{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T09:41:43Z","timestamp":1773654103235,"version":"3.50.1"},"reference-count":28,"publisher":"University of Zielona G\u00f3ra, Poland","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2007,6,1]]},"abstract":"<jats:title>Monitoring of Chlorine Concentration in Drinking Water Distribution Systems Using an Interval Estimator<\/jats:title><jats:p>This paper describes the design of an interval observer for the estimation of unmeasured quality state variables in drinking water distribution systems. The estimator utilizes a set bounded model of uncertainty to produce robust interval bounds on the estimated state variables of the water quality. The bounds are generated by solving two differential equations. Hence the numerical efficiency is sufficient for on-line monitoring of the water quality. The observer is applied to an exemplary water network and its performance is validated by simulations.<\/jats:p>","DOI":"10.2478\/v10006-007-0019-y","type":"journal-article","created":{"date-parts":[[2007,7,25]],"date-time":"2007-07-25T20:06:46Z","timestamp":1185394006000},"page":"199-216","source":"Crossref","is-referenced-by-count":28,"title":["Monitoring of Chlorine Concentration in Drinking Water Distribution Systems Using an Interval Estimator"],"prefix":"10.61822","volume":"17","author":[{"given":"Rafa\u0142","family":"\u0141angowski","sequence":"first","affiliation":[]},{"given":"Mietek","family":"Brdys","sequence":"additional","affiliation":[]}],"member":"37438","reference":[{"issue":"8","key":"1","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1061\/(ASCE)0733-9429(2001)127:8(669)","article-title":"Unsteady-state inverse chlorine modeling in pipe networks","volume":"127","author":"A. Al-Omari","year":"2001","journal-title":"J. Hydr. Eng."},{"key":"2","first-page":"337","article-title":"Application of a robust interval observer to an anaerobic digestion process","volume":"1","author":"V. Alcaraz-Gonz\u00e1lez","year":"2004"},{"issue":"11","key":"3","doi-asserted-by":"crossref","first-page":"2654","DOI":"10.1016\/S0043-1354(03)00067-8","article-title":"A reactive species model for chlorine decay and THM formation under rechlorination conditions","volume":"37","author":"D. Boccelli","year":"2003","journal-title":"Water Res."},{"key":"4","volume-title":"Comprehensive Water Distribution Systems Analysis Handbook","author":"P. Boulos","year":"2004"},{"key":"5","volume-title":"Operational Control of Water Systems: Structures, Algorithms and Applications","author":"M. Brdys","year":"1994"},{"issue":"1","key":"6","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1002\/acs.4480080109","article-title":"Algorithms for state bounding in large-scale systems","volume":"8","author":"M. Brdys","year":"1994","journal-title":"Int. J. Adapt. Contr. Signal Process."},{"issue":"2","key":"7","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1524\/auto.1995.43.2.77","article-title":"Joint estimation of state and parameters in quantity models of water supply and distribution systems","volume":"43","author":"M. Brdys","year":"1995","journal-title":"Automatisierungstechnik"},{"key":"8","first-page":"73","article-title":"Joint estimation of states and parameters of integrated quantity and quality models of dynamic water supply and distribution systems","volume":"1","author":"M. Brdys","year":"1996"},{"key":"9","unstructured":"Chen K. (1997): <i>Set membership estimation of state and parameters and operational control of integrated quantity and quality models of water supply and distribution systems.<\/i> \u2014 Ph.D. thesis, University of Birmingham, Birmingham, UK."},{"issue":"6","key":"10","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1061\/(ASCE)0733-9496(1995)121:6(423)","article-title":"Modeling distribution system water quality: Regulatory implications","volume":"121","author":"R. Clark","year":"1995","journal-title":"J. Water Res. Plann. Manag."},{"issue":"2","key":"11","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1080\/15730620500144043","article-title":"Hierarchical model predictive control of integrated quality and quantity in drinking water distribution systems","volume":"2","author":"K. Duzinkiewicz","year":"2005","journal-title":"Urban Water J."},{"issue":"2","key":"12","first-page":"209","article-title":"Set membership estimation of parameters and variables in dynamic networks by recursive algorithms with a moving measurement window","volume":"16","author":"K Duzinkiewicz","year":"2006","journal-title":"Int. J. Appl. Math. Comput. Sci."