潜射导弹运载器水弹道动力系统建模及其应用研究
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摘要
本文选题来自国家重大工程项目，主要研究了潜射导弹运载器水弹道动力学系
统参数辨识、不确定性建模及发射水动力环境对运载器水弹道影响等方面的理论与
应用问题，对运载器水弹道动力学系统进行了较为全面的数学建模，并具体应用于
某潜射导弹运载器动力学系统辨识和水弹道设计与预报。该导弹运载器的实航试验
结果表明，基于本文提出的方法和数学模型所设计的水弹道是成功的，对水弹道的
预报是准确的。
关于潜射导弹运载器动力学系统辨识问题的研究，本文在国内属首次，并初步
建立了一套较为系统的辨识方法、数学模型与应用技术，具有开拓性，为该领域的
进一步研究奠定了坚实的基础。本文的主要贡献和创新点如下：
1．对于占运载器流体动力主要部分的位置力，不再假设纵、横平面无交联耦合，
而是通过设计运载器模型的空间状态组合风洞实验，对实验数据进行回归分析，来
获得运载器位置力的非线性表达式。
2．将运载器湖上实航试验设计成单项试验与综合试验两个部分，可以充分获得
运载器水弹道动力学系统辨识所需的信息，使某些风洞实验难以测准的弹道敏感参
数，如水平舵及垂直舵舵效参数，得以准确辨识。
3．将改进的单纯形随机搜索策略作为模拟退火算法的随机变化发生器，提出了
基于单纯形的模拟退火参数辨识算法，并采用模拟退火算法对运载器空间运动进行
了参数辨识。结果表明：将一个正的、呈对数分布的随机变量（与温度成比例）添加
到单纯形各顶点的函数值中，再从每个被当作替代点的新点的函数值中减去一个类
似的随机变量的这样一种基于单纯形的随机变化发生器是一种高效的随机变化发生
器。它能使单纯形在向目标函数减少的方向运动的同时，也有能力摆脱局部最小点。
运用模拟退火算法可以获得运载器空间流体动力参数的极大似然估计。
4．将牛顿-拉夫逊、单纯形等优化算法运用于运载器纵向运动参数辨识，对三
种辨识算法进行了收敛速度、准度及全局收敛性比较，结果表明：与牛顿-拉夫逊
算法、单纯形法等常规辨识算法相比，对于待估计参数的不同初始值，模拟退火算
法具有一定的稳定性和较好的全局收敛性。
一
5．运用模拟追火算法对运载器水平尾翼展开过程中由于拍击水流而引起的附加
流体动力进行了辨识建模。有效地解决了运载器水弹道预报的俯仰角数据在过渡段
弹道，明显偏高于运载器湖上实航试验数据这一问题。通过建模后俯仰角数据与试
验数据的对比，表明对运载器在水平尾翼展开过程中由于尾翼拍击水流而引起的附
加流体动力建模是必要的，本文所提出的建模方法是可行的。
6．基于势流理论，建立了艇体扰流场对运载器的附加扰动力数学模型；研究了
流场非定常性的处理方法，及其与水弹道求解在时间步长上的统一性问题；计算了0
艇体扰流场对运载器水弹道的影响；并在运载器完全离开发射管后的艇体扰流场计
＿＿，＿…＿＿、．
算的基础上，对运载器离管过程中的艇体扰流场及其对运载器水弹道的影响进行了
计算。计算结果表明，本文提出的“基于差分法的流场非定常性处理，必须与龙格
－库塔法解弹道方程在时间步长上进行统一处理”及相应的处理方法是可行的；潜
艇运动对运载器横平面的扰动大于纵平面的扰动，包括力与运动；运载器受艇体扰
流影响主要发生在运载器离艇初期。本项研究为解决复杂发射力学环境引起的运载
器出水参数的散布问题奠定了基础。
本文研究成果在鱼雷、水雷、水下无人作战平台等水中兵器领域也具有重要的
应用与参考价值。
This dissertation originates from an important national engineering project. It is mainly
concerned with parameter identification and uncertainty modeling of submarine launched
missile carrier抯 underwater trajectory dynamic system and with the effect of
hydrodynamic environment caused by launch on the carrier抯 trajectory. Overall
mathematical modeling method for carrier抯 underwater trajectory dynamic system is
studied and applied to a certain submarine launched missile carrier抯 trajectory designing
and prediction for the first time in China. The carrier抯 voyage test shows that the
trajectory design based on the methods in this dissertation is successful and the trajectory
prediction is accurate. The main contributions in the dissertation are summarized as
follows:
1. For location force, one major part of fluid motive force of carrier, it抯 no longer
granted that there is no interconnection between vertical and horizontal sections. While
through wind tunnel experiment of combinational spatial states and regression analysis of
experimental data, the nonlinear expressions of location force are acquired.
