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

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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.

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

    Dariusz Uciński & Maciej Patan

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  1. Dariusz Uciński
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Correspondence to Dariusz Uciński.

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Uciński, D., Patan, M. D-optimal design of a monitoring network for parameter estimation of distributed systems. J Glob Optim 39, 291–322 (2007). https://doi.org/10.1007/s10898-007-9139-z

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