Anomaly detection model based on unsupervised learning for multivariate industrial time series

This study focuses on developing an unsupervised anomaly detection model for multivariate time series generated by complex Cyber-Physical Systems (CPS) in shipbuilding and manufacturing enterprises, where strong inter-channel dependencies and regime drifts reduce the sensitivity of traditional Statistical Process Control (SPC) methods. The objective is to design a mathematically grounded model capable of detecting abnormal system behavior under varying operational conditions. The proposed approach includes: (1) representing system states through signature matrices that capture pairwise dependencies among process parameters; (2) reconstructing normal operational patterns using a Long Short-Term Memory (LSTM) neural network and its convolutional variant, Convolutional LSTM (ConvLSTM); (3) applying adaptive thresholds derived from the quantile rule and the Exponentially Weighted Moving Average (EWMA) method to account for process drift; and (4) localizing anomaly sources using residual maps and linking them to the control loop for interpretability. The model ensures scale invariance, sensitivity to cross-channel correlations, and robustness to regime shifts. Its practical application lies in real-time monitoring and early detection of deviations in ship power plants, cooling and fuel systems, and various stages of shipbuilding production, thereby reducing false alarms and providing interpretable diagnostics for operators.

1. Lee, J., B. Bagheri and H-A. Kao. “A Cyber-Physical Systems architecture for Industry 4.0-based manufacturing systems.” Manufacturing Letters 3 (2015): 18–23. DOI: 10.1016/j.mfglet.2014.12.001.

2. Kupriyanovskiy, V. P., D. E. Namiot and S. A. Sinyagov. “Cyber-physical systems as a base for digital economy.” International Journal of Open Information Technologies 4.2 (2016): 18–25.

3. Ozbayoglu, A. M., M. U. Gudelek and O. B. Sezer. “Deep learning for financial applications: A survey.” Applied Soft Computing 93 (2020): 106384. DOI: 10.1016/j.asoc.2020.106384.

4. Adler, Yu. P., O. V. Maksimova and V. L. Shper. “Kontrol’nye karty Shukharta v Rossii i za rubezhom. Chast’ 1.” Standards and Quality 7 (2011): 82–87.

5. Åström K. J. and R. M. Murray. Feedback Systems: An Introduction for Scientists and Engineers. Princeton: Princeton Univ. Press, 2008: 408 p.

6. Zhurilova, O. E., A. V. Bashkirov et al. “Modern methods and problems of spectral analysis of signals: brief discussion and comparison.” Bulletin of Voronezh State Technical University 15.2 (2019): 128–131. DOI: 10.25987/VSTU.2019.15.2.016.

7. Hochreiter, S. and J. Schmidhuber. “Long Short-Term Memory.” Neural Computation 9.8 (1997): 1735–1780. DOI: 10.1162/neco.1997.9.8.1735.

8. SHI, X., W-. WOO, et al. “Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting.” Advances in Neural Information Processing Systems — 28Curran Associates, Inc., 2015.

9. Zhang, C., N. V. Chawla, et al. “A Deep Neural Network for Unsupervised Anomaly Detection and Diagnosis in Multivariate Time Series Data.” Proceedings of the AAAI Conference on Artificial Intelligence 33.01 (2019): 1409–1416. DOI: 10.1609/aaai.v33i01.33011409.

10. Qingning, L., L. Sanglu, et al. “Multi-Scale Anomaly Detection for Time Series with Attention-based Recurrent Autoencoders.” Proceedings of Machine Learning Research — 189PMLR, 2023: 674–689.

11. Jolliffe, I. T. and J. . Cadima. “Principal component analysis: a review and recent developments.” Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 374.2065 (2016): 20150202. DOI: 10.1098/rsta.2015.0202.

12. Namiot, D. E. and E. A. Il’yushin. “Data shift monitoring in machine learning models.” International Journal of Open Information Technologies 10.12 (2022): 84–93.

13. Marchuk, V. I. and K. E. Rumyantsev. “Analysis of the adaptation methods of threshold value at detection of abnormal measurements.” Journal of The Russian Universities. Radioelectronics 1 (2006): 29–34.

14. Hundman, K., T. Soderstrom, et al. “Detecting Spacecraft Anomalies Using LSTMs and Nonparametric Dynamic Thresholding.” KDD ‘18Association for Computing Machinery, 2018: 387–395. DOI: 10.1145/3219819.3219845.

15. Lucas, J. M. and M. S. Saccucci. “Exponentially Weighted Moving Average Control Schemes: Properties and Enhancements.” Technometrics 32.1 (1990): 1–12. DOI: 10.1080/00401706.1990.10484583.

16. NIST/SEMATECH e-Handbook of Statistical Methods. Web. 09 Aug. 2025 https://www.itl.nist.gov/div898/handbook/.

17. Wang, F., X. Pang, et al. “A Survey of Deep Anomaly Detection in Multivariate Time Series: Taxonomy, Applications, and Directions.” Sensors 25.1 (2025). DOI: 10.3390/s25010190.