Novel Fuzzy-Based Optimization Approaches for the Prediction of Ultimate Axial Load of Circular Concrete-Filled Steel Tubes
Abstract
:1. Introduction
2. Research Significance
3. Short Literature Review on Design Codes
4. Modeling Approaches
4.1. Fuzzy System (FS)
4.2. Firefly Algorithm (FFA)
4.3. Differential Evolution (DE)
4.3.1. Generating the Initial Population
4.3.2. Mutation
4.3.3. Crossover
4.3.4. Selection
4.4. Hybridization of FS
5. Data Setup
6. Development of the Hybrid Models
7. Discussion
7.1. Comparison against Alternative Hybrid Models
7.2. Comparison against Design Codes
7.3. Limitations and Future Works
8. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
DE | differential evolution |
D | diameter |
HS | harmony search |
CFST | concrete-filled steel tubular |
CCFST | circular concrete-filled steel tubular |
FS | fuzzy systems |
FFA | firefly algorithm |
fc | the compressive strength |
fy | the steel tube yield stress |
PSO | particle swarm optimization |
L | column length |
t | thickness |
GA | genetic algorithm |
R2 | coefficient of determination |
RMSE | root mean square error |
Pexp | ultimate axial compressive load |
Npop | population |
ML | machine learning |
Appendix A
Dataset Number | fc (MPa) | D (mm) | L (mm) | t (mm) | fy (MPa) | Pexp (KN) |
---|---|---|---|---|---|---|
1 | 34.04 | 60 | 180 | 1.48 | 307 | 215 |
2 | 51.3 | 101.9 | 305.7 | 3.03 | 371 | 926 |
3 | 34.08 | 60 | 180 | 1.48 | 307 | 220 |
4 | 164.4 | 114.3 | 200 | 6.3 | 428 | 2866 |
5 | 103.4 | 100 | 300 | 1.9 | 404 | 1100 |
6 | 103.4 | 100 | 300 | 1.9 | 404 | 1125 |
7 | 103.4 | 100 | 300 | 1.9 | 404 | 1170 |
8 | 51.3 | 101.5 | 304.5 | 3.03 | 371 | 859 |
9 | 23.1 | 101.6 | 304.8 | 3.03 | 371 | 635 |
10 | 23.2 | 101.6 | 304.8 | 3.03 | 371 | 635 |
11 | 40 | 101.6 | 304.8 | 3.03 | 371 | 864 |
12 | 93.6 | 114.57 | 300 | 3.99 | 343 | 1308 |
13 | 34.1 | 101.7 | 203.3 | 3.07 | 605.1 | 1112.10 |
14 | 40 | 101.7 | 305.1 | 3.03 | 371 | 803 |
15 | 48.3 | 165 | 562.5 | 2.82 | 363.3 | 1759 |
16 | 23 | 101.8 | 305.4 | 3.03 | 371 | 679 |
17 | 23.2 | 101.8 | 305.4 | 3.03 | 371 | 632 |
18 | 40.2 | 101.6 | 304.8 | 3.03 | 371 | 864 |
19 | 51 | 101.9 | 305.7 | 3.03 | 371 | 926 |
20 | 34.08 | 60 | 180 | 1.48 | 307 | 215 |
21 | 25.4 | 108 | 324 | 6.47 | 853 | 2275 |
22 | 56.99 | 114.3 | 342.9 | 6 | 342.95 | 1425.3 |
23 | 40.5 | 108 | 324 | 6.47 | 853 | 2402 |
24 | 43.9 | 108 | 1296 | 4 | 336 | 839 |
25 | 43.92 | 108 | 324 | 4 | 336 | 1235 |
26 | 77 | 108 | 324 | 6.47 | 853 | 2713 |
27 | 40.5 | 109 | 327 | 6.47 | 853 | 2446 |
28 | 25 | 114 | 1250 | 5.91 | 486 | 1177 |
29 | 37 | 114 | 850 | 1.79 | 266 | 515 |
30 | 37 | 114 | 850 | 6 | 486 | 1334 |
31 | 31.9 | 114.09 | 300.5 | 3.85 | 343 | 948 |
32 | 97.2 | 114.26 | 300 | 3.93 | 343 | 1359 |
33 | 57.6 | 114.29 | 300 | 3.75 | 343 | 1067 |
