Stage-Based Remaining Useful Life Prediction for Bearings Using GNN and Correlation-Driven Feature Extraction
Abstract
:1. Introduction
2. Methodology
2.1. Methodological Approach to HI Extraction
2.1.1. HIs
2.1.2. Feature Selection Based on Variance
2.1.3. Pearson–Spearman Correlation Analysis
2.1.4. HIs Fusion with KPCA and Autoencoders
- Correlation analysis and grouping: First, perform correlation analysis on the features and set a threshold to group highly correlated features together.
- KPCA processing: Apply KPCA to each group of features, retaining principal components that explain 90% of the cumulative variance.
- Autoencoder optimization: Input the retained principal components and ungrouped features into an autoencoder, adjusting the learning weights according to the original number of features. The output from the bottleneck layer of the autoencoder is used as the final HI, representing the bearing’s degradation state.
2.2. Bearing Degradation Stage Classification
2.2.1. Gaussian Mixture Model (GMM)
- Mean vector :
- Covariance matrix :
- Mixing coefficient :
2.2.2. Graph Convolutional Network
2.2.3. GCN–LSTM
- 1.
- Euclidean distance calculation:
- 2.
- Initial connections:
- 3.
- Additional neighbors selection:
- 4.
- Weight distribution:
Algorithm 1. The pseudocode for constructing the adjacency matrix in the RUL prediction model. |
Input: Feature matrix X, Node count N, Number of neighbors k, Self-loop weight Ws Output: Adjacency matrix A for i in range(1, N) do: for j in range(1, N) do: if i != j: distance(i, j) = compute_distance(X[i], X[j]); end if end for A[i][i] = Ws; for offset in range(−3, 4): neighbor_idx = (i + offset) % N; if neighbor_idx != i: A[i][neighbor_idx] = 1; end if end for sort distances[i] in ascending order; nearest_neighbors = distances[i][:k]; for neighbor in nearest_neighbors do: A[i][neighbor] = 1/(distance(i, neighbor) + epsilon); end for row_sum = sum(A[i]) − A[i][i]; for j in range(1, N) do: if A[i][j] != 0: A[i][j] = (1 − Ws)*A[i][j]/row_sum; end if end for return A; |
2.3. Bearing Remaining Useful Life Prediction
2.3.1. GraphSAGE
2.3.2. Adaptive Attention GraphSAGE–LSTM
- GraphSAGE feature extractor: First, GraphSAGE is used to extract both local and global spatial features from bearing data. These features reflect the bearing’s state during both healthy and degraded phases, providing input for subsequent time-series modeling. The multi-layer structure of GraphSAGE allows it to iteratively aggregate information from neighboring nodes, capturing high-order dependencies. This is especially well-suited for bearing degradation data with complex topologies.
- LSTM temporal dynamics modeling: The extracted spatial features are fed into an LSTM network to capture the temporal dynamics of the bearing degradation process. LSTM effectively models long-term dependencies over time, helping to identify trends and changes across different degradation phases. Given that degradation process features often exhibit significant temporal dependencies, LSTM’s memory mechanism is well-equipped to model these, providing more accurate predictions of degradation states.
- Adaptive attention mechanism: The model incorporates different attention mechanisms at various stages of degradation to better capture critical features. In the early stages of degradation, where it is important to detect overall trends, the model uses a global attention mechanism to identify key features across the entire sequence, aiding in the early detection of degradation trends. In the severe degradation stage, where short-term features become more significant, the model applies a local attention mechanism to focus on rapid changes over short periods, providing a more detailed description of severe degradation.
- Healthy stage: Since feature changes are minimal, the adjacency matrix construction remains simple. Each node is connected to itself, as well as to its preceding and following neighbors, with the weights evenly distributed (each edge weight set to 0.33). This ensures basic connectivity while avoiding overfitting by irrelevant information.
- Slight degradation stage: As feature changes begin to manifest, each node is connected to the two preceding and two following neighbors, as well as to the two other nodes with the smallest Euclidean distances. This results in a total of seven connected nodes, including itself. The self-loop weight is set to 0.1, while the weights for the other connections are assigned based on the inverse of the Euclidean distances, as described in Equations (12) and (13), ensuring that more similar nodes receive higher weights.
