Monitoring Networked Infrastructure with Minimum Data via Sequential Graph Fourier Transforms

Many urban infrastructures contain complex dynamics embedded in spatial networks. Monitoring using Internet-of-Things (IoT) sensors is essential for ensuring safe operations. An open challenge is given an existing sensor network, where best to collect the minimum amount of representative data. Here, we consider an urban underground water distribution network (WDN) and the problem of contamination detection. Existing topology-based approaches link complex network (e.g. Laplacian spectra) to optimal sensing selections, but neglects the underpinning fluid dynamics. Alternative data-driven approaches such as compressed sensing (CS) offer limited data reduction.In this work, we introduce a principal component analysis based Graph Fourier Transform (PCA-GFT) method, which can recover the full networked signal from a dynamic subset of sensors. Specifically, at each time step, we are able to predict which sensors are needed for the next time step. We do so, by exploiting the spatial-time correlations of the WDN dynamics, as well as predicting the sensor set needed using sparse coefficients in the transformed domain. As such, we are able to significantly reduce the number of samples compared with CS approaches. The drawback lies in the computational complexity of a data collection point (DCP) updating the PCA-GFT operator at each time-step. The experimental results show that, on average, with nearly 40% of the sensors reported, the proposed PCA-GFT method is able to fully recover the networked dynamics.