# Predictive Modeling of Mechanical Properties of Silica Fume-Based Green Concrete Using Artificial Intelligence Approaches: MLPNN, ANFIS, and GEP

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## Abstract

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_{2}emissions, cost-effective concrete, increased durability, and mechanical qualities. As environmental issues continue to grow, the development of predictive machine learning models is critical. Thus, this study aims to create modelling tools for estimating the compressive and cracking tensile strengths of silica fume concrete. Multilayer perceptron neural networks (MLPNN), adaptive neural fuzzy detection systems (ANFIS), and genetic programming are all used (GEP). From accessible literature data, a broad and accurate database of 283 compressive strengths and 149 split tensile strengths was created. The six most significant input parameters were cement, fine aggregate, coarse aggregate, water, superplasticizer, and silica fume. Different statistical measures were used to evaluate models, including mean absolute error, root mean square error, root mean squared log error and the coefficient of determination. Both machine learning models, MLPNN and ANFIS, produced acceptable results with high prediction accuracy. Statistical analysis revealed that the ANFIS model outperformed the MLPNN model in terms of compressive and tensile strength prediction. The GEP models outperformed all other models. The predicted values for compressive strength and splitting tensile strength for GEP models were consistent with experimental values, with an R

^{2}value of 0.97 for compressive strength and 0.93 for splitting tensile strength. Furthermore, sensitivity tests revealed that cement and water are the determining parameters in the growth of compressive strength but have the least effect on splitting tensile strength. Cross-validation was used to avoid overfitting and to confirm the output of the generalized modelling technique. GEP develops an empirical expression for each outcome to forecast future databases’ features to promote the usage of green concrete.

## 1. Introduction

_{2}being the most abundant and strongest influence of all GHGs [1,2]. Around 5–7 percent of global CO

_{2}emissions are attributed to the cement industry [3]. Due to its mechanical and durability features, concrete is a widely used building material [4]. Around 8% of CO

_{2}emitted during the concrete making process contributes to global warming [4,5]. Concrete is expected to be manufactured at a rate of 20 billion tons per year, making it the second most frequently utilized substance on the planet after fresh water. Apart from its benefits, concrete is harmful to the Earth and human health and has long-term negative consequences on the natural environment and atmosphere [6]. It expands the human footprint by creating living space out of thin air, spreading across fertile topsoil, and impeding biodiversity. The biodiversity crisis is the primary focus of research, as it is one of the most serious dangers to a sustainable ecosystem and is mostly caused by urbanization. For hundreds of years, humans have longed for the dubious benefits of concrete to overlook this environmental drawback. However, the balance is currently shifting in the opposite direction. At times of unsettling transition, solidity is an alluring quality that can create more problems than it can resolve [7].

_{2}emissions from concrete (produced by calcareous and clay minerals in the kiln). Nearly 900 kg of CO

_{2}is emitted during the manufacturing of a ton of cement. It must be heated to extremely high temperatures during the cement manufacturing process to generate clinkers. Cement is made by grinding clinker to a fine powder and then mixing it with gypsum (Ca

_{3}SiO

_{5}), sometimes called alite. It is generated during the clinker production process and gives an excessive early strength. Alite must be maintained at a temperature of 1500 °C during this process [8,9]. According to some studies, alite can be replaced by various naturally occurring minerals that require a lower roasting temperature than alite. Carbon emissions from concrete have long been a source of concern for both the academic and industrial sectors [10]. Numerous techniques have been proposed to address this issue, one of which asserts that we can achieve sustainability by completely or partially replacing cement with readily available natural materials [11,12,13]. Extra cementitious materials such as silica fume (SF) have been employed to partially replace cement in concrete mixtures to offset the cement industry’s CO2 emissions [14,15,16,17]. SF is a significant by-product of the silicon metal manufacturing sector. Silicon metal is a semi-metallic element that exhibits various metal-like properties. After oxygen, silica is the second most abundant element in the Earth’s crust, occurring primarily in the form of silicon dioxide or silicates but also in its pure state [18].

