The Application of a BiGRU Model with Transformer-Based Error Correction in Deformation Prediction for Bridge SHM
Abstract
1. Introduction
2. Methodology
2.1. BiGRU Model
2.1.1. GRU Neural Network
2.1.2. BiGRU Neural Network
2.2. Transformer Model
2.3. Bridge Deformation Prediction Method
2.3.1. Preliminary Forecasting Stage
2.3.2. Error Correction Stage
2.3.3. Bridge Deformation Prediction Framework
3. Application
3.1. Data Source and Processing
3.2. Model Setup
3.3. Evaluation Metrics
4. Result and Discussion
4.1. Single-Step Prediction Results
4.1.1. Bridge Deformation Prediction Results
4.1.2. Model Comparison
4.2. Multi-Step Prediction Results
4.3. Generalization Performance of the Prediction Method
5. Conclusions
- (1)
- In the bridge deformation prediction experiments, BiGRU outperformed both 1D-CNN and GRU in all evaluation metrics. For example, in the vertical displacement prediction experiment, BiGRU improved prediction accuracy by approximately 11% compared to 1D-CNN and about 2% compared to GRU. This indicates that BiGRU, by learning both forward and backward features of the sequence, enhances its ability to capture complex patterns and long-term dependencies in the deformation data. Thus, its prediction accuracy is further improved compared to other single models.
- (2)
- A comparison of single models and hybrid models incorporating transformer-based error correction was conducted for one-step prediction. The results show that the hybrid models significantly outperform the single models, with their prediction accuracy improving by up to 98.59%. Moreover, when the prediction steps are set to 2, 3, and 4, the hybrid models demonstrate more excellent stability and higher prediction accuracy than single models. This highlights the effectiveness of integrating error correction techniques into the bridge deformation prediction framework.
- (3)
- To improve prediction performance, the BiGRU-Transformer hybrid model employs a two-stage prediction approach, consisting of a preliminary BiGRU prediction followed by transformer-based error correction on SHM data. Compared to other models, the BiGRU-Transformer achieves the highest prediction accuracy, with its prediction error remaining within 5%. This demonstrates the advanced nature and superiority of the BiGRU-Transformer model.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Model | Hyperparameter Name | Hyperparameter Value |
---|---|---|
BiGRU | Input length of BiGRU | 12 |
Number of BiGRU layers | 2 | |
Hidden size of BiGRU | 64, 128 | |
Transformer | Input length of transformer | 5 |
Number of encoder layers | 3 | |
Number of decoder layers | 2 | |
Dimension of model | 128 | |
Dimension of fcn | 128 | |
Number of heads | 8 |
Preliminary Prediction Model | RMSE/mm | MAE/mm | MAPE/% |
---|---|---|---|
1D-CNN | 0.224 | 0.169 | 4.516 |
GRU | 0.195 | 0.149 | 3.985 |
BiGRU | 0.188 | 0.142 | 3.840 |
Hybrid Prediction Model | RMSE/mm | MAE/mm | MAPE/% |
---|---|---|---|
1D-CNN-Transformer | 0.015 | 0.004 | 0.094 |
GRU-Transformer | 0.010 | 0.006 | 0.165 |
BiGRU-Transformer | 0.007 | 0.002 | 0.054 |
Prediction Step | Model | RMSE/mm | MAE/mm | MAPE/% |
---|---|---|---|---|
2 | 1D-CNN | 0.347 | 0.245 | 6.417 |
GRU | 0.301 | 0.212 | 5.536 | |
BiGRU | 0.295 | 0.205 | 5.377 | |
1D-CNN-Transformer | 0.218 | 0.145 | 3.912 | |
GRU-Transformer | 0.204 | 0.116 | 3.034 | |
BiGRU-Transformer | 0.181 | 0.100 | 2.687 | |
3 | 1D-CNN | 0.399 | 0.287 | 7.695 |
GRU | 0.376 | 0.268 | 7.024 | |
BiGRU | 0.371 | 0.262 | 6.907 | |
1D-CNN-Transformer | 0.240 | 0.154 | 4.046 | |
GRU-Transformer | 0.227 | 0.154 | 4.110 | |
BiGRU-Transformer | 0.215 | 0.145 | 3.968 | |
4 | 1D-CNN | 0.451 | 0.325 | 8.525 |
GRU | 0.386 | 0.279 | 7.355 | |
BiGRU | 0.378 | 0.275 | 7.350 | |
1D-CNN-Transformer | 0.288 | 0.196 | 5.303 | |
GRU-Transformer | 0.242 | 0.170 | 4.705 | |
BiGRU-Transformer | 0.248 | 0.168 | 4.515 |
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Wang, X.; Xie, G.; Zhang, Y.; Liu, H.; Zhou, L.; Liu, W.; Gao, Y. The Application of a BiGRU Model with Transformer-Based Error Correction in Deformation Prediction for Bridge SHM. Buildings 2025, 15, 542. https://doi.org/10.3390/buildings15040542
Wang X, Xie G, Zhang Y, Liu H, Zhou L, Liu W, Gao Y. The Application of a BiGRU Model with Transformer-Based Error Correction in Deformation Prediction for Bridge SHM. Buildings. 2025; 15(4):542. https://doi.org/10.3390/buildings15040542
Chicago/Turabian StyleWang, Xu, Guilin Xie, Youjia Zhang, Haiming Liu, Lei Zhou, Wentao Liu, and Yang Gao. 2025. "The Application of a BiGRU Model with Transformer-Based Error Correction in Deformation Prediction for Bridge SHM" Buildings 15, no. 4: 542. https://doi.org/10.3390/buildings15040542
APA StyleWang, X., Xie, G., Zhang, Y., Liu, H., Zhou, L., Liu, W., & Gao, Y. (2025). The Application of a BiGRU Model with Transformer-Based Error Correction in Deformation Prediction for Bridge SHM. Buildings, 15(4), 542. https://doi.org/10.3390/buildings15040542