Surface target damage effect evaluation method and system
Through the Monte Carlo algorithm and random point statistics method, the problem of rough calculation of surface target damage assessment in the existing technology is solved, and efficient and accurate damage area assessment of complex shape surface targets is achieved, and combat decision-making and equipment are supported. R&D.
Patent Information
- Application Number
- CN202311475411.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2023-11-03
- Publication Date
- 2025-02-18
AI Technical Summary
When evaluating the damage effect of multiple shells or missiles on complex irregular targets, the prior art has problems such as rough calculations, low evaluation accuracy, and large computing resources consumption.
The Monte Carlo algorithm is used to calculate the overlapping area of the target area and multiple shells or missile destruction circles. By uniformly generating random points in each destruction circle, counting and calculating the target destruction area, and finally obtaining the average value through multiple simulations to evaluate Effective damage area and rate.
It realizes efficient and accurate damage area calculation for targets of any complex shape plane, reduces computing resource consumption, improves evaluation accuracy, and can effectively evaluate the damage effect of multiple shells or missiles based on different weapon models and aiming points.
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Figure CN119477020A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of military operations data processing, and in particular to a method and system for evaluating damage effects on area targets. Background Art
[0002] A key military application of fire suppression weapons such as mortars, rocket launchers, and missiles is the destruction of opposing target areas. Assessing the damage effects of multiple shells (or missiles) striking opposing targets is fundamental to the development and operational use of these weapons, and holds significant national defense significance.
[0003] When multiple shells (or missiles) strike complex and irregular surface targets, the damage effect is expressed by the effective damage rate, which is the ratio of the effective damage area of the shells in the target area to the area of the target area. The effective damage area is equal to the area of the overlapping part of the damage area of multiple shells and the surface target area. The current development direction of shells (or missiles) is to strike surface targets vertically. The shape of the surface target may be complex and irregular, and the damage area of multiple shells may overlap, which brings challenges to the calculation of the effective damage area. The existing invention patent application document with publication number CN112685944A is "A method for planning aiming points of multiple similar explosive bombs on surface targets". This method divides the plane target into a structured grid for damage assessment simulation, numbers the grid according to the order of the two-dimensional spatial position, and assigns the grid a "damage status" attribute. When calculating the explosion point, the grid number where the explosion point is located is directly calculated according to the coordinates of the explosion point. The existing invention patent application document with publication number CN114722573A, "A Method for Damage Assessment of Surface Targets Using Multiple Types of Explosive Bombs," divides the surface target into a structured grid for damage assessment simulation and assigns physical properties to the numbered grid surfaces. When calculating the intersection of the fragment field and the surface target grid micro-element, the grid number of each fragment is calculated by the impact point coordinates. The aforementioned prior art simplifies the plane target into an equivalent rectangular model, then divides the structured network and assigns the "damage state" attribute to the grid. The paper (Hao Hui, Li Xuerui, Shu Jiansheng, et al. An Analytical Calculation Method for the Damage Area of Missiles Attacking Triangular Targets [J]. Firepower and Command Control, 2013, 38(6):143-147.) provides an analytical calculation method for the damage of a single missile to a triangular target based on Stewart's theorem, and then extends it to the damage effect assessment of a single missile on a regular polygonal target. The paper (Chen Zhijiang, Bi Yiming. Analytical algorithm for damage area of complex-shaped surface targets by multiple missiles [J]. Firepower and Command Control, 2008, 33(10):140-144) uses Green's formula to calculate the loop integral on the effective damage area boundary to obtain the effective damage area. This method can be used to evaluate the damage effect of multiple missiles on complex polygonal targets. The paper (Li Xinqi, Niu Guohua, Wang Minghai, et al. Pixel simulation method for calculating the damage of submunitions to aircraft carrier-based aircraft groups [J]. Journal of System Simulation, 2008, 20(11):3062-3065.) evaluates the damage area by counting the pixels in the intersection area. The paper (Yang Qisong, Wang Ranhui, Wang Shunhong, et al. Evaluation of surface target damage effect based on vector grid method [J]. Firepower and Command Control, 2017, 42(6): 175-180.) divides the surface target into a certain number of grids, and vectorizes each grid. The area of the target damaged by multiple missiles is calculated by statistically analyzing the grid damage.
