Optimal allocation of excitation and measurement for identification of dynamic networks

TL;DR

This paper investigates optimal strategies for allocating excitations and measurements in dynamic network identification to maximize accuracy while minimizing experimental costs, providing analytical guidelines based on network topology.

Contribution

It introduces a formal analysis of optimal excitation and measurement allocation in dynamic networks, with new guidelines derived from network topology and module magnitudes.

Findings

Analytical results for branch and cycle networks

Guidelines based on network topology and module size

Application to more generic network topologies

Abstract

In this paper, the problem of choosing the best allocation of excitations and measurements for the identification of a dynamic network is formally stated and analyzed. The best choice will be one that achieves the most accurate identification with the least costly experiment. Accuracy is assessed by the trace of the asymptotic covariance matrix of the parameters estimates, whereas the cost criterion is the number of excitations and measurements. Analytical and numerical results are presented for two classes of dynamic networks in state space form: branches and cycles. From these results, a number of guidelines for the choice emerge, which are based either on the topology of the network or on the relative magnitude of the modules being identified. An example is given to illustrate that these guidelines can to some extent be applied to networks of more generic topology.