2. By dividing carrier抯 voyage test at lake into two parts of single-factor test and
multiple-factor test, adequate data which is necessary for dynamic system identification
can be gained. And such a test outline makes accurate identification of some parameters
which are sensitive to trajectory but hard to be measured through wind tunnel experiment,
such as horizontal or vertical rudder derivatives, become practicable.
3. Adopting an improved simplex-based random search strategy, a simulated annealing
identification method is derived. The random change generator is proved efficient by
adding a plus random variable, which has logarithmic distribution and scales with
temperature, to each vertex of simplex and then removing a similar random variable from
the new vertex which is a substitution for the worst vertex. Such a generator can make the
simplex not only move downhill but also be capable of free from the local minimum. With
the simulated annealing identification method, the maximum likelihood estimator of
carrier抯 spacious hydrodynamic parameters can be acquired.
4. Newton-Raphson抯 and simplex optimization methods are applied to carrier抯 vertical
hydrodynamic parameters identification respectively. And the three methods are compared
III
LI~k)~眫1~
with each other on convergence speed, accuracy. The results shows that comparing with
general methods, the simulated annealing method has better convergence for various
initial values of parameters.
5. Additional fluid motive force resulting from horizontal rear wings striking water in
the unfolding process is modeled by using the simulated annealing method. The problem
that measured pitching angle data at lake-test is evidently greater than the predicted data
during transitional trajectory is solved effectively. The agreement between measured data
with calculated data after modeling proves that the modeling is necessary and the
modeling method is workable.
6. Based on the theory of potential flow, additional disturbance force and its effect on
the trajectory due to the motion of launching submarine is computed; the method to handle
the unsteady feature of the flow field and the agreement between the method with the time
step for solving trajectory is studied; on the b
统参数辨识、不确定性建模及发射水动力环境对运载器水弹道影响等方面的理论与
应用问题，对运载器水弹道动力学系统进行了较为全面的数学建模，并具体应用于
某潜射导弹运载器动力学系统辨识和水弹道设计与预报。该导弹运载器的实航试验
结果表明，基于本文提出的方法和数学模型所设计的水弹道是成功的，对水弹道的
预报是准确的。
关于潜射导弹运载器动力学系统辨识问题的研究，本文在国内属首次，并初步
建立了一套较为系统的辨识方法、数学模型与应用技术，具有开拓性，为该领域的
进一步研究奠定了坚实的基础。本文的主要贡献和创新点如下：
1．对于占运载器流体动力主要部分的位置力，不再假设纵、横平面无交联耦合，
而是通过设计运载器模型的空间状态组合风洞实验，对实验数据进行回归分析，来
获得运载器位置力的非线性表达式。
2．将运载器湖上实航试验设计成单项试验与综合试验两个部分，可以充分获得
运载器水弹道动力学系统辨识所需的信息，使某些风洞实验难以测准的弹道敏感参
数，如水平舵及垂直舵舵效参数，得以准确辨识。
3．将改进的单纯形随机搜索策略作为模拟退火算法的随机变化发生器，提出了
基于单纯形的模拟退火参数辨识算法，并采用模拟退火算法对运载器空间运动进行
了参数辨识。结果表明：将一个正的、呈对数分布的随机变量（与温度成比例）添加
到单纯形各顶点的函数值中，再从每个被当作替代点的新点的函数值中减去一个类
似的随机变量的这样一种基于单纯形的随机变化发生器是一种高效的随机变化发生
器。它能使单纯形在向目标函数减少的方向运动的同时，也有能力摆脱局部最小点。
运用模拟退火算法可以获得运载器空间流体动力参数的极大似然估计。
4．将牛顿-拉夫逊、单纯形等优化算法运用于运载器纵向运动参数辨识，对三
种辨识算法进行了收敛速度、准度及全局收敛性比较，结果表明：与牛顿-拉夫逊
算法、单纯形法等常规辨识算法相比，对于待估计参数的不同初始值，模拟退火算
法具有一定的稳定性和较好的全局收敛性。
一
5．运用模拟追火算法对运载器水平尾翼展开过程中由于拍击水流而引起的附加
流体动力进行了辨识建模。有效地解决了运载器水弹道预报的俯仰角数据在过渡段
弹道，明显偏高于运载器湖上实航试验数据这一问题。通过建模后俯仰角数据与试
验数据的对比，表明对运载器在水平尾翼展开过程中由于尾翼拍击水流而引起的附
加流体动力建模是必要的，本文所提出的建模方法是可行的。
6．基于势流理论，建立了艇体扰流场对运载器的附加扰动力数学模型；研究了
流场非定常性的处理方法，及其与水弹道求解在时间步长上的统一性问题；计算了0
艇体扰流场对运载器水弹道的影响；并在运载器完全离开发射管后的艇体扰流场计
＿＿，＿…＿＿、．
算的基础上，对运载器离管过程中的艇体扰流场及其对运载器水弹道的影响进行了
计算。计算结果表明，本文提出的“基于差分法的流场非定常性处理，必须与龙格
－库塔法解弹道方程在时间步长上进行统一处理”及相应的处理方法是可行的；潜
艇运动对运载器横平面的扰动大于纵平面的扰动，包括力与运动；运载器受艇体扰
