Machine Learning-Based Models for Shear Strength Prediction of UHPFRC Beams
Abstract
:1. Introduction
2. Experimental Database
3. Parameter Evaluation and Selection
3.1. Parameter Evaluation Method
3.2. Results and Discussions
4. ML Methods
4.1. Prediction Steps
4.2. ML Methods
4.2.1. Artificial Neural Network (ANN)
4.2.2. Support Vector Regression (SVR)
4.2.3. eXtreme-Gradient Boosting (XGBoost)
4.3. Parameter Settings
- (1)
- The number of hidden layers and neurons n was optimized by using the grid search method and cross-validation strategy. Figure 6 shows the variation in the goodness of fit with the number of hidden layers and neurons. As mentioned in Alavi et al.’s work [45], different metrics have different preferences. In this study, we used R2 to perform a grid search and find the optimal values of hyperparameters since traditional models usually R2 use to depict the performance. Moreover, we used mean absolute error as the index to explore the performance of parameter tuning. Results showed that the hyperparameters obtained by using R2 also made models have lower mean absolute errors, i.e., in this study, the selection of metrics does not cause a big difference. Finally, one hidden layer containing 20 units was selected as the final ANN model structure. The activation function dropout was 0.2, and the regularized parameter L2 was 0.001.
- (2)
- SVR uses the kernel function to nonlinearly map low-dimensional data to high-dimensional feature space and then obtains regression function in high-dimensional feature space. The same grid search method and cross-validation strategy were used to optimize the hyperparameters in SVR: penalty coefficient C and kernel function parameter γ. Finally, the hyperparameters C = 3500 and γ = 0.8 were selected.
- (3)
- In XGBoost, at each boosting iteration, the 1st and 2nd order gradient for the objective function “squared error” was calculated for each training case. The model was built using XGBoost′s scikit-learn compatibility. The best results were achieved using tree-based learners in XGBoost, and the parameters are listed in Table 1.
5. Comparative Analysis
5.1. Existing Models for Calculating Shear Strength of Fiber Reinforced Concrete Beams
- (1)
- Qi et al. model for UHPFRC beams [30]Qi et al. [30] suggested a calculating model for UHPFRC beam shear strength. The shear strength of UHPFRC beams is made up of three aspects: the shear capacity (Vc) provided by the shear-compression zone of the cross-section, the shear capacity supplied by the stirrups (Vs), the shear strength (Vfi) provided by the fibers, and the expression of the shear strength is shown as Equations (29) and (30). Vs is calculated using the truss model. The angle of the inclined crack is assumed to be 45°, and the shear strength provided by the fiber is calculated using the Mesoscale Fiber-Matrix Discrete (MFMD) Model.
- (2)
- Ahmad et al. model for UHPFRC beams [31]Based on the shear test data of UHPFRC beams, Ahmad et al. [31] fitted the formula of shear strength, which is expressed as Equation (31).
- (3)
- The method for shear strength of fiber reinforced concrete (FRC) beams in China Association for Engineering Construction Standardization (CECS) 38:2004 [46]This formula (Equation (32)) is suitable for calculating the shear strength of FRC beams. In this paper, the above test data is used to explore its applicability to the shear capacity of UHPFRC beams.
5.2. Comparison and Analysis
6. Conclusions
- (1)
- The ML algorithm of random forest (RF) is used to evaluate the importance of the given parameters for the shear strength of UHPFRC beams, and the studies show that the area of longitudinal reinforcement has the greatest influence on the shear capacity of UHPFRC beam, and its importance coefficient is 0.14. To simplify the calculation and maintain certain calculation accuracy, the first 12 parameters of the area of longitudinal reinforcement, the stirrup strength, the cross-section area, the shear span ratio, fiber volume fraction, etc., are selected as input parameters.
- (2)
- The suggested approach is evaluated for accuracy and reliability using a shear test database, and it is also compared to existing methods for shear strength of UHPFRC and FRC beams. The models of ANN, SVR, and XGBoost have close goodness of fit, and their R2 are, respectively, 0.8825, 0.9016, and 0.8839, the mean value is 0.8893, and it is much larger than those obtained by the existing models for calculating shear strength of UHPFRC beams. The computed to experimental shear strength ratios generated by the suggested ML models (ANN, SVR, XGBoost), respectively, have the average values of 1.08, 1.02, and 1.10, and the coefficients of variation are, respectively, 0.28, 0.21, and 0.28, so the SVR prediction model has better accuracy and reliability. The accuracy and reliability of ML-based models are much better than those of existing models for calculating the shear strength of UHPFRC beams, and the existing analytical methods for determining the shear strength of FRC beams are not applicable for UHPFRC beams.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