34 | 31.7 | 114.3 | 1143 | 3.35 | 287.3 | 563.6 |
35 | 31.7 | 114.3 | 342.9 | 3.35 | 287.3 | 816.2 |
36 | 31.7 | 114.3 | 1143 | 6 | 343 | 909.7 |
37 | 31.7 | 114.3 | 800.1 | 6 | 343 | 1000.4 |
38 | 31.7 | 114.3 | 571.5 | 6 | 343 | 1218.7 |
39 | 31.75 | 114.3 | 342.9 | 3.35 | 287.33 | 816.2 |
40 | 31.75 | 114.3 | 342.9 | 6 | 342.95 | 1380 |
41 | 56.9 | 114.3 | 342.9 | 3.35 | 287.33 | 995.7 |
42 | 25.4 | 108 | 324 | 6.47 | 853 | 2275 |
43 | 57 | 114.3 | 1143 | 3.35 | 287.3 | 904.2 |
44 | 57 | 114.3 | 571.5 | 3.35 | 287.3 | 937 |
45 | 57 | 114.3 | 342.9 | 3.35 | 287.3 | 995.7 |
46 | 57 | 114.3 | 800.1 | 6 | 343 | 1244.4 |
47 | 57 | 114.3 | 571.5 | 6 | 343 | 1389.3 |
48 | 86.1 | 114.3 | 342.9 | 6 | 343 | 1673.9 |
49 | 86.2 | 114.3 | 1143 | 3.35 | 287.3 | 1200 |
50 | 86.2 | 114.3 | 571.5 | 3.35 | 287.3 | 1281.4 |
51 | 86.2 | 114.3 | 1143 | 6 | 343 | 1389.1 |
52 | 86.2 | 114.3 | 800.1 | 6 | 343 | 1509.3 |
53 | 86.2 | 114.3 | 571.5 | 6 | 343 | 1564.7 |
54 | 86.21 | 114.3 | 342.9 | 3.35 | 287.33 | 1242.2 |
55 | 86.21 | 114.3 | 342.9 | 6 | 342.95 | 1673.9 |
56 | 88.8 | 114.3 | 342.9 | 3.35 | 287.3 | 1136.20 |
57 | 88.8 | 114.3 | 571.5 | 3.35 | 287.3 | 1180.70 |
58 | 102.4 | 114.3 | 1143 | 3.35 | 287.3 | 1481.2 |
59 | 102.4 | 114.3 | 800.1 | 3.35 | 287.3 | 1513.5 |
60 | 102.4 | 114.3 | 571.5 | 3.35 | 287.3 | 1598.9 |
61 | 102.4 | 114.3 | 342.9 | 3.35 | 287.3 | 1610.6 |
62 | 102.4 | 114.3 | 1143 | 6 | 343 | 1613.5 |
63 | 102.4 | 114.3 | 800.1 | 6 | 343 | 1788.9 |
64 | 102.4 | 114.3 | 571.5 | 6 | 343 | 1827.1 |
65 | 102.43 | 114.3 | 342.9 | 3.35 | 287.33 | 1610.6 |
66 | 102.43 | 114.3 | 342.9 | 6 | 342.95 | 1943.4 |
67 | 107.2 | 114.3 | 300 | 2.74 | 235 | 1295.10 |
68 | 107.2 | 114.3 | 600 | 5.9 | 355 | 1968.10 |
69 | 164.35 | 114.3 | 200 | 6.3 | 428 | 2595 |
70 | 164.35 | 114.3 | 200 | 6.3 | 428 | 2866 |
71 | 37.5 | 60 | 180 | 1.48 | 307 | 215 |
72 | 173.5 | 114.3 | 250 | 3.6 | 403 | 2340 |
73 | 173.5 | 114.3 | 250 | 3.6 | 403 | 2422 |
74 | 173.5 | 114.3 | 250 | 6.3 | 403 | 2610 |
75 | 31.4 | 114.43 | 300 | 3.98 | 343 | 948 |
76 | 57.6 | 114.49 | 299.3 | 3.75 | 343 | 1038 |
77 | 98.9 | 114.54 | 300 | 3.84 | 343 | 1359 |
78 | 40.2 | 101.7 | 305.1 | 3.03 | 371 | 803 |
79 | 34.7 | 114.88 | 300.5 | 4.91 | 365 | 1380 |
80 | 89.2 | 115 | 300 | 4.92 | 365 | 1787 |
81 | 57.6 | 115.02 | 300.5 | 5.02 | 365 | 1413 |
82 | 104.9 | 115.04 | 300 | 4.92 | 365 | 1787 |
83 | 23.2 | 101.8 | 305.4 | 3.03 | 371 | 679 |
84 | 34.08 | 120 | 360 | 1.48 | 307 | 610 |
85 | 34.08 | 120 | 360 | 1.48 | 307 | 660 |
86 | 36.6 | 159 | 650 | 5 | 390 | 2120 |
87 | 64.2 | 159 | 650 | 4.8 | 433 | 2210 |
88 | 56.1 | 165 | 581 | 2.82 | 363.3 | 2040 |
89 | 110.6 | 121 | 370 | 5 | 295 | 2016 |
90 | 116.7 | 121 | 370 | 5 | 295 | 1996 |
91 | 25.4 | 122 | 366 | 4.54 | 576 | 1509 |
