A method for calculating damage probability based on machine learning classifiers

Abstract

This invention discloses a damage probability calculation method based on a machine learning classifier, comprising: establishing a damage probability calculation model for a fragmentation warhead against a target; performing a large number of random calculations on all random parameters affecting the calculation results according to the damage probability calculation model; approximating the damage probability results in a large number of case data into two classes (0 and 1) or three classes (0, 0.5, and 1); training the above case data using a classifier to obtain a damage probability prediction model; and using the damage probability prediction model to calculate the average single-shot damage probability of the fragmentation warhead against the target under specific projectile-target encounter conditions. Compared with conventional methods for calculating damage probability, this machine learning classifier-based damage probability calculation method ensures a certain level of accuracy while reducing the computational load and significantly shortening the calculation time.

Description

Technical Field

[0001] This invention belongs to the field of damage assessment technology, specifically relating to a damage probability calculation method based on a machine learning classifier. Background Technology

[0002] To accurately assess the damage effect of fragmentation warheads on targets and facilitate research on warhead coordination, it is necessary to establish a corresponding damage probability calculation model based on target vulnerability analysis.

[0003] The commonly used damage probability represents the probability that a warhead will damage a target. Existing methods for calculating the damage probability of fragmentation warheads are computationally intensive. In MATLAB, for complex cases, it often takes hundreds or even thousands of seconds to calculate a single result, and the computational load increases exponentially with the number of fragments. When further calculating the average single-shot damage probability using the Monte Carlo method with 1000 random repetitions, the calculation time can reach days. Therefore, a method is needed to quickly calculate the damage probability of a fragmentation warhead on a target while ensuring a certain level of accuracy. Summary of the Invention

[0004] The purpose of this invention is to overcome the aforementioned shortcomings and provide a damage probability calculation method based on a machine learning classifier. The method includes: establishing a damage probability calculation model for a fragmentation warhead against a target; performing a large number of random calculations based on the Monte Carlo method for all random parameters affecting the calculation results according to the above damage probability calculation model, with each parameter randomly selected in each calculation; approximating the damage probability results in the large number of example data obtained in the previous step into two classes (0 and 1) or three classes (0, 0.5, and 1); training the above example data using a machine learning classifier, and applying an optimization iterative process to some classifier algorithms to improve classifier performance, ultimately obtaining a damage probability prediction model; and using the obtained damage probability prediction model to calculate the average single-shot damage probability of the fragmentation warhead against the target under specific projectile-target encounter conditions. Compared with current conventional methods for calculating damage probability, this machine learning classifier-based damage probability calculation method ensures a certain level of accuracy while reducing the computational load and significantly shortening the calculation time.

[0005] To achieve the above-mentioned objectives, the present invention provides the following technical solution:

[0006] A damage probability calculation method based on a machine learning classifier includes:

[0007] Based on the three-dimensional model of the target, a vulnerability analysis is performed on the target's components; based on the vulnerability analysis results, a calculation model is established for the damage probability of the fragmentation warhead to the target.

[0008] Based on the damage probability calculation model, for all random parameters that affect the calculation results, repeated random calculations based on the Monte Carlo method are carried out more than m times to obtain a large number of damage probability calculation case data for different damage levels; each calculation case data contains a set of random parameter arrays of independent variables and damage probability result values ​​for different levels corresponding to the random parameter arrays; m>10000;

[0009] A large amount of damage probability calculation data is organized into a set of predictive variables and a set of responses; the set of predictive variables is the set of random parameter arrays in all calculation data, and the set of responses is the set of damage probabilities at different levels corresponding to the random parameter arrays; in the set of responses, the damage probability data is approximated to two classes of 0 or 1 or three classes of 0, 0.5 and 1 according to the actual value of the damage probability in the interval [0,1].

[0010] By using a classifier algorithm in machine learning to train the set of prediction variables as input and the set of responses as output, a damage probability prediction model for different damage levels is obtained.

[0011] Under specific projectile-target encounter conditions, the relevant random parameters in the damage probability prediction model, i.e., the random parameters in the input random parameter array that are related to the specific projectile-target encounter conditions, are set to fixed values, while the remaining random parameters in the input random parameter array are still random values ​​within a specific range. The Monte Carlo method is used to perform more than n repeated random calculations based on the damage probability prediction model to predict the average single-shot damage probability of the fragmentation warhead on the target under the specific projectile-target encounter conditions; n>500.

[0012] Furthermore, based on the actual damage probability values ​​in the [0,1] interval, the specific method for approximating the damage probability data as either 0 or 1 (two classes) or 0, 0.5, and 1 (three classes) is as follows:

[0013] The actual value of the damage probability is classified by mathematical approximation through rounding: when the damage probability is below 0.5, it is approximated as 0; when the damage probability is 0.5 or above, it is approximated as 1. Alternatively, when the damage probability is below 0.25, it is approximated as 1; when the damage probability is 0.25 or above but below 0.75, it is approximated as 0.5; and when the damage probability is 0.75 or above, it is approximated as 1.

[0014] Furthermore, the classifier algorithm is one of the following: logistic regression algorithm, naive Bayes algorithm, decision tree algorithm, discriminant analysis algorithm, support vector machine algorithm, nearest neighbor algorithm, or ensemble learning algorithm.

