战术导弹概率设计与蒙特卡罗方法研究
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摘要
为了提高导弹设计过程中的可靠性,本文将概率设计方法引入战术导弹的设计中,以达到对导弹可靠性进行精确设计的目的。论文按照概率设计方法的理论基础、应用基础和实现方法的顺序进行组织,围绕着实现概率设计方法所遇到的问题展开研究。论文主要工作如下：
(1)研究了概率设计方法的理论基础——干涉理论。围绕着如何将‘裕度’和‘可靠性指标’联系起来这一概率设计的核心问题,对应力-强度干涉模型进行了讨论。推导了利用概率密度函数联合积分法和功能密度函数积分法求解可靠度的方法。针对输入变量相关的情况,推导了相关变量可靠度的求解方法,并对干涉理论中的细节问题进行了讨论。
(2)研究了概率设计方法的应用基础——概率密度函数拟合方法。围绕着如何对已收集的偏差量数据进行建模的问题,提出了采用混合Gauss分布作为偏差量的通用拟合模型。并给出了利用期望-极大化算法计算混合Gauss分布参数的方法。在设计通用拟合程序时,加入利用先验分布信息的估计方法。采用χ2拟合度检验方法控制混合Gauss模型分支数递增。算例验证了算法的拟合能力。最后对某型导弹发动机偏斜角试验数据拟合,展开应用研究。
(3)研究了概率设计方法的实现方法——蒙特卡罗法。围绕着如何具体进行概率设计方法的问题,对蒙特卡罗法的原理、步骤、收敛性、误差估计、方差减小方法、打靶次数与可信度等问题进行了讨论。利用Chebyshev不等式和中心极限定理推导出了模拟打靶次数与置信度之间的关系,并计算了置信区间的上下界。
(4)完成了应用概率设计方法设计战术导弹控制系统的实例。按照概率设计法的思想,在确定的可靠度要求指标下,推导了控制系统可靠度与裕度之间的关系。分别对战术导弹弹道和导弹控制系统偏差量进行建模,利用蒙特卡罗法分析了导弹性能对偏差量的灵敏度。最后,通过算例阐明了概率设计方法在控制系统设计中的应用方法,并利用蒙特卡罗方法验证了概率设计方法的合理性。
(5)将新近发展起来的进化算法统一在序贯蒙特卡罗法之中,并以粒子群算法为例,利用序贯蒙特卡罗方法的思想,提出增强粒子活性的方法和引导惩罚函数法对寻优算法进行改进。算例显示改进方法是有效的。
(6)作为对蒙特卡罗方法研究的深入,结合蒙特卡罗基本理论和粒子更新规则,专门讨论了在蒙特卡罗框架下对粒子滤波算法的改进和增广。对粒子滤波算法的两个改进方向：重要性函数的设计和重采样方法的选择分别进行了讨论,并提出增广粒子滤波算法对非线性、非高斯噪声的系统进行参数估计的方法。
In order to solve the problem of margin'blindness'in the designing method of tactical missile, the probability design method was introduced in tactical missile designing to achieve the purpose of reliability accurate designing. In order to sum the theory and application system of probability design method, the structure of this thesis was organized by the sequence of theory fundament, application fundament and implementation method, and some theoretical problems that how to achieve the probability design method were be researched. The main works of this thesis are as follow:
(1):The theory fundament of probability design method--interference theory, was researched. Revolved around the core problem that how to link the 'margin' with 'reliability index', the stress-strength interference model was discussed at length. The method of computing reliability index was derived by the method of joint integral in probability density function and integral in functional density. For the circumstances of relevant input variables, the method of to computing reliable index in this circumstance was derived, and some detailed problems in interference theory were discussed.
(2)The application fundament of probability design method--the probability density function fitting method, was researched. Revolved around the problem of how to model the collected data of deviation, the method that using mixed Gauss distribution to fit experiment data was proposed. The parameters in Gauss mixed distribution was estimated by expectation maximization (EM) algorithm. A universal procedure was designed to fit experiment data. The strategy of combining pre-distribution information and the method to control branches of mixed Gauss distribution were proposed to reduce computational load and make sure the fit accuracy could be satisfied. Some examples were used to illustrate the effectiveness of the method. Finally, the experiment data of angle deviation in a missile engine was taken as an example to show the availability of proposed method in engineering application.
