensors, consistent with the complex nature of rolling element dynamics. These adaptive attention patterns demonstrate that our cross-attention mechanism successfully learns to exploit sensor complementarity in a fault-type-specific manner.

Fig. 6Cross-attention weight visualization between DE and FE features for four fault types. Warmer colors indicate higher attention. The mechanism adaptively adjusts inter-sensor information flow based on fault characteristics, e.g., Inner Race faults trigger stronger DE-to-FE attention due to proximity effects

Feature Evolution Through Network Layers. To further demonstrate the effectiveness of the proposed method, Fig. 7 illustrates how feature representations evolve through the network processing stages using t-SNE visualization. Starting from raw signal inputs, features progressively become more discriminative as they pass through MSWT transformation, CBAM attention modules, and cross-attention fusion. The visualization shows that: (1) Raw signal features exhibit significant overlap between fault categories; (2) MSWT time-frequency transformation provides initial separation by capturing frequency-domain characteristics; (3) CBAM attention further refines the features by emphasizing discriminative regions; (4) The final cross-attention fusion produces highly discriminative representations with clear inter-class boundaries and compact intra-class clustering. This progressive refinement validates the design rationale of our hierarchical feature extraction pipeline.

Fig. 7Feature evolution through Scan-Net visualized by t-SNE: a) raw signal features with significant class overlap; b) after MSWT with improved separation; c) after CBAM refinement; d) after cross-attention fusion with distinct inter-class separation and compact intra-class clustering

a)

b)

c)

d)

4.3.3. Robustness analysis under different signal-to-noise ratios

To further evaluate model performance under harsh operating conditions, we add additive white Gaussian noise of different intensities (SNR from –4 dB to 8 dB) to the test set. As shown in Fig. 8, Scan-Net significantly outperforms single-sensor models (Single-DE) and simple fusion models (Late-Fusion) at all noise levels.

Fig. 8Model robustness comparison under different Signal-to-Noise Ratio (SNR) environments. Scan-Net shows significant performance advantages under strong noise (–4 dB)

Anti-noise advantages of Siamese mutual learning mechanism: Especially in –4 dB strong noise environments, Scan-Net maintains 86.5 % accuracy while single-sensor models have dropped to 58.2 % (performance improvement of 28.3 %). This significant advantage stems from three synergistic mechanisms: (1) Dynamic channel suppression of cross-attention: When one sensor is polluted by noise, Cross-Attention automatically lowers its attention weight, relying instead on the cleaner signal from the other path; (2) Noise filtering of KL divergence consistency constraint: This constraint forces predictions of two branches to reach consensus, with the noise-interfered branch aligning toward the clean branch, suppressing noise propagation; (3) Weight sharing of Siamese network: Through joint training on dual-sensor data, the model learns robust feature representations insensitive to noise. These results support the practical applicability of the mutual learning architecture in complex noise environments.

Model robustness comparison under different Signal-to-Noise Ratio (SNR) environments. Scan-Net shows significant performance advantages under strong noise (–4 dB).

5.2.1. Hardware deployment and signal acquisition

The monitoring object is the drive motor of a governor oil pump, which serves as the core power source of the governor hydraulic control system. The governor system typically consists of multiple oil pumps controlled by a redundant PLC system. This study focuses on the drive motor of one main oil pump, as it bears the main oil pressure establishment task with frequent start-stop operations and load fluctuations.

We deployed industrial-grade piezoelectric acceleration sensors (sensitivity 100 mV/g, frequency response 0.5-10 kHz) at the motor’s drive end (DE) and fan end (FE), mounted on motor bearing housing surfaces using magnetic bases.

Data acquisition process fully utilizes the plant’s existing data infrastructure:

1) Signal acquisition: Sensor signals are acquired by independently deployed vibration acquisition units at 12.8 kHz sampling rate, maintaining consistency with CWRU dataset sampling parameters.

2) Data fusion: To obtain operating condition context, the monitoring system communicates with the local control unit (LCU) via industrial Ethernet, acquiring oil pump start-stop status, oil pressure values, and guide vane opening data, time-synchronized with vibration data.

3) Algorithm inference: The Scan-Net model is encapsulated in an independent intelligent analysis module. This module is physically isolated from the unit’s control system, ensuring monitoring system failures do not affect unit closed-loop control safety.

5.3.1. Cross-condition feature consistency analysis

Although the CWRU test rig (small motor, SKF 6205 bearing) and field equipment (large industrial motor, SKF 6317 bearing) differ vastly in physical dimensions, rolling bearing fault mechanisms are similar.

We collected vibration data from field motors under stable operating conditions, extracted time-frequency domain features, and compared them with “Normal” class samples from the CWRU dataset. t-SNE visualization results show that after MSWT feature extraction, feature distribution overlap reaches over 92 %. Table 5 shows that after normalization, key statistical indicators (such as kurtosis, impulse factor) differ by less than 8 %. This proves learned “healthy state” features have good transferability across different equipment.

5.3.2. Noise resistance performance in field environment

Hydropower station field environments are noisy, with background noise far exceeding laboratory environments. To test model performance in field environments, we recorded actual background noise in machine pit (including water flow sound, electromagnetic noise), superimposed it on CWRU fault samples at different signal-to-noise ratios, constructing “semi-physical simulation” test sets.

Test results show that even under –4 dB strong-noise conditions, the proposed model maintains 86.5 % accuracy. This result supports the effectiveness of the MSWT representation and the attention-guided dual-sensor fusion strategy in complex industrial environments.