A method for evaluating the explosive quantity of air-to-surface ammunition

Abstract

This invention relates to a method for assessing the explosive yield of air-to-surface munitions, belonging to the field of air-to-surface weapon damage assessment technology. It solves the problem of inaccurate explosive yield assessment caused by the incomplete coverage and poor accuracy of existing damage probability calculations. The method includes constructing a three-dimensional model of the target based on its various components, establishing vulnerability curves, shock wave overpressure thresholds, and target damage trees for each component when hit by fragments; then, based on the warhead detonation attitude, establishing a fragment and shock wave power field model at warhead detonation to obtain the target damage probability at all detonation positions, resulting in a damage matrix; based on the circular error radius, obtaining the probability density function, and then obtaining a hit matrix of the same size as the damage matrix, further obtaining the single-shot damage probability; finally, based on the set target expected damage probability, obtaining the explosive yield, which is used as the assessment result for the explosive yield. This achieves accurate assessment of the explosive yield of air-to-surface munitions.

Description

Technical Field

[0001] The invention relates to the technical field of air-to-surface weapon damage assessment, and in particular to a method for assessing the explosive charge of air-to-surface ammunition. Background Art

[0002] In modern warfare, target damage effectiveness assessment technology is an important technology for achieving precision strikes in modern information warfare. The damage assessment of airborne weapons striking ground targets can provide a basis and support for weapon and ammunition selection, formulation of strike plans, and ammunition reserves.

[0003] At present, the existing damage probability calculation methods are based on Monte Carlo sampling, which obtains certain rendezvous postures under a certain CEP (circular error probability) distribution and then calculates the average damage probability. This cannot fully cover all probability deviations, or takes a long time to calculate a large number of samples. Therefore, the existing damage probability calculation cannot fully cover the damage probability, and the damage probability has poor accuracy, which leads to the problem of inaccurate assessment of the explosive amount of the warhead on the target. Summary of the invention

[0004] In view of the above analysis, an embodiment of the present invention aims to provide a method for evaluating the explosive quantity of air-to-surface ammunition, so as to solve the problem that the existing damage probability calculation cannot fully cover the entire area and the damage probability has poor accuracy, which causes inaccurate explosive quantity evaluation.

[0005] The embodiment of the present invention provides a method for evaluating the explosive quantity of air-to-surface ammunition, comprising the following steps:

[0006] Build a three-dimensional model of the target based on each component of the target, and establish the vulnerability curve, shock wave overpressure threshold and target damage tree of each component when hit by fragments;

[0007] According to the detonation posture of the warhead, the fragment and shock wave force field model of the warhead detonation is established, and then the target damage probability of all detonation positions is obtained based on the vulnerability curve of each component, the shock wave overpressure threshold and the target damage tree, and then the damage matrix is ​​obtained; among which, the detonation position is set according to the target;

[0008] Based on the set circular probability error radius, the probability density function is obtained, and then the hit matrix of the same size as the damage matrix is ​​obtained;

[0009] Based on the damage matrix and the hit matrix, the single-shot damage probability is obtained, and then according to the set expected damage probability of the mission, the explosive amount is obtained, and the value of the explosive amount is used as the evaluation result of the explosive amount of air-to-surface ammunition.

[0010] Furthermore, the explosive bomb quantity is obtained by the following formula: :

[0011] ,

[0012] In the formula, represents the expected damage probability of the set mission, represents the single-engine damage probability, Indicates rounding up.

[0013] Furthermore, the single-engine damage probability It is expressed as:

[0014] ,

[0015] In the formula, Indicates the first Line The target damage probability value of the column; Indicates the hit matrix Line The hit probability value of the column; , They represent the number of rows and columns of the damage matrix and the hit matrix respectively; the elements in the damage matrix correspond one to one to the elements in the hit matrix.

[0016] Further, the hit matrix Line The hit probability value of the column It is expressed as:

[0017] ,

[0018] In the formula, , Indicates the hit matrix Line The columns correspond to the damage matrix Line Column elements Axis and Axis coordinate values, It represents the standard deviation under the set circular probability error radius.

[0019] Furthermore, the standard deviation under the set circular probability error radius It is expressed as:

[0020] ,

[0021] In the formula, Indicates the set circular probable error radius.

