# Random Forest Modeling for Fly Ash-Calcined Clay Geopolymer Composite Strength Detection

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}), and MSE (mean squared error) is suggested in the model. The results demonstrated that the RFR model is likely to predict GPC compressive strength (MAE = 1.85 MPa, MSE = 0.05 MPa, RMSE = 2.61 MPa, and R

^{2}= 0.93) and split tensile strength (MAE = 0.20 MPa, MSE = 6.83 MPa, RMSE = 0.24 MPa, and R

^{2}= 0.90) during training.

## 1. Introduction

_{2}solid % in sodium silicate, and superplasticizer (percent P) [5,6]. Because of the porosity in the geopolymer network, the compressive strength is poor. Fly ash, however, needs little H

_{2}O and pushes maximal fill-up of particles to lower porous content due to its round portion shape [7]. Calcined clay and fly ash were mixed and analyzed by roles of the addition, reactiveness, strength due to compression, structural and microstructural characteristics, and CC versus FA ratio. Na

_{2}SiO

_{3}/NaOH was synthesized as an activator with 0, 25, 50, and 75% fly ash and calcined clay percentage in geopolymer mortar [8]. From the academic research, 357 data points were obtained, and the compressive strength of high strength concrete was predicted by using an ensemble random forest (RF) and gene expression programming (GEP) algorithm. A proportioned blend trial mix requires us to determine a specific response. However, engineers are now using mathematical models to simulate a specific response to verify the prediction’s performance, such as linear regression, neural networks (NN), or support vector regression (SVR). Since the relationship between attributes and composite properties is strongly nonlinear, everything is achieved [9]. The dataset provides data on cement ratio, silicate ratio, pulverized time, age of the specimen, and strength due to compression. With an increasing number of trees in random forest regression (RFR), the inaccuracy in predicting data beyond the test dataset decreases, and after 600 tries, the inaccuracy would become steady and very reduced. With an R

^{2}value of 0.89, the random forest model forecasted strength due to compression, using input datasets obtained by laboratory experiments [10]. Cement/fly-ash-based high-performance composite has 56 datasets. RFR was used to detect 28 days’ strength due to compression. The RFR model and the back-propagation neural network (NN) model used a common dataset to predict strength selection of functions with and without [11]. Ground granulated blast furnace slag was gathered with 453 experimental samples, using the RFR model, to calculate the strength due to compression of concrete, including GGBFS [12]. Rubberized concrete (RC) is a cost-effective and eco-sustainable building material. There are a total of 138 datasets collected from the literature. The present study suggested establishing the connection between both the random forest (RF) and beetle antennae algorithm to search the essential factors of random forest. The result analysis showed the beetle antennae algorithm adjusted by RF. The correlation coefficient is strong in this case, as the proposed random forest model can accurately predict rubberized concrete’s compressive strength with a correlation coefficient of 0.96 [13]. Table 1 offers a brief description of previously performed random forest regression studies. Fly-ash-and-calcined-clay-based geopolymer composites have much less research.

_{2}SiO

_{3}, superplasticizer, and added water; and different curing temperatures were used, such as ambient, 80 °C, and 100 °C, with different curing durations, such as 24 and 48 h. The actual compressive strength obtained was predicted by using random forest regression. A total of 80% of samples were tested, and 20% of samples were trained by using RFR. The R square value describes the acceptability of a model. This machine learning approach saves the cost and time of tedious laboratory work.

## 2. Materials and Methods

#### 2.1. Fly Ash

^{3}. The chemical composition of fly ash and % of the mass are mentioned in Table 2. The 5%, 10%, and 15% of fly ash were substituted with calcined clay. The physical properties of fly ash were fineness retained on the 45-micron sieve; activity index test results lie between 80 and 86%, with a specification of minimum 75% at 28 days and 95–103% specification of minimum 85% at 90 days. The particle size distribution of fly ash has a significant impact on geopolymer concrete [14]. Raising the curing temperature has a beneficial compression-strength influence. Because of the porosity in the geopolymer network, the compressive strength declines.

#### 2.2. Calcined Clay

#### 2.3. Sodium Silicate Solution

_{2}SiO

_{3}is called water glass, and it is also accessible as a gel. The ratio of SiO

_{2}to Na

_{2}O in this study was 1.95 to 2.3. It was obtained from the market in liquid solution form. The chemical composition of it was Na

_{2}O 13.5%, SiO

_{2}33%, and water. The chemical composition can be seen in Table 3.

