## 3 Data Analysis Methodology
### The Mixed Learning Approach  
\(DNN_{Train:\ 80K_{t1}}\) and \(DNN_{Train:\ 80K_{t2}}\) demonstrate that each \(K_{t}\) may need a customized DNN using the traditional supervised machine learning tools. This is not a sustainable solution in the long run due to the multitude of DNNs that would be needed for different \(K_{t}\)s [8]. Therefore, in an attempt to avoid the generation of individual DNNs, the mixed learning approach pools in the data from multiple sources to train a single network. As shown in Figure 11, the training data from \(K_{t1}\) and \(K_{t2}\) are used together to train a single DNN denoted by \(DNN_{Train:\ 80K_{t1}+80K_{t2}}\). In doing so, the network is trained to invariably work on both datasets without the need for a \(K_{t}\) identification label.  
The mixed DNN is trained to understand these properties through its multi-layered and fully connected network. Although the procedure remains fairly straightforward, the novel applications to fatigue damage detection engender several questions that need to be thoroughly studied. Specifically, the implications of varying the amount of data from both \(K_{t}\)s can prove to be beneficial to the structural engineering community that often deals with data and testing limitations. For instance, new materials or expensive manufacturing techniques have limited testing information. Under such circumstances, can an accurate damage detection model be built with such mixed learning? How much data is essential to have a reliable DNN for damage detection? To answer such questions, the mixed DNN is further probed with a parametric analysis by varying the training data from both \(K_{t}\)s. A generalized behavior of the mixed DNN is thereby studied by using \(DNN_{Train:\ 80K_{t1}+\beta K_{t2}}^{Test:\{100-\beta\}K_{t1}}\) and \(DNN_{Train:\ 80K_{t1}+\beta K_{t2}}^{Test:\{100-\beta\}K_{t1}+\beta K_{t2}}\) where \(\alpha\) and \(\beta\) represent the training data volume variation from 10% to 80%. Since low data can possibly lead to unreliable, underfitted models, the training-testing split followed in this analysis is such that models trained with a lower percentage of the  
Figure 11: A single mixed DNN (\(DNN_{Train:\ 80K_{t1}+80K_{t2}}\)) trained using a mixed dataset comprising of both \(K_{t1}\) and \(K_{t2}\) data; tested on data from both \(K_{t}\)s separately.  
training data are tested on a higher percentage of testing data. In this way, the reliability of the models is also ensured.  
Note that, in summary, all DNNs are built with the objective of identifying the health of a specimen by just looking at the ultrasonic signals. To achieve this target, a ground truth needs to be established between the healthy and cracked signals. Since these ultrasonic signals (and sensors) are not capable of segregating healthy signals from cracked ones, a confocal microscope is used as an additional information source. The confocal microscope provides the instant at which a crack emerges. During each fatigue test, all signal data acquired after this instant are labeled as cracked. The labeled data from all the specimens are then pooled together, and a training-testing data split is created. The training data are used to train the DNNs, and the testing data (which are previously unseen) are used to evaluate the capability of the DNNs in correctly distinguishing the healthy and cracked signals. This methodology, therefore, attempts to emulate a real scenario where a lab-trained and confocal-aided DNN is deployed to identify a crack by just processing an ultrasonic signal.