Spherical shells are a commonly used structural form in submarine pressure-resistant structures. This study employed machine learning to predict the ultimate strength statistical properties of spherical shells considering inevitable multi-source uncertain imperfections. Thirty nominally identical spherical shells were fabricated, the thickness distribution and geometric imperfections were measured, and the ultimate strength of these shells were obtained by hydrostatic experiments. Then, the measured imperfections were reconstructed and mapped into the finite element model, and the buckling performance of the spherical shells were numerically investigated. Subsequently, two XGBoost models with considerable accuracy were trained to predict the ultimate strength statistical properties. The pole-smoothing double Fourier series expansion was adopted to reconstruct the geometric imperfections with accuracies exceeding 0.985 on all tested shells. The experimental ultimate strength of the spherical shells was consistent with the numerical predictions with an error of 0.81%. The evaluation metrics R2 of the XGBoost models for the mean and standard deviation of spherical shell ultimate strength were 0.9977 and 0.9246, respectively. At a confidence level of 99.74%, the margin of the upper bound prediction was 0.018 MPa, and the margin of the lower bound prediction was 0.624 MPa. The findings of this study propose an innovative method to predict the ultimate strength bounds of spherical shells, offering a generalizable workflow that can potentially inform the design of submarine pressure hulls when extended to application-specific geometric dimensions and materials.
Shi et al. (Mon,) studied this question.