18 Application of a U-Net Convolutional Neural Network to Ultrasonic Wavefield Measurements for Defect Characterization 169 18.2 Background 18.2.1 Convolutional Neural Networks CNN finds its roots in the Neocognitron [12], a neural network framework proposed by Fukushima that can learn visual patterns based on geometrical similarity without a teacher. A CNN takes in a 2D image as an array of pixel information and passes it through a series of hidden layers. In each layer, a set of filters are passed over the input image to produce an array of filtered images—a process known as convolution. The array of filtered images typically pass through a nonlinear activation function, such as the rectified linear unit (ReLu) function, and a max pooling operation to clean the images and reduce parameter size. Grouped together, this set of operations is known as a convolutional layer. The addition of each convolutional layer allows the CNN to detect a hierarchy of features from pixel values, ranging from simple edges and shapes to more complicated figures and features. After passing through several convolutional layers, the array of images passes through several fully connected (dense) layers that eventually connect to the output layer, which is a list of all possible desired object classifications [13]. The CNN contains a set of parameters, weights, and biases that control the propagation of information between each internal layer. The values of these parameters are learned by the CNN by passing several labeled images through the network and computing the total error between the expected output and the output of the CNN. By passing several training images through the network, the total error is minimized by optimizing the set of weights and biases through stochastic gradient descent and backpropagation [14]. A trained CNN model is good at detecting features in an image and classifying objects invariant of viewpoint, perspective, illumination, scale, background, clutter, or intra-class variation. Several hyperparameters must be set before training any CNN model. These hyperparameters include the number, type, order, and depth (number of filters) of each layer, the stride length and size of each filter (kernel), and the learning rate. Several mature software platforms exist for the development of CNN models, including Berkeley’s Caffe platform [15] and Google Brain’s TensorFlow[16]. Because the setting of hyperparameters highly contributes to the success or failure of any CNN model, it is important to understand the functionality of each layer within the CNN for the model’s success in its intended application. The majority of beginning users do not have the depth of experience required to tune these hyperparameters successfully. The lesser-known and forthcoming Fast.ai library [17] achieves greater usability by setting these parameters for the user to enable a faster on-ramp in applying CNN models to solve novel engineering problems. The Fast.ai library with a PyTorch backend [18] was used in the current study. Recent advancements in CNNs have made them a primary tool for a variety of image processing and computer vision applications, including image classification, object detection and tracking, scene labeling, and visual saliency detection [13]. Of interest to the current study are applications of CNNs to the fields of SHM and NDE. Oliveira et al. proposed the application of a CNN to electromagnetic impedance measurements of an aluminum plate [19]. After exciting a boundary-free aluminum plate with a piezoelectronic transducer and measuring the impedance signal of the plate, the signal was converted to an RGB image for classification by a CNN as a damaged or undamaged plate. Ren et al. developed a modified image segmentation-based CNN for the purpose of identifying cracks in concrete civil infrastructure on a pixel-wise basis [20]. The proposed CNN was capable of outperforming conventional crack detection methods. A deep neural network (DNN) was utilized along with a sliding-window approach to locate welding defects in radiographic NDE X-ray images [21]. Munir et al. compared the performance of a CNN and a DNN in classifying weldment flaws from ultrasonic measurements [22]. The authors reported that the CNN outperformed the conventional DNN in nearly every case in classifying cracks, porosity, slags, and other weldment defects from a noisy ultrasonic signal. Ultrasonic weldment flaws were further studied in [23] where noise was first removed from the data by an autoencoder—a type of DNN—before being passed through a CNN for flaw classification. Virkkunen et al. demonstrated extensive data augmentation on phased-array ultrasonic data for flaw classification with a CNN [24]. In the study, the trained CNN model outperformed human inspection in ultrasonic flaw classification. Meng et al. rearranged the wavelet transform coefficients from A-scan ultrasonic signals into a 2D matrix to be fed into a CNN for feature extraction [25]. The proposed algorithm demonstrated better performance than conventional A-scan pattern recognition techniques. These studies demonstrate the applicability and high performance of CNNs in the field of structural damage detection.
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