## 4 Results and Discussion
### Performance of the Mixed Learning Framework  
The poor performance of the transductive analysis provides the motivation for the mixed learning approach. To that end, a single DNN (\(DNN_{Train:80K_{t1}+80K_{t2}}\)) is now trained with 80% of the data from both \(K_{t}\)s. The only difference between the baseline DNNs and this mixed DNN is the elimination of individual networks for each \(K_{t}\). Following the training, \(DNN_{Train:80K_{t1}+80K_{t2}}\) is tested on both datasets separately. The results are shown through confusion matrices in Figure 12e,f. The performance is closely matched to the baseline DNNs in Figure 12a,b. The specificity of the mixed DNN is almost similar to the baselines, whereas sensitivity is impacted by roughly 1.5% due to the new training strategy. This success of the mixed DNN provides several practical advantages that can be reaped for better and more efficient damage detection models in the future. Particularly, mechanical components are bound to have differences in stress concentrations and geometries. The low accuracies in transductive analysis prove the need for DNNs that can work across such changes. The mixed DNN shows that a unified model can help simplify the monitoring of such components. However, the mixed training also highlights the need for massive amounts of data for a single DNN. Since there are no studies that have analyzed the need for data in such problems, a data-dependent parametric analysis is conducted by varying the training data from 10% to 80% for both \(K_{t}\)s. The capabilities of the resulting grid of 64 DNNs are tested on the data from each \(K_{t}\) individually. Through a series of boxplots, Figure 13a shows the nature of the performance metrics of \(K_{t1}\) test data when the training data percentage of \(K_{t1}\) is varied from 10% to 80%. As expected, an increase in the training data shows an overall increase in all three metrics. On an unexpected note, the lowest accuracy for 10% of the data is still admirably at 92%. The lowest sensitivity, however, is close to 87% at 10% training data. In general, as compared to the specificity, sensitivity is consistently lower across all the networks. This indicates that the DNNs are better at detecting healthy data; or as an alternative corollary, learning to identify the cracked signals is a more difficult problem. The performance at 10% training data offers an interesting comparison to the transductive analysis. The transductive analysis is a special case of mixed DNN where the data contribution of one \(K_{t}\) is 0%. The 60% accuracies from the transductive analysis are spiked to 92% with just 10% of the data. This further emphasizes the learning acumen of the mixed DNNs with sparse data. Figure 12: Confusion matrices for (**a**) \(K_{t1}\) baseline DNN and (**b**) \(K_{t2}\) baseline DNN. Confusion matrices for (**c,d**) transductive analysis, and (**e,f**) mixed learning. Reprinted (**a–d**) from [27] with permission under the terms and conditions of the Creative Commons Attribution (CC BY) license. In Figure 13b, the performance distribution of \(K_{t1}\) test data with variations in \(K_{t2}\) training data is shown. The distributions follow no discernible trend, indicating there is no impact of \(K_{t2}\) training data on \(K_{t1}\) performance. This, in turn, indicates the intricate capability of the mixed DNN to learn specific identifiers for each \(K_{t}\). However, due to the low interpretability of such deep networks, an exact learning criterion of these networks for each \(K_{t}\) cannot be explained within the purview of this analysis. While testing on \(K_{t2}\) data, similar trends are observed, as shown in Figure 14a,b. The performance is not impacted by an increase in \(K_{t1}\) data, whereas a steady improvement is seen with an increase in \(K_{t2}\) data. A different perspective on these results is shown through the six contour plots in Figure 15. For both \(K_{t1}\) and \(K_{t2}\) testing data, the accuracy ((a) and (b)) and sensitivity ((c) and (d)) show distinct contours.