# Non-Tuned Machine Learning Approach for Predicting the Compressive Strength of High-Performance Concrete

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Dataset

## 3. Methods

#### 3.1. Extreme Learning Machine

**T**is the target matrix of the training data:

**H**[38], which can be computed using different methods such as orthogonal projection method and singular value decomposition (SVD) [39]. If $\mathbf{H}{\mathbf{H}}^{T}$ is nonsingular, the orthogonal projection method computes ${\mathbf{H}}^{\u2020}$ as ${\mathbf{H}}^{T}{\left(\mathbf{H}{\mathbf{H}}^{T}\right)}^{-1}$; otherwise, ${\mathbf{H}}^{\u2020}$ = ${\left({\mathbf{H}}^{T}\mathbf{H}\right)}^{-1}{\mathbf{H}}^{T}$ when ${\mathbf{H}}^{T}\mathbf{H}$ is nonsingular [40].

#### 3.2. Regularized Extreme Learning Machine

Algorithm 1: Regularized extreme learning machine (RELM) Algorithm |

## 4. Experimental Setting

#### Performance-Evaluation Measures and Cross Validation

## 5. Results and Discussion

## 6. Conclusions

- Although the ELM model achieves good generalization performance (R = 0.929 on average), the RELM model performs even better.
- This research confirms that the use of regularization in ELM could prevent overfitting and improve the accuracy in estimating the HPC compressive strength.
- The RELM model can estimate the HPC compressive strength with higher accuracy than the ensemble methods presented in the literature.
- The proposed RELM model is simple, easy to implement, and has a strong potential for accurate estimation of HPC compressive strength.
- This work provides insights into the advantages of using ELM-based methods for predicting the compressive strength of concrete.
- The prediction performance of the ELM-based models can be improved by optimizing the initial input weights using optimization techniques such as harmony search, differential evolution, or other evolutionary methods.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 5.**Average root mean squared error (RMSE) values of the RELM method with different network architectures.

**Figure 6.**Average Pearson correlation coefficient (R) values of the RELM method with different network architectures.

Variable | Minimum | Maximum | Average | Standard Deviation |
---|---|---|---|---|

C (kg/m${}^{3}$) | 102.00 | 540.00 | 276.51 | 103.47 |

B (kg/m${}^{3}$) | 0.00 | 359.40 | 74.27 | 84.25 |

F (kg/m${}^{3}$) | 0.00 | 260.00 | 62.81 | 71.58 |

W (kg/m${}^{3}$) | 121.80 | 247.00 | 182.99 | 21.71 |

S (kg/m${}^{3}$) | 0.00 | 32.20 | 6.42 | 5.80 |

CA (kg/m${}^{3}$) | 708.00 | 1145.00 | 964.83 | 82.79 |

FA (kg/m${}^{3}$) | 594.00 | 992.60 | 770.49 | 79.37 |

A (Days) | 1.00 | 365.00 | 44.06 | 60.44 |

CS (MPa) | 2.33 | 82.60 | 35.84 | 16.10 |

Variable | C | B | F | W | S | CA | FA | A |
---|---|---|---|---|---|---|---|---|

C | 1.0000 | −0.2728 | −0.4204 | −0.0890 | 0.0674 | −0.0730 | −0.1859 | 0.0906 |

B | −0.2728 | 1.0000 | −0.2889 | 0.0995 | 0.0527 | −0.2681 | −0.2760 | −0.0442 |

F | −0.4204 | −0.2889 | 1.0000 | −0.1508 | 0.3528 | −0.1055 | −0.0062 | −0.1631 |

W | −0.0890 | 0.0995 | −0.1508 | 1.0000 | −0.5882 | −0.2708 | −0.4247 | 0.2420 |

S | 0.0674 | 0.0527 | 0.3528 | −0.5882 | 1.0000 | −0.2747 | 0.1985 | −0.1984 |

CA | −0.0730 | −0.2681 | −0.1055 | −0.2708 | −0.2747 | 1.0000 | −0.1534 | 0.0233 |

FA | −0.1859 | −0.2760 | −0.0062 | −0.4247 | 0.1985 | −0.1534 | 1.0000 | −0.1394 |

A | 0.0906 | −0.0442 | −0.1631 | 0.2420 | −0.1984 | 0.0233 | −0.1394 | 1.0000 |

Model | Dataset | RMSE (MPa) | MAE (MPa) | MAPE (%) | R |
---|---|---|---|---|---|

ELM | Training data | 4.1846 | 3.2062 | 11.3922 | 0.9656 |

Testing data | 6.0377 | 4.4419 | 15.2558 | 0.929 | |

All data | 4.4087 | 3.3298 | 11.7787 | 0.9617 | |

RELM | Training data | 3.6737 | 2.7356 | 9.74 | 0.9736 |

Testing data | 5.5075 | 3.9745 | 13.467 | 0.9403 | |

All data | 3.8984 | 2.8595 | 10.1125 | 0.9702 |

Model | Training Data | Testing Data | All Data |
---|---|---|---|

ELM | 0.1001 | 0.6739 | 0.1401 |

RELM | 0.0405 | 0.5054 | 0.0771 |

**Table 5.**Generalization performance comparison of ELM, RELM, and other methods presented in [3].

Method | Testing Data | |||
---|---|---|---|---|

RMSE (MPa) | MAE (MPa) | MAPE (%) | R | |

ELM | 6.0377 | 4.4419 | 15.2558 | 0.929 |

RELM | 5.5075 | 3.9745 | 13.467 | 0.9403 |

Individual methods [3]: | ||||

ANN | 6.329 | 4.421 | 15.3 | 0.930 |

CART | 9.703 | 6.815 | 24.1 | 0.840 |

CHAID | 8.983 | 6.088 | 20.7 | 0.861 |

LR | 11.243 | 7.867 | 29.9 | 0.779 |

GENLIN | 11.375 | 7.867 | 29.9 | 0.779 |

SVM | 6.911 | 4.764 | 17.3 | 0.923 |

Ensemble methods [3]: | ||||

ANN + CHAID | 7.028 | 4.668 | 16.2 | 0.922 |

ANN + SVM | 6.174 | 4.236 | 15.2 | 0.939 |

CHAID + SVM | 6.692 | 4.580 | 16.3 | 0.929 |

ANN + SVM + CHAID | 6.231 | 4.279 | 15.2 | 0.939 |

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**MDPI and ACS Style**

Al-Shamiri, A.K.; Yuan, T.-F.; Kim, J.H. Non-Tuned Machine Learning Approach for Predicting the Compressive Strength of High-Performance Concrete. *Materials* **2020**, *13*, 1023.
https://doi.org/10.3390/ma13051023

**AMA Style**

Al-Shamiri AK, Yuan T-F, Kim JH. Non-Tuned Machine Learning Approach for Predicting the Compressive Strength of High-Performance Concrete. *Materials*. 2020; 13(5):1023.
https://doi.org/10.3390/ma13051023

**Chicago/Turabian Style**

Al-Shamiri, Abobakr Khalil, Tian-Feng Yuan, and Joong Hoon Kim. 2020. "Non-Tuned Machine Learning Approach for Predicting the Compressive Strength of High-Performance Concrete" *Materials* 13, no. 5: 1023.
https://doi.org/10.3390/ma13051023