Random Forests Machine Learning Applied to PEER Structural Performance Experimental Columns Database
Abstract
:1. Introduction
- According to the authors’ knowledge, the PEER structural performance database is employed for the first time in order to detect the failure mode of RC columns.
- The influence of the main design variables on the column ductility and failure mode is also thoroughly examined.
- Finally, all the performance metrics necessary for the evaluation of the ML methodology in detecting the failure mode of RC columns are provided too.
2. Materials and Methods
2.1. Statistical Representation of the PEER Structural Performance Database
2.2. Influence of Main Design Variables to Column Ductility and Failure Mode
- -
- If no shear damage was reported by the experimentalist, the column was classified as flexure critical.
- -
- If shear damage (diagonal cracks) was reported, the absolute maximum effective force (: absolute maximum measured force in the experimental column response) was compared with the calculated “ideal” force corresponding to a maximum axial compressive strain in the concrete cover set equal to 0.004, which corresponds to the spalling of unconfined concrete (). The failure displacement ductility at an effective force equal to 80% maximum was determined from the experimental envelope. If the maximum effective force or if the failure displacement ductility was less than or equal to 2 (), the column was classified as shear critical. Otherwise, the column was classified as flexure–shear critical. All columns in the database are divided into two sub-groups according to cross-sectional shape (rectangular and circular section columns).
2.3. Supervised ML-Based Prediction of Column Failure Mode with Random Forests
- The estimator number that defines the number of decision trees.
- The maximum feature number that defines the maximum feature number during the separation of nodes in each decision tree.
- The maximum depth: the maximum depth in each decision tree.
- Minimum sample points at each node separation: the minimum sample point number that should be taken into account at each node.
Random Forests with Python [22]
- The question is set and the demanded data are defined.
- The data are obtained in an accessible form.
- Any lack of data or uncertainty is defined and corrected accordingly.
- The data are prepared for the machine learning model.
