## 4 Numerical Application: Simply Supported Beam
#### Results
However, the focus of this work is not to exactly reconstruct the signal, but to extract key elements capable of characterizing the differences between \"normal\" and \"abnormal\" structural responses. Figure 6 displays an example of the SAE reconstructed response when using 50 and 100 internal codes in comparison with their respective original signals. Both plots reveal that just a reduced number of SAE features are enough to fairly represent the original simulated accelerations. For this reason, the authors opted to classify the data with 50 and 100 SAE characteristics (the start and the end of the linear behavior region exhibited in the graph). It can also be noted that the reconstruction errors of the training data are smaller than those obtained for the evaluation data, regardless of the number of SAE characteristics. This is an expected result, given that the first group of data was used to create the SAE models, and the second one has never been presented to them. The performance of the proposed approach for 30 different SAE/SVM models developed with 50 and 100 internal codes, respectively, is presented in Table 3. The classification rate is the mean value of correct identifications achieved in each model (average of the 30 models), only considering the evaluation data. Figures 7 and 8 show the confusion matrices related to the classification rates obtained in Table 3. These matrices point out the classification frequencies of the evaluation examples along with the three structural conditions. The diagonal elements in green are the amount and percentage of correct classifications, whereas the red elements refer to the amount and percentage of misclassified data. The rightmost column of the matrix exposes the precision metric (true positives/(true positives + false positives), and the row at the bottom exposes the recall metric (true positives/(true positives + false negatives). The element in the bottom right of the plot represents the overall accuracy. The \"Output Class\" corresponds to the predicted damage level and the \"Target Class\" to the level which the signal really belongs. They were  
Figure 6: An original response of the numerical beam and its respective signals reconstructed by SAE. constructed with all evaluating subsets, resulting in 13,500 different analyzed examples (450 evaluating examples \(\times\) 30 models). The classification averages are greater than 98% with standard deviation values below 0.5% for all measurement points, indicating the ability of the SAE to interpret and to extract features directly from structural acceleration time histories. Despite the good performance obtained for both quantities of SAE characteristics tested, the accuracy is slightly higher for models with 100 internal codes. For this configuration, practically 100% of the data were correctly classified. The confusion matrices confirm these results. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Mean**} & \multicolumn{2}{c}{**Max.**} & \multicolumn{2}{c}{**Min.**} & \multicolumn{2}{c}{**Std. Deviation**} \\ \hline
**SAE Internal Codes** & **50** & **100** & **50** & **100** & **50** & **100** & **50** & **100** \\ \hline
**Ac1** & 99.32 & 99.96 & 100.00 & 100.00 & 98.22 & 99.78 & 0.46 & 0.08 \\
**Ac2** & 99.56 & 99.99 & 100.00 & 100.00 & 98.22 & 99.78 & 0.43 & 0.04 \\
**Ac3** & 99.50 & 99.93 & 100.00 & 100.00 & 98.67 & 99.56 & 0.35 & 0.12 \\
**Ac4** & 99.50 & 99.94 & 100.00 & 100.00 & 98.89 & 99.56 & 0.38 & 0.13 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simply supported numerical beam: correct classification rates in percentage. Figure 7: Simply supported numerical beam: Confusion matrices—50 SAE internal codes. (**a**) Measurement point Ac1. (**b**) Measurement point Ac2. (**c**) Measurement point Ac3. (**d**) Measurement point Ac4.