UHPFRC | Ultra-high performance fiber reinforced concrete |
RF | Random forest |
ANN | Artificial neural network |
SVR | Support vector regression |
XGBoost | eXtreme-gradient boosting |
RC | Reinforced concrete |
ML | Machine Learning |
SVM | Support vector machine |
k-NN | k-nearest neighbor |
GP | Genetic programming |
TLBO | Teaching–learning-based optimization |
PSO | Particle swarm optimization |
AHS | Harmony search optimization |
BP | Back-propagation |
GC | Gini coefficient |
CoV | Coefficient of variation |
MFMD | Mesoscale Fiber-Matrix Discrete |
FRC | Fiber reinforced concrete |
CECS | China Association for Engineering Construction Standardization |
Appendix A
Ref. | C | lo | ho | λ | l | hw | tw | bf′ | tf′ | bf | tf | Aw | Awo | I | fc | ft | Vf | fy | As | ρs | fy′ | As′ | ρs′ | fyw | dsw | s | ρsw | Fv |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
[2] | I | 760 | 305 | 2.5 | 2000 | 380 | 65 | 270 | 45 | 230 | 105 | 51,250 | 34,000 | 887,612,083 | 203 | 8.5 | 2.5 | 551 | 2061 | 6.06 | 551 | 314 | 0.92 | 0 | 0 | 0 | 0 | 455 |
I | 760 | 305 | 2.5 | 2000 | 380 | 65 | 270 | 45 | 230 | 105 | 51,250 | 34,000 | 887,612,083 | 205 | 8.6 | 2 | 551 | 2061 | 6.06 | 551 | 314 | 0.92 | 0 | 0 | 0 | 0 | 448 | |
I | 760 | 305 | 2.5 | 2000 | 380 | 65 | 270 | 45 | 230 | 105 | 51,250 | 34,000 | 887,612,083 | 187 | 8.2 | 0 | 551 | 2061 | 6.06 | 551 | 314 | 0.92 | 0 | 0 | 0 | 0 | 181 | |
I | 760 | 305 | 2.5 | 2000 | 380 | 65 | 270 | 45 | 230 | 105 | 51,250 | 34,000 | 887,612,083 | 157 | 7.5 | 4.7 | 551 | 2061 | 6.06 | 551 | 314 | 0.92 | 0 | 0 | 0 | 0 | 249 | |
[3] | I | 1100 | 320 | 3.4 | 3000 | 350 | 60 | 200 | 60 | 200 | 60 | 37,800 | 31,800 | 572,635,000 | 185 | 8.2 | 2 | 900 | 2198 | 5.1 | 550 | 251 | 0.79 | 550 | 10 | 125 | 0.63 | 270 |
I | 1100 | 320 | 3.4 | 3000 | 350 | 60 | 200 | 60 | 200 | 60 | 37,800 | 31,800 | 572,635,000 | 184 | 8.1 | 2 | 900 | 2198 | 5.1 | 550 | 251 | 0.79 | 550 | 10 | 125 | 0.63 | 289 | |
I | 1000 | 320 | 3.1 | 3000 | 350 | 60 | 200 | 60 | 200 | 60 | 37,800 | 31,800 | 572,635,000 | 154 | 7.5 | 0 | 900 | 2198 | 5.1 | 550 | 251 | 0.79 | 550 | 10 | 125 | 0.63 | 169 | |
I | 1000 | 320 | 3.1 | 3000 | 350 | 60 | 200 | 60 | 200 | 60 | 37,800 | 31,800 | 572,635,000 | 173 | 7.9 | 0 | 900 | 2198 | 5.1 | 550 | 251 | 0.79 | 550 | 10 | 125 | 0.63 | 185 | |
I | 1000 | 320 | 3.1 | 3000 | 350 | 60 | 200 | 60 | 200 | 60 | 37,800 | 31,800 | 572,635,000 | 170 | 7.8 | 2 | 900 | 2198 | 5.1 | 550 | 251 | 0.79 | 550 | 10 | 200 | 0.39 | 222 | |
I | 1000 | 320 | 3.1 | 3000 | 350 | 60 | 200 | 60 | 200 | 60 | 37,800 | 31,800 | 572,635,000 | 163 | 7.7 | 2 | 900 | 2198 | 5.1 | 550 | 251 | 0.79 | 550 | 10 | 200 | 0.39 | 258 | |
I | 1000 | 320 | 3.1 | 3000 | 350 | 60 | 200 | 60 | 200 | 60 | 37,800 | 31,800 | 572,635,000 | 169 | 7.8 | 1 | 900 | 2198 | 5.1 | 550 | 251 | 0.79 | 550 | 10 | 200 | 0.39 | 223 | |
I | 1000 | 320 | 3.1 | 3000 | 350 | 60 | 200 | 60 | 200 | 60 | 37,800 | 31,800 | 572,635,000 | 168 | 7.8 | 0 | 900 | 2198 | 5.1 | 550 | 251 | 0.79 | 550 | 10 | 200 | 0.39 | 150 | |
I | 1000 | 320 | 3.1 | 3000 | 350 | 60 | 200 | 60 | 200 | 60 | 37,800 | 31,800 | 572,635,000 | 170 | 7.8 | 2 | 900 | 2198 | 5.1 | 550 | 251 | 0.79 | 550 | 10 | 300 | 0.26 | 223 | |
I | 1000 | 320 | 3.1 | 3000 | 350 | 60 | 200 | 60 | 200 | 60 | 37,800 | 31,800 | 572,635,000 | 166 | 7.7 | 1 | 900 | 2198 | 5.1 | 550 | 251 | 0.79 | 550 | 10 | 300 | 0.26 | 199 | |
I | 1000 | 320 | 3.1 | 3000 | 350 | 60 | 200 | 60 | 200 | 60 | 37,800 | 31,800 | 572,635,000 | 175 | 7.9 | 0 | 900 | 2198 | 5.1 | 550 | 251 | 0.79 | 550 | 10 | 300 | 0.26 | 127 | |
I | 1000 | 320 | 3.1 | 3000 | 350 | 60 | 200 | 60 | 200 | 60 | 37,800 | 31,800 | 572,635,000 | 160 | 7.6 | 2 | 900 | 2198 | 5.1 | 550 | 251 | 0.79 | 0 | 0 | 0 | 0 | 126 | |
I | 1000 | 320 | 3.1 | 3000 | 350 | 60 | 200 | 60 | 200 | 60 | 37,800 | 31,800 | 572,635,000 | 188 | 8.2 | 2 | 900 | 2198 | 5.1 | 550 | 251 | 0.79 | 0 | 0 | 0 | 0 | 160 | |
I | 1000 | 320 | 3.1 | 3000 | 350 | 60 | 200 | 60 | 200 | 60 | 37,800 | 31,800 | 572,635,000 | 178 | 8 | 2 | 900 | 2198 | 5.1 | 550 | 251 | 0.79 | 0 | 0 | 0 | 0 | 179 | |
I | 1000 | 320 | 3.1 | 3000 | 350 | 60 | 200 | 60 | 200 | 60 | 37,800 | 31,800 | 572,635,000 | 162 | 7.6 | 1 | 900 | 2198 | 5.1 | 550 | 251 | 0.79 | 0 | 0 | 0 | 0 | 133 | |
I | 1000 | 320 | 3.1 | 3000 | 350 | 60 | 200 | 60 | 200 | 60 | 37,800 | 31,800 | 572,635,000 | 175 | 7.9 | 1 | 900 | 2198 | 5.1 | 550 | 251 | 0.79 | 0 | 0 | 0 | 0 | 99.5 | |
I | 1000 | 320 | 3.1 | 3000 | 350 | 60 | 200 | 60 | 200 | 60 | 37,800 | 31,800 | 572,635,000 | 187 | 8.2 | 1 | 900 | 2198 | 5.1 | 550 | 251 | 0.79 | 0 | 0 | 0 | 0 | 154 | |
