# Prediction of Ecofriendly Concrete Compressive Strength Using Gradient Boosting Regression Tree Combined with GridSearchCV Hyperparameter-Optimization Techniques

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## Abstract

**:**

^{2}) between the observed and forecast strengths were used to evaluate the accuracy of the predictive models. The obtained results indicated that—when compared to the default GBRT model—the GridSearchCV approach can capture more hyperparameters for the GBRT prediction model. Furthermore, the robustness and generalization of the GSC-GBRT model produced notable results, with RMSE and R

^{2}values (for the testing phase) of 2.3214 and 0.9612, respectively. The outcomes proved that the suggested GSC-GBRT model is advantageous. Additionally, the significance and contribution of the input factors that affect the compressive strength were explained using the Shapley additive explanation (SHAP) approach.

## 1. Introduction

## 2. Related Works

^{2}, RMSE, and MAE were 0.9729, 4.9585, and 3.9423, respectively. Han et al. [22] created an innovative hybrid model for calculating the Cs of GGBFS concrete and validated the synergistic benefits of the hybrid algorithm over a single algorithm. The new PSO-BP hybrid neural network model outperformed basic ANNs trained by a single method and was shown to be suited for estimating the Cs of GGBFS concrete. Table 1 provides a comprehensive summary of relevant prior work related to predicting the Cs of eco-friendly concrete.

## 3. Research Significance

## 4. Materials and Methods

#### 4.1. Research Methodology

^{2}measurements. The notion of SHAP was finally introduced throughout the interpretation process, and global and local assessments were carried out. The Python 3.7 Scikit-learn software [44] was used to model and tune the GBRT in order to produce GSC-GBRT.

#### 4.2. Gradient Boosting Algorithm

Algorithm 1: gradient boosting. |

1: ${F}_{0}\left(x\right)=\underset{\rho}{\mathrm{arg}\mathrm{min}}{{\displaystyle \sum}}_{i=1}^{N}L\left({y}_{i},\rho \right)$ |

2: For $m=1$ to M do; |

3: ${\tilde{y}}_{i}=-{\left[\frac{\partial L\left({y}_{i},F\left({x}_{i}\right)\right)}{\partial F\left({x}_{i}\right)}\right]}_{F\left(x\right)={F}_{-1}\left(x\right)}$, $i=1,\dots ,N$ |

4: ${a}_{m}=\underset{a,\beta}{\mathrm{arg}\mathrm{min}}{{\displaystyle \sum}}_{i=1}^{N}{\left[{\tilde{y}}_{i}-\beta h\left({x}_{i};\mathit{a}\right)\right]}^{2}$ |

5: ${\rho}_{m}=\underset{\rho}{\mathrm{arg}\mathrm{min}}{{\displaystyle \sum}}_{i=1}^{N}L\left({y}_{i}-{F}_{m-1}\left({x}_{i}\right)+\rho h\left({x}_{i};{a}_{m}\right)\right)$ |

6: ${F}_{m}\left(x\right)={F}_{m-1}\left(x\right)+{\rho}_{m}h\left(x;{a}_{m}\right)$ |

7: End for |

8: End algorithm |

#### 4.3. Gradient Boosting Regression Tree Algorithm (GBRT)

Algorithm 2: GBRT. |

1:${F}_{0}\left(x\right)=\underset{c}{\mathrm{arg}\mathrm{min}}{{\displaystyle \sum}}_{i=1}^{N}L\left({y}_{i},c\right)$ |

2: $m=1$ to M do; |

3: ${r}_{m,i}=-{\left[\frac{\partial L\left({y}_{i},F\left({x}_{i}\right)\right)}{\partial F\left(x\right)}\right]}_{F\left(x\right)={F}_{m-1}\left(x\right)},i=1,\dots ,N$ |

4: ${c}_{m,j}=\underset{c}{\mathrm{arg}m}{\displaystyle \sum}_{{x}_{i}\in {R}_{m,j}}L\left({y}_{i},{F}_{m-1}\left(x\right)+c\right)$ |

5: ${F}_{m}\left(x\right)={F}_{m-1}\left(x\right)+{{\displaystyle \sum}}_{j=1}^{{J}_{m}}{c}_{m,j}I\left(x\in {R}_{m,j}\right)$ |

6: ${F}_{M}\left(x\right)={F}_{0}\left(x\right)+{{\displaystyle \sum}}_{m=1}^{M}{{\displaystyle \sum}}_{j=1}^{{J}_{m}}{c}_{m,j}I\left(x\in {R}_{m,j}\right)$ |

7: End for |

8: End algorithm |

_{0}(x) is set by the GBRT algorithm using the following equation (step 1).

