基于自校正Broyden拟牛顿法的航空发动机模型数值计算  

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

作　　者：王元[1] 李秋红[1] 黄向华[1] 

机构地区：[1]南京航空航天大学能源与动力学院江苏省航空动力系统重点实验室,南京210016

出　　处：《航空动力学报》2016年第1期249-256,共8页Journal of Aerospace Power

基　　金：国家自然科学基金(61104067);江苏省研究生培养创新工程(KYLX0302);中央高校基本科研业务费专项资金;江苏省航空动力系统重点实验室开放课题

摘　　要：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.A self-tuning Broyden quasi-Newton method combined with computing diver- gence 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 dynam- ic 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-tun- ing 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-Raph- son 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.

关 键 词：自校正 Broyden拟牛顿法 牛顿法 变循环发动机 部件级模型 

分 类 号：V231[航空宇航科学与技术—航空宇航推进理论与工程]