[0015] Furthermore, in the classifier algorithm, the accuracy of the prediction result is adjusted by the misclassification cost; the basis for ending the training of the classifier algorithm is the maximum training time or the maximum number of iterations.

[0016] Classifier validation methods include cross-validation, hold-out validation, or no validation.

[0017] Furthermore, the random parameters include: the detonation position of the fragmentation warhead, the missile's entry angle, the missile's pitch angle, the missile's trajectory angle, the missile's yaw angle, the missile's miss distance, the missile's terminal velocity, the angle between the missile's terminal velocity vector and the ground, or the guidance accuracy probability error.

[0018] The missile's angle of entry is randomly selected from an average distribution within the range of 0° to 360°;

[0019] The missile's trajectory angle is randomly selected from a uniform distribution within the range of -10° to 0°;

[0020] The missile's yaw angle is randomly selected from a uniform distribution within an atmosphere ranging from -2° to 2°.

[0021] The missile's terminal velocity is randomly selected from a uniform distribution between 200m / s and 300m / s;

[0022] The vertical miss distance of the missile is randomly selected from -1m to 1m according to a normal distribution.

[0023] Furthermore, according to the damage probability calculation model, when conducting repeated random calculations based on the Monte Carlo method more than m times for all random parameters affecting the calculation results, it is also necessary to predetermine the input constants. The constants include the physical parameters of the warhead itself, the flight parameters of the warhead, and the detection range and detonation delay of the fuze. The physical parameters of the warhead itself include the structure and number of pre-fragmented fragments, the equivalent TNT charge of the warhead, and the charge coefficient of the warhead. The flight parameters of the warhead include the slip angle of the warhead.

[0024] Furthermore, the damage probability calculation model is as follows:

[0025]

[0026] Where, N or P represents the number of non-redundant components, k represents the number of redundant component groups, and P represents the number of non-redundant components. or,i Let M1, M2, ..., M be the probability of failure for each non-redundant component; k These represent the number of redundant components in each redundant component group; P and,j The probability of damage to each component in the redundant component group is given. The target consists of multiple redundant components and multiple non-redundant components. If all redundant components in any one redundant component group are damaged, the target is considered damaged. If any one non-redundant component is damaged, the target is considered damaged.

[0027] Furthermore, the different damage levels include: M-level mission damage, F-level fire control damage, and K-level catastrophic damage; M-level mission damage indicates that the target's functional components cannot fully perform their intended functions and require 1 to 24 hours to remove the obstruction; F-level fire control damage indicates that the target's functional components have lost their operational capability and require 1 to 7 days and nights to remove the obstruction; K-level catastrophic damage indicates that the target weapon system has lost its combat capability and cannot be repaired or that repairing the damage is economically infeasible.

[0028] Furthermore, the parameters required to be set in the decision tree algorithm include the maximum number of classifications, classification criteria, and alternative decision splits;

[0029] The parameters required to be set in the discriminant analysis algorithm include the covariance structure;

[0030] The parameters required to be set in the support vector machine algorithm include kernel function, box constraint level, and kernel scale mode.

[0031] The parameters required to be set in the nearest neighbor algorithm include the number of neighboring points, distance metric, and distance weight;

[0032] The parameters that need to be set in the ensemble learning algorithm include the ensemble method, learner type, maximum number of splits, and number of learners.

[0033] Furthermore, when the classifier algorithm is an algorithm other than logistic regression, an optimizer is used to iteratively optimize the various adjustment parameters of the classifier algorithm, and after dozens of iterations, an optimized damage probability prediction model is obtained.

[0034] Compared with the prior art, the present invention has the following advantages:

[0035] 1) The method of the present invention uses a damage probability prediction model instead of the original damage probability calculation model, which greatly reduces the amount of calculation and improves the calculation efficiency by more than 20 times.

[0036] 2) The average single-shot damage probability obtained by Monte Carlo calculation using the damage probability prediction model of the present invention can achieve an average accuracy of more than 75% compared with the result obtained by Monte Carlo calculation using the damage probability calculation model.

[0037] 3) The method of the present invention approximates the damage probability, which improves classification efficiency while ensuring accuracy and avoids a huge amount of computation. Attached Figure Description

[0038] Figure 1 This is a flowchart of the damage probability calculation method based on a machine learning classifier according to the present invention. Detailed Implementation

[0039] The features and advantages of the present invention will become clearer and more apparent from the following detailed description.

[0040] The term “exemplary” as used herein means “serving as an example, embodiment, or illustration.” Any embodiment illustrated herein as “exemplary” is not necessarily to be construed as superior to or better than other embodiments. Although various aspects of embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless specifically indicated otherwise.

