{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T03:32:55Z","timestamp":1780630375250,"version":"3.54.1"},"reference-count":62,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,12,20]],"date-time":"2022-12-20T00:00:00Z","timestamp":1671494400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003593","name":"Brasil Energia Inteligente (BEI), NEC Energia, Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico (CNPq)","doi-asserted-by":"publisher","award":["141740\/2019-1"],"award-info":[{"award-number":["141740\/2019-1"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003593","name":"Brasil Energia Inteligente (BEI), NEC Energia, Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico (CNPq)","doi-asserted-by":"publisher","award":["141777\/2019-2"],"award-info":[{"award-number":["141777\/2019-2"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003593","name":"Brasil Energia Inteligente (BEI), NEC Energia, Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico (CNPq)","doi-asserted-by":"publisher","award":["PQ-303119\/2019-5"],"award-info":[{"award-number":["PQ-303119\/2019-5"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Pro-Reitoria de Pesquisa (PRPq) da Universidade Federal de Minas Gerais","award":["141740\/2019-1"],"award-info":[{"award-number":["141740\/2019-1"]}]},{"name":"Pro-Reitoria de Pesquisa (PRPq) da Universidade Federal de Minas Gerais","award":["141777\/2019-2"],"award-info":[{"award-number":["141777\/2019-2"]}]},{"name":"Pro-Reitoria de Pesquisa (PRPq) da Universidade Federal de Minas Gerais","award":["PQ-303119\/2019-5"],"award-info":[{"award-number":["PQ-303119\/2019-5"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Maintenance in small hydroelectric plants (SHPs) is essential for securing the expansion of clean energy sources and supplying the energy estimated to be required for the coming years. Identifying failures in SHPs before they happen is crucial for allowing better management of asset maintenance, lowering operating costs, and enabling the expansion of renewable energy sources. Most fault prognosis models proposed thus far for hydroelectric generating units are based on signal decomposition and regression models. In the specific case of SHPs, there is a high occurrence of data being censored, since the operation is not consistently steady and can be repeatedly interrupted due to transmission problems or scarcity of water resources. To overcome this, we propose a two-step, data-driven framework for SHP prognosis based on time series feature engineering and survival modeling. We compared two different strategies for feature engineering: one using higher-order statistics and the other using the Tsfresh algorithm. We adjusted three machine learning survival models\u2014CoxNet, survival random forests, and gradient boosting survival analysis\u2014for estimating the concordance index of these approaches. The best model presented a significant concordance index of 77.44%. We further investigated and discussed the importance of the monitored sensors and the feature extraction aggregations. The kurtosis and variance were the most relevant aggregations in the higher-order statistics domain, while the fast Fourier transform and continuous wavelet transform were the most frequent transformations when using Tsfresh. The most important sensors were related to the temperature at several points, such as the bearing generator, oil hydraulic unit, and turbine radial bushing.<\/jats:p>","DOI":"10.3390\/s23010012","type":"journal-article","created":{"date-parts":[[2022,12,20]],"date-time":"2022-12-20T04:21:56Z","timestamp":1671510116000},"page":"12","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["A Data-Driven Framework for Small Hydroelectric Plant Prognosis Using Tsfresh and Machine Learning Survival Models"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8454-4512","authenticated-orcid":false,"given":"Rodrigo Barbosa","family":"de Santis","sequence":"first","affiliation":[{"name":"Graduate Program in Industrial Engineering, Universidade Federal de Minas Gerais, Av. Ant\u00f4nio Carlos 6627, Belo Horizonte 31270-901, MG, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tiago Silveira","family":"Gontijo","sequence":"additional","affiliation":[{"name":"Graduate Program in Industrial Engineering, Universidade Federal de Minas Gerais, Av. Ant\u00f4nio Carlos 6627, Belo Horizonte 31270-901, MG, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marcelo Azevedo","family":"Costa","sequence":"additional","affiliation":[{"name":"Graduate Program in Industrial Engineering, Universidade Federal de Minas Gerais, Av. Ant\u00f4nio Carlos 6627, Belo Horizonte 31270-901, MG, Brazil"},{"name":"Department of Industrial Engineering, Universidade Federal de Minas Gerais, Av. Ant\u00f4nio Carlos 6627, Belo Horizonte 31270-901, MG, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,20]]},"reference":[{"key":"ref_1","unstructured":"WEC (2019). World Energy Insights Brief, World Energy Council. Technical Report."},{"key":"ref_2","unstructured":"UNIDO (2016). World Small Hydropower Development Report 2016, United Nations Industrial Development Organization. Technical Report."