# Pipeline Scour Rates Prediction-Based Model Utilizing a Multilayer Perceptron-Colliding Body Algorithm

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## Abstract

**:**

## 1. Introduction

#### Background

## 2. Material and Methods

#### 2.1. Multilayer Perceptron (MLP)

_{i}is the input variable i, ${\beta}_{j}$ is a bias value, ${\omega}_{ij}$ is connection weight, I is the input layer, and j is in the next level. The activation function is utilized in the MLP model based on the results of Equation (2). Different activation functions can be used in the MLP model; according to previous research, the sigmoid function is used most often. This function can be computed based on Equation (2)

#### 2.2. Colliding Body Optimization

_{i}in the previous group. The initial condition of positions is computed as follows:

#### 2.3. Particle Swarm Optimization (PSO)

_{1}is a random number, r

_{2}is a random number, ${\overrightarrow{P}}_{i}\left(t\right)$ is the best solution gained by the ith particle until the tth iteration, and $\overrightarrow{G}\left(t\right)$ is the best solution obtained by all particles until the th iteration (Figure 4).

#### 2.4. Whale Algorithm (WA)

#### 2.5. Optimization Algorithms for Training MLPs

## 3. Datasets

_{w}, and e

_{m}and the outputs were V*

_{H}, V*

_{L}, V*

_{R}, and V*

_{v}. The data published by [33] were used in this study.

## 4. Discussion and Results

#### 4.1. The Selection of Optimization Algorithm Parameters

#### 4.2. The Statistical Results for Different Soft Computing Models

_{R}* forecast, outputs indicated that the MLP-CBO provided a more accurate estimation of scour rates than those using the V

_{L}*.

_{R}*, V

_{V}*, and V

_{L}*. In addition, the error indices of MAE and PBIAS given by the vertical scour rate are lower than those obtained using the V

_{L}* and V

_{R}*. The MAE value given for forecasting the V

_{R}* was 3.12, while this parameter for estimation of the VL* was 3.18. In the V

_{R}* prediction, outputs indicated that the MLP-WA provided more accurate estimation of scour rates than those using the V

_{L}*.

_{H}* prediction, outputs of statistical parameters showed that the MLP-PSO model provided a more accurate prediction of scour rate (MAE: 0.391, NSE: 0.90, and PBIAS: 0.23 in the testing level) than those obtained using the V

_{R}*, V

_{V}*, and V

_{L}*. Table 3 demonstrates the V

_{V}* with high accuracy in terms of MAE: 0.449, PBIAS: 0.32, and NSE: 0.86 (test level) compared to the V

_{R}* and V

_{L}*. In the V

_{R}* prediction, the results indicate that the MLP-PSO provides a more accurate forecast of scour rates than those obtained using the V

_{L}*.

#### 4.3. Comparison of Soft Computing Models

_{L}* prediction, the suggested MLP-PSO model gave inaccurate results with MAE: 0.742 mm/s, PBIAS: 0.45, and NSE 0.80 (test level) compared with those of the MLP-CBO and MLP-WA models. The error indices given by the MLP-CBO model for the V

_{V}* showed a significantly superior result to those of the MLP-PSO and MLP-WA models. In addition, the results showed that the MLP-WA model provided a better estimation than the MLP-PSO model. In Figure 8, a Taylor diagram was drawn for the final simulation outputs of all the applied computing models using three criteria of RMSE (root mean square error), standard deviation, and correlation. According to the obtained results for V

_{H}*, it can be observed that the obtained results of MLP-CBO model were close to and just below the semicircular zone RMSE < 0.5 and gave higher values of the correlation coefficient. The results indicate that the MLP-CBO model provided better results than the other models. Figure 9 indicates the convergence graph for the different optimization algorithms. The results indicate that the CBO model showed faster convergence in comparison to the other algorithms. However, the MLP-CBO model had more accuracy than the other models. The CBO model could find more accurate values for the weights and biases. Thus, the MLP-CBO model had the least value of error function among all the models. The accuracy level of MLP-CBO was high for all parameters V

_{L}*, V

_{V}*, V

_{H}*, and V

_{R}*. Additionally, the MLP-CBO model had faster performance than the other algorithms because of faster convergence. The general results indicate that all models had a better estimation for V

_{H}* in comparison with parameters V

_{L}*, V

_{V}*, V

_{H}*, and V

_{R}*. It should be noted that all models carried out estimations based on four input datasets while the empirical models need more inputs. Although the ANN models gave more accurate estimations, they ignore the physical interactions in the pipes. The numerical models have to consider more detail for boundary conditions for estimation of scour parameters.