[0004] The aforementioned technical means simplifies the surface target into a regular shape with uniform distribution. This technical means not only has a complicated processing process for complex irregular targets, but also has rough calculation results. The pixel simulation method can process surface targets of any shape, but there are two limitations: (1) The pixel density is uneven, which may cause some directions to be too rough and some directions to be too fine, thus affecting the accuracy of the evaluation. (2) The calculation accuracy is greatly affected by the resolution. The higher the resolution, the more accurate the calculation result, but this requires maintaining a large number of pixel points, which consumes a lot of computing resources. The idea of the grid method is similar to that of the pixel method. The grid method requires detailed segmentation of the target. If the segmentation is inaccurate, the evaluation of the target will be inaccurate.
[0005] In summary, the existing technology for evaluating the damage effect of surface targets of arbitrary shapes has technical problems such as rough calculation, low evaluation accuracy, and high consumption of computing resources. Summary of the Invention
[0006] The technical problem to be solved by the present invention is: how to solve the technical problems of the existing technology for evaluating the damage effect of surface targets of arbitrary shapes, such as rough calculation, low evaluation accuracy, and large consumption of computing resources.
[0007] The present invention solves the above technical problems by adopting the following technical solutions: A method for evaluating the damage effect of a surface target comprises:
[0008] S1. Generate the target region based on the input boundary points and calculate the area of the target region;
[0009] S2. Generate N projectile impact points based on the aiming point in the target area and the weapon and ammunition accuracy data;
[0010] S3. Generate damage circles in sequence based on the impact point and damage radius of the shells;
[0011] S4. Generate M random points uniformly within each damage circle;
[0012] S5. Traverse N×M random points and count the number of damage circles that the random points in the target area fall into (how many damage circles they fall into);
[0013] S6. Calculate the target damage area based on the random points and their number, the extent to which the random points in the target area fall within the damage circle, the damage radius, and the area of the damage circle;
[0014] S7, repeating steps S2 to S6, counting the target damage area for more than a preset number of times, and calculating the average value as the effective damage area assessment result;
[0015] S8. Based on the effective damage area assessment result, obtain an effective damage rate as an assessment result of the area target damage effectiveness.
[0016] The present invention uses a Monte Carlo algorithm to calculate the overlapping area between the target area and the damage circles of multiple artillery shells (or missiles). It has high computational efficiency and can calculate the damage area of surface targets of arbitrarily complex shapes. It can effectively evaluate the damage effect of multiple artillery shells (or missiles) hitting the surface target area based on the selection of weapon model, the selection of aiming point, and the distribution of strike ammunition, thereby providing support for combat decision-making and equipment research and development.
[0017] This paper uses the Monte Carlo method to calculate the overlapping area of multiple (damage) circles and complex irregular surface targets. Unlike existing technologies, this method can handle surface targets of arbitrarily complex shapes. This method can handle surface targets of any complex shape and more efficiently and accurately calculate the effective damage area, thereby assessing the effective damage area and effective damage rate of multiple projectiles striking a surface target.
[0018] In a more specific technical solution, in step S1, the logic for obtaining the area of the target region includes: the burdock formula Shoelace.
[0019] In a more specific technical solution, in step S1, the logic for obtaining the target area further includes:
[0020] S11. Calculate the vector cross product using the cross() function in the NumPy library based on the target area.
[0021] S12. Summing the vector cross products to obtain the absolute value of the vector cross products, thereby obtaining the area of the target region.
[0022] In a more specific technical solution, in step S1, the logic for obtaining the target area further includes: using the area() function of the Shapely library in Python to obtain the target area according to the target area.
[0023] In a more specific technical solution, in step S2, the normal distribution standard deviation δ of the shells in the target area is obtained based on the weapon and ammunition data:
[0024] δ=0.8493·CEP
[0025] Where CEP is the circular error probability.
[0026] In a more specific technical solution, in step S5, a ray method is used to imagine a ray from a random point to obtain the parity information of the number of intersections between the random point and the preset polygon, so as to determine the positional relationship between the random point and the preset polygon, and to judge whether the random point is within the target area.
