## 5 Experimental Application: V\(\ddot{\text{\text{\char 2010}}}\)zea Nova Viaduct  
The second application is the V\(\ddot{\text{\text{\char 2010}}}\)zea Nova viaduct situated in Paraiba at the intersection of highways BR-101 and BR-230, between the towns of Joao Pessoa and Campina Grande, in Brazil. The viaduct is 35.7 m long, and due to a traffic accident, one of the four main girders was damaged. To fix it and also to comply with Brazil's current regulation codes, a series of procedures were implemented, including strengthening of pillars, beams, deck, and foundation. Figure 9 shows a perspective view of the viaduct.  
Figure 8: Simply supported numerical beam: Confusion matrices—100 SAE internal codes. (**a**) Measurement point Ac1. (**b**) Measurement point Ac2. (**c**) Measurement point Ac3. (**d**) Measurement point Ac4.  
Figure 9: V\(\ddot{\text{\text{\char 2010}}}\)zea Nova viaduct. (**a**) Before strengthening. (**b**) After strengthening.  
Dynamic tests were conducted before and after structural reinforcement, leading to sets of experimental time histories (accelerations) obtained under traffic loading. A National Instruments NI9215 acquisition system attached to a computer was used to process the vibration signals that were collected by two piezoelectric accelerometers ENDEVCO model 752A13, positioned on the deck above the right border girder at its midspan and at its one-sixth length, as shown in Figure 10. Four dynamic tests were performed for each structural condition, resulting in 8 tests to be analyzed per accelerometer channel. Each structural response has 512 s sampled at 512 Hz. The variation of the first natural frequency--before and after the strengthening--is shown for information purposes in Table 4. As expected, higher values can be observed on the fundamental frequency after the strengthening, since this procedure increased the structure's stiffness without significantly changing it mass.  
To allow a parallel with the beam's signals with respect to the number of sampled points and the number of cycles analyzed per second, the viaduct vibration measurements were divided into more signals before processing the structural responses with SAE. Hence, each accelerometer provided 512 8-s long signals arranged in input matrices (512 \(\times\) 4096), corresponding to 256 dynamic time histories collected before the strengthening procedure and the other 256 collected after. Given the SVM supervised learning, a 512-position target vector was generated specifying the data category through the binary code: 0--before the strengthening, and 1--after the strengthening. In this case, the signal matrices are scaled into (\(-\)10;10) to prevent the quadratic error magnitude from causing significant numerical problems capable of hindering the convergence of the optimization method, as verified in some initial tests.  
For the present application, it was opted to assign approximately 70% of signals to the training phase and 30% to the evaluation phase, as a result of the lower number of structural responses available when compared to the numerical beam. One of the 512 signals of the accelerometer 2 was discarded due to acquisition problems verified  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Structural Scenario** & **1 st Natural Frequency** \\ \hline Before strengthening & 13.37 Hz \\ After strengthening & 13.76 Hz \\ \hline \hline \end{tabular}
\end{table}
Table 4: Variation of the first natural frequency of the Váárzea Nova viaduct.  
Figure 10: Várzea Nova viaduct. (**a**) Top view and experimental setup. (**b**) Typical response for accelerometer 1.  
during the data organization step. Therefore, the input matrices, as well as the target vectors, were subdivided into matrix \(A\) (362 \(\times\) 4096) for both accelerometer channels and into matrix \(C\) (150 \(\times\) 4096) for the accelerometer 1, and into matrix \(C\) (149 \(\times\) 4096) for the accelerometer 2. The architecture and parameters of the achieved SAE and SVM models for the Varzea Nova viaduct are in Table 5.