#### 4.4. Comparison Analysis

_{H}* in comparison with those of Equations (28) and (29) (Table 4). Equation (28) was found to be the best model among other equations. Performance of the empirical equations showed lower accuracy in prediction of scour rates in comparison with those of the soft computing models. NSE, PBIAS, and MAE values given by the Equation (29) for the V

_{H}* forecast gave a superior result to the Equation (28) in this case. Performance of the MLP-PSO and MLP WA models showed notably accurate estimation of the score rates compared with the results estimated using the empirical models.

#### 4.5. Parametric Analysis

_{H}*, while Equation (29) overestimated V

_{H}* (Figure 10a). The results indicate that the MLP-CBO model provided higher accuracy of V

_{H}* compared to those of the other models. For $\alpha =0$ and ${K}_{c}=15.8$, the MLP-PSO and MLP-WA models significantly overestimated the V

_{H}*. The MLP-CBO model provided higher accuracy of scour rate estimation in comparison to those of the other models (Figure 10). From Figure 10c, the outputs indicate that MLP-PSO and MLP-WA models could not present an accurate estimation of V

_{H}* for e/B = 0.1. Figure 10d shows that the MLP-PSO and MLP-WA models indicated a downward trend, which overestimated the V

_{H}in comparison to that of the MLP-CBO model.

- 1
- At the beginning, the fitness g (b) and the uncertainty ranges for the parameters are determined, where mean square error has been chosen as the objective function.
- 2
- The Latin hypercube is performed in the range of [b
_{min}, b_{max}], which is initially set to [b_{j}, abs_mean, b_{j}, abs_max]; the corresponding fitness functions are evaluated and the sensitivity matrix J and the parameters covariance matrix C are calculated.

_{L}* prediction, the suggested MLP-CBO model gave inaccurate results with p: 0.97 and d: 0.12 (test level) compared with those of the MLP-PSO and MLP-WA models. In the V

_{R}* forecast, outputs indicated that the MLP-CBO model provided higher p and lower d values than those using the V

_{L}*.

_{R}*, V

_{V}*, V

_{H}*, and V

_{L}* showed very good performance compared with those of the MLP-PSO and MLP-WA models.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ANFIS | Adaptive Neuro Fuzzy Interface System |

ANN | Artificial Neural Network |

BA | Bat Algorithm |

CBO | Colliding Bodies’ Optimization |

FFA | Firefly Algorithm |

FS | Free Spans |

GA | Genetic Algorithm |

GP | Genetic Programming |

MLP | Multilayer Perceptron |

MLP-CBO | Multilayer Perceptron-Colliding Bodies’ Optimization |

MLP-PSO | Multilayer Perceptron-Particle Swarm Optimization |

MLP-WA | Multilayer Perceptron-Whale Algorithm |

PL | Pipe Line |

PSO | Particle Swarm Optimization |

SA | Shark Algorithm |

WA | Whale Algorithm |

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**Figure 1.**Three-dimensional scour process below the pipeline (PL) [18].

**Figure 2.**The MLP structure for the current study (${\beta}_{I}$: bias for the hidden neuron and ${\beta}_{H}$: bias for the output neuron).

**Figure 3.**The structure of the colliding body (CB) algorithm (NFE: Maximum Number of Objective Function Evaluations).

**Figure 4.**The details of the particle swarm optimization (PSO) components including location and velocity of particles.

**Figure 6.**The details of experimental model [33].

**Figure 7.**Structure of a decision variable in the Salp Swarm Algorithm (SSA) including bias and weight.

**Figure 8.**Taylor diagram for soft computing models. Based on correlation, RMSE, and standard deviation for V

_{R}*, V

_{V}*, V

_{L}*, and V

_{H}*.