92 | 25.4 | 122 | 366 | 4.54 | 576 | 1509 |
93 | 40.2 | 122 | 366 | 4.54 | 576 | 1657 |
94 | 40.5 | 122 | 366 | 4.54 | 576 | 1657 |
95 | 40.5 | 122 | 366 | 4.54 | 576 | 1663 |
96 | 40.5 | 122 | 366 | 4.54 | 576 | 1663 |
97 | 77 | 122 | 366 | 4.54 | 576 | 2100 |
98 | 77.2 | 122 | 366 | 4.54 | 576 | 2100 |
99 | 110.6 | 127.4 | 390 | 5.7 | 295 | 2217 |
100 | 116.7 | 127.4 | 390 | 5.7 | 295 | 2266 |
101 | 116.7 | 127.4 | 390 | 8.5 | 295 | 3106 |
102 | 42.1 | 133 | 465 | 2.9 | 325 | 476 |
103 | 42.1 | 133 | 465 | 4.5 | 325 | 492 |
104 | 42.1 | 133 | 465 | 4.5 | 325 | 576 |
105 | 42.2 | 133 | 2730 | 4.5 | 325 | 282 |
106 | 42.2 | 133 | 2730 | 4.5 | 325 | 293 |
107 | 42.2 | 133 | 1670 | 4.5 | 325 | 335 |
108 | 42.2 | 133 | 1670 | 4.5 | 325 | 347 |
109 | 42.2 | 133 | 1670 | 4.5 | 325 | 412 |
110 | 42.2 | 133 | 1670 | 4.5 | 325 | 430 |
111 | 42.2 | 133 | 465 | 2.9 | 325 | 466 |
112 | 42.2 | 133 | 465 | 2.9 | 325 | 476 |
113 | 42.2 | 133 | 465 | 4.5 | 325 | 500 |
114 | 42.2 | 133 | 465 | 4.5 | 325 | 559 |
115 | 42.2 | 133 | 465 | 4.5 | 325 | 576 |
116 | 42.2 | 133 | 465 | 4.5 | 325 | 591 |
117 | 42.2 | 133 | 1862 | 4.5 | 325 | 715 |
118 | 42.2 | 133 | 2793 | 4.5 | 325 | 784 |
119 | 42.2 | 133 | 2793 | 4.5 | 325 | 800 |
120 | 95 | 133 | 405 | 5 | 295 | 2002 |
121 | 110.6 | 133 | 405 | 5 | 295 | 2142 |
122 | 116.7 | 133 | 405 | 5 | 295 | 2178 |
123 | 28.2 | 140 | 635 | 6.68 | 537 | 2715 |
124 | 52.5 | 140 | 420 | 4.42 | 1020.00 | 3020 |
125 | 52.5 | 140 | 420 | 8.36 | 813 | 4436 |
126 | 52.5 | 140 | 420 | 10.46 | 773 | 5420 |
127 | 125 | 140 | 420 | 6.21 | 359 | 3202 |
128 | 125 | 140 | 420 | 8.19 | 389 | 3354 |
129 | 125 | 140 | 420 | 8.19 | 389 | 3398 |
130 | 125 | 140 | 420 | 11.58 | 367 | 4104 |
131 | 125 | 140 | 420 | 11.58 | 367 | 4300 |
132 | 125 | 140 | 420 | 4.42 | 1020.00 | 4312 |
133 | 125 | 140 | 420 | 4.42 | 1020.00 | 4516 |
134 | 125 | 140 | 420 | 16.72 | 389 | 5120 |
135 | 125 | 140 | 420 | 6.27 | 1153.00 | 5386 |
136 | 125 | 140 | 420 | 8.36 | 813 | 5502 |
137 | 125 | 140 | 420 | 10.46 | 773 | 6187 |
138 | 125 | 140 | 420 | 10.46 | 773 | 6339 |
139 | 40.5 | 149 | 447 | 2.96 | 308 | 1080 |
140 | 77 | 149 | 447 | 2.96 | 308 | 1781 |
141 | 77.1 | 149 | 447 | 2.96 | 308 | 1781 |
142 | 95 | 152 | 465 | 5.5 | 295 | 2662 |
143 | 116.7 | 152 | 465 | 5.5 | 295 | 2851 |
144 | 170 | 152.4 | 942.9 | 8.8 | 392.6 | 3919.9 |
145 | 170 | 152.4 | 551.9 | 8.8 | 392.6 | 4200.8 |
146 | 178.4 | 152.4 | 940.2 | 6.3 | 373.4 | 3584.7 |
147 | 178.4 | 152.4 | 552.7 | 6.3 | 373.4 | 4033 |
148 | 178.8 | 152.4 | 943.8 | 8.8 | 392.6 | 4099.8 |
149 | 180.9 | 152.4 | 949.7 | 5 | 445.9 | 3383.4 |
150 | 182.8 | 152.4 | 950.5 | 5 | 445.9 | 3995.7 |
151 | 182.8 | 152.4 | 540.7 | 5 | 445.9 | 4224 |
152 | 185.7 | 152.4 | 947.3 | 6.3 | 373.4 | 3535.3 |
153 | 185.7 | 152.4 | 554.7 | 6.3 | 373.4 | 3808 |
