# Application of Soft Computing Techniques to Predict the Strength of Geopolymer Composites

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## Abstract

**:**

^{2}), statistical tests, and k-fold analysis were used to determine the validity and comparison of all models. It was discovered that ensembled machine learning techniques outperformed individual machine learning techniques in forecasting the compressive strength of geopolymer composites. However, the outcomes of the individual machine learning model were also within the acceptable limit. R

^{2}values of 0.90, 0.90, and 0.83 were obtained for AdaBoost, random forest, and decision models, respectively. The models’ decreased error values, such as mean absolute error, mean absolute percentage error, and root-mean-square errors, further confirmed the ensembled machine learning techniques’ increased precision. Machine learning approaches will aid the building industry by providing quick and cost-effective methods for evaluating material properties.

## 1. Introduction

_{2}, which substantially add to climate change [8,9,10]. The production of OPC is anticipated to release 1.35 billion tons of greenhouse emissions annually [11,12,13]. Thus, scholars have focused their attempts on minimizing OPC usage through the use of alternate binder types. Alternatives to CBCC may include alkali-activated compounds such as geopolymers [14,15,16]. When precursors and activators react, alkali-activated compounds are formed. They have been categorized into two kinds based on the calcium proportion of the products formed during the reaction: those that are calcium-rich, with a Ca/(Si+Al) fraction above 1, and those that are calcium-deficient, i.e., geopolymers [17,18,19].

^{2}). Additionally, the validity of each strategy was determined using k-fold analysis and error distributions. DT is an individual ML technique, whereas AdaBoost and RF are ensemble ML algorithms. This research is novel in that it estimates the CS of GPC using both individual and ensembled ML techniques, whereas experimental investigations need significant human work, experimental costs, and time for material acquisition, casting, curing, and testing. The use of modern techniques, like ML, in the field of civil engineering to predict material properties will reduce human effort and save time since experimental work for said purpose can be eliminated. ML approaches require a data set that might be retrieved from the literature as considerable research has been conducted to experiment with the material properties, and the data set can be used to train the ML models and estimate the various characteristics of a material. This study aims to identify the most suitable ML technique for the CS of GPCs in terms of results prediction and the influence of input parameters on the model’s performance.

## 2. Methods

#### 2.1. Description of Data

_{2}SiO

_{3}, fly ash, GGBS, and fine aggregate, with CS as the output variable. The number of inputs and datasets have a considerable effect on the model’s outcome [48,49,50]. In the current investigation, 363 data points were used to run ML algorithms. Table 1 summarizes the descriptive statistic evaluation of each input variable. The term “descriptive statistics” refers to a group of concise, factual measurements that generate an outcome, which may be the whole population or a subset of the population. The mean, median, and mode variables represent fundamental tendency, whereas the maximum, minimum, and standard deviation represent variability. The table provides all the mathematical terms for the model’s input variables. The relative frequency distribution of all variables used in the analysis is depicted in Figure 2. It depicts the total number of interpretations related to each value or combination of values. It is intrinsically related to probability dispersal, a widely used statistical term.

#### 2.2. Machine Learning Algorithms Employed

^{2}value for the projected result reflected the validity/precision of all models. The R

^{2}represents the extent of divergence; a value close to zero suggests higher divergence, but a value close to one shows that the model and data are almost completely suited [14]. The sub-sections below detail the ML techniques applied in this research. Additionally, to validate models, statistical and k-fold analysis and error assessments are carried out on all techniques, involving root-mean-square error (RMSE), mean absolute percentage error (MAPE) and mean absolute error (MAE). Moreover, sensitivity analysis is employed to discover the effect of each input parameter on the outcome estimation. The flowchart in Figure 3 depicts the research strategy.

