Computing, Telecommunication and Control Информатика, телекоммуникации и управление 2687-0517 2 10.18721/JCSTCS.19202 TFCA-GRU: A temporal and feature cooperative attention GRU for remaining useful life prediction of bearings across conditions TFCA-GRU: алгоритм GRU с временным и характеристическим кооперативным вниманием для прогнозирования остаточного срока службы подшипников в различных условиях 0000-0002-1497-2893 Guo Chenxi chenxiguo.academic@gmail.com Potekhin Vyacheslav slava.potekhin@mail.ru Peter the Great St. Petersburg Polytechnic University 30 06 2026 19 2 16 30

Accurate prediction of the remaining useful life (RUL) of rolling bearings under different operating conditions is essential to enable proactive maintenance of industrial systems. To address the limitations of traditional recursive models in capturing complex time dependencies and distinguishing sensor contributions, we propose a temporal and feature cooperative attention-based gated recursive unit (TFCA-GRU). By integrating temporal and feature channel attention mechanisms, the model adaptively focuses on degradation-related time steps and key sensor features to build more robust RUL models from multidimensional time-frequency fusion data. Therefore, the TFCA-GRU enables sensitive extraction of critical features from long-term dependencies and local feature information. The validity of the proposed TFCA-GRU is verified using the bearing dataset from the XJTU-SY and the IEEE PHM 2012 Prognostic Challenge. This paper also provides the model’s intrinsic interpretability through structured non-uniform attentional learning across time and feature dimensions. This reveals TFCA-GRU’s selective attention to information time intervals and feature dimensions, which improves the transparency of the model. Experimental results show that the proposed TFCA-GRU performs better than some existing prediction methods in bearing RUL prediction across operating conditions.

 remaining useful life deep learning attention mechanism gated recurrent unit time-frequency feature fusion model interpretability References Sai Van Cuong, Shcherbakov M.V. Architecture of predictive maintenance system of complex multiobject systems in Industry 4.0 concept. Software & Systems, 2020, Vol. 33, No. 2, Pp. 186–194. DOI: 10.15827/0236-235X.130.186-194 Cui L., Shen Q., Xiao Y., Liu D., Wang H. Sparse graph structure fusion convolutional network for machinery remaining useful life prediction. Reliability Engineering & System Safety, 2025, Vol. 254A, Art. no. 110592. DOI: 10.1016/j.ress.2024.110592 Dli M.I., Puchkov A.Yu., Lobaneva E.I. Method for estimating the time of useful use of equipment based on neural networks. Bulletin of the Saint Petersburg State Institute of Technology (Technical University), 2021, Vol. 85, No. 59, Pp. 107–112. DOI: 10.36807/1998-9849-2021-59-85-107-112 Zhang J., Tian J., Yan P., Wu S., Luo H., Yin S. Multi-hop graph pooling adversarial network for cross-domain remaining useful life prediction: A distributed federated learning perspective. Reliability Engineering & System Safety, 2024, Vol. 244, Art. no. 109950. DOI: 10.1016/j.ress.2024.109950 Xu Z., Li C., Yang Y. Fault diagnosis of rolling bearings using an Improved Multi-Scale Convolutional Neural Network with Feature Attention mechanism. ISA Transactions, 2021, Vol. 110, Pp. 379–393. DOI: 10.1016/j.isatra.2020.10.054 Liu H., Sun Y., Ding W., Wu H., Zhang H. Enhancing non-stationary feature learning for remaining useful life prediction of aero-engine under multiple operating conditions. Measurement, 2024, Vol. 227, Art. no. 114242. DOI: 10.1016/j.measurement.2024.114242 Yin Y., Tian J., Liu X. Remaining useful life prediction based on parallel multi-scale feature fusion network. Journal of Intelligent Manufacturing, 2024, Vol. 36, Pp. 3111–3127. DOI: 10.1007/s10845-024-02399-y Fan