Level-Set and Learn: Convolutional Neural Network for Classification of Elements to Identify an Arbitrary Number of Voids in a 2D Solid Using Elastic Waves

We present a new convolutional neural network (CNN)-based element-wise classification method to detect a random number of voids with arbitrary shapes in a two-dimensional (2D) plane-strain solid subjected to elastodynamics. We consider that an elastic wave source excites the solid including a random number of voids, and wave responses are measured by sensors placed around the solid. We present a CNN for resolving the inverse problem, which is formulated as an element-wise classification problem. The CNN is trained to classify each element into a regular or void element from measured wave signals. Element-wise binary classification enables the identification of targeted voids of any shapes and any number without prior knowledge or hint about their locations, shape types, and numbers, while existing methods rely on such prior information. To this end, we generate training data consisting of input-layer features (i.e., measured wave signals at sensors) and output-layer features (i.e., element types of all elements). When the training data are generated, we utilize the level-set method to avoid an expensive remeshing process, which is otherwise needed for each different configuration of voids. We also analyze how effectively the CNN performs on blind test data from a non-level-set wave solver that explicitly models the boundary of voids using an unstructured, fine mesh. Numerical results show that the suggested approach can detect the locations, shapes, and sizes of multiple elliptical and circular voids in the 2D solid domain in the test data set as well as a blind test data set.