# Energy Ratio Variation-Based Structural Damage Detection Using Convolutional Neural Network
## 3 Numerical Validation and Evaluation
### Numerical Simulation  
In order to compare the effects of single damage and multiple damages on the positioning accuracy of different damage locations, 40 different damage scenarios are selected, as shown in Table 4. To simulate the damage in the form of reduction element stiffness, apply the impact load to the fourth node of the simple supported steel beam, and the acceleration signal of the steel beam before and after damage collected by sensor 3 is taken as an example, as shown in Figure 6. Assuming that the damage degree of simple supported steel beam is 1%, 2%, 5%, 10%, and 15% (The elastic modulus of the material changes to the original 0.99, 0.98, 0.95, 0.90, and 0.85 times), the first 10 order frequencies of the second element under five damage degrees are shown in Table 5. It can be seen from the figure that the difference between the signal curves of the intact scenarios and the damage scenarios is small. Therefore, in order to better observe the damage state of the structure, the WPD of the signal is needed to make it easier to distinguish different damage scenarios. Therefore, the concept of wavelet packet mentioned above is introduced, which can decompose low-frequency signals and high-frequency signals at the same time. In the process of signal feature extraction, in order to find more sensitive feature indicators for structural damage, so that the subsequent CNN can be more efficient in feature extraction. In this paper, the selected db15 wavelet is used for ten-layer WPD, the signal is decomposed into 1024 energy bands, and the first 201 energy frequency bands with obvious characteristics are extracted. Combined with the characteristics of energy partial suppression or enhancement before and after structural damage, the ERV of wavelet packet band is used as the damage index. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Scenario**} & \multirow{2}{*}{\begin{tabular}{c} **Scenario** \\ **Number** \\ \end{tabular} } & \multicolumn{6}{c}{**Elastic Modulus**} & \multirow{2}{*}{\
\begin{tabular}{c} **Damage** \\ **Under Different Damage Degrees** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Location** \\ **Element** \\ \end{tabular} } \\ \cline{3-3} \cline{5-8}  & & **15\%** & **10\%** & **5\%** & **2\%** & **1\%** & \\ \hline intact & S0 & E & E & E & E & none & intact \\  & S1 & 0.85 E & 0.90 E & 0.95 E & 0.98 E & 0.99 E & 1 & left end \\  & S2 & 0.85 E & 0.90 E & 0.95 E & 0.98 E & 0.99 E & 2 & left end \\ single & S3 & 0.85 E & 0.90 E & 0.95 E & 0.98 E & 0.99 E & 5 & middle span \\  & S4 & 0.85 E & 0.90 E & 0.95 E & 0.98 E & 0.99 E & 6 & middle span \\  & S5 & 0.85 E & 0.90 E & 0.95 E & 0.98 E & 0.99 E & 9 & right end \\  & S6 & 0.85 E & 0.90 E & 0.95 E & 0.98 E & 0.99 E & 10 & right end \\ multiple & S7 & 0.85 E & 0.90 E & 0.95 E & 0.98 E & 0.99 E & 2, 8 & asymmetry \\  & S8 & 0.85 E & 0.90 E & 0.95 E & 0.98 E & 0.99 E & 5, 6 & symmetry \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Damage scenarios of simple supported steel beam. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Mode No**} &
\begin{tabular}{c} **Intact F** \\ **(Rad/Time)** \\ \end{tabular} & **15\% F** \\ \end{tabular} & **10\% F** \\ \hline
1 & 175.39 & 174.25 & 174.66 & 175.04 & 175.25 & 175.32 \\
2 & 225.74 & 224.24 & 224.77 & 225.27 & 225.55 & 225.64 \\
3 & 440.97 & 437.46 & 438.73 & 439.90 & 440.55 & 440.76 \\
4 & 523.66 & 512.96 & 522.58 & 523.14 & 523.46 & 523.56 \\
5 & 656.09 & 654.04 & 654.78 & 655.46 & 655.84 & 655.97 \\
6 & 762.93 & 756.45 & 759.19 & 761.30 & 762.33 & 762.64 \\
7 & 790.66 & 783.06 & 785.44 & 788.01 & 789.59 & 790.13 \\
8 & 860.51 & 856.58 & 857.92 & 859.23 & 860.00 & 860.26 \\
9 & 925.61 & 917.54 & 920.29 & 922.98 & 924.56 & 925.09 \\
10 & 1048.70 & 1040.10 & 1043.30 & 1046.10 & 1047.70 & 1048.20 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The first ten order frequencies of the intact and damaged scenarios. Figure 6: Acceleration response signals of intact structure and damaged structure.