# Estimating Compressive Strength of Concrete Using Neural Electromagnetic Field Optimization

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## Abstract

**:**

## 1. Introduction

^{2}= 0.84 indicated a high accuracy for the proposed model and its superiority over conventional tools such as ANN. Mai et al. [42] were able to enhance the accuracy of the radial basis function ANN using a firefly algorithm (FFA) for predicting the axial compression capacity of concrete-filled steel columns. Two other metaheuristic techniques, namely genetic algorithm (GA) and differential evolution (DE), which were relatively weaker than FFA, were also used. Ma et al. [43] evaluated the efficiency of four metaheuristic optimizers, namely a salp swarm algorithm (SSA), grasshopper optimization algorithm (GOA), artificial bee colony (ABC), and shuffled frog leaping algorithm (SFLA), to tune the ANN for predicting the CCS. Considering the time and accuracy measures, the SSA and GOA were introduced as the strongest algorithms. In this regard, a notable distinction was observed for the correlation between these two algorithms (around 0.97%) and ABC (70.60%) and SFLA (88.90%). The predictive formula of the SSA and GOA was lastly derived. Notably, ABC emerged as a time-consuming technique. The use of the whale optimization algorithm (WOA) for the same purpose (i.e., neural network tuning for the CCS modeling) was recommended by Bui et al. [44]. The dragonfly algorithm and ant colony optimization were two other optimizers that presented a weaker performance relative to the WOA. A hybrid of the random forest and beetle antennae search (BAS) algorithm was proposed by Zhang et al. [45] for simulating the uniaxial compressive strength of oil palm shell concrete. Due to the high correlation (>95%) obtained for the testing process, the suggested model is a reliable and effective approach to the aforementioned simulation.

## 2. Materials and Methods

#### 2.1. Data Provision

^{3}, 74.27 kg/m

^{3}, 62.81 kg/m

^{3}, 182.98 kg/m

^{3}, 6.42 kg/m

^{3}, 964.83 kg/m

^{3}, 770.49 kg/m

^{3}, and 44.06 days, respectively.

#### 2.2. EFO Algorithm

#### 2.3. Benchmarks Optimizers

#### 2.4. Quality Measures

## 3. Results and Discussion

#### 3.1. Optimization and Training Assessment

_{Iter}) and population size (S

_{Pop}) are two important parameters of all metaheuristic algorithms that need to be selected carefully. Both parameters can be completely different for two algorithms, due to the specific behaviors and strategies executed by them. For the EFO, five S

_{Pop}s (25, 30, 35, 40, and 45) were tested, where the N

_{Iter}equals 30,000, while the WCA, SCA, and CFOA were tested using S

_{Pop}s of 100, 200, 300, 400, and 500, with N

_{Iter}= 1000 [69,70]. In this way, the sensitivity of the algorithms to S

_{Pop}can be monitored, and the best network configuration can be selected. Figure 1 shows the convergence curves obtained after this process. According to this figure and based on the error reduction steps, the optimization proceedings of the algorithms are different from each other. The CFOA, for example, reduced the objective function in the initial iterations more effectively, while the SCA reduced it more gently, in several steps, and the EFO and WCA reduced it by following a smooth trajectory.

_{Pop}of 500, 400, 500, and 40 for the WCA, SCA, CFOA, and EFO, respectively. The obtained RMSEs of ANN-WCA, ANN-SCA, ANN-CFOA, and ANN-EFO were 6.8558, 10.0972, 9.9135, and 6.7992. The magnitude of the error was calculated for all 906 training specimens, and their frequencies are depicted in Figure 2. It is shown that all four models have suitable error histograms, meaning that compared to large errors, much larger frequencies can be observed for small errors. This reliability can be also proven by tolerable MAEs 5.2712, 7.9139, 7.6845, and 5.2653, as well as the PCCs of 0.90493, 0.79004, 0.79200, and 0.90659.

