# Random Forest Algorithm for the Strength Prediction of Geopolymer Stabilized Clayey Soil

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## Abstract

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^{2}= 0.9757 for the testing set, respectively, the RF approach showed to provide excellent results for predicting unknown data within the ranges of examined parameters. Finally, the SHapley Additive exPlanations (SHAP) analysis was implemented to identify the most influential inputs and to quantify their behavior of input variables on the UCS.

## 1. Introduction

_{2}) into the atmosphere. OPC production is considered responsible for about 5 to 8% of the total CO

_{2}worldwide emission [12]. This problem has encouraged academics to design building binders that are less environmentally harmful and more sustainable. Geopolymer is a potential substitute for OPC since it is a synthetic alkali aluminosilicate material produced by reacting solid aluminosilicate [13,14] with hydroxide-silicate combination solution or concentrated aqueous alkali hydroxide. Its manufacturing method requires a lower total amount of fuel energy and generates a lower total amount of greenhouse emissions [11,15]. Geopolymers can be produced using a solid aluminosilicate derived from various industrial waste products, including silicate and/or alumina. These materials may be identified by their acronyms, such as ground-granulated blast-furnace slag (GGBS), metakaolin, and fly ash (FA) [16,17,18].

_{2}-e) produced by all processes required to get raw materials, including concrete production. The assumptions depended on the activities involved in producing one cubic meter of Grade 40 concrete (for example, concrete with a compressive strength of 40 MPa) in the Melbourne Metropolitan area, which included the construction practices, manufacturing methods, and use of locally available materials. Sodium hydroxide with 16M concentration was the alkaline activator used in the geopolymers production. The geopolymer concrete emitted about 9% less CO

_{2}than conventional concrete with 100% OPC binder without any additives or replacement materials. This result was significantly lower than what was predicted by previous research. The inclusion of transport, treatment, and mining of raw materials in the manufacturing process of alkali activators for geopolymers, the expense of energy throughout the manufacturing process of alkali activators, and the requirement for higher curing temperatures for geopolymer concrete in order to gain sensible strength were the primary parameters that caused higher than predicted emissions for geopolymer concrete.

^{2}. The study of Nagaraju and Prasad [37] examined the effectiveness of the particle swarm optimization (PSO) method in forecasting the 28-day UCS of expansive blended clays that have been alkali-activated. An accurate estimate using PSO is still achievable with the minimal experimental data currently available. Gullu [38] used several AI techniques to predict the UCS of soil stabilized with steel, jute fiber, and ash. A strong correlation between the AI algorithms employed and the estimated UCS value was indicated by the outcomes. Mathematical modeling for the UCS values of coal-grout composites was also conducted in [39] by using six ML models. SVM, decision trees (DT), and back-propagation neural network (BPNN) outperformed other models. Several studies highlighted the benefits concerning ML and AI techniques in the areas of road pavements as well as geotechnical engineering [40,41,42,43,44].

## 2. Materials and Methods

#### 2.1. Research Methodology

#### 2.2. Decision Tree

- Start with the root node, which includes all of the cases.
- One of the predictors, ${X}_{j}$, is subjected to a test at each of the tree’s internal nodes.
- Observations are placed into the tree right or left sub-region (branch), depending on how the test turns out.
- In order to make a prediction, keep going back to Step 3 until a terminal leaf or node is reached.

#### 2.3. Random Forests (RF)

- For $b=1$ to $B$:
- From the training data, draw a bootstrap sample with size N.
- The following steps should be repeated recursively for each terminal node of the tree, until the minimum node size ${n}_{min}$ is attained to grow a RF tree ${T}_{b}$ according to the bootstrapped data.
- From the total $p$ variables, choose $m$ variables randomly.
- Among the $m$ variables, choose the best one.
- Generate two subregions by splitting the node.

- Output the ensemble of trees, ${\left\{{T}_{b}\right\}}_{i},i=1,2,\dots ,B$.

#### 2.4. Tuning RF Hyperparameters Using GridSearchCV

^{2}is the most used statistical metric to evaluate models in regression issues. This study used R

^{2}to evaluate the RF predictive performance and goodness of fit together with the RMSE. The GridSearchCV yields the best RF estimator by averaging the R

^{2}scores of the test folds that were left out during the training process.

#### 2.5. Performance Metrics

^{2}[58], which ranges from 0 to 1. The closer to 1 this metric is, the more accurate the forecast. The following equation is used to compute R

^{2}.

## 3. Database Used

## 4. Model Result

#### 4.1. Hyperparameter Optimization: GridSearchCV

^{2}. The models started to overfit when there were more than five predictors. More predictors in a model tend to increase the risk of overfitting the data due to the curse of dimensionality. Additionally, a simpler model lowers the cost of computation. Consequently, 500 trees and five predictors were used to create the final RF model.

