Resolving engineering challenges: Deep learning in frequency domain for 3D inverse identification of heterogeneous composite properties

The inverse identification of heterogeneous composite properties from measured displacement/strain fields is pivotal in engineering. Traditional methodologies and emerging machine learning techniques both confront two major challenges. The first challenge involves achieving rapid identification while maintaining robustness to noise or pollution, and the second pertains to applicability in resolving complex three-dimensional (3D) engineering problems. To address these issues, a novel deep learning in frequency domain method (DLfd) for 3D inverse identification is proposed. Utilizing 3D-discrete cosine transform (3D-DCT), this method reduces input dimension by 98.24%, thereby simplifying the 3D problem to a computationally manageable form. A subsequent U-Net model establishes high-precision mappings between the reduced 3D-DCT coefficients of strain fields and modulus field, and the L1-error for the predicted modulus field is remarkably low at 2.431%. Even facing large noise (5% level) interference, the L1-error increases only 0.1%, demonstrating the robustness of the method. Coupled with Bayesian optimization, DLfd can generate accurate predictions even with incomplete measurements, and has been validated through several case studies involving measured fields missing in various shapes and locations. The method demonstrates general applicability to both 2D and 3D scenarios, and effectively mitigates the challenges posed by noise and data pollution, bringing it a step closer to practical implementation.