[0041] First, a three-dimensional model of the target is established, and its components are subjected to vulnerability analysis. Then, a model for calculating the damage probability of the fragmentation warhead on the target is established. Further, over 10,000 random calculations are performed using the Monte Carlo method for all random parameters affecting the calculation results, such as projectile-target characteristics and encounter conditions. In each calculation, each random parameter takes a value randomly based on its own characteristics. The damage probability results from the large amount of example data obtained in the previous step are approximated as two classes (0 and 1) or three classes (0, 0.5, and 1) according to their distribution in the [0,1] interval. The above example data is trained using a classifier from machine learning, and an optimization iterative process is applied to some classifier algorithms to improve classifier performance. Finally, a damage probability prediction model is obtained, which can predict whether the damage probability is 0 or 1 (or 0, 0.5, or 1) based on the values ​​of each random parameter. The obtained damage probability prediction model is used to replace the original damage probability calculation model, and the Monte Carlo method is used again to calculate the average single-shot damage probability of the warhead on the target under specific projectile-target encounter conditions. The damage probability prediction model can be used to calculate damage probabilities under different projectile-target encounter conditions, and its computational complexity is relatively small, avoiding the enormous computational burden of damage probability calculation models. Therefore, this method can significantly shorten the time required to calculate the average single-shot damage probability while ensuring a certain level of accuracy in the damage probability calculation results.

[0042] like Figure 1 As shown, this invention provides a damage probability calculation method based on a machine learning classifier. The method uses a classifier algorithm from machine learning to train a damage probability prediction model, which is then used to calculate the damage probability of a fragmentation warhead against a target (such as an air defense missile system) under specific conditions. The method includes the following steps:

[0043] S101: Establish a model for calculating the probability of damage to a target by a fragmentation warhead;

[0044] S201: Based on the damage probability calculation model, for all random parameters affecting the calculation results, such as the target's terminal velocity, angle of entry, pitch angle, and miss distance, more than 10,000 repeated random calculations were conducted using the Monte Carlo method to obtain a large number of damage probability calculation examples for different damage levels. In each calculation, each random parameter is randomly selected within a certain range according to a certain probability distribution. Specifically, for example, the missile's angle of entry relative to the target is randomly selected according to a uniform distribution within the range of 0° to 360°; the missile's trajectory angle is randomly selected according to a uniform distribution within the range of -10° to 0°; the missile's yaw angle is randomly selected according to a uniform distribution within the range of -2° to 2°; the missile's terminal velocity is randomly selected according to a uniform distribution between 200m / s and 300m / s; and the missile's vertical miss distance is randomly selected according to a normal distribution between -1m and 1m.

[0045] S301: The large amount of damage probability calculation data (more than 10,000 sets) obtained by calculation is adjusted into two parts: prediction variables and response sets, namely, the set of all random input parameters of the calculation and the corresponding output sets of damage probabilities of level K, level F and level M. According to the distribution of damage probability in the interval [0,1], the damage probability data of each level is approximated to two classes of 0 or 1, or three classes of 0, 0.5 and 1.

[0046] In the damage probability calculation model, the damage probability of the warhead to the target is a real number in the interval [0,1]. However, depending on the specific warhead performance and the vulnerability analysis and geometric modeling of the target, the majority of damage probability results are either 0 or 1, or 0, 0.5, and 1. Therefore, this method classifies the damage probability using a mathematical approximation of "rounding": below 0.5 is approximated as 0, and 0.5 and above is approximated as 1; or below 0.25 is approximated as 1, 0.25 and above but below 0.75 is approximated as 0.5, and 0.75 and above is approximated as 1.

[0047] S301: The above example data is trained using a classifier algorithm in machine learning, and an optimization iteration process is applied to some classifier algorithms to improve classifier performance. Finally, a damage probability prediction model for different damage levels is obtained. This model can predict whether the damage probability is 0 or 1 (or 0, 0.5 or 1) based on the values ​​of each random parameter, avoiding the huge amount of computation in the damage probability calculation model.

[0048] The classifiers mainly employ several algorithms, including logistic regression, Naive Bayes, decision trees, discriminant analysis, support vector machines, nearest neighbor, and ensemble learning.

[0049] The dataset used in the classifier mainly consists of two parts: predictor variables (i.e., independent variables) and responses. The predictor variables are composed of several vectors, each representing the value of a certain input parameter in each of 10,000 calculations. The response (i.e., dependent variable) is a vector representing the damage probability output in each of the 10,000 calculations. Therefore, the three different levels of damage probabilities are three different responses, which must be combined with the predictor variables to form separate datasets and fed into the classifier.

[0050] The main validation methods for classifiers are cross-validation, hold-out validation, and no validation.

[0051] Misclassification cost is one of the adjustable parameters of a classifier. Taking the case where the damage probability is 0 or 1 as an example, the impact of misclassifying 1 as 0 and misclassifying 0 as 1 is different, which can be reflected by the misclassification cost. Generally, it is adjusted appropriately according to the specific prediction results and the actual situation.

[0052] Different algorithms can be selected for the classifier, each with its own different tuning parameters, for example:

[0053] Decision tree algorithms include maximum number of categories (positive integers above 2), classification criteria (Gini diversity index, binary rule, etc.), and alternative decision splits;

[0054] Discriminant analysis algorithms have a covariance structure (diagonal or full);

[0055] Support vector machine algorithms include kernel functions (linear, Gaussian, etc.), box constraint levels, kernel scaling patterns, etc.

[0056] Nearest neighbor algorithms include the number of neighboring points (positive integers), distance metrics (Euclidean, city block, etc.), and distance weights (equal distance and inverse distance, etc.);

[0057] Ensemble learning algorithms include ensemble methods (bag, AdaBoost, and RUSBoost, etc.), learner types, maximum number of splits, and number of learners.

