变循环发动机数学模型求解及有效性研究

Research on Solution and Evaluation of Variable Cycle Engine Mathematical Model

采用部件法建立了变循环发动机的多维非线性隐式方程组模型,该模型具有隐式性,因而求解过程复杂,收敛困难.以变循环发动机为对象,设计了遗传算法,将数学模型转化为最优化问题,并对模型进行求解.提出了算法的有效性评价指标:初值敏感性、计算效率、收敛性、稳定性.与牛顿-拉夫逊法相比,遗传算法初值敏感性较低,收敛性较好.该结果可为变循环发动机模型求解算法的选择与设计提供参考.

A component method is used to build a variable cycle engine mathematical model of multidimension-al nonlinear implicit equations that are not convergent,so as to make it difficult to be solved.Taking the vari-able cycle engine as obj ect,a genetic algorithm is designed to transform the mathematical model into an opti-mization problem,so as to solve the model.Some evaluation indicators such as initial value sensitivity,compu-tation efficiency,convergence and stability of algorithm are proposed to evaluate the method.It is shown that the genetic algorithm is less sensitive to initial value,but more convergent than Newton-Raphson method. The results and conclusions can provide the reference to modeling and solutions of variable cycle engines.