<table><tr><td>5466.96</td><td>40441.00</td><td>7.33</td><td>0.01</td><td>0.02</td><td>0.01</td><td>0.06</td><td>0.06</td><td>0.57</td></tr><tr><td>5949.14</td><td>40762.64</td><td>2.64</td><td>0.01</td><td>0.01</td><td>0.00</td><td>0.03</td><td>0.01</td><td>0.12</td></tr><tr><td>5949.14</td><td>40762.64</td><td>3.67</td><td>0.01</td><td>0.01</td><td>0.01</td><td>0.04</td><td>0.02</td><td>0.16</td></tr><tr><td>5949.14</td><td>40762.64</td><td>4.19</td><td>0.01</td><td>0.01</td><td>0.01</td><td>0.04</td><td>0.02</td><td>0.18</td></tr><tr><td>5949.14</td><td>40762.64</td><td>5.25</td><td>0.01</td><td>0.02</td><td>0.01</td><td>0.05</td><td>0.03</td><td>0.23</td></tr><tr><td>5949.14</td><td>40762.64</td><td>6.27</td><td>0.01</td><td>0.02</td><td>0.01</td><td>0.06</td><td>0.03</td><td>0.28</td></tr><tr><td>5949.14</td><td>40762.64</td><td>7.80</td><td>0.02</td><td>0.03</td><td>0.01</td><td>0.07</td><td>0.04</td><td>0.35</td></tr><tr><td>5882.39</td><td>40806.32</td><td>2.44</td><td>0.00</td><td>0.00</td><td>0.00</td><td>0.01</td><td>0.04</td><td>0.24</td></tr><tr><td>5882.39</td><td>40806.32</td><td>3.39</td><td>0.00</td><td>0.00</td><td>0.00</td><td>0.01</td><td>0.05</td><td>0.34</td></tr><tr><td>5882.39</td><td>40806.32</td><td>3.86</td><td>0.00</td><td>0.01</td><td>0.00</td><td>0.01</td><td>0.06</td><td>0.39</td></tr><tr><td>5882.39</td><td>40806.32</td><td>4.82</td><td>0.00</td><td>0.01</td><td>0.00</td><td>0.02</td><td>0.07</td><td>0.49</td></tr><tr><td>5882.39</td><td>40806.32</td><td>5.78</td><td>0.00</td><td>0.01</td><td>0.00</td><td>0.02</td><td>0.09</td><td>0.58</td></tr><tr><td>5882.39</td><td>40806.32</td><td>7.18</td><td>0.01</td><td>0.01</td><td>0.01</td><td>0.03</td><td>0.11</td><td>0.73</td></tr><tr><td>9251.14</td><td>46569.24</td><td>8.09</td><td>0.46</td><td>0.84</td><td>0.42</td><td>0.10</td><td>0.00</td><td>0.01</td></tr></table>
<table><caption>Table S2. Test sample data.</caption><thead><tr><th>X</th><th>Y</th><th>Leakage volume (L/s)</th><th>Pressure residual 1 (m)</th><th>Pressure residual 2 (m)</th><th>Pressure residual 3 (m)</th><th>Pressure residual 4 (m)</th><th>Pressure residual 5 (m)</th><th>Pressure residual 6 (m)</th></tr></thead><tbody><tr><td>3200.57</td><td>49840.23</td><td>5.00</td><td>0.35</td><td>0.32</td><td>0.00</td><td>0.01</td><td>0.04</td><td>0.35</td></tr><tr><td>7387.58</td><td>48889.82</td><td>3.00</td><td>0.18</td><td>0.17</td><td>0.00</td><td>0.00</td><td>0.03</td><td>0.29</td></tr><tr><td>1164.89</td><td>48975.81</td><td>7.00</td><td>0.48</td><td>0.47</td><td>0.00</td><td>0.01</td><td>0.04</td><td>0.39</td></tr><tr><td>7033.75</td><td>40308.98</td><td>8.00</td><td>0.02</td><td>0.02</td><td>0.03</td><td>0.29</td><td>0.08</td><td>0.03</td></tr><tr><td>11183.13</td><td>39878.88</td><td>5.00</td><td>0.02</td><td>0.02</td><td>0.00</td><td>0.02</td><td>0.10</td><td>0.04</td></tr><tr><td>9251.14</td><td>46569.24</td><td>8.09</td><td>0.46</td><td>0.42</td><