[0022] Furthermore, the fragment and shock wave power field model includes a warhead fragment power field and a warhead shock wave power field; wherein, the warhead fragment power field is constructed based on the average mass of fragment scattering, the number of fragment scattering, the fragment velocity and the spatial distribution of fragments; and the warhead shock wave power field is established based on the shock wave overpressure.

[0023] Furthermore, the damage matrix is ​​obtained by the following method:

[0024] The ground where the target is located is taken as the plane, and the center of the bottom surface of the target is taken as the origin of the coordinate system. A coordinate system is established, and a plane matrix is ​​generated according to the set step size. Each element in the plane matrix corresponds to a position coordinate in the coordinate system, and the initial value of each element is 0.

[0025] The position coordinates of each element of the plane matrix are used as the detonation position coordinates of the warhead in turn, and the target damage probability under each detonation position coordinate is obtained;

[0026] According to the target damage probability under all detonation position coordinates, the element value of the corresponding position of the plane matrix is ​​updated to obtain the damage matrix.

[0027] Furthermore, the target damage probability of the warhead at the detonation position coordinates is obtained by the following method:

[0028] Based on the warhead fragment power field and component vulnerability curve at the detonation position coordinates, the probability of fragment damage to each target component is obtained;

[0029] Based on the warhead shock wave force field and the shock wave overpressure threshold of the component at the detonation position coordinates, the shock wave damage probability of each target component is obtained;

[0030] According to the fragment damage probability and shock wave damage probability of each component of the target, based on the target damage tree, the target damage probability of the warhead at the detonation position coordinates is obtained.

[0031] Furthermore, the probability of damage by fragments of each target component is obtained by the following method:

[0032] Determine the components where the fragment traces intersect the target based on the warhead fragment force field at the detonation position coordinates;

[0033] The corresponding fragment damage probability is obtained according to the vulnerability curves of the intersecting components, and the fragment damage probability of the non-intersecting components is set to 0 to obtain the fragment damage probability of each target component.

[0034] Furthermore, the shock wave damage probability of each target component is obtained by the following method:

[0035] The shock wave overpressure of each target component is obtained according to the warhead shock wave force field at the detonation position coordinates;

[0036] The shock wave damage probability of each target component is obtained by setting the shock wave damage probability of the component whose shock wave overpressure is greater than or equal to the corresponding shock wave overpressure threshold to 1, and setting the shock wave damage probability of the component whose shock wave overpressure is less than the corresponding shock wave overpressure threshold to 0.

[0037] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0038] The present invention provides an explosive quantity evaluation method for air-to-surface ammunition. The method establishes a fragment and shock wave force field model when a warhead is detonated based on a target, obtains the target damage probability of all detonation positions based on the established vulnerability curves of various components, the shock wave overpressure threshold and the target damage tree, and then obtains a damage matrix. Based on a set circular probability error radius, a probability density function is obtained, and then a hit matrix with the same size as the damage matrix is ​​obtained. Thus, the single-shot damage probability is obtained, and then the explosive quantity is obtained. The hit matrix obtained by the probability density function simulates the uncertainty of the warhead during flight, covers various possible deviation problems, and more truly and accurately calculates the damage effect and damage probability of the warhead on the target in each trajectory, thereby realizing accurate evaluation of the explosive quantity. A more accurate and effective reference basis is provided for the formulation of combat indicators such as the attack direction, firepower density and strike posture of a secondary strike.

[0039] In the present invention, the above-mentioned technical solutions can also be combined with each other to achieve more preferred combination solutions. Other features and advantages of the present invention will be described in the subsequent description, and some advantages can become obvious from the description, or can be understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained through the contents particularly pointed out in the description and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The accompanying drawings are only used for the purpose of illustrating specific embodiments and are not to be considered as limiting the present invention. In the entire drawings, the same reference symbols represent the same components;

[0041] Figure 1 A schematic flow chart of a method for evaluating the explosive charge of an air-to-surface ammunition provided by an embodiment of the present invention;

[0042] Figure 2 A schematic diagram of a vulnerability curve provided by an embodiment of the present invention;

[0043] Figure 3 A schematic diagram of a ground aircraft provided by an embodiment of the present invention;

[0044] Figure 4 A schematic diagram of a target damage tree for a ground aircraft provided by an embodiment of the present invention;

[0045] Figure 5 A damage matrix of a certain type of warhead to a certain type of target provided by an embodiment of the present invention;

[0046] Figure 6 A schematic diagram of the hit probability obtained by the probability density function provided by an embodiment of the present invention;

[0047] Figure 7 A hit matrix of a certain type of warhead on a certain type of target provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0048] The preferred embodiments of the present invention are described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not used to limit the scope of the present invention.