#### 2.2.1. Decision Tree

#### 2.2.2. AdaBoost

#### 2.2.3. Random Forest

## 3. Models Results

#### 3.1. Decision Tree Model

^{2}of 0.83 confirms the satisfactory performance of the DT model in forecasting the CS of GPC. The dispersion of predicted and error values for the DT model is represented in Figure 7b. The error values were analyzed, and it was determined that the minimum, average, and highest values were 0.00, 7.02, and 36.59 MPa, respectively. Additionally, the percentage distribution of error values was determined, and it was discovered that 37.4% of values were less than 3 MPa, 38.5% were between 3 and 10 MPa, and only 24.2% were above 10 MPa. Additionally, the dispersion of error values implies that the DT model performs satisfactorily.

#### 3.2. AdaBoost Model

^{2}of 0.90, the AdaBoost model is quite accurate at forecasting the CS of GPC. Figure 8b illustrates the dispersion of predicted and error values for the AdaBoost model. The training set’s lowest, average, and maximum error values were determined to be 0.00, 5.20, and 20.40 MPa, respectively. The error distribution was 46.2%less than 3 MPa, 35.2% between 3 and 10 MPa, and only 18.7% greater than 10 MPa. The distribution of error values indicates the AdaBoost model’s higher precision in forecasting outcomes.

#### 3.3. Random Forest Model

^{2}of 0.90 signifying that the RF model has a comparable precision to the AdaBoost model in estimating the GPCs CS. Figure 9b shows the dispersal of experimental, expected, and error values for the RF model. The lowest, average, and highest error values were determined to be 0.06, 5.33, and 23.45 MPa, respectively. The error distribution was 47.3% less than 3 MPa, 34.1% between 3 and 10 MPa, and only 18.7% larger than 10 MPa. These reduced error values demonstrate the RF model’s higher exactness than the DT model and similar accuracy to the AdaBoost model.

## 4. Validation of Models

^{2}value is high, the model is more accurate. In addition, the operation ought to be reiterated ten times to achieve a reasonable conclusion. This extensive effort contributes significantly to the model’s remarkable accuracy. Furthermore, as shown in Table 2, all models were statistically evaluated in terms of errors (MAE, MAPE, and RMSE). These assessments also confirmed the AdaBoost and RF model’s higher accuracy as a result of their lower error readings when compared to the DT model. The predictive performance of the techniques was determined statistically using Equations (1)–(3), which were acquired from previous studies [38,56,57].

^{2}were calculated, and their values are provided in Table 3. The DT model’s MAE values ranged from 7.02 to 19.78 MPa, with an average of 11.08 MPa. When comparing, the MAE values for the AdaBoost model ranged between 5.20 and 14.68 MPa, with an average of 8.68 MPa. As for the AdaBoost model, the MAE values were between 5.33 and 18.47 MPa, with an average of 8.97 MPa. Similarly, the average MAPE for DT, AdaBoost, and RF models was noted to be 17.04%, 13.16%, and 13.47%, respectively. The average RMSE values for the DT, AdaBoost, and RF models were 15.89, 11.18, and 11.94 MPa. On the other hand, the average R

^{2}values for DT, AdaBoost, and RF models were 0.59, 0.67, and 0.65, respectively. The AdaBoost and RF models with the lower error values and the higher R

^{2}values are more accurate in forecasting the CS of GPC when compared to the DT model.

## 5. Sensitivity Analysis

_{2}SiO

_{3}accounting for 4.80%. Sensitivity analysis generated outcomes related to the number of input parameters and data points employed to construct the models. The influence of an input parameter on the technique’s output was determined using Equations (4) and (5).

## 6. Discussions

#### 6.1. Comparison of Machine Learning Models

^{2}of 0.90, compared to the DT model, which yielded an R

^{2}of 0.83.

^{2}and lower error values. Similarly, Farooq et al. [59] compared the performance of RF with ANN, GEP, and DT techniques and reported the higher precision of the RF model than the others with an R

^{2}of 0.96. However, determining and recommending the optimal ML model for forecasting outcomes through a variety of areas is complicated, as the performance of a model is greatly reliant on the input parameters and quantity of data points utilized to execute the algorithm. The previous studies concluded that up to 300 data points and a minimum of 8 input variables could result in the higher precision of the ML models [56,60]. Hence, the data set retrieved for the current investigation is suitable for the ML model’s best performance.

