Cloud model array construction method and system for power characteristics of dynamic rupture disk field of warhead, storage medium and electronic equipment

Abstract

The invention provides a cloud model array construction method and system for power characteristics of a dynamic rupture disk field of a warhead, a storage medium and electronic equipment, and relates to the technical field of ammunition power tests.According to the method, the power characteristics of the rupture disk field are accurately described through a mixed cloud model, and the density, speed and mass of fragments are obtained in a data collection or simulation mode; the complexity of the array fragment field is comprehensively captured; the generated fragment assessment index assesses the potential power level of a fragment field, and a hybrid cloud model assessment index is generated in combination with an accuracy parameter, a complexity parameter and a generalization ability value and is used for cloud model selection assessment; according to the method, the multi-peak characteristic of the fragment field is identified through a conversion analysis and statistical method, and the density space distribution regularity is explored through clustering analysis; a random sampling consistent EM algorithm and iterative maximum likelihood estimation are adopted to construct a hybrid cloud model, uncertainty characteristics of fragment field power characteristic distribution clustering are fully expressed, and model support is provided for accurate and reliable prediction of fragment field power characteristics.

Description

Technical Field

[0001] The present invention relates to the technical field of ammunition power testing, and in particular to a cloud model array construction method, system, storage medium and electronic equipment for warhead dynamic blasting field power characteristics. Background Art

[0002] In the field of modern warfare and security protection, the study of the power characteristics of fragmentation fields is an important and complex topic. Fragmentation fields are usually generated by explosions and contain a large number of fragments of different shapes, sizes, masses and speeds, which cause damage to surrounding targets. With the development of science and technology, the prediction and analysis methods of the power characteristics of fragmentation fields are also constantly improving. Traditional analysis methods usually rely on experimental data and empirical formulas. These methods can provide basic predictions of the power of fragmentation fields to a certain extent, but they often cannot accurately handle complex fragmentation field distribution characteristics, such as non-convex non-Gaussian distribution and multi-peak distribution. In addition, these traditional methods often encounter challenges in computational efficiency and accuracy when processing large-scale data.

[0003] In the prior art, publication number CN111998739B discloses a method and device for testing the dynamic power fragmentation of a rocket, which relates to the technical field of ammunition power testing. The method includes: using galvanized wire mesh to lay a grid target, wherein the grid target includes a plurality of grids for marking the fragment position A (x0, y0, 0) of the rocket, establishing a ground coordinate system OXYZ and a body coordinate system OdXdYdZd, and determining the coordinate transformation relationship from the ground coordinate system OXYZ to the body coordinate system OdXdYdZd; according to the fragment position A (x0, y0, 0) of the rocket and the coordinate transformation relationship, determining the dynamic scattering angle φ of the fragment and the center angle η of the fragment ray; the method and device can calculate and evaluate the dynamic scattering angle φ of the fragment and the center angle η of the fragment ray under dynamic conditions, wherein the killing area of ​​the rocket fragment can be intuitively determined according to the center angle η of the fragment ray;

[0004] The shortcomings of the existing technology are mainly reflected in the processing of complex fragmentation field distribution. In practical applications, fragmentation fields often present complex distribution forms, such as asymmetric distribution, long-tail distribution, etc. These characteristics make it difficult for traditional Gaussian assumptions and simple statistical models to apply. In addition, since the movement and distribution of fragments under actual conditions are affected by many factors, including the energy distribution of the explosion source, the interference of the surrounding environment, etc., the simulation and prediction of the fragmentation field are more complicated; therefore, there is an urgent need for a new method that can accurately reflect the complex distribution characteristics of the fragmentation field, evaluate the potential power level of the fragmentation field, and be used for model selection evaluation to improve the accuracy and efficiency of power characteristic prediction;

[0005] The above information disclosed in this Background section is only for enhancement of understanding of the background of the present disclosure and therefore it may contain information that does not constitute the prior art that is already known to one of ordinary skill in the art. Summary of the invention

[0006] The object of the present invention is to provide a method, system, storage medium and electronic device for constructing a cloud model array of the dynamic blasting field power characteristics of a warhead, so as to solve the problems raised in the above-mentioned background technology.

