制导炸弹投放区计算研究
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摘要
制导炸弹是一种廉价、高效的精确制导武器,随着现代战争对精确打击需求的增长,其在武器家族中的地位也越来越重要。与常规重力炸弹相比,它不仅打击精度高,而且还可在中高空区域投放,能有效减轻飞行员操作负担,提高载机生存能力。全面评价制导炸弹武器效能,尤其是适用范围是研制方必不可少的一项工作,这个适用范围就是通常意义下的投放区。论文以某典型制导炸弹为研究对象,系统研究制导炸弹投放区的计算问题,并通过实用性分析,增强投放区计算的实用价值。论文主要研究内容包括:
首先,建立制导炸弹投放区的计算模型,包括制导炸弹动力学模型和投放区几何模型。根据工作高度和计算精度构建合适的环境模型,并考虑工程实际需要,将过载作为控制量;为研究射面投放和离轴投放两种情况,分别建立射面质点弹道模型和离轴质点弹道模型。综合各种定义方式,给出较为完整的投放区定义。本质上,投放区边界主要由制导炸弹最优滑翔能力决定。因此,通过简单的平移变换可将投放区边界问题转化为多个最优射程问题。同时,根据制导方法、投弹方向、有无扰动将投放区分为方案型与导引型、射面与离轴、理想与实际三大类。
基于最大值原理,引入同伦方法,提出一种高精度方案型投放区计算方法。首先利用同伦方法的大范围收敛特性,构造原最大射程问题的同伦映射,推导了最大升阻比控制规律,以最大升阻比弹道作为初始解轨迹。随着调节系数从0连续变化至1,同伦轨迹也连续过渡到原最大射程问题的解轨迹。该方法克服了最大值原理求解最优控制问题时对协态初值的过度敏感,且因最大升阻比弹道提供的初始轨迹非常接近原问题的最优解,计算收敛更快。最后,利用所提方法计算了典型条件下的射面方案型投放区和离轴方案型投放区。
根据微分平坦理论,提出了一种基于直接法的导引型投放区计算方法。引入微分平坦变量对弹道模型进行重新描述,以该模型为基础采用直接法计算导引型投放区。导引律既是在线生成弹道的规律,也是一种路径约束。如果仍利用同伦方法进行求解,路径约束处理繁琐,且收敛效果不甚理想。经平坦变量描述的弹道模型,因大部分微分约束被转换为代数约束,需离散化的微分约束和待优化变量减少,计算量也减少,既发挥了直接法善于处理路径约束的优势,又避开了直接法计算量大的缺点。最后,利用所提方法计算了典型条件下的射面导引型投放区和离轴导引型投放区。
由前面的分析与仿真可知,相同条件下导引型投放区的射程范围、离轴能力均小于方案型投放区。其根本原因在于导引型投放区受导引律决定的路径约束,解空间更小。针对该问题,提出一种基于复合制导体制的扩展投放区定义与计算方法,在中制导方案段定义最大水平末速的性能指标,为中末两段的顺利交班设计平滑段,并计算典型条件下的扩展型投放区。仿真结果表明,该型投放区结合了方案型与导引型投放区的优势,具有范围广、制导精度高的特点。
围绕投放区实际使用中存在的几个问题进行了讨论。1)提出了一种选取拟合变量、指定拟合顺序以及规定计量单位的投放区数据预处理方法,并通过实例说明了该处理方法对拟合精度的贡献;2)根据实际投弹扰动因素的作用时刻,将其分成初始状态误差和飞行过程干扰两类。并给出前者独立作用时,投放区命中概率计算式。因后者作用于弹道积分的每个周期,对投放区命中概率的影响可通过拉偏试验展开分析。由综合各类扰动因素的蒙特卡洛试验揭示了投放区相应变化规律;3)从三个角度诠释投放区计算中的通用性涵义,认为提高单条弹道优化的效率、建立批量弹道计算的异常处理机制,以及寻求投放区随弹道参数连续变化的规律,都是增强通用性的途径。
论文引入了数值计算的新方法研究制导炸弹投放区的获取问题,探索了投放区使用时存在的问题并提出了相应的解决方案,通过仿真与分析验证了所提方法的有效性。文中的论述充分结合了制导炸弹的研究背景,算例设计均以实弹参数为参考,分别给出了多种条件下的各型投放区及对比分析,对于新型制导炸弹的研制具有借鉴意义。
As a precision-guided weapon, guided bomb is cheap and highly effective. With the increase of modern warfare demand for precision strike, it is becoming more and more important in arms family. Compared with conventional gravity bomb, it has not only high accuracy but also the ability of mid-high altitude region release. This character can effectively reduce burden on the operation of the pilot and improve carrier survivability. Therefore, a comprehensive evaluation of the performance of guided weapons, particularly the scope of application of guided bomb is essential and critical. Where, the scope is always called as release region of guided bombs. Taking the typical guided bomb as an example, this dissertation studies systematically release region calculation for guided bombs, and through the application analysis of engineering, the practical value of release region is pointed out. The main content of this dissertation is shown as follows:
Release region calculation model of a guided bomb is established, including dynamic model of guided bomb and geometric model of release region. Allowing for altitude scope and calculation accuracy, a suitable environmental model is constructed and overload is taken as control input. Then particle trajectory models on surface-launched and off-axis are set up. Synthesizing various definitions, a general definition of release region is given out. Because release region boundary is related with the utmost trajectory of guided bombs, the boundary issue was put into many rounds of optimal range calculation, through a simple translation transformation. According to guidance mode, release direction and whether or not disturbance, release region are classified into three kinds: guidance and program, on surface-launched and off-axis, ideal and actual.
