## 3 Experiment
### Verification on the Qatar University Grandstand Simulator
#### 3.1.3 Discussions  
The scores of the trained models on the test sets are shown in Table 1. The ID column is the accelerometer's code; the Undamaged and Damaged column is the average anomaly score of the undamaged and damaged data. As indicated in Table 1, the anomaly scores for the undamaged and damaged data can be separated for most accelerometers. Damaged data can be distinguished from undamaged data if an appropriate strategy for selecting an anomaly score threshold is used. The first accelerometer, for example, has an average anomaly score of 0.384 for undamaged data and a value of 5.784 for damaged data, indicating good discrimination. We draw the score distribution density map of the first five accelerometers in Figure 8 to examine the score distribution quickly. The \(x\)-axis represents the score, and the \(y\)-axis represents the density of the score; (a) to (e) are the score distribution density maps of accelerometers 1 to 5. The undamaged and damaged data scores are greatly staggered in the score distribution displayed in Figure 8, indicating that our model successfully enhances the gap between the undamaged and damaged data.  
The ROC-AUC is used as a measurement indicator to evaluate our algorithm's (replaced by MTL + SG \(-\) AE below) performance. The ROC curve depicts the relative trade-off between true positive (TP) and false positive (FP) probabilities, where TP refers to the probability of judging undamaged samples as undamaged samples, and FP refers to the probability of judging damaged samples as undamaged samples [28]. In the process of choosing comparison algorithms, we found that cluster-based methods account for a large proportion of unsupervised structural damage detection, so we chose two classic cluster-based unsupervised methods as comparison algorithms: Gaussian Mixture Model (GMM) and Support Vector Clustering (SVC). At the same time, we noticed that the combination of autoencoder and traditional algorithm has also become a trend of unsupervised structural damage detection, so we also use the algorithm combining autoencoder and one-class support vector machine(AE + OC \(-\) SVM) as one of the comparison algorithms.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline ID & Undamaged & Damaged & ID & Undamaged & Damaged & ID & Undamaged & Damaged \\ \hline
**1** & **0.384** & **5.785** & **11** & **0.802** & **4.108** & **21** & **0.893** & **4.361**  
Finally, to demonstrate the effectiveness of multi-task learning, we also incorporate the algorithm (SG \(-\) AE) without introducing it as our comparative experiment.  
The best ROC curves of the five methods under this dataset are plotted in Figure 9, and the graph demonstrates that MTL + SG \(-\) AE has the maximum area under the curve (AUC). Among the five algorithms, only AE + OC \(-\) SVM, SG \(-\) AE, and MTL + SG \(-\) AE are deep algorithms. Figure 10a shows the AUC values of these three algorithms changes with the training epochs. Figure 10a shows that the performances of SG \(-\) AE and MTL + SG \(-\) AE are significantly better than that of AE + OC \(-\) SVM; additionally, the multi-task learning we implemented improves the performance of MTL + SG \(-\) AE over that of SG \(-\) AE. The mean AUC of the five algorithms is shown in Figure 10b. As can be shown, the average AUC of all algorithms is more than 0.5, implying that these algorithms have unique effects on this dataset. MTL + SG \(-\) AE, on the other hand, has the highest average AUC of 0.708.  
Figure 8: Score distribution of the first five accelerometers, the \(x\)-axis represents the score, and the \(y\)-axis represents the density of the score distribution. (**a**–**e**) represent accelerometer 1 to 5.  
Figure 9: The best ROC curves of five algorithms.