基于微分/代数方程的多体系统动力学设计灵敏度分析的伴随变量方法

ADJIONT VARIABLE METHOD FOR SENSITIVITY ANALYSIS OF MULTIBODY SYSTEM DYNAMICS DESCRIBED BY DIFFERENTIAL/ALGEBRAIC EQUATIONS

基于多体系统动力学微分/代数方程数学模型和通用积分形式的目标函数,建立了多体系统动力学设计灵敏度分析的伴随变量方法,避免了复杂的设计灵敏度计算,对于设计变量较多的多体系统灵敏度分析具有较高的计算效率.文中给出了通用公式以及具体的计算过程和验证方法,并将目标函数及其导数积分形式的计算转化为微分方程的初值问题,进一步提高了计算效率和精度.文末通过一曲柄-滑块机构算例对算法的有效性进行了验证.

An adjoint variable method was established for sensitivity analysis by differential/algebraic equations based on design parameters and avoided the complex parameters. The adjoint variable equations derived, and the detailed processes of the general objective function, which of multibody system dynamics described had high efficiency for systems with many derivatives computation of the generalized coordinates with respect to design for the first order sensitivity analysis and design sensitivity formulations were design sensitivity algorithm were presented. For the purpose of simplification, the objective function and its first derivative were transformed into an initial value problem of ordinary differential equation with one variable. An example of slide-crank system was given to validate the method presented.