Water Distribution Networks (WDNs) are critical infrastructures that ensure safe drinking water. One of the major threats is the accidental or intentional injection of pollutants. Data collection remains challenging in underground WDNs and in order to quantify its threat to end users, modeling pollutant spread with minimal sensor data is can important open challenge. Existing approaches using numerical optimisation suffer from scalability issues and lack detailed insight and performance guarantees. Applying general data-driven approaches such as compressed sensing (CS) offer limited improvements in sample node reduction. Graph theoretic approaches link topology (e.g. Laplacian spectra) to optimal sensing locations, it neglects the complex dynamics.In this work, we introduce a novel Graph Fourier Transform (GFT) that exploits the low-rank property to optimally sample junction nodes in WDNs. The proposed GFT allows us to fully recover the full network dynamics using a subset of data sampled at the identified nodes. The proposed GFT technique offers attractive improvements over existing numerical optimisation, compressed sensing, and graph theoretic approaches. Our results show that, on average, with nearly 30-40% of the junctions monitored, we are able to fully recover the dynamics of the whole network. The framework is useful beyond the application of WDNs and can be applied to a variety of infrastructure sensing for digital twin modeling.
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Precise timing over timestamped packet exchange communication is an enabling technology in the mission-critical industrial Internet of Things, particularly when satellite-based timing is unavailable. The main challenge is to ensure timing accuracy when the clock synchronisation system is subject to disturbances caused by the drifting frequency, time-varying delay, jitter, and timestamping uncertainty. In this work, a Robust Packet-Coupled Oscillators (R-PkCOs) protocol is proposed to reduce the effects of perturbations manifested in the drifting clock, timestamping uncertainty and delays. First, in the spanning tree clock topology, time synchronisation between an arbitrary pair of clocks is modelled as a state-space model, where clock states are coupled with each other by one-way timestamped packet exchange (referred to as packet coupling), and the impacts of both drifting frequency and delays are modelled as disturbances. A static output controller is adopted to adjust the drifting clock. The H∞ robust control design solution is proposed to guarantee that the ratio between the modulus of synchronisation precision and the magnitude of the disturbances is always less than a given value. Therefore, the proposed time synchronisation protocol is robust against the disturbances, which means that the impacts of drifting frequency and delays on the synchronisation accuracy are limited. The one-hour experimental results demonstrate that the proposed R-PkCOs protocol can realise time synchronisation with the precision of six microseconds in a 21-node IEEE 802.15.4 network. This work has widespread impacts in the process automation of automotive, mining, oil and gas industries.
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