^{2}value. The dispersion of R

^{2}values for the AdaBoost and RF sub-models is shown in Figure 13. The minimum, average, and highest R

^{2}values for AdaBoost sub-models were 0.854, 0.876, and 0.900, respectively. Similarly, the minimum, average, and highest R

^{2}values for RF sub-models were 0.872, 0.892, and 0.900, respectively. These results demonstrate that both the AdaBoost and RF sub-models have comparable values and a high degree of precision in forecasting GPC’s CS. Additionally, a sensitivity analysis was done to ascertain the effect of all inputs on the expected CS of GPC. The model’s performance might be affected by the input parameters and the dataset’s size. The sensitivity analysis determined how each of the nine input characteristics contributed to the projected output. Fly ash, GGBS, and NaOH molarity were determined to be the three most significant input variables.

#### 6.2. Comparison of Experimental and Predicted Results

## 7. Conclusions

- Ensemble ML approaches (AdaBoost and RF) performed better than the individual ML technique (DT) at predicting the CS of GPCs, with the AdaBoost and RF models performing with a similar degree of precision. The correlation coefficients (R
^{2}) for the AdaBoost, RF and DT models were 0.90, 0.90, and 0.83, respectively. - Statistical checks and k-fold analysis verified the model’s performance. Furthermore, these checks also confirmed the comparable accuracy of the AdaBoost and RF models. The lower deviation (MAE, MAPE, and RMSE) of the predicted results and higher R
^{2}values of the ensembled models validated their higher precision. - The comparison of the experimental and predicted results further validated the higher accuracy of AdaBoost and RF models due to less deviation of the predicted results than the experimental results. On the other hand, the deviation of the DT model’s results was higher than the AdaBoost and RF models and is less recommended for estimating the CS of GPCs.
- Sensitivity analysis revealed that fly ash, ground granulated blast furnace slag, and NaOH molarity have a greater influence on the model’s outcome and account for 26.37%, 14.74%, and 13.12% of the contribution, respectively. However, NaOH, water/solids ratio, fine aggregate, gravel 4/10 mm, gravel 10/20 mm, and Na
_{2}SiO_{3}contributed 11.60%, 9.52%, 7.53%, 6.48%, 5.84%, and 4.80%, respectively, to the prediction of the outcome. - This type of research will aid the construction sector by enabling the development of quick and cost-effective methods for predicting material strength. Additionally, by promoting eco-friendly construction using these strategies, the acceptance and use of GPC in construction will be expedited.

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Relative frequency dispersal of inputs: (

**a**) Water/solids ratio; (

**b**) NaOH Molarity; (

**c**) Gravel 4/10 mm; (

**d**) Gravel 10/20 mm; (

**e**) NaOH; (

**f**) Na

_{2}SiO

_{3}; (

**g**) Fly ash; (

**h**) GGBS; (

**i**) Fine aggregate.

**Figure 7.**Decision tree model: (

**a**) correlation between experimental and estimated results; (

**b**) dispersal of predicted and error values.

**Figure 8.**AdaBoost model: (

**a**) correlation between experimental and estimated results; (

**b**) dispersal of predicted and error values.

**Figure 9.**Random forest model: (

**a**) correlation between experimental and estimated results; (

**b**) dispersal of predicted and error values.

Parameter | Water/Solids Ratio | NaOH Molarity | Gravel 4/10 mm (kg/m^{3}) | Gravel 10/20 mm (kg/m^{3}) | NaOH (kg/m^{3}) | Na_{2}SiO_{3} (kg/m^{3}) | Fly Ash (kg/m^{3}) | GGBS (kg/m^{3}) | Fine Aggregate (kg/m^{3}) |
---|---|---|---|---|---|---|---|---|---|

Minimum | 0 | 1 | 0 | 0 | 3.5 | 18 | 0 | 0 | 459 |

Maximum | 0.63 | 20 | 1293.4 | 1298 | 147 | 342 | 523 | 450 | 1360 |

Range | 0.63 | 19 | 1293.4 | 1298 | 143.5 | 324 | 523 | 450 | 901 |

Median | 0.34 | 9.2 | 208 | 789 | 56 | 108 | 120 | 300 | 728 |

Mode | 0.53 | 10 | 0 | 0 | 64 | 108 | 0 | 0 | 651 |

Mean | 0.34 | 8.14 | 288.39 | 737.37 | 53.74 | 111.66 | 174.34 | 225.15 | 729.88 |

