Machine Learning Approach for Prediction of Lateral Confinement Coefficient of CFRP-Wrapped RC Columns
Abstract
:1. Introduction
2. Dataset Interpretation
- Corner radii are most significantly due to reduction/curtailments of the stress attack and improved strain distribution during extreme load application. At this moment, RC columns jeopardized maximum load, causing damage to weak zones due to uneven stirrup distribution, proper reinforcement arrangement or mixing proportion.
- By reducing corner radii and wrapping with CFRP material, we can technically ensure that our RC columns have enhanced performance, with improved ductility and comprehensive strength.
- Specimens examined by Ref. [54] showed that the compressive strength ratio (f’cc/f’co) of relatively large-scale square columns confined by CFRP increases almost linearly along with the increase of corner radius.
- Demonstrating that with CFRP, confinement is inconsequential to enlarge the compressive strength of RC columns with sharp corners (r = 0 mm) at the highest loading extents, although the ductility can be increased.
- Ref. [57] pointed out that the strength and strain augmentation effect of sporadically wrapped specimens can be perfected with evenly-distributed overlap regions. Thereupon, respective overlapping zones were staged on a different side and ducked the corner zones.
- Ref. [58] demonstrated the confinement potency model by considering lateral confinement level, corner radius ratio and size effect, proposed for FRP-confined square columns. Juxtaposed with other extant models, the contemplated one provides an enhanced examination of FRP-confined square columns.
3. Methodology
3.1. Genetic Programming (GP)
3.2. Minimax Probability Machine Regression (MPMR)
3.3. Deep Neural Network (DNN)
4. Results and Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Current Study | Doran et al. (2015) [11] | ||
---|---|---|---|
1 | No of Dataset | 293 | 100 |
2 | Models |
| Fuzzy Logic |
3 | No of Inputs | 6 | 5 |
4 | Type of CFRP RC Columns | Rectangular and Square | Rectangular |
5 | Corner Radii | Considered | Not Considered |
b (mm) | H (mm) | r (mm) | tw (mm) | Efrp (mm) | fco (mm) | Ks (mm) | |
---|---|---|---|---|---|---|---|
Min | 20 | 108 | 5 | 0.056 | 10,500 | 10.83 | 0.94 |
Mean | 167.15 | 277.07 | 25.16 | 0.55 | 187,852.90 | 30.54 | 1.69 |
Std | 57.66 | 149.73 | 12.74 | 0.50 | 87,680.16 | 11.61 | 0.69 |
Max | 457 | 1200 | 60 | 3 | 640,000 | 55.36 | 4.79 |
skewness | 1.46 | 2.26 | 0.41 | 2.36 | 0.24 | 0.28 | 1.74 |
Kurtosis | 7.05 | 11.71 | 2.72 | 10.16 | 6.56 | 2.56 | 6.38 |
GP | MPMR | DNN |
---|---|---|
|
|
|
Statistical Parameters | Description | Ideal Condition |
---|---|---|
Coefficient of Determination, | Coefficient of determination calculates the constancy of collaboration between the actual and the predicted values. | The ideal value must be near to unity. |
Mean Absolute Error | MAE enumerates the accuracy error of the predicted and actual data. | MAE value should be 0. When the value of R overtures to 0. |
Root Mean Square Error | Analyze the measured value to the estimated value and calculate the square root of the mean residual error. | RMSE has to be 0. When the value of R overtures to 1, the RMSE value will be near to 0, and vice versa. |