[0049] A specific embodiment of the present invention discloses a method for evaluating the explosive charge of an air-to-surface ammunition, such as Figure 1 As shown, the following steps are included:

[0050] S1. Build a three-dimensional model of the target based on each component of the target, and establish the vulnerability curve, shock wave overpressure threshold and target damage tree of each component when hit by fragments.

[0051] Specifically, a target three-dimensional model is constructed according to the physical properties and component positions of each target component; wherein the physical properties include the size of the component, material density, material yield strength and material ultimate strength.

[0052] More specifically, the target in this embodiment is a ground target, such as a car, an airplane, etc. on the ground.

[0053] Specifically, the vulnerability curve is a curve that shows the probability of being penetrated when being hit by fragments of a certain mass and different speeds, such as Figure 2 As shown, it is the vulnerability curve under two kinds of mass fragments, the horizontal axis represents the fragment velocity, and the vertical axis represents the breakdown probability; in this embodiment, the vulnerability curve when the component is hit by the fragment is established by the following formula:

[0054] ,

[0055] In the formula, represents the probability of damage caused by fragments penetrating components, It represents the specific kinetic energy received by the component surface per unit thickness.

[0056] More specifically, the specific kinetic energy received per unit thickness of the component surface element It is expressed as:

[0057] ,

[0058] In the formula, Indicates the quality of the fragments, Indicates the impact speed of the fragments, represents the fragment shape factor, represents the penetration thickness in the case of surface element breakdown, Indicates the actual thickness of the surface element. It represents the angle between the impact direction of the fragment and the surface normal.

[0059] Specifically, the shock wave overpressure threshold is the damage threshold under the shock wave overpressure, expressed as:

[0060] ,

[0061] Among them, when hour,

[0062] ,

[0063] when hour,

[0064] ,

[0065] in, , , ;

[0066] In the formula, Indicates the half length of the component material side. represents the shock wave load action time, Indicates the material density of the component; Indicates the yield stress of the component material; It means the relative plate thickness of the material minus 1 / 2 of the relative half width of the material; Represents the ultimate strain of the material; It represents the ultimate bending moment per unit width of the component material sheet.

[0067] Specifically, a target damage tree is established based on the following analysis:

[0068] The target is divided into multiple subsystems (for example, ground vehicle targets can be divided into power systems, control systems, fire control systems, fuel supply systems, etc.), and each subsystem can be further divided into one or more components. According to the importance of the components in the subsystem function, they are divided into key components and non-key components, redundant components and non-redundant components. Among them, key components are components that will kill the target when the component is destroyed, while non-key components will not directly cause the target to be destroyed; redundant components are components with redundancy design, and non-redundant components are components without redundancy design.

[0069] For the target The probability of a component being damaged by a single fragment It is through The probability of damage by fragments obtained by the fragility curve of each component and the probability of blast damage derived from the blast overpressure threshold Get, specifically , where if the shock wave overpressure is less than the shock wave overpressure threshold, the shock wave damage probability is 0, otherwise the shock wave damage probability is 1.

[0070] For a single fragment, the probability of a subsystem being damaged is It is expressed as:

[0071] ,

[0072] In the formula, Indicates the subsystem The probability of damage to a key non-redundant component; Represents the number of critical non-redundant components in a subsystem.

[0073] For the subsystem Key non-redundant components, After a fragment hits, the probability of damage is It is expressed as:

[0074] ,

[0075] In the formula, Indicates hitting The number of fragments of a critical non-redundant component, Indicates The key non-redundant components are The probability of damage from a fragment hit.