[0058] To improve the accuracy of the classifier algorithm, Bayesian optimizers are used to further optimize the above-mentioned adjustment parameters of the classifier algorithm. By iteratively adjusting the parameter values, a better machine learning classification model is finally obtained after dozens of iterations.

[0059] Except for logistic regression, all of the aforementioned classifier algorithms can be optimized using iterative optimization. The relevant adjustment parameters include optimizer selection (Bayesian optimization and network search, among which Bayesian optimization is more commonly used), acquisition function (expected improvement per second and expected improvement, etc.), number of iterations (generally an integer of more than 30 times), learning rate (generally 0.001 to 1), and computation time.

[0060] Various algorithms can be used to train a classifier on samples, but ensemble learning algorithms that employ iterative optimization methods are a relatively high-performance choice. The training results of a classifier are primarily measured by accuracy, which is the proportion of correctly predicted samples out of the total number of samples. However, for certain data distributions (e.g., the probability of damage 1 is significantly more common than 0, or vice versa), the classifier's predictions may be completely biased towards the side with the higher probability (i.e., result 1). While this might result in higher accuracy, the prediction model is not reasonable. In such cases, a misclassification cost adjustment is needed to make the classifier training process more inclined to predict the side with the lower probability more accurately. The criteria for ending classifier training are mainly determined by the maximum training time or the number of iterations.

[0061] S401: Using the damage probability classifier prediction model obtained in the previous step, under specific missile-target encounter conditions, some random parameters are fixed according to physical reality. These parameters can be one or more, and the specific fixed parameters are determined by physical reality or research needs, such as the angle of entry and elevation angle. The Monte Carlo method is then used to perform more than 500 repeated random calculations. After statistical analysis, the average single-shot damage probability of the warhead against the target under this specific missile-target encounter condition is obtained. (The damage probability prediction model outputs a single-shot damage probability in a single calculation; if multiple random calculations are performed using the Monte Carlo method, multiple single-shot damage probabilities can be obtained, and the average single-shot damage probability is obtained by averaging them.) By changing the type of fixed parameters, the average single-shot damage probability of the warhead against the target under different conditions can be easily calculated. For example, the missile's angle of entry can be fixed at 270°, or the missile's terminal velocity at 200 m / s, or the missile's trajectory angle at -5°, etc.

[0062] Furthermore, the specific method for establishing a model to calculate the probability of damage to a target by a fragmentation warhead is as follows:

[0063] Step 1: Create a 3D model of the target;

[0064] Establishing a 3D model of a target mainly refers to converting and simplifying the main components of the target into surface elements, which include the coordinates of the quadrilateral nodes of each surface element, as well as information such as the thickness and material of the surface elements, to form a digital model.

[0065] Step 2: Perform vulnerability analysis on each component of the target;

[0066] The vulnerability analysis of each component of the target is mainly based on the theory described in "Target Vulnerability" (Beijing Institute of Technology Press, Li Xiangdong et al.). A vulnerability coefficient is set for each major component of the target to represent the degree of difficulty of damage to each component under certain fragment penetration or explosive shock wave action. The value is equal to the ratio of the vulnerable area of ​​the outer surface of the component to the exposed area. The vulnerability coefficient is assigned to the surface element of each component in the three-dimensional model for damage probability calculation in step 5. Thus, a three-dimensional model of the target containing vulnerability information in the surface element is obtained, which is the basis for calculating the damage probability of the surface element by fragments during the missile-target intersection process.

[0067] Step 3: Establish a damage tree model for destroying the target;

[0068] According to "Target Vulnerability", the degree of damage to a target is generally divided into three levels: M-level damage, F-level damage, and K-level damage.

[0069] Class M damage, or mission-related damage, corresponds to the target's functional components being unable to fully perform their intended functions, requiring maintenance personnel 1 to 24 hours to remove the obstruction; Class F damage, or fire control damage, corresponds to the target's functional components losing their ability to function, requiring specialized maintenance units 1 to 7 days and nights to remove the obstruction; and Class K damage, or destruction damage, corresponds to the target weapon system losing its combat capability, being irreparable, or having damage that is economically infeasible.

[0070] The impact of damage to each component on the overall system function is analyzed. For example, the destruction of the radar antenna or the shelter can lead to the annihilation of the air defense missile system. Finally, three levels of damage trees are formed, and the non-combined or non-redundant components and combined or redundant components in each level of damage tree are given.

[0071] Step 4: Establish a warhead-target encounter model;

[0072] Establish a projectile-target encounter model for the fragmentation warhead, specifically including the following:

[0073] 1) Establish fragmentation field and overpressure field in the warhead coordinate system (field is a physics term referring to the distribution of an object in space; fragmentation field refers to the distribution of each fragment in space, including position and velocity vector information; overpressure field refers to the distribution of the overpressure of the explosion shock wave in space). Regarding the fragmentation field, calculate the spatial distribution, mass distribution, and velocity distribution of fragments after the warhead's static explosion based on the warhead charge, pre-formed fragments, and shell structure. Establish a corresponding spatial analytical model to obtain the random fragmentation field in the warhead coordinate system, i.e., the mass, shape coefficient, and velocity vector information of each fragment. Regarding the overpressure field, calculate the peak overpressure Δp of the shock wave generated by the fragmented warhead explosion. m And the specific impulse i of the positive pressure:

[0074]

[0075]

[0076]

[0077]

[0078]

[0079] In the formula ω e ω is the equivalent charge; α is the charge amount with casing; α is the charge coefficient; r0 / r f γ is the ratio of the initial radius of the shell to the fragmentation radius; γ is the polyhedral index of the detonation products; Δp m The peak value of the shock wave generated when the explosive charge detonates in an infinite air domain, expressed in MPa; m e The equivalent TNT weight is given by , in kg; r is the distance from the explosion point to the detonation center in m; C is a dimensionless constant, and the unit of i is Pa·s.

