A Summability Assisted Machine Learning Framework for Predictive Maintenance of Industrial Equipment

2026-11-05
Published
131-153
Pages
OPEN
Access
AS
Avishek Shah
Faculty of Science, Technology, and Engineering, Rajarshi Janak University, Janakpurdham, Nepal
PN
Prem Kumar Nayak
Faculty of Science, Technology, and Engineering, Rajarshi Janak University, Janakpurdham, Nepal
SS
Suresh Kumar Sahani
Faculty of Science, Technology, and Engineering, Rajarshi Janak University, Janakpurdham, Nepal
Abstract

Purpose: Industrial Predictive Maintenance (PdM) relies on sensor streams that are noisy, irregular, and affected by changing operating regimes, which can cause machine learning models to overreact to transient spikes or miss slow drift. This study develops a summability assisted machine learning framework that converts noisy time series into stable, interpretable features before prediction. 
Research Methodology: The study uses a methodological design that combines a literature synthesis, mathematical definitions of finite Cesàro means, weighted means, cumulative and robust summaries, a leakage resistant evaluation protocol, a cost sensitive decision rule, and simulation based illustrations on a synthetic pump record. 
Results: On the synthetic record, an adjacent window difference and a clipped cumulative sum detected a slow drift that a single sample limit missed while ignoring an isolated spike. Window length governed a clear trade off between false alerts and detection delay, and a worked example showed that a calibrated failure probability of 0.18 justifies inspection when the break even probability is 0.048. 
Conclusions: Summability features are a low cost and interpretable complement to raw signals, but their value must be demonstrated for each asset class and decision horizon. 
Limitations: The framework is not empirically validated, and all numerical results come from synthetic data.
Contributions: The study provides an implementable integration pattern, an evaluation protocol linking smoothing to maintenance decisions, and a real data anchor based on the  Intelligent Maintenance Systems (IMS) bearing tests for future empirical work.

