# Compressive Strength Estimation of Geopolymer Composites through Novel Computational Approaches

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## Abstract

**:**

_{2}SiO

_{3}/NaOH ratio, NaOH molarity, aggregate volume, superplasticizer, and water, with CS as the output variable. Four types of ML models were employed to anticipate the compressive strength of geopolymer concrete, and their performance was compared to find out the most accurate ML model. Two individual ML techniques, support vector machine and multi-layer perceptron neural network, and two ensembled ML methods, AdaBoost regressor and random forest, were employed to achieve the study’s aims. The performance of all models was confirmed using statistical analysis, k-fold evaluation, and correlation coefficient (R

^{2}). Moreover, the divergence of the estimated outcomes from those of the experimental results was noted to check the accuracy of the models. It was discovered that ensembled ML models estimated the compressive strength of the geopolymer concrete with higher precision than individual ML models, with random forest having the highest accuracy. Using these computational strategies will accelerate the application of construction materials by decreasing the experimental efforts.

## 1. Introduction

_{2}) and nitrogen oxide (NO) pollutants are released [11]. With over two billion tons of GHGs emitted yearly as a result of cement manufacture, cement production accounts for approximately 6% of global anthropogenic GHG emissions [12,13,14]. The extensive use of natural raw materials in the manufacture of cement has also resulted in the overexploitation of natural resource reserves, resulting in a degradation of the aesthetics of the environment and the modification of ecosystems [15,16]. Apart from the substantial GHG emissions associated with cement manufacture, the process is extremely energy demanding [17,18]. Recent urbanization, particularly in developing nations, has exacerbated the negative environmental effect of cement manufacturing [19]. As a result, it is critical that sustainable alternatives to cement be utilized in building applications in order to preserve the environment’s sustainability [20,21]. Numerous waste products created by various sectors can be utilized as sustainable substitutes for the traditional resources used in the cement manufacturing process. As a result, the utilization of such wastes in the manufacturing of a sustainable alternative to cement would result in a considerable decrease in GHG emissions, the cost of raw materials, and the use of natural raw resources connected with cement [22]. Materials that have been activated with alkali, such as geopolymers, may be preferred to conventional cement concrete [23,24,25].

_{2}emissions, and low energy consumption [31,32]. These features are intimately connected to the chemical interactions between aluminosilicate and alkali-polysialate [33]. The use of geopolymer concrete (GeoPC) in place of conventional cement concrete results in an embodied carbon reduction of up to 80%, depending on the precursor and activator utilized [34]. GeoPC is mostly composed of waste materials from various industrial and agricultural activities. GeoPC may be considered more ecologically friendly and an efficient method of managing enormous amounts of waste created by industries [35,36,37]. The utilization of locally accessible materials as precursors, such as laterite soil, can help increase the sustainability of GeoPCs [11]. Thus, by utilizing geopolymers as a sustainable alternative to cement, GHG emissions, raw material consumption, and waste management costs would be significantly reduced [38,39,40].

^{2}). Furthermore, k-fold analysis and error distributions were used to determine the validity of each technique. SVM and MLPNN are individual ML techniques, while AR and RF are ensemble ML methods [52]. This study is interesting in that it predicts the C-S of GeoPC utilizing both individual and ensemble ML techniques. However, experimental studies require considerable human effort, the cost for experimentation, and time for material collection, sample casting, curing, and testing. The application of novel methods, such as ML, in the construction field to anticipate material characteristics will decrease the aforesaid issues by obviating the need for experimental work. ML methods need a data set, which may be collected from the past studies since a considerable amount of investigation has been undertaken to determine material characteristics, and the data set might be utilized for training the ML models and forecasting the material properties. The purpose of this work is to ascertain the top appropriate ML method for the C-S estimation of GeoPC based on the results estimation and the effect of input variables on ML model performance.

