## 3 Results and Discussion
### Full Building Validation Results  
Figure 5 shows the BNZ building in Wellington, New Zealand. Unit 3 of the BNZ building has been fully instrumented, allowing for the reconstruction of force-deformation hysteresis loops under earthquakes across all stories. [50]. In Figure 6, the measured hysteresis loops for the six stories of the BNZ building under the 2013 Seddon earthquake [50] are compared with hysteresis loops simulated using the proposed BWBN-VP model. Results show a good match between measured and identified responses with an average correlation coefficient of 0.97 across all stories. Moreover, they reveal the absolute maximum values of the measured and re-simulated inter-story restoring force for the building, as listed in Table 5. Absolute maximum/values of the measured and simulated restoring force for the BNZ building stories under the 2013 Seddon earthquake show an approximately 2% difference on average across all stories. Figure 4: Parity plots comparing BWBN and BWBN-VP hysteresis models for Tests 1–3 results. Figure 7 compares elastic stiffness, \(k_{e}\), evolutions estimated using the HLA-SHM method [43; 50] for the BNZ building stories with those identified using the proposed BWBN-VP model. A similar comparison is also made for pinching stiffness, \(k_{p}\), in Figure 8. Results show that the measured and re-simulated stiffness values are almost identical. There are good matches between the final stiffness values at the end of the damaging earthquake, and major stiffness drops occur at almost the same time for all stories. Therefore, the proposed BWBN-VP hysteresis model not only reconstructs structural responses accurately, but also simulates structural damage inflicted on the building with a high level of accuracy and a very good match to directly measured real-world seismic performance data. Figure 6: Comparison between BNZ building force-deformation hysteresis loops under 2013 Seddon earthquake and those identified using the proposed BWBN-VP model. Figure 7: Comparison between BNZ building elastic stiffness, \(k_{e}\), changes under 2013 Seddon earthquake estimated using HLA-SHM method and those of re-simulated method using the proposed BWBN-VP model. In this study, the column failure tests were conducted at an original sampling rate of 100 Hz, and the measurements on the real building were performed at 200 Hz. These rates were preserved throughout the research without any resampling. This approach ensures the accuracy and reliability of the correlation coefficient values reported in the paper. It is important to highlight that the main advantage of the BWBN-VP model, compared to the original BWBN model, lies in its ability to accurately simulate stiffness degradation and spreading in the pinching region, as demonstrated in Figure 8 for the BNZ building. The original BWBN model does not capture this effect, as it failed for a column with the SF mode in Figure 4. This capability is crucial for precisely simulating and identifying damage mechanisms, which is essential for effective strengthening after damaging earthquakes and helps prevent the wastage of resources. Figure 8: Comparison between BNZ building pinching stiffness, \(k_{p}\), changes under 2013 Seddon earthquake estimated using HLA-SHM method and those of re-simulated method using the proposed BWBN-VP model. The proposed BWBN-VP model can simulate responses of highly nonlinear RC structures with different levels of pinching behavior while accurately capturing the values of elastic and pinching stiffness obtained for the BNZ building using the HLA SHM method. It shows that the proposed BWBN-VP model reproduces realistic behavior and structural damage, simultaneously, for RC buildings. Given the lack of experimental or real data, this capability can be very valuable for civil engineering research and practice, in particular for vibration-based SHM studies, where a connection between measured structural responses and structural damage exists.