[0007] To achieve the above object, the present invention provides the following technical solutions:

[0008] A cloud model array construction method for warhead dynamic blasting field power characteristics, the specific steps comprising:

[0009] Step S1, marking the ammunition fragmentation fields with typical postures and velocities to form a fragmentation field array set {1, 2, ..., u, ..., n}, where u represents the uth fragmentation field, n is the total number of fragmentation fields, and each fragmentation field represents a set of fragments with similar posture and velocity characteristics; and marking the typical intersection radius between the damaged target and the fragment trajectory in the fragmentation field to form {r1, r2, ..., r t , ..., r m}, where t is the tth intersection radius r t The index subscript of m represents the total number of intersection radii in the current debris field. At the same time, the fragments in the t-th intersection radius are marked to form {1, 2, ..., i, ..., l}. For r ti , represents the intersection radius r t The number of the i-th fragment on the previous page, l is the current intersection radius r ti The total number of fragments; and spherical slicing and Euclidean mapping of the typical intersection radius of the fragment field, while collecting fragment density, fragment velocity and fragment mass data under the power characteristic data of the fragment field, and collecting non-convex non-Gaussian distribution data and non-convex segmentation data of the fragment field;

[0010] Step S2, obtaining fragmentation field power characteristic data of non-convex non-Gaussian distribution, and determining its distribution characteristics and regularity through conversion analysis; and the conversion analysis adopts a multi-peak distribution processing method suitable for fragmentation field power characteristics and a conversion function for converting data into an approximate Gaussian distribution;

[0011] Step S3, obtaining a conversion function, and converting the fragmentation field power characteristic data, using a statistical method to analyze the discrete degree and fuzzy degree uncertainty law of the fragmentation field power characteristic slice mapping distribution;

[0012] Step S4, after obtaining the fragment density, fragment velocity and fragment mass data under the fragment field power characteristic data, plane mapping is performed to sequentially form the fragment field target intersection radius spherical slice density mapping, the fragment field target intersection radius spherical slice velocity mapping, and the fragment field target intersection radius spherical slice mass mapping, and calibrate them as the fragment density ρ in sequence. r , fragment speed v r , fragment mass m r , and the fragment density ρ r , fragment speed v r , fragment mass m r Perform analysis and processing to generate a debris assessment index of the t-th intersection radius under the u-th debris field;

[0013] Step S5, obtaining the spatial clustering characteristics of the geodesic distance kernel density of the power characteristic of the fragmentation field, and exploring the regularity of its density spatial distribution; segmenting the non-convex distribution, if the density distribution of the power characteristic of the fragmentation field still does not conform to the Gaussian form after the non-convex distribution segmentation, exploring the change regularity of the conversion function, and determining the optimal conversion function of the Gaussian distribution, the steps of determining the optimal conversion function generation of the Gaussian distribution are data preparation and preliminary processing, kernel density estimation and spatial clustering, non-convex distribution segmentation, conversion function exploration and optimization, multi-convex multi-Gaussian distribution conversion function and mixed model;

[0014] For the problem of distribution uncertainty, a cloud model is used to characterize its discreteness and fuzziness. For the problem of non-convex and non-Gaussian uncertainty of the distribution of power characteristics of the fragmentation field, multiple hybrid cloud models are used to characterize the distribution of power characteristics of the fragmentation field.

[0015] Step S6, obtaining the fragmentation evaluation index and the parameters contained in the hybrid model and analyzing and processing them, constructing the hybrid cloud model evaluation index, and generating an evaluation result of the hybrid cloud model selection according to the hybrid cloud model evaluation index value range;

[0016] Step S7: Based on the density discrimination criterion, a random sampling consistent EM algorithm is used to perform cluster analysis on the converted data, and a mixed cloud model of the non-convex non-Gaussian uncertainty fragmentation field power characteristic distribution is constructed to fully represent the cluster uncertainty characteristics of the fragmentation field power characteristic distribution;

[0017] Step S8, obtaining the fragment assessment index of the t-th intersection radius under the u-th fragment field, the mixed cloud model assessment index, and the non-convex non-Gaussian distribution data and the non-convex segmentation data as the input of the model, and using the sampling consistent iterative maximum likelihood to estimate the mixed cloud model parameters of the fragment field power characteristics. The model is used to predict the power characteristics of the fragment field.