154 | 185.7 | 152.4 | 951.3 | 8.8 | 392.6 | 4178.7 |
155 | 185.7 | 152.4 | 559.7 | 8.8 | 392.6 | 4288.5 |
156 | 185.8 | 152.4 | 951.3 | 5 | 445.9 | 3724.1 |
157 | 185.8 | 152.4 | 548.5 | 5 | 445.9 | 3997.5 |
158 | 188.1 | 152.4 | 553 | 6.3 | 373.4 | 3692.8 |
159 | 188.1 | 152.4 | 948.5 | 6.3 | 373.4 | 3861.1 |
160 | 42 | 152.6 | 304.9 | 4.93 | 633.4 | 2909.10 |
161 | 43.4 | 152.6 | 304.9 | 4.9 | 633.4 | 2913.60 |
162 | 37.5 | 120 | 360 | 1.48 | 307 | 660 |
163 | 36.6 | 159 | 650 | 6.8 | 402 | 2830 |
164 | 36.6 | 159 | 650 | 10 | 355 | 3400 |
165 | 64.1 | 159 | 650 | 4.8 | 433 | 2210 |
166 | 38 | 165 | 571 | 2.82 | 363.3 | 1649 |
167 | 37.5 | 120 | 360 | 1.48 | 307 | 660 |
168 | 48.3 | 190 | 658 | 1.52 | 306.1 | 1841 |
169 | 48.2 | 165 | 562.5 | 2.82 | 363.3 | 1759 |
170 | 64.5 | 159 | 650 | 4.8 | 433 | 2240 |
171 | 93.6 | 159 | 650 | 5 | 390 | 2970 |
172 | 93.6 | 159 | 650 | 10 | 355 | 3400 |
173 | 93.8 | 159 | 650 | 5 | 390 | 2970 |
174 | 93.8 | 159 | 650 | 6.8 | 402 | 3410 |
175 | 106 | 159.6 | 3500 | 4.98 | 270 | 1454 |
176 | 71 | 159.7 | 2500 | 5.2 | 281 | 1562 |
177 | 101 | 159.7 | 3000 | 4.97 | 275 | 1636 |
178 | 70 | 159.8 | 2000 | 5.01 | 283 | 1650 |
179 | 73 | 159.8 | 3000 | 5.1 | 276 | 1468 |
180 | 100 | 159.8 | 2500 | 5.01 | 275 | 1818 |
181 | 102 | 159.8 | 4000 | 4.97 | 270 | 1333 |
182 | 45 | 159.9 | 4000 | 4.98 | 281 | 1091 |
183 | 40 | 160.1 | 2000 | 4.98 | 280 | 1261 |
184 | 74 | 160.1 | 3500 | 4.98 | 276 | 1326 |
185 | 100 | 160.1 | 200 | 4.99 | 275 | 2550 |
186 | 41 | 160.2 | 2500 | 4.96 | 281 | 1244 |
187 | 71 | 160.2 | 4000 | 5.02 | 281 | 1231 |
188 | 43 | 160.3 | 3000 | 5 | 270 | 1236 |
189 | 99 | 160.3 | 2000 | 5.03 | 281 | 2000 |
190 | 158.46 | 164.2 | 652 | 2.5 | 377 | 3501 |
191 | 64.3 | 159 | 650 | 4.8 | 433 | 2210 |
192 | 38.1 | 165 | 571 | 2.82 | 363.3 | 1649 |
193 | 64.2 | 159 | 650 | 4.8 | 433 | 2240 |
194 | 48.1 | 165 | 562.5 | 2.82 | 363.3 | 1759 |
195 | 38.1 | 190 | 657 | 1.13 | 185.7 | 1308 |
196 | 37.5 | 120 | 360 | 1.48 | 307 | 610 |
197 | 34 | 120 | 360 | 1.48 | 307 | 660 |
198 | 95.8 | 168.6 | 645 | 3.9 | 363 | 3339 |
199 | 56.4 | 165 | 581 | 2.82 | 363.3 | 2040 |
200 | 67.9 | 165 | 500 | 2.76 | 350 | 2250 |
201 | 67.94 | 165 | 500 | 2.81 | 350 | 2160 |
202 | 67.94 | 165 | 500 | 2.76 | 350 | 2250 |
203 | 77 | 165 | 571 | 1.82 | 363.3 | 2608 |
204 | 34.08 | 180 | 540 | 1.48 | 307 | 1280 |
205 | 80.2 | 165 | 580.5 | 2.82 | 363.3 | 2295 |
206 | 108 | 165 | 577.5 | 2.82 | 363.3 | 2673 |
207 | 74.7 | 190 | 663.5 | 0.86 | 210.7 | 2451 |
208 | 29.5 | 165.2 | 200 | 3.7 | 366 | 1630.56 |
209 | 43.5 | 165.2 | 200 | 3.7 | 366 | 1676.42 |
210 | 43.5 | 165.2 | 200 | 3.7 | 366 | 1737.94 |
211 | 58 | 165.2 | 200 | 3.7 | 366 | 2094.15 |
212 | 58 | 165.2 | 200 | 3.7 | 366 | 2221.62 |
213 | 81.6 | 165.2 | 200 | 3.7 | 366 | 2511.3 |
