多体系统动力学动态最优化设计与灵敏度分析

DYNAMIC OPTIMIZATION OF MULTIBODY SYSTEM DYNAMICS AND DESIGN SENSITIVITY ANALYSIS

基于多体系统的动态最优化设计过程包括传统的多体系统仿真分析、系统设计灵敏度分析、系统最优化设计等过程,针对多体系统运动学、用二阶常微分方程和微分代数方程描述的动力学,基于含设计参数的通用数学模型及通用的积分型目标函数,采用高效的系统灵敏度分析伴随变量方法及易于实施的惩罚函数最优设计方法,建立了多体系统最优设计数学模犁和算法.通过双摆系统、曲柄-滑块系统、弹簧/阻尼器-滑块系统3个算例对上述算法的有效性进行了验证.

Dynamic optimization based on multibody system dynamics is a complex process, which composed of traditional analysis and simulation of multibody system dynamics, design sensitivity analysis and iterative processes of optimization. A penalty function method for multibody system dynamic optimization is presented based on kinematics described by algebraic equations and dynamics described by second order ordinary differential equations or differential/algebraic equations which include design parameters. Based on the above equations and a general objective functions of integral type, the corresponding adjoint variable methods for sensitivity analysis are constructed. Finally, three numerical examples include double pendulum, slide-crank system and spring-mass system validate the method presented in this paper.