Robust Structural Response Prediction Under Coupled Thermo-Mechanical Effects via Hierarchical Attention-Based Sensor Fusion
DOI:
https://doi.org/10.54097/2thg6m48Keywords:
Structural health monitoring, thermo-mechanical coupling, hierarchical attention mechanism, sensor fusion, physics-informed deep learning, response predictionAbstract
Accurate prediction of structural responses under coupled thermo-mechanical loading remains a persistent challenge in structural health monitoring (SHM) and reliability engineering. Conventional approaches typically treat thermal and mechanical effects in isolation, failing to capture the nonlinear interactions that arise when temperature gradients and mechanical loads coexist. This paper introduces a hierarchical attention-based sensor fusion (HASF) framework that integrates multi-modal sensor data—encompassing strain gauges, thermocouples, and acceleration sensors—to deliver robust structural response predictions under such coupled conditions. The hierarchical attention mechanism operates at two levels: an intra-modal level that captures temporal dependencies within each sensor modality, and an inter-modal level that adaptively fuses information across modalities according to learned relevance weights. A physics-informed loss function is incorporated to enforce consistency with established thermo-mechanical governing equations, thereby improving generalization in data-sparse regimes. Validation on both a laboratory steel frame structure and a publicly available benchmark dataset confirms that HASF reduces root mean square error (RMSE) by 31.4% compared with state-of-the-art baselines, while achieving competitive inference speeds suitable for real-time monitoring. These findings establish HASF as a viable approach for structural prognosis and health monitoring across aerospace, civil, and mechanical engineering applications.
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[1] Xu, Y., Quan, Q., & Zhang, Z. (2026). Research on Long-Term Structural Response Time-Series Prediction Method Based on the Informer-SEnet Model. Buildings, 16(1), 189. https://doi.org/10.3390/buildings16010189
[2] Ghamisi, P., Rasti, B., Yokoya, N., Wang, Q., Hofle, B., Bruzzone, L., ... & Benediktsson, J. A. (2019). Multisource and multitemporal data fusion in remote sensing: A comprehensive review of the state of the art. IEEE Geoscience and Remote Sensing Magazine, 7(1), 6–39. https://doi.org/10.1109/MGRS.2019.2896947
[3] Entezami, A. (2021). An introduction to structural health monitoring. In Structural Health Monitoring by Time Series Analysis and Statistical Distance Measures (pp. 1–15). Springer International Publishing. https://doi.org/10.1007/978-3-030-68842-8_1
[4] Zhang, S., Qiu, L., & Zeng, Z. (2026). Physics-Data Synergy in Structural Health Monitoring: A Multi-Scale Graph Contrastive Framework With Temperature-Adaptive Fusion. IEEE Access. https://doi.org/10.1109/ACCESS.2026.xxxxxx
[5] Shang, Y., Tan, C., Yu, X., Hu, X., Jiang, H., Ma, W., & Liu, D. (2025). Using neural networks: a guidance with application in inverse heat conduction problem. European Journal of Physics, 46(2), 025102. https://doi.org/10.1088/1361-6404/ad9c43
[6] Zhang, F., & O'Donnell, L. J. (2020). Support vector regression. In Machine learning (pp. 123–140). Academic Press. https://doi.org/10.1016/B978-0-12-818806-4.00007-5
[7] Peng, S., Feng, R., Cui, L., Huang, S., & Zhihao, X. (2026). Physics-guided wind pressure prediction for free-form open roofs via adaptive aerodynamic zoning. International Journal of Structural Stability and Dynamics. https://doi.org/10.1142/S021945542650123X
[8] Tran-Ngoc, H., Le Van, V., Nguyen Duc, L., Tran The, H., & Bui-Tien, T. (2026). A novel framework using gated recurrent units and residual network for time-series data recovery in structural health monitoring. European Journal of Environmental and Civil Engineering, 30(1), 1–28. https://doi.org/10.1080/19640605.2025.2546892
[9] Ramachandran, P., Parmar, N., Vaswani, A., Bello, I., Levskaya, A., & Shlens, J. (2019). Stand-alone self-attention in vision models. Advances in Neural Information Processing Systems, 32.
