## 3 Results and Discussion
### Damage Severity Identification of Hinge Joint Based on Artificial Bee Colony
#### Numerical Simulations
**} \\ \cline{3-10} \multicolumn{2}{c}{} & & \multicolumn{2}{c}{**1**} & \multicolumn{2}{c}{**2**} & \multicolumn{2}{c}{**3**} & \multicolumn{2}{c}{**4**} & \multicolumn{2}{c}{**5**} & \multicolumn{2}{c}{**6**} \\ \hline \multirow{4}{*}{5} & \multirow{4}{*}{1} & ABC & 0.05 & 0 & 0 & 0 & 0 & 0 \\  & & ABCG & 0.05 & \(5.740\times 10^{-10}\) & 0 & 0 & 0 & 0 \\  & & ABCLGII & 0.05 & \(5.275\times 10^{-10}\) & 0 & 0 & 0 & \(3.035\times 10^{-9}\) \\  & & HABCDE & 0.05 & \(5.597\times 10^{-10}\) & 0 & 0 & \(1.786\times 10^{-10}\) & 0 \\  & & GA & 0.0625 & 0 & 0 & 0 & 0 & 0 \\ \cline{2-10}  & & PSO & 0.05 & 0 & 0 & 0 & 0 \\ \cline{2-10}  & & ABC & 0.050001 & 0 & 0 & 0 & 0 \\  & & ABCG & 0.05 & 0 & 0 & 0 & 0 \\ \cline{2-10}  & & ABCLGII & 0 & 0.05 & 0 & 0 & 0 \\ \cline{2-10}  & & ABCLGII & 0.05 & \(1.384\times 10^{-9}\) & 0 & \(1.050\times 10^{-9}\) & \(1.486\times 10^{-10}\) & \(3.510\times 10^{-10}\) \\  & & HABCDE & 0.05 & \(1.386\times 10^{-9}\) & 0 & \(1.049\times 10^{-9}\) & \(2.280\times 10^{-10}\) & 0 \\  & & GA & 0.0626 & 0 & 0 & 0 & \(4.768\times 10^{-7}\) & 0 \\  & & PSO & 0.05 & 0 & 0 & 0 & 0 \\ \hline \hline \multirow{4}{*}{6} & \multirow{4}{*}{2} & ABC & 0 & 0 & 0.6 & 0 & 0 \\  & & ABCG & 0 & 0.6 & \(2.644\times 10^{-9}\) & 0 & 0 \\  & & ABCLGII & 0 & 0.6 & \(2.644\times 10^{-9}\) & 0 & 0 \\  & & HABCDE & 0 & 0 & 0.6 & \(2.644\times 10^{-9}\) & 0 \\  & & GA & 0 & 0.6 & \(2.644\times 10^{-9}\) & 0 & 0 \\  & & PSO & 0 & 0.6 & \(2.644\times 10^{-9}\) & 0 & 0 \\ \cline{2-10}  & & GA & 0 & \(6.820\times 10^{-13}\) & 0.6441 & \(2.980\times 10^{-8}\) & 0 & \(7.629\times 10^{-6}\) \\  & & PSO & 0 & 0 & 0.6 & 0 & 0 \\ \hline \hline \multirow{4}{*}{7} & \multirow{4}{*}{1} & ABC & 0 & 0 & 0.6 & 0 & 2.514\(\times 10^{-10}\) \\  & & ABCG & 0 & 0 & 0 & 0 & 0 \\  & & ABCLGII & 2.598 \(\times 10^{-14}\) & 0 & 0.6 & \(5.820\times 10^{-10}\) & \(5.523\times 10^{-10}\) & \(2.002\times 10^{-10}\) \\  & & HABCDE & 9.992 \(\times 10^{-15}\) & 0 & 0.6 & \(5.828\times 10^{-10}\) & \(5.534\times 10^{-10}\) & \(1.996\times 10^{-10}\) \\  & & GA & \(3.074\times 10^{-8}\) & 0 & \(5.9977\) & \(3.243\times 10^{-5}\) & \(2.235\times 10^{-8}\) & \(1.073\times 10^{-6}\) \\  & & PSO & 0 & 0.6 & 0 & 0 & 0 \\ \hline \hline \multirow{4}{*}{7} & \multirow{4}{*}{3} & ABC & 0.1 & \(6.030\times 10^{-9}\) & 0 & 0.5 & 0 & 3.176\(\times 10^{-9}\) \\  & & ABCG & 0.1 & \(0\) & 0 & 0.5 & 0 & 0 \\  & & HABCDE & 0.1 & \(0\) & \(0\) & 0.5 & 0 & 0 \\  & & HABCDE & 0.1 & \(3.608\times 10^{-10}\) & \(7.182\times\) & & 0 \\  & & HABCDE & 0.1 & \(10\)-10 & 0.5 & 0 & 0 \\  & & GA & 0.1250 & \(4.888\times 10^{-6}\) & \(2.328\times\) & \(5.0510\times 10^{-7}\) & \(1.197\times 10^{-7}\) \\  & & PSO & 0.1 & \(0\) & 0.5 & 0 & 0 \\ \hline \hline \multirow{4}{*}{8} & \multirow{4}{*}{4} & ABC & 0.999 & 0.150020 & 0 & 0.40001 & 0.0499 & \(2.300\times 10^{-6}\) \\  & & ABCG & 0.1 & \(0.15\) & 0 & 0.4 & 0.05 & 0 \\ \cline{2-10}  & & ABCLGII & 0.1 & \(0.15\) & 0 & 0.4 & 0.05 & 0 \\ \cline{2-10}  & & ABCLGII & 0.1 & \(0.15\) & 0 & 0.4 & 0.05 & 0 \\ \cline{2-10}  & & ABCLGII & 0.1 & \(0.15\) & 0 & 0.4 & 0.05 & 0 \\ \cline{2-10}  & & ABCLGII & 0.1 & \(0.15\) & 0 & 0.4 & 0.05 & 0 \\ \cline{2-10}  & & GA & 0.0625 & \(0\) & 0.1885 & 0 & 0.419 & \(1.967\times 10^{-6}\) & 0 \\ \cline{2-10}  & & PSO & 0.1012 & \(0.1505\) & 0 & 0.4093 & 0 & 0 \\ \hline \hline \multirow{4}{*}{7} & \multirow{4}{*}{4} & ABC & 0.1 & \(0.1499\) & 0