_{m}(x), whose corresponding leaf node area is ${R}_{m,J}$ j = 1, 2, …, J

_{m}, may be calculated as follows (step 5).

#### 4.4. Hyperparameter Tunning with GridSearchCV

#### 4.5. Model Interpretation with the SHAP Method

#### 4.6. Performance Metrics

^{2}), as indicated by Equation (11), was used to evaluate the accuracy of the training and testing datasets for each model.

^{2}, and VAR become closer to 0, 1, and 100, respectively, the accuracy of the model prediction increases.

## 5. Dataset Used

## 6. Model Results

#### 6.1. Hyperparameter Optimization: GridSearchCV

#### 6.2. Comparison of the Prediction Results of the Two Models

^{2}and RMSE values for the GSC-GBRT model were 0.9612 and 2.3214, respectively, whereas they were 0.9216 and 3.4390 for the GBRT model. This demonstrates that, for the eco-friendly concrete dataset used for the prediction procedure of the Cs, GSC-GBRT could better match the complicated connection between the component factors influencing the Cs and had superior generalization capacity.

^{2}was up 31%, and the RMSE was down 62%. R

^{2}increased by 28%, and RMSE dropped by 61% when compared to the M5P model. Overall, the ensemble learning model appears to perform significantly better for the eco-friendly concrete Cs prediction than the traditional machine learning methods.

## 7. Interpretation of the GBRT Model

## 8. Conclusions

^{2}= 0.9612 and RMSE = 2.3214 when compared to the evaluation metrics of the original GBRT model with R

^{2}= 0.9216 and RMSE = 3.4390 for the test set. The suggested GSC-GBRT model surpasses the initial GBRT model in assessment metrics, and it is suggested to be used as a tool for pre-estimating the Cs of concrete using the mix ratio prior to design and mixing.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Correlations between the Cs and the primary concrete components in the dataset, as well as their statistical distributions.

**Figure 4.**Heatmap showing the correlation between the dataset’s Cs, age, and each eco-friendly concrete component.

**Figure 5.**Results of the GSC-GBRT and GBRT models for the testing and training datasets. (

**a**) GBRT training set. (

**b**) GBRT testing set. (

**c**) GSC-GBRT training set. (

**d**) GSC-GBRT testing set.

**Figure 8.**Results of the M5P and linear regression models for the testing and training datasets. (

**a**) M5P training set. (

**b**) M5P testing set. (

**c**) Linear regression training set. (

**d**) Linear regression testing set.

**Figure 9.**The relative importance of each feature and SHAP summary plot: (

**a**) relative importance; (

**b**) SHAP summary plot.

Algorithm Used | Data Points | Reference | Year | R^{2} | RMSE (MPa) | Replacement Material Used | Limitation |
---|---|---|---|---|---|---|---|

Gene Expression Programming (GEP) | 251 | [23] | 2017 | _ | 7.9 | RCA | No GGBFS material included |

M5 model tree (M5) | 156 | [24] | 2020 | _ | 8.3 | RCA | No GGBFS material included |

Multivariate Adaptive Regression Splines (MARS) | 156 | [24] | 2020 | _ | 9.1 | RCA | No GGBFS material included |

Least Squares Support Vector Regression (LSSVR) | 156 | [24] | 2020 | _ | 7.7 | RCA | No GGBFS material included |

convolutional neural network (CNN) | 74 | [25] | 2018 | _ | _ | RCA | No GGBFS material included |

Multiple nonlinear regression (MNR) | 650 | [26] | 2019 | 0.027 | 11.94 | RCA | No GGBFS material included |

imperialist competitive algorithm-extreme gradient boosting (ICA-XGBoost) | 209 | [27] | 2021 | 0.983 | 1.147 | RCA | No GGBFS material included |

imperialist competitive algorithm—adaptive network-based fuzzy inference system (ICA-ANFIS) | 209 | [27] | 2021 | 0.940 | 2.770 | RCA | No GGBFS material included |

imperialist competitive algorithm-Artificial neural network (ICA-ANN) | 209 | [27] | 2021 | 0.960 | 2.225 | RCA | No GGBFS material included |

imperialist competitive algorithm-Support Vector Regression (ICA-SVR) | 209 | [27] | 2021 | 0.962 | 2.149 | RCA | No GGBFS material included |

Backpropagation neural network models (BPNN) | 344 | [28] | 2020 | 0.828 | 6.639 | RCA | No GGBFS material included |

Random Forest (RF) | 453 | [21] | 2021 | 0.946 | 4.958 | GGBFS | No RCA material included |