},{"issue":"1","key":"13","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/S0304-3800(00)00279-9","article-title":"Interval observers for uncertain biological systems","volume":"13","author":"J. Gouz\u00e9","year":"2000","journal-title":"Ecol. Modell."},{"key":"14","volume-title":"Kalman Filtering: Theory and Practice","author":"M. Grewal","year":"2001"},{"issue":"3","key":"15","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1016\/S0959-1524(99)00074-8","article-title":"Estimating of uncertain models of activated sludge process with interval observers","volume":"11","author":"M. Hadj-Sadok","year":"2001","journal-title":"J. Process Contr."},{"key":"16","doi-asserted-by":"crossref","DOI":"10.3182\/20020721-6-ES-1901.01376","article-title":"Interval observers for interconnected biotechnological systems","author":"J. Harmand","year":"2002"},{"key":"17","volume-title":"Introduction to Dynamic Systems: Theory, Models and Applications","author":"D Luenberger","year":"1979"},{"key":"18","doi-asserted-by":"crossref","DOI":"10.3182\/20060830-2-SF-4903.00007","article-title":"Interval asymptotic estimator for chlorine monitoring in drinking water distribution systems","author":"R. \u0141angowski","year":"2006"},{"issue":"2","key":"19","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1061\/(ASCE)0733-9429(1985)111:2(206)","article-title":"Algorithm for mixing problems in water systems","volume":"111","author":"R. Males","year":"1985","journal-title":"J. Hydr. Eng."},{"issue":"2","key":"20","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1061\/(ASCE)0733-9496(1988)114:2(197)","article-title":"Modeling water quality in distribution systems","volume":"114","author":"R. Males","year":"1988","journal-title":"J. Water Res. Plann. Manag."},{"key":"21","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-9545-5","volume-title":"Bounding Approaches to System Identification","author":"M. Milanese","year":"1996"},{"key":"22","volume-title":"The Finite Difference Method in Partial Differential Equations","author":"A. Mitchel","year":"1980"},{"issue":"10","key":"23","doi-asserted-by":"crossref","first-page":"2255","DOI":"10.1016\/0043-1354(96)00106-6","article-title":"A multi-step computation scheme: decoupling kinetic processes from physical transport in water quality models","volume":"30","author":"K. Park","year":"1999","journal-title":"Water Res."},{"issue":"2","key":"24","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/j.mbs.2004.07.004","article-title":"Interval observers for biochemical processes with uncertain kinetics and inputs","volume":"193","author":"A. Rapaport","year":"2005","journal-title":"Math. Biosci."},{"issue":"5","key":"25","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1061\/(ASCE)0733-9496(1993)119:5(505)","article-title":"Discrete volume element method for network water-quality models","volume":"119","author":"L. Rossman","year":"1993","journal-title":"J. Water Res. Plann. Manag."},{"issue":"4","key":"26","doi-asserted-by":"crossref","first-page":"803","DOI":"10.1061\/(ASCE)0733-9372(1994)120:4(803)","article-title":"Modeling chlorine residuals in drinking water distribution systems","volume":"120","author":"L. Rossman","year":"1994","journal-title":"J. Env. Eng."},{"issue":"2","key":"27","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1061\/(ASCE)0733-9496(1996)122:2(137)","article-title":"Numerical methods for modeling water quality in distribution systems: a Comparison","volume":"122","author":"L. Rossman","year":"1996","journal-title":"J. Water Res. Plann. Manag."},{"key":"28","volume-title":"Monotone Dynamical Systems. An Introduction to the Theory of Competitive and Cooperative Systems","author":"H Smith","year":"1995"}],"container-title":["International Journal of Applied Mathematics and Computer Science"],"original-title":[],"link":[{"URL":"http:\/\/content.sciendo.com\/view\/journals\/amcs\/17\/2\/article-p199.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/view\/j\/amcs.2007.17.issue-2\/v10006-007-0019-y\/v10006-007-0019-y.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,29]],"date-time":"2024-02-29T10:27:33Z","timestamp":1709202453000},"score":1,"resource":{"primary":{"URL":"https:\/\/content.sciendo.com\/doi\/10.2478\/v10006-007-0019-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,6,1]]},"references-count":28,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.2478\/v10006-007-0019-y","relation":{},"ISSN":["1641-876X"],"issn-type":[{"value":"1641-876X","type":"print"}],"subject":[],"published":{"date-parts":[[2007,6,1]]}}}