{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T04:29:52Z","timestamp":1787027392416,"version":"build-2736575974"},"reference-count":44,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,9,3]],"date-time":"2020-09-03T00:00:00Z","timestamp":1599091200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.mdpi.com"],"crossmark-restriction":true},"short-container-title":["Algorithms"],"abstract":"<jats:p>In this paper we propose a novel approach of rule learning called Relaxed Separate-and- Conquer (RSC): a modification of the standard Separate-and-Conquer (SeCo) methodology that does not require elimination of covered rows. This method can be seen as a generalization of the methods of SeCo and weighted covering that does not suffer from fragmentation. We present an empirical investigation of the proposed RSC approach in the area of Predictive Maintenance (PdM) of complex manufacturing machines, to predict forthcoming failures of these machines. In particular, we use for experiments a real industrial case study of a machine which manufactures the plastic bottle. We compare the RSC approach with a Decision Tree (DT) based and SeCo algorithms and demonstrate that RSC significantly outperforms both DT based and SeCo rule learners. We conclude that the proposed RSC approach is promising for PdM guided by rule learning.<\/jats:p>","DOI":"10.3390\/a13090219","type":"journal-article","created":{"date-parts":[[2020,9,3]],"date-time":"2020-09-03T11:22:43Z","timestamp":1599132163000},"page":"219","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Relaxed Rule-Based Learning for Automated Predictive Maintenance: Proof of Concept"],"prefix":"10.3390","volume":"13","author":[{"given":"Margarita","family":"Razgon","sequence":"first","affiliation":[{"name":"Department of Computer Science, Brunel University, Uxbridge, London UB8 3PH, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alireza","family":"Mousavi","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Brunel University, Uxbridge, London UB8 3PH, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Kearns, M.J., and Vazirani, U.V. (1994). An Introduction to Computational Learning Theory, MIT Press.","DOI":"10.7551\/mitpress\/3897.001.0001"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"F\u00fcrnkranz, J., Gamberger, D., and Lavra\u010d, N. (2012). Foundations of Rule Learning, Springer. Cognitive Technologies.","DOI":"10.1007\/978-3-540-75197-7"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1023\/A:1006524209794","article-title":"Separate-and-Conquer Rule Learning","volume":"13","year":"1999","journal-title":"Artif. Intell. Rev."},{"key":"ref_4","unstructured":"Cohen, W.W., and Singer, Y. (1999, January 18\u201322). A Simple, Fast, and Effective Rule Learner. Proceedings of the Sixteenth National Conference on Artificial Intelligence and Eleventh Conference on Innovative Applications of Artificial Intelligence, Orlando, FL, USA."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1023\/A:1022648800760","article-title":"The Strength of Weak Learnability","volume":"5","author":"Schapire","year":"1990","journal-title":"Mach. Learn."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"812","DOI":"10.1109\/TII.2014.2349359","article-title":"Machine Learning for Predictive Maintenance: A Multiple Classifier Approach","volume":"11","author":"Susto","year":"2015","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"6536","DOI":"10.1109\/TIE.2015.2422112","article-title":"A Survey on Wind Turbine Condition Monitoring and Fault","volume":"62","author":"Qiao","year":"2015","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1008","DOI":"10.1016\/j.cie.2018.05.017","article-title":"An HMM and polynomial regression based approach for remaining useful life and health state estimation of cutting tools","volume":"128","author":"Kumar","year":"2019","journal-title":"Comput. Ind. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Mobley, R.K. (2002). An Introduction to Predictive Maintenance, Butterworth-Heinemann.","DOI":"10.1016\/B978-075067531-4\/50006-3"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"106024","DOI":"10.1016\/j.cie.2019.106024","article-title":"A systematic literature review of Machine Learning methods applied to Predictive Maintenance","volume":"137","author":"Carvalho","year":"2019","journal-title":"Comput. Ind. Eng."},{"key":"ref_11","first-page":"23","article-title":"Machine Learning in Manufacturing: Advantages, challenges, and applications","volume":"4","author":"Wuest","year":"2016","journal-title":"Prod. Manuf. Res."