{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:02:15Z","timestamp":1760148135884,"version":"build-2065373602"},"reference-count":9,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,4,3]],"date-time":"2023-04-03T00:00:00Z","timestamp":1680480000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>We consider a time series with real data from a water lift station, equipped with three water pumps which are activated and deactivated depending on certain starting and halting thresholds. Given the water level and the number of active pumps, both read every 5 min, we aim to infer when each pump was activated or deactivated. To do so, we build an algorithm that sets a hierarchy of criteria based on the past and future of a given interval to identify which thresholds have been crossed during that interval. We then fill the gaps between the 5 min time steps, modeling the water level continuously with a piecewise linear function. This filling takes into account not only every water level reading and every previously identified change of status, but also the fact that activation and deactivation of a pump has no immediate effect on water level. This allows for the fulfillment of the ultimate objective of the problem in its real context, which is to provide the water management company an estimate of how long each pump has been working. Additionally, our estimates correct the errors contained in the time series regarding the number of active pumps.<\/jats:p>","DOI":"10.3390\/math11071707","type":"journal-article","created":{"date-parts":[[2023,4,3]],"date-time":"2023-04-03T04:45:33Z","timestamp":1680497133000},"page":"1707","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Automatic Completion of Data Gaps Applied to a System of Water Pumps"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3407-7757","authenticated-orcid":false,"given":"Ricardo","family":"Engui\u00e7a","sequence":"first","affiliation":[{"name":"Departmento de Matem\u00e1tica, Instituto Superior de Engenharia de Lisboa, Instituto Polit\u00e9cnico de Lisboa, Rua Conselheiro Em\u00eddio Navarro, 1, 1959-007 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1304-8041","authenticated-orcid":false,"given":"Filipa","family":"Soares","sequence":"additional","affiliation":[{"name":"Departmento de Matem\u00e1tica, Instituto Superior de Engenharia de Lisboa, Instituto Polit\u00e9cnico de Lisboa, Rua Conselheiro Em\u00eddio Navarro, 1, 1959-007 Lisboa, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"126454","DOI":"10.1016\/j.jhydrol.2021.126454","article-title":"Automatic gap-filling of daily streamflow time series in data-scarce regions using a machine learning algorithm","volume":"598","author":"Arriagada","year":"2021","journal-title":"J. Hydrol."},{"key":"ref_2","unstructured":"Sanjurjo Gonz\u00e1lez, H., Pastor L\u00f3pez, I., Garc\u00eda Bringas, P., Quinti\u00e1n, H., and Corchado, E. Automated Data-Driven Approach for Gap Filling in the Time Series Using Evolutionary Learning. Proceedings of the 16th International Conference on Soft Computing Models in Industrial and Environmental Applications (SOCO 2021)."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1016\/j.jhydrol.2018.11.076","article-title":"Gap-filling of daily streamflow time series using Direct Sampling in various hydroclimatic settings","volume":"569","author":"Oriani","year":"2019","journal-title":"J. Hydrol."},{"key":"ref_4","unstructured":"Karlin, S., Amemiya, T., and Goodman, L.A. (1983). Studies in Econometrics, Time Series, and Multivariate Statistics, Academic Press."},{"key":"ref_5","unstructured":"Findley, D.F. (1981). Applied Time Series Analysis II, Academic Press."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1162","DOI":"10.1016\/j.jhydrol.2014.08.025","article-title":"Infilling missing precipitation records \u2013 A comparison of a new copula-based method with other techniques","volume":"519","author":"Pegram","year":"2014","journal-title":"J. Hydrol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"851","DOI":"10.1080\/02626669609491555","article-title":"Daily flow time series patching or extension: A spatial interpolation approach based on flow duration curves","volume":"41","author":"Hughes","year":"1996","journal-title":"Hydrol. Sci. J."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"9447","DOI":"10.1002\/2015WR017399","article-title":"Reconstruction of missing daily streamflow data using dynamic regression models","volume":"51","author":"Tencaliec","year":"2015","journal-title":"Water Resour. Res."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/j.jhydrol.2011.01.028","article-title":"Evaluation of statistical methods for infilling missing values in high-resolution soil moisture data","volume":"400","author":"Dumedah","year":"2011","journal-title":"J. Hydrol."}],"container-title":["Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2227-7390\/11\/7\/1707\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:08:57Z","timestamp":1760123337000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2227-7390\/11\/7\/1707"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,3]]},"references-count":9,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2023,4]]}},"alternative-id":["math11071707"],"URL":"https:\/\/doi.org\/10.3390\/math11071707","relation":{},"ISSN":["2227-7390"],"issn-type":[{"type":"electronic","value":"2227-7390"}],"subject":[],"published":{"date-parts":[[2023,4,3]]}}}