## 6 Numerical Simulation
### Simulation of the Cantilever Plate  
The cantilever plate model is shown in Figure 14, with its left end fixed. The length, width, and thickness of the cantilever plate are 0.5 m, 0.3 m, and 0.004 m, respectively; the density of the structural material is 7850 kg/m\({}^{3}\); the modulus of elasticity is \(2.06\times 10^{11}\) Pa; the Poisson ratio is 0.3; and it is divided into 15 plate-shell units, with the length and width of each unit being 0.1 m, and the left edge of the plate is fixed. The first five orders of its nature frequencies are 13.61 Hz, 50.21 Hz, 85.46 Hz, 167.02 Hz, and 236.78 Hz. The numbers above the nodes of the units are the node numbers, and the numbers inside the circles are the cell unit numbers. Figure 13: Damage identification results for each beam unit with different frequency points. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**Damage Unit Number/Degree of Damage\%**} \\ \cline{2-4}  & **GA** & **RGA** & **INFO** \\ \hline
2 & 3/16.13\%, 6/17.07\%, 10/13.29\% & 3/14.38\%, 6/15.42\%, 10/13.51\% & 3/17.47\%, 6/15.54\%, 10/13.93\% \\
4 & 3/15.46\%, 6/17.16\%, 10/12.85\% & 3/14.24\%, 6/15.50\%, 10/13.35\% & 3/18.40\%, 6/15.62\%, 10/13.18\% \\
8 & 3/14.39\%, 6/18.20\%, 10/12.34\% & 3/12.45\%, 6/15.61\%, 10/12.97\% & 3/16.89\%, 6/15.33\%, 10/13.37\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Identification results with different frequency-point spacings (Case 2). It can be observed from Figures 15 and 16 that the three intelligent algorithms can accurately localize the two damage sites in Case 3 and the three damage sites in Case 4 without any obvious misjudgment unit in the absence of noise interference. Table 7 shows that the mean errors of the target damage units identified by the GA and the RGA in Case 3 are 7.82% and 7.38%, and 3.36% and 3.11% in Case 4, respectively, whereas there are significant identification errors in both cases for INFO. Then, 1%, 3%, and 10% noise was added to the cantilever plate damage in Case 3. From Figures 17-19, it can be seen that under the influence of 1% and 3% noise, the GA, RGA and INFO can accurately locate the damage position in the cantilever plate; of these, INFO has the best damage identification results without significant misjudgment units, while more significant misjudgment units are found for both the GA and the RGA. However, under the influence of 10% noise, there are many obvious misjudgment units for the three methods. Table 8 (Case 3) shows that under the influence of 1%, 3%, and 10% noise, the mean errors of the target damage units identified by the GA are 14.18%, 28.64%, and 62.47%, 12.77%, 24.02%, and 52.34% by the RGA, and 2.90%, 6.80%, and 45.65% by INFO, respectively. It can be seen that INFO has the highest accuracy, the RGA has the second highest accuracy, and the GA has the lowest accuracy. The results of damage identification after adding 1%, 3%, and 10% noise to Case 4 are shown in Figure 20, Figure 21, and Figure 22, respectively, and summarized in Table 9.  
From Figures 20-22, it is observed that the GA, RGA and INFO are able to accurately locate the damage position in the cantilever plate (Case 4) under 1% as well as 3% noise influence. Under 3% noise, the GA and RGA have more significant misjudgments at units 2 and 6, and INFO has significant misjudgment at unit 2, while under the influence of 10% noise, there are many obvious misjudgment units for the three methods. Table 9 (Case 4) shows that under the influence of 1%, 3% and 10% noise, the mean errors of the target damage units identified by GA are 9.46%, 15.22% and 31.54%, 8.38%, 13.19%, and 28.17% by RGA, and 1.40%, 5.78%, and 23.32% by INFO, respectively. It can be seen that INFO has the highest accuracy in identifying the damage degree of the target unit, the RGA has the second highest accuracy, and the GA has the lowest accuracy.