214 | 81.6 | 165.2 | 200 | 3.7 | 366 | 2922.24 |
215 | 158.7 | 168.1 | 645 | 8.1 | 409 | 5254 |
216 | 48.2 | 190 | 658 | 1.52 | 306.1 | 1841 |
217 | 36.2 | 168.6 | 645 | 3.9 | 363 | 1771 |
218 | 56.3 | 165 | 581 | 2.82 | 363.3 | 2040 |
219 | 95.8 | 168.6 | 645 | 3.9 | 363 | 3339 |
220 | 165.49 | 168.6 | 648 | 3.9 | 363 | 4216 |
221 | 77.1 | 190 | 664 | 0.86 | 210.7 | 2553 |
222 | 158.75 | 168.7 | 645 | 5.2 | 405 | 4751 |
223 | 151.9 | 168.8 | 650 | 5.7 | 452 | 4930 |
224 | 56.4 | 190 | 664.5 | 0.86 | 210.7 | 1940 |
225 | 167.87 | 169 | 645 | 4.8 | 399 | 4330 |
226 | 38.2 | 165 | 571 | 2.82 | 363.3 | 1649 |
227 | 34 | 180 | 540 | 1.48 | 307 | 1280 |
228 | 38.2 | 216.5 | 649.5 | 6.61 | 452 | 4200 |
229 | 34.08 | 180 | 540 | 1.48 | 307 | 1311 |
230 | 37.2 | 180 | 540 | 1.48 | 307 | 1280 |
231 | 64.4 | 159 | 650 | 4.8 | 433 | 2210 |
232 | 37.5 | 180 | 540 | 1.48 | 307 | 1311 |
233 | 158.46 | 189 | 756 | 3 | 398 | 4837 |
234 | 38 | 190 | 657.5 | 0.86 | 210.7 | 1240 |
235 | 38 | 190 | 657 | 1.13 | 185.7 | 1308 |
236 | 38.1 | 190 | 657.5 | 0.86 | 210.7 | 1240 |
237 | 108 | 190 | 660 | 1.94 | 256.4 | 3360 |
238 | 38.1 | 190 | 659.5 | 1.94 | 256.4 | 1652 |
239 | 38.2 | 190 | 657.5 | 0.86 | 210.7 | 1240 |
240 | 41.1 | 300 | 900 | 2.96 | 279 | 3277 |
241 | 77.1 | 165 | 571 | 2.82 | 363.3 | 2608 |
242 | 48.1 | 190 | 658 | 1.52 | 306.1 | 1841 |
243 | 151.91 | 168.8 | 650 | 5.7 | 452 | 4930 |
244 | 77.2 | 190 | 656 | 1.94 | 256.4 | 3083 |
245 | 56.1 | 190 | 664.5 | 0.86 | 210.7 | 1940 |
246 | 56.2 | 190 | 661.5 | 1.13 | 185.7 | 1862 |
247 | 56.2 | 190 | 664.5 | 0.86 | 210.7 | 1940 |
248 | 56.2 | 190 | 655.5 | 1.94 | 256.4 | 2338 |
249 | 56.4 | 190 | 661.5 | 1.13 | 185.7 | 1862 |
250 | 165.5 | 168.6 | 648 | 3.9 | 363 | 4216 |
251 | 37.5 | 180 | 540 | 1.48 | 307 | 1280 |
252 | 74.2 | 190 | 657.5 | 0.86 | 210.7 | 2433 |
253 | 113.5 | 190 | 660 | 2 | 271.9 | 3360 |
254 | 113.5 | 165 | 577.5 | 3 | 364.3 | 2673 |
255 | 74.7 | 190 | 663.5 | 1.94 | 256.4 | 2592 |
256 | 77 | 190 | 664 | 0.86 | 210.7 | 2553 |
257 | 77 | 190 | 658 | 1.52 | 306.1 | 2830 |
258 | 77 | 222 | 666 | 6.47 | 843 | 7304 |
259 | 167.9 | 169 | 645 | 4.8 | 399 | 4330 |
260 | 77.1 | 190 | 658 | 1.52 | 306.1 | 2830 |
261 | 77.1 | 190 | 656 | 1.94 | 256.4 | 3083 |
262 | 39.2 | 318.4 | 955.2 | 10.37 | 335 | 7742 |
263 | 24.3 | 216.5 | 649.5 | 6.61 | 452 | 3568 |
264 | 80.1 | 190 | 662.5 | 1.13 | 185.7 | 2295 |
265 | 80.2 | 190 | 663.5 | 1.52 | 306.1 | 2602 |
266 | 80.2 | 190 | 658.5 | 1.52 | 306.1 | 2870 |
267 | 85.1 | 450 | 1350.00 | 2.96 | 279 | 11,665 |
268 | 108 | 190 | 661 | 1.13 | 185.7 | 3220 |
269 | 108 | 190 | 661.5 | 1.52 | 306.1 | 3260 |
270 | 38.2 | 190 | 659.5 | 1.94 | 256.4 | 1652 |
271 | 108.1 | 190 | 661.5 | 1.13 | 185.7 | 3220 |
272 | 40.5 | 222 | 666 | 6.47 | 843 | 5714 |