#### 2.4. Sodium Hydroxide

#### 2.5. Superplasticizer

#### 2.6. Aggregate

#### 2.6.1. Fine Aggregate/Crushed Stone Dust

#### 2.6.2. Coarse Aggregate

#### 2.7. Sample Preparation and Testing Method

## 3. Modeling Technique

#### 3.1. Random Forest Research (RFR)

#### 3.2. Projected Approach/Proposed Strategy

#### Data Collection

Algorithm 1 Random forest modeling. |

Input-Calcined clay, fly ash geopolymer concrete dataset.Output-Strength due to compression and tension of FACC based geopolymer composite. |

#### 3.3. Analysis of Model Performance

^{2}. These factors are described below in mathematical terms.

_{ref}were reference values in the dataset, and x

_{i}and y

_{pred}were predicted values of models. The performance of the model was also assessed in this paper by using the coefficient of determination (R

^{2}). The reflective practice that reveals the connection between experimental and expected outputs was the value obtained through the model [21].

## 4. Results and Discussion

- (1)
- (2)
- In the case of compressive strength RFR, the R
^{2}was determined to be 0.93 in the training dataset. Similarly, the R^{2}was obtained as 0.58 in the testing phase. Furthermore, RFR was shown to have the best value among the statistical measures used in testing as (MSE = 10.41, RMSE = 3.22, MAE = 3.07). The RFR model excels at capturing the nonlinear interactions between geopolymer mix design proportions and temperatures with compressive strength, which could explain its supremacy. Consequently, since it relies on empirical analytical evaluations, it may be inferred that the RFR model produced the desired results [8,22]. - (3)
- The R
^{2}, MAE, and RMSE of the predicted values, using the RFR, were also calculated [23]. For split tensile strength the training dataset, MSE, RMSE, R^{2}, and MAE values were 0.88, 0.25, 0.88, and 0.0256, respectively. Using the RFR technique, calculate the R^{2}, MAE, and RMSE of the anticipated values [24]. This research could help engineers choose optimal supervised learning models and parameters for geopolymer concrete manufacturing. This graph suggests that employing the RFR model could be beneficial. To forecast the strength due to compression of geopolymer concrete at various temperatures, 12 input variables are sufficient and have reasonable precision. Using a set of 12 input variables could be justified and useful for practical and engineering applications, according to the findings. R^{2}is regarded as very weak, low, medium, or strong if ranges as >0.3, 0.3 < r < 0.5, 0.5 < r < 0.7, or r > 0.7, respectively [25]. - (4)
- The highest R
^{2}score and the fewest other errors have shown some positive results with appropriate dimensions [26]. Figure 3, has an R^{2}score of 0.93, which show that model is highly trained.The mean MSE for RFR is 6.35 and 5.803 for training and testing data. The predictive precision and widespread potential of the RFR are high [11]. There is a loss of training and testing data that can be sorted when the model is taught from an enormous dataset. For MAE, the average MAE is 1.826 and 2.288 for training and testing. Losses are not so much in training as they are in testing data [27]. - (5)
- Figure 4 and Figure 5 show a graphical representation of experiment value (actual) and projected strength due to compression of fly-ash, calcined-clay-based geopolymer concrete at various temperatures, using RFR supervised learning algorithms for the training and testing phases. These data show that RFR models performed as per training and testing in forecasting geopolymer concrete compressive strength at various temperatures in terms of statistical performance.
**Figure 4.**Graphical representation of experimental value (actual) and projected strength due to compression of fly-ash, calcined -clay-based geopolymer concrete.**Figure 5.**Graphical representation of experimental value (actual) and projected split tensile strength of fly-ash, calcined-clay-based geopolymer concrete. - (6)
- Supervised learning models, such as other artificial intelligence systems, have a limited range of scope and are heavily case-dependent. As a result, their generalizability is constrained, and therefore can only be used with a limited collection of trained data. Moreover, in contrast to other models, the created RFR model is capable of correctly and effectively predicting the compressive strength at varying temperatures. However, as the latest data arrive, this model can be adjusted to perform better.

