CN111888767B - Missile ash box simulator trajectory registration method in simulation environment - Google Patents

Missile ash box simulator trajectory registration method in simulation environment Download PDF

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CN111888767B
CN111888767B CN202010639747.7A CN202010639747A CN111888767B CN 111888767 B CN111888767 B CN 111888767B CN 202010639747 A CN202010639747 A CN 202010639747A CN 111888767 B CN111888767 B CN 111888767B
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赵艺阳
朴海音
詹光
杨振
周德云
孔维仁
张凯
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Northwestern Polytechnical University
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Abstract

本发明提供了一种模拟环境中的导弹灰盒仿真器弹道配准方法，采集发射时刻的导弹与敌方飞机初始位置，得到N组典型设计点；将待辨识的导弹仿真系统作为灰盒仿真器，将已知的导弹模型视为白盒仿真器，采集其输出的弹道数据，对每个待辨识参数采用随机方式进行初始化，利用灰盒所生成的弹道轨迹数据，对每条染色体下的白盒仿真器的输出进行评估，并不断优化种群。本发明简单易行，不但避免了繁琐的灵敏度求解，也避免了可能出现的数值问题，而且能使辨识准确性明显增强，从而能够有效地提高参数辨识的可靠性和准确性。

Figure 202010639747

The invention provides a ballistic registration method for a missile gray box simulator in a simulated environment, which collects the initial positions of the missile and the enemy aircraft at the launch moment, and obtains N groups of typical design points; the missile simulation system to be identified is used as a gray box simulation It takes the known missile model as a white-box simulator, collects the output ballistic data, initializes each parameter to be identified in a random way, and uses the ballistic trajectory data generated by the gray box to analyze the trajectory data under each chromosome. The output of the white-box simulator is evaluated and the population is continuously optimized. The invention is simple and easy to implement, not only avoids complicated sensitivity solutions, but also avoids possible numerical problems, and can significantly enhance the identification accuracy, thereby effectively improving the reliability and accuracy of parameter identification.

Figure 202010639747

Description

一种模拟环境中的导弹灰盒仿真器弹道配准方法A Ballistic Registration Method for Missile Grey Box Simulator in Simulation Environment

技术领域technical field

本发明属于参数辨识与计算机仿真技术领域，尤其涉及一种模拟环境中的导弹弹道配准方法。The invention belongs to the technical field of parameter identification and computer simulation, and in particular relates to a missile trajectory registration method in a simulation environment.

背景技术Background technique

弹道配准是指利用现有导弹仿真系统，在相同输入条件下，依照某种算法，从待辨识参数初始值出发，根据导弹模型计算弹道曲线，并与同类型但参数未知的其它导弹仿真系统所输出的弹道曲线进行误差比较，再依照算法逐步调整参数值，使弹道曲线误差达到最小的过程，属于参数辨识下的最值优化问题。需要辨识的整个导弹仿真系统可以看做是一个“灰盒”，该系统遵守基本物理定律，如牛顿第二定律和刚体动力学原理等，即整个系统在已知动力学、运动学方程和其它数学模型及规律的情况下，辨识导弹特定参数。弹道配准的一个典型应用是：空战模拟类游戏往往需要涉及多种导弹的弹道仿真与解算问题，其通常会为每种导弹分别建立弹道模型。在保证一定解算精度的前提下，可以通过设置不同的输入参数来复用某一弹道仿真解算模型，以支持多种导弹的弹道仿真功能并降低软件复杂性。Ballistic registration refers to using the existing missile simulation system, under the same input conditions, according to a certain algorithm, starting from the initial value of the parameters to be identified, calculating the ballistic curve according to the missile model, and comparing it with other missile simulation systems of the same type but with unknown parameters. The output ballistic curve is compared for error, and then the parameter value is adjusted step by step according to the algorithm, so that the ballistic curve error can be minimized, which belongs to the optimization problem under parameter identification. The entire missile simulation system that needs to be identified can be regarded as a "gray box", the system obeys basic physical laws, such as Newton's second law and rigid body dynamics principles, that is, the entire system is in the known dynamics, kinematic equations and other In the case of mathematical models and laws, identify missile-specific parameters. A typical application of ballistic registration is: air combat simulation games often require ballistic simulation and solution problems involving multiple missiles, and a ballistic model is usually established for each missile. On the premise of ensuring a certain solution accuracy, a certain ballistic simulation solution model can be reused by setting different input parameters to support the ballistic simulation function of various missiles and reduce the software complexity.

在导弹参数辨识中得到广泛应用的Newton-Raphson及其改进算法的最大似然法，这类方法具有收敛速度较快，计算量较小的优点。但也有相当的局限性，如当系统存在非线性或时滞时，无法求取梯度值。同时也存在对待辨识参数初值敏感问题，这些方法在优化设计中都始于一组特定参数，使得优化结果极易陷入在起始点附近，形成局部最优解，从而给优化时的参数初值选取造成较大困难。而且在求解灵敏度时，也会带来一些数值问题，从而对参数辨识结果的准确性产生较大的影响，严重时甚至会引起辨识过程的发散，而得不到有效结果。The maximum likelihood method of Newton-Raphson and its improved algorithm, which has been widely used in missile parameter identification, has the advantages of faster convergence speed and less calculation amount. But there are also considerable limitations, such as when the system has nonlinearity or time delay, the gradient value cannot be obtained. At the same time, there is also the problem of sensitivity to the initial value of the parameters to be identified. These methods all start with a set of specific parameters in the optimization design, which makes the optimization result easy to fall into the vicinity of the starting point and form a local optimal solution, thus giving the initial value of the parameters during optimization. selection causes greater difficulty. Moreover, when solving the sensitivity, it will also bring some numerical problems, which will have a great impact on the accuracy of the parameter identification results.

发明内容SUMMARY OF THE INVENTION

为了克服现有技术的不足，本发明提供一种模拟环境中的导弹灰盒仿真器弹道配准方法，采用遗传算法解决参数辨识问题，其辨识思想和方法简单易行，不但避免了繁琐的灵敏度求解，也避免了可能出现的数值问题，而且能使辨识准确性明显增强，从而能够有效地提高参数辨识的可靠性和准确性。In order to overcome the deficiencies of the prior art, the present invention provides a ballistic registration method for a missile gray box simulator in a simulated environment. Genetic algorithm is used to solve the problem of parameter identification. The identification idea and method are simple and easy to implement, and not only avoids cumbersome sensitivity The solution also avoids possible numerical problems, and can significantly enhance the identification accuracy, thereby effectively improving the reliability and accuracy of parameter identification.

本发明解决其技术问题所采用的技术方案包括以下步骤：The technical scheme adopted by the present invention to solve its technical problem comprises the following steps:

步骤1，采集发射时刻的导弹与敌方飞机初始位置作为一组典型设计点，重复该过程N次，得到N组典型设计点；Step 1: Collect the initial position of the missile and the enemy aircraft at the time of launch as a set of typical design points, repeat the process N times, and obtain N groups of typical design points;

步骤2，将待辨识的导弹仿真系统作为灰盒仿真器，采集灰盒仿真器的弹道数据，在第k个典型设计点下的灰盒仿真器所输出的导弹轨迹位置集合Step 2, take the missile simulation system to be identified as a gray box simulator, collect the ballistic data of the gray box simulator, and set the missile trajectory position set output by the gray box simulator under the kth typical design point

Figure GDA0003756956890000021
Figure GDA0003756956890000021

式中：where:

Figure GDA0003756956890000022
—灰盒仿真器在第k个典型设计点下所输出的的导弹第i个位置坐标；
Figure GDA0003756956890000022
- the ith position coordinate of the missile output by the gray box simulator under the kth typical design point;

N—典型设计点个数；N—the number of typical design points;

tk—在输入的第k个典型设计点下，灰盒仿真器所输出的弹道仿真时间；t k — the ballistic simulation time output by the gray box simulator under the input kth typical design point;

T—仿真步长；T—simulation step size;