- A baseline model is set that is intended to be overcome.
- The model is trained with the training data.
- Model predictions are made with the test data.
- The predictions are compared to the known test goals and the performance metrics are computed.
- If the performance is not satisfactory, we adjust the model and obtain more data or another modeling technique is tested too.
3. Results
3.1. Rectangular RC Columns
3.2. Circular RC Columns
3.3. Parametric Sensitivity of Random Forest Algorithm
4. Discussion
5. Conclusions
Author Contributions
Funding
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Feature Values | True Label Values (1 = Flexure, 2 = Flexure–Shear, 3 = Shear) | ||||
---|---|---|---|---|---|
Aspect Ratio | Axial Load Ratio | ρs (%) | fc (MPa) | vmax/√fc | Failure |
2.00 | 0.00 | 0.51 | 37.5 | 0.42 | 2 |
2.00 | 0.00 | 0.51 | 37.2 | 0.29 | 2 |
2.50 | 0.00 | 0.51 | 36 | 0.37 | 2 |
2.00 | 0.00 | 0.51 | 30.6 | 0.42 | 3 |
2.00 | 0.00 | 0.76 | 31.1 | 0.47 | 2 |
1.50 | 0.00 | 0.51 | 30.1 | 0.57 | 3 |
2.00 | 0.00 | 0.38 | 29.5 | 0.41 | 3 |
2.00 | 0.20 | 1.02 | 28.7 | 0.69 | 2 |
2.00 | 0.20 | 1.02 | 31.2 | 0.64 | 2 |
2.00 | 0.20 | 0.51 | 29.9 | 0.59 | 2 |
1.50 | 0.10 | 1.02 | 28.6 | 0.78 | 2 |
2.00 | 0.10 | 1.02 | 36.2 | 0.58 | 2 |
2.00 | 0.00 | 0.51 | 33.7 | 0.43 | 2 |
2.00 | 0.00 | 0.51 | 34.8 | 0.31 | 2 |
2.00 | 0.10 | 0.51 | 33.4 | 0.51 | 3 |
2.50 | 0.10 | 0.51 | 34.3 | 0.44 | 2 |
1.50 | 0.10 | 0.51 | 35 | 0.68 | 3 |
1.50 | 0.10 | 0.38 | 34.4 | 0.59 | 3 |
1.75 | 0.17 | 0.38 | 36.7 | 0.64 | 3 |
2.00 | 0.00 | 0.38 | 33.2 | 0.37 | 3 |
2.00 | 0.00 | 0.39 | 30.9 | 0.41 | 3 |
2.00 | 0.00 | 0.76 | 32.3 | 0.47 | 2 |
2.00 | 0.00 | 0.77 | 33.1 | 0.47 | 2 |
2.00 | 0.19 | 1.42 | 38 | 0.60 | 1 |
2.00 | 0.39 | 0.47 | 37 | 0.64 | 2 |
2.00 | 0.39 | 1.42 | 37 | 0.76 | 1 |
6.22 | 0.05 | 0.63 | 38.8 | 0.07 | 1 |
6.22 | 0.09 | 0.63 | 36.2 | 0.08 | 1 |
2.93 | 0.05 | 0.63 | 35.9 | 0.19 | 2 |
2.92 | 0.10 | 0.63 | 34.4 | 0.21 | 2 |
7.50 | 0.24 | 1.45 | 34.5 | 0.18 | 1 |
3.75 | 0.24 | 1.45 | 34.5 | 0.39 | 1 |
3.75 | 0.35 | 1.45 | 34.5 | 0.40 | 1 |
6.01 | 0.07 | 0.63 | 35.8 | 0.12 | 1 |
3.01 | 0.07 | 1.49 | 34.3 | 0.31 | 1 |
3.00 | 0.10 | 1.41 | 24.1 | 0.27 | 1 |
3.00 | 0.21 | 1.41 | 23.1 | 0.31 | 1 |
6.00 | 0.10 | 0.68 | 25.4 | 0.13 | 1 |
3.00 | 0.10 | 1.41 | 24.4 | 0.26 | 1 |
3.00 | 0.20 | 1.41 | 24.3 | 0.32 | 1 |
6.00 | 0.11 | 0.68 | 23.3 | 0.13 | 1 |
4.50 | 0.09 | 0.94 | 29 | 0.19 | 1 |