**Figure 9.**Convergence curve for algorithms using the number of iterations and objective function value.

**Figure 10.**The variation of parameters versus scour rates. (

**a**) $\propto =0,\text{}{K}_{c}=8.7$; (

**b**) $\propto =0,\text{}{K}_{c}=15.8$; (

**c**) $\propto =15,\text{}{K}_{c}=15.8$; (

**d**) $\propto =15,\text{}{K}_{c}=18$.

Parameters | Range |
---|---|

H (m) (input) | 0.13–0.17 |

T (s) (input) | 1.5–2.0 |

U_{w} (m/s) (input) | 0.29–0.45 |

e_{m} (mm) (input) | 5–20 |

V*_{H} (mm/s) (output) | 1.27–5.162 |

V*_{L} (mm/s) (output) | 1.19–4.527 |

V*_{R} (mm/s) (output) | 1.11–4.49 |

V*_{v} (mm/s) (output) | 0.592–2.405 |

${\mathit{\theta}}_{\mathit{w}}$(input) | 0.18–0.30 |

KC (input) | 8.7–18 |

e/B (input) | 0.10–0.40 |

$\mathit{\alpha}$(rad) (input) | 0.0–0.70 |

**Table 2.**(

**a**) The parameter levels and signal-to-noise (S/N) ratio for the PSO, (

**b**) the best parameters for the colliding bodies’ optimization (CBO), and (

**c**) the best parameters for the whale algorithm (WA).

a | ||||

Parameter | Population Size | Inertia Weight | Individual Coefficient | Social Coefficient |

Level 1 | 100, S/N:0.87 | 0.2, S/N:0.21 | 1.6, S/N:0.32 | 1.6, S/N:0.30 |

Level 2 | 200, S/N:0.76 | 0.40, S/N:0.15 | 1.8, S/N:0.54 | 1.8, S/N:0.41 |

Level 3 | 300 S/N:0.82 | 0.60, S/N:0.42 | 2.0, S/N:0.30 | 2.0, S/N:0.24 |

Level 4 | 400, S/N:0.87 | 0.80, S/N:0.55 | 2.2, S/N:0.45 | 2.2, S/N:0.32 |

b | ||||

Parameter | Population Size | |||

Level 1 | 100, S/N:0.84 | |||

Level 2 | 200, S/N:0.96 | |||

Level 3 | 300 S/N:0.83 | |||

Level 4 | 400, S/N:0.87 | |||

c | ||||

WA, population size: 100, the maximum number of iterations: 200 |

**Table 3.**The statistical results for soft computing models. MAE: mean absolute error; PBIAS: percent bias; NSE: Nash–Sutcliff efficiency; MLP: multilayer perceptron.