步骤3，将已知的导弹模型视为白盒仿真器，将步骤2中的相同输入传入该导弹模型，采集其输出的弹道数据，在第k个典型设计点下的白盒仿真器所输出的导弹轨迹位置集合

Figure GDA0003756956890000023
In step 3, the known missile model is regarded as a white-box simulator, the same input in step 2 is passed into the missile model, and the output ballistic data is collected. The set of output missile trajectory positions
Figure GDA0003756956890000023

其中：in:

Figure GDA0003756956890000024
——白盒仿真器在第k个典型设计点下所输出的的导弹第i个位置坐标；
Figure GDA0003756956890000024
——The i-th position coordinate of the missile output by the white-box simulator under the k-th typical design point;

Figure GDA0003756956890000025
—在输入的第k个典型设计点下，白盒模型所输出的弹道仿真时间；
Figure GDA0003756956890000025
- Ballistic simulation time output by the white-box model under the input k-th typical design point;

步骤4，设灰盒仿真器中的待辨识参数

Figure GDA0003756956890000026
Np为待辨识参数个数，
Figure GDA0003756956890000027
表示第i个待辨识参数θi的寻优范围，pis表示该参数的搜索间隔，满足mod(pimax-pimin,pis)＝0，mod(·)表示取余运算符；对每个待辨识参数采用随机方式进行初始化，染色体编码方式为实数编码，种群生成采用随机初始化方法；Step 4, set the parameters to be identified in the gray box simulator
Figure GDA0003756956890000026
N p is the number of parameters to be identified,
Figure GDA0003756956890000027
Represents the optimization range of the i-th parameter θ i to be identified, p is represents the search interval of this parameter, satisfies mod(p imax -p imin , p is )=0, mod( ) represents the remainder operator; for each The parameters to be identified are initialized in a random manner, the chromosome encoding method is real number encoding, and the population generation adopts a random initialization method;

步骤5，利用灰盒仿真器所生成的弹道轨迹数据，对每条染色体下的白盒仿真器的输出进行评估，分别设计因弹道轨迹和弹道时间无法配准而产生的惩罚项，在第i条染色体的第j个典型设计点下，分别为：Step 5: Use the ballistic trajectory data generated by the gray-box simulator to evaluate the output of the white-box simulator under each chromosome, and design the penalty terms due to the inability to register the ballistic trajectory and the ballistic time. Under the jth typical design point of a chromosome, they are:

Figure GDA0003756956890000028
Figure GDA0003756956890000028

Figure GDA0003756956890000031
Figure GDA0003756956890000031

式中：where:

Figure GDA0003756956890000032
—因弹道轨迹无法配准而产生的惩罚项；
Figure GDA0003756956890000032
- Penalty items due to inability to register ballistic trajectories;

Figure GDA0003756956890000033
—在第i条染色体的第j个典型设计点下，因白盒与灰盒仿真器所输出的弹道轨迹长度在时间序列上无法配准而产生的惩罚项，
Figure GDA0003756956890000034
为当灰盒仿真器所输出的弹道长度大于白盒仿真器时，需要计算的惩罚项，
Figure GDA0003756956890000035
为当白盒仿真器所输出的弹道长度大于灰盒仿真器时，需要计算的惩罚项；
Figure GDA0003756956890000033
- Under the jth typical design point of the ith chromosome, the penalty term due to the inability to register the ballistic trajectory lengths output by the white-box and gray-box simulators in the time series,
Figure GDA0003756956890000034
is the penalty term that needs to be calculated when the ballistic length output by the gray-box simulator is greater than that of the white-box simulator,
Figure GDA0003756956890000035
It is the penalty item that needs to be calculated when the ballistic length output by the white-box simulator is greater than that of the gray-box simulator;

Ts—弹道数据采样间隔；T s —Sampling interval of ballistic data;

Figure GDA0003756956890000036
—两组弹道在时间序列上经过弹道数据采样Ts后重合部分的轨迹数量；
Figure GDA0003756956890000036
- The number of trajectories of the overlapping parts of the two groups of trajectories after the trajectory data sampling T s in the time series;

Figure GDA0003756956890000037
—两组弹道在时间序列上经过弹道数据采样Ts后的非重合部分；
Figure GDA0003756956890000037
- The non-overlapping part of the two sets of ballistics after the ballistic data sampling T s in the time series;

Figure GDA0003756956890000038
Figure GDA0003756956890000038

式中：where:

tj—输入的第j个典型设计点下，灰盒仿真器的弹道仿真时间；t j — the ballistic simulation time of the gray-box simulator under the jth typical design point of the input;

Figure GDA0003756956890000039
—在第i条染色体的第j个典型设计点下，白盒仿真器的弹道仿真时间；
Figure GDA00037569568900000310
—在第i条染色体的第j个典型设计点下，白盒模型和灰盒模型的输出轨迹在时间序列上经过仿真步长T采样后所重合部分的轨迹数量；
Figure GDA0003756956890000039
— Ballistic simulation time of the white-box simulator at the jth typical design point of the ith chromosome;
Figure GDA00037569568900000310
- Under the jth typical design point of the ith chromosome, the output trajectories of the white-box model and the gray-box model in the time series are sampled by the simulation step T and the number of trajectories that overlap;

Figure GDA00037569568900000311
—在第i条染色体的第j个典型设计点下，白盒模型和灰盒模型的输出轨迹在时间序列上经过仿真步长T采样后，取两条轨迹中的最大轨迹数量；
Figure GDA00037569568900000311
- Under the jth typical design point of the ith chromosome, the output trajectories of the white-box model and the gray-box model are sampled by the simulation step T in the time series, and the maximum number of trajectories among the two trajectories is taken;

fix()—向下取整操作；fix()—round down operation;

第i条染色体在第j个典型设计点下的适应度函数为：The fitness function of the i-th chromosome under the j-th typical design point is:

Figure GDA0003756956890000041
Figure GDA0003756956890000041

式中：where:

α1—

Figure GDA0003756956890000042
惩罚项系数；α 1 —
Figure GDA0003756956890000042
penalty term coefficient;

α2—

Figure GDA0003756956890000043
惩罚项系数；α 2 —
Figure GDA0003756956890000043
penalty term coefficient;

第i条染色体的最终适应度函数为

Figure GDA0003756956890000044
The final fitness function of the ith chromosome is
Figure GDA0003756956890000044

步骤6，判断当前迭代次数step是否等于设定的最大迭代次数maxstep，若step＝maxstep则停止算法，输出当前优势染色体；若step≠maxstep，则继续执行下面的步骤；Step 6, judge whether the current iteration number step is equal to the set maximum iteration number maxstep, if step=maxstep, stop the algorithm and output the current dominant chromosome; if step≠maxstep, continue to perform the following steps;

步骤7，对第g代种群θ(g)进行进化，具体进化方法如下：Step 7: Evolve the g-th generation population θ (g) , and the specific evolution method is as follows:

设

Figure GDA0003756956890000048
为第g代种群第i条染色体的解，所对应的适应度函数为fi，计算概率
Figure GDA0003756956890000046
用于选择第i条染色体，
Figure GDA0003756956890000047
是第g代种群所有染色体中的最大适应度值；Assume
Figure GDA0003756956890000048
is the solution of the i-th chromosome of the g-th generation population, and the corresponding fitness function is f i . Calculate the probability
Figure GDA0003756956890000046
is used to select the ith chromosome,
Figure GDA0003756956890000047
is the maximum fitness value of all chromosomes in the gth generation population;

