## 4 Model Verification  
As briefly noted above, our first and second case studies that were conducted to illustrate the application of proposed SVM models utilized different, overlapping sets of building characteristics, numbering 11 and 20, respectively, for the assessment of buildings' capacity curves. The 11 characteristics, from factor 1 to factor 11, are selected from the 20 factors mainly for two reasons. First, either factor 1 to factor 3 or factor 12 to factor 14 can reflect the contribution of columns to a building's lateral stiffness; therefore, only factor 1 to factor 3 are used in the case with 11 characteristics. Second, the data of factor 1 to factor 11 are easy to be collected without special requirement on surveyors' expertise, while the data collection of factor 15 to factor 20 largely relies on the expertise of surveyors regarding structural engineering. The buildings in question were drawn from the previously mentioned NCREE database of more than 5400 Taiwanese schools, which for each building includes all 20 of the characteristics noted in Table 2, and a capacity curve (\(P_{Y}(S_{dy},S_{ay})\) and \(P_{U}(S_{du},S_{au})\)). For verification of the proposed \begin{table}
\begin{tabular}{l l} \hline \hline
**Factors** & **Description** \\ \hline  & (1) Reinforced concrete (RC) frame without masonry infill wall (CF); \\  & (2) RC wall building (CSW); \\  & (3) RC frame building with structural wall (CFSW); \\
1. Structural system & (4) RC frame building with masonry infill wall (CFIW); \\  & (5) RC building with transfer plate (CT); \\  & (6) Masonry building (M); \\  & (7) Steel frame building (S); \\  & (8) Precast building (P) \\ \hline  & (1) Low-rise (1–3), \\
2. Building height (stories) & (2) Mid-rise (4-7), \\  & (3) High-rise (8+) \\ \hline  & (1) High-code, \\
3. Seismic design standard & (2) Medium-code, \\  & (3) Low-code, \\  & (4) Pre-code \\ \hline
4. Built year \\ \hline
5. Total section area of columns in classrooms at ground level \\ \hline
6. Total section area of columns in partitions at ground level \\ \hline
7. Total section area of columns in corridors at ground level \\ \hline
8. Total section area of brick walls at ground level \\ \hline
9. Total section area of reinforced-concrete walls at ground level \\ \hline
10. Total section area of three-sided reinforced-concrete walls at ground level \\ \hline
11. Total section area of four-sided reinforced-concrete walls at ground level \\ \hline
12. Number of columns in classrooms at ground level \\ \hline
13. Number of columns in partitions at ground level \\ \hline
14. Number of columns in corridors at ground level \\ \hline
15. soft story & N/A (1), 2/3 wall inter. (0.9), 1/3 wall inter. (0.8) \\ \hline
16. short column & N/A (1), 50\% col./beam \textless{} 2 (0.9) \\ \hline
17. plan irregularity & N/A (1), \textgreater{}15\% dimension (0.95) \\ \hline
18. vertical irregularity & N/A (1), \textgreater{}15\% dimension (0.95) \\ \hline
19. deterioration & Severe (0.9), Moderate (0.95), Slight (1) \\ \hline
20. retrofitting intervention & Yes (1.2), No (1) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Building characteristics. SVM models, we used our sets of 11 and 20 building characteristics as the inputs, and spectral-yield displacement \(S_{dy}\), spectral-yield acceleration \(S_{ay}\), spectral ultimate displacement \(S_{du}\), and spectral ultimate acceleration \(S_{au}\) as the four outputs. The proposed model set and tested 11 training datasets ranging in size from 400 to 4,400 samples, in intervals of 400. The tests are performed on an Intel(r) CoreTM i7-6700 CPU@ 3.4 GHz with 24 GB RAM in the environment of Microsoft Windows 10. The computational time for each experiment is shown in Table 3. The total computational time is 4077 s (68 min). The computational time increases slightly as the number of building characteristics increases, while it increases significantly as the number of training data increases.