[0018] Furthermore, the collecting of typical intersection radius of the damaged target of each fragmentation field and the intersection of the fragmentation field, and spherical slicing and Euclidean mapping of the typical intersection radius of the fragmentation field specifically include the following contents:

[0019] The contents include determining the location of the damaged target, collecting the typical intersection radius of the fragmentation field, spherical slicing, Euclidean mapping and data recording and analysis steps;

[0020] Among them, the position of the damaged target is determined, and the coordinates of the damaged target for the uth fragment field are set as (x ut ,y ut ,z ut );

[0021] The typical rendezvous radius of the debris field rendezvous is collected to determine the rendezvous radius r of the rendezvous fragments with the damaged target ti ;

[0022] Spherical slicing is used to select the slice radius r s , and obtain a circular slice area;

[0023] The Euclidean mapping is used to map the obtained circular slice area onto a two-dimensional plane through the Euclidean mapping, and the position of each fragment is expressed by the Cartesian coordinates (x i ,y i ), where i is the number of the fragment under the current intersection radius;

[0024] Data records are used to record all relevant fragments (x i ,y i ) coordinates, and their corresponding intersection radius r i , and the intersection radius r of the debris at the intersection point between the target and the debris trajectory ti .

[0025] Further, the multi-modal distribution processing method is a multi-convex distribution method, and the conversion function is a multi-Gaussian distribution conversion function;

[0026] The method of obtaining the conversion function and converting the fragmentation field power characteristic data, and using statistical methods to analyze the discrete degree and fuzzy degree uncertainty law of the fragmentation field power characteristic slice mapping distribution, specifically includes the following contents:

[0027] The Box-Cox transformation function was used to adjust the data to be close to normal distribution;

[0028] Determine the optimal λ value through maximum likelihood estimation, and gradually narrow the search range until the optimal value is found;

[0029] The optimal λ value is used to perform Box-Cox transformation on the fragmentation field characteristic data;

[0030] Standardize the transformed data to ensure that the mean is 0 and the standard deviation is 1;

[0031] Analyze the degree of dispersion of data and calculate variance and standard deviation;

[0032] Quantify the uncertainty of data using information entropy methods;

[0033] Establish a mapping relationship between data, discreteness and uncertainty, and analyze the rules.

[0034] Furthermore, after obtaining the fragment density, fragment velocity and fragment mass data under the fragment field power characteristic data, plane mapping is performed to sequentially form the fragment field target intersection radius spherical slice density mapping, the fragment field target intersection radius spherical slice velocity mapping, and the fragment field target intersection radius spherical slice mass mapping, which specifically include the following contents:

[0035] In the fragmentation field array set {1, 2, ..., u, ..., n}, set the flight trajectory of the uth fragmentation field to T u r i (x, y, z), which is the point set of the fragmentation field flight trajectory changing with time in three-dimensional space coordinates. u r i (x, y, z) converted to azimuth φ-pitch angle Polar coordinate system, where φ = atan(y / x), The azimuth angle φ is used as the x-axis, the pitch angle The Euclidean plane coordinate system of spherical mapping is established for the y-axis. The plane mapping slice fragmentation field power characteristics of the spherical slice with a radius distance r are expressed by the following plane projection slice fragmentation field power characteristic function:

[0036]

[0037] Among them, ρ r is the fragment density under the plane mapping, v r is the fragment velocity under plane mapping, m r is the fragment mass under plane mapping;

[0038] is the debris density function, which maps the debris density in spherical coordinates to the density distribution in plane coordinates, and is quantified by counting the number of debris per unit area on a spherical slice with a specific radius;

[0039] is the debris velocity function, which describes the velocity of the debris at a specific azimuth and elevation angle. This function is related to the initial velocity of the debris and the external force it receives. The velocity distribution function is obtained based on experimental data or theoretical models;

[0040] is the debris mass function, which represents the mass distribution of the debris at a given azimuth and elevation angle. The mass distribution is related to the type, size and distribution of the debris, and its specific expression also depends on the actual distribution of the debris.

[0041] Furthermore, the clustering characteristics of the geodesic distance kernel density of the fragmentation field power characteristics in space are obtained to explore the regularity of its density space distribution; the non-convex distribution is segmented, and if the density distribution of the fragmentation field power characteristics after the non-convex distribution segmentation still does not conform to the Gaussian form, the change regularity of the conversion function is explored to determine the optimal conversion function of the Gaussian distribution; specifically, the following contents are included:

[0042] The steps of determining the optimal conversion function generation of Gaussian distribution are data preparation and preliminary processing, kernel density estimation and spatial clustering, non-convex distribution segmentation, conversion function exploration and optimization, multi-convex multi-Gaussian distribution conversion function and mixed model.