## 2. Data Description

_{2}SiO

_{3}–NaOH solution, respectively. Nine input parameters were employed to run the models, including curing temperature, curing time, specimen age, alkali/fly ash ratio, Na

_{2}SiO

_{3}/NaOH ratio, NaOH molarity, aggregate volume, superplasticizer, and water, with C-S as the output variable. In the present research, a data set of 481 points was utilized for the outcome prediction using ML methods. The quantity of input parameters and data sets have a considerable impact on the technique’s results [54]. According to prior research, a minimum of 300 data points and eight input variables can result in increased precision for ML models [55,56]. As a result, the data set acquired for this research is optimal for the ML model’s performance. Table 1 lists the descriptive statistical analysis of all input variables. The mode, median, and mean values correspond to central propensity, while the standard deviation, minimum, and maximum values correspond to irregularity. Figure 1 depicts the dispersion of input parameters utilized in the research in terms of their relative incidence. It illustrates the overall number of observations linked to each value or sequence of values.

## 3. Machine Learning Methods Employed

^{2}value for the expected outcome indicates the performance/validity of ML methods. The R

^{2}is a statistic that is used to estimate the degree of variation in a response variable specified by a model. In other words, it quantifies the model’s fit to the data. A value close to zero suggests that fitting the mean is similar to fitting the model, whereas a value near one indicates that the date and model are virtually perfectly suited [59]. The data are split: 20% for testing and 80% for training the ML models. The sub-segments underneath describe the ML approaches used in this study. Furthermore, k-fold evaluation, statistical checks, and error measurements (root mean square error (RMSE) and mean absolute error (MAE)) is performed on all ML methods to validate them. In addition, sensitivity analysis (SA) is carried out to find out the influence of every input variable on the results anticipation. The flow diagram in Figure 2 describes the research technique followed in the present study.

#### 3.1. Support Vector Machine

#### 3.2. Multi-Layer Perceptron Neural Network

#### 3.3. AdaBoost Regressor

#### 3.4. Random Forest

## 4. Results and Discussions

#### 4.1. Support Vector Machine Model

^{2}of 0.78 confirms that the SVM model has a lower degree of accuracy in anticipating the C-S of GeoPC. Figure 9 demonstrates the dispersion of experimental, anticipated, and error values for the SVM model for testing data alone, which is 20% of the overall data set. The analysis of the experimental and estimated values discovered that the divergence of outcomes (error) was in the limit of 0.00 to 47.0 MPa, with an average of 7.72 MPa. Moreover, for 8 mixes, the divergence from the experimental results was lower than 1 MPa; for 17 mixes, the divergence was between 1 and 3 MPa; for 21 mixes, the divergence was between 3 and 6 MPa; and for 45 mixes, the variance was greater than 6 MPa. This indicated a higher deviation from the projected findings for the SVM model compared to the experimental results. Thus, the SVM technique is less accurate in anticipating the C-S of GeoPC.

#### 4.2. Multi-Layer Perceptron Neural Network Model

^{2}of 0.81 suggesting that the MLPNN model is more specific than the SVM model in estimating the GeoPC C-S. Figure 11 illustrates the distribution of experimental, estimated, and error values for the MLPNN model. The variation between experimental and estimated values was found to be between 0.06 and 22.77 MPa, with an average of 5.86 MPa. Additionally, the variation from the experimental results was lower than 1 MPa for 10 mixes, between 1 and 3 MPa for 25 mixes, between 3 and 6 MPa for 23 mixes, and greater than 6 MPa for 39 mixes. This also indicates a greater divergence of the MLPNN model’s predicted outcomes when compared to the experimental results. Therefore, the MLPNN technique is also less accurate at predicting GeoPC’s C-S, but slightly more accurate than the SVM model.

#### 4.3. AdaBoost Regressor Model

^{2}of 0.89 indicates that the AR model is reasonably precise at predicting the C-S of GeoPC. The dispersal of the experimental, anticipated, and error readings for the BR model are shown in Figure 13. The difference (error) between the experimental and estimated values ranged from 0.00 to 22.80 MPa, with a mean of 4.03 MPa. Furthermore, for 18 mixes, the variation from the experimental outcomes was lower than 1 MPa; for 26 mixes, it was between 1 and 3 MPa; for 32 mixes, it was between 3 and 6 MPa; and for only 21 mixes it was larger than 6 MPa. When compared to the experimental data, the AR model’s outcomes showed minimal divergence and higher precision, because this technique uses the training data to build a weak learner and then trains it by altering the dispersal of the training data until it forms a strong learner.

