中文摘要：

以混流式水轮发电机组主轴系统为研究对象，用有限单元法建立系统的非线性全局耦合动态方程，并在此动态方程的基础上，运用模糊优化理论，建立以主轴系统动态性能为目标函数、以主轴系统的结构参数为设计变量、具有模糊约束的优化设计数学模型，给出求解此模型的方法，并通过实例对其进行仿真。仿真结果表明：所采用的模糊优化方法体现了主轴系统约束条件的模糊性，比较符合机组设计的实际情况，为进一步研究混流式水轮发电机组的多目标优化设计提供参考。

英文摘要：

A main shaft system of Francis turbine - generator unit is taken as the object of study, and the nonlinear global coupling dynamic equations of it are established by using finite element methods. By the theory of fuzzy optimum, the mathematical model with fuzzy restraints is established by means of the dynamic response of the main shaft system as Objective function, the parameters of the main shaft system as design variables. The method of solving the mathematical model is given, and an example is simulated. The simulation results show that the method of the fuzzy optimum is more suitable for optimization as the system is fuzzy. The research work has certain reference value for further multi - object optimization of the main shaft system.