A Comparative Study of Random Forest and Genetic Engineering Programming for the Prediction of Compressive Strength of High Strength Concrete (HSC)
Abstract
:1. Introduction
2. Research Methodology
2.1. Random Forest Regression
- Collection of trained regression trees using training set.
- Calculating average of the individual regression tree output.
- Cross-validation of the predicted data using validation set.
2.2. Gene Expression Programming
3. Experimental Database Representation
3.1. Dataset Used in Modeling Aspect
3.2. Programming-Based Presentation of Datasets
4. GEP Model Development
5. Model Performance Analysis
6. Results and Discussion
6.1. Random Forest Model Analysis
6.2. Empirical Relation of HSC Using the GEP Model
6.3. GEP Model Evaluation
7. Statistical Analysis Checks on RF and GEP Model
8. Comparison of Models with ANN and Decision Tree
9. Permutation Feature Analysis (PFA)
10. Conclusions
- Random forest is an ensemble approach which gives adamant performance between observed and predicted value. It is due to incorporation of a weak learner as base learner (decision tree) and gives determination of coefficient R2 = 0.96.
- GEP is an individual model rather than an ensemble algorithm. It gives a good relation with the empirical relation. This relation can be used to predict the mechanical aspect of high strength concrete via hand calculation.
- Comparison of the RF and GEP models is made with ANN and DT. However, RF outbursts and gives an obstinate relation of R2 = 0.96. GEP model gives R2 = 0.90. ANN and DT models give 0.89 and 0.90, respectively. Moreover, RF gives less errors as compared to others individual algorithms. This is due to the bagging mechanism of RF.
- Permutation features give an influential parameter in HSC. This help us to check and know the most dominant variables in using experimental work; thus, all the variables have an effect on compressive strength.
Supplementary Materials
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Properties | Data Points | Algorithm | References |
---|---|---|---|
Compressive strength, Slump test | 187 | ANN | [7] |
Elastic modulus | 159 | ANN | [8] |
Elastic modulus | 159 | FUZZY | [9] |
Elastic modulus | 159 | SVM | [10] |
Elastic modulus | 159 | ANFIS and nonlinear | [11] |
Compressive strength | 20 | ANN | [12] |
Compressive strength | 324 | ELM | [13] |
Compressive strength | 357 | GEP | [14] |
Parameters | Cement | Fine/Coarse Aggregate | Water | Superplasticizer |
---|---|---|---|---|
Mean | 384.34 | 0.96 | 173.56 | 2.34 |
Standard Error | 4.92 | 0.01 | 0.82 | 0.14 |
Median | 360 | 0.92 | 170 | 1.25 |
Mode | 360 | 1.01 | 170 | 1 |
Standard Deviation | 93.00 | 0.26 | 15.56 | 2.69 |
Sample Variance | 8650.50 | 0.06 | 242.19 | 7.24 |
Kurtosis | 0.36 | 6.45 | 15.59 | 2.88 |
Skewness | 0.14 | 2.12 | 2.45 | 1.79 |
Range | 440 | 1.86 | 170.08 | 12 |
Minimum | 160 | 0.23 | 132 | 0 |
Maximum | 600 | 2.1 | 302.08 | 12 |
Sum | 137,212.84 | 344.07 | 61,963.8 | 837.61 |
Count | 357 | 357 | 357 | 357 |
Parameters | Cement | Fine/Coarse Aggregate | Water | Superplasticizer |
---|---|---|---|---|
Mean | 383.29 | 0.97 | 173.72 | 2.42 |
Standard Error | 6.06 | 0.01 | 1.08 | 0.17 |
Median | 360 | 0.92 | 170 | 1.37 |
Mode | 320 | 1.01 | 170 | 1 |
Standard Deviation | 95.95 | 0.27 | 17.17 | 2.74 |
Sample Variance | 9206.57 | 0.07 | 295.07 | 7.54 |
Kurtosis | 0.60 | 5.82 | 14.42 | 2.96 |
Skewness | 0.19 | 2.08 | 2.48 | 1.82 |
Range | 420 | 1.86 | 170.08 | 12 |
Minimum | 180 | 0.23 | 132 | 0 |
Maximum | 600 | 2.1 | 302.08 | 12 |
Sum | 95,823.1 | 242.79 | 43,431.75 | 606.43 |
Count | 250 | 250 | 250 | 250 |
Parameters | Cement | Fine/Coarse aggregate | Water | Superplasticizer |