I | 1000 | 320 | 3.1 | 3000 | 350 | 60 | 200 | 60 | 200 | 60 | 37,800 | 31,800 | 572,635,000 | 161 | 7.6 | 0 | 900 | 2198 | 5.1 | 550 | 251 | 0.79 | 0 | 0 | 0 | 0 | 41 | |
I | 1000 | 320 | 3.1 | 3000 | 350 | 60 | 200 | 60 | 200 | 60 | 37,800 | 31,800 | 572,635,000 | 170 | 7.8 | 0 | 900 | 2198 | 5.1 | 550 | 251 | 0.79 | 0 | 0 | 0 | 0 | 31.5 | |
I | 1000 | 320 | 3.1 | 3000 | 350 | 60 | 200 | 60 | 200 | 60 | 37,800 | 31,800 | 572,635,000 | 167 | 7.7 | 0 | 900 | 2198 | 5.1 | 550 | 251 | 0.79 | 0 | 0 | 0 | 0 | 25.5 | |
[4] | R | 1397 | 235 | 5.9 | 3658 | 270 | 180 | 48,600 | 42,300 | 295,245,000 | 167 | 15 | 436 | 398 | 0.94 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 63.3 | |||||
R | 610 | 235 | 2.6 | 3658 | 270 | 180 | 48,600 | 42,300 | 295,245,000 | 167 | 15 | 436 | 531 | 1.26 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 88.6 | ||||||
[5] | I | 504 | 180 | 2.8 | 200 | 20 | 200 | 20 | 110 | 40 | 11,200 | 9000 | 65,853,333 | 150 | 10 | 3 | 500 | 785 | 8.72 | 0 | 0 | 0 | 500 | 0.94 | 115 | |||
I | 504 | 180 | 2.8 | 200 | 20 | 200 | 20 | 110 | 40 | 11,200 | 9000 | 65,853,333 | 150 | 10 | 3 | 500 | 785 | 8.72 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 92 | ||
I | 1120 | 320 | 3.5 | 350 | 58 | 200 | 58 | 200 | 58 | 36,772 | 30,772 | 562,963,969 | 166 | 7.7 | 2 | 900 | 2200 | 7.15 | 0 | 0 | 0 | 550 | 1.35 | 379 | ||||
I | 1120 | 320 | 3.5 | 350 | 58 | 200 | 58 | 200 | 58 | 36,772 | 30,772 | 562,963,969 | 170 | 7.8 | 2 | 900 | 2200 | 7.15 | 0 | 0 | 0 | 550 | 0.9 | 352 | ||||
I | 1120 | 320 | 3.5 | 350 | 58 | 200 | 58 | 200 | 58 | 36,772 | 30,772 | 562,963,969 | 170 | 8 | 2 | 900 | 2200 | 7.15 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 244 | ||
I | 1120 | 320 | 3.5 | 350 | 58 | 200 | 58 | 200 | 58 | 36,772 | 30,772 | 562,963,969 | 166 | 7.7 | 1 | 900 | 2200 | 7.15 | 0 | 0 | 0 | 550 | 0.9 | 314 | ||||
I | 1120 | 320 | 3.5 | 350 | 58 | 200 | 58 | 200 | 58 | 36,772 | 30,772 | 562,963,969 | 174 | 7.9 | 1 | 900 | 2200 | 7.15 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 204 | ||
R | 436 | 218 | 2 | 300 | 150 | 45,000 | 32,700 | 337,500,000 | 156 | 7.5 | 2 | 474 | 2000 | 6.12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 375 | ||||||
R | 327 | 218 | 1.5 | 300 | 150 | 45,000 | 32,700 | 337,500,000 | 152 | 7.4 | 2 | 474 | 2000 | 6.12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 425 | ||||||
R | 660 | 220 | 3 | 290 | 150 | 43,500 | 33,000 | 304,862,500 | 167 | 12 | 1.5 | 618 | 2640 | 8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 476 | ||||||
R | 660 | 220 | 3 | 290 | 150 | 43,500 | 33,000 | 304,862,500 | 167 | 12 | 1.5 | 618 | 2640 | 8 | 0 | 0 | 0 | 538 | 0.6 | 538 | ||||||||
R | 660 | 220 | 3 | 290 | 150 | 43,500 | 33,000 | 304,862,500 | 167 | 12 | 1.5 | 618 | 2640 | 8 | 0 | 0 | 0 | 538 | 0.9 | 552 | ||||||||
[6] | I | 900 | 360 | 2.5 | 4000 | 400 | 60 | 140 | 60 | 140 | 80 | 35,200 | 29,600 | 625,853,333 | 138 | 12 | 1 | 365 | 380 | 1.28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 121 |
I | 828 | 360 | 2.3 | 4000 | 400 | 60 | 140 | 60 | 140 | 80 | 35,200 | 29,600 | 625,853,333 | 138 | 12 | 1 | 365 | 380 | 1.28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 160 | |
I | 900 | 360 | 2.5 | 4000 | 400 | 60 | 140 | 60 | 140 | 80 | 35,200 | 29,600 | 625,853,333 | 138 | 12 | 1 | 365 | 380 | 1.28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 70 | |
I | 828 | 360 | 2.3 | 4000 | 400 | 60 | 140 | 60 | 140 | 80 | 35,200 | 29,600 | 625,853,333 | 138 | 12 | 1 | 365 | 380 | 1.28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 129 | |
I | 828 | 360 | 2.3 | 4000 | 400 | 60 | 140 | 60 | 140 | 80 | 35,200 | 29,600 | 625,853,333 | 138 | 12 | 1 | 365 | 380 | 1.28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 119 | |
I | 900 | 360 | 2.5 | 4000 | 400 | 60 | 140 | 60 | 140 | 80 | 35,200 | 29,600 | 625,853,333 | 138 | 12 | 1 | 365 | 380 | 1.28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 189 | |
I | 828 | 360 | 2.3 | 4000 | 400 | 60 | 140 | 60 | 140 | 80 | 35,200 | 29,600 | 625,853,333 | 138 | 12 | 1 | 365 | 380 | 1.28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 80 | |
I | 900 | 360 | 2.5 | 4000 | 400 | 60 | 140 | 60 | 140 | 80 | 35,200 | 29,600 | 625,853,333 | 138 | 12 | 1 | 365 | 380 | 1.28 | 0 | 0 | 0 | 502 | 8 | 100 | 1.67 | 154 | |
[7] | R | 300 | 130 | 2 | 900 | 150 | 100 | 15,000 | 13,000 | 28,125,000 | 127 | 6.8 | 0 | 550 | 157 | 1.2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 18.2 | ||||
R | 300 | 130 | 2 | 900 | 150 | 100 | 15,000 | 13,000 | 28,125,000 | 127 | 6.8 | 0 | 550 | 226 | 1.7 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 22.1 | |||||
R | 300 | 130 | 2 | 900 | 150 | 100 | 15,000 | 13,000 | 28,125,000 | 130 | 6.8 | 0.5 | 550 | 157 | 1.2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 21 | |||||