流影响主要发生在运载器离艇初期。本项研究为解决复杂发射力学环境引起的运载
器出水参数的散布问题奠定了基础。
本文研究成果在鱼雷、水雷、水下无人作战平台等水中兵器领域也具有重要的
应用与参考价值。
This dissertation originates from an important national engineering project. It is mainly
concerned with parameter identification and uncertainty modeling of submarine launched
missile carrier抯 underwater trajectory dynamic system and with the effect of
hydrodynamic environment caused by launch on the carrier抯 trajectory. Overall
mathematical modeling method for carrier抯 underwater trajectory dynamic system is
studied and applied to a certain submarine launched missile carrier抯 trajectory designing
and prediction for the first time in China. The carrier抯 voyage test shows that the
trajectory design based on the methods in this dissertation is successful and the trajectory
prediction is accurate. The main contributions in the dissertation are summarized as
follows:
1. For location force, one major part of fluid motive force of carrier, it抯 no longer
granted that there is no interconnection between vertical and horizontal sections. While
through wind tunnel experiment of combinational spatial states and regression analysis of
experimental data, the nonlinear expressions of location force are acquired.
2. By dividing carrier抯 voyage test at lake into two parts of single-factor test and
multiple-factor test, adequate data which is necessary for dynamic system identification
can be gained. And such a test outline makes accurate identification of some parameters
which are sensitive to trajectory but hard to be measured through wind tunnel experiment,
such as horizontal or vertical rudder derivatives, become practicable.
3. Adopting an improved simplex-based random search strategy, a simulated annealing
identification method is derived. The random change generator is proved efficient by
adding a plus random variable, which has logarithmic distribution and scales with
temperature, to each vertex of simplex and then removing a similar random variable from
the new vertex which is a substitution for the worst vertex. Such a generator can make the
simplex not only move downhill but also be capable of free from the local minimum. With
the simulated annealing identification method, the maximum likelihood estimator of
carrier抯 spacious hydrodynamic parameters can be acquired.
4. Newton-Raphson抯 and simplex optimization methods are applied to carrier抯 vertical
hydrodynamic parameters identification respectively. And the three methods are compared
III
LI~k)~眫1~
with each other on convergence speed, accuracy. The results shows that comparing with
general methods, the simulated annealing method has better convergence for various
initial values of parameters.
5. Additional fluid motive force resulting from horizontal rear wings striking water in
the unfolding process is modeled by using the simulated annealing method. The problem
that measured pitching angle data at lake-test is evidently greater than the predicted data
during transitional trajectory is solved effectively. The agreement between measured data
with calculated data after modeling proves that the modeling is necessary and the
modeling method is workable.
6. Based on the theory of potential flow, additional disturbance force and its effect on
the trajectory due to the motion of launching submarine is computed; the method to handle
the unsteady feature of the flow field and the agreement between the method with the time
step for solving trajectory is studied; on the b
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