## 4 Artificial Intelligence Approach for Crack Length Prediction
### Network Training  
To build the related CNN for crack length prediction, AE signals were used from the experiment described in Section 3. Here, signals were obtained from the far-field PWAS2 during the experiment when the crack was in the ranges of 3.5-4.5 mm and 7.0-8.0 mm in total length. As previously described in Section 3 and Ref. [22], the fundamental concept is that these AE signals will differ in various characteristics, specifically in the frequency domain. The goal is to build an artificial intelligence system capable of discerning these distinctions and accurately predicting the crack length from the AE signal. Figure 15 shows a schematic of the sensing of the two distinct groups of AE signals used to build an example crack-length estimation CNN. A few examples of the experimental signal CWTs for each of the groups are shown. It is observed from the naked eye that the 7.0-8.0-mm crack length signals have a significant intensity peak near the 410 kHz range, as is also shown in Figure 12, whereas the 3.5-4.5-mm crack length signals do not. Though differentiating other details of the CWT signal subsets may not be easy to the naked eye, training a CNN to do so may yield promising findings.  
The dataset was comprised of a total of 251 CWT figures, 30 of which came from signals of crack lengths 3.5 mm-4.5 mm and 221 of which came from signals of crack lengths 7.0 mm-8.0 mm (as shown in Figure 16). The significant difference in the number of signals from the two groups was a result of more AE signals being captured while the crack was in the 7.0-8.0 mm range due to the more favorable crack surfaces. Due to the small overall dataset, stratified \(k\)-fold cross validation was used to partition the data for training and evaluation of the network capability in classifying crack length.  
Figure 14: [PERSON]–[PERSON] transform of the acoustic emission signals is isolated and augmented to fit the 227 \(\times\) 227-pixel criterion before being entered into the input layer of the AlexNet convolutional neural network architecture.  
The \(k\) value for the stratified \(k\)-fold cross validation was selected as 5, which would partition the dataset into 5 equal subsets, each of which has proportional categorical representation from the total dataset. For this network, which was built using the AlexNet convolutional neural network architecture, the optimizer used is the adaptive moment optimization (Adam). Important training options within the Adam optimizer were selected based on experience. The gradient decay factor and squared gradient decay factor were set to 0.9 and 0.999, respectively. The _max epochs_ for each iteration (\(k=5\)) was set to 15 with a validation frequency of 3. The learning rate was an adaptive learning rate in accordance with the Adam optimizer; the initial learning rate was set to a value of 1 \(\times\) 10\({}^{-4}\). The  
Figure 16: Example CWT figures for both groups used in crack length recognition AlexNet CNN.  
Figure 15: Schematic of signals from different crack lengths, which will be used to train AlexNet CNN for crack length recognition. (CL: crack length).  
mini-batch size for the training was 128. The loss function used in this network is the cross-entropy loss.