## 4 Numerical Simulations
For comparison purposes, the k-means clustering algorithm was applied to the entire dataset, which included both baseline and damage cases. The number of clusters was set to two to evaluate whether the extracted DSFs could naturally separate into distinct healthy and damaged groups based on similarity, without the use of any label information. Since k-means is an unsupervised method and does not involve an explicit training phase, it does not conform to the OCC framework. Therefore, it was included purely as a baseline clustering method to provide additional perspective on the separability of the DSFs in an unlabeled context. The results of the classification for all four models used in this study are listed in the form of a confusion matrix in Table 4. The 'true positive' (actual damaged) side of the matrix shows very satisfactory performance across the models, with one notable exception. The performance of the iForest algorithm is rather unstable; while it accurately predicts the state of the system for some damage cases, its prediction accuracy is significantly lower for others. This variability in iForest's performance may be attributed to its sensitivity to the distribution of the input features and the random nature of its tree construction, which relies on sub-sampling small portions of the dataset to build each isolation tree. In particular, damage scenarios with low-severity effects or overlapping DSF characteristics (e.g., Damage Cases 4 and 6) may limit its ability to effectively isolate anomalies. Furthermore, the presence of noise in the DSFs may affect the algorithm's consistency in distinguishing between healthy and damaged states. In contrast, both the OCSVM and LOF algorithms exhibit very similar performance bordering on perfection. They miss only a few classifications in a single case. Meanwhile, the k-means algorithm demonstrates excellent true-positive predictions without exceptions. The performance across all models seems consistently high on the 'true negative' side of the matrix, suggesting that all are equally suited for the task. Focusing on the safety-critical aspect of the damage detection problem, where predicting an actual damaged case as undamaged (false negative) is of greater concern than raising a false alarm for an undamaged state, the k-means algorithm displays the best performance. Following the detection stage, damage localization results utilizing the proposed index for the simulation cases are obtained and visually summarized in the box plot given in \begin{table}
\begin{tabular}{l l l l l l l l l l l l l l l l l} \hline \hline  & \multicolumn{10}{c}{**Percentage of Occurrences (\%)**} \\ \hline \multicolumn{10}{c}{**Actual Damaged (Test)**} & \multicolumn{10}{c}{**Actual Healthy (Validation)**} \\ \hline \multicolumn{10}{c}{**D.Case No.**} & \multicolumn{10}{c}{**D.Case No.**} & \multicolumn{10}{c}{**D.Case No.**} \\ \cline{3-14}  & & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline \multirow{4}{*}{**OCSVM**} & _OCSVM_ & 100 & 100 & 100 & 100 & 100 & 90 & 100 & 1 & 2 & 7 & 4 & 10 & 3 & 2 \\  & iForest & 98 & 70 & 98 & 4 & 86 & 25 & 100 & 0 & 0 & 3 & 0 & 7 & 0 & 1 \\  & LOF & 100 & 100 & 100 & 100 & 84 & 100 & 1 & 7 & 8 & 4 & 9 & 3 & 2 \\  & _k-means_ & 100 & 100 & 100 & 100 & 100 & 100 & 100 & 0 & 5 & 6 & 4 & 11 & 4 & 0 \\ \hline \multirow{4}{*}{**OCSVM**} & _OCSVM_ & 0 & 0 & 0 & 0 & 0 & 10 & 0 & 99 & 98 & 93 & 96 & 90 & 97 & 98 \\  & iForest & 2 & 30 & 2 & 96 & 14 & 75 & 0 & 100 & 100 & 97 & 100 & 93 & 100 & 99 \\  & _LOF_ & 0 & 0 & 0 & 0 & 0 & 16 & 0 & 99 & 93 & 92 & 96 & 91 & 97 & 98 \\  & _k-means_ & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 100 & 95 & 94 & 96 & 89 & 96 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Confusion matrix data for classification of the 700 damaged and 100 healthy simulation cases. Figure 4 for comparison. It is noteworthy that for all the damage scenarios, the correct location has been identified, with the index reaching its peak at the truly damaged segment.