[0027] In a more specific technical solution, in step S6, the target damage area S is obtained using the following logic: d :
[0028]
[0029] Where R is the damage radius, T k is the number of random points in the damage circle, k is the number of damage circles, M is the number of random points in each damage circle, and N is the number of projectile impact points.
[0030] The present invention evenly generates M random points within each damage circle, avoiding the constraints on assessment accuracy caused by uneven pixel density in traditional technologies. The present invention does not require the maintenance of a large number of pixel points, reducing computing resource consumption.
[0031] In a more specific technical solution, step S7 includes:
[0032] S71, cyclically executing steps S2 to S6 according to a preset number of cycles to calculate the target damage area of the expected number of cycles;
[0033] S72. Calculate the average value of the target damage area
[0034] In a more specific technical solution, in step S8, the following logic is used to process the effective damage area evaluation result to obtain the effective damage rate r:
[0035]
[0036] Where S is the area of the target area.
[0037] In a more specific technical solution, the area target damage effect assessment system includes:
[0038] The target area processing module is used to generate the target area according to the input boundary points and calculate the area of the target area;
[0039] A landing point generation module is used to generate N projectile landing points based on the aiming point and weapon and ammunition data in the target area. The landing point generation module is connected to the target area processing module.
[0040] A damage circle generation module is used to generate a damage circle based on the impact point and damage radius of the projectile. The damage circle generation module is connected to the impact point generation module.
[0041] A random point generation module is used to evenly generate M random points within each damage circle. The random point generation module is connected to the damage circle generation module.
[0042] Overlap calculation module, used to traverse N×M random points and count the number of damage circles that random points in the target area fall into;
[0043] The damage area processing module is used to calculate the target damage area based on the random points and their number, the extent to which the random points in the target area fall within the damage circle, the damage radius, and the area of the damage circle. The damage area processing module is connected to the overlap calculation module;
[0044] An assessment result acquisition module is used to count the target damage area for more than a preset number of times and calculate the average value as the effective damage area assessment result. The assessment result acquisition module is connected to the damage area processing module;
[0045] The effective damage rate calculation module is used to process the effective damage rate according to the effective damage area assessment result, and the effective damage rate calculation module is connected to the assessment result acquisition module.
[0046] Compared with the existing technology, the present invention has the following advantages: the present invention adopts the Monte Carlo algorithm to calculate the overlapping area between the target area and the damage circle of multiple artillery shells (or missiles), with high calculation efficiency. It can calculate the damage area of surface targets of arbitrarily complex shapes, and can effectively evaluate the damage effect of multiple artillery shells (or missiles) hitting the surface target area based on the selection of weapon model, the selection of aiming point, and the distribution of strike ammunition, thereby providing support for combat decision-making and equipment research and development.
[0047] This paper uses the Monte Carlo method to calculate the overlapping area of multiple (damage) circles and complex irregular surface targets. Unlike existing technologies, this method can handle surface targets of arbitrarily complex shapes. This method can handle surface targets of any complex shape and more efficiently and accurately calculate the effective damage area, thereby assessing the effective damage area and effective damage rate of multiple projectiles striking a surface target.
[0048] The present invention evenly generates M random points within each damage circle, avoiding the constraints on assessment accuracy caused by uneven pixel density in traditional technologies. The present invention does not require the maintenance of a large number of pixel points, reducing computing resource consumption.
