Inferring link changes in dynamic networks through power spectral density variations

In this paper, we present a computationally efficient method of detecting and localizing changes in the dynamics of links in networks of LTI systems, represented as a collection of interdependent time series. We define 'link' to mean a dependence of one node process on another. Our method uses only passively obtained second-order statistics. The dynamics of the network are not required to be known. As such, we do not require a least-squares step to find system parameters, nor do we risk using possibly corrupted data to update what we believe is the original system model. As a passive method, it does not require injecting control signals or manipulating the network. The corrupted link is only partially identified, but the scope of the problem is narrowed significantly. We detect a link change by tracking the cross power spectral density between each pair of node processes in the network. When a link changes, many pairs of nodes will experience a change in their power spectral density; we call these 'changed pairs'. We characterize which pairs of nodes in the network will change depending on which link changes. We use this characterization to uniquely find the strongly connected component containing the head of the changed link. We also provide a characterization of when the tail of the changed link can be uniquely identified.