D-optimal design of a monitoring network for parameter estimation of distributed systems

  • Authors:

  • Dariusz Uciński;Maciej Patan

  • Affiliations:

  • Institute of Control and Computation Engineering, University of Zielona Góra, Zielona Góra, Poland 65---246;Institute of Control and Computation Engineering, University of Zielona Góra, Zielona Góra, Poland 65---246

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2007

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Abstract

This paper addresses the design of a network of observation locations in a spatial domain that will be used to estimate unknown parameters of a distributed parameter system. We consider a setting where we are given a finite number of possible sites at which to locate a sensor, but cost constraints allow only some proper subset of them to be selected. We formulate this problem as the selection of the gauged sites so as to maximize the log-determinant of the Fisher information matrix associated with the estimated parameters. The search for the optimal solution is performed using the branch-and-bound method in which an extremely simple and efficient technique is employed to produce an upper bound to the maximum objective function. Its idea consists in solving a relaxed problem through the application of a simplicial decomposition algorithm in which the restricted master problem is solved using a multiplicative algorithm for optimal design. The use of the proposed approach is illustrated by a numerical example involving sensor selection for a two-dimensional convective diffusion process.