QPSO-BP Neural Network Model for Actuator Pressure and Friction Torque in Solid Rocket Ball Joint Nozzles

Friction torque is crucial to the overall design, reliability of motion, and accuracy of a rocket nozzle. The accurate prediction of driving pressure is essential for calculating the friction torque. To address this issue, we propose a prediction method based on quantum particle swarm optimization (QPSO) and a back propagation (BP) neural network. We first derive a formula to calculate the friction torque by using a Lagrangian dynamics equation to establish a theoretical foundation for subsequent analysis. We then obtain driving pressure data under different swing commands and various load conditions by conducting a pendulum test of the rocket nozzle. Using the experimental data as the training set, we perform a nonlinear regression of the driving pressure with the QPSO-BP neural network. The results indicate that, for the two actuators, the average relative errors in driving pressure predictions under dynamic friction are 0.486% and 0.879%, respectively; under static friction, the relative errors in these values are 2.614% and 2.669%, respectively. The findings of this study suggest that the QPSO-BP neural network model achieves an average prediction accuracy of 99.317% under kinetic friction and 97.358% under static friction, highlighting its potential for high-precision driving pressure prediction and friction torque calculation.