Thrust prediction for hybrid rocket motors with aerodynamic throats based on radial basis function neural networks

Hybrid rocket motors with aerodynamic-throat nozzles can mitigate the chamber-pressure drop during deep throttling by using secondary injection to modify the effective throat area, without moving mechanical parts. However, rapid thrust prediction remains challenging because of the nonlinear interaction between secondary injection and the main combustion flow. This study develops a computationally efficient thrust-prediction method based on a radial basis function (RBF) neural network, whose spread factor is optimized by particle swarm optimization (PSO) combined with 5-fold cross-validation. A validated quasi-steady computational fluid dynamics (CFD) dataset covering 100 operating conditions is used for model training and testing, with oxidizer mass flow rate, secondary-injection mass flow rate, and fuel port diameter as inputs. The final model is constructed using all 70 training samples as RBF neuron centres and achieves a root mean square error (RMSE) of 6.86 N and a coefficient of determination (R²) of 0.9959 on 30 independent test samples, indicating accurate in-domain reproduction of the CFD-based thrust map. The trained model is applied to a variable-thrust hot-fire test, where it captures the magnitude and trend of the thrust response, with relative errors generally within 5% during stable operating phases. For a 20-second firing sequence with 1000 prediction steps, the calculation requires only 1000 scalar port-diameter updates and 7 × 10⁴ radial-basis evaluations with output-weight accumulations, making it suitable for rapid design iteration and real-time prediction scenarios. The model is intended for in-domain prediction, and transient deviations may occur during rapid modulation because feed-system dynamics are not explicitly included.