{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T06:54:18Z","timestamp":1781679258889,"version":"3.54.5"},"reference-count":41,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T00:00:00Z","timestamp":1781654400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Evolving fuzzy systems (EFS) offer an incremental learning, making them promising for fault diagnosis (FD) in industrial processes, where unknown faults and changing operation conditions are common. The evolving fuzzy structure enables incremental rule adaptation while maintaining interpretability and reduced computational complexity compared with deep learning approaches. However, the performance of EFS depends heavily on the preprocessing of input data. This study evaluates eight preprocessing strategies for EFS applied to the Tennessee Eastman benchmark process. A one-vs-rest EFS architecture was implemented for ten representative faults (IDV1, IDV2, IDV4, IDV5, IDV6, IDV7, IDV8, IDV10, IDV13 and IDV14) in order to make a comparison with other FD techniques. This approach uses seven variables selected by using the least angle regression. Preprocessing methods were applied to highlight fault signatures. Using the Daubechies-4 in the preprocessing achieved the best overall F1-score (73.68%) with a sensitivity of 97.37%, outperforming the no-preprocessing baseline (F1 = 70.67%). Per-fault analysis showed high performance for faults IDV6, IDV7, and IDV14, while IDV1, IDV2, IDV5, and IDV8 exhibited high sensitivity but lower specificity. These findings indicate that wavelet preprocessing significantly enhances EFS for FD, and that the choice of wavelet should be guided by application priorities: Daubechies-4 is recommended for maximum detection and fewer false alarms. The obtained results demonstrate that wavelet preprocessing substantially improves classification robustness and fault discrimination compared with the non-preprocessed baseline.<\/jats:p>","DOI":"10.3390\/a19060485","type":"journal-article","created":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T05:56:31Z","timestamp":1781675791000},"page":"485","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Wavelet-Based Evolving Fuzzy Framework for Fault Diagnosis in the Tennessee Eastman Process"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2969-9084","authenticated-orcid":false,"given":"Marco Antonio","family":"M\u00e1rquez-Vera","sequence":"first","affiliation":[{"name":"Mechatronics and Automotive Engineering, Polytechnic University of Pachuca, Zempoala 43830, Hidalgo, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4928-5716","authenticated-orcid":false,"given":"Jorge A.","family":"Ruiz-Vanoye","sequence":"additional","affiliation":[{"name":"Mechatronics and Automotive Engineering, Polytechnic University of Pachuca, Zempoala 43830, Hidalgo, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2192-665X","authenticated-orcid":false,"given":"Carlos Antonio","family":"M\u00e1rquez-Vera","sequence":"additional","affiliation":[{"name":"Chemical Engineering, Universidad Veracruzana, Poza Rica 93390, Veracruz, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3482-971X","authenticated-orcid":false,"given":"Alfian","family":"Ma\u2019arif","sequence":"additional","affiliation":[{"name":"Electrical Engineering, Universitas Ahmad Dahlan, Yogyakarta 55166, Indonesia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Edith","family":"Mendoza-Ram\u00edrez","sequence":"additional","affiliation":[{"name":"Mechatronics and Automotive Engineering, Polytechnic University of Pachuca, Zempoala 43830, Hidalgo, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,6,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"112645","DOI":"10.1016\/j.engappai.2025.112645","article-title":"State-of-the-art of machine learning methods for fault detection and health monitoring of wind turbine system components: A comprehensive review","volume":"162","author":"Yimam","year":"2025","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"126801","DOI":"10.1016\/j.apenergy.2025.126801","article-title":"Comprehensive review of gas turbine fault diagnostic strategies","volume":"401","author":"Soleimani","year":"2025","journal-title":"Appl. Energy"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1016\/j.jsr.2022.06.011","article-title":"Prioritization of industry level interventions to improve implementation of design for safety regulations","volume":"82","author":"Asmone","year":"2022","journal-title":"J. Saf. Res."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/j.ifacol.2015.08.199","article-title":"Revision of the Tennessee Eastman process model","volume":"48","author":"Bathelt","year":"2015","journal-title":"IFAC-PapersOnLine"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/0098-1354(93)80018-I","article-title":"A plant-wide industrial process control problem","volume":"17","author":"Downs","year":"1993","journal-title":"Comput. Chem. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1567","DOI":"10.1016\/j.jprocont.2012.06.009","article-title":"A comparison study of basic data-driven fault diagnosis and process monitoring methods on the benchmark Tennessee Eastman process","volume":"22","author":"Yin","year":"2012","journal-title":"J. Process Control"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/j.jprocont.2019.07.006","article-title":"A fault detection and isolation technique using nonlinear support vectors dichotomizing multi-class parity space residuals","volume":"82","author":"Cho","year":"2019","journal-title":"J. Process Control"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"107288","DOI":"10.1016\/j.neunet.2025.107288","article-title":"Neural-network-based practical specified-time resilient formation maneuver control for second-order nonlinear multi-robot systems under FDI attacks","volume":"186","author":"Yang","year":"2025","journal-title":"Neural Netw."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"107147","DOI":"10.1016\/j.jfranklin.2024.107147","article-title":"Observer-based adaptive neural asynchronous H\u221e Control for fuzzy Markov jump systems under FDI attacks","volume":"361","author":"Cao","year":"2024","journal-title":"J. Frankl. Inst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.ins.2011.08.030","article-title":"Adaptive fault detection and diagnosis using an evolving fuzzy classifier","volume":"220","author":"Lemos","year":"2013","journal-title":"Inf. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"113515","DOI":"10.1016\/j.measurement.2023.113515","article-title":"An anomalous frequency band identification method utilising available healthy historical data for gearbox fault detection","volume":"222","author":"Schmidt","year":"2023","journal-title":"Measurement"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/S0098-1354(02)00160-6","article-title":"A review of process fault detection and diagnosis: Part I: Quantitative model-based methods","volume":"27","author":"Venkatasubramanian","year":"2003","journal-title":"Comput. Chem. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.ins.2013.07.002","article-title":"On-line assurance of interpretability criteria in evolving fuzzy systems\u2014Achievements, new concepts and open issues","volume":"251","author":"Lughofer","year":"2013","journal-title":"Inf. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"110814","DOI":"10.1016\/j.compeleceng.2025.110814","article-title":"A high-dimensional data-driven approach for enhancing cyber-physical attack detection in PV-connected distribution power grids using deep Q-networks","volume":"129","author":"Kumar","year":"2026","journal-title":"Comput. Electr. Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"458","DOI":"10.1016\/j.inffus.2022.10.027","article-title":"Evolving multi-user fuzzy classifier system with advanced explainability and interpretability aspects","volume":"91","author":"Lughofer","year":"2023","journal-title":"Inf. Fusion"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1016\/j.ins.2021.08.003","article-title":"Jointly evolving and compressing fuzzy system for feature reduction and classification","volume":"579","author":"Huang","year":"2021","journal-title":"Inf. Sci."},{"key":"ref_17","first-page":"307","article-title":"On-line fault detection with data-driven evolving fuzzy models","volume":"36","author":"Lughofer","year":"2008","journal-title":"Control. Intell. Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1007\/s12530-015-9132-6","article-title":"Generalized smart evolving fuzzy systems","volume":"6","author":"Lughofer","year":"2015","journal-title":"Evol. Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"574","DOI":"10.1109\/TFUZZ.2015.2463732","article-title":"Evolving type-2 fuzzy classifier","volume":"24","author":"Pratama","year":"2016","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"484","DOI":"10.1109\/TSMCB.2003.817053","article-title":"An approach to online identification of Takagi-Sugeno fuzzy models","volume":"34","author":"Angelov","year":"2004","journal-title":"IEEE Trans. Syst. Man  Cybern. Part B"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1393","DOI":"10.1109\/TFUZZ.2008.925908","article-title":"FLEXFIS: A robust incremental learning approach for evolving Takagi-Sugeno fuzzy models","volume":"16","author":"Lughofer","year":"2008","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1109\/91.995117","article-title":"DENFIS: Dynamic evolving neural-fuzzy inference system and its application for time-series prediction","volume":"10","author":"Kasabov","year":"2002","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1109\/TNNLS.2013.2271933","article-title":"PANFIS: A novel incremental learning machine","volume":"25","author":"Pratama","year":"2014","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1109\/TFUZZ.2013.2264938","article-title":"GENEFIS: Toward an effective localist