## 2 Methodology
### Proposed BWBN-VP Model Evaluation
#### 2.3.1 Experimental Verification  
The PEER database [49] provides force-deformation hysteresis loop data for an array of RC column cyclic-loading experiments. Three tests with different column failure types, as listed in Table 2, are selected from the PEER database to demonstrate the applicability and generality of the proposed BWBN-VP model to re-simulate different hysteresis loop shapes and failure modes in RC columns. The parameters of the calibrated model used to simulate Tests 1-3 are presented in Table 3. This validation test verifies the model structure.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Test** & **Author** & **Specimen** & **Failure Type** \\ \hline
1 & [PERSON] et al., 2001 [63] & No. 806040 & Flexural \\ \hline
2 & [PERSON] et al., 1985 [64] & No. 18 & Shear \\ \hline
3 & [PERSON], 2002 [65] & UCI5 & Flexural-shear \\ \hline \hline \end{tabular}
\end{table}
Table 2: RC column cyclic loading tests with three different failure modes, available from PEER database [49].  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Event** & **Parameter** & **Test 1** & **Test 2** & **Test 3** \\ \hline
1 & \(\alpha_{0}\) & \(0.02\) & \(0.10\) & \(0.05\) \\ \hline
2 & \(n\) & \(1\) & \(1\) & \(1\) \\ \hline
3 & \(\beta\) & \(0.6\) & \(0.3\) & \(0.6\) \\ \hline
4 & \(\gamma\) & \(-0.4\) & \(-0.1\) & \(-0.5\) \\ \hline
5 & \(\delta_{\eta}\) & \(0.001\) & \(0.4\) & \(0.5\) \\ \hline
6 & \(\delta_{v}\) & \(0.001\) & \(0.1\) & \(0.1\) \\ \hline
7 & \(\delta_{\psi}\) & \(0.1\) & \(0.1\) & \(0.1\) \\ \hline
8 & \(\xi_{s}\) & \(0\) & \(0\) & \(0\) \\ \hline
9 & \(p\) & \(0.1\) & \(0.9\) & \(0.15\) \\ \hline
10 & \(q\) & \(0.1\) & \(0.1\) & \(0.1\) \\ \hline
11 & \(\psi\) & \(0.1\) & \(0.1\) & \(0.1\) \\ \hline
12 & \(\lambda\) & \(0.1\) & \(0.1\) & \(0.1\) \\ \hline
13 & \(d_{y}\)(mm) & \(10\) & \(3\) & \(4\) \\ \hline
14 & \(C_{1}\) & \(0\) & \(0.5\) & \(10\) \\ \hline
15 & \(C_{2}\) & \(0\) & \(-200\) & \(-0.5\) \\ \hline
16 & \(C_{3}\) & \(1\) & \(10\) & \(0.25\) \\ \hline
17 & \(C_{4}\) & \(-0.5\) & \(-0.75\) & \(-0.5\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Parameters of the proposed BWBN-VP hysteresis model for Tests 1-3.  
2.3.2. Verification for Real-World Structure  
The former BNZ building located in Wellington, New Zealand, is used to demonstrate the performance of the proposed BWBN-VP model in practice. The BNZ building was a six-story concrete building significantly damaged due to a series of earthquakes between 2013 and 2016 [66], and demolished in 2018 [50]. The highly nonlinear hysteresis loops for six stories of the BNZ building under the 2013 Seddon earthquake are used to validate the proposed BWBN-VP model performance in re-simulating force-deformation behavior and modeling structural damage occurring in elastic and plastic stiffnesses of the building across all six stories. The well-proven HLA-SHM method [43; 50] has been used to analyze changes in elastic, \(k_{e}\), and pinching stiffness, \(k_{p}\), and these results are then compared with the proposed BWBN-VP model simulation results. The parameters of the proposed BWBN-VP model calibrated for the stories of the BNZ building are presented in Table 4. This validation test verifies the efficacy of the model for application in design, analysis, and structural health monitoring.