Cesàro Mean Condition Monitoring Machine Learning Predictive Maintenance Summability Methods
How to Cite
Shah, A., Nayak, P. K., & Sahani, S. K. (2026). A Summability Assisted Machine Learning Framework for Predictive Maintenance of Industrial Equipment. Jurnal Teknika Dan Informatika, 6(2), 131-153. https://doi.org/10.52909/jti.v6i2.461
References
  1. Barredo Arrieta, A., Díaz-Rodríguez, N., Del Ser, J., Bennetot, A., Tabik, S., Barbado, A., Garcia, S., Gil-Lopez, S., Molina, D., Benjamins, R., Chatila, R., & Herrera, F. (2020). Explainable artificial intelligence (XAI): Concepts, taxonomies, opportunities and challenges toward responsible AI. Information Fusion, 58, 82–115. https://doi.org/10.1016/j.inffus.2019.12.012
  2. Benatia, M. A., Hafsi, M., & Ben Ayed, S. (2025). A continual learning approach for failure prediction under non stationary conditions: Application to condition monitoring data streams. Computers & Industrial Engineering, 204, Article 111049. https://doi.org/10.1016/j.cie.2025.111049
  3. Breiman, L. (2001). Random forests. Machine Learning, 45(1), 5-32. https://doi.org/10.1023/A:1010933404324
  4. Carvalho, T. P., Soares, F. A. A. M. N., Vita, R., Francisco, R. d. P., Basto, J. P., & Alcalá, S. G. S. (2019). A systematic literature review of machine learning methods applied to predictive maintenance. Computers & Industrial Engineering, 137, Article 106024. https://doi.org/10.1016/j.cie.2019.106024
  5. Cortes, C., & Vapnik, V. (1995). Support vector networks. Machine Learning, 20(3), 273-297. https://doi.org/10.1007/BF00994018
  6. Friedman, J. H. (2001). Greedy function approximation: A gradient boosting machine. Annals of Statistics, 29(5), 1189-1232. https://doi.org/10.1214/aos/1013203451
  7. Guidotti, D., Pandolfo, L., & Pulina, L. (2025). A systematic literature review of supervised machine learning techniques for predictive maintenance in Industry 4.0. IEEE Access, 13, 102479–102504. https://doi.org/10.1109/ACCESS.2025.3578686
  8. Haixiang, G., Yijing, L., Shang, J., Mingyun, G., Yuanyue, H., & Bing, G. (2017). Learning from class imbalanced data: Review of methods and applications. Expert Systems with Applications, 73, 220–239. https://doi.org/10.1016/j.eswa.2016.12.035
  9. Jardine, A. K. S., Lin, D., & Banjevic, D. (2006). A review on machinery diagnostics and prognostics implementing condition based maintenance. Mechanical Systems and Signal Processing, 20(7), 1483-1510. https://doi.org/10.1016/j.ymssp.2005.09.012
  10. Kapoor, S., & Narayanan, A. (2023). Leakage and the reproducibility crisis in machine learning based science. Patterns, 4(9). https://doi.org/10.1016/j.patter.2023.100804
  11. Kushwaha, J. K., Thakur, A. K., Sahani, S. K., & Suryawanshi, H. (2023). Existence and convergence of gamma matrices and their application to infinite series. The Mathematical Education, 57(2), 17-30.
  12. Lee, J., Qiu, H., Yu, G., Lin, J., & Rexnord Technical Services. (2007). Bearing data set [Data set].
  13. Lei, Y., Yang, B., Jiang, X., Jia, F., Li, N., & Nandi, A. K. (2020). Applications of machine learning to machine fault diagnosis: A review and roadmap. Mechanical Systems and Signal Processing, 138, Article 106587. https://doi.org/10.1016/j.ymssp.2019.106587
  14. Li, X., Ding, Q., & Sun, J. Q. (2018). Remaining useful life estimation in prognostics using deep convolution neural networks. Reliability Engineering & System Safety, 172, 1–11. https://doi.org/10.1016/j.ress.2017.11.021
  15. Liu, Z., & Hui, J. (2024). Advancing predictive maintenance: A deep learning approach to sensor and event log data fusion. Sensor Review, 44(5), 563-574. https://doi.org/10.1108/SR-03-2024-0183
  16. Lu, J., Liu, A., Dong, F., Gu, F., Gama, J., & Zhang, G. (2019). Learning under concept drift: A review. IEEE Transactions on Knowledge and Data Engineering, 31(12), 2346-2363. https://doi.org/10.1109/TKDE.2018.2876857
  17. Matzka, S. (2020). Explainable artificial intelligence for predictive maintenance applications. Paper presented at In Proceedings of the Third International Conference on Artificial Intelligence for Industries (AI4I) (pp. 69–74). IEEE.
  18. Murtaza, A. A., Saher, A., Zafar, M. H., Moosavi, S. K. R., Aftab, M. F., & Sanfilippo, F. (2024). Paradigm shift for predictive maintenance and condition monitoring from Industry 4.0 to Industry 5.0: A systematic review, challenges and case study. Results in Engineering, 24, Article 102935. https://doi.org/10.1016/j.rineng.2024.102935