## 5. Conclusions

- In this work, RFR was used to predict the compressive strength at ambient temperature, 80 °C, and 100 °C curing temperature for 24 and 48 h. The best result was shown by FACC geopolymer concrete for 5% calcined clay and 12 M NaOH solution at 100 °C for 48 h curing.
- The RFR model’s predictive skills were evaluated by using statistical measure criteria, such as R
^{2}, MAE, and RMSE. The R^{2}value comes out to be 0.58 for the testing phase of RFR, which is an acceptable value of the coefficient of correlation. The training results of R^{2}as 0.935 are also good for 28 days of compressive strength. - The findings of the testing phase demonstrated that the supervised learning models developed in this work were successful in predicting geopolymer concrete compressive strength at various ranges of temperature. This paper predicted 28 days of compressive and tensile strength.
- Statistics research reveals that the RFR model is effective. Correctness is improved by reducing the erroneous gap between the actual and forecasted parameters. Various metrics, such as MAE, RMSE, R
^{2}, and MSE, were the deciding parameters. - As a result, the use of RFR in the domain of forecasting compressive strength at various temperatures as an alternative to destructive testing methods is reasonable and can be considered as a viable option, and the same is applied to tensile strength.
- Due to the addition of weak classifiers (decision tree), random forest is an ensemble strategy that delivers a consistent performance between observed and forecasted values and gives the coefficient of determination R
^{2}as 0.58.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviation

Designation | Full Form |

FACC | fly ash calcined clay |

RFR | random forest regressor |

NaOH | sodium hydroxide |

Na_{2}SiO_{3} | sodium silicate |

GEP | genetic-algorithm-based |

RMSE | root mean square error |

MAE | mean absolute error |

R^{2} | coefficient of correlation |

MSE | mean squared error |

GGBFs | ground granulated blast furnace slag |

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Reference | Model | Output Description |
---|---|---|

[7] | RFR | Compressive strength of cement |

[8] | RFR and Backpropagation neural network | Strength due to compression of cement/fly-ash-based high-performance composite |

[9] | RFR and GEP | Compressive strength of high strength composite |

[10] | RFR | Strength due to compression of GGBFS composite. |

[11] | RFR | Strength due to compression of GGBFS rubberized geopolymer composite compressive strength |

Component | Composition |
---|---|

Silica | 50–52.5 |

Alumina | 28.5–30.5 |

Ferric oxide | 2–3 |

Calcium oxide | 6–9.5 |

Magnesium oxide | 2–2.5 |

Potassium oxide | <1 |

Na equivalent | <1.5 |

Titanium dioxide | 1.5–2.0 |

Component | SiO_{2} | Water | Na_{2}O |
---|---|---|---|

Composition | 33 | 53.5 | 13.5 |

Serial No. | Property | Natural Sand | Stone Dust | IS Codes |
---|---|---|---|---|

1 | Specific Gravity | 2.6 | 2.53–2.68 | IS2386(Part III)-1963 |

2 | Bulk Density | 1460 | 1710–1850 | IS2386(Part III)-1963 |

3 | Absorption | nil | 1.2–1.5 | IS2386(Part III)-1963 |

4 | Moisture Content | 1.5 | nil | IS2386(Part III)-1963 |

5 | Sieve Analysis | Zone II | Zone II | IS 383-1970 |

Samples | FA (%) | CC (%) | NaOH (M) | Temperature Curing (°C) | Duration of Curing (h) | Aging Time (days) | Added Water |
---|---|---|---|---|---|---|---|