---|---|---|---|---|
Mean | 387.04 | 0.92 | 172.18 | 1.98 |
Standard Error | 12.46 | 0.02 | 1.34 | 0.33 |
Median | 400 | 0.90 | 170 | 1 |
Mode | 360 | 0.75 | 170 | 1 |
Standard Deviation | 95.76 | 0.18 | 10.35 | 2.55 |
Sample Variance | 9170.56 | 0.03 | 107.25 | 6.55 |
Kurtosis | 0.22 | 6.82 | 0.18 | 4.75 |
Skewness | 0.17 | 1.66 | 0.33 | 2.19 |
Range | 440 | 1.22 | 45.2 | 12 |
Minimum | 160 | 0.58 | 154.8 | 0 |
Maximum | 600 | 1.80 | 200 | 12 |
Sum | 22,835.54 | 54.38 | 10,159.18 | 117.09 |
Count | 54 | 54 | 54 | 54 |
Parameters | Cement | Fine/Coarse Aggregate | Water | Superplasticizer |
---|---|---|---|---|
Mean | 390.52 | 0.90 | 173.07 | 2.10 |
Standard Error | 12.58 | 0.02 | 1.21 | 0.34 |
Median | 378 | 0.90 | 175 | 1 |
Mode | 360 | 1.04 | 180 | 0.5 |
Standard Deviation | 89.86 | 0.15 | 8.67 | 2.47 |
Sample Variance | 8076.29 | 0.02 | 75.21 | 6.11 |
Kurtosis | 1.08 | 0.52 | −0.18 | 2.17 |
Skewness | 0.17 | 0.61 | −0.62 | 1.65 |
Range | 440 | 0.73 | 38.32 | 10.5 |
Minimum | 160 | 0.66 | 154 | 0 |
Maximum | 600 | 1.39 | 192.32 | 10.5 |
Sum | 19,916.87 | 46.34 | 8826.8 | 107.57 |
Count | 55 | 55 | 55 | 55 |
Parameters | Settings |
---|---|
General | |
Genes | 4 |
Chromosomes | 30 |
Linking function | Addition |
Head size | 10 |
Function set | +, −, ×, ÷ |
Numerical constants | |
Constant per gene | 10 |
Lower bound | −10 |
Data type | Floating number |
Upper bound | 10 |
Genetic Operators | |
Two-point recombination rate | 0.00277 |
Gene transposition rate | 0.00277 |
Model | RMSE | MAE | R2 | |||
---|---|---|---|---|---|---|
Fc | Validation | Testing | Validation | Testing | Validation | Testing |
1.22 | 1.42 | 0.475 | 0.495 | 0.967 | 0.041 | |
RRMSE | RSE | P(row) | ||||
Validation | Testing | Validation | Testing | Validation | Testing | |
0.0186 | 0.021 | 0.072 | 0.053 | 0.024 | 0.025 |
Model | RMSE | MAE | RSE | |||
---|---|---|---|---|---|---|
Fc | Validation | Testing | Validation | Testing | Validation | Testing |
1.42 | 1.62 | 0.575 | 0.595 | 0.092 | 0.023 | |
RRMSE | R | P(row) | ||||
Validation | Testing | Validation | Testing | Validation | Testing | |
0.0286 | 0.031 | 0.957 | 0.031 | 0.014 | 0.015 |
S.No | Equation | Condition | RF Model | GEP Model |
---|---|---|---|---|
1 | 0.99 | 0.98 | ||
2 | 1.00 | 1.00 | ||
3 | 0.99 | 0.97 | ||
4 | 0.99 | 0.99 |
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Farooq, F.; Nasir Amin, M.; Khan, K.; Rehan Sadiq, M.; Faisal Javed, M.; Aslam, F.; Alyousef, R. A Comparative Study of Random Forest and Genetic Engineering Programming for the Prediction of Compressive Strength of High Strength Concrete (HSC). Appl. Sci. 2020, 10, 7330. https://doi.org/10.3390/app10207330
Farooq F, Nasir Amin M, Khan K, Rehan Sadiq M, Faisal Javed M, Aslam F, Alyousef R. A Comparative Study of Random Forest and Genetic Engineering Programming for the Prediction of Compressive Strength of High Strength Concrete (HSC). Applied Sciences. 2020; 10(20):7330. https://doi.org/10.3390/app10207330
Chicago/Turabian StyleFarooq, Furqan, Muhammad Nasir Amin, Kaffayatullah Khan, Muhammad Rehan Sadiq, Muhammad Faisal Javed, Fahid Aslam, and Rayed Alyousef. 2020. "A Comparative Study of Random Forest and Genetic Engineering Programming for the Prediction of Compressive Strength of High Strength Concrete (HSC)" Applied Sciences 10, no. 20: 7330. https://doi.org/10.3390/app10207330
APA StyleFarooq, F., Nasir Amin, M., Khan, K., Rehan Sadiq, M., Faisal Javed, M., Aslam, F., & Alyousef, R. (2020). A Comparative Study of Random Forest and Genetic Engineering Programming for the Prediction of Compressive Strength of High Strength Concrete (HSC). Applied Sciences, 10(20), 7330. https://doi.org/10.3390/app10207330