Configuring a sensor network for fault detection in distributed parameter systems

Maciej Patan; Dariusz Uciński

International Journal of Applied Mathematics and Computer Science (2008)

  • Volume: 18, Issue: 4, page 513-524
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Maciej Patan, and Dariusz Uciński. "Configuring a sensor network for fault detection in distributed parameter systems." International Journal of Applied Mathematics and Computer Science 18.4 (2008): 513-524. <http://eudml.org/doc/207904>.

@article{MaciejPatan2008,
abstract = {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.},
author = {Maciej Patan, Dariusz Uciński},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {branch-and-bound; constrained experimental design; distributed parameter systems; fault detection; parameter estimation; sensor location},
language = {eng},
number = {4},
pages = {513-524},
title = {Configuring a sensor network for fault detection in distributed parameter systems},
url = {http://eudml.org/doc/207904},
volume = {18},
year = {2008},
}

TY - JOUR
AU - Maciej Patan
AU - Dariusz Uciński
TI - Configuring a sensor network for fault detection in distributed parameter systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2008
VL - 18
IS - 4
SP - 513
EP - 524
AB - 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.
LA - eng
KW - branch-and-bound; constrained experimental design; distributed parameter systems; fault detection; parameter estimation; sensor location
UR - http://eudml.org/doc/207904
ER -

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Citations in EuDML Documents

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  1. Jean-Philippe Georges, Didier Theilliol, Vincent Cocquempot, Jean-Christophe Ponsart, Christophe Aubrun, Fault tolerance in networked control systems under intermittent observations
  2. Dariusz Uciński, Maciej Patan, Sensor network design for the estimation of spatially distributed processes
  3. Maciej Patan, Distributed scheduling of sensor networks for identification of spatio-temporal processes
  4. Dariusz Uciński, Sensor network scheduling for identification of spatially distributed processes

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