{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T01:24:44Z","timestamp":1776821084879,"version":"3.51.2"},"reference-count":36,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T00:00:00Z","timestamp":1648512000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100010607","name":"University of Perugia","doi-asserted-by":"publisher","award":["RICBA19MLF"],"award-info":[{"award-number":["RICBA19MLF"]}],"id":[{"id":"10.13039\/501100010607","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010607","name":"University of Perugia","doi-asserted-by":"publisher","award":["RICBA20MF"],"award-info":[{"award-number":["RICBA20MF"]}],"id":[{"id":"10.13039\/501100010607","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Linear dependence of variables is a commonly used assumption in most diagnostic systems for which many robust methodologies have been developed over the years. In case the system nonlinearities are relevant, fault diagnosis methods, relying on the assumption of linearity, might potentially provide unsatisfactory results in terms of false alarms and missed detections. In recent years, many authors have proposed machine learning (ML) techniques to improve fault diagnosis performance to mitigate this problem. Although very powerful, these techniques require faulty data samples that are representative of any fault scenario. Additionally, ML techniques suffer from issues related to overfitting and unpredictable performance in regions which are not fully explored in the training phase. This paper proposes a non-linear additive model to characterize the non-linear redundancy relationships among the system signals. Using the multivariate adaptive regression splines (MARS) algorithm, these relationships are identified directly from the data. Next, the non-linear redundancy relationships are linearized to derive a local time-dependent fault signature matrix. The faulty sensor can then be isolated by measuring the angular distance between the column vectors of the fault signature matrix and the primary residual vector. A quantitative analysis of fault isolation and fault estimation performance is performed by exploiting real data from multiple flights of a semi-autonomous aircraft, thus allowing a detailed quantitative comparison with state-of-the-art machine-learning-based fault diagnosis algorithms.<\/jats:p>","DOI":"10.3390\/s22072635","type":"journal-article","created":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T21:45:51Z","timestamp":1648590351000},"page":"2635","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Data-Driven Fault Diagnosis Techniques: Non-Linear Directional Residual vs. Machine-Learning-Based Methods"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4908-9769","authenticated-orcid":false,"given":"Nicholas","family":"Cartocci","sequence":"first","affiliation":[{"name":"Department of Engineering, University of Perugia, Via G. Duranti 67, 06125 Perugia, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marcello R.","family":"Napolitano","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Aerospace Engineering, West Virginia University, Morgantown, WV 26506, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Francesco","family":"Crocetti","sequence":"additional","affiliation":[{"name":"Department of Engineering, University of Perugia, Via G. Duranti 67, 06125 Perugia, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8417-9372","authenticated-orcid":false,"given":"Gabriele","family":"Costante","sequence":"additional","affiliation":[{"name":"Department of Engineering, University of Perugia, Via G. Duranti 67, 06125 Perugia, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paolo","family":"Valigi","sequence":"additional","affiliation":[{"name":"Department of Engineering, University of Perugia, Via G. Duranti 67, 06125 Perugia, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3104-8782","authenticated-orcid":false,"given":"Mario L.","family":"Fravolini","sequence":"additional","affiliation":[{"name":"Department of Engineering, University of Perugia, Via G. Duranti 67, 06125 Perugia, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Cartocci, N., Monarca, A., Costante, G., Fravolini, M.L., Dogan, K.M., and Yucelen, T. (2022, January 3\u20137). Linear Control of a Nonlinear Aerospace System via Extended Dynamic Mode Decomposition. Proceedings of the AIAA Scitech 2022 Forum, San Diego, CA, USA.","DOI":"10.2514\/6.2022-2046"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Isermann, R. (2006). Fault-Diagnosis Systems: An Introduction from Fault Detection to Fault Tolerance, Springer.","DOI":"10.1007\/3-540-30368-5"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1016\/S0967-0661(97)00046-4","article-title":"Supervision, Fault-Detection and Fault-Diagnosis Methods\u2014An Introduction","volume":"5","author":"Isermann","year":"1997","journal-title":"Control. Eng. Pract."