Standard Error | 0.01 | 0.24 | 19.54 | 18.82 | 1.67 | 2.53 | 8.82 | 8.52 | 6.87 |

Standard Deviation | 0.11 | 4.56 | 372.31 | 358.55 | 31.91 | 48.16 | 167.95 | 162.27 | 130.97 |

Sum | 124.8 | 2955.1 | 104,684.3 | 267,664.9 | 19,508.8 | 40,532.7 | 63,286.0 | 81,728.1 | 264,947.8 |

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

Decision tree | 7.016 | 16.020 | 10.432 |

AdaBoost | 5.199 | 12.302 | 7.467 |

Random forest | 5.325 | 12.420 | 7.602 |

K-Fold | Decision Tree | AdaBoost | Random Forest | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

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

1 | 16.03 | 18.70 | 21.92 | 0.60 | 8.70 | 13.25 | 13.04 | 0.43 | 10.70 | 12.97 | 13.43 | 0.54 |

2 | 7.02 | 16.93 | 11.57 | 0.76 | 5.65 | 12.30 | 8.01 | 0.49 | 5.33 | 13.76 | 8.09 | 0.72 |

3 | 9.15 | 16.03 | 10.94 | 0.20 | 6.56 | 14.03 | 8.16 | 0.79 | 5.54 | 14.88 | 8.37 | 0.64 |

4 | 11.76 | 17.21 | 10.43 | 0.70 | 8.18 | 12.55 | 8.43 | 0.67 | 8.06 | 13.66 | 11.40 | 0.52 |

5 | 7.31 | 16.02 | 12.41 | 0.59 | 6.11 | 12.98 | 7.47 | 0.90 | 5.34 | 12.90 | 7.85 | 0.77 |

6 | 12.96 | 16.55 | 17.07 | 0.37 | 12.94 | 14.45 | 14.34 | 0.57 | 9.85 | 13.77 | 13.82 | 0.53 |

7 | 7.72 | 18.67 | 19.58 | 0.72 | 9.50 | 13.66 | 12.06 | 0.60 | 9.43 | 12.42 | 15.56 | 0.74 |

8 | 10.92 | 16.03 | 15.26 | 0.41 | 9.33 | 13.08 | 14.33 | 0.86 | 11.12 | 14.02 | 13.93 | 0.34 |

9 | 8.15 | 17.22 | 16.50 | 0.72 | 5.20 | 12.95 | 7.68 | 0.74 | 5.80 | 13.79 | 7.60 | 0.79 |

10 | 19.78 | 17.02 | 23.23 | 0.83 | 14.68 | 12.35 | 18.28 | 0.61 | 18.47 | 12.50 | 19.31 | 0.90 |

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**MDPI and ACS Style**

Wang, Q.; Ahmad, W.; Ahmad, A.; Aslam, F.; Mohamed, A.; Vatin, N.I.
Application of Soft Computing Techniques to Predict the Strength of Geopolymer Composites. *Polymers* **2022**, *14*, 1074.
https://doi.org/10.3390/polym14061074

**AMA Style**

Wang Q, Ahmad W, Ahmad A, Aslam F, Mohamed A, Vatin NI.
Application of Soft Computing Techniques to Predict the Strength of Geopolymer Composites. *Polymers*. 2022; 14(6):1074.
https://doi.org/10.3390/polym14061074

**Chicago/Turabian Style**

Wang, Qichen, Waqas Ahmad, Ayaz Ahmad, Fahid Aslam, Abdullah Mohamed, and Nikolai Ivanovich Vatin.
2022. "Application of Soft Computing Techniques to Predict the Strength of Geopolymer Composites" *Polymers* 14, no. 6: 1074.
https://doi.org/10.3390/polym14061074