#### 4.2. Evaluation of RF Model

^{2}= 0.9949 in the training group. However, the performance of the test set is slightly lower than the one of the training set, with RMSE = 0.9815 and R

^{2}= 09757. A lower R

^{2}generally indicates overfitting in the testing set. However, this is not a significant issue for the RF model study, given the high R

^{2}and low RMSE values that were attained. The RF method uses several regression trees and sets of input variables at random to uncover internal relationships between features. The randomness significantly enhances the resilience of the model. Because it splits at nodes, the RF model’s regression trees can be considered an ensemble approach. Then, the RF model combines such functions to avoid having a lot of variation in a single tree.

#### 4.3. Comparison between RF with Linear Regression

^{2}values from the ridge regression model for both the testing and training sets are 0.7121 and 0.8379, respectively, as shown in Figure 5. A lower R

^{2}value indicates underfitting and suggests that the model cannot adequately account for data variance [49]. In comparison to the RF, the ridge regression performed significantly poorer. This is most likely due to the linear regression model’s inability to handle the UCS and variable nonlinearity.

#### 4.4. Comparison between RF with Previously Developed Models

^{2}, demonstrating that it is the most efficient and robust model. Figure 7 displays the absolute error for the UCS prediction versus the cumulative frequency of the proposed and pre-existing models. The proposed model (RF) predicts the UCS of 70% of the data with an absolute error of fewer than 0.4 MPa and 80% with an absolute error of fewer than 0.57 MPa. On the other hand, the proposed model in this study predicted only 10% of the experimental data with an absolute error higher than 0.93 MPa. The model from Soleimani et al. [34] (MGGP eq.), which was the second most precise model, correctly predicted 14% of the experimental data and 21% of the UCS measurements with absolute relative errors lower than 0.4 MPa and 0.57 MPa, respectively.

## 5. SHAP Analysis

## 6. Conclusions

- The suggested RF model showed a high coefficient of determination of 0.9757 on the test set, indicating that it is highly accurate in forecasting. Additionally, no overfitting was generated, as concluded by the extremely low RMSE values on the training and testing sets.
- The generated model capacity to predict outcomes was contrasted with the one generated by previously proposed models in [34] and [59], which were: multivariable regression model (MLSR), multi-gen genetic programming (MGGP), and multivariable regression (MVR). According to the statistical analysis, the suggested RF model outperformed the current white-box models regarding relative errors and determination coefficients.
- Shap analysis was used to demonstrate the implemented RF’s strong integrity and reliability.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Statistics | (PI) (%) | S (%) | FA(%) | (M) (mol/L) | (A/B) | (Na/Al) | (Si/Al) | UCS (MPa) |
---|---|---|---|---|---|---|---|---|

Standard deviation | 30.73 | 12.92 | 4.66 | 2.73 | 0.14 | 0.44 | 0.35 | 6.49 |

Mean | 38.83 | 15.90 | 2.12 | 12.42 | 0.62 | 1.17 | 1.70 | 5.77 |

Median | 14.07 | 16.00 | 0.00 | 12.00 | 0.65 | 1.18 | 1.49 | 2.91 |

Maximum | 88.46 | 50.00 | 20.00 | 15.00 | 0.85 | 1.98 | 2.49 | 24.26 |

Minimum | 14.07 | 0.00 | 0.00 | 4.00 | 0.45 | 0.24 | 1.49 | 0.00 |

Kurtosis | −1.28 | 0.30 | 4.97 | 2.57 | −1.03 | −0.62 | 0.36 | −0.47 |

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## Share and Cite

**MDPI and ACS Style**

Zeini, H.A.; Al-Jeznawi, D.; Imran, H.; Bernardo, L.F.A.; Al-Khafaji, Z.; Ostrowski, K.A.
Random Forest Algorithm for the Strength Prediction of Geopolymer Stabilized Clayey Soil. *Sustainability* **2023**, *15*, 1408.
https://doi.org/10.3390/su15021408

**AMA Style**

Zeini HA, Al-Jeznawi D, Imran H, Bernardo LFA, Al-Khafaji Z, Ostrowski KA.
Random Forest Algorithm for the Strength Prediction of Geopolymer Stabilized Clayey Soil. *Sustainability*. 2023; 15(2):1408.
https://doi.org/10.3390/su15021408

**Chicago/Turabian Style**

Zeini, Husein Ali, Duaa Al-Jeznawi, Hamza Imran, Luís Filipe Almeida Bernardo, Zainab Al-Khafaji, and Krzysztof Adam Ostrowski.
2023. "Random Forest Algorithm for the Strength Prediction of Geopolymer Stabilized Clayey Soil" *Sustainability* 15, no. 2: 1408.
https://doi.org/10.3390/su15021408