# Indirect Analysis of Concrete Slump Using Different Metaheuristic-Empowered Neural Processors

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Data and Modeling Methodology

#### 2.1. Data

#### 2.2. Methodology

#### 2.2.1. Artificial Neural Network

#### 2.2.2. Metaheuristic Optimizers

#### 2.2.3. Hybridization Process

_{p}) in the range (10, 500) were tested for each ensemble. Similar to previous studies, they performed 1000 iterations to minimize the error. The RMSE was set as the objective function to calculate the learning error. The final RMSEs obtained for each algorithm, as well as the computation time, are shown in Table 1. According to this table, the best complexity of the BBO-MLP, SSA-MLP, MFO-MLP, and WDO-MLP is indicated by the N

_{p}s of 300, 100, 100, and 100, respectively. Furthermore, the convergence (i.e., optimization) curves for the elite configurations are shown in Figure 4.

## 3. Results and Discussion

#### 3.1. Accuracy Criteria

^{2}) is used to represent the correlation between the real slumps with forecasted values (see Equation (3)).

_{i predicted}and Z

_{i observed}, respectively. In addition, $\overline{Z}$

_{observed}symbolizes the mean of real slump values.

#### 3.2. Performance Evaluation

^{2}values (0.7479, 0.7202, 0.6472, and 0.6283) show more than 62% correlation for all predictive models.

^{2}values are 0.7157, 0.5793, 0.6748, and 0.6438.

^{2}s of the BBO-MLP and SSA-MLP indicate a lower correlation in the testing phase.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**The graphical description of (

**a**) X1, (

**b**) X2, (

**c**) X3, (

**d**) X4, (

**e**) X5, (

**f**) X6, (

**g**) X7, and (

**h**) Slump.

**Figure 5.**The training results obtained for (

**a**) BBO-MLP, (

**b**) SSA-MLP, (

**c**) MFO-MLP, and (

**d**) WDO-MLP predictions.

**Figure 6.**The testing errors histograms obtained for (

**a**) BBO-MLP, (

**b**) SSA-MLP, (

**c**) MFO-MLP, and (

**d**) WDO-MLP predictions.

**Figure 7.**The correlation of testing samples for (

**a**) BBO-MLP, (

**b**) SSA-MLP, (

**c**) MFO-MLP, and (

**d**) WDO-MLP models.

N_{p} | BBO-MLP | SSA-MLP | MFO-MLP | WDO-MLP | ||||
---|---|---|---|---|---|---|---|---|

RMSE | Time (s) | RMSE | Time (s) | RMSE | Time (s) | RMSE | Time (s) | |

10 | 5.505577 | 139.4756 | 6.355048 | 144.6717 | 5.8897 | 127.0382 | 6.215144 | 127.2421 |

25 | 4.730596 | 347.3891 | 5.748444 | 344.6891 | 5.540889 | 334.6007 | 5.942362 | 324.4255 |

50 | 4.974088 | 690.5993 | 5.569974 | 666.6998 | 5.610954 | 673.13 | 6.144947 | 632.0315 |

75 | 4.858011 | 1031.498 | 5.522838 | 953.5088 | 5.817214 | 1000.989 | 6.133931 | 986.733 |

100 | 4.816898 | 1310.805 | 4.920222 | 1263.715 | 5.530195 | 1255.081 | 5.664862 | 1398.88 |

200 | 4.74319 | 3025.854 | 5.10271 | 2532.209 | 5.815933 | 2505.335 | 6.285705 | 3270.84 |

300 | 4.692921 | 3870.514 | 5.104293 | 3770.992 | 5.728259 | 4225.847 | 6.166536 | 30,623.5 |

400 | 5.043938 | 5170.186 | 5.553021 | 5051.865 | 5.658828 | 5861.167 | 6.11727 | 5550.942 |

500 | 5.061255 | 6856.051 | 4.950267 | 7814.967 | 5.676524 | 6622.55 | 6.178576 | 6720.605 |

Ensemble Models | Network Results | |||||
---|---|---|---|---|---|---|

Training Phase | Testing Phase | |||||

RMSE | MAE | R^{2} | RMSE | MAE | R^{2} | |

BBO-MLP | 4.6929 | 3.6729 | 0.7479 | 3.6399 | 2.9521 | 0.7157 |

SSA-MLP | 4.9202 | 3.8692 | 0.7202 | 3.8572 | 3.0871 | 0.5793 |

MFO-MLP | 5.5302 | 4.3970 | 0.6472 | 3.3309 | 2.3156 | 0.6748 |

WDO-MLP | 5.6649 | 4.6087 | 0.6283 | 3.7540 | 2.8368 | 0.6438 |

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## Share and Cite

**MDPI and ACS Style**

Safayenikoo, H.; Nejati, F.; Nehdi, M.L.
Indirect Analysis of Concrete Slump Using Different Metaheuristic-Empowered Neural Processors. *Sustainability* **2022**, *14*, 10373.
https://doi.org/10.3390/su141610373

**AMA Style**

Safayenikoo H, Nejati F, Nehdi ML.
Indirect Analysis of Concrete Slump Using Different Metaheuristic-Empowered Neural Processors. *Sustainability*. 2022; 14(16):10373.
https://doi.org/10.3390/su141610373

**Chicago/Turabian Style**

Safayenikoo, Hamed, Fatemeh Nejati, and Moncef L. Nehdi.
2022. "Indirect Analysis of Concrete Slump Using Different Metaheuristic-Empowered Neural Processors" *Sustainability* 14, no. 16: 10373.
https://doi.org/10.3390/su141610373