R | 300 | 130 | 2 | 900 | 150 | 100 | 15,000 | 13,000 | 28,125,000 | 130 | 6.8 | 0.5 | 550 | 226 | 1.7 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 27 | |||||
R | 300 | 130 | 2 | 900 | 150 | 100 | 15,000 | 13,000 | 28,125,000 | 135 | 7 | 0.5 | 550 | 157 | 1.2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 26.9 | |||||
R | 300 | 130 | 2 | 900 | 150 | 100 | 15,000 | 13,000 | 28,125,000 | 135 | 7 | 0.5 | 550 | 226 | 1.7 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 30.2 | |||||
[8] | R | 277 | 350 | 0.8 | 750 | 400 | 80 | 32,000 | 28,000 | 426,666,667 | 173 | 7.9 | 1.5 | 491 | 1017 | 3.63 | 408 | 314 | 1.12 | 400 | 6 | 150 | 0.47 | 445 | ||||
R | 277 | 350 | 0.8 | 750 | 400 | 80 | 32,000 | 28,000 | 426,666,667 | 173 | 7.9 | 1.5 | 491 | 1017 | 3.63 | 408 | 314 | 1.12 | 400 | 8 | 150 | 0.84 | 530 | |||||
R | 329 | 350 | 0.9 | 750 | 400 | 80 | 32,000 | 28,000 | 426,666,667 | 173 | 7.9 | 1.5 | 491 | 1017 | 3.63 | 408 | 314 | 1.12 | 400 | 6 | 150 | 0.47 | 415 | |||||
R | 329 | 350 | 0.9 | 750 | 400 | 80 | 32,000 | 28,000 | 426,666,667 | 173 | 7.9 | 1.5 | 491 | 1017 | 3.63 | 408 | 314 | 1.12 | 400 | 8 | 150 | 0.84 | 455 | |||||
R | 329 | 350 | 0.9 | 750 | 400 | 80 | 32,000 | 28,000 | 426,666,667 | 173 | 7.9 | 1.5 | 491 | 1017 | 3.63 | 408 | 314 | 1.12 | 400 | 8 | 75 | 1.68 | 505 | |||||
[9] | R | 392 | 112 | 3.5 | 1200 | 140 | 100 | 14,000 | 11,200 | 22,866,667 | 78 | 5.5 | 0 | 520 | 401 | 3.4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 35.5 | ||||
R | 392 | 112 | 3.5 | 1200 | 140 | 100 | 14,000 | 11,200 | 22,866,667 | 94 | 9.2 | 0.5 | 520 | 401 | 3.4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 66.5 | |||||
R | 392 | 112 | 3.5 | 1200 | 140 | 100 | 14,000 | 11,200 | 22,866,667 | 98 | 11 | 1 | 520 | 401 | 3.4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 70 | |||||
R | 392 | 112 | 3.5 | 1200 | 140 | 100 | 14,000 | 11,200 | 22,866,667 | 103 | 15 | 1.5 | 520 | 401 | 3.4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 77.5 | |||||
R | 392 | 112 | 3.5 | 1200 | 140 | 100 | 14,000 | 11,200 | 22,866,667 | 110 | 15 | 2 | 520 | 401 | 3.4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 82.5 | |||||
R | 392 | 112 | 3.5 | 1200 | 140 | 100 | 14,000 | 11,200 | 22,866,667 | 110 | 15 | 2 | 589 | 559 | 4.9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 108 | |||||
R | 392 | 112 | 3.5 | 1200 | 140 | 100 | 14,000 | 11,200 | 22,866,667 | 110 | 15 | 2 | 609 | 628 | 5.9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 113 | |||||
R | 392 | 112 | 3.5 | 1200 | 140 | 100 | 14,000 | 11,200 | 22,866,667 | 101 | 14 | 2 | 520 | 401 | 3.4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 77.5 | |||||
R | 392 | 112 | 3.5 | 1200 | 140 | 100 | 14,000 | 11,200 | 22,866,667 | 93 | 13 | 2 | 520 | 401 | 3.4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 75 | |||||
R | 280 | 112 | 2.5 | 1200 | 140 | 100 | 14,000 | 11,200 | 22,866,667 | 110 | 15 | 2 | 520 | 401 | 3.4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 125 | |||||
R | 336 | 112 | 3 | 1200 | 140 | 100 | 14,000 | 11,200 | 22,866,667 | 110 | 15 | 2 | 520 | 401 | 3.4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 97.5 | |||||
R | 280 | 112 | 2.5 | 1200 | 140 | 100 | 14,000 | 11,200 | 22,866,667 | 98 | 11 | 1 | 520 | 401 | 3.4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 100 | |||||
R | 504 | 112 | 4.5 | 1200 | 140 | 100 | 14,000 | 11,200 | 22,866,667 | 98 | 11 | 1 | 520 | 401 | 3.4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 55 | |||||
R | 392 | 112 | 3.5 | 1200 | 140 | 100 | 14,000 | 11,200 | 22,866,667 | 125 | 17 | 2 | 520 | 401 | 3.4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 94 | |||||
[10] | I | 2000 | 600 | 3.3 | 4000 | 650 | 50 | 400 | 100 | 250 | 100 | 87,500 | 75,000 | 5,349,479,167 | 161 | 19 | 2.5 | 1750 | 1716 | 2.29 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 430 |
I | 2000 | 600 | 3.3 | 4000 | 650 | 50 | 400 | 100 | 250 | 100 | 87,500 | 75,000 | 5,349,479,167 | 160 | 21 | 2.5 | 1750 | 1716 | 2.29 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 497 | |
I | 2000 | 600 | 3.3 | 4000 | 650 | 50 | 400 | 100 | 250 | 100 | 87,500 | 75,000 | 5,349,479,167 | 149 | 22 | 2.5 | 1750 | 1716 | 2.29 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 428 | |
I | 2000 | 600 | 3.3 | 4000 | 650 | 50 | 400 | 100 | 250 | 100 | 87,500 | 75,000 | 5,349,479,167 | 164 | 18 | 1.3 | 1750 | 1716 | 2.29 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 337 | |
I | 2000 | 600 | 3.3 | 4000 | 650 | 50 | 400 | 100 | 250 | 100 | 87,500 | 75,000 | 5,349,479,167 | 171 | 22 | 2.5 | 1750 | 1716 | 2.29 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 440 | |
I | 2000 | 600 | 3.3 | 4000 | 650 | 50 | 400 | 100 | 250 | 100 | 87,500 | 75,000 | 5,349,479,167 | 157 | 18 | 2.5 | 1750 | 1716 | 2.29 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 330 | |