^{2}values of 0.99 and 0.96 for compressive and flexural strength, respectively. Naderpour et al. [48] used ANN to forecast the compressive strength of recycled aggregate concrete and building waste concrete.

^{2}) and root mean square error (RMSE) were used for the evaluation of models. Based on these statistical indicators, it was concluded that RF predicted the best results, followed by ANN. Han et al. [53] also highlighted the utility of machine learning algorithms for calculating the strength of reinforced concrete materials with high accuracy. Similarly, Table 1 outlines research on machine learning conducted by researchers employing waste materials.

## 2. Algorithms for Machine Learning

#### 2.1. Multilayer Perceptron Neural Network (MLPNN)

#### 2.2. Adaptive Neural Fuzzy Detection System (ANFIS)

^{th}rule’s firing strength to the total of all firing strengths is the normalized value. The fourth layer is known as the defuzzification layer. In each node of this layer, weighted values of rules are determined. The summation layer is the fifth layer. The actual output of ANFIS is obtained by summing the outputs obtained for each rule in the defuzzification layer.

#### 2.3. Genetic Algorithm and Gene Expression Programming

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## 3. Modeling Dataset and Model Development

## 4. Models Evaluation Criteria

^{2}). However, the R

^{2}value, also known as the coefficient of determination, is considered the best of these for model evaluation. With advancements in the field of artificial intelligence, several modelling techniques have been used to construct prediction models for the resulting concrete’s mechanical properties. To promote the use of SF in concrete on an industrial scale, we attempted to develop regression and GEP models between compressive strength and split tensile strength with a mixed proportion of SFC and then compared them to determine the model that best predicts the output with the least or no deviation. The models are tested in this work using statistical analysis and the computation of error metrics. These metrics can provide a variety of insights regarding the flaws in your model. Additionally, the coefficient of variance and standard deviations are used to evaluate the model’s performance. The correctness and validation of the model are justified in this study by its coefficient of determination. R

^{2}values between 0.65 and 0.75 indicate satisfactory findings, whereas values less than 0.50 indicate disappointing results. R

^{2}can be determined using Equation (2).

## 5. Results and Discussion

#### 5.1. Formulation of the Compressive Strength and Split Tensile Strength of SFC

^{2}) values. R

^{2}values for several models are shown in Table 7 for each outcome.

#### 5.1.1. Model Outcome of MLPNN

^{2}= 0.85. The error distribution of the targeted values with the model values is shown in Figure 8b. The MLPNN compressive model shows an average error of 5.28 MPa, with the maximum and minimum errors of 19.34 MPa and 0.048 MPa. Moreover, data indicate imprecision of 57.90% below 5 MPa, 24.56% between 5–10 MPa, 12.28 percent between 10–15 MPa, and 5.26 % between 15–20 MPa.

^{2}= 0.90 as shown in Figure 8c. The error distribution of the models obtained is depicted in Figure 8d. The MLPNN tensile strength model shows an average error of 0.41 MPa with maximum and minimum error values of 1.05 MPa and 0.02 MPa, respectively. In addition, 96.67% of error is below 1 MPa, and only 3.34% of the error lies in between 1 to 2 MPa. The results of the model are satisfactory and can be used to predict the split tensile strength of the model. Based on the above stats, the MLPNN is capable of predicting the compressive strength and split tensile strength of SFC with appreciable accuracy.

#### 5.1.2. Model Outcomes of ANFIS

^{2}= 0.91 for ANFIS compressive strength. Figure 9b depicts maximum and minimum errors of 22.94 MPa and 0.001 MPa, respectively, with an average error of 4.18 MPa for the ANFIS compressive strength model. Moreover, data indicates an error of 71.93% below 5 MPa, 21.05% between 5–10 MPa, 5.26% between 10–15 MPa, 0% between 15–20 MPa and 1.75 % between 20–25 MPa. The error distribution of MLPNN shows a higher peak in comparison to the ANFIS model but the overall performance of both models gives approximately the same results.