#### 3.2. Testing Performance

#### 3.3. Discussion and More Evaluation

## 4. Conclusions

_{Pop}of 40 vs. 500, 400, and 500) for optimizing the ANN. Moreover, despite the EFO being implemented with a N

_{Iter}s 30 times that of other algorithms, it was the fastest algorithm. Therefore, the ANN-EFO may be a potent indirect method for evaluating CCS. Comparisons with some previous studies demonstrated the superiority of the models offered in this work. Additionally, recommendations were presented for practical usages of the models in the concrete and construction industries. However, the authors believe that this work can be built upon by extending the methodologies, optimizing the dataset, and performing cross-validation with real-world concrete data.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

Parameter | Unit | Mean | Standard Error | Standard Deviation | Sample Variance | Skewness | Minimum | Maximum |
---|---|---|---|---|---|---|---|---|

C | kg/m^{3} | 276.50 | 3.07 | 103.47 | 10,706.03 | 0.53 | 102.00 | 540.00 |

${S}_{BF}$ | 74.27 | 2.50 | 84.25 | 7097.52 | 0.77 | 0.00 | 359.40 | |

$F{A}_{1}$ | 62.81 | 2.13 | 71.58 | 5124.15 | 0.61 | 0.00 | 260.00 | |

W | 182.98 | 0.65 | 21.71 | 471.49 | 0.09 | 121.75 | 247.00 | |

SP | 6.42 | 0.17 | 5.80 | 33.60 | 0.84 | 0.00 | 32.20 | |

${A}_{C}$ | 964.83 | 2.46 | 82.79 | 6853.89 | −0.17 | 708.00 | 1145.00 | |

$F{A}_{2}$ | 770.49 | 2.36 | 79.37 | 6300.21 | −0.19 | 594.00 | 992.60 | |

${A}_{T}$ | Day | 44.06 | 1.80 | 60.44 | 3653.15 | 3.47 | 1.00 | 365.00 |

CCS | MPa | 35.84 | 0.48 | 16.10 | 259.23 | 0.42 | 2.33 | 82.60 |

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**Figure 2.**The frequency of errors in the training process (Error = $CC{S}_{{i}_{\mathrm{Laboratory}}}-CC{S}_{{i}_{\mathrm{Estimate}}}$).

**Figure 3.**The trend of errors over the testing dataset (Error =$CC{S}_{{i}_{\mathrm{Laboratory}}}-CC{S}_{{i}_{\mathrm{Estimate}}}$ ).

Training | Testing | |||||||
---|---|---|---|---|---|---|---|---|

ANN-WCA | ANN-SCA | ANN-CFOA | ANN-EFO | ANN-WCA | ANN-SCA | ANN-CFOA | ANN-EFO | |

RMSE | 6.8558 | 10.0972 | 9.9135 | 6.7992 | 7.8044 | 10.0340 | 9.8392 | 7.4595 |

MAE | 5.2712 | 7.9139 | 7.6845 | 5.2653 | 5.8363 | 7.8248 | 7.6538 | 5.6236 |

PCC | 0.90493 | 0.79004 | 0.79200 | 0.90659 | 0.87666 | 0.80249 | 0.79832 | 0.88633 |

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**MDPI and ACS Style**

Akbarzadeh, M.R.; Ghafourian, H.; Anvari, A.; Pourhanasa, R.; Nehdi, M.L.
Estimating Compressive Strength of Concrete Using Neural Electromagnetic Field Optimization. *Materials* **2023**, *16*, 4200.
https://doi.org/10.3390/ma16114200

**AMA Style**

Akbarzadeh MR, Ghafourian H, Anvari A, Pourhanasa R, Nehdi ML.
Estimating Compressive Strength of Concrete Using Neural Electromagnetic Field Optimization. *Materials*. 2023; 16(11):4200.
https://doi.org/10.3390/ma16114200

**Chicago/Turabian Style**

Akbarzadeh, Mohammad Reza, Hossein Ghafourian, Arsalan Anvari, Ramin Pourhanasa, and Moncef L. Nehdi.
2023. "Estimating Compressive Strength of Concrete Using Neural Electromagnetic Field Optimization" *Materials* 16, no. 11: 4200.
https://doi.org/10.3390/ma16114200