Application of Intelligent Optimization Machine Learning Method Based on Cross-Validation in Nozzle Profile Optimization

The expansion section profile of two-dimensional axisymmetric nozzles, with fixed expansion ratio and expansion section length, was optimized with the aim of maximizing nozzle thrust. The optimization parameter considered was the radial position of the control points on the Bezier curve. The hyperparameters of three machine learning models, BP neural network, support vector regression, and extreme learning machine, were optimized by combining a ten-fold cross-validation method with an optimization algorithm, which in turn evaluated their performance on the task of predicting nozzle thrust. The machine learning model with the highest fitting accuracy was used for the optimization calculation in combination with the agent optimization algorithm. Simulation results reveal that, following the optimization of hyperparameters, the three machine learning models demonstrate high prediction accuracy on the test set, with the BP neural network achieving the highest accuracy under the proposed model. The machine learning-based surrogate model optimization method leads to a 1.958% increase in optimized nozzle thrust, and the BP neural network estimates the optimized nozzle thrust with a mere 0.0249% error. Compared to the optimization results based on direct computational fluid dynamics (CFD) calculations, it is proven that the proposed method offers higher optimization efficiency and accuracy. The discrepancy in optimized nozzle thrust is only 0.0075%, and the optimization time is reduced by 16.5%.