叶片基元叶型椭圆形前缘拟合方法
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摘要
针对叶片基元叶型建模时对前缘的椭圆形转接需求,采用最小二乘法获得椭圆初始参数值,基于此参数引入改进粒子群算法进一步求解,以点到椭圆垂直距离作为目标函数,建立椭圆参数优化数学模型,从而提高拟合精度。基于上述研究结果,利用VC++软件及UG平台完成前缘椭圆拟合,实例表明,对于数据点集中分布于一侧且存在大量噪声的情况,该方法与最小二乘法相比能获得更高的拟合精度,且响应时间符合设计需求。
According to the elliptical leading edge's connecting demand of elementary blade profile modeling, the least square method is used to figure out initial elliptic parameters. With these parameters, improved particle swarm optimization algorithm is introduced to make a further solving, which takes Euclidean Distance from point to ellipse as an objective function and then establishes a mathematical model for parameter optimization of ellipse, in order to improve the accuracy of ellipse fitting. Based on the results of the study above, VC ++ and UG are applied to accomplishing the ellipse fitting.As a result, some examples are given to prove the better response time and higher accuracy of using this method, especially for the situation that discrete points contain lots of noise and mostly distribute at one side.
According to the elliptical leading edge's connecting demand of elementary blade profile modeling, the least square method is used to figure out initial elliptic parameters. With these parameters, improved particle swarm optimization algorithm is introduced to make a further solving, which takes Euclidean Distance from point to ellipse as an objective function and then establishes a mathematical model for parameter optimization of ellipse, in order to improve the accuracy of ellipse fitting. Based on the results of the study above, VC ++ and UG are applied to accomplishing the ellipse fitting.As a result, some examples are given to prove the better response time and higher accuracy of using this method, especially for the situation that discrete points contain lots of noise and mostly distribute at one side.
引文
[1]陆宏志,徐力平,方韧.压气机叶片前缘形状的改进设计[J].航空动力学报,2000,15(2):129-132.
[2]Fitzgibbon A,Pilu M,Fisher R B.Direct least square fitting of ellipses[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,1999,21(5):476-480.
[3]陈燕新,戚飞虎.一种新的基于随机Hough变换椭圆检测方法[J].红外与毫米波学报,2000,19(1):43-47.
[4]靳军,刘波,南向谊,等.超声速叶型前缘几何形状对叶栅气动性能的影响[J].航空动力学报,2007,22(4):660-665.
[5]Zhang Zhengyou.Parameter estimation techniques:a tutorial with application to conic fitting[J].Image and Computing Vision,1997,15(1):59-76.
[6]Eberhart R,Kennedy J.A new optimizer using particle swarm theory[C]//Proceedings of the Sixth International Symposium on Micro-Machine and Human Science.Nogoya,Japan:IEEE,1995:39-43.
[7]Arumugam M S,Rao M V C,Chandramohan A.A new and improved version of particle swarm optimization algorithm with global-local best parameters[J].Journal of Knowledge and Information Systems,2008,16(3):324-350.
[2]Fitzgibbon A,Pilu M,Fisher R B.Direct least square fitting of ellipses[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,1999,21(5):476-480.
[3]陈燕新,戚飞虎.一种新的基于随机Hough变换椭圆检测方法[J].红外与毫米波学报,2000,19(1):43-47.
[4]靳军,刘波,南向谊,等.超声速叶型前缘几何形状对叶栅气动性能的影响[J].航空动力学报,2007,22(4):660-665.
[5]Zhang Zhengyou.Parameter estimation techniques:a tutorial with application to conic fitting[J].Image and Computing Vision,1997,15(1):59-76.
[6]Eberhart R,Kennedy J.A new optimizer using particle swarm theory[C]//Proceedings of the Sixth International Symposium on Micro-Machine and Human Science.Nogoya,Japan:IEEE,1995:39-43.
[7]Arumugam M S,Rao M V C,Chandramohan A.A new and improved version of particle swarm optimization algorithm with global-local best parameters[J].Journal of Knowledge and Information Systems,2008,16(3):324-350.