[0076] Then the probability of damage to the subsystem when it is hit by multiple fragments is expressed as:

[0077] ,

[0078] The damage mode analysis of the target when hit by the warhead is actually based on the target damage tree, that is, to analyze and determine each possible damage, analyze its local and final impact on the target, and the final result depends on the functional composition of the target itself. The damage tree is generally built in a top-down manner, that is, first divide the target into several subsystems according to the function or reliability model, and clarify the corresponding structural composition of the subsystem, and each subsystem damage is regarded as a damage tree item event; then divide the subsystem into several functional units, and the damage of the functional unit is regarded as an intermediate event; then divide the functional unit into the component level, and the component damage is regarded as the bottom event of the damage, and clarify the key components of the target, explain the vulnerability of the key components and the possible fragment damage and shock wave damage; finally, use appropriate logic gates to connect the events at all levels, so as to establish the target damage tree. Among them, vulnerability includes vulnerability curve and shock wave overpressure threshold.

[0079] Due to the characteristics of ground targets and the damage mode, degree, troubleshooting and time required to restore combat capability of each subsystem and its components after being hit by fragments and the shock wave overpressure, these are the main factors affecting the combat effectiveness of the entire system, reflecting the degree of damage to the target. Based on the above analysis, the damage of the ground target system is divided into different damage levels. According to the damage of targets of different damage levels, the structure and function of each key component and its vulnerability under the action of fragments and overpressure are analyzed. According to the materials and structures of different components, the vulnerability curve affected by fragment penetration is constructed, and the shock wave overpressure threshold affected by shock wave overpressure is analyzed. The relationship between each key component and the impact of key component damage on the overall target function are analyzed, and finally the damage tree of each level is established. Among them, "or" means that damage is caused if a single component is damaged, and "and" means that damage is satisfied if all components are damaged.

[0080] Based on this, in this embodiment, the target damage tree is established in the following manner:

[0081] Classify damage levels according to combat requirements;

[0082] Based on the divided damage levels, the functions of each damage level are determined by analyzing the target characteristics; that is, by analyzing the target characteristics, the functions that can meet the requirements of the damage level are obtained; wherein the functions here are functions realized by the subsystems or target components of the target.

[0083] Based on the relationship between the target components, subsystems and the functions of each damage level, a logic gate is established to generate a target damage tree; among them, based on the vulnerability of each target component, the damage criterion of each target component is established, and the damage criterion is the damage probability of the component determined by the vulnerability curve and the shock wave overpressure threshold. For example, if the classification level includes F-level damage and M-level damage, where F-level damage means that it cannot be repaired within 24 hours and M-level damage means that it is impossible to continue the action, then when constructing the damage tree, the M-level damage tree will consider the power system, fuel system and control system, and the F-level damage tree will consider some components and subsystems that can be repaired by replacing parts.

[0084] For example, Figure 3 The key components of a ground aircraft shown in the figure are the engine, the weapon compartment, and the fuel tank A and fuel tank B. The target damage tree of these four key components is as follows: Figure 4 shown.

[0085] S2. According to the warhead detonation posture, a fragment and shock wave force field model is established when the warhead is detonated. Then, based on the vulnerability curve of each component, the shock wave overpressure threshold and the target damage tree, the target damage probability of all detonation positions is obtained, and then the damage matrix is ​​obtained; among them, the detonation position is set according to the target.

[0086] Specifically, the warhead detonation posture includes pitch angle, yaw angle and roll angle.

[0087] During implementation, in step S2, the fragment and shock wave power field model includes the warhead fragment power field and the warhead shock wave power field; wherein, the warhead fragment power field is established based on the average mass of fragment scattering, the number of fragment scattering, the fragment velocity and the spatial distribution of fragments; and the warhead shock wave power field is established based on the shock wave overpressure.

[0088] In specific implementation, in the warhead fragmentation force field:

[0089] Spatial distribution of fragments:

[0090] ,

[0091] In the formula, represents the spatial distribution function of fragments, Indicates the fragment dispersion angle, Indicates the number of fragments within the cone formed by the fragment dispersion angle. Indicates that the cone range changes to The change in the number of fragments is Indicates the total number of fragments formed by the warhead explosion.

[0092] Average mass of scattered fragments :

[0093] ,

[0094] In the formula, represents the average thickness of the shell, represents the average inner diameter of the shell, Represents the mass of the shell, Indicates the mass of explosive charge, Indicates the coefficient determined according to the explosive.

[0095] The number of fragments scattered is the mass of a single fragment. to The cumulative number between , expressed as:

[0096] ,

[0097] In the formula, Indicates fragment velocity, Indicates the total number of fragments produced by the warhead.