4.50 | 0.09 | 0.94 | 29 | 0.19 | 1 |
4.50 | 0.09 | 0.94 | 35.5 | 0.17 | 1 |
4.50 | 0.09 | 0.94 | 35.5 | 0.21 | 1 |
4.50 | 0.09 | 0.94 | 35.5 | 0.18 | 1 |
4.50 | 0.09 | 0.94 | 32.8 | 0.19 | 1 |
4.50 | 0.09 | 0.94 | 32.8 | 0.17 | 1 |
4.50 | 0.09 | 0.94 | 32.5 | 0.18 | 1 |
4.50 | 0.10 | 0.94 | 27 | 0.20 | 1 |
4.50 | 0.10 | 0.94 | 27 | 0.19 | 1 |
4.50 | 0.10 | 0.94 | 27 | 0.19 | 1 |
1.50 | 0.06 | 0.28 | 30 | 0.26 | 2 |
1.50 | 0.06 | 0.17 | 30 | 0.37 | 2 |
6.00 | 0.15 | 0.89 | 41.1 | 0.19 | 1 |
1.99 | 0.31 | 1.14 | 38.3 | 0.61 | 1 |
1.99 | -0.10 | 1.14 | 39.2 | 0.28 | 2 |
1.99 | 0.15 | 1.14 | 39.4 | 0.54 | 1 |
1.99 | 0.15 | 2.70 | 35 | 1.02 | 2 |
1.99 | -0.08 | 0.85 | 35.2 | 0.41 | 2 |
1.99 | 0.33 | 3.04 | 35 | 1.14 | 1 |
8.00 | 0.30 | 0.92 | 36.6 | 0.19 | 1 |
8.00 | 0.27 | 1.38 | 40 | 0.17 | 1 |
8.00 | 0.28 | 0.92 | 38.6 | 0.19 | 1 |
4.00 | 0.07 | 0.70 | 31 | 0.18 | 1 |
8.00 | 0.07 | 0.70 | 31 | 0.09 | 1 |
10.00 | 0.07 | 0.70 | 31 | 0.06 | 1 |
4.00 | 0.07 | 0.70 | 31 | 0.11 | 1 |
4.00 | 0.07 | 0.70 | 31 | 0.30 | 1 |
3.00 | 0.09 | 0.89 | 34.5 | 0.32 | 1 |
8.00 | 0.09 | 0.89 | 34.5 | 0.12 | 1 |
10.00 | 0.09 | 0.89 | 34.5 | 0.11 | 1 |
3.00 | 0.04 | 0.54 | 34.6 | 0.26 | 1 |
3.00 | 0.04 | 0.81 | 33 | 0.28 | 1 |
6.58 | 0.31 | 1.54 | 65 | 0.18 | 1 |
6.58 | 0.31 | 3.49 | 65 | 0.17 | 1 |
6.58 | 0.42 | 1.74 | 90 | 0.17 | 1 |
6.58 | 0.21 | 1.54 | 90 | 0.16 | 1 |
6.58 | 0.42 | 1.54 | 90 | 0.17 | 1 |
2.58 | 0.00 | 0.10 | 34.7 | 0.19 | 2 |
2.58 | 0.00 | 0.26 | 35.4 | 0.23 | 2 |
2.00 | 0.00 | 0.13 | 29.8 | 0.25 | 3 |
2.00 | 0.00 | 0.13 | 26.8 | 0.22 | 3 |
2.00 | 0.00 | 0.13 | 31.2 | 0.20 | 3 |
Feature Values | True Label Values (1 = Flexure, 2 = Flexure–Shear, 3 = Shear) | ||||
---|---|---|---|---|---|
Aspect Ratio | Axial Load Ratio | ρs (%) | fc (MPa) | vmax/√fc | Failure |
2.18 | 0.26 | 1.50 | 23.1 | 0.48 | 1 |
2.18 | 0.21 | 2.30 | 41.4 | 0.42 | 1 |
2.18 | 0.42 | 2.00 | 21.4 | 0.48 | 1 |
2.18 | 0.60 | 3.50 | 23.5 | 0.47 | 1 |
4.00 | 0.38 | 2.83 | 23.6 | 0.25 | 1 |
4.00 | 0.21 | 2.22 | 25 | 0.21 | 1 |
4.00 | 0.10 | 0.86 | 46.5 | 0.18 | 1 |
4.00 | 0.30 | 1.22 | 44 | 0.26 | 1 |
4.00 | 0.30 | 0.80 | 44 | 0.26 | 1 |
4.00 | 0.30 | 0.57 | 40 | 0.26 | 1 |
4.00 | 0.22 | 1.56 | 28.3 | 0.25 | 1 |
4.00 | 0.39 | 1.99 | 40.1 | 0.27 | 1 |
4.00 | 0.50 | 0.66 | 41 | 0.29 | 1 |
4.00 | 0.50 | 0.32 | 40 | 0.29 | 1 |
4.00 | 0.70 | 1.26 | 42 | 0.29 | 1 |
4.00 | 0.70 | 0.70 | 39 | 0.30 | 1 |