设交叉概率Pic，根据上述在选择策略中所计算的第g代种群各染色体被选择概率Pi (g)，使用轮盘赌方法选择染色体C1和C2，对应的适应度值为fc1和fc2，对第i个待辨识参数按交叉概率Pic进行交叉操作，产生两个新个体C'1和C'2，新个体的适应度值f'c1和f'c2通过步骤5进行计算，若f'c1＞fc1，则接受C'1；若f'c2＞fc2，则接受C'2；Set the crossover probability P ic , according to the selected probability P i (g) of each chromosome of the g-th generation population calculated in the selection strategy above, use the roulette method to select chromosomes C 1 and C 2 , and the corresponding fitness value is f c1 and f c2 , perform the crossover operation on the i-th parameter to be identified according to the crossover probability P ic to generate two new individuals C' 1 and C' 2 , and the fitness values of the new individuals f' c1 and f' c2 pass step 5 Calculate, if f' c1 >f c1 , accept C'1; if f' c2 >f c2 , accept C'2;

设变异概率Pim，根据上述在选择策略中所计算的第g代种群各染色体被选择概率Pi (g)，使用轮盘赌方法选择染色体M1，其适应度值为fm1，对第i个待辨识参数按变异概率Pim进行变异操作，产生新个体M'1，新个体的适应度值f'm1通过步骤5进行计算，若f'm1＞fm1，则接受M'1，否则接受M1；Set the mutation probability P im , according to the selected probability P i (g) of each chromosome of the g-th generation population calculated in the selection strategy above, use the roulette method to select the chromosome M 1 , and its fitness value is f m1 . The i parameters to be identified are mutated according to the mutation probability P im to generate a new individual M' 1 , and the fitness value f' m1 of the new individual is calculated in step 5. If f' m1 >f m1 , M' 1 is accepted, otherwise accept M 1 ;

步骤8，计算当前进化后新种群的最优解，并令迭代次数step加1，返回步骤6。Step 8: Calculate the optimal solution of the new population after the current evolution, add 1 to the iteration number step, and return to step 6.

所述的步骤1中，N取[5，10]范围内的整数。In the step 1, N takes an integer in the range of [5, 10].

所述的步骤2中，仿真步长T取值范围为[0.02，0.5]。In the step 2, the value range of the simulation step size T is [0.02, 0.5].

所述的步骤5中，弹道数据采样间隔Ts取[1，5]之间的整数；

Figure GDA0003756956890000051
惩罚项系数α1取2；
Figure GDA0003756956890000052
惩罚项系数α2取2。In the step 5, the ballistic data sampling interval T s is an integer between [1, 5];
Figure GDA0003756956890000051
The penalty term coefficient α 1 is taken as 2;
Figure GDA0003756956890000052
The penalty term coefficient α 2 is taken as 2.

所述的步骤6中，maxstep取50。In the step 6, maxstep is set to 50.

所述的步骤7中，交叉概率Pic＝0.66，变异概率Pim＝0.34。In the step 7, the crossover probability P ic =0.66, and the mutation probability P im =0.34.

本发明的有益效果是：采用遗传算法解决参数辨识问题，其辨识思想和方法简单易行，不但避免了繁琐的灵敏度求解，也避免了可能出现的数值问题，而且能使辨识准确性明显增强，从而能够有效地提高参数辨识的可靠性和准确性。基于遗传算法的参数辨识，对初值问题不敏感，同时也不要求目标函数具有连续性和可导性，不存在传统优化方法对搜索空间的苛刻要求，因而具有极强的鲁棒性。此外，作为一种随机性优化方法，遗传算法在每一代可以同时搜索待辨识参数空间的不同区域，并将搜索方向指向具有较高概率找到更优解的区域，因此具有良好的全局优化特性，它可以同时处理搜索空间中的多个点，增加了收敛到全局最优解的可能性，因此特别适合处理参数辨识问题。The beneficial effects of the invention are: adopting the genetic algorithm to solve the parameter identification problem, the identification idea and method are simple and easy to implement, not only avoids the complicated sensitivity solution, but also avoids possible numerical problems, and can obviously enhance the identification accuracy, Therefore, the reliability and accuracy of parameter identification can be effectively improved. The parameter identification based on genetic algorithm is not sensitive to the initial value problem, and also does not require the objective function to have continuity and derivability. There is no strict requirement on the search space of traditional optimization methods, so it has strong robustness. In addition, as a random optimization method, the genetic algorithm can simultaneously search different regions of the parameter space to be identified in each generation, and point the search direction to the region with a higher probability of finding a better solution, so it has good global optimization characteristics. It can process multiple points in the search space at the same time, increasing the possibility of convergence to the global optimal solution, so it is especially suitable for dealing with parameter identification problems.

附图说明Description of drawings

图1是本发明的系统结构框图；Fig. 1 is the system structure block diagram of the present invention;

图2是本发明的方法流程图。Figure 2 is a flow chart of the method of the present invention.

具体实施方式Detailed ways

本发明提供了一种基于改进遗传算法的弹道配准方法以对导弹特定参数进行辨识，将空战模拟类游戏里需要被复用的导弹模型视为灰盒仿真器，将游戏中的通用导弹模型视为白盒仿真器，通过确定白盒仿真器中的待辨识参数来对灰盒仿真器所生成的弹道轨迹进行拟合的过程，从而实现弹道配准。辨识系统结构框图如图1所示。The present invention provides a ballistic registration method based on an improved genetic algorithm to identify specific parameters of missiles. The missile model that needs to be reused in air combat simulation games is regarded as a gray box simulator, and the general missile model in the game is regarded as a gray box simulator. Considered as a white-box simulator, the process of fitting the ballistic trajectory generated by the gray-box simulator by determining the parameters to be identified in the white-box simulator, so as to achieve ballistic registration. The block diagram of the identification system is shown in Figure 1.

该方法的流程包括：The flow of the method includes:

步骤1：在空战模拟类游戏中，采集导弹在发射时刻的导弹与敌方飞机初始位置作为一组典型设计点，重复该步骤N次；每组典型设计点反应了当前环境中的敌我态势。N的取值大小会影响算法运行时间及轨迹拟合精度，为保证算法性能，N可取[5，10]之间的整数；将这N组典型设计点作为灰盒/白盒仿真器的输入；Step 1: In the air combat simulation game, collect the initial position of the missile and the enemy aircraft at the launch moment as a set of typical design points, and repeat this step N times; each group of typical design points reflects the situation of the enemy and the enemy in the current environment. The value of N will affect the running time of the algorithm and the accuracy of trajectory fitting. In order to ensure the performance of the algorithm, N can be an integer between [5, 10]; these N groups of typical design points are used as the input of the gray-box/white-box simulator ;

步骤2：将待辨识的导弹仿真系统作为灰盒仿真器，采集灰盒仿真器的弹道数据，记为：Step 2: Take the missile simulation system to be identified as the gray box simulator, and collect the ballistic data of the gray box simulator, which is recorded as:

Figure GDA0003756956890000061
Figure GDA0003756956890000061

式中：where:

Bk—在第k个典型设计点下的灰盒仿真器所输出的导弹轨迹位置集合；B k —the set of missile trajectory positions output by the gray box simulator under the kth typical design point;

Figure GDA0003756956890000062
—灰盒仿真器在第k个典型设计点下所输出的的导弹第i个位置坐标；
Figure GDA0003756956890000062
- the ith position coordinate of the missile output by the gray box simulator under the kth typical design point;

N—典型设计点个数，取值大小在步骤1中指定；N—the number of typical design points, the value is specified in step 1;

tk—在输入的第k个典型设计点下，灰盒模型所输出的弹道仿真时间；t k — the ballistic simulation time output by the gray-box model under the input k-th typical design point;

T—仿真步长；其取值大小会影响算法运行时间及轨迹拟合精度，为保证算法性能，T可取范围为[0.02，0.5]；T—simulation step size; its value will affect the running time of the algorithm and the accuracy of trajectory fitting. To ensure the performance of the algorithm, the range of T is [0.02, 0.5];

步骤3：将游戏中的通用导弹模型视为白盒仿真器，将步骤2中的相同输入传入该仿真模型，采集其输出的弹道数据，，记为Step 3: Treat the general missile model in the game as a white-box simulator, pass the same input in step 2 into the simulation model, and collect its output ballistic data, denoted as