[0080] 2) Establish a warhead-target intersection model. This mainly involves establishing the fragmentation field and overpressure field in the target coordinate system based on the intersection relationship between the warhead and the target. Then, determine whether each fragment in the fragmentation field intersects with each surface element of the target, whether penetration is possible if they intersect, and whether the overpressure field can damage each specific surface element of the target. The intersection relationship between the fragmentation field and the target is jointly determined by the warhead's terminal attitude and the direction of its terminal velocity.

[0081] Step 5: Establish a model for calculating the probability of damage to the target by the fragmentation warhead.

[0082] Calculating the probability of damage to a target by a fragmentation warhead includes the following steps:

[0083] 1) Calculate the probability of damage to the target component by the fragmentation field:

[0084] Calculate the damage probability of each component of the target. Some components are considered as a whole. For these components, the total number of fragments penetrating all surface elements is used as the effective killing fragments to calculate the damage probability of the entire component. Taking all fragments penetrating the t-th component of this type as the effective damaging fragments, the damage probability of the t-th component of this type is calculated according to the following formula:

[0085] p t =1-e -ξ·n

[0086] In the formula, ζ is the vulnerability coefficient, and n is the total number of fragments that are penetrated by the t-th component;

[0087] Some components are calculated based on non-redundancy for each face. That is, if any one face of the surface elements that make up this component is damaged, the entire component is considered damaged. Then, the formula for calculating the damage probability of the s-th component in this type of component is:

[0088]

[0089] In the formula p m R is the probability of damage to the m-th face element in the s-th component, and R is the total number of face elements in the s-th component.

[0090] There is another type of component that has some redundant surface units. That is, if a certain percentage (e.g., 20%) of the total number of surface units are destroyed (the probability of destruction is 1), then the component is considered destroyed (the probability of destruction is 1).

[0091] 2) Calculate the probability of damage to the target component from the overpressure field:

[0092] First, calculate the shock wave overpressure on a certain surface element. If the shock wave overpressure is greater than the pressure bearing threshold of the surface element, then the overpressure damage probability of the surface element is considered to be 1.

[0093] The damage criteria for shock waves are calculated using the following formula:

[0094] (ΔP-P * (II) * )≥K

[0095] Where ΔP and I are the peak overpressure and specific impulse of the shock wave, respectively, and P * and I * Here, K represents the critical overpressure and critical specific impulse of the shock wave, respectively, and K is a constant that depends on the vulnerability of the target. When the above equation is satisfied, the target element is considered to have a 100% probability of being destroyed. The maximum value of the damage probability of a certain element by the fragmentation field and overpressure field is taken as the final damage probability of that element. Then, based on the damage situation of the element, the damage probability of the component is further calculated according to the content of Section 1) above.

[0096] 3) Calculate the total damage probability of the system.

[0097] According to target vulnerability analysis theory, there are two damage calculation scenarios for the components of a target: one is that the target is damaged when at least one non-combined or non-redundant component is damaged; the other is that the target is damaged only when all combined or redundant components are damaged. Therefore, based on the damage probabilities of each target component and the results of three levels of damage tree analysis, the total damage probability of the warhead on the target system can be calculated separately for each of the three levels, using the following formula:

[0098]

[0099] Where, Nor P represents the number of non-redundant component elements, k represents the number of redundant component groups, and P represents the number of non-redundant component elements. or,i Let M1, M2, ..., M be the probability of failure for each non-redundant component. k P represents the number of redundant components in each redundant component group. and,i This represents the probability of damage to each component in the redundant component group.

[0100] Furthermore, the specific method for conducting more than 10,000 repeated random calculations based on the Monte Carlo method for all random parameters affecting the calculation results is as follows:

[0101] Step 1: Determine the constants that need to be input when calculating the probability of damage, that is, the constants that remain unchanged when performing random calculations;

[0102] The constants required to calculate the probability of damage are mainly: the physical parameters of the warhead itself, such as the structure and number of pre-fragmented fragments, the equivalent TNT charge of the warhead, the charge coefficient of the warhead, etc.; the flight parameters of the warhead, such as the slip angle of the warhead, etc.; and the detection range and detonation delay of the fuze, etc.

[0103] Step 2: Determine the random parameters that need to be randomly calculated using the Monte Carlo method when calculating the probability of damage;

[0104] The random parameters that need to be calculated using the Monte Carlo method when calculating the probability of destruction mainly include: the detonation position of the fragmentation warhead and the missile's entry angle, elevation angle, miss distance, terminal velocity, the angle between the terminal velocity vector and the ground, and the guidance accuracy probability error, i.e., circular error.