(3)The implementation method of probability design method-Monte Carlo method, was researched. Revolved around the problem of how to implement the probability design method concretely, the principle of the Monte Carlo method, steps, convergence, error estimates, variance reduction methods, the relationship between the numbers of targeting and the credibility and the application of sequence Monte Carlo thought in selecting of optimum parameters were discussed. The relationship between the numbers of targeting and the credibility was derived by Chebyshev inequality and Central Limit Theorem, the upper bound and lower bound of credibility interval was computed respectively. The newly developed evolutionary algorithms such as genetic algorithms, particle swarm algorithm, fish swarm algorithm etc. were united in the sequential Monte Carlo method. In order to describe how to improve the evolution algorithm by sequence Monte Carlo thought, the particle swam optimization algorithm was taken as an example.
(4) An instance of how to design the tactical missile control system in probability design method was demonstrated. According to the thought of probability design method, under the fixed reliability index, the relationship between margin and reliability index was derived. The trajectory and control system of tactical missile were modeled, and the sensitivity of missile performances with deviation was analyzed by the Monte Carlo method. At the end, the implementation method of probability design method in the designing of missile control system was described by an example.
(5) Taking the newly developing Evolutionary-algorithm (Genetic Algorithm, Particle Swarm Optimization Algorithm, Fish Swarm Algorithm) into the system of Mote Carlo method, and taking PSO algorithm as an example to demonstrate how to use the thoughts of Monte Carlo to improve Evolutionary Algorithm by increasing the activity of particles and leading penalty function method. The effective of this improvement was proved by this example.
(6) Do as a deeper research on Monte Carlo method, combined the basic theory of Monte Carlo with the regular of particles update, the improvement and extend of particle filtering algorithm were discussed. Two directions of particle filtering algorithm: the design of import function and strategy of re-sampling were discussed respectively, and the extend particle filtering algorithm was proposed to estimate parameters in nonlinear, non-Gauss noise system.
(1)研究了概率设计方法的理论基础——干涉理论。围绕着如何将‘裕度’和‘可靠性指标’联系起来这一概率设计的核心问题,对应力-强度干涉模型进行了讨论。推导了利用概率密度函数联合积分法和功能密度函数积分法求解可靠度的方法。针对输入变量相关的情况,推导了相关变量可靠度的求解方法,并对干涉理论中的细节问题进行了讨论。
(2)研究了概率设计方法的应用基础——概率密度函数拟合方法。围绕着如何对已收集的偏差量数据进行建模的问题,提出了采用混合Gauss分布作为偏差量的通用拟合模型。并给出了利用期望-极大化算法计算混合Gauss分布参数的方法。在设计通用拟合程序时,加入利用先验分布信息的估计方法。采用χ2拟合度检验方法控制混合Gauss模型分支数递增。算例验证了算法的拟合能力。最后对某型导弹发动机偏斜角试验数据拟合,展开应用研究。
(3)研究了概率设计方法的实现方法——蒙特卡罗法。围绕着如何具体进行概率设计方法的问题,对蒙特卡罗法的原理、步骤、收敛性、误差估计、方差减小方法、打靶次数与可信度等问题进行了讨论。利用Chebyshev不等式和中心极限定理推导出了模拟打靶次数与置信度之间的关系,并计算了置信区间的上下界。
(4)完成了应用概率设计方法设计战术导弹控制系统的实例。按照概率设计法的思想,在确定的可靠度要求指标下,推导了控制系统可靠度与裕度之间的关系。分别对战术导弹弹道和导弹控制系统偏差量进行建模,利用蒙特卡罗法分析了导弹性能对偏差量的灵敏度。最后,通过算例阐明了概率设计方法在控制系统设计中的应用方法,并利用蒙特卡罗方法验证了概率设计方法的合理性。
(5)将新近发展起来的进化算法统一在序贯蒙特卡罗法之中,并以粒子群算法为例,利用序贯蒙特卡罗方法的思想,提出增强粒子活性的方法和引导惩罚函数法对寻优算法进行改进。算例显示改进方法是有效的。
(6)作为对蒙特卡罗方法研究的深入,结合蒙特卡罗基本理论和粒子更新规则,专门讨论了在蒙特卡罗框架下对粒子滤波算法的改进和增广。对粒子滤波算法的两个改进方向：重要性函数的设计和重采样方法的选择分别进行了讨论,并提出增广粒子滤波算法对非线性、非高斯噪声的系统进行参数估计的方法。
In order to solve the problem of margin'blindness'in the designing method of tactical missile, the probability design method was introduced in tactical missile designing to achieve the purpose of reliability accurate designing. In order to sum the theory and application system of probability design method, the structure of this thesis was organized by the sequence of theory fundament, application fundament and implementation method, and some theoretical problems that how to achieve the probability design method were be researched. The main works of this thesis are as follow:
(1):The theory fundament of probability design method--interference theory, was researched. Revolved around the core problem that how to link the 'margin' with 'reliability index', the stress-strength interference model was discussed at length. The method of computing reliability index was derived by the method of joint integral in probability density function and integral in functional density. For the circumstances of relevant input variables, the method of to computing reliable index in this circumstance was derived, and some detailed problems in interference theory were discussed.
(2)The application fundament of probability design method--the probability density function fitting method, was researched. Revolved around the problem of how to model the collected data of deviation, the method that using mixed Gauss distribution to fit experiment data was proposed. The parameters in Gauss mixed distribution was estimated by expectation maximization (EM) algorithm. A universal procedure was designed to fit experiment data. The strategy of combining pre-distribution information and the method to control branches of mixed Gauss distribution were proposed to reduce computational load and make sure the fit accuracy could be satisfied. Some examples were used to illustrate the effectiveness of the method. Finally, the experiment data of angle deviation in a missile engine was taken as an example to show the availability of proposed method in engineering application.
(3)The implementation method of probability design method-Monte Carlo method, was researched. Revolved around the problem of how to implement the probability design method concretely, the principle of the Monte Carlo method, steps, convergence, error estimates, variance reduction methods, the relationship between the numbers of targeting and the credibility and the application of sequence Monte Carlo thought in selecting of optimum parameters were discussed. The relationship between the numbers of targeting and the credibility was derived by Chebyshev inequality and Central Limit Theorem, the upper bound and lower bound of credibility interval was computed respectively. The newly developed evolutionary algorithms such as genetic algorithms, particle swarm algorithm, fish swarm algorithm etc. were united in the sequential Monte Carlo method. In order to describe how to improve the evolution algorithm by sequence Monte Carlo thought, the particle swam optimization algorithm was taken as an example.
(4) An instance of how to design the tactical missile control system in probability design method was demonstrated. According to the thought of probability design method, under the fixed reliability index, the relationship between margin and reliability index was derived. The trajectory and control system of tactical missile were modeled, and the sensitivity of missile performances with deviation was analyzed by the Monte Carlo method. At the end, the implementation method of probability design method in the designing of missile control system was described by an example.
(5) Taking the newly developing Evolutionary-algorithm (Genetic Algorithm, Particle Swarm Optimization Algorithm, Fish Swarm Algorithm) into the system of Mote Carlo method, and taking PSO algorithm as an example to demonstrate how to use the thoughts of Monte Carlo to improve Evolutionary Algorithm by increasing the activity of particles and leading penalty function method. The effective of this improvement was proved by this example.
(6) Do as a deeper research on Monte Carlo method, combined the basic theory of Monte Carlo with the regular of particles update, the improvement and extend of particle filtering algorithm were discussed. Two directions of particle filtering algorithm: the design of import function and strategy of re-sampling were discussed respectively, and the extend particle filtering algorithm was proposed to estimate parameters in nonlinear, non-Gauss noise system.
引文
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