Data-driven modeling of a four-dimensional stochastic projectile system

Abstract

The dynamical modelling of projectile systems with sufficient accuracy is of great difficulty due to the high-dimensional space and various perturbations. With the rapid development of data science and scientific tools of measurement recently, there are numerous data-driven methods devoted to discovering governing laws from data. In this work, a data-driven method is employed to perform the modelling of the projectile based on Kramers-Moyal formulas. More specifically, the four-dimensional projectile system is assumed as an Itô stochastic differential equation. Then the least square method and sparse learning are applied to identify the drift coefficient and diffusion matrix from sample path data, which agree well with the real system. The effectiveness of the data-driven method demonstrates that it will become a powerful tool in extracting governing equations and predicting complex dynamical behaviors of the projectile.

Sparse identification method of extracting hybrid energy harvesting system from observed data

“…Lu and Lermusiaux [31] devised a Bayesian learning technique to model stochastic dynamical systems. Huang and Li [32] used the SINDy to discover the equations of a four-dimensional stochastic projectile system. Wu et al [33] obtained the mean residence time and escape probability of SDEs from data by using the devised approach.…”