4.00 | 0.70 | 2.33 | 40 | 0.31 | 1 |
4.00 | 0.20 | 2.55 | 25.6 | 0.21 | 1 |
4.00 | 0.20 | 2.55 | 25.6 | 0.21 | 1 |
4.00 | 0.20 | 2.55 | 25.6 | 0.22 | 1 |
4.00 | 0.20 | 2.55 | 25.6 | 0.21 | 1 |
3.00 | 0.10 | 1.70 | 32 | 0.23 | 1 |
3.00 | 0.10 | 1.70 | 32 | 0.24 | 1 |
3.00 | 0.30 | 2.08 | 32.1 | 0.36 | 1 |
3.00 | 0.30 | 2.08 | 32.1 | 0.36 | 1 |
2.97 | 0.10 | 2.17 | 26.9 | 0.32 | 1 |
1.50 | 0.33 | 1.18 | 20.6 | 0.57 | 1 |
1.50 | 0.17 | 0.81 | 21.6 | 0.47 | 3 |
1.50 | 0.35 | 1.39 | 21 | 0.61 | 2 |
4.00 | 0.03 | 0.32 | 24.8 | 0.15 | 1 |
4.00 | 0.03 | 0.32 | 24.8 | 0.14 | 1 |
4.00 | 0.03 | 0.32 | 24.8 | 0.14 | 1 |
2.00 | 0.14 | 0.57 | 32 | 0.45 | 2 |
2.00 | 0.15 | 0.57 | 29.9 | 0.51 | 2 |
1.65 | 0.05 | 0.36 | 27.1 | 0.45 | 3 |
2.00 | 0.80 | 0.73 | 21.1 | 0.58 | 2 |
2.00 | 0.80 | 0.73 | 21.1 | 0.61 | 1 |
2.00 | 0.90 | 1.75 | 21.1 | 0.57 | 2 |
3.00 | 0.70 | 0.73 | 28.8 | 0.41 | 2 |
3.00 | 0.70 | 0.73 | 28.8 | 0.40 | 2 |
3.00 | 0.70 | 1.75 | 28.8 | 0.38 | 2 |
3.00 | 0.11 | 0.38 | 27.9 | 0.25 | 1 |
3.00 | 0.11 | 0.38 | 27.9 | 0.24 | 1 |
3.00 | 0.11 | 0.38 | 27.9 | 0.25 | 1 |
3.00 | 0.12 | 0.38 | 24.8 | 0.27 | 1 |
3.00 | 0.11 | 0.38 | 27.9 | 0.25 | 1 |
3.00 | 0.11 | 0.38 | 27.9 | 0.23 | 1 |
1.25 | 0.18 | 0.21 | 31.8 | 0.71 | 3 |
1.25 | 0.45 | 0.21 | 33 | 0.72 | 3 |
2.50 | 0.40 | 1.61 | 85.7 | 0.66 | 1 |
2.50 | 0.63 | 1.61 | 85.7 | 0.65 | 1 |
2.50 | 0.63 | 1.61 | 85.7 | 0.67 | 1 |
2.50 | 0.25 | 1.61 | 115.8 | 0.59 | 1 |
2.50 | 0.25 | 1.61 | 115.8 | 0.59 | 1 |
2.50 | 0.42 | 1.61 | 115.8 | 0.67 | 1 |
2.50 | 0.42 | 1.61 | 115.8 | 0.67 | 1 |
1.50 | 0.26 | 0.91 | 25.8 | 0.64 | 2 |
1.50 | 0.62 | 0.91 | 25.8 | 0.67 | 2 |
2.00 | 0.35 | 0.50 | 99.5 | 0.66 | 1 |
2.00 | 0.35 | 0.75 | 99.5 | 0.66 | 1 |
2.00 | 0.35 | 0.61 | 99.5 | 0.69 | 1 |
2.00 | 0.35 | 0.50 | 99.5 | 0.65 | 1 |
2.00 | 0.35 | 0.50 | 99.5 | 0.65 | 1 |
2.00 | 0.35 | 0.50 | 99.5 | 0.67 | 1 |
2.00 | 0.35 | 0.50 | 99.5 | 0.65 | 1 |
1.16 | 0.74 | 0.89 | 46.3 | 0.98 | 2 |
2.88 | 0.12 | 0.33 | 34.7 | 0.36 | 2 |
2.88 | 0.12 | 0.33 | 34.7 | 0.37 | 1 |
2.88 | 0.15 | 0.48 | 26.1 | 0.44 | 2 |
2.88 | 0.15 | 0.48 | 26.1 | 0.41 | 1 |
2.88 | 0.11 | 0.33 | 33.6 | 0.35 | 2 |
2.88 | 0.11 | 0.33 | 33.6 | 0.39 | 1 |
2.88 | 0.07 | 0.33 | 33.6 | 0.33 | 3 |
2.88 | 0.07 | 0.33 | 33.6 | 0.35 | 1 |
2.88 | 0.11 | 0.67 | 33.4 | 0.38 | 2 |
2.88 | 0.11 | 0.67 | 33.4 | 0.37 | 1 |
2.88 | 0.11 | 1.47 | 33.5 | 0.45 | 2 |
2.88 | 0.11 | 1.47 | 33.5 | 0.45 | 1 |