273 | 113.5 | 190 | 660 | 1.15 | 184.8 | 3058 |
274 | 113.5 | 190 | 662 | 0.95 | 211.2 | 3070 |
275 | 113.5 | 190 | 661.5 | 1.55 | 315.3 | 3260 |
276 | 25.4 | 337 | 1011.00 | 6.47 | 823 | 8475 |
277 | 46.7 | 216.4 | 649.2 | 6.61 | 452 | 4283 |
278 | 24.1 | 216.5 | 649.5 | 6.61 | 452 | 3568 |
279 | 56.4 | 190 | 655.5 | 1.94 | 256.4 | 2338 |
280 | 38.1 | 216.5 | 649.5 | 6.61 | 452 | 4200 |
281 | 41.1 | 337 | 1011 | 6.47 | 823 | 9835 |
282 | 108 | 219 | 708 | 6.3 | 300 | 5410 |
283 | 148.8 | 219.1 | 600 | 6.3 | 300 | 6838 |
284 | 163 | 219.1 | 600 | 6.3 | 300 | 6915 |
285 | 174.5 | 219.1 | 600 | 6.3 | 300 | 7569 |
286 | 175.4 | 219.1 | 600 | 6.3 | 300 | 7407 |
287 | 185.1 | 219.1 | 600 | 5 | 380 | 7837 |
288 | 185.1 | 219.1 | 600 | 10 | 381 | 9085 |
289 | 25.4 | 222 | 666 | 6.47 | 843 | 4964 |
290 | 108.2 | 190 | 661 | 1.13 | 185.7 | 3220 |
291 | 26.9 | 550 | 1000.00 | 16 | 546 | 28,830 |
292 | 77 | 222 | 666 | 6.47 | 843 | 7304 |
293 | 77.2 | 190 | 658 | 1.52 | 306.1 | 2830 |
294 | 40.5 | 238 | 714 | 4.54 | 507 | 3583 |
295 | 40.5 | 238 | 714 | 4.54 | 507 | 3647 |
296 | 25.4 | 239 | 717 | 4.54 | 507 | 3035 |
297 | 74.7 | 190 | 657.5 | 0.86 | 210.7 | 2433 |
298 | 34.08 | 240 | 720 | 1.48 | 307 | 2150 |
299 | 34.08 | 240 | 720 | 1.48 | 307 | 2300 |
300 | 41.1 | 337 | 1011.00 | 6.47 | 823 | 9668 |
301 | 37.5 | 240 | 720 | 1.48 | 307 | 2150 |
302 | 41.1 | 361 | 1083 | 4.54 | 525 | 7260 |
303 | 38.2 | 190 | 657 | 1.13 | 185.7 | 1308 |
304 | 25.4 | 301 | 903 | 2.96 | 279 | 2382 |
305 | 80.3 | 301 | 903 | 2.96 | 279 | 5540 |
306 | 52.2 | 318.3 | 954.9 | 10.37 | 335 | 9297 |
307 | 39.1 | 318.4 | 955.2 | 10.37 | 335 | 7742 |
308 | 77 | 190 | 656 | 1.94 | 256.4 | 3083 |
309 | 24.2 | 318.5 | 955.5 | 10.37 | 335 | 6901 |
310 | 92.3 | 323.9 | 1000.00 | 5.6 | 443.9 | 11,481 |
311 | 25.4 | 337 | 1011 | 6.47 | 823 | 8475 |
312 | 34.01 | 240 | 720 | 1.48 | 307 | 2300 |
313 | 41.1 | 337 | 1011 | 6.47 | 823 | 9668 |
314 | 158.75 | 168.1 | 645 | 8.1 | 409 | 5254 |
315 | 37.5 | 240 | 720 | 1.48 | 307 | 2300 |
316 | 41.1 | 337 | 1011.00 | 6.47 | 823 | 9835 |
317 | 85.1 | 337 | 1011 | 6.47 | 823 | 13,776 |
318 | 41.1 | 360 | 1080 | 4.54 | 525 | 7045 |
319 | 85.1 | 360 | 1080 | 4.54 | 525 | 11,505 |
320 | 37.2 | 240 | 720 | 1.48 | 307 | 2300 |
321 | 41.1 | 361 | 1083.00 | 4.54 | 525 | 7260 |
322 | 25.4 | 450 | 1350 | 2.96 | 279 | 4415 |
323 | 41.1 | 450 | 1350 | 2.96 | 279 | 6870 |
324 | 41.1 | 450 | 1350 | 2.96 | 279 | 6985 |
325 | 85.1 | 450 | 1350 | 2.96 | 279 | 11,665 |
326 | 108 | 190 | 660 | 1.13 | 185.7 | 3058 |
327 | 40.5 | 222 | 666 | 6.47 | 843 | 5714 |
328 | 26.9 | 550 | 1000.00 | 16 | 546 | 29,590 |
329 | 37.5 | 60 | 180 | 1.48 | 307 | 215 |
330 | 103.4 | 100 | 300 | 1.9 | 404 | 1085.00 |
331 | 51.3 | 101.5 | 304.5 | 3.03 | 371 | 859 |
