Fourier Neural Operator and Self-attention Mechanism for Damage Identification on a Steel Beam

Machine learning has been extensively applied in structural health monitoring, with modal-parameter-based damage identification being one of the most actively studied areas. However, existing studies often suffer from limited generalization ability and insufficient robustness to diverse damage patterns, hindering their practical application in real-world engineering. To address these challenges, this study proposes a deep learning framework composed of a middle-fusion processing block, a Fourier Neural Operator (FNO) block, and a self-attention-based post-processing block. The framework takes the first to third mode shapes and corresponding frequencies as input and predicts the stiffness distribution along the beam. Specifically, the middle-fusion block integrates modal information into a unified latent feature tensor, which is subsequently processed by the FNO block to learn the inverse mapping from modal parameters to stiffness. The self-attention post-processing block then refines the prediction to enhance accuracy. The framework is trained on numerically generated datasets, where stiffness variations are simulated using Gaussian Random Fields (GRFs). A total of 8000 samples is used for training. Both numerical and experimental validations are conducted to demonstrate the feasibility and robustness of the proposed framework.