[0043] The data preparation and preliminary processing are to obtain fragmentation field array data, damage targets and typical rendezvous radius, and prepare fragment characteristic data;

[0044] The kernel density estimation and spatial clustering are to calculate the kernel density estimation and apply the clustering method to identify high-density areas;

[0045] The non-convex distribution is divided into analyzing convexity, and the non-convex distribution data is divided into convex areas;

[0046] The conversion function exploration and optimization is to try basic conversion functions, explore advanced methods such as VAE, and determine the optimal conversion function;

[0047] The multi-convex multi-Gaussian distribution conversion function and the mixed model are to fit the characteristic distribution of the fragmentation field using a mixed Gaussian model and a mixed cloud model;

[0048] Wherein, the hybrid cloud model generation consists of model construction and model quantification indicators;

[0049] The model building means combining the segmented regions and the results of the conversion function to build a hybrid cloud model to characterize the overall structure of the power characteristic distribution of the fragmentation field, and the model can describe the distribution characteristics of each region and the relationship between them;

[0050] The model quantification index represents the evaluation index of the defined model, and the evaluation index is the accuracy parameter, complexity parameter and generalization ability value of the model, and the accuracy parameter is calibrated as ZQd, the complexity parameter is calibrated as FZd, and the generalization ability value is calibrated as FHl;

[0051] Assume that the fragmentation field power characteristic density contains k cloud models, and the expectation is Ex j, which indicates the clustering of the density distribution of the power characteristics of the fragmentation field; Entropy is En j The random variable represents the uncertainty of the density distribution of the power characteristics of the fragmentation field; the super entropy is He j , represents the uncertainty of the distribution uncertainty of the power characteristic density of the fragmentation field; and j = 1, 2, ..., k, where k is a hyperparameter;

[0052] Define the certainty function μ of the power characteristic density of the cloud model fragmentation field j for:

[0053]

[0054] Because it is a hybrid cloud model, there are not only expected Ex j 、Entropy j 、Super entropy He j Model parameters need to be estimated, and there are also hyperparameters k and entropy En of the number of hybrid clouds. j Type and Super Entropy He j Hyperparameter estimation of type T, hyperentropy He j The type T represents different standard covariance matrices, the same standard covariance matrix, different diagonal covariance matrices and different slice covariance matrices; according to the different types of T, the corresponding super entropy calculation method is selected.

[0055] Furthermore, the fragment density ρ under the plane projection slice fragment field power characteristic function is obtained r , fragment speed v r , fragment mass m r , and analyze and process to generate the debris evaluation index E of the t-th intersection radius under the u-th fragment field ti,u , the calculation formula is as follows:

[0056]

[0057] Among them, E ti,u is the debris assessment index of the tth intersection radius in the uth debris field; l u is the intersection radius r in the uth fragment field ti The total number of fragments; v r,i 、m r,i and ρ r,i are the velocity, mass and density of the i-th fragment at the current intersection radius, Z is the normalization factor, ensuring that E ti,u The maximum value of does not exceed 1;

[0058] v max 、m max and ρ max are the maximum velocity, maximum mass, and maximum density among all fragments, respectively, for normalization;

[0059] w1, w2 and w3 are weight factors used to balance the effects of speed, mass and density in the evaluation index, and w1+w2+w3=1, w1, w2 and w3 are all non-negative numbers;

[0060] a1, a2 and a3 are adjustment factors used to adjust the influence of speed, mass and density;

[0061] is a fragment azimuth angle φ i and the pitch angle φ i is a function of φ0, which is used to consider the influence of the flight direction of the fragments on their potential power; φ0 and are the azimuth and elevation angles of the reference direction, respectively, which are used to determine the reference value of the potential power of debris in a specific direction;

[0062] Based on weight factors, adjustment factors and Setting E ti,u The value range of is [0,1];

[0063] The [0,1] value range is divided into several level intervals, and the potential power level of the fragmentation field corresponding to each interval is defined. The larger the value, the higher the potential power level of the fragmentation field, and vice versa.