5C1FA | 95 | 5 | 12 | 30 | 24 | 28 | 56.92 |

5C2FA | 95 | 5 | 12 | 80 | 24 | 28 | 56.92 |

5C3FA | 95 | 5 | 12 | 80 | 48 | 28 | 56.92 |

5C4FA | 5 | 5 | 12 | 100 | 24 | 28 | 56.92 |

5C5FA | 95 | 5 | 12 | 100 | 48 | 28 | 56.92 |

5C6FA | 95 | 5 | 14 | 30 | 24 | 28 | 39.5 |

5C7FA | 95 | 5 | 14 | 80 | 24 | 28 | 39.5 |

5C8FA | 95 | 5 | 14 | 80 | 48 | 28 | 39.5 |

5C9FA | 95 | 5 | 14 | 100 | 24 | 28 | 39.5 |

5C10FA | 95 | 5 | 14 | 100 | 48 | 28 | 39.5 |

5C11FA | 95 | 5 | 16 | 30 | 24 | 28 | 47.36 |

5C12FA | 95 | 5 | 16 | 80 | 24 | 28 | 47.36 |

5C13FA | 95 | 5 | 16 | 80 | 48 | 28 | 47.36 |

5C14FA | 95 | 5 | 16 | 100 | 24 | 28 | 47.36 |

5C15FA | 95 | 5 | 16 | 100 | 48 | 28 | 47.36 |

10C1FA | 90 | 10 | 12 | 30 | 24 | 28 | 59.2 |

10C2FA | 90 | 10 | 12 | 80 | 24 | 28 | 59.2 |

10C3FA | 90 | 10 | 12 | 80 | 48 | 28 | 59.2 |

10C4FA | 90 | 10 | 12 | 100 | 24 | 28 | 59.2 |

10C5FA | 90 | 10 | 12 | 100 | 48 | 28 | 59.2 |

10C6FA | 90 | 10 | 14 | 30 | 24 | 28 | 49.3 |

10C7FA | 90 | 10 | 14 | 80 | 24 | 28 | 49.3 |

10C8FA | 90 | 10 | 14 | 80 | 48 | 28 | 49.3 |

10C9FA | 90 | 10 | 14 | 100 | 24 | 28 | 49.3 |

10C10FA | 90 | 10 | 14 | 100 | 48 | 28 | 49.3 |

15C1FA | 85 | 15 | 14 | 30 | 24 | 28 | 45.3 |

15C2FA | 85 | 15 | 14 | 80 | 24 | 28 | 45.3 |

15C3FA | 85 | 15 | 14 | 80 | 48 | 28 | 45.3 |

15C4FA | 85 | 15 | 14 | 100 | 24 | 28 | 45.3 |

15C5FA | 85 | 15 | 14 | 100 | 48 | 28 | 45.3 |

15C6FA | 85 | 15 | 16 | 30 | 24 | 28 | 51.3 |

15C7FA | 85 | 15 | 16 | 80 | 24 | 28 | 51.3 |

15C8FA | 85 | 15 | 16 | 80 | 48 | 28 | 51.3 |

15C9FA | 85 | 15 | 16 | 100 | 24 | 28 | 51.3 |

15C10FA | 85 | 15 | 16 | 100 | 48 | 28 | 51.3 |

**Table 6.**The training phase (compressive strength) with available RFR models’ yielded statistical data from the applied prediction models.

Model | Results of Training Performance | |||
---|---|---|---|---|

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

RFR | 6.83 | 2.61 | 0.93 | 1.85 |

**Table 7.**The testing phase (compressive strength) with available RFR models’ yielded statistical data from the applied prediction models.

Model | Results of Testing Performance | |||
---|---|---|---|---|

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

RFR | 10.41 | 3.23 | 0.58 | 3.07 |

**Table 8.**The training phase (split tensile strength) with available RFR models’ yielded statistical data from the applied prediction models.

Model | Results of Training Performance | |||
---|---|---|---|---|

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

RFR | 0.065 | 0.256 | 0.88 | 0.213 |

**Table 9.**The testing phase (split tensile strength) with available RFR models’ yielded statistical data from the applied prediction models.

Model | Results of Testing Performance | |||
---|---|---|---|---|

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

RFR | 0.28 | 0.53 | 0.57 | 0.36 |

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## Share and Cite

**MDPI and ACS Style**

Gupta, P.; Gupta, N.; Saxena, K.K.; Goyal, S. Random Forest Modeling for Fly Ash-Calcined Clay Geopolymer Composite Strength Detection. *J. Compos. Sci.* **2021**, *5*, 271.
https://doi.org/10.3390/jcs5100271

**AMA Style**

Gupta P, Gupta N, Saxena KK, Goyal S. Random Forest Modeling for Fly Ash-Calcined Clay Geopolymer Composite Strength Detection. *Journal of Composites Science*. 2021; 5(10):271.
https://doi.org/10.3390/jcs5100271

**Chicago/Turabian Style**

Gupta, Priyanka, Nakul Gupta, Kuldeep K. Saxena, and Sudhir Goyal. 2021. "Random Forest Modeling for Fly Ash-Calcined Clay Geopolymer Composite Strength Detection" *Journal of Composites Science* 5, no. 10: 271.
https://doi.org/10.3390/jcs5100271