基于自校正Broyden拟牛顿法的航空发动机模型数值计算

王元; 李秋红; 黄向华

doi:10.13224/j.cnki.jasp.2016.01.032

基于自校正Broyden拟牛顿法的航空发动机模型数值计算

doi: 10.13224/j.cnki.jasp.2016.01.032

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

基金项目:

国家自然科学基金(61104067)

江苏省航空动力系统重点实验室开放课题

中央高校基本科研业务费专项资金

江苏省研究生培养创新工程(KYLX0302)

详细信息

作者简介:
王元(1988-),男,江苏泰州人,博士生,主要从事航空发动机建模与控制研究.

中图分类号: V231
计量
- 文章访问数: 709
- HTML浏览量: 4
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- 被引次数: 0
出版历程
- 收稿日期: 2014-05-05
- 刊出日期: 2016-01-28

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

Jiangsu Province Key Laboratory of Aerospace Power System, College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

摘要

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.
- 自校正 /
- Broyden拟牛顿法 /
- 牛顿法 /
- 变循环发动机 /
- 部件级模型
Abstract: 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.
- self-tuning /
- Broyden quasi-Newton method /
- Newton-Raphson method /
- variable cycle engine /
- component-level model

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参考文献(18)

[1]	John R.Real-time simulation of F100-PW-100 turbofan engine using the hybrid computer[R].NASA TMX-3261,1975.
[2]	廉筱纯,吴虎.航空发动机原理[M].西安:西北工业大学出版社,2005.
[3]	骆广琦,桑增产,王如根,等.航空燃气涡轮发动机数值仿真[M].北京:国防工业出版社,2007.
[4]	李家瑞,孙健国,张绍基.航空发动机总体性能数学模型的1种收敛算法[J].航空发动机,2005,31(4):48-50. LI Jiarui,SUN Jianguo,ZHANG Shaoji.A convergence algorithm of aeroengine performance mathematical model[J].Aeroengine,2005,31(4):48-50.(in Chinese)
[5]	Biazar J,Ghanbary B.A new technique for solving systems of nonlinear equations[J].Applied Mathematical Sciences,2008,2(55):2699-2703.
[6]	Noor M A,Waseem M.Some iterative methods for solving a system of nonlinear equations[J].Computers and Mathematics with Applications,2009,57(1):101-106.
[7]	Dhamacharoen A.An efficient hybrid method for solving systems of nonlinear equations[J].Journal of Computational and Applied Mathematics,2014,263:59-68.
[8]	苏三买,陈永琴.基于混合遗传算法的航空发动机数学模型解法[J].推进技术,2007,28(6):661-664. SU Sanmai,CHEN Yongqin.Hybrid genetic algorithm in solving aeroengine nonlinear mathematical model[J].Journal of Propulsion Technology,2007,28(6):661-664.(in Chinese)
[9]	王军,隋岩峰.求解航空发动机数学模型的迭代算法及其改进算法的收敛性研究[J].系统仿真学报,2014,26(2):310-314. WANG Jun,SUI Yanfeng.Study on convergence and im provement of iteration methods in aero-engine mathematical models[J].Journal of System Simulation,2014,26(2):310-314.(in Chinese)
[10]	陈玉春,徐思远,杨云铠.改善航空发动机特性计算收敛性的方法[J].航空动力学报,2008,23(12):2242-2248. CHEN Yuchun,XU Siyuan,YANG Yunkai.Research on the method to solve convergence problem in aero turbo engine performance computation[J].Journal of Aerospace Power,2008,23(12):2242-2248.(in Chinese)
[11]	杨伟,冯雷星,彭靖波,等.求解航空发动机数学模型的混合智能方法[J].推进技术,2008,29(5):614-616. YANG Wei,FENG Leixing,PENG Jingbo,et al.An intelligent algorithm for solution of nonlinear mathematical model for aeroengine[J].Journal of Propulsion Technology,2008,29(5):614-616.(in Chinese)
[12]	陆军,郭迎清,张书刚.航空发动机非线性模型实时计算的迭代方法研究[J].航空动力学报,2010,25(3):681-686. LU Jun,GUO Yingqing,ZHANG Shugang.Research on the iteration methods in aero-engine non-linear model real time computation[J].Journal of Aerospace Power,2010,25(3):681-686.(in Chinese)
[13]	倪健,马昌凤.解非线性方程牛顿迭代法的一种新的加速技巧[J].广西科学院学报,2010,26(1):1-3. NI Jian,MA Changfeng.A new acceleration technique of Newton iterative method for solving nonlinear equation[J].Journal of Guangxi Academy of Sciences,2010,26(1):1-3.(in Chinese)
[14]	黄旭,王占学,张晓博.基于Broyden改进算法的航空发动机性能模拟研究[J].科学技术与工程,2012,12(21):5231-5234. HUANG Xu,WANG Zhanxue,ZHANG Xiaobo.Research of a corrected Broyden's method on the aero-engine performance simulation[J].Science Technology and Engineering,2012,12(21):5231-5234.(in Chinese)
[15]	叶纬,陈玉春,崔高峰,等.拟牛顿法在航空发动机特性仿真中的应用[J].计算机仿真,2007,10(10):78-82. YE Wei,CHEN Yuchun,CUI Gaofeng,et al.Application of quasi-Newton method to aero-engine performance simulation[J].Computer Simulation,2007,10(10):78-82.(in Chinese)
[16]	苟学中,周文祥,黄金泉.变循环发动机部件级建模技术[J].航空动力学报,2013,28(1):104-111. GOU Xuezhong,ZHOU Wenxiang,HUANG Jinquan.Component-level modeling technology for variable cycle engine[J].Journal of Aerospace Power,2013,28(1):104-111.(in Chinese)
[17]	王元,李秋红,黄向华.变循环发动机建模技术研究[J].航空动力学报,2013,28(4):954-960. WANG Yuan,LI Qiuhong,HUANG Xianghua.Research of variable cycle engine modeling techniques[J].Journal of Aerospace Power,2013,28(4):954-960.(in Chinese)
[18]	蒲志林.非线性代数系统的一种拟牛顿迭代法[J].四川师范大学学报,1995,18(2):35-41. PU Zhilin.A nonlinear algebraic systems quasi-Newton iterative method[J].Journal of Sichuan Normal University,1995,18(2):35-41.(in Chinese)