Characterizing the Impact of Hydrants on Transients ^†

To determine the impact of the hydrant and its ancillary features modelling work has been conducted using TSNet [4] which is transient modelling software that uses the method of characteristics. Each feature is given its own length, wavespeed, and diameter, with relevant characteristics shown in Table 1. A wavespeed of 400 m/s would represent a plastic pipe, which would have corresponding viscoelastic properties; however, for the purposes of this study, steady friction alone has been modelled. The valve closure time is 5 ms, which is realistic for a mechanical valve closure attached to a hydrant [5].

The connector pipe which attaches the hydrant to the main pipeline has been given a variable wavespeed of between 400 and 1400 m/s. The purpose of this is to determine whether accurately characterizing the ancillary features has a significant impact on the transient waves. The ‘modelled’ transient wave reflected back from the leak has been correlated with the ‘measured’ pressure signal to identify the location of the leak from the correlation peak. This process of identifying the leak location has been replicated for various levels of additional white Gaussian noise to verify the impact in more realistic conditions. The ‘Correlation confidence’ (Equation (1)) is then plotted for the various levels of additional noise.

To identify the leak time determined by the correlations, the largest peak between 0.35 and 0.45 s has been identified. As there are multiple peaks in the signal, an identification ‘boundary’ had to be imposed, and this range was deemed appropriate.

The standpipe and hydrant properties can be determined in advance through a combination of physical measurement and fitting transient data. This is because the same standpipe can be used for testing and its features determined beforehand, and hydrants are built to the same standard and are relatively invariant. Of the ancillary features this alone leaves the connector as uncharacterized. To determine connector properties an initial transient test is proposed using a high sampling frequency and solenoid valve, followed by an inverse transient analysis (ITA) approach to fit the ‘modelled’ transient signal before any reflections are received from the main pipeline to the ‘measured’ transient signal. All work conducted is based on a modelling approach; however, for the purposes of this paper, the ‘measured’ signal is assumed to be when the connector has a wavespeed of 700 m/s, diameter of 0.05 m, and length of 2 m. The three properties of the connector—wavespeed, diameter, and length—are varied using a brute force optimization algorithm with the root mean squared error (RMSE) being the output. This is carried out to characterize the search space when connector properties are varied giving an indication of what optimization techniques may be appropriate.

Results from Figure 2c show the correlation confidence (Equation (1)) results and how they vary with different levels of additional noise. With no noise and the correct connector wavespeed (700 m/s), the correlation confidence is 1, and this confidence decreases as noise is added and incorrect connector wavespeeds are used. This shows that correctly identifying the connector wavespeed increases the leakage localization accuracy, and this relationship is maintained even when the noise added to the signal becomes large enough so as to obscure any discernable pattern in the leak reflection (Figure 2a). These results support the conclusion that correctly determining the properties of ancillary features is important for accurate transient based leakage detection even in noisy conditions.

The optimization results show clearly that the correct connector properties are identified when using a brute force optimization method. Local minima are identified for Figure 3c (diameter and length), but not for Figure 3a (length and wavespeed) or Figure 3b (diameter and wavespeed). This suggests that if the length or diameter of the connector can be identified beforehand, the problem is convex and a simple gradient-based optimization algorithm will work for determining the connector properties. Otherwise, if length and diameter are unknown, a more sophisticated optimization technique will be required to avoid local minima traps. However, the principle of using the initial transient signal as a basis for an ITA-based approach to determine connector properties is shown to work.