Data-driven modeling of a four-dimensional stochastic projectile system
Yong Huang(黄勇)1 and Yang Li(李扬)2,†
1 School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094, China; 2 School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China
Abstract The dynamical modeling of projectile systems with sufficient accuracy is of great difficulty due to 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 modeling of the projectile based on the 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.
Fund: This research was supported by the Six Talent Peaks Project in Jiangsu Province, China (Grant No. JXQC-002).
Corresponding Authors:
Yang Li
E-mail: liyangbx5433@163.com
Cite this article:
Yong Huang(黄勇) and Yang Li(李扬) Data-driven modeling of a four-dimensional stochastic projectile system 2022 Chin. Phys. B 31 070501
[1] Brunton S L, Proctor J and Kutz J 2016 Proc. Natl. Acad. Sci. USA113 3932 [2] Champion K, Lusch B, Kutz J N and Brunton S L 2019 Proc. Natl. Acad. Sci. USA116 22445 [3] Schaeffer H, Caisch R, Hauck C D and Osher S 2013 Proc. Natl. Acad. Sci. USA110 6634 [4] Rudy S, Alla A, Brunton S L and Kutz J N 2019 SIAM J. Appl. Dyn. Systems18 643 [5] Lee S, Kooshkbaghi M, Spiliotis K, Siettos C I and Kevrekidis I G 2020 Chaos30 013141 [6] Boninsegna L, Nüske F and Clementi C 2018 J. Chem. Phys.148 241723 [7] Li Y and Duan J 2021 Physica D417 132830 [8] Li Y and Duan J 2022 J. Stat. Phys.186 30 [9] Williams M O, Kevrekidis I G and Rowley C 2015 J. Nonlinear Sci.25 1307 [10] Klus S, Nüske F, Peitz S, Niemann J H, Clementi C and Schütte C 2020 Physica D406 132416 [11] Lu Y and Duan J 2020 Chaos30 093110 [12] Raissi M, Perdikaris P and Karniadakis G 2019 J. Comput. Phys.378 686 [13] Chen X, Yang L, Duan J and Karniadakis G E 2021 SIAM J. Sci. Comput.43 B811 [14] Lu Y, Li Y and Duan J 2021 arXiv:2108.12570[math.DS] [15] Chen R T Q, Rubanova Y, Bettencourt J and Duvenaud D 2018 Advances in Neural Information Processing Systems (Curran Associates, Inc.) Vol. 31 [16] Wu D, Fu M and Duan J 2019 Chaos29 093122 [17] Zhang Y, Duan J, Jin Y and Li Y 2020 Chaos30 113112 [18] Li Y, Duan J and Liu X 2021 Phys. Rev. E103 012124 [19] Dai M, Gao T, Lu Y, Zheng Y and Duan J 2020 Chaos30 113124 [20] Han Z P 2008 Exterior Ballistics for projectiles (Beijing:Beijing University of Technology Press) (in Chinese) [21] Duan J 2015 An Introduction to Stochastic Dynamics (New York:Cambridge University Press) [22] M Reza Rahimi Tabar 2019 Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems (Springer) 11
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