Figure GDA0003756956890000063
Figure GDA0003756956890000063

其中：in:

wk—在第k个典型设计点下的白盒仿真器所输出的导弹轨迹位置集合；w k —the set of missile trajectory positions output by the white-box simulator under the k-th typical design point;

Figure GDA0003756956890000064
——白盒仿真器在第k个典型设计点下所输出的的导弹第i个位置坐标；
Figure GDA0003756956890000064
——The i-th position coordinate of the missile output by the white-box simulator under the k-th typical design point;

N—典型设计点个数，取值大小在步骤1中指定；N—the number of typical design points, the value is specified in step 1;

Figure GDA0003756956890000065
—在输入的第k个典型设计点下，白盒模型所输出的弹道仿真时间；
Figure GDA0003756956890000065
- Ballistic simulation time output by the white-box model under the input k-th typical design point;

T—仿真步长；其取值大小与步骤2中一致；T—simulation step size; its value is consistent with that in step 2;

步骤4：种群初始化，设灰盒模型中的待辨识参数

Figure GDA0003756956890000066
Np为待辨识参数个数，
Figure GDA0003756956890000067
表示第i个待辨识参数θi的寻优范围，pis表示该参数的搜索间隔，满足mod(pimax-pimin,pis)＝0，mod(·)表示取余运算符。对每个待辨识参数采用随机方式进行初始化。染色体编码方式为实数编码，种群生成采用随机初始化方法。Step 4: Population initialization, set the parameters to be identified in the grey box model
Figure GDA0003756956890000066
N p is the number of parameters to be identified,
Figure GDA0003756956890000067
Represents the optimization range of the i-th parameter θ i to be identified, p is represents the search interval of this parameter, and satisfies mod( pimax -p imin , p is )=0, and mod(·) represents the remainder operator. Each parameter to be identified is initialized in a random manner. The chromosome coding method is real number coding, and the population generation adopts the random initialization method.

步骤5：适应度函数计算，利用灰盒所生成的弹道轨迹数据，对每条染色体下的白盒仿真器的输出进行评估，为提高参数辨识精度，分别设计了因弹道轨迹和弹道时间无法配准而产生的惩罚项，在第i条染色体的第j个典型设计点下，分别为：Step 5: Calculate the fitness function. Use the ballistic trajectory data generated by the gray box to evaluate the output of the white box simulator under each chromosome. In order to improve the parameter identification accuracy, the ballistic trajectory and the ballistic time cannot be matched. The penalty terms generated by the calibration, under the jth typical design point of the ith chromosome, are:

Figure GDA0003756956890000071
Figure GDA0003756956890000071

Figure GDA0003756956890000072
Figure GDA0003756956890000072

式中：where:

Figure GDA0003756956890000073
—因弹道轨迹无法配准而产生的惩罚项；其计算方式为白盒与灰盒仿真器在第i条染色体的第j个典型设计点下，二者所输出的弹道轨迹在时间序列上的重合部分所产生的位置误差累加和；
Figure GDA0003756956890000073
- Penalty term due to the inability to register ballistic trajectories; its calculation method is that the ballistic trajectories output by the white-box and gray-box simulators at the j-th typical design point of the i-th chromosome are calculated in the time series. The cumulative sum of the position errors generated by the coincident part;

Figure GDA0003756956890000074
—在第i条染色体的第j个典型设计点下，因白盒与灰盒仿真器所输出的弹道轨迹长度在时间序列上无法配准而产生的惩罚项，
Figure GDA0003756956890000075
为当灰盒仿真器所输出的弹道长度大于白盒仿真器时，需要计算的惩罚项，
Figure GDA0003756956890000076
为当白盒仿真器所输出的弹道长度大于灰盒仿真器时，需要计算的惩罚项；
Figure GDA0003756956890000074
- Under the jth typical design point of the ith chromosome, the penalty term due to the inability to register the ballistic trajectory lengths output by the white-box and gray-box simulators in the time series,
Figure GDA0003756956890000075
is the penalty term that needs to be calculated when the ballistic length output by the gray-box simulator is greater than that of the white-box simulator,
Figure GDA0003756956890000076
It is the penalty item that needs to be calculated when the ballistic length output by the white-box simulator is greater than that of the gray-box simulator;

Ts—弹道数据采样间隔，一般取[1，5]之间的整数；T s — ballistic data sampling interval, generally an integer between [1, 5];

Figure GDA0003756956890000077
—两组弹道在时间序列上经过弹道数据采样Ts后重合部分的轨迹数量。
Figure GDA0003756956890000077
- The number of trajectories of the overlapping parts of the two sets of trajectories after the trajectory data sampling T s in the time series.

Figure GDA0003756956890000078
—两组弹道在时间序列上经过弹道数据采样Ts后的非重合部分；
Figure GDA0003756956890000078
- The non-overlapping part of the two sets of ballistics after the ballistic data sampling T s in the time series;

Figure GDA0003756956890000079
表达式如下：
Figure GDA0003756956890000079
The expression is as follows:

Figure GDA00037569568900000710
Figure GDA00037569568900000710

式中：where:

tj—输入的第j个典型设计点下，灰盒模型的弹道仿真时间；t j - the ballistic simulation time of the gray-box model under the input jth typical design point;

Figure GDA0003756956890000081
—在第i条染色体的第j个典型设计点下，白盒模型的弹道仿真时间；
Figure GDA0003756956890000081
— Ballistic simulation time of the white-box model at the jth typical design point of the ith chromosome;

T—仿真步长；其取值大小与步骤2中一致；T—simulation step size; its value is consistent with that in step 2;

Figure GDA0003756956890000082
—在第i条染色体的第j个典型设计点下，白盒模型和灰盒模型的输出轨迹在时间序列上经过仿真步长T采样后所重合部分的轨迹数量；
Figure GDA0003756956890000082
- Under the jth typical design point of the ith chromosome, the output trajectories of the white-box model and the gray-box model in the time series are sampled by the simulation step T and the number of trajectories that overlap;

Figure GDA0003756956890000083
—在第i条染色体的第j个典型设计点下，白盒模型和灰盒模型的输出轨迹在时间序列上经过仿真步长T采样后，取两条轨迹中的最大轨迹数量；
Figure GDA0003756956890000083
- Under the jth typical design point of the ith chromosome, the output trajectories of the white-box model and the gray-box model are sampled by the simulation step T in the time series, and the maximum number of trajectories among the two trajectories is taken;

Ts—弹道数据采样间隔，一般取[1，5]之间的整数；T s — ballistic data sampling interval, generally an integer between [1, 5];

fix()—向下取整操作；fix()—round down operation;

第i条染色体在第j个典型设计点下的适应度函数为：The fitness function of the i-th chromosome under the j-th typical design point is:

Figure GDA0003756956890000084
Figure GDA0003756956890000084

式中：where:

α1—

Figure GDA0003756956890000085
惩罚项系数，一般取2；α 1 —
Figure GDA0003756956890000085
Penalty term coefficient, generally take 2;

α2—

Figure GDA0003756956890000086
惩罚项系数，一般取2；α 2 —
Figure GDA0003756956890000086
Penalty term coefficient, generally take 2;

第i条染色体的最终适应度函数为：The final fitness function of the ith chromosome is:

Figure GDA0003756956890000087
Figure GDA0003756956890000087

步骤6：判断当前迭代次数step是否等于最大迭代次数maxstep，若step＝maxstep则停止算法，输出当前优势染色体；若step≠maxstep，则继续执行下面的步骤。为兼顾拟合精度与算法性能，maxstep可以取50。Step 6: Determine whether the current number of iterations step is equal to the maximum number of iterations maxstep, if step=maxstep, stop the algorithm and output the current dominant chromosome; if step≠maxstep, continue to perform the following steps. In order to take into account the fitting accuracy and algorithm performance, maxstep can be taken as 50.

