<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>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 <italic>D<sub>s</sub></italic>-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 <italic>a priori</italic> 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.</p></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.

Configuring A Sensor Network for Fault Detection in Distributed Parameter Systems

Institute of Control and Computation Engineering, University of Zielona Góra, ul. Podgórna 50, 65-246 Zielona Góra, Poland

International Journal of Applied Mathematics and Computer Science

The problem of fault detection in distributed parameter systems (DPSs) is formulated as that of maximizing the power of a parametric hypothesis test which...

Configuring A Sensor Network for Fault Detection in Distributed Parameter Systems

Published Online: Dec 30, 2008

Page range: 513 - 524

DOI: https://doi.org/10.2478/v10006-008-0045-4

Keywords
branch-and-bound, constrained experimental design, distributed parameter systems, fault detection, parameter estimation, sensor location

This content is open access.

Configuring A Sensor Network for Fault Detection in Distributed Parameter Systems

Published Online: Dec 30, 2008

Page range: 513 - 524

DOI: https://doi.org/10.2478/v10006-008-0045-4

Keywordsbranch-and-bound, constrained experimental design, distributed parameter systems, fault detection, parameter estimation, sensor location

This content is open access.

Keywords
branch-and-bound, constrained experimental design, distributed parameter systems, fault detection, parameter estimation, sensor location