The homotopy method based on maximum principle is developed to calculate program release region whose demand for precision is higher than efficiency. The homotopy map for maximum range problem is built by using homotopy method with a large scope convergence property, and the control law of maximum lift-drag ratio is deduced. Then the maximum lift-drag ratio trajectory is regarded as the initial solution, and the optimal solution of original maximum range is obtained through successively increasing the adjustment parameter from zero to one. The method overcomes initial costates guess puzzle and has a fast convergence rate which thanks to maximum lift-drag ratio trajectory close to true optimal solution. Finally, program release regions on surface-launched and off-axis are calculated by using proposed method.
Proper flat outputs are introduced and used to reformulate trajectory model, then the direct method is adopted to calculate guidance release region on the basis of the reformulated trajectory model. Guidance law is not only used to generate trajectory online but also as a path constraint. If above homotopy method is adopted to calculate release region of guidance type, the path constraint is complicated to deal with and the convergence rate is low. Most differential constraints of reformulated trajectory model are transformed into algebraic ones. Hence, less differential constraints need discretizing and less decision variables need optimizing. When direct method is utilized to solve maximum range problem, the cost on computation is not a troublesome problem. Finally, guidance release regions on surface-launched and off-axis are calculated based on the reformulated trajectory model.
Range and off-axis angle of the release region of guidance type are smaller than those of program type under the same conditions. The reason is that solution space becomes smaller while guidance path constraint is imposed. Therefore, compound guidance scheme is adopted to expand release region. After maximum final velocity in horizon for midcourse is taken as performance indicator and smooth handover is designed from the midcourse to the terminal, the expanding type release region is calculated. Expanding type release region has both advantages of program type and guidance type through analysis of the calculation results.
The problems are discussed from the practical application of release region. 1) A data preprocessing method is brought forward in order to select appropriate fitting variables, fitting queue and units of measurement, and effectiveness of proposed method is validated by illustration. 2) According to the time span of effection, the disturbances are divided into two classes: initial state error and flight course interference. The hit probability expressions are given when the former acts individually. But the latter influences each period of trajectory integral, deflection tests are necessary to analyze hit probability when flight course interference acts individually. After that, the shift mode of ideal release region is obtained by monte carlo examination considering disturbances of both classes. 3) The generality of release region calculation is expatiated from three points of view, so the conclusion is that efficiency of trajectory optimization, error disposal on group trajectories computation and relation between release region and trajectory parameters are the ways to generality.