2.88 | 0.11 | 0.92 | 33.5 | 0.45 | 2 |
2.88 | 0.11 | 0.92 | 33.5 | 0.45 | 1 |
5.50 | 0.10 | 1.54 | 29.1 | 0.12 | 1 |
5.50 | 0.09 | 0.93 | 30.7 | 0.12 | 1 |
5.50 | 0.10 | 1.54 | 29.2 | 0.12 | 1 |
5.50 | 0.10 | 0.93 | 27.6 | 0.15 | 1 |
5.50 | 0.20 | 1.54 | 29.4 | 0.15 | 1 |
5.50 | 0.18 | 0.93 | 31.8 | 0.14 | 1 |
5.50 | 0.26 | 1.54 | 33.3 | 0.15 | 1 |
5.50 | 0.27 | 0.93 | 32.4 | 0.15 | 1 |
5.50 | 0.28 | 1.54 | 31 | 0.16 | 1 |
5.50 | 0.27 | 0.93 | 31.8 | 0.15 | 1 |
1.11 | 0.16 | 0.28 | 34.9 | 0.58 | 3 |
1.98 | 0.16 | 0.31 | 34.9 | 0.47 | 3 |
1.11 | 0.27 | 0.28 | 42 | 0.67 | 3 |
1.50 | 0.10 | 0.26 | 29.9 | 0.42 | 3 |
3.00 | 0.21 | 2.19 | 39.3 | 0.36 | 1 |
3.00 | 0.31 | 1.26 | 39.8 | 0.37 | 1 |
2.86 | 0.00 | 0.85 | 43.6 | 0.34 | 1 |
2.86 | 0.14 | 1.69 | 34.8 | 0.38 | 1 |
2.86 | 0.15 | 2.54 | 32 | 0.47 | 1 |
2.86 | 0.13 | 1.95 | 37.3 | 0.46 | 1 |
2.86 | 0.13 | 1.95 | 39 | 0.45 | 1 |
4.56 | 0.30 | 1.22 | 80 | 0.23 | 1 |
4.56 | 0.30 | 1.22 | 80 | 0.22 | 1 |
4.56 | 0.20 | 1.22 | 80 | 0.18 | 1 |
4.56 | 0.20 | 1.22 | 80 | 0.25 | 1 |
4.56 | 0.20 | 1.83 | 80 | 0.25 | 1 |
4.56 | 0.30 | 1.83 | 80 | 0.23 | 1 |
4.56 | 0.30 | 1.83 | 80 | 0.23 | 1 |
4.56 | 0.20 | 1.83 | 80 | 0.20 | 1 |
4.56 | 0.20 | 3.66 | 80 | 0.18 | 1 |
4.56 | 0.30 | 3.66 | 80 | 0.23 | 1 |
4.56 | 0.20 | 3.66 | 80 | 0.24 | 1 |
4.56 | 0.30 | 3.66 | 80 | 0.24 | 1 |
4.56 | 0.20 | 1.22 | 80 | 0.31 | 1 |
4.56 | 0.30 | 1.22 | 80 | 0.30 | 1 |
4.56 | 0.30 | 1.22 | 80 | 0.31 | 1 |
4.56 | 0.20 | 1.22 | 80 | 0.37 | 1 |
4.56 | 0.20 | 1.83 | 80 | 0.29 | 1 |
4.56 | 0.20 | 1.83 | 80 | 0.35 | 1 |
4.56 | 0.30 | 1.83 | 80 | 0.31 | 1 |
4.56 | 0.30 | 1.83 | 80 | 0.31 | 1 |
4.56 | 0.20 | 3.66 | 80 | 0.31 | 1 |
4.56 | 0.20 | 3.66 | 80 | 0.31 | 1 |
4.56 | 0.30 | 3.66 | 80 | 0.30 | 1 |
4.56 | 0.30 | 3.66 | 80 | 0.32 | 1 |
3.83 | 0.10 | 0.37 | 27.2 | 0.30 | 1 |
3.83 | 0.24 | 0.37 | 27.2 | 0.33 | 1 |
3.83 | 0.09 | 0.48 | 28.1 | 0.31 | 1 |
3.83 | 0.23 | 0.48 | 28.1 | 0.35 | 1 |
3.22 | 0.09 | 0.08 | 26.9 | 0.26 | 3 |
3.22 | 0.07 | 0.08 | 33.1 | 0.20 | 2 |
3.22 | 0.28 | 0.08 | 25.5 | 0.29 | 2 |
3.22 | 0.26 | 0.08 | 27.6 | 0.30 | 3 |
3.22 | 0.26 | 0.25 | 27.6 | 0.32 | 3 |
3.22 | 0.09 | 0.08 | 26.9 | 0.25 | 3 |
3.22 | 0.07 | 0.08 | 33.1 | 0.19 | 2 |
3.22 | 0.28 | 0.25 | 25.5 | 0.35 | 2 |
2.00 | 0.10 | 3.67 | 76 | 0.58 | 1 |
2.00 | 0.20 | 3.67 | 76 | 0.67 | 1 |
2.00 | 0.10 | 3.67 | 86 | 0.46 | 1 |
2.00 | 0.19 | 3.67 | 86 | 0.53 | 1 |
2.00 | 0.10 | 1.63 | 86 | 0.45 | 2 |
