## 5 Conclusions and Future Work  
This paper presents a fatigue crack detection paradigm using ultrasonic signals through deep learning across different \(K_{t}\)s. Two baseline DNNs are trained for two different stress concentration factors (\(K_{t1}\) and \(K_{t2}\)). An accuracy of 95.8% and 96.1% is observed, respectively, for \(K_{t1}\) and \(K_{t2}\). A transductive analysis is conducted to understand the capability of these pre-trained DNNs to detect damage in different \(K_{t}\)s. The analysis shows a steep drop in performance with accuracies of roughly 60%, indicating the disparity in the seemingly identical data from both the \(K_{t}\)s. To build a unified damage detection DNN, a mixed learning approach is developed by combining the data from both \(K_{t}\)s and training a single network. The mixed approach successfully demonstrates performance closer to the baseline DNNs. Delving further into the properties of mixed DNNs, a parametric analysis is conducted by varying the amount of training data used from each \(K_{t}\). A gradual increase in performance is observed with an increase in the percentage of training data from 10% to 80% for both \(K_{t}\)s. Incredibly, even with low training data, accuracies above 90% are observed in the analysis. The study, therefore, provides a basis for retraining with scarcely available data. All DNNs in this analysis are developed in-house without using any of the existing pretrained networks. A study on fatigue-crack detection using a scattered-wave two-dimensional cross-correlation imaging method [38] shows an accuracy of 96% for the detection of 5-mm-long cracks and an accuracy of 99% for the detection of 10-mm-long cracks. However, the proposed method is able to detect cracks of the order of 3 micrometers of crack opening displacements with a maximum accuracy of 96% using relatively inexpensive ultrasonic sensors, thus showing that this method is not just feasible but actually superior to the existing techniques under certain scenarios. From a data analysis perspective, a common competitor to the mixed learning approach is transfer learning [35], which can also be used to solve a similar problem. A preceding study [27] with transfer learning shows similar accuracies to the mixed learning approach. However, mixed learning tri-umphs over transfer learning by eliminating the need for multiple DNNs. The combination of high accuracy, ease of deployment, and parametric retraining can, therefore, make DNNs a fantastic choice in fatigue-damage detection across industries. However, the study does have some shortcomings that need to be addressed. The current approach investigates the question at hand as a binary classification problem without taking into consideration the sequence information present inside the time series. This is a reason why most of the erroneous predictions are around the area in the time  
Figure 15: Contour plots showing variations in (**a,b**) Accuracy, (**c,d**) Sensitivity, and (**e,f**) Specificity for \(K_{t1}\) and \(K_{t2}\), respectively. series where the crack first appears. Such behavior is expected because there is very little visual or mathematical difference between the signals immediately before and after the short crack initiation. Incorporating sequence information within the models, using long short-term memory (LSTM) or generative adversarial network (GAN), might be able to boost our accuracy further. Moreover, DNNs serve very much as a 'black-box' model: it is difficult to understand what features the model has learned in order to solve the problem of fatigue crack detection. Employing an encoder-decoder-based structure can allow the extraction of features from a 2D latent space. A systemic study of these features may allow us to gain a deeper understanding of the mechanics of fatigue failure and, thus, serve as an area of interest for future investigations. Conceptualization, A.B. ; methodology, A.B., S.D. and R.R. ; software, R.R. and S.D. ; validation, S.D. and R.R. ; formal analysis, S.D. and R.R. ; investigation, R.R. and S.D.