基于遗传规划的炸弹弹道分组拟合模型
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摘要
针对传统弹道拟合方法需要事先设定拟合方程的函数结构形式且不能很好适应大范围投射条件的问题,提出了一种分组遗传规划的炸弹弹道拟合方法。首先,依据动力学仿真实验得到炸弹在不同投射条件下的弹道样本。然后,采用分组遗传规划对样本数据中弹道诸元和投射初值进行输入-输出映射拟合训练,得到了多组弹道拟合方程,并进行了未分组和分组拟合方程式之间的精度和泛化性比较。大量检测验算说明,采用分组遗传规划得到的弹道拟合方程式组具有物理关系明确、拟合精度高、泛化好、实时解算快等特性。
The traditional trajectory fitting method always needs a priori enactment about the structure form of the fitting equation and is not adaptable when it is used to fit trajectory under the large range launching condition.In view of these deficiencies,a bomb trajectory fitting method based on group genetic programming(GGP)is proposed.First,the GGP model samples data of different launching conditions are obtained through bomb dynamics simulation.Then,on the basis of mapping input-output training of these trajectory data and initial launching value by the GGP,multiple trajectory fitting equations are provided.The accuracy between ungroup and group equations is compared based on modeling errors as well as generalization ability for untrained samples.A lot of checking calculation shows that the GGP method has clear physical relations,a high precision,good generalization and can fast calculate.
The traditional trajectory fitting method always needs a priori enactment about the structure form of the fitting equation and is not adaptable when it is used to fit trajectory under the large range launching condition.In view of these deficiencies,a bomb trajectory fitting method based on group genetic programming(GGP)is proposed.First,the GGP model samples data of different launching conditions are obtained through bomb dynamics simulation.Then,on the basis of mapping input-output training of these trajectory data and initial launching value by the GGP,multiple trajectory fitting equations are provided.The accuracy between ungroup and group equations is compared based on modeling errors as well as generalization ability for untrained samples.A lot of checking calculation shows that the GGP method has clear physical relations,a high precision,good generalization and can fast calculate.
引文
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[12]王备,周韬,董长虹.拦截弹道快速设计方法[J].北京航空航天大学学报,2015,41(2):358-363.WANG B,ZHOU T,DONG C H.Rapid design algorithm for intercept missile trajectory[J].Journal of Beijing University of Aeronautics and Astronautics,2015,41(2):358-363.
[13]唐万梅.BP神经网络网络结构优化问题的研究[J].系统工程理论与实践,2005,25(10):95-100.TANG W M.The study of the optimal structure of BP neural network[J].Systems Engineering-Theory&Practice,2005,25(10):95-100.
[14]ATIYA A,JI C.How initial conditions affect generalization performance in large networks[J].IEEE Trans.on Neural Networks,1997,8(2):448.
[15]SHAO G F,ZHOU Q F,CHEN G Q.Data fitting based on improved genetic programming[J].Application Research of Computers,2009,26(2):481-484.
[16]冯琦,张才坤,张华涛.基于遗传规划的激光制导炸弹弹道拟合[J].弹箭与制导学报,2014,34(4):1-4.FENG Q,ZHANG C K,ZHANG H T.Ballistic trajectory fitting of laser-guided bomb based on genetic programming[J].Journal of Projectiles,Rockets,Missiles and Guidance,2014,34(4):1-4.
[17]PUROHIT A,BHARDWAJ A,TIWARI A,et al.Handling the problem of code bloating to enhance the performance of classifier designed using genetic programming[J].Journal of Algebra,2011,213(1):369-377.
[18]GONCALVES I,SILVA S.Balancing learning and overfitting in genetic programming with interleaved sampling of training data[M].Berlin Heidelberg:Springer,2013:73-84.
[19]徐德坤,戚堂有,陈芳.飞行试验弹道重建技术[J].导航与控制,2011,10(1):1-4.XU D K,QI T Y,CHEN F.The ballistic reproduction technique for flight test[J].Navigation and Control,2011,10(1):1-4.
[20]秦丽,张文栋,潘峰.大攻角飞行载体运动学建模的四元数方法研究[J].中北大学学报(自然科学版),2006,27(3):276-279.QIN L,ZHANG W D,PAN F.Quaternion method for kinematics modeling of high attack-angle flying carrier[J].Journal of North University of China(Natural Science Edition),2006,27(3):276-279.
[21]曹化飞,朱柏荣,姚菲,等.激光制导炸弹的弹道解算与仿真[J].海军航空工程学院学报,2004,19(1):171-174.CAO H F,ZHU B R,YAO F.The solution and simulation of the laser-guided bomb’s trajectory[J].Journal of Naval Aeronautical and Astronautical University,2004,19(1):171-174.
[22]PAL N,LIM W K.Estimation of circular error probable and measuring the accuracy of a missile system[J].Stat Methods,2003,2(2):97-120.
[2]张滢,杨任农,左家亮,等.激光制导炸弹无偏置上仰投放战术机动规划[J].系统工程与电子技术,2016,38(5):1074-1080.ZHANG Y,YANG R L,ZUO J L.Tactic maneuver planning of loft delivery of laser-guided bomb with no offset[J].Systems Engineering and Electronics,2016,38(5):1074-1080.
[3]TONG Z C,SUN X Q,HAN C L,et al.Modeling and simulation of laser jam for laser-guiding weapon[J].Journal of System Simulation,2007,19(22):5115-5119.
