## 3 Experiment
### Verification on Experimental Phase II of the SHM Benchmark Data
#### 3.2.3 Discussions  
The experimental results are shown in Table 3. As far as the entire structure is concerned, with the increase in the overall damage degree of the structure, the mean anomaly score shows a steady upward trend. For the undamaged case (Case 1), the average anomaly score is 0.824, the lowest average anomaly score compared to the average anomaly scores in the other cases, indicating that the current situation has the lowest probability of overall structural stability damage. In Case 2, removing a single diagonal brace increased the value to 1.115. When additional braces were removed in Cases 3-6, the average anomaly scores gradually climbed from 1.298 in Case 3 to 1.792 in Case 6. In Case 7, however, when all of the remaining diagonal braces were eliminated, the anomaly score jumped to 2.118. Finally, the anomaly score has grown to 3.655 due to loosened bolts in Cases 8 and 9, revealing a significant gap inside the entire structure. As far as a single sensor is concerned, it can be observed that the proposed algorithm exhibits remarkable results on most accelerometers. As the damage degree increases, the anomaly score also increases. In Case 9, most anomaly scores are more extensive than 4, and the anomaly scores of some accelerometers are even more significant than 5, gradually approaching 6. Figure 12 has drawn the score distribution of the 1 st accelerometer in 9 cases. The figure shows that as the degree of damage increases, the anomaly score becomes larger and larger, and there are clear boundaries between the different degrees of damage. Interestingly, the trained model can also better detect the degree of structural damage in the remaining cases, despite only using a portion of the data from Cases 1 and 9. In other words, even though the acceleration signals in Cases 2-8 and the remaining frames in Cases 1 and 9 were unfamiliar to the algorithm, it was able to assign a good anomaly score that accurately reflected the actual degree of damage in all cases. We also compare our proposed method with the four algorithms mentioned in Section 3.1.3. Figure 13 shows the best ROC curves of the five algorithms; in this figure, the ROC curves of \(\mathrm{SG}\,-\,\mathrm{AE}\) and \(\mathrm{MTL}\,+\,\mathrm{SG}\,-\,\mathrm{AE}\) overlap, and the AUC values are both 1. According to [28], we know that when the value of AUC is 1, the model is perfect. Therefore, these two algorithms are perfect for this dataset. Figure 14a shows the variation trends of the AUC values of the three depth algorithms during training. It is not difficult to find that the final AUC values are all 1, but during the training process, the initial AUC value of \(\mathrm{MTL}\,+\,\mathrm{SG}\,-\,\mathrm{AE}\) is 0.8, while the other two algorithms are 0. Compared with the other two algorithms, \(\mathrm{MTL}\,+\,\mathrm{SG}\,-\,\mathrm{AE}\) has a faster speed converging to 1, reflecting the algorithm's excellent training. Figure 14b depicts the average AUC of the five algorithms. The figure shows that the performance of \(\mathrm{MTL}\,+\,\mathrm{SG}\,-\,\mathrm{AE}\) is much better than that of GMM, SVC, \(\mathrm{AE}\,+\,\mathrm{OC}\,-\,\mathrm{SVM}\). Moreover, compared with \(\mathrm{SG}\,-\,\mathrm{AE}\), the average AUC is also improved from 0.961 to 0.998, which shows the effectiveness of multi-task learning. Figure 12: Score density plot of the 1 st accelerometer in 9 cases. To make the claims more substantiated, we also compared with other method using SHM benchmark data. Literature [5] used SHM benchmark data to verify the performance of the proposed unsupervised method, this method utilizes the distribution of the PoD values throughout the structure to identify the location of structural damage will be investigated. In their study, Case 1 has the smallest value of PoD and the Case 9 has the biggest value of PoD, which is similar to the distribution of anomaly score under this dataset.