Efficient Numerical Calibration of Water Delivery Network Using Short-Burst Hydrant Trials

Abstract

Calibration is a critical process for reducing uncertainty in Water Distribution Network Hydraulic Models (WDN HM). However, features of certain WDNs, such as oversized pipelines, lead to shallow pressure gradients under normal daily conditions, posing a challenge for effective calibration. This study proposes a calibration methodology using short hydrant trials conducted at night, which increase the pressure gradient in the WDN. The data is resampled to align with hourly consumption patterns. In a unique real-world case study of a WDN zone, we demonstrate the statistically significant superiority of our method compared to calibration based on daily usage. The experimental methodology, inspired by a machine learning cross-validation framework, utilises two state-of-the-art calibration algorithms, achieving a reduction in absolute error of up to 45% in the best scenario.

Figures (6)

• Figure 1: The entrance to the study area, coloured by elevation above sea level. Key regions include: (a) the reservoir, (b) an area of rapid residential expansion with a subsystem of pipes of varying diameters and materials, and (c) the main pipe connecting to the rest of the DMA to the west.
• Figure 2: Pressure head and flow rate during two subsequent hydrant trials performed in the WDN zone. The peak water discharge during hydrant probes is marked by the blue rectangle between (a) 1:17 and 1:19, and (b) 1:41 and 1:45. In both cases, the water flow rate (blue line) in the WDN rises from nearly no usage to around $10\: \mathrm{m^3/h}$, which was the maximum flow rate set on the hydrants. Also, both trials indicate a significant drop in pressure head on all sensors.
• Figure 3: The change of the absolute error $\mathbf{\Delta e}$ in leave-one-scenario-out experiments. The abbreviations are as follows: 'HH'--experiment with hydrant trials training set and unseen hydrant trial test set; 'DH' --experiment with daily usages training set and hydrant trial test set; 'HD'-- experiment with hydrant trials training set and daily usage test set; 'DD' --experiment with daily usages training set and unseen daily usage test set; 'AP'--ANN-PSO algorithm; 'C'--clustering-COBYLA algorithm (refer to Sec. \ref{['subsec:exp_setup']}). Green-shaded area marks a region of negative $\mathbf{\Delta e}$, which is also the area of effective error reduction due to calibration. Sensor numbers in (a) and (b) are sorted by experimental scatter series of the biggest error reduction
• Figure 4: The change of the absolute error $\mathbf{\Delta e}$ in leave-one-sensor-out experiments on test sensor in (a) hydrant trials scenarios H1, …, H4; (b) daily usage scenarios D1, …, D4. Each point represents the test stage result of the experiment with the test ('left') sensor number indicated on the X-axis. 'AP' stands for ANN-PSO algorithm, while 'C' stands for clustering-COBYLA algorithm. Green-shaded area marks a region of negative $\mathbf{\Delta e}$, which is also the area of effective error reduction due to calibration. Sensor numbers are sorted by experimental scatter series of the biggest error reduction.
• Figure 5: Visualization of the study area graph fragment with results of ANN-PSO calibration approach on example scenario from the training stage of the main experiment. Nodes marked as $\circ$ represent the absolute error between the pressure head simulated from the calibrated hydraulic model and the pressure head estimated by ANN. Nodes marked as $\triangledown$ represent the absolute error between the pressure head simulated from the calibrated hydraulic model and the pressure head measured in the sensor points.