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1016\/0005-1098(84)90098-0","article-title":"Process Fault Detection Based on Modeling and Estimation Methods-A Survey","volume":"20","author":"Isermann","year":"1984","journal-title":"Automatica"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"783","DOI":"10.1016\/S0005-1098(97)00004-6","article-title":"Information Criteria for Residual Generation and Fault Detection and Isolation","volume":"33","author":"Basseville","year":"1997","journal-title":"Automatica"},{"key":"ref_6","unstructured":"Basseville, M., and Nikiforov, I.V. (1993). Detection of Abrupt Changes: Theory and Application, Prentice Hall Englewood Cliffs."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/0005-1098(88)90073-8","article-title":"Detecting Changes in Signals and Systems-A Survey","volume":"24","author":"Basseville","year":"1988","journal-title":"Automatica"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Gertler, J.J. (2017). Fault Detection and Diagnosis in Engineering Systems, CRC Press.","DOI":"10.1201\/9780203756126"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1080\/00207179508921908","article-title":"Optimal Residual Decoupling for Robust Fault Diagnosis","volume":"61","author":"Gertler","year":"1995","journal-title":"Int. J. Control"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/S1474-6670(17)51119-2","article-title":"Analytical Redundancy Methods in Fault Detection and Isolation\u2014Survey and Synthesis","volume":"24","author":"Gertler","year":"1991","journal-title":"IFAC Proc. Vol."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Cartocci, N., Costante, G., Napolitano, M.R., Valigi, P., Crocetti, F., and Fravolini, M.L. (2020, January 15\u201318). PCA Methods and Evidence Based Filtering for Robust Aircraft Sensor Fault Diagnosis. Proceedings of the 2020 28th Mediterranean Conference on Control and Automation, MED 2020, Saint-Rapha\u00ebl, France.","DOI":"10.1109\/MED48518.2020.9182973"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Cartocci, N., Napolitano, M.R., Costante, G., Crocetti, F., Valigi, P., and Fravolini, M.L. (2021, January 22\u201325). A Robust Data-Driven Fault Diagnosis Scheme Based on Recursive Dempster-Shafer Combination Rule. Proceedings of the 2021 29th Mediterranean Conference on Control and Automation, MED 2021, Puglia, Italy.","DOI":"10.1109\/MED51440.2021.9480256"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Cartocci, N., Napolitano, M.R., Costante, G., and Fravolini, M.L. (2021). A Comprehensive Case Study of Data-Driven Methods for Robust Aircraft Sensor Fault Isolation. Sensors, 21.","DOI":"10.3390\/s21051645"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Cartocci, N., Crocetti, F., Costante, G., Valigi, P., and Fravolini, M.L. (2021). Robust Multiple Fault Isolation Based on Partial-Orthogonality Criteria. Int. J. Control Autom. Syst.","DOI":"10.1007\/s12555-021-0428-y"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"108668","DOI":"10.1016\/j.ymssp.2021.108668","article-title":"Aircraft Robust Data-Driven Multiple Sensor Fault Diagnosis Based on Optimality Criteria\", Mechanical Systems and Signal Processing","volume":"170","author":"Cartocci","year":"2021","journal-title":"Mech. Syst. Signal Processing"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Cartocci, N., Crocetti, F., Costante, G., Valigi, P., Napolitano, M.R., and Fravolini, M.L. (2021, January 6\u201310). Data-Driven Sensor Fault Diagnosis Based on Nonlinear Additive Models and Local Fault Sensitivity. Proceedings of the 2021 20th International Conference on Advanced Robotics (ICAR), Ljubljana, Slovenia.","DOI":"10.1109\/ICAR53236.2021.9659449"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.promfg.2018.01.016","article-title":"Comparison of Different Classification Algorithms for Fault Detection and Fault Isolation in Complex Systems","volume":"19","author":"Jung","year":"2018","journal-title":"Procedia Manuf."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1016\/j.conengprac.2018.08.013","article-title":"Combining Model-Based Diagnosis and Data-Driven Anomaly Classifiers for Fault Isolation","volume":"80","author":"Jung","year":"2018","journal-title":"Control Eng. Pract."