Design of experiments for eigenvalue identification in distributed-parameter systems

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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 experiment, which consists of the spectral density of a stochastic input signal and a 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 eases, Application of the results is illustrated in case of a vibrating system.