^{2}= 0.92 for the ANFIS tensile strength model. The average, maximum and minimum errors observed from Figure 9d are 0.26, 1.09, and 0.001 MPa, respectively, for the ANFIS split tensile strength model. Data of the ANFIS tensile strength model shows an error of 93.33% below 1 MPa, whereas a 6.67% error between 1–2 MPa. The ANFIS model can predict the targeted results with an ignorable deviation observed by the value of errors.

#### 5.2. Evaluation of GEP Models for Compressive Strength and Split Tensile Strength

^{2}. In this section, genetic expression models are made to predict the compressive strength and split tensile strength of concrete containing a different amount of SF. The outcome of both properties was obtained based on expression trees as shown in Figure 10 and Figure 11.

#### Model Outcomes of Gene Expression Programming (GEP)

^{2}, by employing GEP, is close to 1. Moreover, Figure 12b represents an average of 3.52 MPa, with the maximum and minimum errors of 4.46 and 2.70 MPa, respectively. The data of the GEP model for compressive strength indicate that all the errors lie below 5 MPa. A comparison is drawn between the actual and the predicted compressive strength to evaluate the model accuracy and to measure the deviation of the model from the experimental results. Figure 12c shows the coefficient of correlation for the split tensile strength model with R

^{2}= 0.93, whereas Figure 12d shows the error distribution of predicted results with actual results. The GEP model for fst may show high error peaks as compared to the models obtained by DT, MLPNN, SVM, but the overall performance of the model is better comparatively as can be seen in the statistical parameters in Table 8. Average, maximum, and minimum errors for the tensile strength GEP model are 0.3, 0.4, and 0.23 MPa, respectively. Moreover, the data indicate that 100% of the error lies below 0.5 MPa. The expression tree for the GEP split tensile strength model is shown in Figure 11. The relationship that developed between tensile strength and input parameters is shown in Equation (7).

#### 5.3. Comparison between Ensemble Models and the GEP Model

#### 5.4. Sensitivity Analysis

#### 5.5. Cross-Validation

^{2}), mean absolute error (MAE), mean square logarithmic error (RMSLE), and root mean square error (RMSE) are used to evaluate the outcomes of cross-validation, as depicted in Figure 16 and Figure 17 for compressive strength and splitting tensile strength, respectively. The GEP model shows fewer errors and better R

^{2}as compared to supervised machine learning techniques. The average R

^{2}for GEP modeling is 0.84 for a compressive strength of ten folds with maximum and minimum values of 0.97 and 0.61, as shown in Figure 16. Similarly, the average R

^{2}= 0.83 for tensile strength with a maximum and minimum value of 0.98 and 0.71, respectively, is shown in Figure 17. Each model shows fewer errors for validation. The validation indicator result shows that mean values of MAE, RMSE, and RMSLE come to be 5.33, 6.54, and 0.039, respectively, for the compressive strength GEP model and 0.49, 0.63, and 0.031 for the splitting tensile strength GEP model. Similarly, the ensemble models show the same trend by showing comparatively more errors.

## 6. Conclusions

^{2}, MAE, RMSE, and RMSLE. The values of statistical parameters indicated that all models are capable of accurately predicting the compressive and split tensile strengths of concrete. The outcomes of the machine learning models and the GEP model are compared. External validation and sensitivity assessments were also done for additional assurance. R

^{2}values of 0.97 for compressive strength and 0.93 for tensile strength were achieved using the best model (GEP).

- The results of this study indicated that GEP models have higher accuracy for the prediction of data than other ML models.
- After a detailed study, it was observed that the order of accuracy followed by the compressive strength and tensile strength models is: GEP > ANFIS > MLPNN.
- The benefit of GEP is it gives us a new mathematical equation that can be used to predict the properties for another database.
- Sensitivity analysis showed that water and cement are the governing factors in the model development for compressive strength. However, these factors have least effect in tensile strength model development.
- Statistical parameters including R
^{2}, MAE, RMSE, and RMSLE were used to check the k-fold validation results. These parameters depicted satisfactory results for all the models. - Accurate expressions and models can be used to increase the industrial-level utilization of hazardous SF in concrete in construction procedures, rather than accumulating it as industrial waste. This research contributes to sustainable development by lowering energy usage, landfill waste, and greenhouse gas emissions.