- Severe degradation stage: As feature changes become more pronounced, each node is connected to the two preceding and two following neighbors, along with the four other nodes with the smallest Euclidean distances. This forms connections to a total of nine nodes, including itself. The self-loop weight remains at 0.1, and the weights for the other nodes are distributed according to the inverse of the Euclidean distances, as described in Equations (12) and (13).
Algorithm 2. The pseudocode for constructing the adjacency matrix in the RUL prediction model. |
Input: Feature matrix X, Node count N, Stage type (Healthy, Slight Degradation, Severe Degradation), Self-loop weight Ws Output: Adjacency matrix A for i in range(1, N) do: for j in range(1, N) do: if i != j: distance(i, j) = compute_distance(X[i], X[j]); end if end for if stage_type == “Healthy”: A[i][i] = Ws; for offset in range(−1, 2): neighbor_idx = (i + offset) % N; if neighbor_idx != i: A[i][neighbor_idx] = 0.33; end if end for else if stage_type == “Slight Degradation”: A[i][i] = Ws; for offset in range(−2, 3): neighbor_idx = (i + offset) % N; if neighbor_idx != i: A[i][neighbor_idx] = 1; end if end for sort distances[i] in ascending order; nearest_neighbors = distances[i][:2]; for neighbor in nearest_neighbors do: A[i][neighbor] = 1/(distance(i, neighbor) + epsilon); end for else if stage_type == “Severe Degradation”: A[i][i] = Ws; for offset in range(−2, 3): neighbor_idx = (i + offset) % N; if neighbor_idx != i: A[i][neighbor_idx] = 1; end if end for sort distances[i] in ascending order; nearest_neighbors = distances[i][:4]; for neighbor in nearest_neighbors do: A[i][neighbor] = 1/(distance(i, neighbor) + epsilon); end for end if if stage_type != “Healthy”: row_sum = sum(A[i]) − A[i][i]; for j in range(1, N) do: if A[i][j] != 0: A[i][j] = (1 − Ws)*A[i][j]/row_sum; end if end for end if end for return A; |
3. Experimental Results
3.1. HI Extraction
3.2. Stage Classification
- Healthy stage vs. slight degradation stage classification network: This network is used to distinguish between the healthy stage and the slight degradation stage of bearings.
- Slight degradation stage vs. severe degradation stage classification network: This network is used to differentiate between the slight degradation and severe degradation stages.
3.3. RUL Prediction
3.4. Parameter Analysis
4. Discussion
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Feature | Formula | Feature | Formula |
---|---|---|---|
Interquartile range | Peak to peak | ||
Kurtosis | Root mean square | ||
Kurtosis indicator | Signal entropy | ||
Waveform indicator | RMSEE | ||
Margin indicator | Modulus maximum | ||
Skewness | Teager energy mean | ||
Peak indicator | Variance | ||
Pulse indicator | Mean absolute deviation |
Feature | Formula |
---|---|
Center frequency | |
Frequency domain amplitude average | |
Root mean square frequency | |
Standard deviation frequency | |
Peak frequency | |
Spectral energy | |
Spectral entropy | |
Spectral flatness | |
Spectral kurtosis | |
Spectral skewness | |
Spectral spread |
Features Before Initial Selection | Features After Initial Selection | ||
---|---|---|---|
IQR | FDAA | IQR | Spectral entropy |
Kurtosis | Peak frequency | Kurtosis | Spectral flatness |
Kurtosis indicator | RMSF | Kurtosis indicator | Spectral kurtosis |
MAD | Spectral energy | MAD | Spectral skewness |
Margin indicator | Spectral entropy | Margin indicator | Spectral spread |
LSS | Spectral flatness | Modulus max | SDF |
Mean | Spectral kurtosis | Peak indicator | EMD1 |
