Combination of iFEM and CNN for rapid reconstruction of nonlinear buckling deformations of cylindrical shell

Accurate and fast shape sensing algorithms are essential to ensure the safety and improve the maintenance of ocean engineering structures. The purpose of this paper is to propose a novel method for the rapid reconstruction of nonlinear buckling deformations of cylindrical shell structures based on the inverse finite element method (iFEM) and convolutional neural networks (CNN). This hybrid method is called iFEM-CNN, which can reconstruct the nonlinear buckling deformation of cylindrical shell structures in real time without requiring prior knowledge of material properties and load conditions. First, a nonlinear iFEM suitable for cylindrical shell structures is derived. Using nonlinear iFEM, the discrete strains are reconstructed as full-field displacements. Subsequently, an integrated iFEM-CNN model is developed using the reconstructed full-field displacements as labels. Numerical results indicate that the iFEM-CNN method exhibits high reconstruction accuracy and fast computational speed. It is more suitable than using iFEM or CNN alone in real engineering applications. Moreover, the iFEM-CNN method can quickly and accurately reconstruct nonlinear buckling deformations of cylindrical shell under both dense and sparse sensor networks. Under dense configurations, the maximum percentage displacement error does not exceed 3% even with noisy measurements, and the reconstruction time is within 0.03 s. Under sparse configurations, with as few as 5% of elements instrumented, the mean PD error remains below 3%.