A Noise Scaled Semi Parametric Gaussian Process Model for Real Time Water Network Leak Detection in the Presence of Heteroscedasticity

The timely detection of leaks in water distribution systems is critical to the sustainable provision of clean water to consumers. Increasingly, water companies are deploying remote sensors to measure water flow in real-time in order to detect such leaks. However, in practice, for typical District Metering Zones (DMZ), financial constraints limit the number of deployable real time flow sensors/meters to one or two, thus constraining leak detection to be based on the aggregated flow being monitored at these point. Such aggregated flow data typically exhibits input signal dependence whereby both noise and leaks are dependent on the flow being measured. This limited monitoring and input signal dependance make conventional approaches based on simple thresholds unreliable for real time leak detection. To address this, we propose a Gaussian process (GP) model with an additive diagonal noise covariance that is able to handle the input dependant noise observed in this setting. A parameterised mean step change function is used to detect leaks and to estimate their size. Using prior water distribution systems (WDS) knowledge we dynamically bound and discretize the detection parameters of the step change mean function, reducing and pruning the parameter search space considerably. We evaluate the proposed noise scaled GP (NSGP) against both the latest research work on GP based fault detection methods and the current state of the art and applied leak detection approaches in water distribution systems. We show that our proposed method out performs other approaches, on real water network data with synthetically generated time varying leaks, with a detection accuracy of 99%, almost zero false positive detections and the lowest root mean squared error in leak magnitude estimation (0.065 l/s).