[0049] The present invention solves the technical problems in the existing technology of damage assessment for surface targets of arbitrary shapes and multiple artillery shells (or missiles), such as overlapping calculations, uneven pixel density, inaccurate segmentation resulting in low assessment accuracy, and large consumption of computing resources. BRIEF DESCRIPTION OF THE DRAWINGS
[0050] Figure 1 Schematic diagram of the basic steps of the method for evaluating the damage effect on a surface target according to Example 1 of the present invention;
[0051] Figure 2 This is a schematic diagram of the operation flow of the area target damage effect assessment system according to Example 2 of the present invention;
[0052] Figure 3This is an interface diagram of a surface target damage effect assessment system according to Example 2 of the present invention;
[0053] Figure 4 This is a diagram showing the evaluation result interface of the damage effect on a surface target according to Example 2 of the present invention;
[0054] Figure 5 This is a diagram showing the effect of a random simulated strike in Example 3 of the present invention;
[0055] Figure 6 This is a schematic diagram of a military target area according to Example 3 of the present invention;
[0056] Figure 7 This is a schematic diagram of selecting an aiming point for strike according to embodiment 3 of the present invention;
[0057] Figure 8 This is a schematic diagram of generating the impact points of 12 shells according to Example 3 of the present invention;
[0058] Figure 9a This is the first picture of the random damage effect of 12 shells in Example 3 of the present invention;
[0059] Figure 9b This is the second picture of the random damage effect of 12 shells in Example 3 of the present invention;
[0060] Figure 9c This is the third picture showing the random damage effect of 12 shells in Example 3 of the present invention;
[0061] Figure 9d This is the fourth picture of the random damage effect of 12 shells in Example 3 of the present invention. DETAILED DESCRIPTION
[0062] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.
[0063] Example 1
[0064] like Figure 1 As shown, the method for evaluating the damage effect of a surface target provided by the present invention includes the following basic steps:
[0065] S1. Generate target area and calculate the area of target area;
[0066] In this embodiment, a target region is generated based on the input boundary points, and the area S of the target region is calculated. In this embodiment, the calculation logic of the target region includes but is not limited to:
[0067] The area of the irregular target region was calculated using the Shoelace formula;
[0068] Alternatively, convert each vertex of the polygon into a vector, calculate the vector cross product using the cross() function in the NumPy library, and then sum and calculate the absolute value to obtain the area of the polygon;
[0069] Or directly use the area() function of the Shapely library in Python to calculate the area of an irregular polygon.
[0070] S2. Generate N impact points based on the aiming point and the projectile CEP;
[0071] In this embodiment, N is the total number of projectiles fired; CEP (circular error probable) is the circular error probability that takes into account both the system error and random error of the artillery. The standard deviation of the normal distribution is:
[0072] δ=0.8493·CEP.
[0073] S3. Generate a corresponding damage circle based on the impact point and damage radius of the projectile;
[0074] S4. Generate M points uniformly within each damage circle. In this embodiment, M is determined based on the actual damage scenario, and M is greater than a preset threshold.
[0075] S5. Traverse N×M points and calculate the overlap of each point falling into the target area;
[0076] In this embodiment, the number of random points in the target area that fall within the k damage circles is T k For example, the number of random points that fall into one damage circle is T1, the number of random points that fall into two damage circles is T2, ..., the number of random points that fall into N damage circles is T N In the processing logic of this embodiment, to determine whether a point is within the target area, for example, a ray method may be used, i.e., a ray is imagined from the point to infinity, and the positional relationship between the point and the polygon is determined by determining whether the number of intersections between the ray and the polygon is odd or even.
[0077] S6. Calculate the target damage area:
[0078]
[0079] S7. Counting the simulation calculation results for more than a preset number of times and calculating the average value, which is the assessment result of the effective damage area;
[0080] In this embodiment, the calculation is repeated from the above step S1, and the simulation calculation results of Q times (Q is large enough) are counted to obtain the average value. This is the assessment result of the effective damage area.
[0081] S8. Calculate the damage rate.
[0082] In this embodiment, the evaluation result of the effective damage rate is calculated:
[0083]
[0084] Example 2
[0085] like Figure 2 As shown, in this embodiment, the operation process of the area target damage effect assessment system includes:
[0086] S1', input artillery performance parameters;
[0087] S2', input the data of the target area;
[0088] S3', sequentially input multiple aiming point data and the corresponding number of fired shells;
[0089] S4', calculation of damage effect on area targets;
[0090] S5'. Output damage assessment results.
[0091] like Figure 3 As shown, in this embodiment, the input content of the operating software interface of the area target damage effect evaluation system includes but is not limited to: "Please enter the artillery CEP / m", "Please enter the damage radius / m", "Load target area data", "Load target area data", "Bind aiming point coordinates", "Corresponding number of shots" and other input content. The output content includes but is not limited to: "Effective damage area m 2 ”, “Effective damage rate”.