network","volume":"22","author":"Pratama","year":"2014","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Lughofer, E. (2011). On Improving Performance and Increasing Useability of EFS. Evolving Fuzzy Systems\u2014Methodologies, Advanced Concepts and Applications, Springer.","DOI":"10.1007\/978-3-642-18087-3"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Lughofer, E. (2016). Evolving fuzzy systems: Fundamentals, reliability, interpretability, and applications. Handbook of Computational Intelligence, World Scientific.","DOI":"10.1142\/9789814675017_0003"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.ins.2015.04.008","article-title":"Fuzzy fault isolation using gradient information and quality criteria from system identification models","volume":"316","author":"Serdio","year":"2015","journal-title":"Inf. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1016\/j.engappai.2017.10.020","article-title":"Evolving model identification for process monitoring and prediction of non-linear systems","volume":"68","author":"Adonovski","year":"2018","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2487","DOI":"10.1016\/j.asoc.2010.10.004","article-title":"Identifying static and dynamic prediction models for NOx emissions with evolving fuzzy systems","volume":"11","author":"Lughofer","year":"2011","journal-title":"Appl. Soft Comput."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.sigpro.2013.04.015","article-title":"Wavelets for fault diagnosis of rotary machines: A review with applications","volume":"96","author":"Yan","year":"2014","journal-title":"Signal Process."},{"key":"ref_31","unstructured":"Mallat, S. (2009). A Wavelet Tour of Signal Processing: The Sparse Way, Academic Press."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"676","DOI":"10.1016\/j.asoc.2016.08.040","article-title":"A new fault classification approach applied to Tennessee Eastman benchmark process","volume":"49","author":"Palhares","year":"2016","journal-title":"Appl. Soft Comput."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/j.isatra.2018.05.002","article-title":"Fault detection and isolation in the challenging Tennessee Eastman process by using image processing techniques","volume":"79","author":"Hajihosseini","year":"2018","journal-title":"ISA Trans."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"103631","DOI":"10.1016\/j.engappai.2020.103631","article-title":"Fault diagnosis using novel AdaBoost based discriminant locality preserving projection with resamples","volume":"91","author":"He","year":"2020","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"103132","DOI":"10.1016\/j.compind.2019.103132","article-title":"Compound fault diagnosis of gearboxes via multi-label convolutional neural network and wavelet transform","volume":"113","author":"Liang","year":"2019","journal-title":"Comput. Ind."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"107499","DOI":"10.1016\/j.cie.2021.107499","article-title":"Inverse fuzzy fault model for fault detection and isolation with least angle regression for variable selection","volume":"159","year":"2021","journal-title":"Comput. Ind. Eng."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ymssp.2015.08.023","article-title":"Wavelet transform based on inner product in fault diagnosis of rotating machinery: A review","volume":"70","author":"Chen","year":"2016","journal-title":"Mech. Syst. Signal Process"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"101974","DOI":"10.1016\/j.measen.2025.101974","article-title":"Wavelet-based denoising of structural health monitoring strain measurements","volume":"42","author":"Mansi","year":"2025","journal-title":"Meas. Sens."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"132506","DOI":"10.1016\/j.neucom.2025.132506","article-title":"A two-stage framework for early failure detection in predictive maintenance: A case study on metro trains","volume":"670","author":"Toribio","year":"2026","journal-title":"Neurocomputing"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"114358","DOI":"10.1016\/j.engappai.2026.114358","article-title":"An interpretable Transformer\u2013LSTM denoising autoencoder for semi-supervised fault diagnosis in chemical processes","volume":"172","author":"Guo","year":"2026","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_41","first-page":"164","article-title":"Fault diagnosis using an LSTM and an elastic net","volume":"18","year":"2021","journal-title":"Rev. Iberoam. Autom. Inf. Ind."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/19\/6\/485\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T06:05:45Z","timestamp":1781676345000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/19\/6\/485"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,17]]},"references-count":41,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2026,6]]}},"alternative-id":["a19060485"],"URL":"https:\/\/doi.org\/10.3390\/a19060485","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,17]]}}}