<p>Various sensors are mounted on pipelines to acquire hydraulic data and transmit them to data centers to detect leakages.</p> Full article ">Figure 2
<p>The overall architecture of the proposed model. (1) Instead of performing the direct addition of position embeddings and inputs as in most attention mechanisms, we concatenate position embeddings with pressure data. (2) We consider the dependency of contemporaneous pressure data and take them as the input to the decoder. (3) We use the MSE loss function to evaluate the reconstruction residuals.</p> Full article ">Figure 3
<p>A comparison of pressure data between normal operation and leakage of the pipe network in several scenarios. The left column (<b>a1</b>,<b>b1</b>,<b>c1</b>,<b>d1</b>) and middle column (<b>a2</b>,<b>b2</b>,<b>c2</b>,<b>d2</b>) show the water demands (in m<sup>3</sup>) and pressure (in m) under normal operation. The right column (<b>a3</b>,<b>b3</b>,<b>c3</b>,<b>d3</b>) shows pressure changes in different leakage scenarios.</p> Full article ">Figure 4
<p>Comparison of pressure (in m, normalized) before and after normalization. Lines with different colors represent different scenarios. (<b>a</b>) Concatenated pressure data in different scenarios without normalization. (<b>b</b>) Concatenated pressure data in different scenarios with normalization. (<b>c</b>) Pressure data with the same distribution according to KS statistics after normalization for each scenario. (<b>d</b>) Pressure data with different distributions according to KS statistics.</p> Full article ">Figure 5
<p>A comparison of pressure data and data with the addition of position embeddings. The top figure illustrates the pressure data (in m, normalized) without the addition of the position embeddings, and the bottom one presents the corresponding pressure data after the addition of the position embeddings. The leakage point is indicated by the area shaded in orange.</p> Full article ">Figure 6
<p>Local attention layers of encoder and decoder. In the attention layer of the encoder, <span class="html-italic">Q</span>, <span class="html-italic">K</span>, and <span class="html-italic">V</span> are obtained from the historical pressure data. In the first attention layer of the decoder, <span class="html-italic">Q</span>, <span class="html-italic">K</span>, and <span class="html-italic">V</span> are obtained from the pressure data at the same time on different days. In the second attention layer of the decoder, <span class="html-italic">Q</span> is obtained from pressure data at the same time on different days, and <span class="html-italic">K</span> and <span class="html-italic">V</span> are obtained from the historical pressure data.</p> Full article ">Figure 7
<p>Latent features from normal pressure and leakage data. Each point represents a latent feature at a time step, and the color of the points varies according to the change in the time steps. (<b>a</b>) The t-SNE embeddings of the latent features with one week of pressure data; (<b>b</b>) the t-SNE embeddings of the latent features at the same hour of different days; (<b>c</b>) the comparison of the t-SNE embeddings of the pressure data under normal operation and the data for leakages, denoted by points in green and orange, respectively.</p> Full article ">Figure 8
<p>Visualization of leakage detection. The green line denotes pressure data, the yellow line denotes MSE loss between input pressure and reconstructed pressure (in m, normalized), and the orange shade denotes leakages.</p> Full article ">Figure 9
<p>The network topologies of Anytown, Hanoi, and Net1. Each point represents a junction with Pressure Transducer and Flow Transducer.</p> Full article ">Figure 10
<p>The components of the demand data. (<b>a</b>) The fundamental periodicity to simulate the seasonal trends; (<b>b</b>) random noise used to generate the variance in daily usage and operations on the pipelines; (<b>c</b>) daily consumption-based demand periodicity.</p> Full article ">Figure 11
<p>Performance comparison of historical pressure data (<b>a</b>–<b>c</b>) and pressure data at the same hour on different days (<b>d</b>–<b>f</b>) for different window sizes. Various training epochs were considered. We use the green color to indicate the performance of “F1-score” and blue to indicate the performance of “Accuracy”. The window size was set to [1 day, 2 days, and 7 days] for the historical pressure data, and to [2 days, 7 days, 30 days] for the pressure data at the same hour on different days.</p> Full article ">