## 7. Limitations and Directions for Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 5.**Flow chart of the GEP [73].

**Figure 6.**Relative frequency distribution of parameters to compressive strength; (

**a**) cement, (

**b**) sand, (

**c**) gravel, (

**d**) water, (

**e**) silica fume, (

**f**) super plasticizer.

**Figure 7.**Relative frequency distribution of parameters to tensile strength; (

**a**) cement, (

**b**) sand, (

**c**) gravel, (

**d**) water, (

**e**) silica fume, (

**f**) super plasticizer.

**Figure 8.**MLPNN model for; (

**a**) compressive strength and (

**b**) its error distribution between; (

**c**) splitting tensile strength and (

**d**) its error distribution.

**Figure 9.**ANFIS model for (

**a**) compressive strength and (

**b**) its error distribution between actual and target values; (

**c**) split tensile strength model and (

**d**) its error distribution between actual and target values.

**Figure 10.**GEP expression tree for compressive strength (

**a**) sub-ET 1; (

**b**) sub-ET2; (

**c**) sub-ET 3; (

**d**) sub-ET4; (

**e**) sub-ET5; (

**f**) sub-ET6.

**Figure 11.**GEP expression tree for splitting tensile strength (

**a**) sub-ET 1; (

**b**) sub-ET2; (

**c**) sub-ET 3; (

**d**) sub-ET4; (

**e**) sub-ET5.

**Figure 12.**GEP model for (

**a**) compressive strength and (

**b**) its error distribution; (

**c**) split tensile strength and (

**d**) its error distribution.

**Figure 16.**K-fold cross validation of compressive strength for MLPNN, ANFIS and GEP; (

**a**) Based on R

^{2}; (

**b**) Based on MAE; (

**c**) based on RMSE; (

**d**) based on RMSLE.

**Figure 17.**K-fold cross validation of tensile strength for MLPNN, ANFIS and GEP; (

**a**) Based on R

^{2}; (

**b**) Based on MAE; (

**c**) based on RMSE; (

**d**) based on RMSLE.

S. No | Algorithm Name | Notation | Dataset | Prediction Properties | Year | Waste Material Used | References |
---|---|---|---|---|---|---|---|

1 | Artificial neural network | ANN | 300 | Compressive strength | 2009 | FA | [54] |

2 | Artificial neural network | ANN | 80 | Compressive strength | 2011 | FA | [55] |

3 | Artificial neural network | ANN | 169 | Compressive strength | 2016 | THE | [56] |

4 | Artificial neural network | ANN | 69 | Compressive strength | 2017 | FA | [33] |

5 | Artificial neural network | ANN | 114 | Compressive strength | 2017 | FA | [57] |

6 | An adaptive neuro-fuzzy inference system | ANFIS | 55 | Compressive strength | 2018 | [58] | |

7 | Random Kitchen Sink algorithm | RKSA | 40 | V-funnel test J-ring test Slump test Compressive strength | 2018 | FA | [59] |

8 | Multivariate adaptive regression spline | M5 MARS | 114 | Compressive strength Slump test L-box test V-funnel test | 2018 | FA | [60] |

9 | Artificial neural network | ANN | 205 | Compressive strength | 2019 | FA GGBFS SF RHA | [61] |

10 | Random forest | RF | 131 | Compressive strength | 2019 | FA GGBFS SF | [62] |

11 | Intelligent rule-based enhanced multiclass support vector machine and fuzzy rules | IREMSVM-FR with RSM | 114 | Compressive strength | 2019 | FA | [63] |

12 | Support vector machine | SVM | Compressive strength | 2020 | FA | [64] | |

13 | Multivariate | MV | 21 | Compressive strength | 2020 | Crumb rubber with SF | [65] |

14 | Biogeographical-based programming | BBP | 413 | Elastic modulus | SF FA SLAG | [66] | |

15 | Support vector machine | SVM | 115 | Slump test L-box test V-funnel test Compressive strength | 2020 | FA | [67] |