W., Chang Z., Xu S., Fan Z., Yuan Y. RUL Prediction of Rolling Bearings with MVGA-DSAL: A Multiscale Variant Gaussian Attention Model with Depth-Wise Sparse Attention LSTM. IEEE Transactions on Instrumentation and Measurement, 2025, Vol. 74, Art no. 3523111. DOI: 10.1109/TIM.2025.3551998 Qu Y., Fu S., Yong M., Tian J., Lv Z., Li R. Health Indicator Construction and Remaining Useful Life Prediction Based on MSC-LSTM-AE Model for Working Bearings. IEEE Sensors Journal, 2025, Vol. 25, No. 9, Pp. 15525–15535. DOI: 10.1109/JSEN.2025.3548675 Yang T., Li G., Huo J., Li X., Zhou X., Han Q. The DRTS-Net Framework: Enhanced Probabilistic Health Perception for Wind Turbine Bearings Under Complex Operating Conditions with Improved Interpretability. IEEE Transactions on Instrumentation and Measurement, 2025, Vol. 74, Art no. 3517412. DOI: 10.1109/TIM.2025.3545504 Ma P., Li G., Zhang H., Wang C., Li X. Prediction of Remaining Useful Life of Rolling Bearings Based on Multiscale Efficient Channel Attention CNN and Bidirectional GRU. IEEE Transactions on Instrumentation and Measurement, 2024, Vol. 73, Art no. 2508413. DOI: 10.1109/TIM.2023.3347787 Guo D., Cao Z., Fu H., Li Z. Remaining Useful Life Estimation for Rolling Bearings Using MSGCNN-TR. IEEE Sensors Journal, 2022, Vol. 22, No. 24, Pp. 24333–24343. DOI: 10.1109/JSEN.2022.3221753 Que Z., Jin X., Xu Z. Remaining Useful Life Prediction for Bearings Based on a Gated Recurrent Unit. IEEE Transactions on Instrumentation and Measurement, 2021, Vol. 70, Art no. 3511411. DOI: 10.1109/TIM.2021.3054025 Vaswani A., Shazeer N., Parmar N., Uszkoreit J., Jones L., Gomez A.N., Kaiser L., Polosukhin I. Attention is all you need. arXiv:1706.03762, 2017. DOI: 10.48550/arXiv.1706.03762 Nectoux P., Gouriveau R., Medjaher K., Ramasso E., Chebel-Morello B. et al. PRONOSTIA: An experimental platform for bearings accelerated degradation tests. IEEE International Conference on Prognostics and Health Management (PHM’12), 2012, pp. 1–8. Wang B., Lei Y., Li N., Li N. A hybrid prognostics approach for estimating remaining useful life of rolling element bearings. IEEE Transactions on Reliability, 2020, Vol. 69, No. 1, Pp. 401–412. DOI: 10.1109/TR.2018.2882682 Wang T., Liu H., Guo D., Sun X.-M. Continual residual reservoir computing for remaining useful life prediction. IEEE Transactions on Industrial Informatics, 2024, Vol. 20, No. 1, Pp. 931–940. DOI: 10.1109/TII.2023.3271661 Qin Y., Chen D., Xiang S., Zhu C. Gated Dual Attention Unit Neural Networks for Remaining Useful Life Prediction of Rolling Bearings. IEEE Transactions on Industrial Informatics, 2021, Vol. 17, No. 9, Pp. 6438–6447. DOI: 10.1109/TII.2020.2999442 Babu G.S., Zhao P., Li X.-L. Deep Convolutional Neural Network Based Regression Approach for Estimation of Remaining Useful Life. Database Systems for Advanced Applications (DASFAA 2016), 2016, Vol. 9642, Pp. 214–228. DOI: 10.1007/978-3-319-32025-0_14 Zhu J., Chen N., Peng W. Estimation of Bearing Remaining Useful Life Based on Multiscale Convolutional Neural Network. IEEE Transactions on Industrial Electronics, 2019, Vol. 66, No. 4, Pp. 3208–3216. DOI: 10.1109/TIE.2018.2844856 Wang Y., Deng L., Zheng L., Gao R.X. Temporal convolutional network with soft thresholding and attention mechanism for machinery prognostics. Journal of Manufacturing Systems, 2021, Vol. 60, Pp. 512–526. DOI: 10.1016/j.jmsy.2021.07.008 Zou H., Zhu J. DCTCN: Deep Complex Temporal Convolutional Network for Real Time Speech Enhancement. 2021 11th International Conference on Intelligent Control and Information Processing (ICICIP), 2021, Pp. 112–118. DOI: 10.1109/ICICIP53388.2021.9642159 Hu K., Yan A. Multitarget Robust Deep Stochastic Configuration Network Parameter Modeling Method. 2024 6th International Conference on Industrial Artificial Intelligence (IAI), 2024, Pp. 1–5. DOI: 10.1109/IAI63275.2024.10729968