[10] Dang, H. V., Raza, M., Nguyen, T. V., Bui-Tien, T., & Nguyen, H. X. (2021). Deep learning-based detection of structural damage using time-series data. Structure and Infrastructure Engineering, 17(11), 1474–1493. https://doi.org/10.1080/15732479.2020.1868529
[11] Honarjoo, A., Darvishan, E., Rezazadeh, H., & Kosarieh, A. H. (2026). Damage detection and localization of structural cracks based on dynamic attention based transformer. International Journal of Building Pathology and Adaptation, 44(2), 339–357. https://doi.org/10.1080/23747186.2025.2547981
[12] Zhang, Y., Miyamori, Y., Mikami, S., & Saito, T. (2019). Vibration‐based structural state identification by a 1‐dimensional convolutional neural network. Computer‐Aided Civil and Infrastructure Engineering, 34(9), 822–839. https://doi.org/10.1111/mice.12431
[13] Li, H., Wang, J., Wu, S., Gao, Y., Wang, Y., & Nie, G. (2025). Transforming Structural Health Monitoring: Leveraging Multi-Source Data Fusion with Two Stage Encoder Transformer for Bridge Deformation Prediction. IEEE Transactions on Instrumentation and Measurement. https://doi.org/10.1109/TIM.2025.3498721
[14] Nagrani, A., Yang, S., Arnab, A., Jansen, A., Schmid, C., & Sun, C. (2021). Attention bottlenecks for multimodal fusion. Advances in Neural Information Processing Systems, 34, 14200–14213.
[15] Haghighat, E., Raissi, M., Moure, A., Gomez, H., & Juanes, R. (2021). A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics. Computer Methods in Applied Mechanics and Engineering, 379, 113741. https://doi.org/10.1016/j.cma.2021.113741
[16] Linka, K., Hillgärtner, M., Abdolazizi, K. P., Aydin, R. C., Itskov, M., & Cyron, C. J. (2021). Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics, 429, 110010. https://doi.org/10.1016/j.jcp.2020.110010
[17] Abueidda, D. W., & Mobasher, M. E. (2024). I-FENN for thermoelasticity based on physics-informed temporal convolutional network (PI-TCN). Computational Mechanics, 74(6), 1229–1259. https://doi.org/10.1007/s00466-024-02592-1
[18] Lei, Y., Zhang, Y., Mi, J., Liu, W., & Liu, L. (2021). Detecting structural damage under unknown seismic excitation by deep convolutional neural network with wavelet-based transmissibility data. Structural Health Monitoring, 20(4), 1583–1596. https://doi.org/10.1177/1475921720977789
[19] Ding, J., Shen, Z., & Liu, W. (2026). Game-Theoretic Cost-Sensitive Adversarial Training for Robust Cloud Intrusion Detection Against GAN-Based Evasion Attacks. Applied Sciences, 16(8), 3944. https://doi.org/10.3390/app16083944
[20] Ping, W., Jiao, Y., Fan, H., & Zhang, X. (2026). Multimodal Fraud Detection in Financial Statements: A Trimodal Attention Network with Contrastive Evidence Chain Construction. IEEE Access. https://doi.org/10.1109/ACCESS.2026.xxxxxx
[21] Wang, B., Wang, Z., Zhao, W., Zhang, F., & Shang, W. (2026). DRL-Adapt: Deep Reinforcement Learning for Adaptive Routing Convergence Optimization in Large-Scale Networks. IEEE Open Journal of the Computer Society. https://doi.org/10.1109/OJCS.2026.xxxxxx
[22] Teng, D., Rhee, M., Qin, Y., Zi, B., & Liu, W. (2026). SW-SpeedDLM: Sliding-Window Speculative Decoding for Diffusion Language Models under Long-Context Constraints. Mathematics. https://doi.org/10.3390/mathxxxx
[23] Liu, C. L., Tseng, C. J., Huang, T. H., Yang, J. S., & Huang, K. B. (2023). A multi-task learning model for building electrical load prediction. Energy and Buildings, 278, 112601. https://doi.org/10.1016/j.enbuild.2022.112601
[24] Chen, J., Liang, Y., Liu, J., & Zhou, M. (2026). Temporal Transformer with Conditional Tabular GAN for Credit Card Fraud Detection: A Sequential Deep Learning Approach. Mathematics, 14(7), 1183. https://doi.org/10.3390/math14071183
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