16 | Adaptive neuro fuzzy inference system | ANFIS with ANN | 7 | Compressive strength | 2020 | POFA | [68] |

17 | Data envelopment analysis | DEA | 114 | Compressive strength Slump test L-box test V-funnel test | 2021 | FA | [69] |

Parameters | Cement | Fine Aggregate | Coarse Aggregate | Water | Silica Fume | Superplasticizer |
---|---|---|---|---|---|---|

Statistical Description | ||||||

Mean | 393.48 | 702.90 | 1062.41 | 185.15 | 38.25 | 2.56 |

Std error | 3.92 | 13.44 | 10.88 | 1.84 | 2.27 | 0.35 |

Median | 383.15 | 653.00 | 1040.00 | 175.00 | 26.25 | 0.00 |

variance | 4359.48 | 51,138.84 | 33,530.89 | 963.29 | 1469.97 | 34.80 |

Std. dev | 66.02 | 226.13 | 183.11 | 31.03 | 38.34 | 5.89 |

Kurtosis | −0.15 | −0.51 | 0.20 | 3.66 | 0.57 | 30.00 |

Skewness | 0.15 | 0.11 | 0.61 | 1.50 | 1.11 | 4.97 |

Range | 376.00 | 985.36 | 728.00 | 178.87 | 150.00 | 43.00 |

Min | 224.00 | 184.63 | 702.00 | 135.00 | 0.00 | 0.00 |

Max | 600.00 | 1170.00 | 1430.00 | 313.87 | 150.00 | 43.00 |

Sum | 111,354.90 | 198,941.50 | 300,663.20 | 52,397.59 | 10,827.33 | 726.11 |

Count | 283.00 | 283.00 | 283.00 | 283.00 | 283.00 | 283.00 |

Training Dataset | ||||||

Mean | 393.14 | 697.76 | 1067.67 | 185.80 | 36.78 | 2.65 |

Std error | 4.41 | 14.67 | 11.94 | 2.15 | 2.56 | 0.42 |

Median | 382.82 | 653.00 | 1040.00 | 176.00 | 26.25 | 0.00 |

variance | 4404.11 | 48,659.21 | 32,197.86 | 1045.27 | 1483.09 | 40.60 |

Std. dev | 66.36 | 220.59 | 179.44 | 32.33 | 38.51 | 6.37 |

Kurtosis | −0.14 | −0.38 | 0.28 | 3.70 | 0.52 | 27.05 |

Skewness | 0.13 | 0.11 | 0.65 | 1.57 | 1.11 | 4.83 |

Range | 376.00 | 985.37 | 728.00 | 178.88 | 150.00 | 43.00 |

Min | 224.00 | 184.63 | 702.00 | 135.00 | 0.00 | 0.00 |

Max | 600.00 | 1170.00 | 1430.00 | 313.88 | 150.00 | 43.00 |

Sum | 88,848.53 | 157,693.90 | 240,1294.40 | 41,990.32 | 8313.19 | 599.42 |

Count | 226.00 | 226.00 | 226.00 | 226.00 | 226.00 | 226.00 |

Testing Dataset | ||||||

Mean | 394.85 | 723.64 | 1041.56 | 182.58 | 44.11 | 2.22 |

Std error | 8.64 | 32.84 | 26.13 | 3.36 | 4.96 | 0.46 |

Median | 390.00 | 653.00 | 990.00 | 175.00 | 29.62 | 0.00 |

variance | 4255.64 | 61,470.40 | 38,931.08 | 642.77 | 1399.90 | 11.97 |

Std. dev | 65.24 | 247.93 | 197.31 | 25.35 | 37.42 | 3.46 |

Kurtosis | −0.17 | −0.93 | 0.05 | 0.46 | 1.07 | 9.21 |

Skewness | 0.28 | 0.09 | 0.57 | 0.73 | 1.24 | 2.55 |

Range | 302.00 | 932.82 | 728.00 | 125.70 | 150.00 | 19.00 |

Min | 238.00 | 237.19 | 702.00 | 135.20 | 0.00 | 0.00 |

Max | 540.00 | 1170.00 | 1430.00 | 260.90 | 150.00 | 19.00 |

Sum | 22,506.35 | 41,247.52 | 59,368.84 | 10,407.28 | 2514.14 | 126.69 |

Count | 57.00 | 57.00 | 57.00 | 57.00 | 57.00 | 57.00 |

Parameters | Cement | Fine Aggregate | Coarse Aggregate | Water | Silica Fume | Superplasticizer |
---|---|---|---|---|---|---|