[0092] like Figure 4 As shown in FIG. 1 , in this embodiment, the CEP of the shell is 15 m and the damage radius is 30 m. In this embodiment, the enemy target area is an irregular surface target area formed by (-90, 25), (-80, -25), (0, -50), (80, -25), (90.25), and (0, 15).
[0093] In this embodiment, three aiming points are set: (-60, 0), (0, -25), and (60, 0). The number of shells fired at these three aiming points is 3, 6, and 3 respectively.
[0094] In this example, pressing "Execute Evaluation" results in Figure 3 The assessment results shown show that the effective damage area is 9251m 2 , the effective damage rate is 96.4%.
[0095] Example 3
[0096] like Figure 5 As shown, in this embodiment, pressing the "Random Effect Picture" button will display a random simulated strike effect picture. Figure 5 The blue target area is 9600m 2 , 12 shells hit the blue target area, the damage area is 8856m 2 , the damage rate was 92.2%.
[0097] like Figure 6 As shown, in this embodiment, to strike Figure 6 For example, the blue target area in the figure is input as follows: (-90, 25), (-80, -25), (0, -50), (80, -25), (90, 25), (0, 15). The target area is 9600m 2 . It is planned to fire 12 artillery shells to hit the target area.
[0098] like Figure 7 As shown, in this embodiment, the binding aiming point, the red x point is the aiming point.
[0099] like Figure 8 As shown, in this embodiment, three, six, and three shells are fired from the left, right, and right aiming points, respectively. Assume that the impact point CEP of this type of shell is 15 meters and the damage radius is 30 meters. Twelve impact points are randomly generated based on the performance parameters of the artillery.
[0100] like Figure 9a 、 Figure 9b 、 Figure 9c 、 Figure 9d As shown, in this embodiment, a damage circle is generated based on the impact point and the effective damage rate is calculated. Figure 9a The effective damage rate is 92.1%; Figure 9b The effective damage rate is 95.6%; Figure 9c The effective damage rate is 98.5%; Figure 9d The effective damage rate is 90.0%.
[0101] In this embodiment, the simulation results of 500 times (Q=500) are counted and the average value is obtained. This is the damage effect assessment result. In this example, the effective damage area assessment result is 9251m2 The effective damage rate evaluation result is 96.4%. From this embodiment, it can be seen that the system can be used to evaluate the damage effect caused by the strike plan (weapon model selection, aiming point selection, and strike ammunition allocation) and select a satisfactory strike plan based on the evaluation results.
[0102] In summary, the present invention uses the Monte Carlo algorithm to calculate the overlapping area between the target area and the damage circles of multiple artillery shells (or missiles). The calculation efficiency is high and the damage area of surface targets of arbitrarily complex shapes can be calculated. According to the selection of weapon model, the selection of aiming point, and the distribution of strike ammunition, the damage effect of multiple artillery shells (or missiles) hitting the surface target area can be effectively evaluated, thereby providing support for combat decision-making and equipment research and development.
[0103] The present invention uses the Monte Carlo method to calculate the overlapping area of multiple damage circles and complex irregular surface targets. Unlike existing technologies, this method can handle surface targets of arbitrarily complex shapes. This method can more efficiently and accurately calculate the effective damage area, thereby assessing the effective damage area and effective damage rate of multiple projectiles striking a surface target.
[0104] The present invention evenly generates M random points within each damage circle, avoiding the constraints on assessment accuracy caused by uneven pixel density in traditional technologies. The present invention does not require the maintenance of a large number of pixel points, reducing computing resource consumption.
[0105] The present invention solves the technical problems in the existing technology of damage assessment for surface targets of arbitrary shapes and multiple artillery shells (or missiles), such as overlapping calculations, uneven pixel density, inaccurate segmentation resulting in low assessment accuracy, and large consumption of computing resources.
[0106] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.
