# Structural Health Monitoring Using Machine Learning and Cumulative Absolute Velocity Features
## 4 Applications
### MDOF Systems
#### 4.1.2 Results  
Table 4 shows the damage state and location accuracy values for the two MDOF models. Results reveal that MODF-US achieved damage state detection accuracy of 91% and 84% when tested with TE-1 and TE-2, respectively. The higher accuracy with TE-1 was expected since the test set came from the same distribution as the training set. The damage state detection accuracy for MDOF-US and MDOF-NS (91%) tested with TE-1 significantly improved to 97% for MDOF-NS when tested with TE-2.  
Although accuracy is a widely used performance metric for ML models, other metrics can further explain the results, e.g., the recall value. Herein, the recall is defined as the proportion of the actual damages identified correctly for each damage state. The closer the recall value to 1, the better the performance of the model. The recall value for the undamaged state was computed using Equation (22).  
\[\text{Recall}_{\text{undamaged}}=\frac{\text{TU}}{\text{TD1}+\text{TD2}+\text{ TD3}} \tag{22}\]  
where TU = true undamaged cases, TD1 = true minor damage cases, TD2 = true moderate damage cases, and TD3 = true major damage cases. Similarly, recall values were calculated for the other damage states. Table 5 presents the class-specific recall values for the two MDOF systems. From this table, it is evident that for MDOF-US, the model predicted very well the undamaged class (0.99) and the major damage class (0.92). For moderate damage, it did fairly with a 0.78 recall value. However, minor damage was mostly misclassified due to the definition of the damage states. Since minor damage was defined as \(1\leq\mu\leq 2\), with this narrow range, the model performed poorly to detect minor damages which was further worsened by the lack of data from minor damage states. Similar performance of the model was observed for MDOF-NS. Major damage class had a higher recall value (0.97) than the MDOF-US, because of more data available for this damage state. Both MDOF-US and MDOF-NS had the same recall for the undamaged class.  
Table 4 also shows that damage locations were detected with 97.5% accuracy for MDOF-US with both TE-1 and TE-2. It is noted that three inaccurate cases were detected where the worst damage took place in both first and second stories, i.e., the first story was labeled as the correct location, but the model only identified the second story as the worst damage location. The damage locations were detected with 93% and 95% accuracy with TE-1 and TE-2, respectively, for MDOF-NS. Damage location detection for this model was more critical since the non-uniformity of stiffness introduced significant uncertainty about the damage locations. Thus, the results show that the damage location was identified with high confidence, even for non-uniform structural properties, using the proposed method.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Task** & **Test Set** & **MDOF-US** & **MDOF-NS** \\ \hline \multirow{2}{*}{**Damage State**} & TE-1 & 90.67 & 90.67 \\  & TE-2 & 84.33 & 96.67 \\ \hline \multirow{2}{*}{**Location**} & TE-1 & 97.50 & 93.00 \\  & TE-2 & 97.50 & 95.00 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Damage state and location accuracy (%) for the two MDOF models.