2.00 | 0.19 | 1.63 | 86 | 0.54 | 2 |
2.00 | 0.60 | 0.90 | 118 | 0.61 | 1 |
2.00 | 0.60 | 1.41 | 118 | 0.66 | 1 |
2.00 | 0.60 | 1.82 | 118 | 0.74 | 1 |
2.00 | 0.35 | 1.41 | 118 | 0.67 | 1 |
2.00 | 0.35 | 1.82 | 118 | 0.67 | 1 |
7.64 | 0.34 | 0.12 | 40.6 | 0.13 | 1 |
6.04 | 0.50 | 3.15 | 72.1 | 0.19 | 1 |
6.04 | 0.36 | 2.84 | 71.7 | 0.19 | 1 |
6.04 | 0.50 | 2.84 | 71.8 | 0.19 | 1 |
6.04 | 0.50 | 5.12 | 71.9 | 0.19 | 1 |
6.04 | 0.45 | 4.02 | 101.8 | 0.21 | 1 |
6.04 | 0.46 | 6.74 | 101.9 | 0.21 | 1 |
6.04 | 0.45 | 2.72 | 102 | 0.18 | 1 |
6.04 | 0.47 | 4.29 | 102.2 | 0.19 | 1 |
4.70 | 0.43 | 1.00 | 34 | 0.27 | 1 |
4.70 | 0.43 | 2.00 | 34 | 0.27 | 1 |
4.70 | 0.20 | 2.00 | 34 | 0.23 | 1 |
4.70 | 0.46 | 1.33 | 34 | 0.29 | 1 |
4.70 | 0.46 | 2.66 | 34 | 0.33 | 1 |
4.70 | 0.46 | 2.66 | 34 | 0.31 | 1 |
4.70 | 0.46 | 1.26 | 34 | 0.30 | 1 |
4.70 | 0.23 | 1.26 | 34 | 0.28 | 1 |
4.70 | 0.46 | 1.26 | 34 | 0.31 | 1 |
4.70 | 0.46 | 2.66 | 34 | 0.33 | 1 |
3.00 | 0.05 | 1.00 | 69.6 | 0.20 | 1 |
3.00 | 0.05 | 1.00 | 69.6 | 0.20 | 1 |
3.00 | 0.10 | 1.00 | 67.8 | 0.28 | 1 |
3.00 | 0.10 | 1.00 | 67.8 | 0.28 | 1 |
3.00 | 0.21 | 1.00 | 65.5 | 0.32 | 1 |
3.00 | 0.21 | 1.00 | 65.5 | 0.31 | 1 |
3.00 | 0.00 | 1.00 | 37.9 | 0.23 | 1 |
3.00 | 0.00 | 1.00 | 37.9 | 0.23 | 1 |
3.00 | 0.14 | 1.00 | 48.3 | 0.25 | 1 |
3.00 | 0.14 | 1.00 | 48.3 | 0.25 | 1 |
3.00 | 0.36 | 1.00 | 38.1 | 0.33 | 1 |
3.00 | 0.36 | 1.00 | 38.1 | 0.33 | 1 |
3.50 | 0.11 | 0.76 | 24.9 | 0.31 | 1 |
3.50 | 0.16 | 0.76 | 26.7 | 0.32 | 1 |
3.50 | 0.22 | 0.76 | 26.1 | 0.37 | 1 |
3.50 | 0.11 | 0.73 | 25.3 | 0.31 | 1 |
3.50 | 0.16 | 0.73 | 27.1 | 0.34 | 1 |
3.50 | 0.21 | 0.73 | 26.8 | 0.37 | 1 |
3.50 | 0.11 | 0.71 | 26.38 | 0.31 | 1 |
3.50 | 0.15 | 0.71 | 27.48 | 0.34 | 1 |
3.50 | 0.21 | 0.71 | 26.9 | 0.36 | 1 |
2.67 | 0.00 | 0.04 | 21.9 | 0.23 | 3 |
1.33 | 0.00 | 0.09 | 16 | 0.38 | 3 |
3.92 | 0.00 | 0.96 | 102.7 | 0.20 | 1 |
3.92 | 0.20 | 0.96 | 86.3 | 0.34 | 1 |
3.92 | 0.00 | 0.96 | 87.5 | 0.19 | 1 |
3.92 | 0.10 | 0.96 | 83.4 | 0.26 | 1 |
3.92 | 0.20 | 0.96 | 90 | 0.30 | 1 |
3.92 | 0.00 | 0.96 | 67.5 | 0.21 | 1 |
3.92 | 0.10 | 0.96 | 74.6 | 0.26 | 1 |
3.92 | 0.20 | 0.96 | 81.8 | 0.27 | 1 |
3.92 | 0.20 | 0.77 | 75.8 | 0.28 | 1 |
3.92 | 0.20 | 0.64 | 87 | 0.29 | 1 |
3.92 | 0.20 | 0.54 | 71.2 | 0.27 | 1 |
3.22 | 0.15 | 0.25 | 21.1 | 0.33 | 2 |
3.22 | 0.61 | 0.25 | 21.1 | 0.37 | 2 |
3.22 | 0.15 | 0.25 | 21.8 | 0.30 | 2 |