[0064] Furthermore, the accuracy parameter ZQd, complexity parameter FZd, generalization capability value FHl and fragmentation evaluation index E are obtained. ti,u After analysis and processing, a hybrid cloud model evaluation index is constructed and defined as HMEI. The calculation formula is as follows:

[0065]

[0066] Among them, ZQd represents the accuracy parameter of the model, which is calculated by mean square error MSE or mean absolute error MAE. For classification problems, the accuracy rate is used; FZd represents the complexity parameter of the model, which is estimated by the number of model parameters;

[0067] FHl represents the generalization ability value of the model, which is evaluated by the average performance index of k-fold cross validation;

[0068] e1, e2, and e3 are the weight parameters of accuracy, the inverse function of complexity, and generalization ability respectively, and e1, e2, and e3 are all non-negative numbers, e1 + e2 + e3 = 1. The value range of HMEI is limited within [-1, 1]. Among them, the value of HMEI close to 1 indicates better comprehensive performance of the model, and the value close to -1 indicates worse comprehensive performance of the model. The value range [-1, 1] of HMEI is divided into intervals [0.8, 1], [0.5, 0.8), [0, 0.5), [-0.5, 0), and [-1, -0.5) in turn, and corresponding model selection evaluation results are generated for each interval;

[0069] Based on the density discrimination criterion, using the random sample consensus EM algorithm, perform clustering analysis on the transformed data to construct a hybrid cloud model of the non-convex and non-Gaussian uncertainty blast field power characteristic distribution, so as to fully represent the clustering uncertainty characteristics of the blast field power characteristic distribution; specifically include the following contents:

[0070] If the transformed data is close to a Gaussian distribution, use the random sample consensus EM algorithm for clustering analysis;

[0071] Select the corresponding density discrimination criterion to identify the clustering structure in the data and determine the density discrimination criterion;

[0072] Use the random sample consensus algorithm to perform clustering analysis on the transformed data;

[0073] According to the results of the clustering analysis, construct a hybrid cloud model of the non-convex and non-Gaussian uncertainty blast field power characteristic distribution;

[0074] The parameters of the blast field power characteristic hybrid cloud model are estimated by sampling consensus iterative maximum likelihood. This model is used to predict the power characteristics of the blast field, specifically including the following contents:

[0075] Initialize the number of categories k = 0 of the cloud model, the type T of the covariance matrix, set the radius of the adjacent area around a point as Rn, and the minimum number of points contained in the adjacent area as Nn;

[0076] Randomly sample a blast field power characteristic point in the densest area. If there is no point to sample, end; if there is a point to sample, increase the number of categories k of the cloud model by 1, and perform non-convex segmentation using characteristic density and spatial strategy clustering;

[0077] Count the number Nn of blast field power characteristic points in the k-th category k , Nn is the minimum number of blast field power characteristic points contained in the category. If Nn k < Nn, decrease the number of categories k of the cloud model by 1, continue to randomly sample a blast field power characteristic point, and count and compare;

[0078] The Box-Cox transformation is performed on the power characteristics of the k-th type of fragmentation field to make it approximately conform to the Gaussian uncertainty distribution, and the expected Ex is calculated using the maximum likelihood MLE. i , Entropy i , super entropy He i , we get the cloud model Cl of the power characteristics of the k-th type of fragmentation field k .

[0079] A cloud model array construction system for warhead dynamic blasting fragment power characteristics, the system is used to execute the cloud model array construction method for warhead dynamic blasting fragment power characteristics, comprising:

[0080] Data acquisition module: used to mark the ammunition fragmentation fields with typical postures and velocities to form a fragmentation field array set {1, 2, ..., u, ..., n}, where u represents the uth fragmentation field, n is the total number of fragmentation fields, and each fragmentation field represents a set of fragments with similar posture and velocity characteristics; and to mark the typical intersection radius between the damaged target and the fragment trajectory in the fragmentation field to form {r1, r2, ..., r t , ..., r m}, where t is the tth intersection radius r t The index subscript of m represents the total number of intersection radii in the current debris field. At the same time, the fragments in the t-th intersection radius are marked to form {1, 2, ..., i, ..., l}. For r ti , represents the intersection radius r t The number of the i-th fragment on the previous page, l is the current intersection radius r ti The total number of fragments; and spherical slicing and Euclidean mapping of the typical intersection radius of the fragment field, while collecting fragment density, fragment velocity and fragment mass data under the power characteristic data of the fragment field, and collecting non-convex non-Gaussian distribution data and non-convex segmentation data of the fragment field;

[0081] Conversion analysis module: used to obtain the power characteristic data of the fragmentation field with non-convex and non-Gaussian distribution, and determine its distribution characteristics and regularity through conversion analysis; and the conversion analysis adopts a multi-peak distribution processing method suitable for the power characteristics of the fragmentation field and a conversion function that converts the data into an approximate Gaussian distribution;

