Failure detection for transport processes on networks

Diffusion on complex networks is a convenient framework to simulate a great variety of transport systems. The effects of failures in the network links may be used to cascade phenomena or the congestion formation in the system. A real time detection of failures can mitigate their effect and allow to optimize the control procedures on the transport network. The main objective of this work is to provide a dimensionality reduction technique for a transport network where a diffusive dynamics takes place, to detect presence of a failure by a limited number of observations. Our approach is based on the susceptibility response of the network state under random perturbations of the link weights. The correlations among the nodes fluctuations is exploited in order to provide the clustering procedure. The network dimensionality is therefore reduced introducing `representative nodes' for each cluster and generating a reduced network model, whose dynamical state is detected by the limited observations. We realize a failure identification procedure for the whole network, studying the dynamics of the coarse-grained network. The localization efficiency of the proposed clustering algorithm, averaging over all possible single-edge failures, is compared with traditional structure-based clustering using different graph configurations. We show that the proposed clustering algorithm is more sensitive than traditional clustering techniques to detect link failure with high stationary fluxes.