基于自校正Broyden拟牛顿法的航空发动机模型数值计算

以Broyden拟牛顿法为基础结合计算发散判断和校正机制,提出自校正Broyden拟牛顿法.该算法结合牛顿法(Newton-Raphson method)平方收敛和Broyden拟牛顿法超线性收敛特性,通过自适应调整计算步长和校正函数,在非线性系统中具有更好的计算性能.以变循环发动机部件级模型为对象,应用自校正Broyden拟牛顿法进行稳态及动态仿真计算,并与牛顿法和Broyden拟牛顿法作对比.结果表明:自校正Broyden拟牛顿法对恶劣的初始计算条件适应性更高,计算速度更快且收敛能力性更强,动态计算中部件模型计算调用次数为牛顿法的15%,模型动态误差低于Broyden拟牛顿法的15%,同时也低于牛顿法的28%,动态计算最大残差量低于其他两种算法的25%.验证结果表明了自校正Broyden拟牛顿法的优越性. 

Numerical calculation of aero-engine model based on self-tuning Broyden quasi-Newton method

A self-tuning Broyden quasi-Newton method combined with computing divergence mechanism judging and tuning was proposed. By combining the quadratic convergence of Newton-Raphson method and the super-linear convergence of Broyden quasi-Newton method, the proposed method had higher computing performance in calculation of nonlinear system. Targeting variable cycle engine component-level model, the steady state and dynamic simulation have been calculated by Newton-Raphson method, Broyden quasi-Newton method and the self-tuning Broyden quasi-Newton method. Results shows that, the self-tuning Broyden quasi-Newton method has greater adaptability, faster calculation speed and stronger convergence. The component computing times of the self-tuning Broyden quasi-Newton method is 15% of the Newton-Raphson method in dynamic simulation, the dynamic error is lower than 15% of the Broyden quasi-Newton method and 28% of the Newton-Raphson method, the maximum amount of residual is lower than 25% of other methods. These results prove the self-tuning Broyden quasi-Newton method superiority, the objective of the proposed method has been achieved.