Predictive Modeling of Mechanical Properties of Silica Fume-Based Green Concrete Using Artificial Intelligence Approaches: MLPNN, ANFIS, and GEP
Abstract
:1. Introduction
2. Algorithms for Machine Learning
2.1. Multilayer Perceptron Neural Network (MLPNN)
2.2. Adaptive Neural Fuzzy Detection System (ANFIS)
2.3. Genetic Algorithm and Gene Expression Programming
3. Modeling Dataset and Model Development
4. Models Evaluation Criteria
5. Results and Discussion
5.1. Formulation of the Compressive Strength and Split Tensile Strength of SFC
5.1.1. Model Outcome of MLPNN
5.1.2. Model Outcomes of ANFIS
5.2. Evaluation of GEP Models for Compressive Strength and Split Tensile Strength
Model Outcomes of Gene Expression Programming (GEP)
5.3. Comparison between Ensemble Models and the GEP Model
5.4. Sensitivity Analysis
5.5. Cross-Validation
6. Conclusions
- 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 R2, 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
References
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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 |
Assessment Criteria | Range | Accurate Model |
---|---|---|
MAE | [0, ∞) | The Smaller the Better |
RMSE | [0, ∞) | The Smaller the Better |
MSLE | [0, ∞) | The Smaller the Better |
R2 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 | R2 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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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
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 StyleNafees, 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