Fracture characterization from noisy displacement data using artificial neural networks

Mechanical characterization of fractures, i.e., identifying their characteristic parameters such as energy release rate, is crucial to assess the safety and stability of structural members. This is generally achieved using a combination of finite element analysis and optimization. Machine learning models are increasingly used to characterize engineering problems. While such models have shown impressive performance on smooth data, their performance diminishes significantly on data with discontinuities and sharp gradients. For fractures, this issue is more severe due to the singular solutions in the vicinity of the fracture tips. To resolve this difficulty, leveraging classical fracture mechanics, we construct custom functions, using neural networks, containing fundamental solutions of fracture mechanics. Through a series of examples, we demonstrate the proposed framework not only captures the singular solution and characteristic parameters accurately on both noise-free and noisy data, but also is highly efficient due to its simplicity and small number of parameters.