Coupled Kernel Extreme Learning Machine and Cuckoo Search for Aerodynamic Modeling and Stability Analysis of Spinning Projectiles

The deformation of spinning projectiles induces alterations in their aerodynamic characteristics, thereby influencing flight stability. To assess the stability of spinning projectiles, the kernel extreme learning machine (KELM) is employed to develop the aerodynamic model of spinning projectiles. A mixed kernel is formulated by incorporating Gaussian and polynomial kernel functions to enhance the generalization ability of the model. The parameters of model are subsequently optimized using the cuckoo search (CS). Based on verifying the accuracy of the model by comparing the prediction results with the CFD results, the Lyapunov exponent method is adopted to investigate the impact of elastic deformation on the nonlinear angular motion stability of spinning projectiles, thereby revealing the mechanism of deformation on the attraction basin and stability for the angular motion. The findings reveal that the CS-based KELM with mixed kernel exhibits good reliability and accuracy in predicting the aerodynamic characteristics of spinning projectiles, with the maximum error between the predicted results and the CFD results remaining below 5%; as the deformation amplitude increases, the deformation-induced variation of yawing moment plays a leading role in the reduction of attraction basin; during the transition from convergence to divergence in the angular motion, the deformation can induce cluster oscillations prior to divergence, where the deformation-induced decrease of pitching damping moment significantly shapes the progression of the angular motion instability.