332 | 33.9 | 101.7 | 203.3 | 3.07 | 605.1 | 1067.60 |
333 | 23.2 | 101.8 | 305.4 | 3.03 | 371 | 632 |
334 | 40.5 | 109 | 327 | 6.47 | 853 | 2446 |
335 | 25 | 114 | 1280 | 5.94 | 486 | 1285 |
336 | 37 | 114 | 850 | 3.35 | 291 | 785 |
337 | 37 | 114 | 850 | 4.44 | 332 | 902 |
338 | 31.7 | 114.3 | 800.1 | 3.35 | 287.3 | 736.8 |
339 | 31.7 | 114.3 | 571.5 | 3.35 | 287.3 | 749.4 |
340 | 31.7 | 114.3 | 342.9 | 6 | 343 | 1380 |
341 | 31.9 | 114.3 | 300 | 3.85 | 343 | 998 |
342 | 57 | 114.3 | 800.1 | 3.35 | 287.3 | 932.9 |
343 | 57 | 114.3 | 1143 | 6 | 343 | 1141.3 |
344 | 57 | 114.3 | 342.9 | 6 | 343 | 1425.3 |
345 | 86.2 | 114.3 | 800.1 | 3.35 | 287.3 | 1206.5 |
346 | 86.2 | 114.3 | 342.9 | 3.35 | 287.3 | 1242.2 |
347 | 102.4 | 114.3 | 342.9 | 6 | 343 | 1943.4 |
348 | 105.5 | 114.3 | 571.5 | 3.35 | 287.3 | 1407.10 |
349 | 105.5 | 114.3 | 342.9 | 3.35 | 287.3 | 1453.10 |
350 | 107.2 | 114.3 | 600 | 2.74 | 235 | 1296.60 |
351 | 107.2 | 114.3 | 300 | 5.9 | 355 | 1989.90 |
352 | 173.5 | 114.3 | 250 | 6.3 | 403 | 2633 |
353 | 98.9 | 114.37 | 299.5 | 3.85 | 343 | 1182 |
354 | 34.7 | 114.43 | 300 | 3.82 | 343 | 929 |
355 | 84.1 | 114.5 | 300 | 3.84 | 343 | 1359 |
356 | 79.6 | 114.6 | 300 | 3.99 | 343 | 1308 |
357 | 77.1 | 190 | 662 | 1.13 | 185.7 | 2630 |
358 | 95 | 127.4 | 390 | 8.5 | 295 | 2544 |
359 | 110.6 | 127.4 | 390 | 8.5 | 295 | 2623 |
360 | 42.2 | 133 | 2730 | 4.5 | 325 | 268 |
361 | 42.2 | 133 | 1670 | 4.5 | 325 | 416 |
362 | 42.2 | 133 | 465 | 4.5 | 325 | 568 |
363 | 42.2 | 133 | 465 | 4.5 | 325 | 582 |
364 | 42.2 | 133 | 1862 | 4.5 | 325 | 882 |
365 | 52.5 | 140 | 420 | 6.27 | 1153.00 | 4274 |
366 | 125 | 140 | 420 | 6.21 | 359 | 3215 |
367 | 125 | 140 | 420 | 16.72 | 389 | 5135 |
368 | 125 | 140 | 420 | 6.27 | 1153.00 | 5354 |
369 | 95 | 127.4 | 390 | 5.7 | 295 | 2078 |
370 | 25.4 | 149 | 447 | 2.96 | 308 | 941 |
371 | 40.5 | 149 | 447 | 2.96 | 308 | 1064 |
372 | 110.6 | 152 | 465 | 5.5 | 295 | 2734 |
373 | 178.8 | 152.4 | 549.8 | 8.8 | 392.6 | 4354.1 |
374 | 93.8 | 159 | 650 | 10 | 355 | 3400 |
375 | 77.1 | 190 | 662.5 | 1.13 | 185.7 | 2630 |
376 | 80 | 190 | 658.5 | 1.52 | 306.1 | 2870 |
377 | 158.5 | 164.2 | 652 | 2.5 | 377 | 3501 |
378 | 67.9 | 165 | 500 | 2.81 | 350 | 2160 |
379 | 41 | 160.2 | 3500 | 4.97 | 273 | 1193 |
380 | 29.5 | 165.2 | 200 | 3.7 | 366 | 1428.32 |
381 | 36.2 | 168.6 | 645 | 3.9 | 363 | 1771 |
382 | 158.7 | 168.7 | 645 | 5.2 | 405 | 4751 |
383 | 158.5 | 189 | 756 | 3 | 398 | 4837 |
384 | 38.2 | 190 | 659.5 | 1.94 | 256.4 | 1652 |
385 | 56.4 | 190 | 661.5 | 1.13 | 185.7 | 1862 |
386 | 56.4 | 190 | 655.5 | 1.94 | 256.4 | 2338 |
387 | 74.7 | 190 | 657.5 | 0.86 | 210.7 | 2433 |
388 | 77.1 | 190 | 664 | 0.86 | 210.7 | 2553 |
389 | 93.8 | 159 | 650 | 6.8 | 402 | 3410 |
390 | 125 | 140 | 420 | 8.36 | 813 | 5531 |
391 | 77.1 | 190 | 662 | 1.13 | 185.7 | 2630 |