I | 2000 | 600 | 3.3 | 4000 | 650 | 50 | 400 | 100 | 250 | 100 | 87,500 | 75,000 | 5,349,479,167 | 169 | 25 | 2.5 | 1750 | 1716 | 2.29 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 400 | |
[11] | I | 1000 | 230 | 4.3 | 2300 | 250 | 40 | 150 | 40 | 150 | 40 | 18,800 | 15,800 | 150,276,667 | 148 | 7.3 | 0 | 471 | 157 | 0.8 | 0 | 0 | 0 | 0 | 0 | 100 | 0 | 15.8 |
I | 1000 | 230 | 4.3 | 2300 | 250 | 40 | 150 | 40 | 150 | 40 | 18,800 | 15,800 | 150,276,667 | 163 | 7.7 | 1 | 472 | 157 | 0.8 | 0 | 0 | 0 | 0 | 0 | 100 | 0 | 26.4 | |
I | 1000 | 230 | 4.3 | 2300 | 250 | 40 | 150 | 40 | 150 | 40 | 18,800 | 15,800 | 150,276,667 | 163 | 7.7 | 1 | 472 | 226 | 1.2 | 0 | 0 | 0 | 0 | 0 | 100 | 0 | 46.9 | |
I | 1000 | 230 | 4.3 | 2300 | 250 | 40 | 150 | 40 | 150 | 40 | 18,800 | 15,800 | 150,276,667 | 163 | 7.7 | 1 | 468 | 308 | 1.7 | 0 | 0 | 0 | 0 | 0 | 100 | 0 | 39.4 | |
I | 1000 | 230 | 4.3 | 2300 | 250 | 40 | 150 | 40 | 150 | 40 | 18,800 | 15,800 | 150,276,667 | 163 | 7.7 | 1 | 467 | 402 | 2.2 | 0 | 0 | 0 | 0 | 0 | 100 | 0 | 55.3 | |
[12] | R | 750 | 380 | 2 | 2300 | 400 | 200 | 80,000 | 76,000 | 1,066,666,667 | 107 | 9.9 | 0.5 | 475 | 760 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 147 | ||||
[13] | R | 952 | 280 | 3.4 | 350 | 200 | 70,000 | 56,000 | 714,583,333 | 198 | 12 | 0 | 445 | 2453 | 4.38 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 120 | |||||
R | 952 | 280 | 3.4 | 350 | 200 | 70,000 | 56,000 | 714,583,333 | 198 | 12 | 0 | 445 | 2453 | 4.38 | 0 | 0 | 0 | 422 | 9.5 | 150 | 0.47 | 258 | ||||||
R | 952 | 280 | 3.4 | 350 | 200 | 70,000 | 56,000 | 714,583,333 | 117 | 7.8 | 2 | 445 | 2453 | 4.38 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 259 | ||||||
R | 560 | 280 | 2 | 350 | 200 | 70,000 | 56,000 | 714,583,333 | 198 | 12 | 0 | 445 | 2453 | 4.38 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 236 | ||||||
R | 560 | 280 | 2 | 350 | 200 | 70,000 | 56,000 | 714,583,333 | 217 | 15 | 2 | 445 | 2453 | 4.38 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 568 | ||||||
R | 560 | 280 | 2 | 350 | 200 | 70,000 | 56,000 | 714,583,333 | 117 | 7.8 | 2 | 445 | 2453 | 4.38 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 493 | ||||||
[14] | I | 1588 | 397 | 4 | 460 | 50 | 230 | 70 | 220 | 120 | 56,000 | 42,140 | 1,495,429,167 | 148 | 20 | 2 | 450 | 2280 | 5.41 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 130 | |
I | 1588 | 397 | 4 | 460 | 50 | 230 | 70 | 220 | 120 | 56,000 | 42,140 | 1,495,429,167 | 144 | 14 | 1 | 450 | 3040 | 7.21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 120 | ||
I | 1588 | 397 | 4 | 460 | 50 | 230 | 70 | 220 | 120 | 56,000 | 42,140 | 1,495,429,167 | 146 | 20 | 2 | 450 | 3040 | 7.21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 120 | ||
I | 1588 | 397 | 4 | 460 | 50 | 230 | 70 | 220 | 120 | 56,000 | 42,140 | 1,495,429,167 | 152 | 25 | 3 | 450 | 3040 | 7.21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 165 | ||
I | 1890 | 315 | 6 | 380 | 50 | 170 | 60 | 165 | 110 | 38,850 | 28,125 | 651,852,500 | 147 | 20 | 2 | 450 | 1700 | 6.05 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 80 | ||
I | 2520 | 315 | 8 | 380 | 50 | 170 | 60 | 165 | 110 | 38,850 | 28,125 | 651,852,500 | 149 | 21 | 2 | 450 | 1700 | 6.05 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 70 | ||
I | 1260 | 315 | 4 | 380 | 50 | 170 | 60 | 165 | 110 | 38,850 | 28,125 | 651,852,500 | 146 | 20 | 2 | 450 | 1963 | 6.98 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 110 | ||
I | 1890 | 315 | 6 | 380 | 50 | 170 | 60 | 165 | 110 | 38,850 | 28,125 | 651,852,500 | 147 | 20 | 2 | 450 | 1963 | 6.98 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 90 | ||
[15] | R | 660 | 220 | 3 | 1320 | 290 | 150 | 43,500 | 33,000 | 304,862,500 | 167 | 12 | 1.5 | 618 | 2641 | 0.78 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 229 | ||||
[16] | R | 1600 | 640 | 2.5 | 3200 | 700 | 50 | 500 | 100 | 500 | 110 | 129,500 | 99,500 | 9,873,704,167 | 175 | 10 | 1 | 1600 | 2176 | 2.19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 244 |
R | 1600 | 640 | 2.5 | 3200 | 700 | 50 | 500 | 100 | 500 | 110 | 129,500 | 99,500 | 9,873,704,167 | 181 | 9.4 | 1 | 1600 | 2176 | 2.19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 257 | |
R | 1600 | 640 | 2.5 | 3200 | 700 | 50 | 500 | 100 | 500 | 110 | 129,500 | 99,500 | 9,873,704,167 | 188 | 14 | 1.5 | 1600 | 2176 | 2.19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 264 | |
R | 1600 | 640 | 2.5 | 3200 | 700 | 50 | 500 | 100 | 500 | 110 | 129,500 | 99,500 | 9,873,704,167 | 184 | 14 | 1.5 | 1600 | 2176 | 2.19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 295 | |
R | 1600 | 640 | 2.5 | 3200 | 700 | 50 | 500 | 100 | 500 | 110 | 129,500 | 99,500 | 9,873,704,167 | 186 | 17 | 2 | 1600 | 2176 | 2.19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 356 | |
