## 4 Data Classification Results
### Results of the Rule-Based Classification  
The rule-based classification was applied to the acceleration data from the Hyatae Bridge along with added artificial data to investigate its applicability. The threshold values used in the rule-based classification are listed in Table 2. The selection of the specific values is discussed later in this section. Acceleration data were obtained from December 2020 to May 2021 for all 36 channels. During the classification, _Normal_, _Missing_, _Outlier_, _Trend_, and _Drift_ classes were identified in the actual acceleration data. Examples of these classes representing 10 min acceleration data are shown in Figure 11.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Class** & **Criteria** & **Threshold** \\ \hline _Missing_ & Existence of a missing data point & Not applicable \\ \hline _Minor_ & Quantization lines in data & 64 \\ \hline \multirow{3}{*}{_Outlier_} & \(r_{outlier,1}\) & 30 \\  & \(r_{outlier,2}\) & 3 \\  & \(r_{outlier,3}\) & 3 \\ \hline \multirow{3}{*}{_Square_} & \(t_{1}\) & 0.05 \\  & \(t_{2}\) & 0.05 \\ \hline _Trend_ & \(r_{trend}\) & 0.00035 \\ \hline _Drift_ & \(d_{drift}\) & 0.3 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Threshold values for the data anomaly classes.  
Figure 10: Examples of artificially generated classes: (**a**) _Minor_ and (**b**) _Square_.  
A critical issue in applying a rule-based method is that the measured data have an intrinsic ambiguity in the anomaly classes. In particular, certain data are difficult to identify as the _Trend_, _Drift_, or _Normal_ class because the data do not exhibit distinctive features for classification. To better describe the phenomenon, the index defined for the _Trend_ class, \(r_{trend}\), for all acceleration data is plotted in Figure 12a, showing an almost continuous distribution without clear patterns that can be used for classifying the _Trend_ class. Thus, we selected two threshold values for \(r_{trend}\) to separate data clearly for both _Trend_ and _Normal_ classes, such that data above the red line (i.e., the first threshold of \(r_{trend}=0.00035\)) and below the green line (i.e., the second threshold of \(r_{trend}=0.00005\)) in Figure 12b, c are observed as obvious _Trend_ and _Normal_ classes, respectively. The data between the red and green lines are defined as _Trend-ambiguous_. A procedure similar to that for _the \(d_{drift}\)_ distribution shown in Figure 13a was used for the _Drift_ class. Time history examples for the _Drift_ and _Normal_ classes above and below the green lines are shown in Figures 13b and 13c, respectively. The data between the red and green lines correspond to _Drift-ambiguous_.  
Figure 11: Example data for anomaly classes: (**a**) _Normal_, (**b**) _Missing_, (**c**) _Outlier_, (**d**) _Trend_, and (**e**) _Drift_.  
Examples of both _Trend-ambiguous_ and _Drift-ambiguous_ classes are shown in Figure 14. One can clearly see the difficulty of considering it as a perfect _Normal_, _Trend_, or _Drift_ class. In total, 7216 _Trend-ambiguous_ samples and 3489 _Drift-ambiguous_ samples were selected from the measured acceleration data with pre-defined thresholds. Using rule-based classification, the total numbers of samples for each class and their proportions with respect to the total number of samples labeled in the database are listed in Table 3.  
Figure 14: Examples of (**a**) _Trend-ambiguous_ class and (**b**) _Drift-ambiguous_ class.  
Figure 12: (**a**) _Trend_ class classification index distribution, (**b**) time history example right above the red line, and (**c**) time history example right below the green line.