#### 4.4. Random Forest Model

^{2}value of 0.95 specifies that the RF model performs with the highest precision compared to the other models employed in this study. Figure 15 exemplifies the scattering of experimental, projected, and error values for the RF model. The variation (error) between the experimental and estimated values was found to be between 0.05 and 14.99 MPa, with an average of 2.34 MPa. In addition, the variation from the experimental outcomes was lower than 1 MPa for 38 mixes, between 1 and 3 MPa for 29 mixes, between 3 and 6 MPa for 24 mixes, and greater than 6 MPa for only 6 mixes. This indicates a smaller variation between the experimental and predicted outcomes. Therefore, the RF technique is more suitable, demonstrating the highest precision in estimating the C-S of GeoPC.

## 5. Model’s Validation

^{2}values suggest the higher precision of a model [69]. Moreover, the process must be repeated 10 times to obtain a suitable decision. This broad endeavor provides the notable precision of a model. Moreover, as displayed in Table 2, each ML method was statistically assessed based on errors (MAE and RMSE). These evaluations also supported the ensemble ML model’s greater precision in comparison to the individual techniques, owing to its lower error readings. The projecting accuracy of the models was ascertained statistically through Equations (1) and (2), taken from previous work [55,74,75].

_{i}= experimental values, and P

_{i}= predicted values.

^{2}, MAE, and RMSE were calculated, and the resulting values for the SVM, MLPNN, AR, and RF techniques are summarized in Table 3. To compare the MAE values for all of the models from the k-fold analysis, Figure 16 was generated. The MAE values for the SVM model were in the range of 6.72 to 14.26 MPa, with an average of 10.53 MPa. The same values for the MLPNN model were between 5.86 and 13.79 MPa, with an average of 9.39 MPa. Additionally, for the AR method, these values were between 4.03 and 11.94 MPa, with an average of 8.20 MPa. The MAE values for the RF model were in the range of 2.34 to 11.10 MPa, with an average of 6.90 MPa. This analysis validated the higher accuracy of ensemble ML models, with the RF model having the lowest error/deviation from the experimental results. This was further confirmed by the results of RMSE, as depicted in Figure 17. The average RMSE value for the SVM, MLPNN, AR, and RF models was 13.29, 11.08, 9.91, and 7.97, respectively. The results of R

^{2}from the k-fold analysis were compared and are presented in Figure 18. It was determined that the RF model has higher R

^{2}values with an average of 0.71, compared to the other models, which yielded an average R

^{2}of 0.42, 0.49, and 0.62 for the SVM, MLPNN, and AR models, respectively. The RF model with smaller deviations from the experimental results and higher R

^{2}values outperformed the other models in estimating the C-S of GeoPC. Hence, this analysis suggests the use of an RF model for this purpose.

## 6. Sensitivity Analysis

_{2}SiO

_{3}/NaOH ratio, and aggregate volume, had a contribution of 12.5%, 9.4%, 4.8%, 4.2%, 4.1%, and 3.9%, respectively. SA revealed relationships between the quantity of input factors and the data points used to build the ML models. The impact of input parameters on the ML model’s results was ascertained using Equations (3) and (4).

_{i}is the attained impact percentage for the specific input parameter.

## 7. Discussions

_{2}emissions, better material properties, and green construction materials [27].

^{2}of 0.95, compared to the AR, MLPNN, and SVM models, which yielded R

^{2}of 0.89, 0.81, and 0.78, respectively. Furthermore, all models’ performance was confirmed by k-fold and statistical analysis techniques. The fewer errors in the model, the more precise it is. However, establishing and suggesting the ideal ML method for forecasting outcomes across a number of areas is challenging, since any model’s performance is highly dependent on the input parameters and data set utilized to execute the algorithm. Ensembled ML methods frequently make use of the weak learner by building sub-models that may be trained on data and tweaked to maximize the R

^{2}value.

