## 3 Results and Discussion  
The particularity of the quality classification in this study can be illustrated by the feature distribution of normal welds and abnormal welds shown in Figure 8. The \(\text{Lim}_{\text{L}}\) and \(\text{Lim}_{\text{U}}\) of \(\Delta Q_{10}\) are selected to -0.1 and 0.1, respectively, because 97.5% welds are at this interval. According to the statistical analysis, 52,291 welds meet the conditions of \(\Delta Q_{10\text{N}}\in\)[0.4, 0.6) and \(\Delta S_{10\text{N}}\in\)[0.0, 0.2), and 79.6% (89, 094) welds meet the conditions of \(\Delta Q_{10\text{N}}\in\)[0.3, 0.7) and \(\Delta S_{10\text{N}}\in\)[0.0, 0.5). This reflects the fact that most welds are similar to their 'near neighbors' in terms of \(Q_{E}\) and \(R_{t}\) profile. It can be observed that in this imbalanced dataset, abnormal welds overlap with normal welds in part of the two-dimensional characteristic space. The combination of class imbalance and class overlap makes it difficult to construct the frontier of each class, which adds complexity for quality classification. The dataset of normal welds may contain certain abnormal welds because of misjudgment, which may make abnormal welds overlap 'normal' (misjudged) welds. However, the amount of such polluted data was limited, since the weld quality was inspected by two inspectors in this experiment. The weld failure detection methods based on traditional classification models appear to be unsuitable to detect abnormal welds from the imbalanced data. First, such models generally adopt global performance measures such as prediction accuracy in the learning process. If all welds are predicted as normal welds, a high accuracy score (>99.75%) can be obtained because of the low defect rate (<0.25%), leading to poor detection of weld failure in this application. Second, traditional classification models are based on supervised learning for the class-balanced data in general, while there is not enough real data of weld failure available for model training and testing in this study, since the abnormal welds do not often occur in reality. Third, the problem of class overlap also makes it difficult to distinguish between normal welds and abnormal welds by traditional classification models. \begin{table}
\begin{tabular}{c c} \hline \hline
**Algorithm** & **Major Parameters** \\ \hline iForest & trees = 100, subsampling size = 256, contamination (\(c\)) \(\in\) [0.01, 0.02,..., 0.49, 0.49999] \\ OCSVM & kernel = ‘rbf’, gamma = ‘scale’, \(nu\) [0.01, 0.02,..., 0.49, 0.49999] \\ LOF & neighbors = 20, contamination (\(c\)) \(\in\) [0.01, 0.02,..., 0.49, 0.49999] \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Anomaly detection algorithms and their major parameters. It is an essential task to find out abnormal welds in the quality monitoring of MRSW. Figure 9 shows the performance difference of anomaly detection for three models and four defect types. The parameter \(c\) or \(nu\) provided in the packages is used to adjust the model decision function. Figure 8: Feature distribution of normal welds and abnormal welds: (**a**) characteristic space; (**b**) frequency distribution. Figure 9: Comparison of detection performance: (**a**) iForest, (**b**) OCSVM; (**c**) LOF. For the detection of incomplete fusion welds, both iForest and OCSVM can distinguish all the incomplete fusion welds from normal welds, at the cost of the decrease in the specificity. The LOF model appears to be unsuitable for this application because its recall of incomplete fusion welds cannot reach 100% when \(c\) is near its upper limit 0.5. For the detection of other defect types, none of these models can identify the abnormal welds effectively, since no valid features have been extracted from \(u_{t}\), \(i_{t}\) and variables calculated from them so far.