外弹道优化设计的随机模型

Random Model for Optimum Design of Exterior Ballistics

该文给出了供弹箭弹道优化设计的随机弹道模型。模型包括弹箭飞行动力学方程、各干扰因素及其相关函数。外弹道方程以状态变量形式表示。采用协方差分析描述函数法，对阵风、推力偏心、动不平衡和起始扰动所引起的散布，可作为弹道系统的动态响应加以分析研究。其中风场随机过程采用ＰＲＥＳＳ模型；推力偏心作用过程被视为弱平稳随机过程，对其实验曲线的统计分析表明，其自协方差函数为指数衰减型。基于干扰函数与状态变量间的协方差关系，文中给出了该协方差的微分方程。将它与弹道状态变量方差矩阵方程联立，便可得到角偏差的解。以火箭弹道优化设计为例，论述了优化的一般原则，确定设计变量、目标函数和约束条件的方法。实例计算表明，该模型是实用可行的。

This paper gives a random ballistic model for ballistic optimum design of missiles.The model includes flight dynamic equation of missilles,disturbing factors and their related functions.The exterior ballistic equation is expressed as state vaviable one.The dispersion caused by gust,thrust mallignment,dynamic unbalance and initial disturbances is studied with description function of coveriance analysis.The dispersion is dynamic responce of ballistic system.PRESS model is used in the gust random process.The forcing process of thrust malalignment is thought of as weak stable random one.The related function is obtained by doing statistical analysis for thrust mallignment process.It is an attenuation index model.Based on the covariance relation between disturbing random function and state variables,this paper gives differential equation of the covariance.When the equation is simultaneous with variance matrix equation about the ballistic state variables,the solutions of angular deflections are obtained.Take the optimum design of rocket ballistics as an example,the general principle of the ballistic optimum design and determination method of design variables,objective function and restraint conditions are discussed.Concrete computation shows that this model is practicable.