Acta Scientiarum Naturalium Universitatis Pekinensis ›› 2021, Vol. 57 ›› Issue (5): 795-803.DOI: 10.13209/j.0479-8023.2021.035

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Application of Particle Swarm Optimization on the Multi-body System Dynamics with Singular Positions

YANG Liusong1, YAO Wenli2,†, XUE Shifeng1,†   

  1. 1. College of Pipeline and Civil Engineering, China University of Petroleum (East China), Qingdao 266580 2. College of Science, Qingdao University of Technology, Qingdao 266520
  • Received:2020-09-13 Revised:2021-03-31 Online:2021-09-20 Published:2021-09-20
  • Contact: YAO Wenli, E-mail: ywenli1969(at); XUE Shifeng, E-mail: sfeng(at)


杨流松1, 姚文莉2,†, 薛世峰1,†   

  1. 1. 中国石油大学(华东)储运与建筑工程学院, 青岛 266580 2. 青岛理工大学理学院, 青岛 266520
  • 通讯作者: 姚文莉, E-mail: ywenli1969(at); 薛世峰, E-mail: sfeng(at)
  • 基金资助:


Different from the traditional method, the mathematical optimization model is established with Gauss principle to handle the singular problems to deal with the singular problems. Traditional optimization method and intelligent optimization method (particle swarm optimization algorithm, PSO) are combined to solve the above optimization problem, which can fully utilize the fast convergence of the traditional optimization method and the characteristic of global searching of the intelligent algorithm. The numerical example is simulated by Lagrangian formulation, null space method and Gauss optimization method respectively. The simulation results show that Gauss optimization method has higher computational accuracy, keeps the stability of the numerical calculation and would not lead to simulation failure due to the sudden changes of the system degree of freedom, which validates the effectiveness and universality of the proposed method.

Key words: multi-body system, singular problem, Gauss principle, particle swarm optimization (PSO)


以广义坐标形式的高斯原理作为建模方法, 采用传统优化与智能优化方法(粒子群算法)相结合的思路, 充分发挥传统算法的快速收敛和智能算法的全局搜索的优势, 实现约束优化问题的全局寻优目的, 从而有效地克服构型奇异给计算造成的困难。分别采用增广拉格朗日方法、零空间方法和高斯优化方法进行仿真, 结果表明, 高斯优化方法不仅具有较高的计算精度, 而且可以长时间保持数值计算的稳定, 不会因多体系统自由度的突变而导致仿真失败, 证明了所提方法的有效性和普适性。

关键词: 多体系统, 奇异问题, 高斯优化方法, 粒子群算法(PSO)