Statistical Description | ||||||

Mean | 386.48 | 756.67 | 1102.91 | 186.36 | 55.33 | 3.57 |

Std error | 4.64 | 23.17 | 18.24 | 3.05 | 12.57 | 0.18 |

Median | 375.00 | 912.00 | 980.00 | 169.53 | 26.25 | 3.90 |

variance | 3212.04 | 79,963.57 | 49,589.84 | 1388.00 | 23,545.85 | 4.98 |

Std. dev | 56.67 | 282.78 | 222.69 | 37.26 | 153.45 | 2.23 |

Kurtosis | −0.12 | −1.07 | −0.83 | 2.72 | 30.06 | 1.27 |

Skewness | 0.73 | −0.39 | 0.28 | 1.68 | 5.49 | 0.40 |

Range | 234.60 | 985.37 | 728.00 | 178.68 | 953.98 | 10.48 |

Min | 289.49 | 184.63 | 702.00 | 135.20 | 0.00 | 0.00 |

Max | 524.09 | 1170.00 | 1430.00 | 313.88 | 953.98 | 10.48 |

Sum | 57,586.23 | 112,744.40 | 164,334.20 | 27,766.94 | 8244.31 | 531.91 |

Count | 149.00 | 149.00 | 149.00 | 149.00 | 149.00 | 149.00 |

Training Dataset | ||||||

Mean | 388.13 | 749.54 | 1109.50 | 187.36 | 57.08 | 3.55 |

Std error | 5.79 | 28.83 | 22.72 | 3.85 | 16.18 | 0.22 |

Median | 375.00 | 912.00 | 980.00 | 169.53 | 26.25 | 3.90 |

variance | 3212.04 | 79,963.57 | 49,589.84 | 1388.00 | 23,545.85 | 4.98 |

Std. dev | 57.92 | 288.26 | 227.22 | 38.52 | 161.78 | 2.22 |

Kurtosis | −0.32 | −1.10 | −0.87 | 2.35 | 27.33 | 1.29 |

Skewness | 0.60 | −0.33 | 0.18 | 1.61 | 5.25 | 0.38 |

Range | 234.60 | 985.37 | 728.00 | 178.68 | 953.98 | 10.48 |

Min | 289.49 | 184.63 | 702.00 | 135.20 | 0.00 | 0.00 |

Max | 524.09 | 1170.00 | 1430.00 | 313.88 | 953.98 | 10.48 |

Sum | 38,813.39 | 74,954.21 | 110,950.07 | 18,736.21 | 5707.68 | 354.82 |

Count | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |

Testing Dataset | ||||||

Mean | 383.12 | 771.23 | 1089.47 | 184.30 | 51.77 | 3.61 |

Std error | 7.78 | 39.08 | 30.69 | 4.97 | 19.48 | 0.32 |

Median | 375.00 | 920.00 | 980.00 | 165.00 | 26.25 | 3.90 |

variance | 2966.32 | 74,850.46 | 46,145.30 | 1212.64 | 18,596.89 | 5.17 |

Std. dev | 54.46 | 273.59 | 214.81 | 34.82 | 136.37 | 2.27 |

Kurtosis | 0.63 | −0.97 | −0.61 | 4.14 | 42.05 | 1.47 |

Skewness | 1.08 | −0.54 | 0.51 | 1.89 | 6.29 | 0.46 |

Range | 201.59 | 985.37 | 728.00 | 178.68 | 953.98 | 10.48 |

Min | 322.50 | 184.63 | 702.00 | 135.20 | 0.00 | 0.00 |

Max | 524.09 | 1170.00 | 1430.00 | 313.88 | 953.98 | 10.48 |

Sum | 18,772.84 | 37,790.19 | 53,384.14 | 9030.73 | 2536.63 | 177.09 |

Count | 49.00 | 49.00 | 49.00 | 49.00 | 49.00 | 49.00 |

Parameters | Abbreviation | Minimum | Maximum |
---|---|---|---|

Input Variables | |||

Binder | C | 224 | 600 |

Fine Aggregate Coarse Aggregate | FA CA | 184.6 702 | 1170 1430 |