步骤7：对第g代种群θ(g)进行进化。进化算子共分为两种，第一种为选择算子，第二种为交叉算子，具体进化方法如下：Step 7: Evolve the g-th generation population θ (g) . There are two kinds of evolution operators. The first is the selection operator, and the second is the crossover operator. The specific evolution methods are as follows:

1选择策略：设

Figure GDA0003756956890000088
为第g代种群第i条染色体的解，所对应的适应度函数为fi，根据概率Pi (g)来选择第i条染色体的计算方法为：1 Choose a strategy: set
Figure GDA0003756956890000088
is the solution of the i-th chromosome of the g-th generation population, and the corresponding fitness function is f i . The calculation method for selecting the i-th chromosome according to the probability P i (g) is:

Figure GDA0003756956890000091
Figure GDA0003756956890000091

式中：where:

Figure GDA0003756956890000092
—第g代种群所有染色体中的最大适应度值；
Figure GDA0003756956890000092
—The maximum fitness value among all chromosomes in the gth generation population;

2交叉算子：设交叉概率Pic，一般取Pic＝0.66，根据上述在选择策略中所计算的第g代种群各染色体被选择概率Pi (g)，使用轮盘赌方法选择染色体C1和C2，它们的适应度值为fc1和fc2，对第i个待辨识参数按交叉概率Pic进行交叉操作，产生两个新个体C'1和C'2，新个体的适应度值f'c1和f'c2通过步骤5进行计算，若f'c1＞fc1，则接受C'1；若f'c2＞fc2，则接受C'2。2 Crossover operator: set the crossover probability P ic , generally take P ic =0.66, according to the selected probability P i (g) of each chromosome of the g-th generation population calculated in the selection strategy above, use the roulette method to select chromosome C 1 and C 2 , their fitness values are f c1 and f c2 , perform crossover operation on the i-th parameter to be identified according to the crossover probability P ic to generate two new individuals C' 1 and C' 2 , the adaptation of the new individual The degree values f' c1 and f' c2 are calculated in step 5. If f' c1 >f c1 , accept C'1; if f' c2 >f c2 , accept C' 2 .

3变异算子：设变异概率Pim，一般取Pim＝0.34，根据上述在选择策略中所计算的第g代种群各染色体被选择概率Pi (g)，使用轮盘赌方法选择染色体M1，其适应度值为fm1，对第i个待辨识参数按变异概率Pim进行变异操作，产生新个体M'1，新个体的适应度值f'm1通过步骤5进行计算，若f'm1＞fm1，则接受M'1，否则接受M1。3 Mutation operator: set the mutation probability P im , generally take P im = 0.34, and use the roulette method to select chromosome M according to the selected probability P i (g) of each chromosome of the g-th generation population calculated in the selection strategy above 1 , its fitness value is f m1 , the i-th parameter to be identified is subjected to mutation operation according to the mutation probability P im to generate a new individual M' 1 , and the fitness value f' m1 of the new individual is calculated through step 5, if f ' m1 > f m1 , accept M' 1 , otherwise accept M 1 .

步骤8：计算当前进化后新种群的最优解，并令迭代次数step加1，返回步骤6。Step 8: Calculate the optimal solution of the new population after the current evolution, increase the number of iterations step by 1, and return to step 6.

该流程说明了一种对弹道进行配准的方法。通过多组不同条件下的典型设计点作为该灰盒模型的输入，采集弹道数据；然后将该输入传入另一待调导弹白盒仿真器，利用所采集的弹道数据对其输出结果进行评估，通过改进的遗传算法对白盒模型中的关键参数进行寻优搜索，进行弹道配准。本发明可以得到较为满意的配准结果。This procedure illustrates a method for registering ballistics. The ballistic data is collected by using multiple groups of typical design points under different conditions as the input of the gray-box model; then the input is passed to another white-box simulator of the missile to be adjusted, and the output results are evaluated using the collected ballistic data. , the key parameters in the white-box model are optimized and searched by the improved genetic algorithm, and the ballistic registration is carried out. The present invention can obtain relatively satisfactory registration results.

将以上步骤综合起来的本发明方法流程图如图2所示。The flow chart of the method of the present invention that combines the above steps is shown in FIG. 2 .

下面结合附图和实施例对本发明进一步说明，本发明包括但不仅限于下述实施例。The present invention will be further described below with reference to the accompanying drawings and embodiments, and the present invention includes but is not limited to the following embodiments.

本发明按照图2所示的流程图实施如下步骤：The present invention implements the following steps according to the flow chart shown in Figure 2:

步骤1：在空战模拟类游戏中，采集导弹在发射时刻的导弹与敌方飞机初始位置作为一组典型设计点，重复该步骤N次；每组典型设计点反应了当前环境中的敌我态势。N的取值大小会影响算法运行时间及轨迹拟合精度，为保证算法性能，N可取[5，10]之间的整数；将这N组典型设计点作为灰盒/白盒仿真器的输入；Step 1: In the air combat simulation game, collect the initial position of the missile and the enemy aircraft at the launch moment as a set of typical design points, and repeat this step N times; each group of typical design points reflects the situation of the enemy and the enemy in the current environment. The value of N will affect the running time of the algorithm and the accuracy of trajectory fitting. In order to ensure the performance of the algorithm, N can be an integer between [5, 10]; these N groups of typical design points are used as the input of the gray-box/white-box simulator ;

步骤2：将待辨识的导弹仿真系统作为灰盒仿真器，通过N组典型设计点作为仿真器的输入来采集弹道数据，记为：Step 2: Take the missile simulation system to be identified as a gray box simulator, and collect ballistic data through N groups of typical design points as the input of the simulator, which is recorded as:

Figure GDA0003756956890000101
Figure GDA0003756956890000101

式中：where:

Bk—在第k个典型设计点下的灰盒仿真器所输出的导弹轨迹位置集合；B k —the set of missile trajectory positions output by the gray box simulator under the kth typical design point;

Figure GDA0003756956890000102
—灰盒仿真器在第k个典型设计点下所输出的的导弹第i个位置坐标；
Figure GDA0003756956890000102
- the ith position coordinate of the missile output by the gray box simulator under the kth typical design point;

N—典型设计点个数，取值大小在步骤1中指定；N—the number of typical design points, the value is specified in step 1;

tk—在输入的第k个典型设计点下，灰盒模型所输出的弹道仿真时间；t k — the ballistic simulation time output by the gray-box model under the input k-th typical design point;

T—仿真步长；其取值大小会影响算法运行时间及轨迹拟合精度，为保证算法性能，T可取范围为[0.02，0.5]；T—simulation step size; its value will affect the running time of the algorithm and the accuracy of trajectory fitting. To ensure the performance of the algorithm, the range of T is [0.02, 0.5];

步骤3：将游戏中的通用导弹模型视为白盒仿真器，将步骤2中的相同输入传入该仿真模型，采集其输出的弹道数据，记为：Step 3: Treat the general missile model in the game as a white-box simulator, pass the same input in step 2 into the simulation model, and collect the output ballistic data, recorded as:

Figure GDA0003756956890000103
Figure GDA0003756956890000103

其中：in:

wk—在第k个典型设计点下的白盒仿真器所输出的导弹轨迹位置集合；w k —the set of missile trajectory positions output by the white-box simulator under the k-th typical design point;

Figure GDA0003756956890000104
——白盒仿真器在第k个典型设计点下所输出的的导弹第i个位置坐标；
Figure GDA0003756956890000104
——The i-th position coordinate of the missile output by the white-box simulator under the k-th typical design point;

N—典型设计点个数，取值大小在步骤1中指定；N—the number of typical design points, the value is specified in step 1;

Figure GDA0003756956890000105
—在输入的第k个典型设计点下，白盒模型所输出的弹道仿真时间；
Figure GDA0003756956890000105
- Ballistic simulation time output by the white-box model under the input k-th typical design point;

T—仿真步长；其取值大小与步骤2中一致；T—simulation step size; its value is consistent with that in step 2;

步骤4：种群初始化，设灰盒模型中的待辨识参数

Figure GDA0003756956890000106
Np为待辨识参数个数，
Figure GDA0003756956890000107
表示第i个待辨识参数θi的寻优范围，pis表示该参数的搜索间隔，满足mod(pimax-pimin,pis)＝0，mod(·)表示取余运算符。对每个待辨识参数采用随机方式进行初始化。染色体编码方式为实数编码，种群生成采用随机初始化方法。Step 4: Population initialization, set the parameters to be identified in the grey box model
Figure GDA0003756956890000106
N p is the number of parameters to be identified,
Figure GDA0003756956890000107
Represents the optimization range of the i-th parameter θ i to be identified, p is represents the search interval of this parameter, and satisfies mod( pimax -p imin , p is )=0, and mod(·) represents the remainder operator. Each parameter to be identified is initialized in a random manner. The chromosome coding method is real number coding, and the population generation adopts the random initialization method.