R | 1600 | 640 | 2.5 | 3200 | 700 | 50 | 500 | 100 | 500 | 110 | 129,500 | 99,500 | 9,873,704,167 | 190 | 17 | 2 | 1600 | 2176 | 2.19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 359 | |
R | 2200 | 640 | 3.4 | 4400 | 700 | 50 | 500 | 100 | 500 | 110 | 129,500 | 99,500 | 9,873,704,167 | 169 | 10 | 1 | 1600 | 2176 | 2.19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 140 | |
R | 2200 | 640 | 3.4 | 4400 | 700 | 50 | 500 | 100 | 500 | 110 | 129,500 | 99,500 | 9,873,704,167 | 167 | 9.2 | 1 | 1600 | 2176 | 2.19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 154 | |
R | 2200 | 640 | 3.4 | 4400 | 700 | 50 | 500 | 100 | 500 | 110 | 129,500 | 99,500 | 9,873,704,167 | 193 | 14 | 1.5 | 1600 | 2176 | 2.19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 202 | |
R | 2200 | 640 | 3.4 | 4400 | 700 | 50 | 500 | 100 | 500 | 110 | 129,500 | 99,500 | 9,873,704,167 | 189 | 14 | 1.5 | 1600 | 2176 | 2.19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 187 | |
R | 2200 | 640 | 3.4 | 4400 | 700 | 50 | 500 | 100 | 500 | 110 | 129,500 | 99,500 | 9,873,704,167 | 189 | 17 | 2 | 1600 | 2176 | 2.19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 219 | |
R | 2200 | 640 | 3.4 | 4400 | 700 | 50 | 500 | 100 | 500 | 110 | 129,500 | 99,500 | 9,873,704,167 | 182 | 17 | 2 | 1600 | 2176 | 2.19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 239 | |
[17] | I | 700 | 230 | 3 | 2300 | 250 | 50 | 150 | 40 | 150 | 40 | 20,500 | 17,500 | 154,370,833 | 121 | 10 | 0 | 470 | 402 | 2.3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 33.4 |
I | 700 | 230 | 3 | 2300 | 250 | 50 | 150 | 40 | 150 | 40 | 20,500 | 17,500 | 154,370,833 | 143 | 18 | 2 | 470 | 157 | 0.9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 36.8 | |
I | 700 | 230 | 3 | 2300 | 250 | 50 | 150 | 40 | 150 | 40 | 20,500 | 17,500 | 154,370,833 | 143 | 18 | 2 | 470 | 226 | 1.29 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 49.9 | |
I | 700 | 230 | 3 | 2300 | 250 | 50 | 150 | 40 | 150 | 40 | 20,500 | 17,500 | 154,370,833 | 143 | 18 | 2 | 470 | 308 | 1.76 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 62.7 | |
I | 700 | 230 | 3 | 2300 | 250 | 50 | 150 | 40 | 150 | 40 | 20,500 | 17,500 | 154,370,833 | 143 | 18 | 2 | 470 | 402 | 2.3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 60.1 | |
[18] | R | 279 | 223 | 1.3 | 1400 | 240 | 50 | 120 | 90 | 120 | 90 | 24,600 | 22,560 | 136,980,000 | 136 | 21 | 1.5 | 512 | 308 | 1.37 | 512 | 155 | 0.69 | 0 | 0 | 0 | 0 | 100 |
R | 279 | 223 | 1.3 | 1400 | 240 | 50 | 120 | 90 | 120 | 90 | 24,600 | 22,560 | 136,980,000 | 138 | 24 | 1.5 | 512 | 308 | 1.37 | 512 | 155 | 0.69 | 0 | 0 | 0 | 0 | 80 | |
[19] | R | 390 | 260 | 1.5 | 1350 | 350 | 165 | 57,750 | 42,900 | 589,531,250 | 119 | 2.5 | 0 | 474 | 3215 | 7.5 | 490 | 760 | 1.77 | 0 | 0 | 0 | 0 | 245 | ||||
R | 390 | 260 | 1.5 | 1350 | 350 | 165 | 57,750 | 42,900 | 589,531,250 | 115 | 3.2 | 0.8 | 474 | 3215 | 7.49 | 490 | 760 | 1.77 | 0 | 0 | 0 | 0 | 288 | |||||
R | 390 | 260 | 1.5 | 1350 | 350 | 165 | 57,750 | 42,900 | 589,531,250 | 124 | 6.3 | 1.5 | 474 | 3215 | 7.49 | 490 | 760 | 1.77 | 0 | 0 | 0 | 0 | 454 | |||||
R | 390 | 260 | 1.5 | 1350 | 350 | 165 | 57,750 | 42,900 | 589,531,250 | 112 | 2.1 | 0.8 | 474 | 3215 | 7.49 | 490 | 760 | 1.77 | 0 | 0 | 0 | 0 | 296 | |||||
R | 390 | 260 | 1.5 | 1350 | 350 | 165 | 57,750 | 42,900 | 589,531,250 | 105 | 4.3 | 2.3 | 474 | 3215 | 7.49 | 490 | 760 | 1.77 | 0 | 0 | 0 | 0 | 334 | |||||
R | 390 | 260 | 1.5 | 1350 | 350 | 165 | 57,750 | 42,900 | 589,531,250 | 126 | 2.3 | 0.8 | 474 | 3215 | 7.49 | 490 | 760 | 1.77 | 0 | 0 | 0 | 0 | 347 | |||||
R | 390 | 260 | 1.5 | 1350 | 350 | 165 | 57,750 | 42,900 | 589,531,250 | 107 | 4.9 | 1.5 | 474 | 3215 | 7.49 | 490 | 760 | 1.77 | 0 | 0 | 0 | 0 | 377 | |||||
R | 390 | 260 | 1.5 | 1350 | 350 | 165 | 57,750 | 42,900 | 589,531,250 | 124 | 5.6 | 2.3 | 474 | 3215 | 7.49 | 490 | 760 | 1.77 | 0 | 0 | 0 | 0 | 466 | |||||
R | 390 | 260 | 1.5 | 1350 | 350 | 165 | 57,750 | 42,900 | 589,531,250 | 123 | 5.1 | 1.5 | 474 | 3215 | 7.49 | 490 | 760 | 1.77 | 0 | 0 | 0 | 0 | 474 | |||||
R | 390 | 260 | 1.5 | 1350 | 350 | 165 | 57,750 | 42,900 | 589,531,250 | 119 | 7 | 2.3 | 474 | 3215 | 7.49 | 490 | 760 | 1.77 | 0 | 0 | 0 | 0 | 547 | |||||
R | 390 | 260 | 1.5 | 1350 | 350 | 165 | 57,750 | 42,900 | 589,531,250 | 114 | 6 | 2.3 | 474 | 3215 | 7.49 | 490 | 760 | 1.77 | 0 | 0 | 0 | 0 | 500 | |||||
R | 390 | 260 | 1.5 | 1350 | 350 | 165 | 57,750 | 42,900 | 589,531,250 | 98 | 4.4 | 2 | 474 | 3215 | 7.49 | 490 | 760 | 1.77 | 0 | 0 | 0 | 0 | 419 | |||||
R | 858 | 260 | 3.3 | 1900 | 350 | 165 | 57,750 | 42,900 | 589,531,250 | 95 | 2.6 | 0 | 474 | 3215 | 7.49 | 490 | 760 | 1.77 | 0 | 0 | 0 | 0 | 70.2 | |||||
R | 858 | 260 | 3.3 | 1900 | 350 | 165 | 57,750 | 42,900 | 589,531,250 | 117 | 2.3 | 0.8 | 474 | 3215 | 7.49 | 490 | 760 | 1.77 | 0 | 0 | 0 | 0 | 193 | |||||