[0082] Law analysis module: used to obtain the conversion function and convert the fragmentation field power characteristic data, and use statistical methods to analyze the discrete degree and fuzzy degree uncertainty law of the fragmentation field power characteristic slice mapping distribution;

[0083] The first index generation module is used to obtain the fragment density, fragment velocity and fragment mass data under the fragment field power characteristic data and then perform plane mapping to sequentially form the fragment field target intersection radius spherical slice density mapping, fragment field target intersection radius spherical slice velocity mapping, fragment field target intersection radius spherical slice mass mapping, and sequentially generate the plane projection slice fragment density ρ under the fragment field power characteristic function r , fragment speed v r , fragment mass m r , and the fragment density ρ r , fragment speed v r , fragment mass m r Perform analysis and processing to generate a debris assessment index of the t-th intersection radius under the u-th debris field;

[0084] Optimal determination module: used to obtain the spatial clustering characteristics of the geodesic distance kernel density of the power characteristics of the fragmentation field, and explore the regularity of its density spatial distribution; segment the non-convex distribution. If the density distribution of the power characteristics of the fragmentation field still does not conform to the Gaussian form after the non-convex distribution segmentation, explore the change regularity of the conversion function and determine the optimal conversion function of the Gaussian distribution. The steps for determining the optimal conversion function of the Gaussian distribution are data preparation and preliminary processing, kernel density estimation and spatial clustering, non-convex distribution segmentation, conversion function exploration and optimization, multi-convex multi-Gaussian distribution conversion function and mixed model;

[0085] For the problem of distribution uncertainty, a cloud model is used to characterize its discreteness and fuzziness. For the problem of non-convex and non-Gaussian uncertainty of the distribution of power characteristics of the fragmentation field, multiple hybrid cloud models are used to characterize the distribution of power characteristics of the fragmentation field.

[0086] The second index generation module is used to obtain the fragmentation evaluation index and the parameters contained in the hybrid model and analyze and process them, construct the hybrid cloud model evaluation index, and generate the evaluation result of the hybrid cloud model selection according to the hybrid cloud model evaluation index value range;

[0087] Hybrid cloud model building module: It is used to perform cluster analysis on the converted data based on the density discrimination criterion and adopt the random sampling consistent EM algorithm to build a hybrid cloud model of the power characteristic distribution of the non-convex and non-Gaussian uncertainty fragmentation field, so as to fully represent the cluster uncertainty characteristics of the power characteristic distribution of the fragmentation field;

[0088] A computer-readable storage medium stores a computer program, which implements the steps of the method when executed by a processor.

[0089] An electronic device comprises a processor, a memory and a computer program stored in the memory and executable on the processor, wherein the steps of the above method are implemented when the processor executes the program.

[0090] Compared with the prior art, the invention has the following beneficial effects: the power characteristics of the fragmentation field are accurately described through the hybrid cloud model; each fragmentation field is marked and data collected in detail, or the density, velocity, mass and non-convex and non-Gaussian distribution characteristics of the fragments are collected through simulation. This method can fully capture the complexity of the fragmentation field;

[0091] Obtain the fragment density ρ under the power characteristic function of the plane projection slice fragment field r , fragment speed v r , fragment mass m r The generated fragment assessment index can evaluate the potential power level of the fragmentation field; and then obtain the accuracy parameter ZQd, complexity parameter FZd, generalization capability value FHl and fragment assessment index E ti,u Perform analysis and processing to generate a hybrid cloud model evaluation index, and generate an evaluation result for cloud model selection;

[0092] By using transformation analysis and statistical methods, this method can not only identify the multi-peak characteristics of the fragmentation field distribution, but also explore the regularity of its density spatial distribution through cluster analysis; this method adopts the random sampling consistent EM algorithm and the sampling consistent iterative maximum likelihood estimation, and obtains the debris assessment index, the hybrid cloud model assessment index, as well as non-convex non-Gaussian distribution data and non-convex segmentation data as the input of the model, to construct a hybrid cloud model that can fully represent the clustering uncertainty characteristics of the power characteristics distribution of the fragmentation field, thereby improving the accuracy and reliability of the prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0093] Figure 1 It is a schematic diagram of the overall method flow of the present invention;

[0094] Figure 2 It is a flow chart of the system modules of the present invention;

[0095] Figure 3 A schematic diagram for constructing a hybrid cloud model to characterize the distribution of fragmentation field power characteristics. DETAILED DESCRIPTION

[0096] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with specific embodiments.

