{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,4]],"date-time":"2025-12-04T14:35:57Z","timestamp":1764858957485,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2017,1,14]],"date-time":"2017-01-14T00:00:00Z","timestamp":1484352000000},"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>This article is focused on the detection of errors using an approach that is signal based. The proposed algorithm considers several criteria: soft, hard and very hard recognition error. After the recognition of the error, the error is replaced. In this sense, different strategies for data reconciliation are associated with the proposed criteria error detection. Algorithms in several industrial software platforms are used for detecting errors of sensors. Computer simulations confirm the validation of the presented applications. Results with actual sensor measurements in industrial processes are presented.<\/jats:p>","DOI":"10.3390\/a10010013","type":"journal-article","created":{"date-parts":[[2017,1,16]],"date-time":"2017-01-16T09:44:02Z","timestamp":1484559842000},"page":"13","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["A Fault Detection and Data Reconciliation Algorithm in Technical Processes with the Help of Haar Wavelets Packets"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3288-5280","authenticated-orcid":false,"given":"Paolo","family":"Mercorelli","sequence":"first","affiliation":[{"name":"Institute of Product and Process Innovation, Leuphana University of Lueneburg, Volgershall 1, D-21339 Lueneburg, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2017,1,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2841","DOI":"10.1002\/aic.690421014","article-title":"Data reconciliation and gross-error detection for dynamic systems","volume":"42","author":"Albuquerque","year":"1996","journal-title":"AIChE J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"712","DOI":"10.1109\/18.119732","article-title":"Entropy based algorithm for best basis selection","volume":"38","author":"Coifman","year":"1992","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"865","DOI":"10.1016\/S0967-0661(99)00039-8","article-title":"Wavelets and non linear principal component analysis for process monitoring","volume":"7","author":"Shao","year":"1999","journal-title":"Control Eng. Pract."},{"key":"ref_4","unstructured":"Beheshti, S., and Dahleh, M. (2002, January 9\u201312). On denoising and signal representation. Proceedings of the 10th Mediterranean Conference on Control and Automation (MED2002), Lisbon, Portugal."},{"key":"ref_5","unstructured":"Menold, P., Pearson, R., and Allg\u00f6wer, F. (1999, January 28\u201330). Online outlier detection and removal. Proceedings of the 7th Mediterranean Conference on Control and Automation (MED1999), Heifa, Israel."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/S0959-1524(00)00046-9","article-title":"Exploring process data","volume":"11","author":"Pearson","year":"2001","journal-title":"J. Process Control"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1109\/87.974338","article-title":"Outliers in process modelling and identification","volume":"10","author":"Pearson","year":"2002","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_8","unstructured":"Beheshti, S., and Dahleh, M. (2003, January 6\u201310). Noise variance and signal denoising. Proceedings of the 2003 IEEE International Conference on Acustic Speech, and Signal Processing (ICASSP), Hong Kong, China."},{"key":"ref_9","unstructured":"Schimmack, M., Mc Gaw, D., and Mercorelli, P. (2015, January 11\u201313). Wavelet based Fault Detection and RLS Parameter Estimation of Conductive Fibers with a Simultaneous Estimation of Time-Varying Disturbance. Proceedings of the 15th IFAC Symposium on Information Control Problems in Manufacturing, INCOM 2015, Ottawa, ON, Canada."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Nadjah, A.A.N., and Mourelle, L. (2007). Computational Intelligence in Information Assurance and Security, Springer-Verlag.","DOI":"10.1007\/978-3-540-71078-3"},{"key":"ref_11","unstructured":"Mercorelli, P. (2015, January 3\u201315). Using Haar Wavelets for Fault Detection in Technical Processes. Proceedings of the 13th IFAC and IEEE Conference on Programmable Devices and Embedded Systems, Cracow, Poland."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1109\/18.382009","article-title":"Denoising by soft thresholding","volume":"41","author":"Donoho","year":"1995","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"331","DOI":"10.2478\/eletel-2014-0044","article-title":"Prefiltering in Wavelet Analysis Applying Cubic B-Splines","volume":"60","author":"Rakowski","year":"2014","journal-title":"Int. J. Electron. Telecommun."},{"key":"ref_14","unstructured":"Frick, A., and Mercorelli, P. (2003). Spurious Measurement Value Detection Method Uses Wavelet Functions in Defining a Reporting Window for Rejecting Spurious Values in a Continuous Digital Sequence of Measurement Values. (10225343 (A1)), DE Patent, (In German)."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1109\/18.382009","article-title":"Denoising and soft Thresholding","volume":"41","author":"Donoho","year":"1995","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"508","DOI":"10.1214\/aos\/1032894451","article-title":"Density estimation by wavelet thesholding","volume":"24","author":"Donoho","year":"1996","journal-title":"Ann. Stat."},{"key":"ref_17","unstructured":"Mercorelli, P. (2015). Advances in Intelligent Systems Research, Atlantis Press."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/10\/1\/13\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:26:14Z","timestamp":1760207174000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/10\/1\/13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1,14]]},"references-count":17,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2017,3]]}},"alternative-id":["a10010013"],"URL":"https:\/\/doi.org\/10.3390\/a10010013","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2017,1,14]]}}}