{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,2]],"date-time":"2025-10-02T06:11:58Z","timestamp":1759385518277},"reference-count":86,"publisher":"University of Zielona G\u00f3ra, Poland","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012,3,1]]},"abstract":"<jats:title>Sensor network scheduling for identification of spatially distributed processes<\/jats:title><jats:p>The work treats the problem of fault detection for processes described by partial differential equations as that of maximizing the power of a parametric hypothesis test which checks whether or not system parameters have nominal values. A simple node activation strategy is discussed for the design of a sensor network deployed in a spatial domain that is supposed to be used while detecting changes in the underlying parameters which govern the process evolution. The setting considered relates to a situation where from among a finite set of potential sensor locations only a subset of them can be selected because of the cost constraints. As a suitable performance measure, the<jats:italic>D<jats:sub>s<\/jats:sub><\/jats:italic>-optimality criterion defined on the Fisher information matrix for the estimated parameters is applied. The problem is then formulated as the determination of the density of gauged sites so as to maximize the adopted design criterion, subject to inequality constraints incorporating a maximum allowable sensor density in a given spatial domain. The search for the optimal solution is performed using a simplicial decomposition algorithm. The use of the proposed approach is illustrated by a numerical example involving sensor selection for a two-dimensional diffusion process.<\/jats:p>","DOI":"10.2478\/v10006-012-0002-0","type":"journal-article","created":{"date-parts":[[2012,3,23]],"date-time":"2012-03-23T15:15:45Z","timestamp":1332515745000},"page":"25-40","source":"Crossref","is-referenced-by-count":19,"title":["Sensor network scheduling for identification of spatially distributed processes"],"prefix":"10.61822","volume":"22","author":[{"given":"Dariusz","family":"Uci\u0144ski","sequence":"first","affiliation":[]}],"member":"37438","reference":[{"key":"1","first-page":"4238","volume-title":"Systems & Control Encyclopedia. Theory, Technology, Applications","volume":"6","author":"M. Amouroux","year":"1988"},{"key":"2","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-58727-6","volume-title":"Basic Linear Geostatistics","author":"M. 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Cassandras","year":"2005","journal-title":"European Journal of Control"},{"key":"12","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4471-0347-9","volume-title":"Fault Detection and Diagnosis in Industrial Systems","author":"L. Chiang","year":"2001"},{"issue":"8","key":"13","doi-asserted-by":"crossref","first-page":"1247","DOI":"10.1109\/JPROC.2003.814918","article-title":"Sensor networks: Evolution, opportunities, and challenges","volume":"91","author":"C.-Y. Chong","year":"2003","journal-title":"Proceedings of the IEEE"},{"key":"14","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0185-4","volume-title":"Nonlinear and Robust Control of PDE Systems: Methods and Applications to Transport-Reaction Processes","author":"P. Christofides","year":"2001"},{"key":"15","unstructured":"COMSOL AB (1995). <i>Partial Differential Equation Toolbox for Use withMatlab. 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