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. 2025 Sep 26;15:33299. doi: 10.1038/s41598-025-17150-7

Table 10.

Performance checking variables for different equations and models.

Load type Model and equation considering eccentric load Equations considering concentric load Machine learning model
Method ANN Proposed equation (GMDH) Proposed equation (GEP) CSA- S806-12 AS-3600 Mohammed et al. (A) Mohammed et al. (B) Hadhood et al Tobbi et al Arora et al
MAE 121.539 169.941 209.010 536.84 280.32 302.89 245.61 316.62 309.26 232.04
RMSE 206.612 239.070 309.417 695.68 439.25 461.27 407.22 475.28 440.10 346.73
MAPE 9.325 17.011 18.505 23.44 13.11 13.88 12.13 14.05 16.09 29.22
Inline graphic 0.974 0.966 0.942 0.708 0.883 0.871 0.90 0.863 0.883 0.951