This dissertation introduces new methods for numerical calculation to obtain release region of guided bomb, and explored the problems in the appliction of release region and puts forward corresponding solutions. Referring the actual guided bomb’s characters during shooting, some typical instances are designed and release regions are worked out by using proposed methods under various release conditions. What’s more, detailed analysis is made and some conclusions are drawn according to above calculated results, which shows proposed methods will be helpful in development of new types of guided bombs.
首先,建立制导炸弹投放区的计算模型,包括制导炸弹动力学模型和投放区几何模型。根据工作高度和计算精度构建合适的环境模型,并考虑工程实际需要,将过载作为控制量;为研究射面投放和离轴投放两种情况,分别建立射面质点弹道模型和离轴质点弹道模型。综合各种定义方式,给出较为完整的投放区定义。本质上,投放区边界主要由制导炸弹最优滑翔能力决定。因此,通过简单的平移变换可将投放区边界问题转化为多个最优射程问题。同时,根据制导方法、投弹方向、有无扰动将投放区分为方案型与导引型、射面与离轴、理想与实际三大类。
基于最大值原理,引入同伦方法,提出一种高精度方案型投放区计算方法。首先利用同伦方法的大范围收敛特性,构造原最大射程问题的同伦映射,推导了最大升阻比控制规律,以最大升阻比弹道作为初始解轨迹。随着调节系数从0连续变化至1,同伦轨迹也连续过渡到原最大射程问题的解轨迹。该方法克服了最大值原理求解最优控制问题时对协态初值的过度敏感,且因最大升阻比弹道提供的初始轨迹非常接近原问题的最优解,计算收敛更快。最后,利用所提方法计算了典型条件下的射面方案型投放区和离轴方案型投放区。
根据微分平坦理论,提出了一种基于直接法的导引型投放区计算方法。引入微分平坦变量对弹道模型进行重新描述,以该模型为基础采用直接法计算导引型投放区。导引律既是在线生成弹道的规律,也是一种路径约束。如果仍利用同伦方法进行求解,路径约束处理繁琐,且收敛效果不甚理想。经平坦变量描述的弹道模型,因大部分微分约束被转换为代数约束,需离散化的微分约束和待优化变量减少,计算量也减少,既发挥了直接法善于处理路径约束的优势,又避开了直接法计算量大的缺点。最后,利用所提方法计算了典型条件下的射面导引型投放区和离轴导引型投放区。
由前面的分析与仿真可知,相同条件下导引型投放区的射程范围、离轴能力均小于方案型投放区。其根本原因在于导引型投放区受导引律决定的路径约束,解空间更小。针对该问题,提出一种基于复合制导体制的扩展投放区定义与计算方法,在中制导方案段定义最大水平末速的性能指标,为中末两段的顺利交班设计平滑段,并计算典型条件下的扩展型投放区。仿真结果表明,该型投放区结合了方案型与导引型投放区的优势,具有范围广、制导精度高的特点。
围绕投放区实际使用中存在的几个问题进行了讨论。1)提出了一种选取拟合变量、指定拟合顺序以及规定计量单位的投放区数据预处理方法,并通过实例说明了该处理方法对拟合精度的贡献;2)根据实际投弹扰动因素的作用时刻,将其分成初始状态误差和飞行过程干扰两类。并给出前者独立作用时,投放区命中概率计算式。因后者作用于弹道积分的每个周期,对投放区命中概率的影响可通过拉偏试验展开分析。由综合各类扰动因素的蒙特卡洛试验揭示了投放区相应变化规律;3)从三个角度诠释投放区计算中的通用性涵义,认为提高单条弹道优化的效率、建立批量弹道计算的异常处理机制,以及寻求投放区随弹道参数连续变化的规律,都是增强通用性的途径。
论文引入了数值计算的新方法研究制导炸弹投放区的获取问题,探索了投放区使用时存在的问题并提出了相应的解决方案,通过仿真与分析验证了所提方法的有效性。文中的论述充分结合了制导炸弹的研究背景,算例设计均以实弹参数为参考,分别给出了多种条件下的各型投放区及对比分析,对于新型制导炸弹的研制具有借鉴意义。
As a precision-guided weapon, guided bomb is cheap and highly effective. With the increase of modern warfare demand for precision strike, it is becoming more and more important in arms family. Compared with conventional gravity bomb, it has not only high accuracy but also the ability of mid-high altitude region release. This character can effectively reduce burden on the operation of the pilot and improve carrier survivability. Therefore, a comprehensive evaluation of the performance of guided weapons, particularly the scope of application of guided bomb is essential and critical. Where, the scope is always called as release region of guided bombs. Taking the typical guided bomb as an example, this dissertation studies systematically release region calculation for guided bombs, and through the application analysis of engineering, the practical value of release region is pointed out. The main content of this dissertation is shown as follows:
Release region calculation model of a guided bomb is established, including dynamic model of guided bomb and geometric model of release region. Allowing for altitude scope and calculation accuracy, a suitable environmental model is constructed and overload is taken as control input. Then particle trajectory models on surface-launched and off-axis are set up. Synthesizing various definitions, a general definition of release region is given out. Because release region boundary is related with the utmost trajectory of guided bombs, the boundary issue was put into many rounds of optimal range calculation, through a simple translation transformation. According to guidance mode, release direction and whether or not disturbance, release region are classified into three kinds: guidance and program, on surface-launched and off-axis, ideal and actual.
