A Self-Evolving Physics-Constrained Multi-Round Strain Augmentation Framework for Sparse-Data iFEM Shape Sensing of Ship Plate Structures

Accurate reconstruction of thin-walled marine structures, such as ship hull plates and stiffened panels, via the conventional inverse Finite Element Method (iFEM) is severely limited by strain data scarcity in real-world deployments. Existing augmentation approaches either lack explicit physical constraints or rely on prior knowledge, restricting generality. This paper proposes a self-evolving physics-constrained multi-round strain augmentation framework (SPMR iFEM) that extracts deformation physics, specifically curvature trends, from iFEM-reconstructed displacements using only sparse measurements, without any prior knowledge. This extracted physics serves as a self-evolving reference to guide multi-round strain augmentation, progressively refining the displacement field through controlled steps. The method is demonstrated on two representative transverse deformation modes of ship plates: pure transverse deformation and a complex S-shaped transverse deformation. Quantitative results show that SPMR-iFEM reduces the maximum reconstruction error from 91.73% (conventional iFEM) to −11.68% for pure transverse deformation, and from 228.29% to −22.44% with four rounds and to −47.69% even with a single round for S-shaped deformation. The proposed prior knowledge-free, physics-constrained framework offers a robust shape sensing solution for marine structural health monitoring under data-sparse conditions, with potential for SHM in marine engineering involving complex deformations.