Based on the obtained results, the MB4, MS5 and MI3 models are selected as the best models for simulating scour depth for the ski-jump bucket, sharp-crested weir and inclined slope controlled structure cases, respectively. The MB4 model includes four dimensionless parameters, i.e. . Table 6 shows the results of the sensitivity analysis of the GEP and FFNN models. According to the table,
is the most important parameter affecting the scour depth simulation downstream of the ski-jump bucket, while
shows the lowest impact.
Sensitivity analyses of the best data driven models
Omitted variable . | Model . | CC . | R2 . | RMSE . | MAE . |
---|---|---|---|---|---|
Ski-jump bucket (MB4 model) | |||||
| GEP | 0.318 | 0.439 | 0.065 | 0.052 |
FFNN | 0.203 | 0.261 | 0.189 | 0.085 | |
| GEP | 0.411 | 0.457 | 0.064 | 0.045 |
FFNN | 0.535 | 0.581 | 0.060 | 0.039 | |
| GEP | 0.623 | 0.694 | 0.048 | 0.037 |
FFNN | 0.741 | 0.817 | 0.038 | 0.029 | |
| GEP | 0.598 | 0.651 | 0.051 | 0.036 |
FFNN | 0.477 | 0.511 | 0.081 | 0.046 | |
Sharp edge overflow (MS5 model) | |||||
| GEP | 0.224 | 0.304 | 0.273 | 0.159 |
FFNN | 0.345 | 0.567 | 0.207 | 0.146 | |
| GEP | 0.763 | 0.817 | 0.150 | 0.086 |
FFNN | 0.821 | 0.852 | 0.126 | 0.062 | |
| GEP | 0.613 | 0.709 | 0.174 | 0.097 |
FFNN | 0.736 | 0.826 | 0.142 | 0.074 | |
| GEP | 0.588 | 0.649 | 0.191 | 0.111 |
FFNN | 0.711 | 0.771 | 0.163 | 0.086 | |
| GEP | 0.491 | 0.519 | 0.219 | 0.128 |
FFNN | 0.628 | 0.679 | 0.192 | 0.090 | |
Inclined slope controlled structure (MI3 model) | |||||
| GEP | 0.411 | 0.498 | 0.282 | 0.246 |
FFNN | 0.398 | 0.439 | 0.187 | 0.095 | |
| GEP | 0.122 | 0.232 | 0.338 | 0.290 |
FFNN | 0.233 | 0.394 | 0.302 | 0.243 | |
| GEP | 0.321 | 0.413 | 0.298 | 0.232 |
FFNN | 0.285 | 0.382 | 0.306 | 0.237 |
Omitted variable . | Model . | CC . | R2 . | RMSE . | MAE . |
---|---|---|---|---|---|
Ski-jump bucket (MB4 model) | |||||
| GEP | 0.318 | 0.439 | 0.065 | 0.052 |
FFNN | 0.203 | 0.261 | 0.189 | 0.085 | |
| GEP | 0.411 | 0.457 | 0.064 | 0.045 |
FFNN | 0.535 | 0.581 | 0.060 | 0.039 | |
| GEP | 0.623 | 0.694 | 0.048 | 0.037 |
FFNN | 0.741 | 0.817 | 0.038 | 0.029 | |
| GEP | 0.598 | 0.651 | 0.051 | 0.036 |
FFNN | 0.477 | 0.511 | 0.081 | 0.046 | |
Sharp edge overflow (MS5 model) | |||||
| GEP | 0.224 | 0.304 | 0.273 | 0.159 |
FFNN | 0.345 | 0.567 | 0.207 | 0.146 | |
| GEP | 0.763 | 0.817 | 0.150 | 0.086 |
FFNN | 0.821 | 0.852 | 0.126 | 0.062 | |
| GEP | 0.613 | 0.709 | 0.174 | 0.097 |
FFNN | 0.736 | 0.826 | 0.142 | 0.074 | |
| GEP | 0.588 | 0.649 | 0.191 | 0.111 |
FFNN | 0.711 | 0.771 | 0.163 | 0.086 | |
| GEP | 0.491 | 0.519 | 0.219 | 0.128 |
FFNN | 0.628 | 0.679 | 0.192 | 0.090 | |
Inclined slope controlled structure (MI3 model) | |||||
| GEP | 0.411 | 0.498 | 0.282 | 0.246 |
FFNN | 0.398 | 0.439 | 0.187 | 0.095 | |
| GEP | 0.122 | 0.232 | 0.338 | 0.290 |
FFNN | 0.233 | 0.394 | 0.302 | 0.243 | |
| GEP | 0.321 | 0.413 | 0.298 | 0.232 |
FFNN | 0.285 | 0.382 | 0.306 | 0.237 |