Claims
1. A method for evaluating the damage effect of a surface target, characterized in that: The method comprises: S1. Generate the target area according to the input boundary points and calculate the area of the target area; S2, generating N shell landing points according to the aiming point and weapon and ammunition accuracy data in the target area; S3, generating damage circles in sequence according to the shell landing point and damage radius; S4. Generate M random points uniformly in each damage circle; S5, traversing the N×M random points, and counting the number of random points in the target area falling into the damage circle; S6. Calculate a target damage area according to the random points and their number, the random points in the target area falling into the damage circle, the damage radius, and the area of the damage circle; S7, repeating the steps S2 to S6, counting the target damage area for more than a preset number of times, and calculating an average value as an effective damage area assessment result; S8. According to the evaluation result of the effective damage area, an effective damage rate is obtained as the evaluation result of the surface target damage effectiveness.
2. The method for evaluating the damage effect of a surface target according to claim 1, characterized in that: In the step S1, the logic for obtaining the target region area includes: the burdock formula Shoelace.
3. The method for evaluating the damage effect of a surface target according to claim 1, characterized in that: In step S1, the logic for obtaining the target area further includes: S11, according to the target area, using the cross() function in the NumPy library to calculate the vector cross product; S12. Summing the vector cross products to obtain the absolute value of the vector cross products, thereby obtaining the area of the target region.
4. The method for evaluating the damage effect of a surface target according to claim 1, characterized in that: In the step S1, the logic for obtaining the target region area further includes: using the area() function of the Shapely library in Python to obtain the target region area according to the target region.
5. The method for evaluating the damage effect of a surface target according to claim 1, characterized in that: In step S2, the following logic is used to obtain the normal distribution standard deviation δ of the shells in the target area based on the weapon and ammunition data: δ=0.8493·CEP Where CEP is the circular error probability.
6. The method for evaluating the damage effect of a surface target according to claim 1, characterized in that: In step S5, a ray method is used to imagine a ray from the random point to determine whether the random point is within the target area.
7. The method for evaluating the damage effect of a surface target according to claim 1, characterized in that: In step S6, the target damage area S is obtained using the following logic: d : Where R is the damage radius, T k is the number of random points in the damage circle, k is the number of damage circles, M is the number of random points in each damage circle, and N is the number of shell impact points.
8. The method for evaluating the damage effect of a surface target according to claim 1, characterized in that: The step S7 comprises: S71, according to a preset number of cycles, cyclically executing the steps S2 to S6 to count the target damage area of the expected number of cycles; S72, obtaining the average value of the target damage area 9. The method for evaluating the damage effect of a surface target according to claim 1, characterized in that: In step S8, the effective damage area evaluation result is processed using the following logic to obtain the effective damage rate r: Wherein, S is the area of the target area.
10. The surface target damage effect assessment system is characterized by: The system comprises: The target area processing module is used to generate the target area according to the input boundary points and calculate the area of the target area; A landing point generation module, used for generating N shell landing points according to the aiming point in the target area and the weapon and ammunition accuracy data, wherein the landing point generation module is connected to the target area area processing module; A damage circle generation module, used for generating a damage circle according to the projectile landing point and the damage radius, wherein the damage circle generation module is connected to the landing point generation module; A random point generation module, used to uniformly generate M random points in each damage circle, wherein the random point generation module is connected to the damage circle generation module; An overlap calculation module, used to traverse the N×M random points and count the number of random points in the target area falling into the damage circle, the overlap calculation module is connected to the random point generation module; A damage area processing module, used for calculating the target damage area according to the random points and their number, the number of random points in the target area falling into the damage circle, the damage radius and the area of the damage circle, and the damage area processing module is connected to the overlap calculation module; An evaluation result acquisition module, used for counting the target damage area for more than a preset number of times and obtaining an average value as an effective damage area evaluation result, wherein the evaluation result acquisition module is connected to the damage area processing module; The effective damage rate obtaining module is used to obtain the effective damage rate according to the effective damage area assessment result, and the effective damage rate obtaining module is connected to the assessment result acquisition module.
Citation Information
Patent Citations
Method for planning target aiming point opposite to multiple similar explosion-killing bullets
CN112685944A
Method for evaluating damage to opposite target by multiple types of multiple explosive bombs
CN114722573A
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