Prediction of natural vibration characteristics of double-layer cylindrical shells based on machine learning

Objective To address the challenges of frequent parameter iterations and high computational costs associated with finite element analysis (FEA) in ship structural design, this study proposes a machine learning-based surrogate model for predicting the natural vibration characteristics of double-layer cylindrical shells, aiming to achieve fast and accurate prediction of the structural modal frequencies.

Method Six design parameters of the double-layer cylindrical shell, including length, radius, and thickness, were selected as input features, with modal frequencies defined as the prediction targets. Data samples were generated through co-simulation using MATLAB and ANSYS. Latin Hypercube Sampling (LHS) was adopted to construct training datasets containing 50–600 samples, along with an independent test set comprising 20 samples. Four machine learning techniques—Kriging, Support Vector Machine (SVM), Backpropagation Neural Network (BP), and Random Forest (RF)—were adopted to develop surrogate models. Model performance was evaluated using the coefficient of determination (R²), Mean Absolute Error (MAE), and Root Mean Square Error (RMSE), and the effects of sample size and parameter feature importance were analyzed.

Results The results show that all surrogate models achieved an R² value greater than 0.95. Among them, the relative errors of the Kriging, BP, and SVM models were controlled within 3%, and the Kriging model exhibited the highest accuracy and robustness. A training sample size of 200 was found to be sufficient to meet the accuracy and stability requirements of engineering applications, and the cylindrical shell radius and the number of ribs were identified as the most influential parameters affecting the modal frequencies.

Conclusion The machine learning-based surrogate modeling approach can effectively replace conventional FEA for the rapid prediction of the natural vibration characteristics of double-layer cylindrical shells. The findings provide a reliable reference for the optimal design of underwater structures.