Index of Agreement, | Index was employed to analyze the precision of the measurable models in this investigation. | The IA value should be 1 to enumerate the performance model. |
Fractional Variance | FV emphases computed variance of actual and predicted data. | FV ideal value must be 0. |
Factor of Two (FA2) | Indicates the range of the output results data between 0.5–2 as benchmark model accuracy. | Based on the model performance, the range output result data should lie between 0.5–2. |
Coefficient of Variation (%) | It symbolizes the ratio of the RMSE variance to the actual data variance. It is exhibited in percentage. | The ideal value of CV should be 0. RMSE is also 0. |
Durbin–Watson (DW) statistics, where, | It measures the predictive accuracy. To validate the predictive capability of the prediction models, | The ideal value of DW must be close to 2. |
Normalized Mean Bias Error (NMBE), | NMBE estimates the aptitude of the model to anticipate a value, which is staged away from the mean value. It is expressed in percentage. | A positive NMBE reveals over-prediction, and a negative value depicts under-prediction |
Doran et al. (2015) [11] (Fuzzy Logic) Overall | Training GP | Testing GP | Training MPMR | Testing MPMR | Training DNN | Testing DNN | |
---|---|---|---|---|---|---|---|
Number of Dataset | 100 | 220 | 73 | 220 | 73 | 220 | 73 |
R2 | 0.919 | 0.89 | 0.89 | 0.885 | 0.712 | 0.806 | 0.712 |
MAE | 0.133 | 0.041 | 0.054 | 0.041 | 0.064 | 0.036 | 0.070 |
RMSE | 0.174 | 0.056 | 0.073 | 0.057 | 0.097 | 0.076 | 0.117 |
IA | 0.976 | 0.970 | 0.960 | 0.969 | 0.937 | 0.947 | 0.883 |
FV | 0.111 | 0.116 | 0.389 | 0.123 | 0.067 | 0.071 | 0.499 |
FA2 | 0.993 | 0.836 | 1.135 | 1.237 | 1.283 | 1.184 | 1.454 |
CV(%) | 10.74 | 30.777 | 31.933 | 31.185 | 42.794 | 41.421 | 51.411 |
DW statistic | 1.513 | 1.453 | 1.004 | 1.491 | 0.978 | 0.842 | 0.877 |
NMBE (%) | - | 0.001 | −9.596 | 0.130 | −3.974 | −2.666 | −20.767 |
Training (GP) | Testing (GP) | Training (MPMR) | Testing (MPMR) | Training (DNN) | Testing (DNN) | |
---|---|---|---|---|---|---|
R2 | 3 | 3 | 2 | 1 | 1 | 1 |
MAE | 1 | 3 | 2 | 2 | 3 | 1 |
RMSE | 3 | 3 | 2 | 2 | 1 | 1 |
IA | 1 | 3 | 3 | 2 | 2 | 1 |
FV | 2 | 2 | 1 | 3 | 3 | 1 |
FA2 | 1 | 1 | 3 | 3 | 2 | 1 |
CV (%) | 3 | 3 | 2 | 2 | 1 | 1 |
DW statistic | 2 | 2 | 3 | 1 | 1 | 1 |
NMBE (%) | 3 | 1 | 2 | 2 | 1 | 1 |
Total Points | 19 | 21 | 20 | 18 | 15 | 9 |
Overall Points | 40 | 38 | 24 |
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Xue, X.; Makota, C.; Khalaf, O.I.; Jayabalan, J.; Samui, P.; Abdulsahib, G.M. Machine Learning Approach for Prediction of Lateral Confinement Coefficient of CFRP-Wrapped RC Columns. Symmetry 2023, 15, 545. https://doi.org/10.3390/sym15020545
Xue X, Makota C, Khalaf OI, Jayabalan J, Samui P, Abdulsahib GM. Machine Learning Approach for Prediction of Lateral Confinement Coefficient of CFRP-Wrapped RC Columns. Symmetry. 2023; 15(2):545. https://doi.org/10.3390/sym15020545
Chicago/Turabian StyleXue, Xingsi, Celestine Makota, Osamah Ibrahim Khalaf, Jagan Jayabalan, Pijush Samui, and Ghaida Muttashar Abdulsahib. 2023. "Machine Learning Approach for Prediction of Lateral Confinement Coefficient of CFRP-Wrapped RC Columns" Symmetry 15, no. 2: 545. https://doi.org/10.3390/sym15020545