Orbit correction based on machine learning

Dengjie Xiao; Yusi Qiao; Zhongming Chu

doi:10.11884/HPLPB202133.200352

Journals >High Power Laser and Particle Beams >Volume 33 >Issue 5 >Page 054004 > Article

High Power Laser and Particle Beams
Vol. 33, Issue 5, 054004 (2021)

Orbit correction based on machine learning

Dengjie Xiao^1,2, Yusi Qiao^1,2, and Zhongming Chu³

Author Affiliations

¹School of Nuclear Science and Technology, University of Chinese Academy of Sciences, Beijing 100049, China

²Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China

³College of Engineering and Applied Science, Nanjing University, Nanjing 210023, China

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DOI: 10.11884/HPLPB202133.200352 Cite this Article

Dengjie Xiao, Yusi Qiao, Zhongming Chu. Orbit correction based on machine learning[J]. High Power Laser and Particle Beams, 2021, 33(5): 054004 Copy Citation Text

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Abstract

Orbit correction is one of the most fundamental processes used for beam control in accelerators. Algorithms have been developed at various laboratories to meet specific demands. Typically, linear algebraic tools are applied to various response matrices to solve related problems. However, there are still many problems faced by orbit correction algorithms such as lengthy measurement and computation time. A new approach based on machine learning to develop an orbit correction program is introduced. In this method a machine learning program is trained with correctors data and BPMs data for applying to orbit correction. Mathematical formulation, algorithms prototyped and tested on simulated and real data, and future possibilities are discussed.

Keywords

data cleaning machine learning magnet error operation data orbit correction

$ \Vert {{r}}{\Vert }^{2}=\Vert {{z}} -{{R}}{{\theta}} {\Vert }_{2}^{2}$

(1)

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$ {{R}}={{US}}{{{V}}}^{{\rm{T}}}={\sum\limits_{i}{\lambda }_{i}}{{{u}}}_{i}{{{v}}}_{i}^{{\rm{T}}}$

(2)

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${{{R}}^ + } = \sum\limits_i {\frac{1}{{{\lambda _i}}}} {{{v}}_i}{{u}}_i^r = {{V}}{\rm{diag}} \left( {\frac{1}{{{\lambda _i}}}, \cdots ,\frac{1}{{{\lambda _r}}},0, \cdots ,0} \right){{{U}}^r}$

(3)

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$ J({{\beta}} )={\sum {({{y}}-{{X}}{{\beta}} )}^{2}}+\lambda \Vert {{\beta}} {\Vert }_{2}^{2}$

(4)

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$ J({{\beta}} ) = \displaystyle\sum {{{({{y}} - {{X}}{{\beta}} )}^2}} + \displaystyle\sum \lambda {{{\beta}} ^2} = {({{y}} - {{X}}{{\beta}} )^{\rm{T}}}({{y}} - {{X}}{{\beta}} ) + \lambda {{{\beta}} ^{\rm{T}}}{{\beta}} ={{{y}}^{\rm{T}}}{{y}} - {{{y}}^{\rm{T}}}{{X}}{{\beta}} - {{{\beta}} ^{\rm{T}}}{{{X}}^{\rm{T}}}{{y}} + {{{\beta}} ^{\rm{T}}}{{{X}}^{\rm{T}}}{{X}}{{\beta}} + \lambda {{{\beta}} ^{\rm{T}}}{{\beta}} $

(5)