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"9779","DOI":"10.1021\/acs.iecr.7b05189","article-title":"Reconstruction-Based Multivariate Process Fault Isolation Using Bayesian Lasso","volume":"57","author":"Yan","year":"2018","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1080\/0740817X.2010.523769","article-title":"A Nonparametric Fault Isolation Approach through One-Class Classification Algorithms","volume":"43","author":"Kim","year":"2011","journal-title":"IIE Trans."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"912","DOI":"10.1115\/1.1962019","article-title":"Degradation Assessment and Fault Modes Classification Using Logistic Regression","volume":"127","author":"Yan","year":"2005","journal-title":"J. Manuf. Sci. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/j.patcog.2016.03.028","article-title":"High-Dimensional and Large-Scale Anomaly Detection Using a Linear One-Class SVM with Deep Learning","volume":"58","author":"Erfani","year":"2016","journal-title":"Pattern Recognit."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1007\/s11760-016-0935-0","article-title":"An Efficient System for Anomaly Detection Using Deep Learning Classifier","volume":"11","author":"Revathi","year":"2017","journal-title":"Signal Image Video Processing"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.renene.2017.03.051","article-title":"Data Driven Sensor and Actuator Fault Detection and Isolation in Wind Turbine Using Classifier Fusion","volume":"116","author":"Pashazadeh","year":"2018","journal-title":"Renew. Energy"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Mousavi, M., Moradi, M., Chaibakhsh, A., Kordestani, M., and Saif, M. (2020, January 11\u201314). Ensemble-Based Fault Detection and Isolation of an Industrial Gas Turbine. Proceedings of the 2020 IEEE International Conference on Systems, Man, and Cybernetics (SMC), Toronto, ON, Canada.","DOI":"10.1109\/SMC42975.2020.9282904"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Hastie, T.J., and Tibshirani, R.J. (2017). Generalized Additive Models, Routledge.","DOI":"10.1201\/9780203753781"},{"key":"ref_27","first-page":"152","article-title":"Additive Model Applications for the Fault Detection of Actuators","volume":"55","year":"2009","journal-title":"Pomiary Autom. Kontrola"},{"key":"ref_28","first-page":"1","article-title":"Multivariate Adaptive Regression Splines","volume":"19","author":"Friedman","year":"1991","journal-title":"Ann. Stat."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"3639","DOI":"10.1007\/s10462-020-09934-2","article-title":"A Review on Fault Detection and Diagnosis Techniques: Basics and Beyond","volume":"54","author":"Abid","year":"2020","journal-title":"Artif. Intell. Rev."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.jlp.2016.03.010","article-title":"A Review on Different Pipeline Fault Detection Methods","volume":"41","author":"Datta","year":"2016","journal-title":"J. Loss Prev. Process Ind."},{"key":"ref_31","unstructured":"(2022, February 20). Gints J\u0113kabsons ARESLab: Adaptive Regression Splines Toolbox for Matlab\/Octave. Available online: http:\/\/www.cs.rtu.lv\/jekabsons\/regression.html."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1016\/j.ins.2020.08.068","article-title":"A Distributed Sensor-Fault Detection and Diagnosis Framework Using Machine Learning","volume":"547","author":"Jan","year":"2021","journal-title":"Inf. Sci."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Lo, N.G., Flaus, J.M., and Adrot, O. (2019, January 2\u20134). Review of Machine Learning Approaches in Fault Diagnosis Applied to IoT Systems. Proceedings of the 2019 International Conference on Control, Automation and Diagnosis, ICCAD 2019, Grenoble, France.","DOI":"10.1109\/ICCAD46983.2019.9037949"},{"key":"ref_34","unstructured":"(2022, February 20). Tecnam P92. Available online: https:\/\/www.tecnam.com\/aircraft\/p92-echo-mkii\/."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1077","DOI":"10.1016\/j.conengprac.2007.01.004","article-title":"Design and Flight-Testing of Non-Linear Formation Control Laws","volume":"15","author":"Campa","year":"2007","journal-title":"Control Eng. Pract."},{"key":"ref_36","unstructured":"Grandini, M., Bagli, E., and Visani, G. (2020). Metrics for Multi-Class Classification: An Overview. arXiv."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/7\/2635\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:46:02Z","timestamp":1760136362000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/7\/2635"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,29]]},"references-count":36,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2022,4]]}},"alternative-id":["s22072635"],"URL":"https:\/\/doi.org\/10.3390\/s22072635","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,3,29]]}}}