Xinchao Liu, Xiao Liu, T. Kaman, Xiaohua Lu, Guang Lin
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Statistical Learning for Nonlinear Dynamical Systems with Applications to Aircraft-UAV Collisions
ABSTRACT This article investigates a physics-informed statistical approach capable of (i) learning nonlinear system dynamics by using data generated from a nonlinear system as well as the underlying governing physics, and (ii) predicting system dynamics with reasonable accuracy and a computational speed much faster than numerical methods. The proposed approach obtains the reduced-order model from the full-order governing equations. A function-to-function regression, based on multivariate Functional Principal Component Analysis, establishes the mapping between external forcing and system dynamics, while a multivariate Gaussian Process is used to capture the relationship between parameters and external forcing. In the application, the proposed approach is applied to predict aircraft nose skin deformation after Unmanned Aerial Vehicle (UAV) collisions at different impact attitudes (i.e., pitch, yaw and roll degrees). We show that the proposed physics-informed statistical model can achieve a 12% out-of-sample mean relative error, and is more than 103 times faster than Finite Element Analysis (FEA). Computer code and sample data are available on GitHub.
期刊介绍:
Technometrics is a Journal of Statistics for the Physical, Chemical, and Engineering Sciences, and is published Quarterly by the American Society for Quality and the American Statistical Association.Since its inception in 1959, the mission of Technometrics has been to contribute to the development and use of statistical methods in the physical, chemical, and engineering sciences.