Sensor Placement for Discrimination between Rival Models of Distributed Parameter Systems

The problem under consideration is to plan the locations of pointwise stationary sensors along with the percentage of experimental effort spent at them in such a way as to maximize the reliability of discrimination between competing models of a distributed parameter system. The worst-case criterion of optimality adopted here is based on the sum of squares of deviations between model responses, and picks up the sensor locations yielding the maximum divergence for the least favourable values of model parameters. The approach converts the problem to an optimum experimental design formulation, in which the idea of continuous designs interpreted as probability measures on the set of admissible sensor positions is exploited. Numerical solutions are obtained through a relaxation algorithm being a nontrivial generalization of an exchange method for solving semi-infinite programming problems to the space of probability measures. The algorithm makes an iterative refinement to the existing solution at each step and adapts the number of support points if necessary