Detecting link failures in complex network processes using remote monitoring

• We study detection of network changes from remote noisy time-series measurements.
• A Maximum A-Posteriori Probability hypothesis testing scheme is employed.
• Relationships between the network topology and MAP detector performance are developed.
• Detector performance depends on presence of certain paths in the network.
• Simulations demonstrate the analytical results developed.

We study whether local structural changes in a complex network can be distinguished from passive remote time-course measurements of the network’s dynamics. Specifically the detection of link failures in a network synchronization process from noisy measurements at a single network component is considered. By phrasing the detection task as a Maximum A Posteriori Probability hypothesis testing problem, we are able to obtain conditions under which the detection is (1) improved over the a priori and (2) asymptotically perfect, in terms of the network spectrum and graph. We find that, in the case where the detector has knowledge of the network’s state, perfect detection is possible under general connectivity conditions regardless of the measurement location. When the detector does not have state knowledge, a remote signature permits improved but not perfect detection, under the same connectivity conditions. At its essence, detectability is achieved because of the close connection between a network’s topology, its eigenvalues and local response characteristics.