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1303","DOI":"10.1007\/s10845-015-1179-5","article-title":"Review, analysis and synthesis of prognostic-based decision support methods for condition based maintenance","volume":"29","author":"Bousdekis","year":"2018","journal-title":"J. Intell. Manuf."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/s00170-009-2482-0","article-title":"Current status of machine prognostics in condition-based maintenance: A review","volume":"50","author":"Peng","year":"2010","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1803","DOI":"10.1016\/j.ymssp.2010.11.018","article-title":"Prognostic modelling options for remaining useful life estimation by industry","volume":"25","author":"Sikorska","year":"2011","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1016\/j.chemolab.2009.01.002","article-title":"Moving window kernel PCA for adaptive monitoring of nonlinear processes","volume":"96","author":"Liu","year":"2009","journal-title":"Chemom. Intell. Lab. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1016\/j.jsv.2016.01.046","article-title":"EEMD-based multiscale ICA method for slewing bearing fault detection and diagnosis","volume":"370","author":"Zupan","year":"2016","journal-title":"J. Sound Vib."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"4436","DOI":"10.1177\/0142331219860279","article-title":"A hybrid approach for measuring the vibrational trend of hydroelectric unit with enhanced multi-scale chaotic series analysis and optimized least squares support vector machine","volume":"41","author":"Fu","year":"2019","journal-title":"Trans. Inst. Meas. Control."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"350148","DOI":"10.1155\/2015\/350148","article-title":"Forecasting Models for Hydropower Unit Stability Using LS-SVM","volume":"2015","author":"Qiao","year":"2015","journal-title":"Math. Probl. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/j.jsv.2012.08.019","article-title":"Towards an automatic spectral and modal identification from operational modal analysis","volume":"332","author":"Vu","year":"2013","journal-title":"J. Sound Vib."},{"key":"ref_11","first-page":"86","article-title":"Vibration fault diagnosis of hydroelectric unit based on LS-SVM and information fusion technology","volume":"27","author":"Peng","year":"2007","journal-title":"Zhongguo Dianji Gongcheng Xuebao\/Proc. Chin. Soc. Electr. Eng."},{"key":"ref_12","unstructured":"Gregg, S.W., Steele, J.P., and Van Bossuyt, D.L. (2017). Feature selection for monitoring erosive cavitation on a hydroturbine. Int. J. Progn. Health Manag., 8."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2054","DOI":"10.1021\/ie061083g","article-title":"Process monitoring based on independent Component Analysis-Principal Component Analysis (ICA-PCA) and similarity factors","volume":"46","author":"Ge","year":"2007","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/j.measurement.2014.08.026","article-title":"A novel KICA-PCA fault detection model for condition process of hydroelectric generating unit","volume":"58","author":"Zhu","year":"2014","journal-title":"Meas. J. Int. Meas. Confed."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1402","DOI":"10.1109\/TPWRD.2013.2251752","article-title":"Detection and classification of faults in power transmission lines using functional analysis and computational intelligence","volume":"28","author":"Costa","year":"2013","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"de Santis, R.B., and Costa, M.A. (2020). Extended isolation forests for fault detection in small hydroelectric plants. Sustainability, 12.","DOI":"10.3390\/su12166421"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Hara, Y., Fukuyama, Y., Arai, K., Shimasaki, Y., Osada, Y., Murakami, K., Iizaka, T., and Matsui, T. (2021, January 13\u201315). Fault Detection of Hydroelectric Generators by Robust Random Cut Forest with Feature Selection Using Hilbert-Schmidt Independence Criterion. Proceedings of the 2021 IEEE International Conference on Smart Internet of Things (SmartIoT), Jeju Island, Republic of Korea.","DOI":"10.1109\/SmartIoT52359.2021.00030"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"488","DOI":"10.1016\/j.isatra.2019.09.020","article-title":"Incipient winding fault detection and diagnosis for squirrel-cage induction motors equipped on CRH trains","volume":"99","author":"Wu","year":"2020","journal-title":"ISA Trans."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ejor.2010.11.018","article-title":"Remaining useful life estimation\u2013a review on the statistical data driven approaches","volume":"213","author":"Si","year":"2011","journal-title":"Eur. J. Oper. Res."