The homotopy method based on maximum principle is developed to calculate program release region whose demand for precision is higher than efficiency. The homotopy map for maximum range problem is built by using homotopy method with a large scope convergence property, and the control law of maximum lift-drag ratio is deduced. Then the maximum lift-drag ratio trajectory is regarded as the initial solution, and the optimal solution of original maximum range is obtained through successively increasing the adjustment parameter from zero to one. The method overcomes initial costates guess puzzle and has a fast convergence rate which thanks to maximum lift-drag ratio trajectory close to true optimal solution. Finally, program release regions on surface-launched and off-axis are calculated by using proposed method.
Proper flat outputs are introduced and used to reformulate trajectory model, then the direct method is adopted to calculate guidance release region on the basis of the reformulated trajectory model. Guidance law is not only used to generate trajectory online but also as a path constraint. If above homotopy method is adopted to calculate release region of guidance type, the path constraint is complicated to deal with and the convergence rate is low. Most differential constraints of reformulated trajectory model are transformed into algebraic ones. Hence, less differential constraints need discretizing and less decision variables need optimizing. When direct method is utilized to solve maximum range problem, the cost on computation is not a troublesome problem. Finally, guidance release regions on surface-launched and off-axis are calculated based on the reformulated trajectory model.
Range and off-axis angle of the release region of guidance type are smaller than those of program type under the same conditions. The reason is that solution space becomes smaller while guidance path constraint is imposed. Therefore, compound guidance scheme is adopted to expand release region. After maximum final velocity in horizon for midcourse is taken as performance indicator and smooth handover is designed from the midcourse to the terminal, the expanding type release region is calculated. Expanding type release region has both advantages of program type and guidance type through analysis of the calculation results.
The problems are discussed from the practical application of release region. 1) A data preprocessing method is brought forward in order to select appropriate fitting variables, fitting queue and units of measurement, and effectiveness of proposed method is validated by illustration. 2) According to the time span of effection, the disturbances are divided into two classes: initial state error and flight course interference. The hit probability expressions are given when the former acts individually. But the latter influences each period of trajectory integral, deflection tests are necessary to analyze hit probability when flight course interference acts individually. After that, the shift mode of ideal release region is obtained by monte carlo examination considering disturbances of both classes. 3) The generality of release region calculation is expatiated from three points of view, so the conclusion is that efficiency of trajectory optimization, error disposal on group trajectories computation and relation between release region and trajectory parameters are the ways to generality.
This dissertation introduces new methods for numerical calculation to obtain release region of guided bomb, and explored the problems in the appliction of release region and puts forward corresponding solutions. Referring the actual guided bomb’s characters during shooting, some typical instances are designed and release regions are worked out by using proposed methods under various release conditions. What’s more, detailed analysis is made and some conclusions are drawn according to above calculated results, which shows proposed methods will be helpful in development of new types of guided bombs.
引文
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