## 8 Conclusions and Extensions  
In this study, to overcome the constraints of stationary conditions in TS modeling and promote the automatic ML technology in SHM applications, we proposed a two-stage framework, namely ARIMA-ML. In stage 1, through the **pre-processing module**, the raw non-stationary TS data was processed to be stationary to satisfy the assumptions of the ARMA modeling. Through the **model parameter determination module**, multiple candidate models were selected to increase the robustness of the framework. In stage 2, the segmented data were processed by the selected candidate model to obtain feature-label pairs in the **feature extraction module**. Subsequently, an ensemble classifier EVC engaged with multiple single classifiers was trained and tested in the **classification module**. This was followed by repeating stage 2 for all candidate models, such that the best model, from a performance accuracy point of view, was finally determined for use with future predictions. The effectiveness of the ARIMA-ML framework on the damage recognition of building structures was validated using TS data (mostly non-stationary) from shaking table tests for a steel structure subjected to different earthquake hazard levels producing several scenarios of damage detection tasks. Three classification experiments were designed: (1) global damage detection, (2) local damage detection, and (3) local damage pattern recognition. The validation experimental results demonstrated the robustness and accurate performance of the ARIMA-ML in all tasks, where nearly 97%, 98%, and 80% average segment accuracy were obtained for these three tasks, respectively. For the simpler binary Tasks 1 and 2, the confusion matrix analysis results further indicated the unbiased model performance even under an imbalanced-class distribution. Along with different experiments, discussions were made to explore the influence of overlapping pattern for data augmentation in the SSND procedure and the effect of higher order terms of the extracted features based on the \(FI\) scores to assess the feature performance. Our specific conclusions are listed as follows:  
1. The ARIMA coefficients were sensitive to the changes in stiffness both globally and locally. Using these coefficients as features, the developed framework accurately distinguished between the undamaged and damaged states with accurate performance in the more fine-grained damage categories, i.e., multiple damage patterns representing different damage levels. 2. The overlapping pattern (OL) used in the sliding window did not significantly affect the results, which we attributed to the size of the dataset (over 7000 segments) generated by Non-OL. This dataset contained sufficient information to accurately train a classifier for global damage detection, and applying OL slightly improved the classification accuracy (0.1%\(\sim\)0.3%). However, the OL increased the computational  
Figure 14: \(FI\) score of features extracted by the ARI(7,1) model. cost, and a trade-off between efficiency and accuracy should be considered in different practical applications involving real-time SHM field implementations. 3. Compared to previous studies, the candidate model mechanism made the framework more robust. In our case, the simpler TS model, ARI(\(p\), \(I\)), achieved better classification performance compared with the other complex ones, ARIMA(\(p\), \(I\), \(q\)), where \(p=6\) or \(7\), \(I=1\), and \(q=6\). This was mainly due to some overfitting in these more complex models, which degraded the classification performance. However, the complex models were shown to have better fitting results through the AIC value evaluation and residual diagnosis. Thus, considering several candidate models instead of using one best fitted model can reduce the risk of overfitting. 4. Due to the good performance of RF, its important characteristic of feature importance (\(FI\)) score was evaluated to understand how each feature was weighted using this ML classifier for making the final decision.