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Salomon, C.P., Ferreira, C., Sant\u2019Ana, W.C., Lambert-Torres, G., da Silva, L.E.B., Bonaldi, E.L., de Lacerda de Oliveira, L.E., and Torres, B.S. (2019). A study of fault diagnosis based on electrical signature analysis for synchronous generators predictive maintenance in bulk electric systems. Energies, 12.","DOI":"10.3390\/en12081506"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1016\/j.ymssp.2017.11.016","article-title":"Machinery health prognostics: A systematic review from data acquisition to RUL prediction","volume":"104","author":"Lei","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/j.ymssp.2018.05.050","article-title":"Deep learning and its applications to machine health monitoring","volume":"115","author":"Zhao","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_23","first-page":"631","article-title":"Condition-based maintenance in hydroelectric plants: A systematic literature review","volume":"236","author":"Gontijo","year":"2021","journal-title":"Proc. Inst. Mech. Eng. Part J. Risk Reliab."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1074","DOI":"10.1177\/0142331214532998","article-title":"Condition parameter degradation assessment and prediction for hydropower units using Shepard surface and ITD","volume":"36","author":"An","year":"2014","journal-title":"Trans. Inst. Meas. Control."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"015012","DOI":"10.1088\/1361-6501\/aaf377","article-title":"Vibration trend measurement for hydropower generator based on optimal variational mode decomposition and LSSVM improved with chaotic sine cosine algorithm optimization","volume":"30","author":"Fu","year":"2018","journal-title":"Meas. Sci. Technol."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Zhou, K.B., Zhang, J.Y., Shan, Y., Ge, M.F., Ge, Z.Y., and Cao, G.N. (2019). A hybrid multi-objective optimization model for vibration tendency prediction of hydropower generators. Sensors, 19.","DOI":"10.3390\/s19092055"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Dindorf, C., Teufl, W., Taetz, B., Bleser, G., and Fr\u00f6hlich, M. (2020). Interpretability of input representations for gait classification in patients after total hip arthroplasty. Sensors, 20.","DOI":"10.3390\/s20164385"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Tam, I., Kalech, M., Rokach, L., Madar, E., Bortman, J., and Klein, R. (2020). Probability-based algorithm for bearing diagnosis with untrained spall sizes. Sensors, 20.","DOI":"10.3390\/s20051298"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Khan, I., Choi, S., and Kwon, Y.W. (2020). Earthquake detection in a static and dynamic environment using supervised machine learning and a novel feature extraction method. Sensors, 20.","DOI":"10.3390\/s20030800"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Voronov, S., Krysander, M., and Frisk, E. (2020). Predictive maintenance of lead-acid batteries with sparse vehicle operational data. Int. J. Progn. Health Manag., 11.","DOI":"10.36001\/ijphm.2020.v11i1.2608"},{"key":"ref_31","unstructured":"Gurung, R.B. (2020). Random Forest for Histogram Data: An Application in Data-Driven Prognostic Models for Heavy-Duty Trucks. [Ph.D. Thesis, Department of Computer and Systems Sciences, Stockholm University]."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"04021019","DOI":"10.1061\/(ASCE)IS.1943-555X.0000629","article-title":"Combining machine learning and survival statistics to predict remaining service life of watermains","volume":"27","author":"Snider","year":"2021","journal-title":"J. Infrastruct. Syst."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1117\/12.434239","article-title":"Reasoning and modeling systems in diagnosis and prognosis","volume":"4389","author":"Mathur","year":"2001","journal-title":"Proceedings of the Component and Systems Diagnostics, Prognosis, and Health Management"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1016\/j.ymssp.2007.08.009","article-title":"Higher-order cumulants and spectral kurtosis for early detection of subterranean termites","volume":"22","year":"2008","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1109\/89.905996","article-title":"Robust voice activity detection using higher-order statistics in the LPC residual domain","volume":"9","author":"Nemer","year":"2001","journal-title":"IEEE Trans. Speech Audio Process."},{"key":"ref_36","unstructured":"Welling, M. (2005, January 6\u20138). Robust higher order statistics. Proceedings of the International Workshop on Artificial Intelligence and Statistics, PMLR, Bridgetown, Barbados."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/j.neucom.2018.03.067","article-title":"Time series feature extraction on basis of scalable hypothesis tests (tsfresh\u2013a python package)","volume":"307","author":"Christ","year":"2018","journal-title":"Neurocomputing"},{"key":"ref_38","first-page":"15","article-title":"Fourier transforms and the fast Fourier transform (FFT) algorithm","volume":"2","author":"Heckbert","year":"1995","journal-title":"Comput. Graph."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1016\/S0165-1684(02)00140-8","article-title":"Continuous wavelet transform with arbitrary scales and O (N) complexity","volume":"82","author":"Munoz","year":"2002","journal-title":"Signal Process."