Mean square value | Spectral skewness | Peak to peak | EMD2 |
Median | Spectral spread | Pulse indicator | EMD3 |
Modulus max | SDF | RMSEE | EMD4 |
Peak indicator | EMD1 | Root mean square | EMD5 |
Peak to peak | EMD2 | Signal entropy | WPE2 |
Pulse indicator | EMD3 | Skewness | WPE3 |
RMSEE | EMD4 | Teager energy mean | WPE4 |
Root mean square | EMD5 | Variance | WPE5 |
Signal entropy | WPE1 | Waveform indicator | |
Skewness | WPE2 | Center frequency | |
Teager energy mean | WPE3 | FDAA | |
Variance | WPE4 | Peak frequency | |
Waveform indicator | WPE5 | RMSF | |
Center frequency | Spectral energy |
Group1 | Group2 | Group3 | Group4 |
---|---|---|---|
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 35, 36, 37, 38, 41, 42, 43, 44, 45, 46, 48, 50, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72 | 33, 34, 39, 40 | 17, 25 | 47, 49 |
Group1 | Group2 |
---|---|
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 35, 36, 37, 40, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72 | 33, 34, 38, 39 |
Parameters | Parameter Value | Parameters | Parameter Value |
---|---|---|---|
GCN layers | 3 | Activation function | ReLU |
GCN channels | 32 | Optimizer | NAdam |
LSTM layers | 6 | Learning rate | 0.0001 |
LSTM hidden layers | 64 | Loss function | CrossEntropyLoss |
Parameters | Parameter Value | Parameters | Parameter Value |
---|---|---|---|
GCN layers | 3 | Activation function | ReLU |
GCN channels | 64 | Optimizer | NAdam |
LSTM layers | 8 | Learning rate | 0.00015 |
LSTM hidden layers | 64 | Loss function | CrossEntropyLoss |
Models | Bearing 1-4 | Bearing 2-1 | Bearing 3-3 |
---|---|---|---|
GCN–LSTM | 99.31%/98.92% | 98.42%/98.50% | 99.53%/97.33% |
CNN | 82.27%/76.13% | 79.81%/80.29% | 72.45%/69.88% |
GCN | 88.40%/83.44% | 84.62%/82.46% | 86.91%/87.69% |
CCN–LSTM | 94.57%96.83% | 89.45%/90.68% | 93.40%/94.74% |
Bearings | RMSE | MAE | MAPE | R2 | Adjusted R2 |
---|---|---|---|---|---|
Bearing 1-4 | 0.00706 | 0.00599 | 0.04994 | 0.997555 | 0.997552 |
Bearing 2-1 | 0.00494 | 0.00403 | 0.07415 | 0.998545 | 0.998542 |
Bearing 3-3 | 0.00265 | 0.00180 | 0.17506 | 0.978568 | 0.978509 |
Models | 1-4 | 2-1 | 3-3 |
---|---|---|---|
AAGL | 0.00706 | 0.00494 | 0.00265 |
[43] | 0.00772 | 0.00525 | 0.00732 |
[44] | 0.1739 | - | - |
[45] | 0.0691 | 0.1071 | 0.0822 |
Models | 1-4 | 2-1 | 3-3 |
---|---|---|---|
LSTM | 0.02732 | 0.01492 | 0.02346 |
CNN–LSTM | 0.01613 | 0.00963 | 0.01372 |
GCN–LSTM | 0.00967 | 0.007670 | 0.00663 |
AAGL | 0.00706 | 0.00494 | 0.00265 |
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Huang, G.; Lei, W.; Dong, X.; Zou, D.; Chen, S.; Dong, X. Stage-Based Remaining Useful Life Prediction for Bearings Using GNN and Correlation-Driven Feature Extraction. Machines 2025, 13, 43. https://doi.org/10.3390/machines13010043
Huang G, Lei W, Dong X, Zou D, Chen S, Dong X. Stage-Based Remaining Useful Life Prediction for Bearings Using GNN and Correlation-Driven Feature Extraction. Machines. 2025; 13(1):43. https://doi.org/10.3390/machines13010043
Chicago/Turabian StyleHuang, Guangzhong, Wenping Lei, Xinmin Dong, Dongliang Zou, Shijin Chen, and Xing Dong. 2025. "Stage-Based Remaining Useful Life Prediction for Bearings Using GNN and Correlation-Driven Feature Extraction" Machines 13, no. 1: 43. https://doi.org/10.3390/machines13010043
APA StyleHuang, G., Lei, W., Dong, X., Zou, D., Chen, S., & Dong, X. (2025). Stage-Based Remaining Useful Life Prediction for Bearings Using GNN and Correlation-Driven Feature Extraction. Machines, 13(1), 43. https://doi.org/10.3390/machines13010043