[0097] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The words "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0098] Embodiment 1:

[0099] See also Figure 1 , the present invention provides a technical solution:

[0100] This application is a method for constructing a cloud model array of the dynamic blasting field power characteristics of a warhead, and the specific steps include:

[0101] Step S1, marking the ammunition fragmentation fields with typical postures and velocities to form a fragmentation field array set {1, 2, ..., u, ..., n}, where u represents the uth fragmentation field, n is the total number of fragmentation fields, and each fragmentation field represents a set of fragments with similar posture and velocity characteristics; and marking the typical intersection radius between the damaged target and the fragment trajectory in the fragmentation field to form {r1, r2, ..., r t , ..., r m}, where t is the tth intersection radius r t The index subscript of m represents the total number of intersection radii in the current debris field. At the same time, the fragments in the t-th intersection radius are marked to form {1, 2, ..., i, ..., l}. For r ti , represents the intersection radius r t The number of the i-th fragment on the previous page, l is the current intersection radius r ti The total number of fragments; and spherical slicing and Euclidean mapping of the typical intersection radius of the fragment field, while collecting fragment density, fragment velocity and fragment mass data under the power characteristic data of the fragment field, and collecting non-convex non-Gaussian distribution data and non-convex segmentation data of the fragment field;

[0102] Step S2, obtaining fragmentation field power characteristic data of non-convex non-Gaussian distribution, and determining its distribution characteristics and regularity through conversion analysis; and the conversion analysis adopts a multi-peak distribution processing method suitable for fragmentation field power characteristics and a conversion function for converting data into an approximate Gaussian distribution;

[0103] Step S3, obtaining a conversion function, and converting the fragmentation field power characteristic data, using a statistical method to analyze the discrete degree and fuzzy degree uncertainty law of the fragmentation field power characteristic slice mapping distribution;

[0104] Step S4, after obtaining the fragment density, fragment velocity and fragment mass data under the fragment field power characteristic data, plane mapping is performed to sequentially form the fragment field target intersection radius spherical slice density mapping, the fragment field target intersection radius spherical slice velocity mapping, and the fragment field target intersection radius spherical slice mass mapping, and calibrate them as the fragment density ρ in sequence. r , fragment speed v r , fragment mass m r , and the fragment density ρ r , fragment speed v r , fragment mass m r Perform analysis and processing to generate a debris assessment index of the t-th intersection radius under the u-th debris field;

[0105] Step S5, obtaining the spatial clustering characteristics of the geodesic distance kernel density of the power characteristic of the fragmentation field, and exploring the regularity of its density spatial distribution; segmenting the non-convex distribution, if the density distribution of the power characteristic of the fragmentation field still does not conform to the Gaussian form after the non-convex distribution segmentation, exploring the change regularity of the conversion function, and determining the optimal conversion function of the Gaussian distribution, the steps of determining the optimal conversion function generation of the Gaussian distribution are data preparation and preliminary processing, kernel density estimation and spatial clustering, non-convex distribution segmentation, conversion function exploration and optimization, multi-convex multi-Gaussian distribution conversion function and mixed model;

[0106] For the problem of distribution uncertainty, a cloud model is used to characterize its discreteness and fuzziness. For the problem of non-convex and non-Gaussian uncertainty of the distribution of power characteristics of the fragmentation field, multiple hybrid cloud models are used to characterize the distribution of power characteristics of the fragmentation field.

[0107] Step S6, obtaining the fragmentation evaluation index and the parameters contained in the hybrid model and analyzing and processing them, constructing the hybrid cloud model evaluation index, and generating an evaluation result of the hybrid cloud model selection according to the hybrid cloud model evaluation index value range;

[0108] Step S7: Based on the density discrimination criterion, a random sampling consistent EM algorithm is used to perform cluster analysis on the converted data, and a mixed cloud model of the non-convex non-Gaussian uncertainty fragmentation field power characteristic distribution is constructed to fully represent the cluster uncertainty characteristics of the fragmentation field power characteristic distribution;

[0109] Step S8, obtaining the fragment assessment index of the t-th intersection radius under the u-th fragment field, the mixed cloud model assessment index, and the non-convex non-Gaussian distribution data and the non-convex segmentation data as the input of the model, and using the sampling consistent iterative maximum likelihood to estimate the mixed cloud model parameters of the fragment field power characteristics. The model is used to predict the power characteristics of the fragment field.