步骤5：适应度函数计算，利用灰盒所输出的弹道轨迹数据，对每条染色体下的白盒仿真器所输出的弹道轨迹进行评估，为提高参数辨识精度，分别设计了因弹道轨迹和弹道时间无法配准而产生的惩罚项，在第i条染色体的第j个典型设计点下，分别为：Step 5: Calculate the fitness function. Use the ballistic trajectory data output by the gray box to evaluate the ballistic trajectory output by the white box simulator under each chromosome. In order to improve the parameter identification accuracy, the ballistic trajectory and the ballistic trajectory are designed respectively. The penalty terms generated by the inability to register time, under the jth typical design point of the ith chromosome, are:

Figure GDA0003756956890000111
Figure GDA0003756956890000111

Figure GDA0003756956890000112
Figure GDA0003756956890000112

式中：where:

Figure GDA0003756956890000113
—因弹道轨迹无法配准而产生的惩罚项；其计算方式为白盒与灰盒仿真器在第i条染色体的第j个典型设计点下，二者所输出的弹道轨迹在时间序列上的重合部分所产生的位置误差累加和；
Figure GDA0003756956890000113
- Penalty term due to the inability to register ballistic trajectories; its calculation method is that the ballistic trajectories output by the white-box and gray-box simulators at the j-th typical design point of the i-th chromosome are calculated in the time series. The cumulative sum of the position errors generated by the coincident part;

Figure GDA0003756956890000114
—在第i条染色体的第j个典型设计点下，因白盒与灰盒仿真器所输出的弹道轨迹长度在时间序列上无法配准而产生的惩罚项，
Figure GDA0003756956890000115
为当灰盒仿真器所输出的弹道长度大于白盒仿真器时，需要计算的惩罚项，
Figure GDA0003756956890000116
为当白盒仿真器所输出的弹道长度大于灰盒仿真器时，需要计算的惩罚项；
Figure GDA0003756956890000114
- Under the jth typical design point of the ith chromosome, the penalty term due to the inability to register the ballistic trajectory lengths output by the white-box and gray-box simulators in the time series,
Figure GDA0003756956890000115
is the penalty term that needs to be calculated when the ballistic length output by the gray-box simulator is greater than that of the white-box simulator,
Figure GDA0003756956890000116
It is the penalty item that needs to be calculated when the ballistic length output by the white-box simulator is greater than that of the gray-box simulator;

Ts—弹道数据采样间隔，一般取[1，5]之间的整数；T s — ballistic data sampling interval, generally an integer between [1, 5];

Figure GDA0003756956890000117
—两组弹道在时间序列上经过弹道数据采样Ts后重合部分的轨迹数量。
Figure GDA0003756956890000117
- The number of trajectories of the overlapping parts of the two sets of trajectories after the trajectory data sampling T s in the time series.

Figure GDA0003756956890000118
—两组弹道在时间序列上经过弹道数据采样Ts后的非重合部分；
Figure GDA0003756956890000118
- The non-overlapping part of the two sets of ballistics after the ballistic data sampling T s in the time series;

Figure GDA0003756956890000119
表达式如下：
Figure GDA0003756956890000119
The expression is as follows:

Figure GDA00037569568900001110
Figure GDA00037569568900001110

式中：where:

tj—输入的第j个典型设计点下，灰盒模型的弹道仿真时间；t j - the ballistic simulation time of the gray-box model under the input jth typical design point;

Figure GDA0003756956890000121
—在第i条染色体的第j个典型设计点下，白盒模型的弹道仿真时间；
Figure GDA0003756956890000121
— Ballistic simulation time of the white-box model at the jth typical design point of the ith chromosome;

T—仿真步长；其取值大小与步骤2中一致；T—simulation step size; its value is consistent with that in step 2;

Figure GDA0003756956890000122
—在第i条染色体的第j个典型设计点下，白盒模型和灰盒模型的输出轨迹在时间序列上经过仿真步长T采样后所重合部分的轨迹数量；
Figure GDA0003756956890000122
- Under the jth typical design point of the ith chromosome, the output trajectories of the white-box model and the gray-box model in the time series are sampled by the simulation step T and the number of trajectories that overlap;

Figure GDA0003756956890000123
—在第i条染色体的第j个典型设计点下，白盒模型和灰盒模型的输出轨迹在时间序列上经过仿真步长T采样后，取两条轨迹中的最大轨迹数量；
Figure GDA0003756956890000123
- Under the jth typical design point of the ith chromosome, the output trajectories of the white-box model and the gray-box model are sampled by the simulation step T in the time series, and the maximum number of trajectories among the two trajectories is taken;

Ts—弹道数据采样间隔，一般取[1，5]之间的整数；T s — ballistic data sampling interval, generally an integer between [1, 5];

fix()—向下取整操作；fix()—round down operation;

第i条染色体在第j个典型设计点下的适应度函数为：The fitness function of the i-th chromosome under the j-th typical design point is:

Figure GDA0003756956890000124
Figure GDA0003756956890000124

式中：where:

α1—

Figure GDA0003756956890000125
惩罚项系数，一般取2；α 1 —
Figure GDA0003756956890000125
Penalty term coefficient, generally take 2;

α2—

Figure GDA0003756956890000126
惩罚项系数，一般取2；α 2 —
Figure GDA0003756956890000126
Penalty term coefficient, generally take 2;

第i条染色体的最终适应度函数为：The final fitness function of the ith chromosome is:

Figure GDA0003756956890000127
Figure GDA0003756956890000127

步骤6：判断当前迭代次数step是否等于最大迭代次数maxstep，若step＝maxstep则停止算法，输出当前优势染色体；若step≠maxstep，则继续执行下面的步骤。为兼顾拟合精度与算法性能，maxstep可以取50。Step 6: Determine whether the current number of iterations step is equal to the maximum number of iterations maxstep, if step=maxstep, stop the algorithm and output the current dominant chromosome; if step≠maxstep, continue to perform the following steps. In order to take into account the fitting accuracy and algorithm performance, maxstep can be taken as 50.

步骤7：对第g代种群θ(g)进行进化。进化算子共分为两种，第一种为选择算子，第二种为交叉算子，具体进化方法如下：Step 7: Evolve the g-th generation population θ (g) . There are two kinds of evolution operators. The first is the selection operator, and the second is the crossover operator. The specific evolution methods are as follows:

4选择策略：设

Figure GDA0003756956890000128
为第g代种群第i条染色体的解，所对应的适应度函数为fi，根据概率Pi (g)来选择第i条染色体的计算方法为：4Choose a strategy: set
Figure GDA0003756956890000128
is the solution of the i-th chromosome of the g-th generation population, and the corresponding fitness function is f i . The calculation method for selecting the i-th chromosome according to the probability P i (g) is:

Figure GDA0003756956890000129
Figure GDA0003756956890000129

式中：where:

Figure GDA0003756956890000131
—第g代种群所有染色体中的最大适应度值；
Figure GDA0003756956890000131
—The maximum fitness value among all chromosomes in the gth generation population;

5交叉算子：设交叉概率为Pic，一般取Pic＝0.66，根据上述在选择策略中所计算的第g代种群各染色体被选择概率Pi (g)，使用轮盘赌方法选择染色体C1和C2，它们的适应度值为fc1和fc2，对第i个待辨识参数按交叉概率Pic进行交叉操作，产生两个新个体C'1和C'2，新个体的适应度值f'c1和f'c2通过步骤5进行计算，若f'c1＞fc1，则接受C'1；若f'c2＞fc2，则接受C'2。5 Crossover operator: set the crossover probability as P ic , generally take P ic = 0.66, according to the selected probability P i (g) of each chromosome of the g-th generation population calculated in the selection strategy above, use the roulette method to select chromosomes C 1 and C 2 , their fitness values are f c1 and f c2 , perform crossover operation on the i-th parameter to be identified according to the crossover probability P ic to generate two new individuals C' 1 and C' 2 . The fitness values f' c1 and f' c2 are calculated in step 5. If f' c1 >f c1 , C' 1 is accepted; if f' c2 >f c2 , C' 2 is accepted.

