Skip to main content
. 2026 May 15;16:22198. doi: 10.1038/s41598-026-49985-z

Table 7.

Comparison ML models with design codes and literatures.

No. Authors Shape of CFST Type of comparison FEM description R 2 RMSE (kN) MAE (kN) MAPE (%)
1 Present study All shapes of polygon CFST SVR – 0.7367 4102.71 2111.74 30.51
RF 0.9839 1015.16 538.15 8.95
GB 0.9619 1560.01 899.61 24.03
DNN 0.9979 362.83 253.07 6.61
2 Ren et al.34 Triangular CFST DBJ13-51-2010 – EXP – 0.8498 98.40 76.50 5.83
Eurocode 4 – EXP 0.7543 79.08 71.17 5.21
3 Zhu and Chan49 Triangular CFST FE – EXP Observed by themselves or the authors of the work. 1 60.12 43.50 3.60
4 Liu and Williamns36 Square CFST FE – EXP Observed by Ayough9 0.9999 155.49 144.60 6.69
AISC 360 – EXP - 0.9314 1270.23 863.33 29.26
Eurocode 4 – EXP 1 119.39 119.33 6.33
ACI – EXP 1 278.88 262 12.25746
5 Huang et al.37 Square CFST FE – EXP Observed by Ayough9 The sample is only one available and not possible to count R2.
6 Schneider35 Square CFST FE – EXP Observed by Ayough9 0.9880 109.04 83.76 5.99
7 Zhu and Chan39 Square CFST Eurocode 4 – EXP – 0.9963 308.74 260.14 4.73
ACI – EXP 0.9964 701.97 601.14 10.72
8 Zhong55 Square CFST Eq. M. Yu et al.59 – EXP – 0.5362 313.37 245.89 10.83
9 Liu57 Square CFST Eq. M. Yu et al.59 – EXP – 0.8787 194.24 164.50 7.42
10 Liu et al.56 Square CFST Eq. M. Yu et al.59 – EXP – 0.9949 98.04 81.13 3.87
11 Zhang et al.56 Square CFST Eq. M. Yu et al.59 – EXP – 0.9436 248.62 218.59 11.79
12 Yu et al.59 Square CFST Eq. M. Yu et al.59 – EXP – 0.7174 90.82 76.33 4.84
13 Zhu et al.60 Square CFST AISC 360 – EXP – 0.9974 1225.85 1201.75 38.60
Eurocode 4 – EXP 0.9974 1581.80 1529.25 48.38
14 Hilo et al.62 Square CFST Eurocode 4 – FE Parametric study of FEM 0.8206 134.02 105.03 7.80
15 Ayough et al.9 Square, Hexagon, & Octagon CFST AISC 360 – EXP – Comparison with literatures is only show the mean of Nu formula/Nu EXP.
Eurocode 4 – EXP
16 Li et al.30 Rectangular CFST FE – EXP Observed by Ami and Patel31 0.9735 78.43 64.75 3.96
AISC 360 – EXP – 0.9615 571.62 568.50 34.17
GB50936 – EXP 0.9598 240.69 234.05 13.94
CECS 28:90 - EXP 0.9682 205.93 200.13 12.01
Eq. Li et al.30 – EXP 0.9506 61.44 55.83 3.48
17 Hilo et al.62 Rectangular CFST Eurocode 4 – FE Parametric study of FEM 0.8080 247.48 232.44 17.40
18 Hilo et al.62 Pentagon CFST Eurocode 4 – FE Parametric study of FEM 0.8047 205.81 186.08 13
19 Ding et al.29 Hexagon CFST FE – EXP Observed by themselves or the authors of the work. 0.9320 289.22 278.13 4.54
Eq. M. Yu et al.59 – EXP – 0.9261 491.50 419.88 7.08
Eq. Ding et al.29 – EXP 0.9263 513.81 445.75 7.49
20 Ding et al.29 Hexagon CFST FE – EXP Observed by Ami and Patel31 0.9805 195.20 155.75 2.57
21 Ding et al.29 Hexagon CFST FE – EXP Observed by Ayough9 0.9112 444.75 382.16 6.07
22 Xu et al.47 Hexagon CFST FE – EXP Observed by themselves or the authors of the work. 0.9122 99.71 73.50 4.25
DBJ13-51-2010 – EXP – 0.9008 108.58 83.83 4.54
Eurocode 4 - EXP 0.8957 86.25 74.83 4.33
AIJ 2008 – EXP 0.8969 162.58 141.83 7.51
23 Liu et al.48 Hexagon CFST FE – EXP Observed by Ahmed and Liang50 Not possible to count R2.
24 Zhu and Chan49 Hexagon CFST FE – EXP Observed by themselves or the authors of the work 1 26 26 1.38
FE – EXP Observed by Ahmed and Liang50 1 31.02 29 1.54
AISC 360 – EXP – Not possible to count R2.
GB50936 – EXP Not possible to count R2.
Eurocode 4 - EXP Not possible to count R2.
25 Shen et al.52 Hexagon CFST with/without inner steel tube FE – EXP Observed by themselves or the authors of the work. 0.9851 582.02 393.46 4.83