[0098] Fragment speed :

[0099] ,

[0100] In the formula, It indicates the ratio of charge mass to shell mass; Indicates the Gurney velocity, which is determined by factors such as the type of explosive and the filling density.

[0101] During specific implementation, in the warhead shock wave force field:

[0102] Shock wave overpressure , expressed as:

[0103] when hour,

[0104] ,

[0105] when hour,

[0106] ,

[0107] when hour,

[0108] ,

[0109] In the formula, Indicates the equivalent TNT bare charge mass of the warhead, Indicates the distance from the center of the explosion.

[0110] During implementation, in step S2, the damage matrix is ​​obtained by:

[0111] S21. Take the ground where the target is located as a plane and the center of the bottom surface of the target as the origin of the coordinate system, establish a coordinate system, and generate a plane matrix according to the set step size; wherein each element in the plane matrix corresponds to a position coordinate of the coordinate system, and the initial value of each element is 0.

[0112] S22. The position coordinates of each element of the plane matrix are used as the detonation position coordinates of the warhead in turn to obtain the target damage probability at each corresponding detonation position coordinate.

[0113] S23. Update the element value of the corresponding position of the plane matrix according to the target damage probability under all detonation position coordinates to obtain a damage matrix.

[0114] It should be noted that when obtaining the target damage probability at each detonation position coordinate, except for the change in the detonation position coordinate, other settings remain unchanged.

[0115] Specifically, in step S21, the plane matrix is ​​the minimum matrix containing the coordinates of all the target projection points on the ground; by projecting the target vertically onto the ground, based on the coordinates of all the projection points, the maximum and minimum values ​​on each coordinate axis are statistically obtained, and the maximum value minus the minimum value on the X-axis is used as the number of columns of the plane matrix, and the maximum value minus the minimum value on the Y-axis is used as the number of rows of the plane matrix, so as to generate the plane matrix.

[0116] More specifically, the step size is set according to actual capabilities and needs. The smaller the step size is, the longer the calculation time is and the higher the accuracy is. Exemplarily, the step size is set to 1m.

[0117] It can be understood that by establishing a coordinate system on the plane and fixing the warhead detonation position on each target plane, situations that are impossible to occur in actual combat can be avoided when randomly sampling the trajectory, making the results of the numerical simulation more realistic and reliable.

[0118] In specific implementation, in step S22, the target damage probability of the warhead at the detonation position coordinates is obtained by the following method:

[0119] S221. Based on the warhead fragment power field and component vulnerability curves at the detonation position coordinates, obtain the fragment damage probability of each target component.

[0120] Specifically, the probability of damage by fragments of each target component is obtained in the following way:

[0121] Determine the components where the fragment traces intersect the target based on the warhead fragment force field at the detonation position coordinates;

[0122] According to the vulnerability curves of the intersecting components, the corresponding fragment damage probabilities are obtained, and the fragment damage probabilities of the non-intersecting components are set to 0, and the fragment damage probabilities of the target components are obtained. Among them, the same component includes one or more fragment damage probabilities. It can be understood that a single component may intersect with multiple fragment traces, and the fragment damage probabilities of the component under each intersecting fragment trace are obtained.

[0123] Among them, the fragment trajectory can be drawn according to the average mass of fragments scattered in the fragment power field, the number of fragments scattered, the fragment speed and the fragment spatial distribution, and the components intersecting with the target can be obtained. The drawing method can be realized by existing technology and will not be repeated here.

[0124] S222. Based on the warhead shock wave force field and the shock wave overpressure threshold of the component at the detonation position coordinates, obtain the shock wave damage probability of each target component.

[0125] Specifically, the shock wave damage probability of each target component is obtained by the following method:

[0126] The shock wave overpressure of each target component is obtained according to the warhead shock wave force field at the detonation position coordinates;

[0127] The shock wave damage probability of each target component is obtained by setting the shock wave damage probability of the component whose shock wave overpressure is greater than or equal to the corresponding shock wave overpressure threshold to 1, and setting the shock wave damage probability of the component whose shock wave overpressure is less than the corresponding shock wave overpressure threshold to 0.

[0128] S223. According to the fragment damage probability and shock wave damage probability of each target component, based on the target damage tree, obtain the target damage probability of the warhead at the detonation position coordinates.

