大型多体系统动力学的多DAE求解器分布式仿真技术研究

Traditionally, the approach to simulate the dynamics of a large-scale multi-body system (MBS) were performed by solving the entire system using a single differential-algebraic equation (DAE) integrator. The object of this proposal is to solve that large-scale MBS through a distributive approach with multiple DAE integrators. According to the dynamical characteristics, the large-scale MBS can be partitioned into multiple subsystems, which are coupled through constraint equations and/or elastic connections. The generalized coordinates of a subsystem serve as its state variables, and those of the other subsystems are its environment variables. Hence the dynamics of a subsystem can be integrated by a DAE integrator which is mostly suitable for its own dynamics, and then the state variables of each subsystem can be swapped and updated in proper coupled times by iterations, such that all the generalized coordinates of the MBS are converged. As a result, the dynamics of the large-scale MBS can be integrated distributively on a parallel computer with multiple CPUs and/or GPUs. This work is based on a previous research on performance improvement on the simulation of large-scale flexible multi-body system dynamics, where a DAE integrator and a Duhamel integrator are adopted to solve the system interactively. The distributed approach of multiple DAE integrator approaches are superior to the traditional approaches as follows. Firstly, each subsystem is solved according to its own dynamical properties, but not effected by local high frequencies in other subsystems, such that the computational load is greatly reduced. Secondly, large-scale MBS dynamics can be simulated naturally on a parallel computer or several computers connected by high-speed networks, where the matrix size of each subsystem is small enough for a processor unit in a cluster or a generic computer, which resolved the matrix computational complexity issues in most large-scale computational problems. Thirdly, this methodology is consistent with the modeling principles in MBS, such that the simulation strategy can be optimized systematically from top down. Lastly, the results and algorithms from this proposal will provide a theoretical foundation for further studies on the co-simulation of large-scale simulation problems by multiple softwares.

传统的多体系统动力学仿真过程是用单个代数微分方程求解器来计算整个系统的时间响应，而本项目的目标是用多个求解器来对大型系统进行分布式仿真。多体系统根据动力学特性可划分为若干个子系统，各个子系统之间通过约束方程或弹性连接相互耦合。每个子系统以自身的自由度为状态变量，而以其他子系统的自由度及拉格朗日乘子为环境参量, 因此可以用最适合其动力学特性的求解器进行仿真，然后与其他子系统在耦合时间节点上交换状态变量并迭代修正，最终实现计算结果的整体性收敛。本项目的出发点是申请人对柔性多体系统提出的DAE求解器与Duhamel积分器共同仿真的思路。多求解器方法有如下优点：首先，每个子系统用独立的积分步长进行仿真而不受其他局部高频的子系统动力学的影响，大大减小了计算量；其次，子系统分布式仿真方法解决了大型多体系统的求解规模问题；再次，该方法自然符合多体系统的建模思想；最后，为多软件的合作仿真提供了理论准备。

本项目的研究背景：.多体系统动力学的计算规模和仿真性能的提高对工业界和国防科技的发展有着非常重要的现实意义。对大型多体系统进行分布式建模，得到大型代数微分方程组，然后用基于多积分器技术的求解器来积分，在实用中是非常有效的动力学建模和仿真思路。..本项目的主要研究内容：.将大型多体系统根据动力学特性划分为若干个子系统；根据每个子系统的特点，选择用最适合其特性的求解器，用独立的自适应的积分时间步长进行计算仿真，并在耦合时间节点上进行数据交换和迭代修正，从而实现对整个系统动力学的高效仿真。..本项目的重要结果：.1..提出了参考节点坐标方法，解决了高速旋转柔性系统动力学仿真中的关键问题；基于该方法完成了柔性电动太阳风帆（E-sail）系统的建模、仿真与控制器设计；该方法可以一般性地应用于车辆、轮船、飞行器和航天器建模、仿真和控制；.2..完成了代数微分方程组（DAE）的理论和算法方面的设计工作；完成了李群积分器的设计和开发，解决了多体软件中旋转问题中固有的奇异性问题；提出了DAE系统的显式积分器，为协同仿真的发展打下基础；.3..完成了多求解器仿真计算中的核心技术，并基于此提出了一套新的多体系统的软件设计方法，其程序架构现有商业软件ADAMS、SIMPACK和RecurDyn都不同的另一种核心架构模式，可用于开发自主产权的多体动力学软件。..本项目的关键数据：.1..参考节点坐标方法可以将高速旋转柔性系统的仿真效率提高了两到三个量级；.2..李群积分器的计算效率可以突破香农采样定律的限制，将多体系统动力学的仿真效率提高十倍以上。..本项目的科学意义：. 本项目的研究结果可以大大提高现有多体系统动力学软件的仿真效率，已经被某国产商业软件作为核心程序的算法，助力解决工业软件方面的卡脖子问题。