A Hybrid Semi-Supervised Framework for Full Life-Cycle Degradation Trajectory Learning and RUL Estimation
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Abstract
Deep Learning (DL) has substantially expanded its role in Prognostics and Health Management (PHM), particularly by enabling automated feature extraction for Remaining Useful Life (RUL) prediction. Despite this progress, existing DL models such as Long Short-Term Memory (LSTM) networks still face challenges in accurately capturing complete life-cycle degradation trajectories. To address this limitation, this study introduces a hybrid semi-supervised model that integrates a Time-Transformer (TT) with a Denoising Autoencoder (DAE), termed TT-DAE. The DAE first extracts spatial features and suppresses noise through signal reconstruction from degraded inputs. These extracted features are then separated into source and target domains and normalized to a uniform sequence length using a padding strategy. Subsequently, the TT module leverages both source features and a Sliding Variable-Length Window (SVW) mechanism to learn full degradation trajectories. A comprehensive experimental evaluation conducted on the C-MAPSS dataset demonstrates the effectiveness of the proposed approach, achieving an average Pearson Correlation Coefficient (PCC) of 0.89 between the predicted and actual target signals.
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Time-Transformer, Denoise Auto-Encoder, Turbofan engine, Remaining Useful Life, Complete life cycle degradation trajectory learning
Frederick, D. K., DeCastro, J. A., & Litt, J. S. (2007). User’s Guide for the Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) (p. NASA/TM-2007-215026) [Technical Memorandum (TM)]. NASA. https://ntrs.nasa.gov/citations/20070034949
Guo, L., Li, N., Jia, F., Lei, Y., & Lin, J. (2017). A recurrent neural network based health indicator for remaining useful life prediction of bearings. Neurocomputing, 240, 98–109. https://doi.org/10.1016/j.neucom.2017.02.045
Heng, A., Zhang, S., Tan, A. C. C., & Mathew, J. (2009). Rotating machinery prognostics: State of the art, challenges and opportunities. Mechanical Systems and Signal Processing, 23(3), 724–739. https://doi.org/10.1016/j.ymssp.2008.06.009
Jia, X., Li, W., Wang, W., Li, X., & Lee, J. (2020). Development of Multivariate Failure Threshold with Quantifiable Operation Risks in Machine Prognostics. Annual Conference of the PHM Society, 12(1), 9. https://doi.org/10.36001/phmconf.2020.v12i1.1288
Ma, J., Su, H., Zhao, W., & Liu, B. (2018). Predicting the Remaining Useful Life of an Aircraft Engine Using a Stacked Sparse Autoencoder with Multilayer Self-Learning. Complexity, 2018, 1–13. https://doi.org/10.1155/2018/3813029
Qiao, X., Jauw, V. L., Chin Seong, L., & Banda, T. (2024). Advances and limitations in machine learning approaches applied to remaining useful life predictions: A critical review. The International Journal of Advanced Manufacturing Technology. https://doi.org/10.1007/s00170-024-14000-0
Qiao, X., Liow, H. Y., Jauw, V. L., & Lim, C. S. (2025). Comparative Study of Deep Learning Model Based Equipment Fault Diagnosis and Prognosis. International Journal of Prognostics and Health Management, 16(1). https://doi.org/10.36001/ijphm.2025.v16i1.4254
Saxena, A., Goebel, K., Simon, D., & Eklund, N. (2008). Damage propagation modeling for aircraft engine run-to-failure simulation. 2008 International Conference on Prognostics and Health Management, 1–9. https://doi.org/10.1109/PHM.2008.4711414
Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., Kaiser, L., & Polosukhin, I. (2017). Attention Is All You Need. 652–658. https://doi.org/10.48550/arXiv.1706.03762
Wang, Z., Chen, Y., Cai, Z., Gao, Y., & Wang, L. (2020). Methods for predicting the remaining useful life of equipment in consideration of the random failure threshold. Journal of Systems Engineering and Electronics, 31(2), 415–431. https://doi.org/10.23919/JSEE.2020.000018
Wu, J., Hu, K., Cheng, Y., Zhu, H., Shao, X., & Wang, Y. (2020). Data-driven remaining useful life prediction via multiple sensor signals and deep long short-term memory neural network. ISA Transactions, 97, 241–250. https://doi.org/10.1016/j.isatra.2019.07.004
Xia, T., Shu, J., Xu, Y., Zheng, Y., & Wang, D. (2022). Multiscale similarity ensemble framework for remaining useful life prediction. Measurement, 188, 110565. https://doi.org/10.1016/j.measurement.2021.110565
Ye, Z., Zhang, Q., Shao, S., Niu, T., & Zhao, Y. (2022). Rolling Bearing Health Indicator Extraction and RUL Prediction Based on Multi-Scale Convolutional Autoencoder. Applied Sciences, 12(11), 5747. https://doi.org/10.3390/app12115747
Zhang, C., Lim, P., Qin, A. K., & Tan, K. C. (2017). Multiobjective Deep Belief Networks Ensemble for Remaining Useful Life Estimation in Prognostics. IEEE Transactions on Neural Networks and Learning Systems, 28(10), 2306–2318. https://doi.org/10.1109/TNNLS.2016.2582798
Zhang, J., Li, X., Tian, J., Luo, H., & Yin, S. (2023). An integrated multi-head dual sparse self-attention network for remaining useful life prediction. Reliab. Eng. Syst. Saf., 233, 109096. https://doi.org/10.1016/j.ress.2023.109096
Zhou, H., Zhang, S., Peng, J., Zhang, S., Li, J., Xiong, H., & Zhang, W. (2021). Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting. Proceedings of the AAAI Conference on Artificial Intelligence, 35(12), 11106–11115. https://doi.org/10.1609/aaai.v35i12.17325

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