## 6 Results and Discussion
### Error Distribution Analysis  
To quantify improvements in our hybrid approach, we conducted error distribution analyses across six methods: the original dataset, noise-based augmentation, and four GAN-based techniques (GAN, DCGAN, TSAGAN, WGAN). Each method was evaluated 10 times for model variability. We calculated mean Euclidean distance errors between predicted and actual source locations for each run. Figure 9 presents box plots of these errors, with each box representing the distribution of mean errors across 10 runs per method. This approach provides a statistically sound comparison of augmentation strategies for improving AE source localization accuracy.  
Figure 8: The comparison of acoustic emission (AE) source localization performance. (**a**) Results from the hybrid deep learning model with GAN-based data augmentation and Inception network. (**b**) Results from the Inception network alone without GAN-based augmentation. Square markers represent actual source locations, star markers show predicted locations, and the large circular marker indicates the sensor position. The x and y axes represent dimensions in inches.  
The original data show that the highest median error was 6.2 inches with a 1.1-inch interquartile range. Noise-based augmentation marginally improves this to 5.2 inches (median) with a 0.3-inch range, indicating increased consistency but persistent substantial errors. Among the GAN methods, the standard GAN demonstrated superior performance, achieving a median error of 2.9 inches and a 0.7-inch interquartile range. This represents a 53% reduction from the original data and a 44% improvement over noise-based augmentation. The DCGAN and TSAGAN also perform well, with median errors of 3.4 and 3.6 inches respectively, showing 45% and 42% in improvements over the original data. Surprisingly, the WGAN underperforms with a 5.7-inch median error, only marginally better than the original data. This unanticipated performance of the WGAN, which theoretically should provide more stable training, demands further investigations. Its median error of 5.7 inches, only slightly better than noise-based augmentation, may be attributed to specific characteristics of AE signals or potential issues in implementation. We assume that the Wasserstein loss might be less effective in capturing the nuanced features of AE signals compared to the binary cross-entropy loss used in the standard GAN for this particular application.  
While our hybrid approach demonstrates significant improvements, it is also important to acknowledge its limitations. This study focused on a specific 24\" \(\times\) 24\" \(\times\) 0.1\" aluminum plate configuration, and further research is needed to validate its performance on larger structures and different materials. In conclusion, our innovative hybrid deep learning approach with GAN-based augmentation exhibits superior performance in AE source localization. The standard GAN architecture emerges as the most effective method, reducing median localization error by 53% compared to the original data, and by 44% compared to noise-based augmentation. These quantitative improvements underscore the value of advanced data augmentation techniques in enhancing model accuracy and reliability for structural health monitoring applications.