R | 858 | 260 | 3.3 | 1900 | 350 | 165 | 57,750 | 42,900 | 589,531,250 | 103 | 3.9 | 1.5 | 474 | 3215 | 7.49 | 490 | 760 | 1.77 | 0 | 0 | 0 | 0 | 223 | |||||
R | 858 | 260 | 3.3 | 1900 | 350 | 165 | 57,750 | 42,900 | 589,531,250 | 115 | 1.6 | 0.8 | 474 | 3215 | 7.49 | 490 | 760 | 1.77 | 0 | 0 | 0 | 0 | 115 | |||||
R | 858 | 260 | 3.3 | 1900 | 350 | 165 | 57,750 | 42,900 | 589,531,250 | 94 | 5.8 | 2.3 | 474 | 3215 | 7.49 | 490 | 760 | 1.77 | 0 | 0 | 0 | 0 | 174 | |||||
R | 858 | 260 | 3.3 | 1900 | 350 | 165 | 57,750 | 42,900 | 589,531,250 | 134 | 1.5 | 0.8 | 474 | 3215 | 7.49 | 490 | 760 | 1.77 | 0 | 0 | 0 | 0 | 130 | |||||
R | 858 | 260 | 3.3 | 1900 | 350 | 165 | 57,750 | 42,900 | 589,531,250 | 132 | 3.8 | 1.5 | 474 | 3215 | 7.49 | 490 | 760 | 1.77 | 0 | 0 | 0 | 0 | 219 | |||||
R | 858 | 260 | 3.3 | 1900 | 350 | 165 | 57,750 | 42,900 | 589,531,250 | 117 | 5.1 | 2.3 | 474 | 3215 | 7.49 | 490 | 760 | 1.77 | 0 | 0 | 0 | 0 | 234 | |||||
R | 858 | 260 | 3.3 | 1900 | 350 | 165 | 57,750 | 42,900 | 589,531,250 | 110 | 3.7 | 2.3 | 474 | 3215 | 7.49 | 490 | 760 | 1.77 | 0 | 0 | 0 | 0 | 254 | |||||
R | 858 | 260 | 3.3 | 1900 | 350 | 165 | 57,750 | 42,900 | 589,531,250 | 124 | 5.4 | 2.3 | 474 | 3215 | 7.49 | 490 | 760 | 1.77 | 0 | 0 | 0 | 0 | 277 | |||||
R | 858 | 260 | 3.3 | 1900 | 350 | 165 | 57,750 | 42,900 | 589,531,250 | 113 | 4.6 | 2 | 474 | 3215 | 7.49 | 490 | 760 | 1.77 | 0 | 0 | 0 | 0 | 221 | |||||
T | 1000 | 300 | 3.3 | 3000 | 350 | 100 | 300 | 50 | 142 | 45,000 | 40,000 | 53,4375,000 | 152 | 7.4 | 0 | 557 | 1256 | 3.58 | 557 | 1256 | 3.58 | 552 | 6 | 380 | 0.15 | 113 | ||
[20] | T | 361 | 114 | 3.2 | 1140 | 140 | 40 | 120 | 35 | 53 | 8400 | 7360 | 14,577,500 | 116 | 7.1 | 2 | 761 | 226 | 4.96 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 38 | |
T | 361 | 114 | 3.2 | 1140 | 140 | 40 | 120 | 35 | 53 | 8400 | 7360 | 14,577,500 | 96 | 5.2 | 0.5 | 761 | 226 | 4.96 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 26.1 | ||
T | 361 | 114 | 3.2 | 1140 | 140 | 40 | 120 | 35 | 53 | 8400 | 7360 | 14,577,500 | 94 | 6.1 | 1 | 761 | 226 | 4.96 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 26.3 | ||
T | 285 | 114 | 2.5 | 1140 | 140 | 40 | 120 | 35 | 53 | 8400 | 7360 | 14,577,500 | 116 | 7.1 | 2 | 761 | 226 | 4.96 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 52 | ||
T | 428 | 114 | 3.8 | 1140 | 140 | 40 | 120 | 35 | 53 | 8400 | 7360 | 14,577,500 | 116 | 7.1 | 2 | 761 | 226 | 4.96 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 44 | ||
T | 361 | 114 | 3.2 | 1140 | 140 | 40 | 120 | 35 | 53 | 8400 | 7360 | 14,577,500 | 121 | 7.7 | 2 | 761 | 226 | 4.96 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 34.5 | ||
T | 361 | 114 | 3.2 | 1140 | 140 | 40 | 120 | 35 | 53 | 8400 | 7360 | 14,577,500 | 113 | 6.5 | 2 | 761 | 226 | 4.96 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 33.1 | ||
T | 361 | 114 | 3.2 | 1140 | 140 | 40 | 120 | 35 | 53 | 8400 | 7360 | 14,577,500 | 121 | 7.7 | 2 | 761 | 226 | 4.96 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 23.6 | ||
T | 361 | 114 | 3.2 | 1140 | 140 | 40 | 120 | 35 | 53 | 8400 | 7360 | 14,577,500 | 113 | 6.5 | 2 | 761 | 226 | 4.96 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 38.5 | ||
[21] | R | 620 | 310 | 2 | 2000 | 350 | 200 | 70,000 | 62,000 | 714,583,333 | 125 | 7.1 | 2 | 474 | 2944 | 4.75 | 474 | 981 | 1.58 | 568 | 8 | 200 | 0.25 | 991 | ||||
R | 465 | 310 | 1.5 | 2000 | 350 | 200 | 70,000 | 62,000 | 714,583,333 | 125 | 7.1 | 2 | 474 | 2943 | 4.75 | 474 | 981 | 1.58 | 568 | 8 | 200 | 0.25 | 778 | |||||
R | 620 | 310 | 2 | 2000 | 350 | 200 | 70,000 | 62,000 | 714,583,333 | 125 | 7.1 | 2 | 474 | 2943 | 4.75 | 474 | 981 | 1.58 | 568 | 8 | 200 | 0.25 | 646 | |||||
R | 775 | 310 | 2.5 | 2000 | 350 | 200 | 70,000 | 62,000 | 714,583,333 | 119 | 5.2 | 1 | 474 | 2943 | 4.75 | 474 | 981 | 1.58 | 568 | 8 | 200 | 0.25 | 687 | |||||
R | 620 | 310 | 2 | 2000 | 350 | 200 | 70,000 | 62,000 | 714,583,333 | 132 | 8.9 | 3 | 474 | 2943 | 4.75 | 474 | 981 | 1.58 | 568 | 8 | 200 | 0.25 | 805 | |||||
R | 620 | 310 | 2 | 2000 | 350 | 200 | 70,000 | 62,000 | 714,583,333 | 125 | 7.1 | 2 | 474 | 2943 | 4.75 | 474 | 981 | 1.58 | 0 | 0 | 0 | 0 | 689 | |||||
R | 620 | 310 | 2 | 2000 | 350 | 200 | 70,000 | 62,000 | 714,583,333 | 125 | 7.1 | 2 | 474 | 2943 | 4.75 | 474 | 981 | 1.58 | 568 | 8 | 100 | 0.5 | 867 | |||||
R | 620 | 310 | 2 | 2000 | 350 | 200 | 70,000 | 62,000 | 714,583,333 | 125 | 7.1 | 2 | 474 | 2943 | 4.75 | 474 | 981 | 1.58 | 568 | 8 | 300 | 0.17 | 748 | |||||
[22] | R | 313 | 125 | 2.5 | 1300 | 150 | 100 | 15,000 | 12,500 | 28,125,000 | 118 | 6.5 | 2 | 570 | 509 | 4.1 | 340 | 57 | 0.45 | 0 | 0 | 0 | 0 | 85.5 | ||||
R | 313 | 125 | 2.5 | 1300 | 150 | 100 | 15,000 | 12,500 | 28,125,000 | 118 | 6.5 | 2 | 570 | 509 | 4.1 | 340 | 57 | 0.46 | 340 | 6 | 200 | 0.28 | 87.5 | |||||