6.56 | 0.14 | 2.50 | 92.4 | 0.14 | 1 |
6.56 | 0.28 | 2.50 | 93.3 | 0.18 | 1 |
6.56 | 0.39 | 2.50 | 98.2 | 0.21 | 1 |
6.56 | 0.14 | 1.16 | 94.8 | 0.12 | 1 |
6.56 | 0.26 | 1.16 | 97.7 | 0.18 | 1 |
6.56 | 0.37 | 1.16 | 104.3 | 0.19 | 1 |
6.56 | 0.40 | 2.50 | 78.7 | 0.21 | 1 |
6.56 | 0.41 | 2.50 | 109.2 | 0.22 | 1 |
6.56 | 0.35 | 1.93 | 109.5 | 0.20 | 1 |
6.56 | 0.37 | 1.33 | 104.2 | 0.21 | 1 |
6.56 | 0.53 | 1.93 | 104.5 | 0.21 | 1 |
6.56 | 0.51 | 2.50 | 109.4 | 0.22 | 1 |
2.25 | 0.08 | 0.57 | 33.7 | 0.42 | 1 |
2.25 | 0.08 | 0.57 | 33.7 | 0.42 | 1 |
2.25 | 0.09 | 1.64 | 32.1 | 0.44 | 1 |
2.25 | 0.09 | 1.64 | 32.1 | 0.44 | 1 |
2.25 | 0.10 | 0.82 | 29.9 | 0.45 | 1 |
2.25 | 0.10 | 0.82 | 29.9 | 0.45 | 1 |
2.25 | 0.10 | 1.09 | 27.4 | 0.47 | 1 |
2.25 | 0.10 | 1.09 | 27.4 | 0.47 | 1 |
2.25 | 0.16 | 0.82 | 36.4 | 0.47 | 1 |
2.25 | 0.16 | 0.82 | 36.4 | 0.47 | 1 |
2.25 | 0.08 | 1.09 | 34.9 | 0.42 | 1 |
2.25 | 0.08 | 1.09 | 34.9 | 0.42 | 1 |
2.25 | 0.08 | 1.09 | 36.5 | 0.42 | 1 |
2.25 | 0.08 | 1.09 | 36.5 | 0.42 | 1 |
2.50 | 0.30 | 0.59 | 37.6 | 0.52 | 1 |
2.50 | 0.60 | 0.59 | 37.6 | 0.49 | 1 |
2.00 | 0.57 | 0.99 | 39.2 | 0.55 | 1 |
2.00 | 0.57 | 0.99 | 39.2 | 0.59 | 1 |
2.14 | 0.59 | 0.99 | 32.2 | 0.67 | 1 |
3.11 | 0.03 | 0.23 | 35.9 | 0.16 | 1 |
3.11 | 0.03 | 0.23 | 35.7 | 0.15 | 1 |
3.11 | 0.03 | 0.23 | 34.3 | 0.16 | 1 |
3.11 | 0.03 | 0.23 | 33.2 | 0.17 | 1 |
3.11 | 0.03 | 0.23 | 36.8 | 0.16 | 1 |
3.11 | 0.03 | 0.23 | 35.9 | 0.18 | 1 |
3.49 | 0.20 | 1.85 | 64.1 | 0.35 | 1 |
3.49 | 0.33 | 1.85 | 62.1 | 0.40 | 1 |
3.49 | 0.22 | 1.48 | 62.1 | 0.36 | 1 |
3.49 | 0.32 | 1.48 | 62.1 | 0.40 | 1 |
3.49 | 0.20 | 1.23 | 64.1 | 0.34 | 1 |
3.49 | 0.20 | 1.23 | 64.1 | 0.34 | 1 |
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Rectangular Reinforced (306 Tests) | Spiral Reinforced (177 Tests) | |||||
---|---|---|---|---|---|---|
Column Property | Mean | Std | CoV | Mean | Std | CoV |
Depth (mm) | 323.43 | 116.5 | 0.36 | 420.97 | 202.11 | 0.48 |
Aspect Ratio | 3.44 | 1.44 | 0.42 | 3.31 | 1.96 | 0.59 |
Axial-Load Ratio | 0.27 | 0.19 | 0.73 | 0.14 | 0.14 | 1.04 |
ρl (%) | 2.45 | 1.00 | 0.41 | 2.62 | 1.02 | 0.39 |
ρs (%) | 1.34 | 1.07 | 0.80 | 0.93 | 0.74 | 0.80 |
Confusion Matrix in Numbers * | ||||
---|---|---|---|---|
True Values | Flexure | 55 | 2 | 0 |
Flexure–Shear | 2 | 2 | 0 | |
Shear | 0 | 0 | 1 | |
Flexure | Flexure–Shear | Shear | ||
Predicted Values |
Performance Metrics * | |||||||
