多场耦合不确定性多体系统动力学快速计算方法研究

The influence of uncertainties and multi-field coupling effects on the dynamic characteristics of mechanical systems is becoming more and more dramatically. It is very difficult to evaluate the dynamic characteristics of multibody systems with uncertainties under multi-field coupling effect due to the lack of means of efficient calculation. This project is based on the research background of typical controlled thermonuclear fusion Tokamak device with uncertainties under the heat-flow-electromagnetic multi-field coupling effect. In this project, a brand new transfer equation and transfer matrix of the typical elements of multibody systems with uncertainties under multi-field coupling effect will be derived, an adaptive multi-time step iterative algorithm will be established, and the corresponding numerical simulation system will be developed, then the innovation of rapid calculation of dynamic characteristics of multibody system with uncertainties under multi-field coupling effect will be formed, distinguishing feature of the multi-field coupling uncertain multibody system transfer matrix method is without a global dynamic equation, but the transfer matrix order is lower and programming degree is higher. Based on above, a new method for dynamic analysis and reliability evaluation of Tokamak could be established based on the multi-field coupling uncertain multibody system transfer matrix method, the influence mechanism of uncertainties and multi-field coupling effect on the dynamic characteristics of the system can be analyzed, and the application of this method in engineering field is realized. The research of the project will provide the basic theory and the fast algorithm for the dynamic analysis, the optimization and the reliability evaluation of multibody systems with uncertainties under multi-field coupling effect.

不确定性和多场耦合效应对机械系统动态特性影响大，缺乏多场耦合不确定性多体系统动力学快速计算手段导致系统动态特性难以准确分析评估已成为该类系统动态设计、研制过程中急需解决的难题。为此，本项目以热、流、电磁多场耦合作用下不确定性受控核聚变托卡马克装置为研究背景，展开多场耦合不确定多体系统传递矩阵法研究，推导多场耦合和不确定性条件下系统典型元件的传递方程和传递矩阵，提出自适应多时间步长迭代算法并开发相应数值仿真系统，形成无需系统总体动力学方程、矩阵阶次低、程式化程度高的多场耦合不确定性多体系统动力学快速计算新方法；在此基础上，建立基于多场耦合不确定多体系统传递矩阵法的托卡马克装置动力学分析及可靠性评估模型，探索不确定性和多场耦合效应对系统动态特性的影响机理，实现重大工程应用。项目研究将为多场耦合不确定性机械系统动力学分析、优化和可靠性评估提供基础理论和快速算法，具有重要的理论和工程价值。

不确定性和热、流、电磁等多场耦合效应对机械系统动态特性影响显著。当前工程技术领域缺乏多场耦合条件下不确定性多体系统动力学高效建模方法和快速计算手段导致其动态特性难以准确分析和评估。本项目考虑不确定性和多场耦合效应，开展了多场耦合不确定性多体系统传递矩阵法研究，包括：多场耦合不确定性线性多体系统传递矩阵法、多场耦合不确定性多体系统有限元传递矩阵法、时变非线性多场耦合不确定性多体系统传递矩阵法，推导了计及不确定性和多物理场作用的多体系统典型元件的传递方程和传递矩阵，实现了无需系统总体动力学方程、矩阵阶次低、程式化程度高的多场耦合不确定性机械系统（结构）动力学的高效建模。对多物理场作用下随机不确定性线性多体系统（结构）固有振动特性分析问题，不确定性线性多体系统传递矩阵法或不确定性多体系统有限元传递矩阵法，通过引入表征随机参数的随机变量，将随机参数表示成确定性部分和随机部分之和，利用小参数摄动技术，建立系统各元件传递矩阵和随机参数的摄动关系，推导系统特征值和特征矢量的摄动递归传递方程，获得系统特征值和特征矢量的各阶摄动量及其均值、方差，实现了不确定性固有振动特性的高效分析；对多场耦合不确定性机械系统（结构）动力响应问题，考虑非侵入式不确定性分析方法（如：自适应稀疏混沌多项式展开方法、BP神经网络法、Chebyshev多项式展开方法、响应面法等），将含不确定性参量的多体系统传递方程和耦合场控制方程的联合求解问题转换为少量确定性求解问题，提高了不确定性分析的计算效率。考虑概率不确定性和电磁-结构单向耦合情况，结合多体系统有限元传递矩阵法、子结构法以及循环对称约束条件，实现了受控核聚变托卡马克装置真空室高效动力学建模仿真，并结合响应面法和一阶可靠性方法，建立了真空室概率可靠性分析方法，研究了不确定性和电磁场作用对真空室动态特性的影响，为系统可靠性评估、动态设计与后期安全运行提供了理论支撑。