## 6 Numerical Simulation
### Simulation of a Simply Supported Beam  
The model of the simply supported beam is shown in Figure 4. Its one section is fixed, and the bottom end of the other section is connected to a movable hinge support. The beam has an axial length of 1.2 m and is divided into 12 units, and the cross-section is a rectangle with a width of 0.05 m and a height of 0.015 m. The modulus of elasticity of the material is set to 2.061011 Pa, while Poisson's ratio is 0.3, and the density is 7850 kg/m\({}^{3}\). The first five orders of the nature frequencies of the model are 24.19 Hz, 96.66 Hz, 217.07 Hz, 384.76 Hz, and 598.42 Hz. Two damage cases, as shown in Table 1, are set up in the model of the simply supported beam. The numbers after \"/ \" in Table 1 and the subsequent tables represent the degree of damage of the unit. \begin{table}
\begin{tabular}{c c} \hline
**Damage Case Number** & **Damage Unit Number/Degree of Damage\%** \\ \hline
1 & 5/13\%, 9/9\% \\
2 & 3/19\%, 6/15\%, 10/15\% \\ \hline \end{tabular}
\end{table} 
Table 1: Damage case settings for the simply supported beam. Figure 4: Numerical simulation model of the simply supported beam. and 1.60%, respectively, while INFO has the highest identification accuracy without obvious errors for the two cases. However, the measured response data will inevitably be affected by different levels of noise in practical engineering applications. Two levels of noise (1% and 3%) were added to Case 1, and the damage identification results for each beam unit under the influence of these different levels of noise are shown in Figures 7 and 8, respectively. From Figures 7 and 8, it can be seen that all the three algorithms accurately identify the damage location in the simply supported beam under the influence of 1% as well as 3% noise, but only under the influence of 3% noise is there a significant misjudment by the GA in the damage identification of the simply supported beam model at units 1, 2 and 12. Figure 9 shows the damage identification results for each unit when 10% noise was added to Case 1. Figure 8: Damage identification results for each beam unit under 3% noise (Case 1). Figure 7: Damage identification results for each beam unit under 1% noise (Case 1). Figure 9: Damage identification results for each beam unit under 10% noise (Case 1). From Figure 9, it can be seen that under the influence of 10% noise, the three algorithms' damage identification results are significantly worse compared with ones under the influence of 1% and 3% noise, and there are many obvious misjudgment units; GA is relatively more affected by this level of noise, while the other two algorithms' damage identification results are better than that of GA. The identification results under the influence of 1%, 3%, and 10% noise are shown in Table 3.  
Table 3 (Case 1) shows that under the influence of 1%, 3%, and 10% noise, the mean errors of the target damage units identified by the GA are 7.74%, 16.68%, and 59.31%, while those identified by the RGA are 6.52%, 12.39%, and 38.40% and those identified by INFO are 1.67%, 5.18%, and 31.29%, respectively. It can be seen that INFO has the highest accuracy while RGA has the second highest, and GA has the lowest accuracy in identifying the damage degree of the target unit. The mean error of the three algorithms in identifying the damage in the target unit in Case 1 increases significantly when the results of the 10% noise are compared with those with 1% and 3% noise, which is mainly due to the fact that too high a level of noise seriously affects the transfer ratio obtained and, ultimately, results in the failure to obtain a more accurate damage degree of the target unit, even if the value of the objective function converges more closely to the global optimum. Sub  
From Figures 10 and 11, it can be seen that the three algorithms can accurately identify the damage location in the simply supported beam under the influence of 1% and 3% noise.