R | 313 | 125 | 2.5 | 1300 | 150 | 100 | 15,000 | 12,500 | 28,125,000 | 118 | 6.5 | 2 | 570 | 509 | 4.1 | 340 | 57 | 0.46 | 340 | 6 | 150 | 0.38 | 91.5 | |||||
R | 313 | 125 | 2.5 | 1300 | 150 | 100 | 15,000 | 12,500 | 28,125,000 | 118 | 6.5 | 2 | 570 | 509 | 4.1 | 340 | 57 | 0.46 | 340 | 6 | 100 | 0.56 | 93.5 | |||||
R | 313 | 125 | 2.5 | 1300 | 150 | 100 | 15,000 | 12,500 | 28,125,000 | 110 | 6.3 | 1 | 570 | 509 | 4.1 | 340 | 57 | 0.46 | 0 | 0 | 0 | 0 | 79 | |||||
R | 313 | 125 | 2.5 | 1300 | 150 | 100 | 15,000 | 12,500 | 28,125,000 | 100 | 6 | 0.5 | 570 | 509 | 4.1 | 340 | 57 | 0.46 | 0 | 0 | 0 | 0 | 71 | |||||
R | 313 | 125 | 2.5 | 1300 | 150 | 100 | 15,000 | 12,500 | 28,125,000 | 129 | 6.8 | 2 | 570 | 509 | 4.1 | 340 | 57 | 0.46 | 0 | 0 | 0 | 0 | 89 | |||||
[23] | R | 312 | 260 | 1.2 | 1000 | 300 | 150 | 45,000 | 39,000 | 337,500,000 | 108 | 4.1 | 0 | 526 | 1963 | 5.23 | 476 | 226 | 0.58 | 466 | 6 | 200 | 0.19 | 445 | ||||
R | 312 | 260 | 1.2 | 1000 | 300 | 150 | 45,000 | 39,000 | 337,500,000 | 118 | 6.4 | 1 | 526 | 1963 | 5.23 | 476 | 226 | 0.58 | 466 | 6 | 200 | 0.19 | 645 | |||||
R | 312 | 260 | 1.2 | 1000 | 300 | 150 | 45,000 | 39,000 | 337,500,000 | 118 | 6.4 | 1 | 526 | 1963 | 5.23 | 476 | 226 | 0.58 | 0 | 0 | 0 | 0 | 580 | |||||
R | 312 | 260 | 1.2 | 1000 | 300 | 150 | 45,000 | 39,000 | 337,500,000 | 118 | 6.4 | 1 | 526 | 1963 | 5.23 | 476 | 226 | 0.58 | 466 | 6 | 100 | 0.38 | 670 | |||||
R | 312 | 260 | 1.2 | 1000 | 300 | 150 | 45,000 | 39,000 | 337,500,000 | 118 | 6.4 | 1 | 526 | 1963 | 5.23 | 476 | 226 | 0.58 | 466 | 6 | 150 | 0.25 | 655 | |||||
R | 312 | 260 | 1.2 | 1000 | 300 | 150 | 45,000 | 39,000 | 337,500,000 | 118 | 6.4 | 1 | 520 | 1741 | 4.65 | 476 | 226 | 0.58 | 466 | 6 | 200 | 0.19 | 560 | |||||
R | 312 | 260 | 1.2 | 1000 | 300 | 150 | 45,000 | 39,000 | 337,500,000 | 118 | 6.4 | 1 | 519 | 1520 | 4.06 | 476 | 226 | 0.58 | 466 | 6 | 200 | 0.19 | 490 | |||||
R | 364 | 260 | 1.4 | 1000 | 300 | 150 | 45,000 | 39,000 | 337,500,000 | 118 | 6.4 | 1 | 526 | 1963 | 5.23 | 476 | 226 | 0.58 | 466 | 6 | 200 | 0.19 | 525 | |||||
R | 416 | 260 | 1.6 | 1000 | 300 | 150 | 45,000 | 39,000 | 337,500,000 | 118 | 6.4 | 1 | 526 | 1963 | 5.23 | 476 | 226 | 0.58 | 466 | 6 | 200 | 0.19 | 475 | |||||
[25] | R | 203 | 124 | 1.6 | 610 | 152 | 152 | 23,104 | 18,848 | 44,482,901 | 121 | 4.9 | 0 | 406 | 603 | 3.2 | 485 | 85 | 0.45 | 0 | 103 | |||||||
[26] | R | 601 | 258 | 2.3 | 1200 | 300 | 150 | 45,000 | 38,700 | 337,500,000 | 125 | 5.6 | 3 | 543 | 2454 | 6.34 | 540 | 226 | 0.58 | 423 | 6 | 50 | 0.75 | 565 | ||||
R | 599 | 255 | 2.4 | 1200 | 300 | 150 | 45,000 | 38,250 | 337,500,000 | 125 | 5.6 | 3 | 543 | 1610 | 4.21 | 540 | 226 | 0.59 | 423 | 6 | 100 | 0.38 | 463 | |||||
R | 601 | 272 | 2.2 | 1200 | 300 | 150 | 45,000 | 40,800 | 337,500,000 | 125 | 5.6 | 3 | 543 | 1473 | 3.61 | 540 | 226 | 0.55 | 423 | 6 | 150 | 0.25 | 436 | |||||
R | 601 | 272 | 2.2 | 1200 | 300 | 150 | 45,000 | 40,800 | 337,500,000 | 125 | 5.6 | 3 | 543 | 1473 | 3.61 | 540 | 226 | 0.55 | 423 | 6 | 200 | 0.19 | 364 | |||||
R | 601 | 259 | 2.3 | 1200 | 300 | 150 | 45,000 | 38,850 | 337,500,000 | 138 | 6.8 | 5 | 543 | 1884 | 4.85 | 540 | 226 | 0.58 | 423 | 6 | 100 | 0.38 | 518 | |||||
R | 600 | 262 | 2.3 | 1200 | 300 | 150 | 45,000 | 39,300 | 337,500,000 | 138 | 6.8 | 5 | 543 | 1572 | 4 | 540 | 226 | 0.58 | 423 | 6 | 200 | 0.19 | 406 |
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Parameters | Values |
---|---|
Number of estimators | 30 |
Learning rate | 0.2 |
Max depth | 3 |
Min child weight | 2 |
Gamma | 2000 |
Subsample | 0.3 |
Colsample bytree | 0.4 |
Scale pos weight | 0.7 |
Methods | R2 | Vpre/Vexp | |||
---|---|---|---|---|---|
Max | Min | Mean | CoV | ||
ANN | 0.8825 | 1.91 | 0.64 | 1.08 | 0.28 |
SVR | 0.9016 | 1.74 | 0.62 | 1.02 | 0.21 |
XGBBOOST | 0.8839 | 1.91 | 0.63 | 1.1 | 0.28 |
Qi et al. | 0.6427 | 2 | 0.27 | 0.72 | 0.36 |
Ahmad et al. | 0.7026 | 2.05 | 0.25 | 1.1 | 0.41 |
CECS 38:2004 | 0.7149 | 1.95 | 0.37 | 1.04 | 0.49 |
Sharma et al. | 0.5618 | 3 | 0.21 | 1.35 | 0.54 |
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Ni, X.; Duan, K. Machine Learning-Based Models for Shear Strength Prediction of UHPFRC Beams. Mathematics 2022, 10, 2918. https://doi.org/10.3390/math10162918
Ni X, Duan K. Machine Learning-Based Models for Shear Strength Prediction of UHPFRC Beams. Mathematics. 2022; 10(16):2918. https://doi.org/10.3390/math10162918
Chicago/Turabian StyleNi, Xiangyong, and Kangkang Duan. 2022. "Machine Learning-Based Models for Shear Strength Prediction of UHPFRC Beams" Mathematics 10, no. 16: 2918. https://doi.org/10.3390/math10162918
APA StyleNi, X., & Duan, K. (2022). Machine Learning-Based Models for Shear Strength Prediction of UHPFRC Beams. Mathematics, 10(16), 2918. https://doi.org/10.3390/math10162918