6变异算子：设变异概率Pim，一般取Pim＝0.34，根据上述在选择策略中所计算的第g代种群各染色体被选择概率Pi (g)，使用轮盘赌方法选择染色体M1，其适应度值为fm1，对第i个待辨识参数按变异概率Pim进行变异操作，产生新个体M'1，新个体的适应度值f'm1通过步骤5进行计算，若f'm1＞fm1，则接受M'1，否则接受M1。6 Mutation operator: set the mutation probability P im , generally take P im = 0.34, and use the roulette method to select chromosome M according to the selected probability P i (g) of each chromosome of the g-th generation population calculated in the selection strategy above 1 , its fitness value is f m1 , the i-th parameter to be identified is subjected to mutation operation according to the mutation probability P im to generate a new individual M' 1 , and the fitness value f' m1 of the new individual is calculated through step 5, if f ' m1 > f m1 , accept M' 1 , otherwise accept M 1 .

步骤8：计算当前进化后新种群的最优解，并令迭代次数step加1，返回步骤6。Step 8: Calculate the optimal solution of the new population after the current evolution, increase the number of iterations step by 1, and return to step 6.

该流程说明了一种对弹道进行配准的方法。通过多组不同条件下的典型设计点作为该灰盒模型的输入，采集弹道数据；然后将该输入传入另一待调导弹白盒仿真器，利用所采集的弹道数据对其输出结果进行评估，通过改进的遗传算法对白盒模型中的关键参数进行寻优搜索，进行弹道配准。本发明可以得到较为满意的配准结果。This procedure illustrates a method for registering ballistics. The ballistic data is collected by using multiple groups of typical design points under different conditions as the input of the gray-box model; then the input is passed to another white-box simulator of the missile to be adjusted, and the output results are evaluated using the collected ballistic data. , the key parameters in the white-box model are optimized and searched by the improved genetic algorithm, and the ballistic registration is carried out. The present invention can obtain relatively satisfactory registration results.

将以上步骤综合起来的本发明方法流程图如图2所示。The flow chart of the method of the present invention that combines the above steps is shown in FIG. 2 .

Claims (6)