  19. Njor, E., Hasanpour, M. A., Madsen, J., & Fafoutis, X. (2024). A holistic review of the TinyML stack for predictive maintenance. IEEE Access, 12, 184861–184882. https://doi.org/10.1109/ACCESS.2024.3512860
  20. Pang, G., Shen, C., Cao, L., & van den Hengel, A. (2022). Deep learning for anomaly detection: A review. ACM Computing Surveys, 54(2). https://doi.org/10.1145/3439950
  21. Parisi, G. I., Kemker, R., Part, J. L., Kanan, C., & Wermter, S. (2019). Continual lifelong learning with neural networks: A review. Neural Networks, 113, 54–71. https://doi.org/10.1016/j.neunet.2019.01.012
  22. Pokharel, J. K., Pahari, N. P., & Sahani, S. K. (2023). Critical analyzing on some new application of almost decreasing sequence to Legendre series associated with [B] sum. Advances in Nonlinear Variational Inequalities, 26(2), 36-40. https://doi.org/10.52783/anvi.v26.253
  23. Qiu, H., Lee, J., Lin, J., & Yu, G. (2006). Wavelet filter based weak signature detection method and its application on rolling element bearing prognostics. Journal of Sound and Vibration, 289(4–5), 1066–1090.
  24. Rudin, C. (2019). Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead. Nature Machine Intelligence, 1(5), 206-215. https://doi.org/10.1038/s42256-019-0048-x
  25. Sahani, S. K., & Mishra, L. N. (2021). Degree of approximation of signals by Nörlund summability of derived Fourier series. The Nepali Mathematical Sciences Report, 38(2), 13-19. https://doi.org/10.3126/nmsr.v38i2.42845
  26. Sahani, S. K., & Mishra, V. N. (2020). A certain study on Nörlund summability of series. Journal of Linear and Topological Algebra, 9(4), 311-321.
  27. Sahani, S. K., & Mishra, V. N. (2023). Degree of approximation of functions by Nörlund summability of double Fourier series. Mathematical Sciences and Applications E Notes, 11(2), 80-88. https://doi.org/10.36753/mathenot.1008750
  28. Sahani, S. K., Mishra, V. N., & Rathour, L. (2022). On Nörlund summability of double Fourier series. Open Journal of Mathematical Sciences, 6(1), 99-107. https://doi.org/10.30538/oms2022.0180
  29. Saxena, A., Goebel, K., Simon, D., & Eklund, N. (2008). Damage propagation modeling for aircraft engine run to failure simulation. Paper presented at In Proceedings of the International Conference on Prognostics and Health Management (PHM08). IEEE.
  30. Serradilla, O., Zugasti, E., Rodriguez, J., & Zurutuza, U. (2022). Deep learning models for predictive maintenance: A survey, comparison, challenges and prospects. Applied Intelligence, 52(10), 10934-10964. https://doi.org/10.1007/s10489-021-03004-y
  31. Sullivan, G. P., Pugh, R., Melendez, A. P., & Hunt, W. D. (2010). Operations and maintenance best practices: A guide to achieving operational efficiency (Release 3.0).
  32. Syed, M. A. B., Hasan, M. R., Chowdhury, N. I., Rahman, M. H., & Ahmed, I. (2025). A systematic review of time series algorithms and analytics in predictive maintenance. Decision Analytics Journal, 15, Article 100573. https://doi.org/10.1016/j.dajour.2025.100573
  33. Tsallis, C., Papageorgas, P., Piromalis, D., & Munteanu, R. A. (2025). Application wise review of machine learning based predictive maintenance: Trends, challenges, and future directions. Applied Sciences, 15(9). https://doi.org/10.3390/app15094898
  34. Yadav, D. K., Kaushik, A., & Yadav, N. (2024). Predicting machine failures using machine learning and deep learning algorithms. Sustainable Manufacturing and Service Economics, 3, Article 100029. https://doi.org/10.1016/j.smse.2024.100029
  35. Zhao, R., Yan, R., Chen, Z., Mao, K., Wang, P., & Gao, R. X. (2019). Deep learning and its applications to machine health monitoring. Mechanical Systems and Signal Processing, 115, 213–237. https://doi.org/10.1016/j.ymssp.2018.05.050
  36. Zonta, T., da Costa, C. A., da Rosa Righi, R., de Lima, M. J., da Trindade, E. S., & Li, G. P. (2020). Predictive maintenance in the Industry 4.0: A systematic literature review. Computers & Industrial Engineering, 150, Article 106889. https://doi.org/10.1016/j.cie.2020.106889

How to Cite

Shah, A., Nayak, P. K., & Sahani, S. K. (2026). A Summability Assisted Machine Learning Framework for Predictive Maintenance of Industrial Equipment. Jurnal Teknika Dan Informatika, 6(2), 131-153. https://doi.org/10.52909/jti.v6i2.461
Downloads
View PDF PDF · Open Access
Statistics