[0129] Specifically, damage is determined when damage is caused by any one of the damage elements, fragments and shock waves. Based on formula (5), the damage probability of a single component being hit by multiple fragments can be obtained. Based on this, based on the subsystem damage probability formula of formula (6) and the logical gate relationship of the target damage tree, the target damage probability can be obtained.

[0130] For example, Figure 4 In the target damage tree shown in the figure, the engine is hit by fragments 1 and 2, the probability of damage by fragments is 0.5, and the probability of damage by shock waves is 0. Then the probability of damage to the engine is ; The weapon compartment is hit by fragment 3, the probability of damage by fragments is 0.5, and the probability of damage by shock waves is 0, then the probability of damage to the weapon compartment is Fuel tank 1 is hit by fragment 4, and fuel tank 2 is hit by fragment 5. The probability of damage by fragments is 0.5. The probability of damage by shock wave to fuel tank 1 is 0, and the probability of damage to fuel tank 2 is 1. Based on the logical relationship of "and" between fuel tank 1 and fuel tank 2, the damage probability of the fuel system is Based on the logical relationship of "or" among the engine, weapon bay and fuel system, the target damage probability of the ground aircraft can be deduced as .

[0131] Specifically, after obtaining the target damage probability at all detonation position coordinates, the target damage probability at each coordinate position is used as the element value of the corresponding coordinate position of the plane matrix, and the plane matrix at this time is used as the damage matrix.

[0132] S3. Based on the set circular probability error radius, a probability density function is obtained, and then a hit matrix of the same size as the damage matrix is ​​obtained.

[0133] During implementation, the hit matrix Line The hit probability value of the column It is expressed as:

[0134] ,

[0135] In the formula, , Indicates the hit matrix Line The columns correspond to the damage matrix Line Column elements Axis and Axis coordinate values, It represents the standard deviation under the set circular probability error radius.

[0136] Specifically, the standard deviation under the set circular probability error radius is It is expressed as:

[0137] ,

[0138] In the formula, Indicates the set circular probable error radius.

[0139] It should be noted that the hit matrix is ​​obtained by the following derivation:

[0140] It is generally believed that the x and y coordinates of the bomb's landing point are independent random variables and follow a normal distribution about the center of distribution. According to the two-dimensional normal distribution law, when the system error is not considered, the probability density function of the two-dimensional normal distribution of the landing point on the plane where the target is located is expressed as:

[0141] ,

[0142] In the formula, Indicates that the drop point appears at The probability of being at , Respectively represent the standard deviation in the x-axis direction and the y-axis direction, reflecting the degree of discreteness of the data set; , Respectively represent the expected values ​​of the landing point in the x-axis direction and the y-axis direction, represents the joint distribution.

[0143] When considering the drop point, the drop point appears in the x-axis and y-axis directions with the same degree of discreteness, so ; The aiming position is the center point (0,0), so the joint distribution .

[0144] After simplification, we can get:

[0145] ,

[0146] When the area of ​​the target region is When the probability density function of the projectile drop distribution is known, the hit probability can be obtained by integrating the probability density function in the target area. , that is, the landing point appears at Probability in the region for:

[0147] ,

[0148] Substituting into formula (17), we get

[0149] ,

[0150] The circular error probability (CEP) is a circle with a radius of 50% with the aiming point as the center. Under stable shooting conditions, 50% of the landing points will be within this circle. According to the definition, the circular error probability is calculated by integrating the circular area with the origin at the aiming center using formula (19):

[0151] ,

[0152] By trigonometric substitution, , Converting the rectangular coordinate system to the polar coordinate system yields:

[0153] ,

[0154] In the formula, Represents the polar diameter in polar coordinates; Represents the polar angle in polar coordinates; It represents the circular probability deviation radius, that is, the radius of the circle that contains 50% of the impact points in the circular probability deviation; It represents the standard deviation, which reflects the degree of dispersion of a data set.

[0155] Points:

[0156] ,

[0157] The circular probability deviation radius is obtained as follows:

[0158] ,

[0159] The relationship between the circular probability deviation radius and the standard deviation is obtained from equation (23). Let the coincidence point between the center of the damage matrix and the center of the two-dimensional normal distribution probability density function be the origin. , at this time, the probability density function represents the hit probability of each coordinate position in the coordinate system, which is expressed as:

[0160] ,

[0161] in, ;

[0162] Therefore, based on the coordinates corresponding to each element of the damage matrix and the obtained probability density function, a hit matrix equal to the size of the damage matrix is ​​obtained, and the elements in the damage matrix correspond one to one to the elements in the hit matrix.