[0105] Step 3: Based on the damage probability calculation model, and after determining the constants in Step 1, the Monte Carlo method is used to perform more than 10,000 repeated random calculations on all random parameters in Step 2, ultimately obtaining a large amount of damage probability calculation data (more than 10,000 sets). In each calculation, each random parameter is randomly selected within a certain range according to a certain probability distribution. Specifically, for example, the missile's angle of entry relative to the target is randomly selected according to an average distribution within the range of 0° to 360°; the missile's trajectory angle is randomly selected according to a uniform distribution within the range of -10° to 0°; the missile's yaw angle is randomly selected according to a uniform distribution within the range of -2° to 2°; the missile's terminal velocity is randomly selected according to a uniform distribution between 200m / s and 300m / s; and the missile's vertical miss distance is randomly selected according to a normal distribution between -1m and 1m, etc.

[0106] Furthermore, the damage probability results from the large number of case studies obtained through the Monte Carlo random calculations are approximated as two classes (0 and 1) or three classes (0, 0.5, and 1) based on their distribution in the [0,1] interval. The specific method is as follows:

[0107] In the damage probability calculation model, the damage probability of the warhead to the target is a real number in the interval [0,1]. However, depending on the specific warhead performance and the vulnerability analysis and geometric modeling of the target, the majority of damage probability results often fall around 0 and 1, or around 0, 0.5, and 1. Therefore, the damage probability is classified here by a mathematical approximation using "rounding": below 0.5 is approximated as 0, and 0.5 and above is approximated as 1; or below 0.25 is approximated as 1, and 0.25 and above but below 0.75 is approximated as 0.5, and 0.75 and above is approximated as 1.

[0108] After the above processing, the damage probability calculation data can be analyzed using classifier algorithms in machine learning to extract a prediction model.

[0109] Furthermore, the specific method for training the large number of damage probability example data after result approximation using machine learning classifier algorithms to generate a damage probability prediction model is as follows:

[0110] Step 1: Determine the algorithm, dataset structure, and validation method to be used when training data for a classifier algorithm employing machine learning methods;

[0111] Training data with classifier algorithms using machine learning methods first requires selecting an algorithm and defining the dataset structure. Common classifier algorithms include logistic regression, Naive Bayes, decision trees, discriminant analysis, support vector machines, nearest neighbor algorithms, and ensemble learning. These algorithms have different mathematical principles and varying performance on different specific problems and data sets. Therefore, it is necessary to analyze various algorithms to find the relatively optimal one.

[0112] The dataset used in the classifier mainly consists of two parts: predictor variables (i.e., independent variables) and responses. The predictor variables are composed of several vectors, each representing the value of a certain input parameter in each of 10,000 calculations. The response (i.e., dependent variable) is a vector representing the damage probability output (0 and 1, or 0, 0.5, and 1) in each of the 10,000 calculations. Therefore, the three different levels of damage probabilities are three different responses, which must be combined with the predictor variables to form separate datasets and fed into the classifier.

[0113] The machine learning analysis process of classifiers requires selecting a validation method to analyze and validate the performance of the prediction model on the dataset. Generally, there are three types: cross-validation, hold-out validation, and no validation. Cross-validation involves dividing a dataset into X parts, using one part as the test set, and the remaining X-1 parts as the training set, repeating this process until each part has been used as the test set. Ten-fold cross-validation is commonly used. Hold-out validation involves directly dividing the dataset into two mutually exclusive sets, one as the training set and the other as the test set. After training the model on the training set, the error is tested on the test set to estimate the generalization error. Ten-fold cross-validation is typically chosen.

[0114] Step 2: Determine the parameters for training the classifier using machine learning methods on the training data;

[0115] The main parameters that need to be set when using machine learning methods to train data based on classifiers are:

[0116] Misclassification cost is one of the adjustable parameters of a classifier. Taking the case where the damage probability is 0 or 1 as an example, the impact of misclassifying 1 as 0 and misclassifying 0 as 1 is different, which can be reflected by the misclassification cost. Generally, it is adjusted appropriately according to the specific prediction results and the actual situation.

[0117] Different algorithms in classifiers have their own different tuning parameters, for example:

[0118] Decision tree algorithms include maximum number of categories (positive integers above 2), classification criteria (Gini diversity index, binary rule, etc.), and alternative decision splits;

[0119] Discriminant analysis algorithms have a covariance structure (diagonal or full);

[0120] Support vector machine algorithms include kernel functions (linear, Gaussian, etc.), box constraint levels, kernel scaling patterns, etc.

[0121] Nearest neighbor algorithms include the number of neighboring points (positive integers), distance metrics (Euclidean, city block, etc.), and distance weights (equal distance and inverse distance, etc.);

[0122] Ensemble learning algorithms include ensemble methods (bag, AdaBoost, and RUSBoost, etc.), learner types, maximum number of splits, and number of learners.

[0123] Using the above parameters, subsequent training on example data can be performed based on the classifier.