392 | 77 | 165 | 571 | 2.82 | 363.3 | 2608 |
393 | 80.2 | 190 | 658.5 | 1.52 | 306.1 | 2870 |
394 | 108 | 190 | 662 | 0.86 | 210.7 | 3070 |
395 | 46.7 | 216.4 | 649.2 | 6.61 | 452 | 4283 |
396 | 25.4 | 222 | 666 | 6.47 | 843 | 4964 |
397 | 40.4 | 222 | 666 | 6.47 | 843 | 5638 |
398 | 40.5 | 222 | 666 | 6.47 | 843 | 5638 |
399 | 77 | 238 | 714 | 4.54 | 507 | 5578 |
400 | 77 | 238 | 714 | 4.54 | 507 | 5578 |
401 | 41.1 | 300 | 900 | 2.96 | 279 | 3152 |
402 | 80.3 | 301 | 903 | 2.96 | 279 | 5540 |
403 | 52.2 | 318.3 | 954.9 | 10.37 | 335 | 9297 |
404 | 24.2 | 318.5 | 955.5 | 10.37 | 335 | 6901 |
405 | 85.1 | 337 | 1011.00 | 6.47 | 823 | 13,776 |
406 | 41.1 | 360 | 1080.00 | 4.54 | 525 | 7045 |
407 | 85.1 | 360 | 1080.00 | 4.54 | 525 | 11,505 |
408 | 25.2 | 361 | 1083.00 | 4.54 | 525 | 5633 |
409 | 25.4 | 361 | 1083 | 4.54 | 525 | 5633 |
410 | 26.9 | 550 | 1000.00 | 16 | 546 | 29,050 |
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Code | (MPa) | (MPa) | Section Slenderness | Other |
---|---|---|---|---|
EN1994 [71] | ||||
AISC 360 [72] | ||||
AIJ [73] |
Parameter | Unit | Min | Average | Max | SDT |
---|---|---|---|---|---|
L | mm | 180 | 720.73 | 4000 | 594.56 |
D | mm | 60 | 169.41 | 550 | 74.04 |
t | mm | 0.86 | 4.47 | 16.72 | 2.59 |
fy | MPa | 184.8 | 388.38 | 1153 | 170.29 |
fc | MPa | 23.2 | 74.98 | 188.1 | 44.01 |
Pexp | KN | 215 | 2992.71 | 29590 | 3213.2 |
Model | Training | Testing | ||||
---|---|---|---|---|---|---|
a20-Index | R2 | RMSE | a20-Index | R2 | RMSE | |
FS-FFA | 0.9604 | 0.9854 | 482.0362 | 0.8659 | 0.9880 | 415.4471 |
FS-DE | 0.9634 | 0.9571 | 655.4708 | 0.8659 | 0.9876 | 419.4502 |
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Liao, J.; Asteris, P.G.; Cavaleri, L.; Mohammed, A.S.; Lemonis, M.E.; Tsoukalas, M.Z.; Skentou, A.D.; Maraveas, C.; Koopialipoor, M.; Armaghani, D.J. Novel Fuzzy-Based Optimization Approaches for the Prediction of Ultimate Axial Load of Circular Concrete-Filled Steel Tubes. Buildings 2021, 11, 629. https://doi.org/10.3390/buildings11120629
Liao J, Asteris PG, Cavaleri L, Mohammed AS, Lemonis ME, Tsoukalas MZ, Skentou AD, Maraveas C, Koopialipoor M, Armaghani DJ. Novel Fuzzy-Based Optimization Approaches for the Prediction of Ultimate Axial Load of Circular Concrete-Filled Steel Tubes. Buildings. 2021; 11(12):629. https://doi.org/10.3390/buildings11120629
Chicago/Turabian StyleLiao, Jinsong, Panagiotis G. Asteris, Liborio Cavaleri, Ahmed Salih Mohammed, Minas E. Lemonis, Markos Z. Tsoukalas, Athanasia D. Skentou, Chrysanthos Maraveas, Mohammadreza Koopialipoor, and Danial Jahed Armaghani. 2021. "Novel Fuzzy-Based Optimization Approaches for the Prediction of Ultimate Axial Load of Circular Concrete-Filled Steel Tubes" Buildings 11, no. 12: 629. https://doi.org/10.3390/buildings11120629