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

TL;DR

The paper addresses crack detection in 2D linear elastic solids from strain data by casting the problem as an inverse optimization solved with genetic algorithms. It introduces holomorphic neural networks to learn KM potentials, enabling boundary-only training that automatically satisfies crack-face conditions, and employs transfer learning within a two-stage long-range/short-range search to accelerate convergence. Across three benchmark problems, the GA–HNN–TL framework achieves 7–23x faster performance than a standard GA–XFEM approach while maintaining comparable solution accuracy, with an identified optimal training epoch count around 200. Although demonstrated on a single internal straight crack, the authors show the method can generalize to other crack configurations and potentially multiple cracks via domain-decomposition strategies.

Abstract

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.

Figures (9)

• Figure 1: Linear elastic solid containing a straight internal crack.
• Figure 2: Reference crack detection algorithm proposed by waisman_detection_2010, which combines genetic optimization with XFEM.
• Figure 3: New algorithm for short-range search, which exploits HNNs and TL to efficiently evaluate the model response.
• Figure 4: Geometry, boundary conditions, sensor placement (indicated by the red crosses), and search space (indicated by the red dashed box) for the numerical experiments. (a) Plate with central crack subjected to uniform tensile loading. (b) Same as in (a), but with 16 strain sensors instead of 10. (c) Same as in (a), but with slanted crack.
• Figure 5: Impact of the number of epochs on the number of generations and computation time for the long-range search of the GA-HNN crack detection strategy. The problem of \ref{['fig:num_exp_1']} is considered, and the markers indicate the mean of five runs per epoch with identical initial population.