The HGB and RF results with 10% pressure uncertainty are shown in Figure 10(a) and 10(b), respectively, and in more detail, in Tables 8 and 9, respectively. Generally, the obtained results show that the accuracy of the prediction classification and regression prediction truly is reduced by introducing pressure uncertainty, but not tremendously. When comparing the leak node prediction of the HGB model a considerable drop in precision can be observed when adding the first 5% of uncertainty, specifically more than 15% of accuracy is taken away (see Tables 4 and 6) for the top 1 probability at 1 million input simulations. However, when comparing the drop in accuracy of the model with 5% uncertainty with that of 10% pressure uncertainty, the accuracy is diminished by a negligible amount.
Table 8

Probabilities percentages for top nodes of the HGB model with 10% added uncertainty

Percentages of total inputsTop 1 (%)Top 3 (%)Top 5 (%)Top 10 (%)
60.75 66.62 70.06 74.93 
67.37 72.43 75.58 80.56 
68.87 73.98 77.06 81.98 
10 69.89 74.9 77.90 82.89 
20 69.75 75.21 78.55 83.46 
30 69.82 75.29 78.76 84.06 
50 70.27 75.97 79.48 84.54 
60 70.52 76.21 79.71 84.83 
80 70.40 76.32 79.86 85.01 
100 70.34 76.39 80.10 85.38 
Percentages of total inputsTop 1 (%)Top 3 (%)Top 5 (%)Top 10 (%)
60.75 66.62 70.06 74.93 
67.37 72.43 75.58 80.56 
68.87 73.98 77.06 81.98 
10 69.89 74.9 77.90 82.89 
20 69.75 75.21 78.55 83.46 
30 69.82 75.29 78.76 84.06 
50 70.27 75.97 79.48 84.54 
60 70.52 76.21 79.71 84.83 
80 70.40 76.32 79.86 85.01 
100 70.34 76.39 80.10 85.38 
Table 9

Probabilities percentages for top nodes of the RF model with 10% added uncertainty

Percentages of total inputsTop 1 (%)Top 3 (%)Top 5 (%)Top 10 (%)
8.812 16.68 21.12 30.68 
12.02 20.70 25.97 37.04 
12.51 21.98 27.33 37.70 
10 13.44 22.51 28.69 39.55 
20 14.40 23.59 29.43 40.65 
30 15.09 24.21 29.71 40.51 
50 15.25 24.23 29.99 41.03 
60 15.26 24.19 29.91 40.91 
80 15.40 24.23 29.72 40.77 
100 15.32 24.21 29.83 40.61 
Percentages of total inputsTop 1 (%)Top 3 (%)Top 5 (%)Top 10 (%)
8.812 16.68 21.12 30.68 
12.02 20.70 25.97 37.04 
12.51 21.98 27.33 37.70 
10 13.44 22.51 28.69 39.55 
20 14.40 23.59 29.43 40.65 
30 15.09 24.21 29.71 40.51 
50 15.25 24.23 29.99 41.03 
60 15.26 24.19 29.91 40.91 
80 15.40 24.23 29.72 40.77 
100 15.32 24.21 29.83 40.61 
Figure 9

R2 score validation curve for the (a) HGB model and (b) RF model with 5% added uncertainty for the leak start time.

Figure 9

R2 score validation curve for the (a) HGB model and (b) RF model with 5% added uncertainty for the leak start time.

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