Methodology Development of a Free-Flight Parameter Estimation Technique Using Physics-Informed Neural Networks

Unstable free-flight rigid body motion, consisting of 3D translational motion and large angular rates about all axes and orientations outside of typical flight envelopes, is a complex dynamical system with significant challenges in modeling and simulation. Current methods in predicting this type of flight rely on aerodynamic models dependent on large databases consisting of non-linear aerodynamic stability coefficients determined primarily through computational simulations and a combination of static and dynamic wind-tunnel tests. Due to the complex nature of this type of unstable free-flight motion, experimental flight data is needed to study the full dynamics and is well suited to aircraft system identification and parameter estimation, which has greatly affected how non-linear aerodynamic models are developed. While these methods have been proven effective in a wide array of flight conditions, significant research efforts are still going into improving these methods in extreme flight conditions similar to the fully unstable free-flight motion de-scribed. Similarly, the development of Physics-Informed Neural Networks (PINNs) has significantly changed scientific machine learning by introducing physical knowledge of a system directly into the neural network training. In this work, we develop three methods of using PINNs to extract aerodynamic parameters from flight data. First, Determinant PINNs consist of a trajectory network and a parameter estimation module which can be used to estimate parameters that vary due to a known or estimated functional form caused by changes in explanatory variables. Secondly, Non-Determinant PINNs consisting of a trajectory network and a parameter estimation network can be used to estimate parameters that vary due to a set of explanatory variables with no known form. Thirdly, a Modified Non-Determinant PINN is developed to demonstrate the use of a parameter estimation network independent of a trajectory network while still implementing physical constraints into the training process. Each method is introduced with simulated case studies based on 2D projectile motion. Then an F-16 non-linear 6-DOF simulation case study is used to demonstrate the potential application of PINNs as an aircraft parameter estimation and modeling tool.