Water | W | 135 | 313.9 |

Silica Fume Superplasticizer | SF SP | 0 0 | 150 43 |

Output Variable | |||

Compressive Strength | fc’ | 5.66 | 95.9 |

Parameters | Abbreviation | Minimum | Maximum |
---|---|---|---|

Input Variables | |||

Binder | C | 289.5 | 524.1 |

Fine Aggregate Coarse Aggregate | FA CA | 184.6 702 | 1170 1430 |

Water | W | 135 | 313.9 |

Silica Fume Superplasticizer | SF SP | 0 0 | 954 10.5 |

Output Variable | |||

Split Tensile Strength | fst’ | 6.97 | 0.66 |

**Table 6.**Range of Errors for Statistical Parameters [91]

Assessment Criteria | Range | Accurate Model |
---|---|---|

MAE | [0, ∞) | The Smaller the Better |

RMSE | [0, ∞) | The Smaller the Better |

MSLE | [0, ∞) | The Smaller the Better |

R^{2} Value | (0,1] | The Bigger the Better |

Output Parameter | Approach Employed | R Value |
---|---|---|

Compressive Strength | MLPNN | 0.85 |

ANFIS | 0.91 | |

GEP | 0.97 | |

Split Tensile Strength | MLPNN | 0.90 |

ANFIS | 0.92 | |

GEP | 0.93 |

Models | MAE | RMSE | RMSLE | R^{2} Value |
---|---|---|---|---|

MLPNN | ||||

Compressive Strength | 5.28 | 7.25 | 0.065 | 0.85 |

Split Tensile Strength | 0.41 | 0.51 | 0.059 | 0.90 |

ANFIS | ||||

Compressive Strength | 4.18 | 5.69 | 0.056 | 0.91 |

Split Tensile Strength | 0.26 | 0.40 | 0.052 | 0.92 |

GEP | ||||

Compressive Strength | 3.52 | 3.56 | 0.046 | 0.97 |

Split Tensile Strength | 0.31 | 0.31 | 0.037 | 0.93 |

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**MDPI and ACS Style**

Nafees, A.; Javed, M.F.; Khan, S.; Nazir, K.; Farooq, F.; Aslam, F.; Musarat, M.A.; Vatin, N.I.
Predictive Modeling of Mechanical Properties of Silica Fume-Based Green Concrete Using Artificial Intelligence Approaches: MLPNN, ANFIS, and GEP. *Materials* **2021**, *14*, 7531.
https://doi.org/10.3390/ma14247531

**AMA Style**

Nafees A, Javed MF, Khan S, Nazir K, Farooq F, Aslam F, Musarat MA, Vatin NI.
Predictive Modeling of Mechanical Properties of Silica Fume-Based Green Concrete Using Artificial Intelligence Approaches: MLPNN, ANFIS, and GEP. *Materials*. 2021; 14(24):7531.
https://doi.org/10.3390/ma14247531

**Chicago/Turabian Style**

Nafees, Afnan, Muhammad Faisal Javed, Sherbaz Khan, Kashif Nazir, Furqan Farooq, Fahid Aslam, Muhammad Ali Musarat, and Nikolai Ivanovich Vatin.
2021. "Predictive Modeling of Mechanical Properties of Silica Fume-Based Green Concrete Using Artificial Intelligence Approaches: MLPNN, ANFIS, and GEP" *Materials* 14, no. 24: 7531.
https://doi.org/10.3390/ma14247531