ELM-based joint model identification for flight dynamics under unknown moments of inertia

Flight dynamics modeling typically requires prior knowledge of the aircraft’s moments of inertia, which is not always available in practice. This paper focuses on the dependency of aircraft dynamics modeling on inertial parameters and proposes a joint identification algorithm for scenarios with unknown moments of inertia. First, to overcome the strong coupling between unknown inertial parameters and aerodynamic parameters in the standard dynamic equations, which renders the latter unidentifiable, the present study reformulates the standard equations and defines equivalent aerodynamic moment derivatives. This transformation thereby leads to a joint identification model that enables simultaneous estimation of both inertial parameters and equivalent aerodynamic derivatives. Second, the unknown inertial parameters in the coupling terms introduce nonlinearities and potential instability into the joint model, making its numerical solution prone to divergence. To this end, the Extreme Learning Machine (ELM) trained on flight test data is employed to replace the direct numerical integration of the joint model in the original output error method for output prediction. Third, to reduce sensitivity to initial guesses of unknown parameters, the Gauss–Newton algorithm is replaced with a Levenberg–Marquardt (LM) algorithm enhanced by Particle Swarm Optimization (PSO). Finally, the improved output error method integrating ELM and PSO is applied to estimate the parameters of the proposed joint model. The proposed algorithm is applied to both F-16 simulation flight data and real flight data from a small fixed-wing UAV. The Theil's Inequality Coefficient indicates that the dynamic modeling accuracy of the joint model is comparable to that of the standard model with known moments of inertia. Moreover, the estimation error for inertial parameters is below 5%, demonstrating that the proposed approach provides a novel and effective means of estimating inertia parameters through flight tests.