ANN | 284 | [29] | 2009 | 0.981 | 2.511 | GGBFS | No RCA material included |

ANFIS | 284 | [29] | 2009 | 0.968 | 3.379 | GGBFS | No RCA material included |

Hybridized multiobjective ANN and a multiobjective slap swarm algorithm (MOSSA) | 624 | [30] | 2020 | 0.941 | 2.39 | GGBFS | No RCA material included |

M5P model tree algorithm | 624 | [30] | 2020 | 0.883 | 4.60 | GGBFS | No RCA material included |

ANN model | 269 | [22] | 2019 | 0.961 | 3.332 | GGBFS | No RCA material included |

Data Category | Statistics | Sp (kg) | RA% | Age (days) | W/B | GGBFS% | CS (MPa) |
---|---|---|---|---|---|---|---|

Training data | Standard deviation | 2.12 | 38.22 | 29.52 | 0.10 | 26.14 | 11.52 |

Mean | 1.57 | 58.70 | 34.54 | 0.48 | 33.47 | 33.81 | |

Median | 0.76 | 50.00 | 28.00 | 0.50 | 30.00 | 33.30 | |

Maximum | 7.80 | 100.00 | 90.00 | 0.75 | 90.00 | 65.00 | |

Minimum | 0.00 | 0.00 | 7.00 | 0.25 | 0.00 | 11.00 | |

Kurtosis | 2.56 | −1.48 | −0.30 | 1.34 | −1.14 | −0.49 | |

Testing data | Standard deviation | 2.27 | 38.80 | 31.27 | 0.10 | 24.91 | 11.89 |

Mean | 1.71 | 70.91 | 35.85 | 0.46 | 31.21 | 35.38 | |

Median | 0.76 | 100.00 | 28.00 | 0.50 | 40.00 | 35.28 | |

Maximum | 7.80 | 100.00 | 90.00 | 0.75 | 80.00 | 68.00 | |

Minimum | 0.00 | 0.00 | 7.00 | 0.25 | 0.00 | 12.00 | |

Kurtosis | 2.73 | −0.80 | −0.62 | 1.14 | −1.31 | 0.53 |

Tunning Hyperparameter | Values and Ranges | Optimal Hyperparameters |
---|---|---|

$n$ Estimators | [100, 500, 1000] | 1000 |

Learning Rate | [0.01, 0.05, 0.1, 0.2] | 0.05 |

Max Depth | [4, 6, 8, 10] | 4 |

Subsample | [0.9, 0.5, 0.2, 0.1] | 0.5 |

Sets | Model | RMSE | R^{2} | VAF(%) |
---|---|---|---|---|

Training | GSC-GBRT | 0.2619 | 0.9995 | 99.95 |

GBRT | 1.3273 | 0.9870 | 98.66 | |

Testing | GSC-GBRT | 2.3214 | 0.9612 | 96.07 |

GBRT | 3.4390 | 0.9216 | 91.40 |

**Table 5.**GSC-GBRT, linear regression, and M5P models’ performance in predicting Cs for training and test datasets.

Model | RMSE | R^{2} | VAF(%) |
---|---|---|---|

GSC-GBRT | 2.3214 | 0.9612 | 96.07 |

Linear regression | 6.031 | 0.735 | 73.49 |

M5P | 5.903 | 0.7493 | 74.87 |

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**MDPI and ACS Style**

Alhakeem, Z.M.; Jebur, Y.M.; Henedy, S.N.; Imran, H.; Bernardo, L.F.A.; Hussein, H.M.
Prediction of Ecofriendly Concrete Compressive Strength Using Gradient Boosting Regression Tree Combined with GridSearchCV Hyperparameter-Optimization Techniques. *Materials* **2022**, *15*, 7432.
https://doi.org/10.3390/ma15217432

**AMA Style**

Alhakeem ZM, Jebur YM, Henedy SN, Imran H, Bernardo LFA, Hussein HM.
Prediction of Ecofriendly Concrete Compressive Strength Using Gradient Boosting Regression Tree Combined with GridSearchCV Hyperparameter-Optimization Techniques. *Materials*. 2022; 15(21):7432.
https://doi.org/10.3390/ma15217432

**Chicago/Turabian Style**

Alhakeem, Zaineb M., Yasir Mohammed Jebur, Sadiq N. Henedy, Hamza Imran, Luís F. A. Bernardo, and Hussein M. Hussein.
2022. "Prediction of Ecofriendly Concrete Compressive Strength Using Gradient Boosting Regression Tree Combined with GridSearchCV Hyperparameter-Optimization Techniques" *Materials* 15, no. 21: 7432.
https://doi.org/10.3390/ma15217432