## 7 Stage 2: ML Recognition
### Task 1: Global Damage Detection  
The results of Task 1 are presented in Table 5. There was no significant difference in the accuracy between Non-OL and OL, \(\leq\)0.3% in EVC. Accordingly, the generated feature-label pairs without OL (\(\approx\)7000) contained sufficient information to accurately train a classifier for global damage detection. Therefore, the ARIMA-ML is proposed to be applicable in practice since it does not require a very large dataset. In addition, due to the similar performance of Non-OL and OL and for computational efficiency, only the Non-OL pattern was considered in Tasks 2 and 3.  
Among different individual ML classifiers, SVM and NN classifiers achieved the highest accuracy, while RF and LR were slightly lower. Moreover, the ensemble classifier EVC achieved a stable and robust performance, comparable to the best individual classifier [36; 39]. This confirmed the effectiveness of using ensemble learning in this study. In general, the best classification performance using features extracted from these candidate models were similar (96.6\(\sim\)97.7%), and the EVC classifier using features extracted by ARI(7,1) was slightly better than the other two, i.e., the best fitting model may not be best feature extractor. This is mainly attributed to some overfitting in more complex models, e.g., ARIMA(6,1,6) and ARIMA(7,1,6). The candidate model mechanism resolved such issues by increasing the accuracy and robustness.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dataset** & **Pattern** & **ARI(7,1)** & **ARIMA(6,1,6)** & **ARIMA(7,1,6)** \\ \hline \multirow{2}{*}{Training} & Non-OL & 7396 & 7155 & 7132 \\ \cline{2-5}  & OL & 14,771 & 14,287 & 14,273 \\ \hline \multirow{2}{*}{Test} & Non-OL & 2559 & 2488 & 2471 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The number of feature-label pairs generated by different models.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model** & **Pattern** & **SVM** & **NN** & **RF** & **LR** & **EVC** \\ \hline \multirow{3}{*}{ARI(7,1)} & Non-OL & 97.2 & 97.5 & 96.4 & 97.0 & 97.6 \\ \cline{2-6}  & OL & 97.3 & 97.5 & 96.8 & 97.2 & 97.7 \\ \hline \multirow{3}{*}{ARIMA(6,1,6)} & Non-OL & 96.4 & 96.7 & 91.3 & 93.4 & 96.7 \\ \cline{2-6}  & OL & 96.6 & 96.9 & 92.5 & 93.5 & 96.9 \\ \hline \multirow{3}{*}{ARIMA(7,1,6)} & Non-OL & 96.6 & 96.3 & 92.1 & 93.5 & 96.6 \\ \cline{2-6}  & OL & 96.9 & 96.4 & 92.9 & 93.7 & 96.9 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Accuracy (%) of the global damage detection for different candidate models. Ensemble voting classifier (EVC).  
According to Figure 9, the labels of the dataset were somewhat imbalanced. Thus, a confusion matrix analysis was conducted to check the possible existence of biased predictions. For brevity, only the best result of ARI(7,1) without OL is presented in Figure 12a. It is evident that high values were achieved on the diagonal cells, while low values were achieved on the off-diagonal ones, which indicates that the classifier predicted each class accurately without a large bias. Thus, for Task 1, the best pipeline selected in stage 2 (step 5 in Figure 1) was the EVC classifier using features extracted from ARI(7,1).  
From the shaking table tests, Table 1, the natural period of the test structure varied from 0.56 s (UD) to 1.36 s (AL). As mentioned in Section 5.1, the floor information was not considered in Task 1 where the whole structure was treated as a SDOF system with damage detected as changes in its global stiffness and natural period, Figure 7. From the results, the ML classifiers were sensitive to the changes in the ARIMA coefficients corresponding to the changes in the first natural period. This is consistent with findings of high damage correlations with the AR coefficients of the ARMA models [2,21].