[4]王凯,付昭旺,张晓飞.激光制导炸弹弹道分析与仿真[J].弹箭与制导学报,2009,29(3):179-182.WANG K,FU Z W,ZHANG X F.The analysis and simulation of the laser-guided bomb’s trajectory[J].Journal of Projectiles,Rockets,Missiles and Guidance,2009,29(3):179-182.
[5]张道驰,夏群利,何晓夫,等.激光制导炸弹捕获域快速解算方法[J].红外与激光工程,2015,44(12):3535-3540.ZHANG D C,XIA L Q,HE X F,et al.Rapid calculation method for capture area of laser guided bomb[J].Infrared and Laser Engineering,2015,44(12):3535-3540.
[6]HE P,YANG J J.Feasibility analysis of near space un-powered guided bomb when attacking aerial target based on genetic algorithm[C]∥Proc.of the International Conference on Information Engineering and Computer Science,2009:1-4.
[7]严大卫,孙瑞胜,陈洁卿,等.基于混合BTT/STT控制的滑翔制导炸弹自动驾驶仪设计[J].弹道学报,2016,28(4):47-51.YAN D W,SUN R S,CHEN J Q,et al.Hybrid BTT/STT autopilot design for glide guided bomb[J].Journal of Ballistics,2016,28(4):47-51.
[8]袁震宇,钟志通,张林,等.导弹末端弹道拟合方法研究[J].舰船电子工程,2015,35(11):52-54.YUAN Z Y,ZHONG Z T,ZHANG L.Missile terminal ballistic curve fitting methods[J].Ship Electronic Engineering,2015,35(11):52-54.
[9]李元生,陈礼国.舰炮弹道拟合对岸校射方法研究[J].火炮发射与控制学报,2016,37(4):25-28.Li Y S,Chen L G.Study on naval gun trajectory fitting firing correction method against shore targets[J].Journal of Gun Launch&Control,2016,37(4):25-28.
[10]杜昌平,周德云,阳治平.基于遗传算法的空空导弹弹道拟合方法[J].西北工业大学学报,2003,21(2):172-175.DU C P,ZHOU D Y,YANG Z P.A method for approximating air-to-air missile trajectory based on genetic algorithm[J].Journal of Northwestern Polytechnical University,2003,21(2):172-175.
[11]李飞飞,吕颖,南英.炸弹弹道落点参数拟合算法[J].电光与控制,2013,20(9):84-87.LI F F,LV Y,NAN Y.A combined algorithm for ballistic parameters of bomb trajectory[J].Electronics Optics&Control,2013,20(9):84-87.
[12]王备,周韬,董长虹.拦截弹道快速设计方法[J].北京航空航天大学学报,2015,41(2):358-363.WANG B,ZHOU T,DONG C H.Rapid design algorithm for intercept missile trajectory[J].Journal of Beijing University of Aeronautics and Astronautics,2015,41(2):358-363.
[13]唐万梅.BP神经网络网络结构优化问题的研究[J].系统工程理论与实践,2005,25(10):95-100.TANG W M.The study of the optimal structure of BP neural network[J].Systems Engineering-Theory&Practice,2005,25(10):95-100.
[14]ATIYA A,JI C.How initial conditions affect generalization performance in large networks[J].IEEE Trans.on Neural Networks,1997,8(2):448.
[15]SHAO G F,ZHOU Q F,CHEN G Q.Data fitting based on improved genetic programming[J].Application Research of Computers,2009,26(2):481-484.
[16]冯琦,张才坤,张华涛.基于遗传规划的激光制导炸弹弹道拟合[J].弹箭与制导学报,2014,34(4):1-4.FENG Q,ZHANG C K,ZHANG H T.Ballistic trajectory fitting of laser-guided bomb based on genetic programming[J].Journal of Projectiles,Rockets,Missiles and Guidance,2014,34(4):1-4.
[17]PUROHIT A,BHARDWAJ A,TIWARI A,et al.Handling the problem of code bloating to enhance the performance of classifier designed using genetic programming[J].Journal of Algebra,2011,213(1):369-377.
[18]GONCALVES I,SILVA S.Balancing learning and overfitting in genetic programming with interleaved sampling of training data[M].Berlin Heidelberg:Springer,2013:73-84.
[19]徐德坤,戚堂有,陈芳.飞行试验弹道重建技术[J].导航与控制,2011,10(1):1-4.XU D K,QI T Y,CHEN F.The ballistic reproduction technique for flight test[J].Navigation and Control,2011,10(1):1-4.
[20]秦丽,张文栋,潘峰.大攻角飞行载体运动学建模的四元数方法研究[J].中北大学学报(自然科学版),2006,27(3):276-279.QIN L,ZHANG W D,PAN F.Quaternion method for kinematics modeling of high attack-angle flying carrier[J].Journal of North University of China(Natural Science Edition),2006,27(3):276-279.
[21]曹化飞,朱柏荣,姚菲,等.激光制导炸弹的弹道解算与仿真[J].海军航空工程学院学报,2004,19(1):171-174.CAO H F,ZHU B R,YAO F.The solution and simulation of the laser-guided bomb’s trajectory[J].Journal of Naval Aeronautical and Astronautical University,2004,19(1):171-174.
[22]PAL N,LIM W K.Estimation of circular error probable and measuring the accuracy of a missile system[J].Stat Methods,2003,2(2):97-120.