Model | MAE (mm/s) | PBIAS | NSE |
---|---|---|---|

Train | |||

MLP-CBO (V_{H}*) | 0.345 | 0.12 | 0.95 |

MLP-WA (V_{H}*) | 0.389 | 0.17 | 0.93 |

MLP-PSO (V_{H}*) | 0.393 | 0.22 | 0.92 |

Test | |||

MLP-CBO (V_{H}*) | 0.367 | 0.14 | 0.92 |

MLP-WA (V_{H}*) | 0.379 | 0.19 | 0.91 |

MLP-PSO (V_{H}*) | 0.391 | 0.23 | 0.90 |

Train | |||

MLP-CBO (V_{V}*) | 0.412 | 0.18 | 0.91 |

MLP-WA (V_{V}*) | 0.422 | 0.22 | 0.89 |

MLP-PSO (V_{V}*) | 0.434 | 0.25 | 0.87 |

Test | |||

MLP-CBO (V_{V}*) | 0.416 | 0.20 | 0.90 |

MLP-WA (V_{V}*) | 0.432 | 0.29 | 0.88 |

MLP-PSO (V_{V}*) | 0.449 | 0.32 | 0.86 |

Train | |||

MLP-CBO (V_{R}*) | 0.512 | 0.27 | 0.89 |

MLP-WA (V_{R}*) | 0.522 | 0.32 | 0.87 |

MLP-PSO (V_{R}*) | 0.523 | 0.34 | 0.85 |

Test | |||

MLP-CBO (V_{R}*) | 0.534 | 0.29 | 0.87 |

MLP-WA (V_{R}*) | 0.541 | 0.35 | 0.86 |

MLP-PSO (V_{R}*) | 0.555 | 0.37 | 0.85 |

Train | |||

MLP-CBO (V_{L}*) | 0.612 | 0.31 | 0.86 |

MLP-WA (V_{L}*) | 0.621 | 0.39 | 0.84 |

MLP-PSO (V_{L}*) | 0.629 | 0.42 | 0.83 |

Test | |||

MLP-CBO (V_{L}*) | 0.714 | 0.33 | 0.85 |

MLP-WA (V_{L}*) | 0.738 | 0.42 | 0.82 |

MLP-PSO (V_{L}*) | 0.742 | 0.45 | 0.80 |

MODEL | MAE (MM/S) | PBIAS | NSE |
---|---|---|---|

EQUATION (28) | 1.59 | 0.55 | 0.87 |

EQUATION (29) | 1.34 | 0.52 | 0.86 |

EQUATION (30) | 1.37 | 0.56 | 0.85 |

EQUATION (31) | 1.42 | 0.55 | 0.81 |

EQUATION (32) | 1.45 | 0.54 | 0.80 |

MLP-CBO (VH*) | 0.367 | 0.14 | 0.90 |

MLP-WA (VH*) | 0.391 | 0.23 | 0.89 |

MLP-PSO (VH*) | 0.399 | 0.25 | 0.87 |

MLP-CBO (VL*) | 0.721 | 0.42 | 0.89 |

MLP-WA (VL*) | 0.745 | 0.45 | 0.87 |

MLP-PSO (VL*) | 0.814 | 0.49 | 0.86 |

MLP-CBO (VR*) | 0.621 | 0.32 | 0.85 |

MLP-WA (VR*) | 0.634 | 0.36 | 0.82 |

MLP-PSO (VR*) | 0.642 | 0.38 | 0.80 |

MLP-CBO (VV*) | 0.521 | 0.23 | 0.88 |

MLP-WA (VV*) | 0.555 | 0.25 | 0.89 |

MLP-PSO (VV*) | 0.591 | 0.27 | 0.89 |

**Table 5.**General performance rating for the RMSE-observations standard deviation ratio (RSR) index [35].

Performance Rating | RSR Value |
---|---|

Very Good | 0.00 ≤ RSR ≤ 0.5 |

Good | 0.500 ≤ RSR ≤ 0.600 |

Satisfactory | 0.600 ≤ RSR ≤ 0.700 |

Unsatisfactory | RSR > 0.7 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Ehteram, M.; Ahmed, A.N.; Ling, L.; Fai, C.M.; Latif, S.D.; Afan, H.A.; Banadkooki, F.B.; El-Shafie, A. Pipeline Scour Rates Prediction-Based Model Utilizing a Multilayer Perceptron-Colliding Body Algorithm. *Water* **2020**, *12*, 902.
https://doi.org/10.3390/w12030902

**AMA Style**

Ehteram M, Ahmed AN, Ling L, Fai CM, Latif SD, Afan HA, Banadkooki FB, El-Shafie A. Pipeline Scour Rates Prediction-Based Model Utilizing a Multilayer Perceptron-Colliding Body Algorithm. *Water*. 2020; 12(3):902.
https://doi.org/10.3390/w12030902

**Chicago/Turabian Style**

Ehteram, Mohammad, Ali Najah Ahmed, Lloyd Ling, Chow Ming Fai, Sarmad Dashti Latif, Haitham Abdulmohsin Afan, Fatemeh Barzegari Banadkooki, and Ahmed El-Shafie. 2020. "Pipeline Scour Rates Prediction-Based Model Utilizing a Multilayer Perceptron-Colliding Body Algorithm" *Water* 12, no. 3: 902.
https://doi.org/10.3390/w12030902