Configuring a sensor network for fault detection in distributed parameter systems

Patan, M. ; Uciński, D.

International Journal of Applied Mathematics and Computer Science, Tome 18 (2008) no. 4, pp. 513-524.

Résumé

The problem of fault detection in distributed parameter systems (DPSs) is formulated as that of maximizing the power of a parametric hypothesis test which checks whether or not system parameters have nominal values. A computational scheme is provided for the design of a network of observation locations in a spatial domain that are supposed to be used while detecting changes in the underlying parameters of a distributed parameter system. The setting considered relates to a situation where from among a finite set of potential sensor locations only a subset can be selected because of the cost constraints. As a suitable performance measure, the Ds-optimality criterion defined on the Fisher information matrix for the estimated parameters is applied. Then, the solution of a resulting combinatorial problem is determined based on the branch-and-bound method. As its essential part, a relaxed problem is discussed in which the sensor locations are given a priori and the aim is to determine the associated weights, which quantify the contributions of individual gauged sites. The concavity and differentiability properties of the criterion are established and a gradient projection algorithm is proposed to perform the search for the optimal solution. The delineated approach is illustrated by a numerical example on a sensor network design for a two-dimensional convective diffusion process.

Détail

Keywords: branch-and-bound, constrained experimental design, distributed parameter system, fault detection, parameter estimation, sensor location
Mots-clés : metoda podziału i ograniczeń, ograniczony plan eksperymentu, układ o parametrach rozłożonych, detekcja uszkodzeń, estymacja parametryczna, rozmieszczanie czujników

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