^{2}values for the AR and RF sub-models is represented in Figure 20. The lowest, average, and maximum R

^{2}values for AR sub-models were 0.811, 0.864, and 0.892, respectively. The lowest, average, and maximum R

^{2}values for RF sub-models were 0.938, 0.947, and 0.952, respectively. These figures indicate the superior exactness of the RF method in comparison to the AR in estimating the C-S of GeoPC. Other researchers have also observed that the AR and RF models are more accurate in predicting outcomes [68,77,78]. Feng et al. [68] observed that the AR model outperformed individual models, including ANN and SVM, in terms of R

^{2}and error values. Likewise, Farooq et al. [78] assessed the accuracy of RF with that of the decision tree, gene expression programming, and artificial neural network methods and found that the RF model had a greater precision than the others, with an R

^{2}of 0.96.

## 8. Conclusions

- Ensemble ML methods (AR and RF) outperformed individual ML techniques (SVM and MLPNN) in forecasting the C-S of GeoPC, with the RF model performing with the highest accuracy. The correlation coefficients (R
^{2}) were 0.95, 0.89, 0.81, and 0.78 for RF, AR, MLPNN, and SVM models, respectively. - The comparison of experimental and anticipated results verified the AR and RF models’ superior accuracy, as the projected values deviated less from the experimental values. On the other hand, the MLPNN and SVM model results deviated more from the experimental results, making them less suitable for predicting the C-S of GeoPC.
- Statistical analysis and k-fold evaluation were used to validate the model performance. These evaluations validated the RF model’s superior accuracy. The ensembled models’ decreased deviation (MAE and RMSE) and higher R
^{2}values supported their increased accuracy over individual models. - Sensitivity analysis discovered that curing time, curing temperature, and specimen age were the most significant elements influencing the ML model’s performance in predicting GeoPC’s C-S, accounting for 22.5%, 20.1%, and 18.5%, respectively. The other input variables, including superplasticizer, NaOH molarity, water, alkali/fly ash ratio, Na
_{2}SiO_{3}/NaOH ratio, and aggregate volume, contributed 12.5%, 9.4%, 4.8%, 4.2%, 4.1%, and 3.9%, respectively. - This kind of study will benefit the construction industry by allowing for the progress of rapid and cost-efficient strategies for estimating the strength of materials. Moreover, by applying these methods to encourage eco-responsive construction, the acceptance and usage of GeoPC in the building sector will be enhanced.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Support vector machine model mapping. Reprinted/adapted with permission from [60].

**Figure 5.**Sequence of a multi-layer perceptron neural network modeling process. Reprinted/adapted with permission from [67].

**Figure 6.**Sequence of AdaBoost regressor modeling process [69].

**Figure 7.**Sequence of random forest modeling process. Reprinted/adapted with permission from [70].

**Figure 8.**Relationship between experimental and estimated results for the support vector machine model.

**Figure 9.**Distribution of experimental, estimated, and error values for the support vector machine model.

**Figure 10.**Relationship between experimental and estimated results for the multi-layer perceptron neural network model.

**Figure 11.**Distribution of experimental, estimated, and error values for the multi-layer perceptron neural network model.

**Figure 12.**Relationship between experimental and estimated results for the AdaBoost regressor model.

**Figure 13.**Distribution of experimental, estimated, and error values for the AdaBoost regressor model.

Parameter | Curing Temperature (°C) | Curing Time (h) | Age of Specimen (days) | Alkali/Fly Ash Ratio | Na_{2}SiO_{3}/NaOH Ratio | NaOH Molarity (M) | Aggregate Volume (%) | Superplasticizer (%) | Water (%) |
---|---|---|---|---|---|---|---|---|---|

Mean | 68.94 | 27.46 | 21.53 | 0.43 | 2.25 | 11.89 | 59.98 | 1.93 | 53.56 |

Median | 70.00 | 24.00 | 7.00 | 0.40 | 2.50 | 12.00 | 70.00 | 1.55 | 55.90 |

Mode | 60.00 | 24.00 | 7.00 | 0.35 | 2.50 | 10.00 | 70.00 | 2.00 | 55.90 |

Standard Deviation | 25.19 | 13.24 | 45.33 | 0.11 | 0.53 | 2.73 | 28.97 | 2.41 | 3.82 |

