## 5 Conclusions  
In this research, we introduce an innovative approach for developing an online damage localization technique. Utilizing the BP-ANN algorithm, we established multiple neural networks to emulate the transfer matrices among various bridge cross-sections. Based on these networks, a mapping network was developed to link data from two reference cross-sections to the other sections of interest. Subsequently, real-time monitoring data from these reference cross-sections were employed as inputs to reconstruct the dynamic responses at other locations. By comparing these reconstructed responses with actual monitored data, potential structural damage could be effectively identified. Figure 16: Ratio between measured responses and reconstructed responses at \(-\)2.4 m and 2.4 m in the intact and damaged scenarios. We conducted a comprehensive series of finite element simulations and laboratory experiments to validate the efficacy of our proposed method. The key findings from this study are summarized as follows:  
1. In the theoretical section, we introduced the concept of a transfer matrix for responses between different bridge cross-sections, which is independent of traffic loading. This key physical characteristic establishes the basis for the proposed damage localization algorithm's applicability under multiple vehicle conditions without requiring any traffic condition information. Furthermore, we provided a physical explanation for damage localization using the transfer matrix and the application of BP-ANNs. 2. In the numerical simulation section, we constructed comparative models for simple VBI systems with both an intact beam and a damaged beam. For these systems, the transfer matrix for displacement corresponding to the intact beam between two reference points and three other observation points was simulated using multiple regression analysis. It was confirmed that the transfer matrix undergoes significant changes following the occurrence of damage, and the reconstructed displacement for the damaged beam exhibited clear divergence from the measured displacement. Moreover, this divergence decreases with increasing distance between the damaged region and the observation point, thereby validating the physical foundation of the proposed method. 3. In our laboratory experiment, we constructed and tested a large-scale, three-span bridge with artificial damage to evaluate the efficacy of the proposed method. For the intact scenario, the accurately reconstructed inclination time histories validated the precision of the proposed reconstruction method that utilizes BP-ANN. Additionally, a series of comparisons were performed to assess potential divergences between the reconstructed and measured inclination time histories. The observed divergence in the comparison results distinctly pinpointed the location of the damaged area. Moreover, in the undamaged regions where the impact of the damage was minimal, the reconstructed responses closely aligned with the measured data, with negligible divergence. These results further corroborate the reliability of our proposed damage localization technique. Compared to existing studies, the proposed method stands out as a purely data-driven approach, offering high efficiency suitable for engineering applications. It is based on bridge mode shapes, which are independent of fluctuating traffic conditions, making it adaptable even under unknown and complex traffic scenarios. Unlike existing methods that rely on influence line functions and are limited to single-vehicle inspections, our method is designed to facilitate online monitoring in the presence of multiple moving vehicles. Furthermore, while the method is grounded in mode shapes, it does not require explicit mode shape functions during application. This eliminates the challenges associated with mode shape identification, especially when sensor coverage is not comprehensive. Additionally, the use of inclination measurements tends to be less susceptible to the impact of measurement noise, enhancing the reliability of the data.