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. 2024 Jun 25;14:14590. doi: 10.1038/s41598-024-64386-w

Table 1.

Summary of previous ML models in predicting RCDBs shear strength.

Reference Category (number)* Models: Statistical criteria
Wakjira10 WOR (371) GP: Vth=0.0456fc0.619ρl0.411ad-0.874bwd μ = 0.82, COV = 0.305
Ashour4 All (141) GP: V=bwhfc-4.56+1.68adρl2+2.45+0.1ad2-1.16ad+3.12ρtρl+0.3ρhw+0.4ρvw μ = 1.11, Std = 0.21
Shahnewaz9 All (381)

GA: Vu=bwhfc25-14ad0.23+0.85ρlρhwρvw0.1-35adρhwρvw116-200adρlρhwρvw2.65 μ = 0.99, CoV = 0.232

GA: Vu=bwhfc1.74-2ad0.044+0.5ρ0.14 μ = 1.01, CoV = 0.257

Cheng5 All (106)

EMARS, BPNN, RBFNN, SVM. EMARS is the best model. Grid search with cross-validation

EMARS: training MAPE = 5.67, R2 = 0.989, testing MAPE = 5.887, R2 = 0.973

Feng6 All (271)

DT, SVM, ANN, RF, AdaBoost, GBRT, XGBoost. XGboost is the best model. Grid search with cross-validation

XGboost: Training R2 = 0.999, MAPE = 0.74, testing R2 = 0.928, MAPE = 10.44% (overfitting)

Hameed11 All (271)

LWR, RF, MLR, ELM. LWR is the best model. Grid search with cross-validation

LWR: Training: RMSE = 22.563, MAE = 13.249, a20-index = 98.89, testing: RMSE = 57.776, MAE = 33.933, a20-index = 85.87

Liu8 All (267)

LR, SVR, ANN, RF, XGBoost, NGBoost using Bayesian optimisation technique. NGBoost is the best model

NGboost: R2 = 0.9045, RMSE = 38.7976 kN

Tiwari7 All (271)

DT, SVR, RF, GB, Adaptive boosting, XGBoost, voting regression. XGboost is the best model. Grid search with cross-validation

XGboost: Training R2 = 0.999, MAPE = 0.78, RMSE = 1.45 kN, testing R2 = 0.928, MAPE = 9.79, RMSE = 47.76 (overfitting). μ = 1.00, CoV = 6.38%

Nguyen3 All (518)

LR, ANN, SVR, DT, GPR, XGBoost using Bayesian optimisation technique. GPR is the best model

GPR: Training R2 = 0.99, MAE = 12.77, RMSE = 18.84 kN, validation R2 = 0.89, MAE = 41.72, RMSE = 71.06 kN, testing R2 = 0.94, MAE = 38.44, RMSE = 63.38

Ma2 All (457)

kNN, DTM RFM GBDT, CatBoost, XGboost. XGboost is the best model. Grid search with cross-validation

XGboost: Training R2 = 0.992, MAE = 0.148, RMSE = 0.26, testing R2 = 0.917, MAE = 0.531, RMSE = 0.777

WOR*: μ = 1.03, Std = 0.128, WVR*: μ = 1.005, Std = 0.073, WHR*: μ = 1.003, Std = 0.077, WVHR*: μ = 1.01, Std = 0.084

This study All (840)

CATBoost: Training: μ = 1.005, CoV = 0.062, a20-index = 0.9894, MAPE = 4.41, RMSE = 36.8 kN

Testing: μ = 1.026, CoV = 0.141, a20-index = 0.899, MAPE = 9.32, RMSE = 160.9 kN

SR: (WOR)* μ = 1.003, CoV = 0.207, a20-index = 0.68, MAPE = 16.80, RMSE = 115.9 kN

SR: (WWR)* μ = 1.004, CoV = 0.192, a20-index = 0.78, MAPE = 13.70, RMSE = 196.7 kN

*WOR and WWR stand for without web reinforcement and with web reinforcement cases.