Locating line and node disturbances in networks of diffusively coupled dynamical agents

A wide variety of natural and human-made systems consist of a large set of dynamical units coupled into a complex structure. Breakdown of such systems can have a dramatic impact, as in the case of neurons in the brain or lines in an electric grid, to name but a few. Preventing such catastrophic events requires in particular to be able to detect and locate the source of disturbances as fast as possible. We propose a simple method to identify and locate disturbances in networks of coupled dynamical agents, relying only on time series measurements and on the knowledge of the (possibly Kron-reduced) network structure. The strength and the appeal of the present approach lies in its simplicity paired with the ability to precisely locate disturbances and even to differentiate between line and node disturbances. If we have access to measurement at only a subset of nodes, our method is still able to identify the location of the disturbance if the disturbed nodes are measured. If not, we manage to identify the region of the network where the disturbance occurs.