Crack detection by holomorphic neural networks and transfer-learning-enhanced genetic optimization

A new strategy for detecting cracks in 2D solids based on strain data is introduced. Crack detection is formulated as an inverse problem and solved using genetic optimization. The novelty lies in the evaluation of the model response at each generation. Specifically, the solution to the corresponding plane elasticity problem is expressed via holomorphic potentials, which are determined by training two holomorphic neural networks. As the potentials satisfy equilibrium and traction-free conditions along the crack faces a priori, the training proceeds quickly based solely on boundary information. Training efficiency is further improved by splitting the genetic search into long-range and short-range stages, enabling the use of transfer learning in the latter. The new strategy is tested on three benchmark problems, showing that an optimal number of training epochs exists that provides the best overall performance. A comparison is also made with a popular crack detection approach that uses XFEM to compute the model response. Under the assumption of identical stress-field representation accuracy, the proposed method is found to be between 7 and 23 times faster than the XFEM-based approach. While the strategy is presented here for the simplified case of a single internal crack, generalization is feasible. Overall, the present findings demonstrate that combining genetic optimization with holomorphic neural networks and transfer learning offers a promising avenue for developing crack detection strategies with higher efficiency than those currently available.