## 6 Numerical Simulation
### Simulation of a Simply Supported Beam
Compared with the aforementioned Case 1 (simply supported beam), under the influence of 3% noise, damage identification using the GA does not result in obvious misjuddment units, mainly because the damage degree of the damage unit in Case 2 is larger, and the identification is not easily affected by the noise. Further studies were carried out by adding 10% noise to the Case 2 (simply supported beam), and the results of the damage identification for each beam unit are shown in Figure 12.  
From Figures 10-12, it can be seen that there is the same pattern as for Case 1. But under the influence of 3% noise, the results are not the same as for Case 1; damage identification using the GA does not appear to present obvious misjuddment units, mainly because the damage degree of the damage unit in Case 2 is larger, and the identification results are not easily affected by the noise. The results of identifying the target damage units (Case 2) under the influence of 1%, 3%, and 10% noise are shown in Table 4.  
Table 4 (Case 2) shows that under the influence of 1%, 3%, and 10% noise, the mean errors of the target damage units identified by the GA are 7.10%, 9.67%, and 32.43%, while they are 5.75%, 7.31%, and 24.09% by the RGA, and 1.00%, 3.82%, and 17.24% by INFO, respectively. Comparing the mean errors, it can be seen that INFO has the highest accuracy in identifying the damage degree of the target unit, while RGA has the second highest accuracy, and GA has the lowest accuracy. In the aforementioned simulation, more frequency points in a larger frequency range were used, leading to increased computation. So, reducing the frequency points was considered. Keeping the frequency range from 1 Hz to 400 Hz unchanged, the following three scenarios were simulated for Case 2: (1) Taking points at equal intervals of 2 Hz for a total of 200 frequency points. (2) Taking points at equal intervals of 4 Hz for a total of 100 frequency points. (3) Taking points at equal intervals of 8 Hz for a total of 50 frequency points. The damage identification results from adding 3% noise are shown in Figure 13 and Table 5. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**Damage Unit Number/Degree of Damage\%**} \\ \cline{2-4}
**Noise Level/\%** & **GA** & **RGA** & **INFO** \\ \hline
1 & 3/17.65\%, 6/16.18\%, 10/14.05\% & 3/17.04\%, 6/15.25\%, 10/14.21\% & 3/18.72\%, 6/15.07\%, 10/14.84\% \\
3 & 3/19.42\%, 6/17.08\%, 10/13.06\% & 3/15.87\%, 6/14.56\%, 10/14.62\% & 3/17.57\%, 6/15.22\%, 10/14.63\% \\
10 & 3/9.71\%, 6/18.01\%, 10/10.75\% & 3/8.69\%, 6/14.51\%, 10/12.79\% & 3/13.58\%, 6/16.17\%, 10/12.69\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Identification results for the target damage units of the simply supported beam under three different levels of noise (Case 2). Figure 12: Damage identification results for each beam unit under 10% noise (Case 2). From Figure 13, it can be observed that under the influence of the same noise, the three algorithms obtained slightly worse damage identification results for each beam unit at the 2 Hz spacing than at the 1 Hz spacing (aforementioned results in Figure 11), but there is no obvious difference in the identification results when comparing the 4 Hz and 8 Hz spacings. Table 5 shows that under the influence of the same noise, the mean errors of the target damage identified by the three methods are 13.44%, 12.35%, and 6.26% at a 2 Hz spacing, 15.79%, 13.13%, and 6.47% at a 4 Hz spacing, and 21.11%, 17.36%, and 8.06% at an 8 Hz spacing, respectively. The identification accuracy for the three algorithms becomes lower and lower with the gradual increase in the taking-point spacing within the same frequency range, and the identification accuracy of INFO is the highest, with the second highest identification accuracy for the RGA, and the lowest identification accuracy for the GA.