[0124] Step 3: Input more than 10,000 sets of damage probability calculation examples obtained randomly from S201 into a machine learning classifier tool for training;

[0125] 1) Adjust the more than 10,000 sets of damage probability calculation examples obtained by random calculation in S201 into two parts: input and output, namely, the set of all input parameters of the calculation examples and the corresponding output sets of K-level, F-level and M-level damage probabilities;

[0126] 2) Input the input and output datasets into various machine learning classifier software tools for training (K-level, F-level and M-level training are carried out separately). Available tools include Matlab and Python.

[0127] Step 4: By continuously training the classifier multiple times (dozens of times) on the damage probability example data, and adjusting some learning parameters, such as changing the training algorithm or the cost of misclassification, a damage probability prediction model with the highest accuracy (the proportion of correctly predicted samples out of the total samples) can eventually be found. Using this model, the probability of K-level, F-level, and M-level damage under different input conditions can be predicted based on the values ​​of each parameter, avoiding the enormous computational burden in damage probability calculation models.

[0128] Step 5: Further optimization can be performed using an optimizer to refine the various parameters of the classifier algorithm, thereby improving accuracy;

[0129] To improve the accuracy of the classifier algorithm, Bayesian optimizers can be used to optimize the various parameters of the classifier algorithm. By iterating and continuously adjusting the parameter values, a better machine learning classification prediction model can be obtained after dozens of iterations.

[0130] Except for logistic regression, all of the aforementioned classifier algorithms can be optimized using iterative optimization. The relevant adjustment parameters include optimizer selection (Bayesian optimization and network search, among which Bayesian optimization is more commonly used), number of learners (generally an integer of 10 or more), acquisition function (expected improvement per second and expected improvement, etc.), number of iterations (generally an integer of 30 or more), and learning rate (generally 0.001 to 1).

[0131] Various algorithms can be used to train a classifier on samples, but ensemble learning algorithms that employ iterative optimization methods are a relatively high-performance choice. The training results of a classifier are primarily measured by accuracy, which is the proportion of correctly predicted samples out of the total number of samples. However, for certain data distributions (e.g., the probability of damage 1 is significantly more common than 0, or vice versa), the classifier's predictions may be completely biased towards the more common outcome (i.e., outcome 1). While this might result in higher accuracy, the prediction model is not reasonable. In such cases, a misclassification cost adjustment is needed to make the classifier training process more inclined to predict the less common outcome more accurately.

[0132] Furthermore, using the damage probability prediction model obtained from S301 and employing the Monte Carlo method, the specific method for calculating the average single-shot damage probability of the warhead against the target under specific projectile-target encounter conditions is as follows:

[0133] Step 1: Determine the required missile-target rendezvous conditions based on user needs;

[0134] The specific projectile-target rendezvous conditions required for calculation are determined by the actual needs of the user of this method. Under these conditions, a portion of random parameters, such as the entry angle and elevation angle, are fixed according to physical reality or research needs. The values ​​of other parameters remain unchanged and are still randomly selected within a specific range, thus obtaining the input dataset corresponding to the projectile-target rendezvous conditions.

[0135] Step 2: Using the obtained damage probability prediction model, perform more than 500 repeated random calculations using the Monte Carlo method on the input dataset from Step 1. After statistical analysis, obtain the average single-shot damage probability of the fragmentation warhead against the target under the target encounter conditions in Step 1. In each calculation, the values ​​of all random parameters, except for the specific target encounter conditions, remain unchanged. This allows the damage probability prediction model, obtained through 10,000 repeated random calculations of the damage probability calculation model and then trained by a classifier, to replace the original damage probability calculation model, while reducing the computational load and avoiding the enormous computational burden of the original model. Furthermore, by changing the target encounter conditions and the corresponding input dataset (i.e., changing the fixed parameter types), the average single-shot damage probability of the warhead against the target under different conditions can be easily calculated.

[0136] The average single-shot damage probability obtained by Monte Carlo calculation using the damage probability prediction model of this method can achieve an average accuracy of more than 75% compared with the result obtained by Monte Carlo calculation using the damage probability calculation model directly. At the same time, this method significantly reduces the amount of calculation and improves the calculation efficiency by more than 20 times.

[0137] The present invention has been described in detail above with reference to specific embodiments and exemplary examples; however, these descriptions should not be construed as limiting the present invention. Those skilled in the art will understand that various equivalent substitutions, modifications, or improvements can be made to the technical solutions and embodiments of the present invention without departing from the spirit and scope of the invention, and all such modifications and improvements fall within the scope of the present invention. The scope of protection of the present invention is defined by the appended claims.