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2213","DOI":"10.1109\/JSYST.2019.2905565","article-title":"Data-Driven Methods for Predictive Maintenance of Industrial Equipment: A Survey","volume":"13","author":"Zhang","year":"2019","journal-title":"IEEE Syst. J."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Durbhaka, G.K., and Selvaraj, B. (2016, January 21\u201324). Predictive Maintenance for Wind Turbine Diagnostics using vibration signal analysis based on collaborative recommendation approach. Proceedings of the 2016 International Conference on Advances in Computing, Communications and Informatics, Jaipur, India.","DOI":"10.1109\/ICACCI.2016.7732316"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/j.ress.2015.02.001","article-title":"Hybrid PSOSVMbased method for forecasting of the Remaining Useful Life for aircraft engines and Evaluation of its reliability","volume":"138","year":"2015","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Mathew, J., Luo, M., and Pang, C.K. (2017, January 12\u201315). Regression kernel for prognostics with Support Vector Machines. Proceedings of the 2017 22nd IEEE International Conference on Emerging Technologies and Factory Automation (ETFA), Limassol, Cyprus.","DOI":"10.1109\/ETFA.2017.8247740"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Mathew, V., Toby, T., Singh, V., Rao, B.M., and Kumar, M.G. (2017, January 20\u201321). Prediction of Remaining Useful Lifetime (RUL) of turbofan engine using machine learning. Proceedings of the 2017 IEEE International Conference on Circuits and Systems (ICCS), Thiruvananthapuram, India.","DOI":"10.1109\/ICCS1.2017.8326010"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Sipos, R., Fradkin, D., M\u00f6rchen, F., and Wang, Z. (2014, January 24\u201327). Log-based Predictive Maintenance. Proceedings of the The 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, New York, NY, USA.","DOI":"10.1145\/2623330.2623340"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/j.measurement.2015.03.017","article-title":"A novel bearing fault diagnosis model integrated permutation entropy, ensemble empirical mode decomposition and optimized SVM","volume":"69","author":"Zhang","year":"2015","journal-title":"Measurement"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1600","DOI":"10.1016\/j.ymssp.2008.12.006","article-title":"Intelligent Condition\u00e2 based Prediction of Machinery Reliability","volume":"23","author":"Heng","year":"2009","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Kolokas, N., Vafeiadis, T., Ioannidis, D., and Tzovaras, D. (2018, January 3\u20135). Forecasting faults of industrial equipment using Machine Learning Classifiers. Proceedings of the 2018 Innovations in Intelligent Systems and Applications (INISTA), Thessaloniki, Greece.","DOI":"10.1109\/INISTA.2018.8466309"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"775","DOI":"10.1016\/j.ejor.2018.02.033","article-title":"Degradation data analysis and Remaining Useful Life estimation: A review on Wiener-process-based methods","volume":"271","author":"Zhang","year":"2018","journal-title":"Eur. J. Oper. Res."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.promfg.2018.06.009","article-title":"Cluster identification of sensor data for Predictive Maintenance in a Selective Laser Melting machine tool","volume":"24","author":"Uhlmann","year":"2018","journal-title":"Procedia Manuf."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Lewis, A.D., and Groth, K.M. (2020). A Dynamic Bayesian Network Structure for Joint Diagnostics and Prognostics of Complex Engineering Systems. Algorithms, 13.","DOI":"10.3390\/a13030064"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1016\/j.ress.2012.03.008","article-title":"Ensemble of Data-Driven Prognostic Algorithms for Robust Prediction of Remaining Useful Life","volume":"103","author":"Hu","year":"2012","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Xiao, Y., and Hua, Z. (2020). Misalignment Fault Prediction of Wind Turbines Based on Combined Forecasting Model. Algorithms, 13.","DOI":"10.3390\/a13030056"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1109\/TR.2018.2882682","article-title":"A Hybrid Prognostics Approach for Estimating Remaining Useful Life of Rolling Element Bearings","volume":"69","author":"Wang","year":"2020","journal-title":"IEEE Trans. Reliab."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1292","DOI":"10.1016\/j.applthermaleng.2017.10.013","article-title":"An improved Decision Tree-based fault diagnosis method for practical variable refrigerant flow system using virtual sensor-based fault indicators","volume":"129","author":"Li","year":"2017","journal-title":"Appl. Therm. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.trc.2014.04.013","article-title":"Improving Rail Network Velocity: A Machine Learning Approach to Predictive Maintenance","volume":"45","author":"Li","year":"2014","journal-title":"Transp. Res. Part C: Emerg. Technol."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Canizo, M., Onieva, E., Conde, A., Charramendieta, S., and Trujillo, S. (2017, January 19\u201321). Real-time Predictive Maintenance for Wind Turbines using Big Data frameworks. Proceedings of the 2017 IEEE International Conference on Prognostics and Health Management, Dallas, Texas, USA.","DOI":"10.1109\/ICPHM.2017.7998308"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1007\/s10845-015-1110-0","article-title":"Identifying maximum imbalance in datasets for fault diagnosis of gearboxes","volume":"29","author":"Santos","year":"2018","journal-title":"J. Intell. Manuf."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1080\/00986445.2017.1292259","article-title":"Application and Evaluation of Random Forest Classifier Technique for Fault Detection in Bioreactor Operation","volume":"204","author":"Shrivastava","year":"2017","journal-title":"Chem. Eng. Commun."},{"key":"ref_32","first-page":"151","article-title":"Predicting Cargo Train Failures: A Machine Learning Approach for a Lightweight Prototype","volume":"Volume 9956","author":"Kauschke","year":"2016","journal-title":"Discovery Science, Proceedings of the 19th International Conference, DS 2016, Bari, Italy, 19\u201321 October 2016"},{"key":"ref_33","first-page":"123","article-title":"An Analysis of Stopping and Filtering Criteria for Rule Learning","volume":"Volume 3201","author":"Flach","year":"2004","journal-title":"Machine Learning: ECML 2004, Proceedings of the 15th European Conference on Machine Learning, Pisa, Italy, 20\u201324 September 2004"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1007\/978-3-540-88411-8_7","article-title":"An Empirical Investigation of the Trade-Off between Consistency and Coverage in Rule Learning Heuristics","volume":"Volume 5255","author":"Janssen","year":"2008","journal-title":"Discovery Science, Proceedings of the 11th International Conference, DS 2008, Budapest, Hungary, 13\u201316 October 2008"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Mossel, E., O\u2019Donnell, R., and Servedio, R.A. (2003, January 9\u201311). Learning juntas. Proceedings of the 35th Annual ACM Symposium on Theory of Computing, San Diego, CA, USA.","DOI":"10.1145\/780572.780574"},{"key":"ref_36","first-page":"2825","article-title":"Scikit-learn: Machine Learning in Python","volume":"12","author":"Pedregosa","year":"2011","journal-title":"J. Mach. Learn. Res."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Clark, P., and Boswell, R. (1991). Rule Induction with CN2: Some Recent Improvements. Machine Learning-EWSL-91, European Working Session on Learning, Springer.","DOI":"10.1007\/BFb0017011"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1010933404324","article-title":"Random Forests","volume":"45","author":"Breiman","year":"2001","journal-title":"Mach. Learn."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1023\/A:1006314320276","article-title":"Heavy-Tailed Phenomena in Satisfiability and Constraint Satisfaction Problems","volume":"24","author":"Gomes","year":"2000","journal-title":"J. Autom. Reason."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Cohen, W.W. (1995, January 9\u201312). Fast Effective Rule Induction. Machine Learning. In Proceedings of the Twelfth International Conference on Machine Learning, Tahoe City, CA, USA.","DOI":"10.1016\/B978-1-55860-377-6.50023-2"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"F\u00fcrnkranz, J., and Widmer, G. (1994, January 10\u201313). Incremental Reduced Error Pruning. Machine Learning. Proceedings of the Eleventh International Conference, New Brunswick, NJ, USA.","DOI":"10.1016\/B978-1-55860-335-6.50017-9"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1023\/A:1007329424533","article-title":"Pruning Algorithms for Rule Learning","volume":"27","year":"1997","journal-title":"Mach. Learn."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/j.neucom.2018.05.017","article-title":"Anomaly Detection and Predictive Maintenance for photovoltaic systems","volume":"310","author":"Benedetti","year":"2018","journal-title":"Neurocomputing"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/2898359","article-title":"Unsupervised Rare Pattern Mining: A Survey","volume":"10","author":"Koh","year":"2016","journal-title":"ACM Trans. Knowl. Discov. 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