Probabilistic leak detection and quantification using multi-output Gaussian processes

Abstract

A water distribution system WDS is often divided into smaller isolated and independent zones called district metering areas (DMA). A DMA can have anywhere from a few hundred to a few thousand properties. Normally only three locations within a district metering area are actively monitored for pressure or flow readings. These are the supply point pressure and flow and the critical point pressure which is the point of the lowest pressure in the DMA. As leakage rates are typically directly proportional to average pressures in the DMA, keeping the network pressure as low as possible while maintaining desired serviceability is an effective and widely used method for leak reduction. With advancement in technology this network pressure reduction is now done in real-time, where the network pressure is increased or decreased based on the demand. However, such real-time optimisation changes the DMA dynamics making it different from traditional unoptimised DMAs. We consider the problem of detecting and quantifying leaks in pressure optimised DMA, using only these three DMA-level hydraulic measurements. The DMA-level measurements represent the current aggregate water demand/consumption within the DMA. Detecting leaks at this point is challenging, particularly small leaks, as they do not produce a significant increase in the aggregated DMA-level measurements. Furthermore, the DMA-level data exhibits input signal dependence whereby both noise and leaks are dependent on the flow and pressure being measured, making leak detection task more difficult. To address this, we first propose a Gaussian process (GP) based approach that uses only the DMA-level flow to detect leaks (NSGP). We devise an additive diagonal noise covariance for the GP that is able to handle the input dependant noise observed in this setting. A parameterised mean step change function is used to detect and approximate leaks. As accurate leak data is often not available due to poor record keeping, we develop a detailed simulated model of a pressure optimised DMA and use it for analysing proposed leak detection methods. We show that active pressure optimisation changes the dynamics of a DMA. In light of the change in DMA dynamics, we proposed a domain specific, data driven, multi output gaussian process model, to detect and quantify leaks in pressure optimised DMAs (SMOGP). The novelty of the model is, firstly its ability to use all available information from a DMA to detect leaks, secondly the ability to model the pressure dependant leak process mathematically within the GP framework. We compare the performance of the proposed methods with the current state of the art leak detection method. We show that our proposed method out perform other approaches considerably both in terms of the accuracy of leak detection and leak magnitude estimation.

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