[0163] S4. Based on the damage matrix and the hit matrix, the single-shot damage probability is obtained, and then the explosive amount is obtained according to the set expected damage probability of the mission, and the value of the explosive amount is used as the evaluation result of the explosive amount of air-to-surface ammunition.

[0164] When implemented, the single-engine damage probability It is expressed as:

[0165] ,

[0166] In the formula, Indicates the first Line The target damage probability value of the column; Indicates the hit matrix Line The hit probability value of the column; , They represent the number of rows and columns of the damage matrix and the hit matrix respectively; the elements in the damage matrix correspond one to one to the elements in the hit matrix.

[0167] During implementation, the explosive bomb quantity is obtained by the following formula: :

[0168] ,

[0169] In the formula, represents the expected damage probability of the set mission, represents the single-engine damage probability, Indicates rounding up.

[0170] Specifically, under normal circumstances, the probability of damage from a single projectile cannot reach 100%. In order to meet the needs of combat missions, it is necessary to evaluate the explosive quantity. The explosive quantity refers to the minimum amount of ammunition required to project ammunition until the probability of damage to the target meets the mission expectations, that is, to meet:

[0171] ,

[0172] After simplification, we can get the explosive bomb quantity :

[0173] ,

[0174] In the formula, represents the expected damage probability of the set mission, represents the single-engine damage probability, Indicates rounding up.

[0175] The explosive amount As an evaluation result of the explosive bomb quantity, it provides an accurate and effective reference basis for the formulation of combat indicators such as attack direction, firepower density, and strike posture of the subsequent secondary strike.

[0176] For example, taking a certain type of warhead against a certain type of target as an example, a certain missile-target intersection posture is selected, assuming that the target is fixed at the center of the horizontal plane, and the probability of the warhead causing damage to the target at any position on the target plane is calculated, and the damage matrix is ​​drawn, such as Figure 5 shown.

[0177] Assuming that the circular probability deviation radius of the modified air-to-surface warhead is 20m, the standard deviation is:

[0178] ,

[0179] According to the probability density function, the probability of the warhead hitting the horizontal plane can be obtained, as follows: Figure 6 As shown in the figure, any point on the probability density function The meaning is that the warhead appears in The probability value at Discretizing the probability density function into a matrix of the same size as the damage matrix yields the hit matrix, as Figure 7 shown.

[0180] Get the single-engine damage probability :

[0181] ,

[0182] Assuming that the expected probability of damage to the target during combat is 80%, the amount of explosive bombs is:

[0183] ,

[0184] Therefore, the evaluation result of the explosive bomb quantity is 3.

[0185] Compared with the prior art, the present embodiment provides a method for evaluating the explosive quantity of air-to-surface ammunition, which establishes a fragment and shock wave force field model when the warhead is detonated based on the target, and then obtains the target damage probability of all detonation positions based on the established vulnerability curves of each component and the shock wave overpressure threshold and target damage tree, and then obtains the damage matrix, and then obtains the probability density function based on the set circular probability error radius, and then obtains the hit matrix of the same size as the damage matrix; thereby, the single-shot damage probability is obtained, and then the explosive quantity is obtained. The hit matrix obtained by the probability density function simulates the uncertainty of the warhead during flight, covers various possible deviation problems, and more realistically and accurately calculates the damage effect and damage probability of the warhead on the target in each trajectory, thereby achieving accurate evaluation of the explosive quantity, and more accurately and effectively providing a reference basis for the formulation of combat indicators such as the attack direction, firepower density, and strike posture of the secondary strike.

[0186] Those skilled in the art will appreciate that all or part of the processes of the above-mentioned embodiments can be implemented by instructing related hardware through a computer program, and the program can be stored in a computer-readable storage medium, wherein the computer-readable storage medium is a disk, an optical disk, a read-only storage memory, or a random access memory, etc.