[0138] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A method for calculating damage probability based on a machine learning classifier, characterized in that, include: Based on the three-dimensional model of the target, a vulnerability analysis is performed on the target's components; based on the vulnerability analysis results, a model is established to calculate the probability of damage to the target by the fragmentation warhead. Based on the damage probability calculation model, for all random parameters that affect the calculation results, repeated random calculations based on the Monte Carlo method are carried out more than m times to obtain a large number of damage probability calculation case data for different damage levels; each calculation case data contains a set of random parameter arrays and damage probabilities of different levels corresponding to the random parameter arrays; m>10000; A large amount of damage probability calculation data is organized into a set of predictive variables and a set of responses; the set of predictive variables is the set of random parameter arrays in all calculation data, and the set of responses is the set of damage probabilities at different levels corresponding to the random parameter arrays; in the set of responses, the damage probability data is approximated to two classes of 0 or 1 or three classes of 0, 0.5 and 1 according to the actual value of the damage probability in the interval [0,1]. By using a classifier algorithm in machine learning to train the set of prediction variables as input and the set of responses as output, a damage probability prediction model for different damage levels is obtained. Under specific projectile-target encounter conditions, the relevant random parameters in the damage probability prediction model are set to fixed values. The Monte Carlo method is used to perform more than n repeated random calculations based on the damage probability prediction model to predict the average single-shot damage probability of the fragmentation warhead to the target under the specific projectile-target encounter conditions; n>500. The damage probability calculation model is as follows: Where, N or P represents the number of non-redundant components, k represents the number of redundant component groups, and P represents the number of non-redundant components. or,i Let M1, M2, ..., M be the probability of failure for each non-redundant component; k These represent the number of redundant components in each redundant component group; P and,j The probability of damage to each component in the redundant component group is given. The target consists of multiple redundant components and multiple non-redundant components. If all redundant components in any one redundant component group are damaged, the target is considered damaged. If any one non-redundant component is damaged, the target is considered damaged.

2. The damage probability calculation method based on a machine learning classifier according to claim 1, characterized in that, Based on the actual damage probability values ​​in the [0,1] interval, the specific method for approximating the damage probability data as either 0 or 1, or 0, 0.5, and 1, is as follows: The actual value of the damage probability is classified by mathematical approximation through rounding: when the damage probability is below 0.5, it is approximated as 0; when the damage probability is 0.5 or above, it is approximated as 1. Alternatively, when the damage probability is below 0.25, it is approximated as 1; when the damage probability is 0.25 or above but below 0.75, it is approximated as 0.5; and when the damage probability is 0.75 or above, it is approximated as 1.

3. The damage probability calculation method based on a machine learning classifier according to claim 1, characterized in that, The classifier algorithm is one of the following: logistic regression, naive Bayes, decision tree, discriminant analysis, support vector machine, nearest neighbor, or ensemble learning.

4. The damage probability calculation method based on a machine learning classifier according to claim 1, characterized in that, In the classifier algorithm, the accuracy of the prediction result is adjusted by the misclassification cost; the classification algorithm training ends based on the maximum training time or the maximum number of iterations. Classifier validation methods include cross-validation, hold-out validation, or no validation.

5. The damage probability calculation method based on a machine learning classifier according to claim 1, characterized in that, The random parameters include: the detonation position of the fragmentation warhead, the missile's entry angle, the missile's elevation angle, the missile's trajectory angle, the missile's yaw angle, the missile's miss distance, the missile's terminal velocity, the angle between the missile's terminal velocity vector and the ground, or the guidance accuracy probability error. The missile's angle of entry is randomly selected from a uniform distribution within the range of 0° to 360°; The missile's trajectory angle is randomly selected from a uniform distribution within the range of -10° to 0°; The missile's yaw angle is randomly selected from a uniform distribution within an atmosphere ranging from -2° to 2°. The missile's terminal velocity is randomly selected from a uniform distribution between 200m / s and 300m / s; The vertical miss distance of the missile is randomly selected from -1m to 1m according to a normal distribution.

6. The damage probability calculation method based on a machine learning classifier according to claim 5, characterized in that, According to the damage probability calculation model, when performing repeated random calculations based on the Monte Carlo method more than m times for all random parameters that affect the calculation results, it is also necessary to predetermine the input constants. The constants include the physical parameters of the warhead itself, the flight parameters of the warhead, and the detection range and detonation delay of the fuse. The physical parameters of the warhead itself include the structure and number of pre-fragmented fragments, the equivalent TNT charge of the warhead, and the charge coefficient of the warhead. The flight parameters of the warhead include the slip angle of the warhead.

7. The damage probability calculation method based on a machine learning classifier according to claim 1, characterized in that, The different damage levels include: M-level mission damage, F-level fire control damage, and K-level catastrophic damage; M-level mission damage indicates that the target's functional components cannot fully perform their intended functions and require 1 to 24 hours to remove the obstruction; F-level fire control damage indicates that the target's functional components have lost their operational capability and require 1 to 7 days and nights to remove the obstruction; K-level catastrophic damage indicates that the target weapon system has lost its combat capability and cannot be repaired or that repairing the damage is economically infeasible.

8. The damage probability calculation method based on a machine learning classifier according to claim 3, characterized in that, The parameters required to be set in the decision tree algorithm include the maximum number of classifications, classification criteria, and alternative decision splits. The parameters required to be set in the discriminant analysis algorithm include the covariance structure; The parameters required to be set in the support vector machine algorithm include kernel function, box constraint level, and kernel scale mode. The parameters required to be set in the nearest neighbor algorithm include the number of neighboring points, distance metric, and distance weight; The parameters that need to be set in the ensemble learning algorithm include the ensemble method, learner type, maximum number of splits, and number of learners.

9. The damage probability calculation method based on a machine learning classifier according to claim 8, characterized in that, When the classifier algorithm is an algorithm other than logistic regression, an optimizer is used to iteratively optimize the various adjustment parameters of the classifier algorithm. After dozens of iterations, an optimized damage probability prediction model is obtained.

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