---|---|---|---|---|---|---|---|
True Positive | True Negative | False Positive | False Negative | Accuracy | Precision | Recall | |
Flexure | 55 | 2 + 1 + 0 + 0 = 3 | 2 + 0 = 2 | 2 + 0 = 2 | (55 + 3)/(55 + 3 + 2 + 2) = 58/62 = 94% | (55)/(55 + 2) = 55/57 = 97% | (55)/(55 + 2) = 55/57 = 97% |
Flexure–Shear | 2 | 55 + 0 + 0 + 1= 56 | 2 + 0 = 2 | 2 + 0 = 2 | (2 + 56)/(2 + 56 + 2 + 2) = 58/62 = 94% | (2)/(2 + 2) = 2/4 = 50% | (2)/(2 + 2) = 2/4 = 50% |
Shear | 1 | 55 + 2 + 2 + 2 = 61 | 0 + 0 = 0 | 0 + 0 = 0 | (1 + 61)/(1 + 61 + 0 + 0) = 62/62 = 100% | (1)/(1 + 0) = 1/1 = 100% | (1)/(1 + 0) = 1/1 = 100% |
Confusion Matrix in Numbers * | ||||
---|---|---|---|---|
True Values | Flexure | 12 | 0 | 0 |
Flexure–Shear | 1 | 5 | 1 | |
Shear | 0 | 1 | 1 | |
Flexure | Flexure–Shear | Shear | ||
Predicted Values |
Performance Metrics * | |||||||
---|---|---|---|---|---|---|---|
True Positive | True Negative | False Positive | False Negative | Accuracy | Precision | Recall | |
Flexure | 12 | 5 + 1 + 1 + 1 = 8 | 1 + 0 = 1 | 0 + 0 = 0 | (12 + 8)/(12 + 8 + 1 + 0) = 20/21 = 95% | (12)/(12 + 1) = 12/13 = 92% | (12)/(12 + 0) = 12/12 = 100% |
Flexure–Shear | 5 | 12 + 0 + 0 + 1 = 13 | 0 + 1 = 1 | 1 + 1 = 2 | (5 + 13)/(5 + 13 + 1 + 2) = 18/21 = 95% | (5)/(5 + 1) = 5/6 = 83% | (5)/(5 + 2) = 5/7 = 71% |
Shear | 1 | 12 + 0 + 1 + 5 = 18 | 0 + 1 = 1 | 0 + 1 = 1 | (1 + 18)/(1 + 18 + 1 + 1) = 19/21 = 90% | (1)/(1 + 1) = 1/2 = 50% | (1)/(1 + 1) = 1/2 = 50% |
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Megalooikonomou, K.G.; Beligiannis, G.N. Random Forests Machine Learning Applied to PEER Structural Performance Experimental Columns Database. Appl. Sci. 2023, 13, 12821. https://doi.org/10.3390/app132312821
Megalooikonomou KG, Beligiannis GN. Random Forests Machine Learning Applied to PEER Structural Performance Experimental Columns Database. Applied Sciences. 2023; 13(23):12821. https://doi.org/10.3390/app132312821
Chicago/Turabian StyleMegalooikonomou, Konstantinos G., and Grigorios N. Beligiannis. 2023. "Random Forests Machine Learning Applied to PEER Structural Performance Experimental Columns Database" Applied Sciences 13, no. 23: 12821. https://doi.org/10.3390/app132312821
APA StyleMegalooikonomou, K. G., & Beligiannis, G. N. (2023). Random Forests Machine Learning Applied to PEER Structural Performance Experimental Columns Database. Applied Sciences, 13(23), 12821. https://doi.org/10.3390/app132312821