26 Ramadan et al.28 Hexagon CFST with/without inner steel tube FE – EXP Observed by themselves or the authors of the work. 0.9887 271.75 235.20 5.15
27 Ramadan et al.28 Hexagon CFST Nu with fscy modified MOHURD76 – FE Parametric study of FEM 0.9659 244.53 170.71 8.03
Nu with fscy modified Han et al.77 – FE 0.9919 268.35 212.58 9.90
Nu with fscy modified Shen et al.33 – FE 0.9961 61.76 48.54 2.63
Ramadan et al.28 – FE 0.9946 172.00 149.25 7.84
28 Hilo et al.62 Hexagon CFST Eurocode 4 – FE Parametric study of FEM 0.7868 240.55 222.28 15.20
29 Hilo et al.62 Heptagon CFST Eurocode 4 – FE Parametric study of FEM 0.7832 256.58 239.40 16.20
30 Ding et al.26 Octagon CFST FE – EXP Observed by themselves or the authors of the work. 0.9868 501.08 469.25 4.22
FE – EXP Observed by Hassanein et al. (2018) 0.9764 490.71 427.88 3.87
FE – EXP Observed by Ayough9 1 691.77 591.20 5.68
Eq. Ding et al.26 – EXP – 0.9881 1234.93 1197.25 10.46
Eq. M. Yu et al.59 – EXP 0.9883 1238.86 1225.75 11.06
31 Tomii et al.24 Octagon CFST FE – EXP Observed by Ding et al.26 0.9231 33.36 33.33 3.00
FE – EXP Observed by Ayough9 0.9440 48.34 47.48 4.59
FE – EXP Observed by Hassanein et al.25 0.9714 43.10 39.75 3.92
Eq. Ding et al.26 – EXP – 0.9478 214.52 212.00 18.88
Eq. M. Yu et al.59 - EXP 0.9490 58.62 52.33 4.73
32 Fang et al.38 Octagon CFST FE - EXP Observed by themselves or the authors of the work. 0.9978 51.34 43.45 2.25
33 Zhu and Chan39 Octagon CFST Eurocode 4 - EXP – 0.9984 605.10 604.57 17.41
ACI - EXP 0.9984 868.31 862.71 24.37
34 Ahmed and Liang40 Octagon CFST Ahmed and Liang50 - FE Parametric study of FEM 0.9908 1497.27 1161.33 4.77
35 Chen and Chan8 Octagon CFST Eurocode 4 - EXP – 0.9948 243.10 215.60 6.14
Nu ic - EXP 0.9937 110.60 83.20 2.27
Nu cc - EXP 0.9928 111.93 87.45 2.38
36 Hassanein et al.25 Octagon CFST Eq. Ding et al.26 - FE Parametric study of FEM 0.9910 720.02 559.60 3.44
Eq. M. Yu et al.59 - FE 0.9754 3453.61 2986.69 16.97
Eq. Patel et al., 2016 - FE 0.9905 2344.07 2093.38 12.31
37 Fang et al.42 Octagon CFST FE - EXP Observed by themselves or the authors of the work. 0.9937 133.69 118.50 3.24
38 Manigandan et al.43 Octagon CFST with/without inner steel tube FE - EXP Observed by themselves or the authors of the work. 0.9938 37.97 36.75 4.51
39 Alqawzai et al.41 Octagon CFST with/without inner steel tube Parametric study of FEM and not compared to design codes/proposed equations of literatures
40 Ami and Zahrai51 Octagon CFST with/without inner steel tube Parametric study of FEM and not compared to design codes/proposed equations of literatures
41 Zha53 Octagon CFST Eq. M. Yu et al.59 - EXP Not possible to count R2.
42 Zhang et al.54 Octagon CFST Eq. M. Yu et al.59 - EXP – 0.9958 376.72 346.82 13.63
43 Zhu et al.60 Octagon CFST AISC 360 - EXP 0.9830 888.67 865.57 22.96
Zhu and Chan39 - EXP 0.9832 381.03 341.57 8.65
Liu et al.75 – EXP 0.9829 255.21 222.86 6.76
44 Hilo et al.62 Octagon CFST Eurocode 4 - FE Parametric study of FEM 0.7699 327.96 313.27 20.40
45 Almamoori et al.27 Triangular, Square, Rectangular, Rhombic, Pentagon, Hexagon, and Octagon CFST Not compared to design codes/proposed equations of literatures
46 Bai et al.32 Square CFST Not compared to design codes/proposed equations of literatures
47 Samir et al.61 Hexagon, Square, & Triangle CFST Not compared to design codes/proposed equations of literatures
48 Hassanein et al.45 Hexagon Not compared to design codes/proposed equations of literatures
49 Evirgen et al.46 Hexagon CFST Not compared to design codes/proposed equations of literatures