Design of Experiments for Eigenvalue Identification in Distributed-Parameter Systems

Abstract

The problem of optimal design of experiments for identification of distributed systems described by a linear, parabolic partial differential equation is considered. Conditions of an experiments, which consists of the spectral density of a stochastic input signal and probability measure corresponding to positions of sensors, are chosen such as to maximize the accuracy of a finite number of the system's eigenvalue estimates. Conditions for optimality of the experiment design are derived. In particular, it is shown that the optimal input consists of a finite number sinusoids and optimal positions of the sensors can be found analytically in some cases. Application of the results is illustrated in case of a vibrating system. 1 Introduction A wide interest in the identification of parameters of distributed-parameter systems, DPS, (see Polis and Goodson 1976 and Kubrusly 1977 for survey papers) poses new problems concerned with the choice of experimental conditions (inputs and sensor locatio..