1.一种模拟环境中的导弹灰盒仿真器弹道配准方法，其特征在于包括以下步骤：1. a missile gray box simulator ballistic registration method in a simulated environment, is characterized in that comprising the following steps: 步骤1，采集发射时刻的导弹与敌方飞机初始位置作为一组典型设计点，重复该过程N次，得到N组典型设计点；Step 1: Collect the initial position of the missile and the enemy aircraft at the time of launch as a set of typical design points, repeat the process N times, and obtain N groups of typical design points; 步骤2，将待辨识的导弹仿真系统作为灰盒仿真器，采集灰盒仿真器的弹道数据，在第k个典型设计点下的灰盒仿真器所输出的导弹轨迹位置集合Step 2, take the missile simulation system to be identified as a gray box simulator, collect the ballistic data of the gray box simulator, and set the missile trajectory position set output by the gray box simulator under the kth typical design point
Figure FDA0003756956880000011
Figure FDA0003756956880000011
 式中：where:
Figure FDA0003756956880000012
—灰盒仿真器在第k个典型设计点下所输出的导弹第j个位置坐标；
Figure FDA0003756956880000012
—The jth position coordinate of the missile output by the gray box simulator under the kth typical design point; N—典型设计点个数；N—the number of typical design points; tk—在输入的第k个典型设计点下，灰盒仿真器所输出的弹道仿真时间；t k — the ballistic simulation time output by the gray box simulator under the input kth typical design point; T—仿真步长；T—simulation step size; 步骤3，将已知的导弹模型视为白盒仿真器，将步骤2中的相同输入传入该导弹模型，采集其输出的弹道数据，在第k个典型设计点下的白盒仿真器所输出的导弹轨迹位置集合
Figure FDA0003756956880000013
In step 3, the known missile model is regarded as a white-box simulator, the same input in step 2 is passed into the missile model, and the output ballistic data is collected. The set of output missile trajectory positions
Figure FDA0003756956880000013
 其中：in:
Figure FDA0003756956880000014
——白盒仿真器在第k个典型设计点下所输出的导弹第j个位置坐标；
Figure FDA0003756956880000014
——The jth position coordinate of the missile output by the white box simulator under the kth typical design point;
Figure FDA0003756956880000015
—在输入的第k个典型设计点下，白盒模型所输出的弹道仿真时间；
Figure FDA0003756956880000015
- Ballistic simulation time output by the white-box model under the input k-th typical design point; 步骤4，设灰盒仿真器中的待辨识参数
Figure FDA0003756956880000016
Np为待辨识参数个数，
Figure FDA0003756956880000017
表示第i个待辨识参数θi的寻优范围，pis表示该参数的搜索间隔，满足mod(pimax-pimin,pis)＝0，mod(·)表示取余运算符；对每个待辨识参数采用随机方式进行初始化，染色体编码方式为实数编码，种群生成采用随机初始化方法；Step 4, set the parameters to be identified in the gray box simulator
Figure FDA0003756956880000016
N p is the number of parameters to be identified,
Figure FDA0003756956880000017
Represents the optimization range of the i-th parameter θ i to be identified, p is represents the search interval of this parameter, satisfies mod( pimax -p imin , p is )=0, mod( ) represents the remainder operator; for each The parameters to be identified are initialized in a random manner, the chromosome encoding method is real number encoding, and the population generation adopts a random initialization method; 步骤5，利用灰盒仿真器所生成的弹道轨迹数据，对每条染色体下的白盒仿真器的输出进行评估，分别设计因弹道轨迹和弹道时间无法配准而产生的惩罚项，在第i条染色体的第j个典型设计点下，分别为：Step 5: Use the ballistic trajectory data generated by the gray-box simulator to evaluate the output of the white-box simulator under each chromosome, and design the penalty terms due to the inability to register the ballistic trajectory and the ballistic time. Under the jth typical design point of a chromosome, they are:
Figure FDA0003756956880000021
Figure FDA0003756956880000021
Figure FDA0003756956880000022
Figure FDA0003756956880000022
 式中：where:
Figure FDA0003756956880000023
—因弹道轨迹无法配准而产生的惩罚项；
Figure FDA0003756956880000023
- Penalty items due to inability to register ballistic trajectories;
Figure FDA0003756956880000024
—在第i条染色体的第j个典型设计点下，因白盒与灰盒仿真器所输出的弹道轨迹长度在时间序列上无法配准而产生的惩罚项，
Figure FDA0003756956880000025
为当灰盒仿真器所输出的弹道长度大于白盒仿真器时，需要计算的惩罚项，
Figure FDA0003756956880000026
为当白盒仿真器所输出的弹道长度大于灰盒仿真器时，需要计算的惩罚项；
Figure FDA0003756956880000024
- Under the jth typical design point of the ith chromosome, the penalty term due to the inability to register the ballistic trajectory lengths output by the white-box and gray-box simulators in the time series,
Figure FDA0003756956880000025
is the penalty term that needs to be calculated when the ballistic length output by the gray-box simulator is greater than that of the white-box simulator,
Figure FDA0003756956880000026
It is the penalty item that needs to be calculated when the ballistic length output by the white-box simulator is greater than that of the gray-box simulator; Ts—弹道数据采样间隔；T s —Sampling interval of ballistic data;
Figure FDA0003756956880000027
—两组弹道在时间序列上经过弹道数据采样Ts后重合部分的轨迹数量；
Figure FDA0003756956880000027
- The number of trajectories of the overlapping parts of the two groups of trajectories after the trajectory data sampling T s in the time series;
Figure FDA0003756956880000028
—两组弹道在时间序列上经过弹道数据采样Ts后的非重合部分；
Figure FDA0003756956880000028
- The non-overlapping part of the two sets of ballistics after the ballistic data sampling T s in the time series;
Figure FDA0003756956880000029
Figure FDA0003756956880000029
 式中：where: tj—输入的第j个典型设计点下，灰盒仿真器的弹道仿真时间；t j — the ballistic simulation time of the gray-box simulator under the jth typical design point of the input;
Figure FDA00037569568800000210
—在第i条染色体的第j个典型设计点下，白盒仿真器的弹道仿真时间；
Figure FDA00037569568800000210
— Ballistic simulation time of the white-box simulator at the jth typical design point of the ith chromosome;
Figure FDA00037569568800000211
—在第i条染色体的第j个典型设计点下，白盒模型和灰盒模型的输出轨迹在时间序列上经过仿真步长T采样后所重合部分的轨迹数量；
Figure FDA00037569568800000211
- Under the jth typical design point of the ith chromosome, the output trajectories of the white-box model and the gray-box model in the time series are sampled by the simulation step T and the number of trajectories that overlap;
Figure FDA00037569568800000212
—在第i条染色体的第j个典型设计点下，白盒模型和灰盒模型的输出轨迹在时间序列上经过仿真步长T采样后，取两条轨迹中的最大轨迹数量；
Figure FDA00037569568800000212
- Under the jth typical design point of the ith chromosome, the output trajectories of the white-box model and the gray-box model are sampled by the simulation step T in the time series, and the maximum number of trajectories among the two trajectories is taken; fix()—向下取整操作；fix()—round down operation; 第i条染色体在第j个典型设计点下的适应度函数为：The fitness function of the i-th chromosome under the j-th typical design point is:
Figure FDA0003756956880000031
Figure FDA0003756956880000031
 式中：where: α1—
Figure FDA0003756956880000032
惩罚项系数；α 1 —
Figure FDA0003756956880000032
penalty term coefficient; α2—
Figure FDA0003756956880000033
惩罚项系数；α 2 —
Figure FDA0003756956880000033
penalty term coefficient; 第i条染色体的最终适应度函数为
Figure FDA0003756956880000034
The final fitness function of the ith chromosome is
Figure FDA0003756956880000034
 步骤6，判断当前迭代次数step是否等于设定的最大迭代次数maxstep，若step＝maxstep则停止算法，输出当前优势染色体；若step≠maxstep，则继续执行下面的步骤；Step 6, judge whether the current iteration number step is equal to the set maximum iteration number maxstep, if step=maxstep, stop the algorithm and output the current dominant chromosome; if step≠maxstep, continue to perform the following steps; 步骤7，对第g代种群θ(g)进行进化，具体进化方法如下：Step 7: Evolve the g-th generation population θ (g) , and the specific evolution method is as follows: 设
Figure FDA0003756956880000035
为第g代种群第i条染色体的解，所对应的适应度函数为fi，计算概率
Figure FDA0003756956880000036
用于选择第i条染色体，
Figure FDA0003756956880000037
是第g代种群所有染色体中的最大适应度值；Assume
Figure FDA0003756956880000035
is the solution of the i-th chromosome of the g-th generation population, and the corresponding fitness function is f i . Calculate the probability
Figure FDA0003756956880000036
is used to select the ith chromosome,
Figure FDA0003756956880000037
is the maximum fitness value of all chromosomes in the gth generation population; 设交叉概率Pic，根据上述在选择策略中所计算的第g代种群各染色体被选择概率Pi (g)，使用轮盘赌方法选择染色体C1和C2，对应的适应度值为fc1和fc2，对第i个待辨识参数按交叉概率Pic进行交叉操作，产生两个新个体C'1和C'2，新个体的适应度值f'c1和f'c2通过步骤5进行计算，若f'c1＞fc1，则接受C'1；若f'c2＞fc2，则接受C'2；Set the crossover probability P ic , according to the selected probability P i (g) of each chromosome of the g-th generation population calculated above in the selection strategy, use the roulette method to select chromosomes C 1 and C 2 , and the corresponding fitness value is f c1 and f c2 , perform crossover operation on the i-th parameter to be identified according to the crossover probability P ic to generate two new individuals C' 1 and C' 2 , and the fitness values of the new individuals f' c1 and f' c2 pass step 5 Calculate, if f' c1 >f c1 , accept C'1; if f' c2 >f c2 , accept C'2; 设变异概率Pim，根据上述在选择策略中所计算的第g代种群各染色体被选择概率Pi (g)，使用轮盘赌方法选择染色体M1，其适应度值为fm1，对第i个待辨识参数按变异概率Pim进行变异操作，产生新个体M'1，新个体的适应度值f'm1通过步骤5进行计算，若f'm1＞fm1，则接受M'1，否则接受M1；Set the mutation probability P im , according to the selected probability P i (g) of each chromosome of the g-th generation population calculated in the above selection strategy, use the roulette method to select the chromosome M 1 , and its fitness value is f m1 , for the first The i parameters to be identified are subjected to mutation operation according to the mutation probability P im to generate a new individual M' 1 , and the fitness value f' m1 of the new individual is calculated through step 5. If f' m1 >f m1 , M' 1 is accepted, otherwise accept M 1 ; 步骤8，计算当前进化后新种群的最优解，并令迭代次数step加1，返回步骤6。Step 8: Calculate the optimal solution of the new population after the current evolution, add 1 to the iteration number step, and return to step 6. 2.根据权利要求1所述的模拟环境中的导弹灰盒仿真器弹道配准方法，其特征在于：所述的步骤1中，N取[5,10]范围内的整数。2 . The ballistic registration method for a missile gray box simulator in a simulated environment according to claim 1 , wherein in the step 1, N is an integer in the range of [5, 10]. 3 . 3.根据权利要求1所述的模拟环境中的导弹灰盒仿真器弹道配准方法，其特征在于：所述的步骤2中，仿真步长T取值范围为[0.02,0.5]。3 . The ballistic registration method for a missile gray box simulator in a simulation environment according to claim 1 , wherein in the step 2, the simulation step size T is in the range of [0.02, 0.5]. 4 . 4.根据权利要求1所述的模拟环境中的导弹灰盒仿真器弹道配准方法，其特征在于：所述的步骤5中，弹道数据采样间隔Ts取[1,5]之间的整数；
Figure FDA0003756956880000041
惩罚项系数α1取2；
Figure FDA0003756956880000042
惩罚项系数α2取2。4. The ballistic registration method of the missile grey box simulator in the simulation environment according to claim 1, wherein in the step 5, the ballistic data sampling interval T s is an integer between [1,5] ;
Figure FDA0003756956880000041
The penalty term coefficient α 1 is taken as 2;
Figure FDA0003756956880000042
The penalty term coefficient α 2 is taken as 2. 5.根据权利要求1所述的模拟环境中的导弹灰盒仿真器弹道配准方法，其特征在于：所述的步骤6中，maxstep取50。5 . The ballistic registration method of the missile gray box simulator in the simulation environment according to claim 1 , wherein: in the described step 6, maxstep is 50. 6 . 6.根据权利要求1所述的模拟环境中的导弹灰盒仿真器弹道配准方法，其特征在于：所述的步骤7中，交叉概率Pic＝0.66，变异概率Pim＝0.34。6 . The ballistic registration method for a missile gray box simulator in a simulated environment according to claim 1 , wherein in the step 7, the crossover probability P ic =0.66, and the mutation probability P im =0.34. 7 .
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