# Open Channel Sluice Gate Scouring Parameters Prediction: Different Scenarios of Dimensional and Non-Dimensional Input Parameters

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## Abstract

**:**

## 1. Introduction

## 2. Laboratory Experiment of Scouring in Sluice Gate

## 3. Description of the Models

#### 3.1. Extreme Learning Machine (ELM) Model

#### 3.2. Multivariate Adaptive Regression Spline

_{1}, x

_{2}, …, x

_{N}), the MARS model estimates the target variable as,

#### 3.3. Model Development

## 4. Results and Discussion

^{2}is always not the measure of best prediction as it is based on linear agreement between the predicted and the observed values.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Flow patterns in the downstream of a sluice gate, (

**a**) water jets along the bed surface, (

**b**) jet rising to the water surface, (

**c**) surface jet [5].

**Figure 2.**(

**a**) Schematic diagram of the experimental setup, (

**b**) Sieve analysis graphs of bed materials.

**Figure 4.**Scatter plots including the least square regression line and the coefficient of determination for the predicted scour-hole characteristics (Ls, Ds, Lsm) obtained using dimensional variables in (

**a**) ELM and (

**b**) MARS models.

**Figure 5.**Scatter plots including the least square regression line and the coefficient of determination for the predicted scour-hole characteristics (Ls, Ds, Lsm) obtained using non-dimensional variables in (

**a**) ELM and (

**b**) MARS models.

**Figure 6.**The relative error distribution percentages during validation of ELM and MARS models using dimensional variables.

**Figure 7.**The relative error distribution percentages during validation of ELM and MARS models using dimensional variables.

Bed Material Samples | Geometric Standard Deviation ${\mathit{\sigma}}_{\mathit{g}}$ | Mean Diameter (mm) ${\mathit{D}}_{50}$ |
---|---|---|

A | 2 | 0.345 |

B | 3.51 | 0.6309 |

C | 3.79 | 1.31 |

**Table 2.**The statistical performance of ELM models during validation period in prediction of $\mathrm{Ls}$, $\mathrm{Ds}$ and $\mathrm{Lsm}$ using dimensional data.

Predicted Value | SI | MAPE | RMSE | MAE | RMSRE | R |
---|---|---|---|---|---|---|

$\mathrm{Ls}$ | 0.0482 | 0.0219 | 0.6611 | 0.2366 | 0.0691 | 0.98 |

$\mathrm{Ds}$ | 0.0961 | 0.0393 | 0.3634 | 0.1430 | 0.0995 | 0.97 |

$\mathrm{Lsm}$ | 0.0349 | 0.0128 | 0.2563 | 0.0871 | 0.0391 | 0.97 |

**Table 3.**The statistical performance of MARS models during validation period in prediction of $\mathrm{Ls}$, $\mathrm{Ds}$ and $\mathrm{Lsm}$ using dimensional data.

Predicted Value | SI | MAPE | RMSE | MAE | RMSRE | R |
---|---|---|---|---|---|---|

$\mathrm{Ls}$ | 0.2760 | 0.0580 | 3.7876 | 0.9721 | 0.2171 | 0.86 |

$\mathrm{Ds}$ | 0.1375 | 0.0454 | 0.5201 | 0.1654 | 0.1420 | 0.77 |

$\mathrm{Lsm}$ | 0.0631 | 0.0223 | 0.4637 | 0.1673 | 0.0589 | 0.90 |

**Table 4.**The statistical performance of ELM models during validation period in prediction of $\mathrm{Ls}$, $\mathrm{Ds}$ and $\mathrm{Lsm}$ using non-dimensional data.

Predicted Value | SI | MAPE | RMSE | MAE | RMSRE | R |
---|---|---|---|---|---|---|

$\mathrm{Ls}$ | 0.0232 | 0.0090 | 0.6724 | 0.2637 | 0.0225 | 0.90 |

$\mathrm{Ds}$ | 0.0249 | 0.0093 | 0.2008 | 0.0742 | 0.0253 | 0.89 |

$\mathrm{Lsm}$ | 0.0230 | 0.0080 | 0.3590 | 0.1257 | 0.0227 | 0.92 |

**Table 5.**The statistical performance of MARS models during validation period in prediction of $\mathrm{Ls}$, $\mathrm{Ds}$ and $\mathrm{Lsm}$ using non-dimensional data.

Predicted Value | SI | MAPE | RMSE | MAE | RMSRE | R |
---|---|---|---|---|---|---|

$\mathrm{Ls}$ | 0.0902 | 0.0312 | 2.6107 | 0.9213 | 0.0867 | 0.71 |

$\mathrm{Ds}$ | 0.1232 | 0.0456 | 0.9925 | 0.3717 | 0.1207 | 0.72 |

$\mathrm{Lsm}$ | 0.0804 | 0.0266 | 1.2525 | 0.4236 | 0.0772 | 0.64 |

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## Share and Cite

**MDPI and ACS Style**

Yousif, A.A.; Sulaiman, S.O.; Diop, L.; Ehteram, M.; Shahid, S.; Al-Ansari, N.; Yaseen, Z.M.
Open Channel Sluice Gate Scouring Parameters Prediction: Different Scenarios of Dimensional and Non-Dimensional Input Parameters. *Water* **2019**, *11*, 353.
https://doi.org/10.3390/w11020353

**AMA Style**

Yousif AA, Sulaiman SO, Diop L, Ehteram M, Shahid S, Al-Ansari N, Yaseen ZM.
Open Channel Sluice Gate Scouring Parameters Prediction: Different Scenarios of Dimensional and Non-Dimensional Input Parameters. *Water*. 2019; 11(2):353.
https://doi.org/10.3390/w11020353

**Chicago/Turabian Style**

Yousif, Ali A., Sadeq Oleiwi Sulaiman, Lamine Diop, Mohammad Ehteram, Shamsuddin Shahid, Nadhir Al-Ansari, and Zaher Mundher Yaseen.
2019. "Open Channel Sluice Gate Scouring Parameters Prediction: Different Scenarios of Dimensional and Non-Dimensional Input Parameters" *Water* 11, no. 2: 353.
https://doi.org/10.3390/w11020353