td>0.00</td><td>0.01</td><td>0.10</td><td>0.84</td></tr><tr><td>10260.17</td><td>46725.03</td><td>2.71</td><td>0.14</td><td>0.13</td><td>0.00</td><td>0.01</td><td>0.04</td><td>0.25</td></tr><tr><td>1040.00</td><td>51851.00</td><td>8.11</td><td>0.73</td><td>0.54</td><td>0.00</td><td>0.01</td><td>0.05</td><td>0.49</td></tr><tr><td>1047.15</td><td>52011.69</td><td>4.35</td><td>0.39</td><td>0.29</td><td>0.00</td><td>0.00</td><td>0.03</td><td>0.26</td></tr><tr><td>8546.14</td><td>39434.60</td><td>3.84</td><td>0.01</td><td>0.01</td><td>0.01</td><td>0.09</td><td>0.04</td><td>0.02</td></tr><tr><td>5652.58</td><td>40577.76</td><td>5.71</td><td>0.00</td><td>0.00</td><td>0.09</td><td>0.60</td><td>0.02</td><td>0.01</td></tr><tr><td>2719.06</td><td>49944.59</td><td>3.95</td><td>0.28</td><td>0.25</td><td>0.00</td><td>0.00</td><td>0.03</td><td>0.26</td></tr><tr><td>7169.97</td><td>47567.15</td><td>8.15</td><td>0.49</td><td>0.46</td><td>0.00</td><td>0.01</td><td>0.09</td><td>0.89</td></tr><tr><td>11079.78</td><td>39173.00</td><td>4.65</td><td>0.02</td><td>0.01</td><td>0.00</td><td>0.02</td><td>0.08</td><td>0.03</td></tr><tr><td>414.27</td><td>43688.32</td><td>4.64</td><td>0.00</td><td>0.00</td><td>0.09</td><td>0.09</td><td>0.00</td><td>0.00</td></tr></tbody></table>
<table><caption>**Table S3.** Genetic algorithm configuration</caption><thead><tr><th>Parameter</th><th>Value/Method</th><th>Description</th></tr></thead><tbody><tr><td>Maximum generations</td><td>100</td><td>Evolution stopping criterion (balanced for convergence speed vs computational cost)</td></tr><tr><td>Population size</td><td>20</td><td>Number of chromosomes per generation (smaller size for faster iteration)</td></tr><tr><td>Crossover probability</td><td>0.5</td><td>Arithmetic crossover: child = α×parent<sub>1</sub> + (1-α)×parent<sub>2</sub> where α~U(0,1)</td></tr><tr><td>Mutation probability</td><td>0.2</td><td>Adaptive boundary mutation: Δ = (bound-x)×(rand*(1-gen/maxgen))<sup>2</sup></td></tr><tr><td>Parameter bounds</td><td>[-3, 3]</td><td>Constrained search space for all neural network weights and biases<br>Direct encoding of:<ul><li>Input→hidden weights (7×6 matrix)</li><li>Hidden biases (6×1 vector)</li><li>Hidden→output weights (6×2 matrix)</li><li>Output biases (2×1 vector)</li></ul></td></tr><tr><td>Encoding scheme</td><td>Real-valued</td><td>• Input→hidden weights (7×6 matrix)<br>• Hidden biases (6×1 vector)<br>• Hidden→output weights (6×2 matrix)<br>• Output biases (2×1 vector)</td></tr><tr><td>Selection operator</td><td>Roulette Wheel</td><td>Probability proportional to scaled fitness (10/fitness) with rejection sampling</td></tr><tr><td>Crossover operator</td><td>Single-point arithmetic</td><td>Random gene position selected, convex combination applied</td></tr><tr><td>Mutation operator</td><td>Generation-scaled boundary</td><td>Mutates toward parameter bounds with strength decreasing over generations<br>Σ|NN(inputn)-outputn| after limited BP training (50k epochs max). (All input features were normalized to [-1, 1] using MATLAB's mapminmax function, denoted as inputn to distinguish from raw inputs.)</td></tr><tr><td>Fitness function</td><td>Sum Absolute Error</td><td></td></tr></tbody></table>
