In Figure 7(a) and 7(b), the top node results for the HGB and RF model with pressure uncertainty are shown. Through the obtained results (which are also presented in Tables 6 and 7), it can be concluded that the model trained with the HGB algorithm greatly outperforms the RF model. When the model training and testing (86 and 14% split) is done with 1 million input data, it is shown that the HGB model has an accuracy (the predicted node being the actual leak node) of around 71%. The decrease in accuracy is noticeable when compared to a less realistic case when no pressure uncertainty is incorporated into the model (as presented in Table 4) when the accuracy is around 86%.
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Table 6
Probabilities percentages for top nodes of the HGB model with 5% added uncertainty
| Percentages of total inputs | Top 1 (%) | Top 3 (%) | Top 5 (%) | Top 10 (%) |
|---|---|---|---|---|
| 1 | 57.68 | 65.75 | 69.37 | 75.75 |
| 3 | 66.60 | 72.35 | 75.62 | 80.39 |
| 5 | 67.82 | 73.25 | 76.61 | 81.61 |
| 10 | 69.38 | 75.06 | 78.46 | 83.63 |
| 20 | 69.52 | 75.14 | 78.48 | 83.90 |
| 30 | 70.30 | 75.85 | 79.45 | 84.5 |
| 50 | 70.87 | 76.69 | 80.39 | 85.67 |
| 60 | 70.78 | 76.66 | 80.39 | 85.72 |
| 80 | 70.63 | 76.62 | 80.37 | 85.76 |
| 100 | 70.98 | 77.06 | 80.80 | 86.05 |
| Percentages of total inputs | Top 1 (%) | Top 3 (%) | Top 5 (%) | Top 10 (%) |
|---|---|---|---|---|
| 1 | 57.68 | 65.75 | 69.37 | 75.75 |
| 3 | 66.60 | 72.35 | 75.62 | 80.39 |
| 5 | 67.82 | 73.25 | 76.61 | 81.61 |
| 10 | 69.38 | 75.06 | 78.46 | 83.63 |
| 20 | 69.52 | 75.14 | 78.48 | 83.90 |
| 30 | 70.30 | 75.85 | 79.45 | 84.5 |
| 50 | 70.87 | 76.69 | 80.39 | 85.67 |
| 60 | 70.78 | 76.66 | 80.39 | 85.72 |
| 80 | 70.63 | 76.62 | 80.37 | 85.76 |
| 100 | 70.98 | 77.06 | 80.80 | 86.05 |
Table 7
Probabilities percentages for top nodes of the RF model with 5% added uncertainty
| Percentages of total inputs | Top 1 (%) | Top 3 (%) | Top 5 (%) | Top 10 (%) |
|---|---|---|---|---|
| 1 | 7.81 | 15.56 | 20.12 | 30.87 |
| 3 | 11.77 | 20.72 | 27.06 | 37.72 |
| 5 | 12.75 | 22.15 | 28.16 | 40.33 |
| 10 | 13.8 | 23.82 | 30.06 | 42.51 |
| 20 | 15.02 | 24.76 | 31.13 | 43.14 |
| 30 | 15.13 | 24.54 | 30.66 | 42.79 |
| 50 | 15.54 | 24.87 | 31.20 | 43.22 |
| 60 | 15.55 | 24.76 | 30.82 | 42.86 |
| 80 | 15.60 | 25.03 | 31.17 | 42.99 |
| 100 | 15.48 | 24.88 | 30.93 | 42.72 |
| Percentages of total inputs | Top 1 (%) | Top 3 (%) | Top 5 (%) | Top 10 (%) |
|---|---|---|---|---|
| 1 | 7.81 | 15.56 | 20.12 | 30.87 |
| 3 | 11.77 | 20.72 | 27.06 | 37.72 |
| 5 | 12.75 | 22.15 | 28.16 | 40.33 |
| 10 | 13.8 | 23.82 | 30.06 | 42.51 |
| 20 | 15.02 | 24.76 | 31.13 | 43.14 |
| 30 | 15.13 | 24.54 | 30.66 | 42.79 |
| 50 | 15.54 | 24.87 | 31.20 | 43.22 |
| 60 | 15.55 | 24.76 | 30.82 | 42.86 |
| 80 | 15.60 | 25.03 | 31.17 | 42.99 |
| 100 | 15.48 | 24.88 | 30.93 | 42.72 |
Figure 6
Stratified KFold cross-validation accuracy mean with standard deviation for (a) HGB model and (b) RF model with no pressure uncertainty added.
Figure 6
Stratified KFold cross-validation accuracy mean with standard deviation for (a) HGB model and (b) RF model with no pressure uncertainty added.