[0187] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for evaluating the explosive quantity of air-to-surface ammunition, characterized in that: The following steps are involved: Build a three-dimensional model of the target based on each component of the target, and establish the vulnerability curve, shock wave overpressure threshold and target damage tree of each component when hit by fragments; According to the detonation posture of the warhead, the fragment and shock wave force field model of the warhead detonation is established, and then the target damage probability of all detonation positions is obtained based on the vulnerability curve of each component, the shock wave overpressure threshold and the target damage tree, and then the damage matrix is ​​obtained; among which, the detonation position is set according to the target; Based on the set circular probability error radius, the probability density function is obtained, and then the hit matrix of the same size as the damage matrix is ​​obtained; Based on the damage matrix and the hit matrix, a single-shot damage probability is obtained, and then according to the set expected damage probability of the mission, the explosive amount is obtained, and the value of the explosive amount is used as an evaluation result of the explosive amount of air-to-surface ammunition; The explosive charge is obtained by the following formula : ， In the formula, represents the expected damage probability of the set mission, represents the single-engine damage probability, Indicates rounding up; The single-engine damage probability It is expressed as: ， In the formula, Indicates the first Line The target damage probability value of the column; Indicates the hit matrix Line The hit probability value of the column; , Respectively represent the number of rows and columns of the damage matrix and the hit matrix; the elements in the damage matrix correspond one to one with the elements in the hit matrix; The hit matrix Line Hit probability value of the column It is expressed as: ， In the formula, , Indicates the hit matrix Line The columns correspond to the damage matrix Line Column elements Axis and Axis coordinate values, It represents the standard deviation under the set circular probability error radius.

2. The method for evaluating the explosive quantity of air-to-surface ammunition according to claim 1, characterized in that: The standard deviation under the set circular probability error radius It is expressed as: ， In the formula, Indicates the set circular probable error radius.

3. The method for evaluating the explosive quantity of air-to-surface ammunition according to claim 1, characterized in that: The fragment and shock wave power field model includes a warhead fragment power field and a warhead shock wave power field; wherein, the warhead fragment power field is constructed according to the average mass of fragment scattering, the number of fragment scattering, the fragment velocity and the spatial distribution of fragments; and the warhead shock wave power field is established according to the shock wave overpressure.

4. The method for evaluating the explosive quantity of air-to-surface ammunition according to claim 3, characterized in that: The damage matrix is ​​obtained by: The ground where the target is located is taken as the plane, and the center of the bottom surface of the target is taken as the origin of the coordinate system. A coordinate system is established, and a plane matrix is ​​generated according to the set step size. Each element in the plane matrix corresponds to a position coordinate in the coordinate system, and the initial value of each element is 0. The position coordinates of each element of the plane matrix are used as the detonation position coordinates of the warhead in turn, and the target damage probability under each detonation position coordinate is obtained; According to the target damage probability under all detonation position coordinates, the element value of the corresponding position of the plane matrix is ​​updated to obtain the damage matrix.

5. The method for evaluating the explosive quantity of air-to-surface ammunition according to claim 4, characterized in that: The target damage probability of the warhead at the detonation position coordinates is obtained by the following method: Based on the warhead fragment power field and component vulnerability curve at the detonation position coordinates, the probability of fragment damage to each target component is obtained; Based on the warhead shock wave force field and the shock wave overpressure threshold of the component at the detonation position coordinates, the shock wave damage probability of each target component is obtained; According to the fragment damage probability and shock wave damage probability of each component of the target, based on the target damage tree, the target damage probability of the warhead at the detonation position coordinates is obtained.

6. The method for evaluating the explosive quantity of air-to-surface ammunition according to claim 5, characterized in that: The probability of fragment damage of each target component is obtained by the following method: Determine the components where the fragment traces intersect the target based on the warhead fragment force field at the detonation position coordinates; The corresponding fragment damage probability is obtained according to the vulnerability curves of the intersecting components, and the fragment damage probability of the non-intersecting components is set to 0 to obtain the fragment damage probability of each target component.

7. The method for evaluating the explosive quantity of air-to-surface ammunition according to claim 5, characterized in that: The shock wave damage probability of each target component is obtained by the following method: The shock wave overpressure of each target component is obtained according to the warhead shock wave force field at the detonation position coordinates; The shock wave damage probability of each target component is obtained by setting the shock wave damage probability of the component whose shock wave overpressure is greater than or equal to the corresponding shock wave overpressure threshold to 1, and setting the shock wave damage probability of the component whose shock wave overpressure is less than the corresponding shock wave overpressure threshold to 0.

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