edfas.org 7 ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 26 NO. 3 To evaluate the performance of the trained models, F1 score and intersection over union (IoU) metrics are used.[33] The IoU score is mathematically represented as: (Eq 1) where J is Jaccard distance, A is ground truth, and B is prediction. A higher IoU score signifies a greater degree of overlap between model predictions and manually annotated image regions like voids, indicating better model performance. The F1 score is calculated as: (Eq 2) where TP is number of true positives, FP is number of false positives, and FN is number of false negatives. RESULTS AND DISCUSSION The quantitative and comparative analysis of the tested U-Net models for void detection in BGA solder joints is presented in Table 1. The score present here is achieved from the test set, which is not part of the training process. Among all four models, the U-Net 2D with Dice loss and U-Net++ with CCE loss outperform the other models. Both models achieved the same IoU and F1 score, 87.7% and 92.5%, respectively. U-Net with CCE loss was not the best-performing model among other loss functions, it provided a score very near to the best-performing model, U-Net++ with CCE loss and U-Net 2D with Dice loss. U-Net with CCE provided 87.5% IoU score and 92.2% F1 score. U-Net 3D with Jaccard loss exhibited the lowest performance among all models, achieving an IoU score of 73% and an F1 score of 63%. This suggests that the architecture selection may have a significant impact on model performance. From Table 1, it is observed that overall 2D models performed better than 3D models in terms of IoU and F1 score, particularly U-Net 2D with Dice loss and U-Net++ with CCE loss outperformed other models. Figure 4 presents the results obtained from the U-Net 2D model, showing the segmentation of voids within the XRM scan of solder balls. Figure 4a is the XRM scan of solder balls from the test set, with the background Table 1 Quantitative and comparative analysis of different U-Net architectures with different loss functions tested in this study. The results shown in the table are obtained on the test set. Deep learning model Lossfunction Mean IoU,% Mean F1,% U-Net 3D CCE 81.90 88.60 Dice loss 66.50 76.80 Jaccard loss 63.10 73.10 U-Net 2D CCE 87.50 92.20 Dice loss 87.70 92.50 Jaccard loss 86.60 91.80 U-Net++ 2D CCE 87.70 92.50 Dice loss 84.90 91.10 Jaccard loss 86.60 91.80 U-Net 2D (Dropout) CCE 85.80 90.60 Dice loss 86.80 91.80 Jaccard loss 87.30 92.20 Fig. 4 Qualitative analysis of model prediction for void detection. (a) 3D XRM scan visualization from test set having nine solder balls containing voids in it, and (b) corresponding segmentation from the U-Net 2D model, visualized in 3D and overlaid on the original image, where red color is voids in the solder ball and background is removed for better visualization. (a) (b)
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