Range | 100.00 | 92.00 | 539.00 | 0.70 | 3.60 | 12.00 | 80.00 | 11.30 | 18.90 |

Minimum | 20.00 | 4.00 | 1.00 | 0.30 | 0.40 | 8.00 | 0.00 | 0.00 | 45.10 |

Maximum | 120.00 | 96.00 | 540.00 | 1.00 | 4.00 | 20.00 | 80.00 | 11.30 | 64.00 |

Model | MAE | RMSE |
---|---|---|

Support vector machine | 6.720 | 8.145 |

Multi-layer perceptron neural network | 5.864 | 7.492 |

AdaBoost regressor | 4.027 | 5.543 |

Random forest | 2.338 | 3.394 |

K-Fold | SVM | MLPNN | AR | RF | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

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

1 | 14.26 | 18.02 | 0.67 | 9.10 | 12.19 | 0.25 | 7.56 | 11.05 | 0.22 | 8.10 | 9.34 | 0.91 |

2 | 9.09 | 11.53 | 0.57 | 8.81 | 11.62 | 0.81 | 6.23 | 6.04 | 0.79 | 7.48 | 9.36 | 0.32 |

3 | 13.15 | 15.48 | 0.58 | 6.46 | 9.53 | 0.34 | 11.09 | 14.76 | 0.21 | 2.34 | 13.46 | 0.84 |

4 | 10.96 | 17.65 | 0.78 | 13.79 | 19.49 | 0.26 | 10.21 | 10.06 | 0.89 | 11.10 | 3.39 | 0.39 |

5 | 7.56 | 11.24 | 0.26 | 5.86 | 9.43 | 0.72 | 7.46 | 8.46 | 0.58 | 7.49 | 9.13 | 0.76 |

6 | 6.72 | 9.16 | 0.13 | 7.67 | 8.40 | 0.21 | 4.74 | 5.54 | 0.81 | 4.26 | 4.81 | 0.80 |

7 | 11.94 | 13.45 | 0.60 | 11.21 | 7.49 | 0.63 | 8.08 | 8.87 | 0.50 | 7.81 | 10.31 | 0.60 |

8 | 9.94 | 13.45 | 0.18 | 12.60 | 8.92 | 0.40 | 11.94 | 12.23 | 0.64 | 8.65 | 4.11 | 0.84 |

9 | 14.23 | 15.82 | 0.32 | 10.05 | 15.75 | 0.58 | 10.62 | 15.35 | 0.85 | 9.38 | 12.10 | 0.95 |

10 | 7.43 | 8.15 | 0.14 | 8.34 | 8.03 | 0.69 | 4.03 | 6.69 | 0.71 | 2.44 | 3.72 | 0.66 |

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## Share and Cite

**MDPI and ACS Style**

Amin, M.N.; Khan, K.; Ahmad, W.; Javed, M.F.; Qureshi, H.J.; Saleem, M.U.; Qadir, M.G.; Faraz, M.I.
Compressive Strength Estimation of Geopolymer Composites through Novel Computational Approaches. *Polymers* **2022**, *14*, 2128.
https://doi.org/10.3390/polym14102128

**AMA Style**

Amin MN, Khan K, Ahmad W, Javed MF, Qureshi HJ, Saleem MU, Qadir MG, Faraz MI.
Compressive Strength Estimation of Geopolymer Composites through Novel Computational Approaches. *Polymers*. 2022; 14(10):2128.
https://doi.org/10.3390/polym14102128

**Chicago/Turabian Style**

Amin, Muhammad Nasir, Kaffayatullah Khan, Waqas Ahmad, Muhammad Faisal Javed, Hisham Jahangir Qureshi, Muhammad Umair Saleem, Muhammad Ghulam Qadir, and Muhammad Iftikhar Faraz.
2022. "Compressive Strength Estimation of Geopolymer Composites through Novel Computational Approaches" *Polymers* 14, no. 10: 2128.
https://doi.org/10.3390/polym14102128