<figure><img src="image_12.png" /></figure>
<table><caption>**Table S4.** Evaluation criteria for pipeline security levels.</caption><thead><tr><th>Indicator</th><th>Excellent</th><th>Good</th><th>Moderate</th><th>Poor</th></tr></thead><tbody><tr><td>Pipe Material</td><td>Ductile cast iron</td><td>Plastic</td><td>Steel</td><td>-</td></tr><tr><td>Pipe Length (m)</td><td>≤ 100</td><td>100 - 200</td><td>200 - 500</td><td>> 500</td></tr><tr><td>Pipe Diameter (mm)</td><td>≤ 300</td><td>300 - 500</td><td>500 - 700</td><td>> 700</td></tr><tr><td>Pipe Age (years)</td><td>≤ 1</td><td>1 - 5</td><td>5 - 10</td><td>> 10</td></tr><tr><td>Joint Type</td><td>Flexible</td><td>-</td><td>Rigid</td><td>-</td></tr><tr><td>Water Flow (L/s)</td><td>≤ 50</td><td>50 - 100</td><td>100 - 200</td><td>> 200</td></tr><tr><td>Water Pressure (m)</td><td>≤ 20</td><td>20 - 30</td><td>30 - 40</td><td>> 40</td></tr><tr><td>Geographic Location</td><td>Branch road</td><td>Secondary main road</td><td>Primary main road</td><td>-</td></tr><tr><td>Population Density (persons/km²)</td><td>≤ 200</td><td>200 - 500</td><td>500 - 1000</td><td>> 1000</td></tr><tr><td>Burial Depth (m)</td><td>≤ 0.8</td><td>0.8 - 1.5</td><td>1.5 - 2.0</td><td>> 2.0</td></tr></tbody></table>
<table><caption>**Table S5.** RF prediction error results.</caption><thead><tr><th>Sample number</th><th>Horizontal coordinate<br>error value (m)</th><th>Vertical coordinate<br>error value (m)</th><th>Prediction error<br>value (m)</th></tr></thead><tbody><tr><td>1</td><td>94.11</td><td>437.90</td><td>447.90</td></tr><tr><td>2</td><td>1273.26</td><td>410.54</td><td>1337.81</td></tr><tr><td>3</td><td>375.12</td><td>1330.04</td><td>1381.93</td></tr><tr><td>4</td><td>8.81</td><td>23.47</td><td>25.07</td></tr><tr><td>5</td><td>31.29</td><td>807.26</td><td>807.86</td></tr><tr><td>6</td><td>112.74</td><td>10.37</td><td>113.21</td></tr><tr><td>7</td><td>163.31</td><td>62.83</td><td>174.98</td></tr><tr><td>8</td><td>31.63</td><td>502.70</td><td>503.69</td></tr><tr><td>9</td><td>133.21</td><td>126.31</td><td>183.58</td></tr><tr><td>10</td><td>285.03</td><td>152.10</td><td>323.07</td></tr><tr><td>11</td><td>960.38</td><td>62.40</td><td>962.40</td></tr><tr><td>12</td><td>543.02</td><td>94.52</td><td>551.18</td></tr><tr><td>13</td><td>45.86</td><td>432.78</td><td>435.21</td></tr><tr><td>14</td><td>28.14</td><td>24.05</td><td>37.02</td></tr><tr><td>15</td><td>57.60</td><td>584.75</td><td>587.58</td></tr></tbody></table>