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1048","DOI":"10.1177\/0954411917731592","article-title":"Using multiple classifiers for predicting the risk of endovascular aortic aneurysm repair re-intervention through hybrid feature selection","volume":"231","author":"Attallah","year":"2017","journal-title":"Proc. Inst. Mech. Eng. Part J. Eng. Med."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1002\/(SICI)1097-0258(19960229)15:4<361::AID-SIM168>3.0.CO;2-4","article-title":"Multivariable prognostic models: Issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors","volume":"15","author":"Lee","year":"1996","journal-title":"Stat. Med."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1105","DOI":"10.1002\/sim.4154","article-title":"On the C-statistics for evaluating overall adequacy of risk prediction procedures with censored survival data","volume":"30","author":"Uno","year":"2011","journal-title":"Stat. Med."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1146\/annurev.publhealth.20.1.145","article-title":"Time-dependent covariates in the Cox proportional-hazards regression model","volume":"20","author":"Fisher","year":"1999","journal-title":"Annu. Rev. Public Health"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1111\/j.2517-6161.1972.tb00899.x","article-title":"Regression models and life-tables","volume":"34","author":"Cox","year":"1972","journal-title":"J. R. Stat. Soc. Ser."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1","DOI":"10.18637\/jss.v039.i05","article-title":"Regularization paths for Cox\u2019s proportional hazards model via coordinate descent","volume":"39","author":"Simon","year":"2011","journal-title":"J. Stat. Softw."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1214\/08-AOAS169","article-title":"Random survival forests","volume":"2","author":"Ishwaran","year":"2008","journal-title":"Ann. Appl. Stat."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1016\/S0167-9473(01)00065-2","article-title":"Stochastic gradient boosting","volume":"38","author":"Friedman","year":"2002","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_48","first-page":"172","article-title":"The state of boosting","volume":"31","author":"Ridgeway","year":"1999","journal-title":"Comput. Sci. Stat."},{"key":"ref_49","unstructured":"Van Rossum, G., and Drake, F.L. (2009). Python 3 Reference Manual, CreateSpace."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1038\/s41592-019-0686-2","article-title":"SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python","volume":"17","author":"Virtanen","year":"2020","journal-title":"Nat. Methods"},{"key":"ref_51","unstructured":"McKinney, W. (July, January 28). Data Structures for Statistical Computing in Python. Proceedings of the 9th Python in Science Conference, Austin, TX, USA."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1038\/s41586-020-2649-2","article-title":"Array programming with NumPy","volume":"585","author":"Harris","year":"2020","journal-title":"Nature"},{"key":"ref_53","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_54","first-page":"1","article-title":"scikit-survival: A Library for Time-to-Event Analysis Built on Top of scikit-learn","volume":"21","year":"2020","journal-title":"J. Mach. Learn. Res."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1109\/MCSE.2007.55","article-title":"Matplotlib: A 2D graphics environment","volume":"9","author":"Hunter","year":"2007","journal-title":"Comput. Sci. Eng."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"3021","DOI":"10.21105\/joss.03021","article-title":"seaborn: Statistical data visualization","volume":"6","author":"Waskom","year":"2021","journal-title":"J. Open Source Softw."},{"key":"ref_57","unstructured":"McDonald, J. (2014). Handbook of Biological Statistics, Sparky House Publishing. [3rd ed.]."},{"key":"ref_58","unstructured":"Tukey, J.W. (1977). Exploratory Data Analysis, Pearson."},{"key":"ref_59","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_60","unstructured":"Wang, X., Li, J., and Yu, R. (2022). Modeling disruption durations of subway service via random survival forests: The case of Shanghai. J. Transp. Saf. Secur., 1\u201323."},{"key":"ref_61","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Zhao, X., Zuo, Y., Ren, L., and Wang, L. (2017). The development of the renewable energy power industry under feed-in tariff and renewable portfolio standard: A case study of China\u2019s photovoltaic power industry. Sustainability, 9.","DOI":"10.3390\/su9040532"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1080\/08982112.2020.1766692","article-title":"Reinforcement learning for dynamic condition-based maintenance of a system with individually repairable components","volume":"32","author":"Yousefi","year":"2020","journal-title":"Qual. Eng."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/1\/12\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:44:32Z","timestamp":1760147072000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/1\/12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,20]]},"references-count":62,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["s23010012"],"URL":"https:\/\/doi.org\/10.3390\/s23010012","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,20]]}}}