<table><caption>**Table S6.** Single BP neural network prediction error results.</caption><thead><tr><th>Sample number</th><th>Horizontal coordinate<br>error value (m)</th><th>Vertical coordinate<br>error value (m)</th><th>Prediction error<br>value (m)</th></tr></thead><tbody><tr><td>1</td><td>152.82</td><td>74.25</td><td>169.90</td></tr><tr><td>2</td><td>151.86</td><td>208.34</td><td>257.81</td></tr><tr><td>3</td><td>41.57</td><td>377.57</td><td>379.85</td></tr><tr><td>4</td><td>226.71</td><td>109.76</td><td>251.89</td></tr><tr><td>5</td><td>4.98</td><td>126.09</td><td>126.18</td></tr><tr><td>6</td><td>139.91</td><td>147.70</td><td>203.45</td></tr><tr><td>7</td><td>65.33</td><td>42.38</td><td>77.87</td></tr><tr><td>8</td><td>166.87</td><td>85.16</td><td>187.34</td></tr><tr><td>9</td><td>116.74</td><td>26.17</td><td>119.64</td></tr><tr><td>10</td><td>195.62</td><td>5.45</td><td>195.69</td></tr><tr><td>11</td><td>17.47</td><td>151.73</td><td>152.73</td></tr><tr><td>12</td><td>177.18</td><td>86.33</td><td>197.09</td></tr><tr><td>13</td><td>33.57</td><td>33.14</td><td>47.17</td></tr><tr><td>14</td><td>25.60</td><td>14.48</td><td>29.41</td></tr><tr><td>15</td><td>11.00</td><td>26.05</td><td>28.28</td></tr></tbody></table>
<table><caption>**Table S7.** GA-BP neural network prediction error results.</caption><thead><tr><th>Sample number</th><th>Horizontal coordinate<br>error value (m)</th><th>Vertical coordinate<br>error value (m)</th><th>Prediction<br>error<br>value(m)</th></tr></thead><tbody><tr><td>1</td><td>47.88</td><td>59.02</td><td>76.00</td></tr><tr><td>2</td><td>67.84</td><td>77.76</td><td>103.19</td></tr><tr><td>3</td><td>55.18</td><td>99.30</td><td>113.60</td></tr><tr><td>4</td><td>47.83</td><td>53.49</td><td>71.75</td></tr><tr><td>5</td><td>84.67</td><td>46.26</td><td>96.48</td></tr><tr><td>6</td><td>70.39</td><td>64.39</td><td>95.39</td></tr><tr><td>7</td><td>13.80</td><td>48.60</td><td>50.52</td></tr><tr><td>8</td><td>30.06</td><td>107.13</td><td>111.26</td></tr><tr><td>9</td><td>93.57</td><td>13.42</td><td>94.52</td></tr><tr><td>10</td><td>85.78</td><td>33.48</td><td>92.08</td></tr><tr><td>11</td><td>79.31</td><td>92.29</td><td>121.69</td></tr><tr><td>12</td><td>57.93</td><td>33.63</td><td>66.98</td></tr><tr><td>13</td><td>40.08</td><td>9.53</td><td>41.19</td></tr><tr><td>14</td><td>6.99</td><td>12.68</td><td>14.48</td></tr><tr><td>15</td><td>62.49</td><td>91.49</td><td>110.79</td></tr></tbody></table>
<figure><img src="image_13.png" /><figcaption>Fig. S1. Flowchart of BP neural network algorithm for genetic algorithm optimization.</figcaption></figure>

The structure of BP network includes the number of hidden layers, the number of nodes in the hidden layers, and the transfer function of each layer. Genetic algorithm includes coding method, fitness function, selection, crossover operation and mutation operation.

<figure><img src="image_14.png" /><figcaption>Fig. S2. Random forest training results (Horizontal coordinate error value).</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>Fig. S3. Random forest training results (Vertical coordinate error value).</figcaption></figure>