[0110] Embodiment 2:

[0111] Further illustrating on the basis of the first embodiment, the method of collecting the typical intersection radius of the damaged target and the fragmentation field of each fragmentation field, and performing spherical slicing and Euclidean mapping on the typical intersection radius of the fragmentation field, sequentially includes the steps of determining the position of the damaged target, collecting the typical intersection radius of the fragmentation field, spherical slicing, Euclidean mapping, and data recording and analysis;

[0112] Among them, the position of the damaged target is determined, and the coordinates of the damaged target corresponding to the t-th intersection radius of the u-th fragment field are set as (x ut ,y ut ,z ut );

[0113] The typical rendezvous radius of the debris field is collected to determine the rendezvous radius r of the rendezvous fragments with the damaged target ti ;

[0114] Spherical slicing is used to select the slice radius r s , and obtain a circular slice area;

[0115] The Euclidean mapping is used to map the obtained circular slice area onto a two-dimensional plane through the Euclidean mapping, and the position of each fragment is expressed by the Cartesian coordinates (x i ,y i ), where i is the number of the fragment under the current intersection radius;

[0116] Data records are used to record all relevant fragments (x i ,y i ) coordinates, and their corresponding typical intersection radius r i , and the intersection radius r of the debris at the intersection point between the target and the debris trajectory ti ;

[0117] Step 1: Determine the location of the target:

[0118] Target positioning: First, the specific location of the target in the fragmentation field needs to be determined, which can be achieved through optical, radar or other remote sensing technologies. The coordinates of the target in the uth fragmentation field are set as (x ut ,y ut ,z ut );

[0119] Step 2: Collect the typical intersection radius of the fragmentation field intersection:

[0120] Fragmentation field modeling: The fragmentation field is modeled as a spherical area centered on the explosion point of the explosive, and its radius depends on the farthest distance of fragment diffusion, which is assumed to be r meters;

[0121] Definition of intersection radius: The typical intersection radius is the distance from the explosion point of the explosive to the specific fragment location in the fragmentation field, denoted by r. i , where i is the number of the fragment under the current intersection radius;

[0122] Intersection calculation: Calculate the intersection point of the target and the debris trajectory, and then determine the intersection radius r of the debris that intersects with the target. ti , which can be done through geometric analysis or numerical simulation;

[0123] It should be noted that: the typical intersection radius contains m intersection radii, so for r ti Use the intersection radius, and for the fragmentation field as a whole, use the typical intersection radius overview;

[0124] Step 3, spherical slices:

[0125] Slice radius selection: Select a slice radius r s , this radius should be less than or equal to the intersection radius r ti ; r s =0.9×r ti .

[0126] Execute slice: On the spherical debris field model, with the explosive explosion point as the center and a radius of r s Slice the sphere to obtain a circular slice area, which will contain the trajectory of some fragments;

[0127] Step 4, Euclidean mapping:

[0128] Mapping to a two-dimensional plane: The obtained circular slice area is mapped to a two-dimensional plane through Euclidean mapping, which is achieved by converting spherical coordinates into Cartesian coordinates;

[0129] Quantitative description: On a two-dimensional plane, the position of each fragment is expressed by Cartesian coordinates (x i ,y i ), where i is the number of the fragment under the current intersection radius, so that the distribution of the fragments can be quantitatively described by two-dimensional coordinates;

[0130] Step 5, data recording:

[0131] Data Record: Record all relevant fragments (x i ,yi ) coordinates, and their corresponding intersection radius r ti ;

[0132] The debris density at the t-th intersection radius is denoted by ρ i , the fragment velocity is denoted as v i , the fragment mass is marked as m i ;

[0133] Debris density: refers to the number or distribution of debris per unit volume or area in a debris field. Density data can help determine the distribution and density of debris in a specific area, which is important for assessing potential risks and dangers;

[0134] Debris velocity: refers to the speed of movement of debris in the debris field. These data can describe the movement pattern and velocity distribution of debris in the debris field, which is crucial for assessing the impact of debris on the surrounding environment and objects, as well as for the formulation of safety measures;

[0135] Debris mass: refers to the total mass of debris in the debris field or the number of debris per unit mass. Knowing the total mass of the debris field or the number of debris per unit mass can help assess the degree of damage and power of the debris field, which is crucial for disaster management and emergency response.

[0136] Non-convex segmentation: describes the situation where the shape of the fragmentation field intersection radius map is not convex, which is often considered when studying fragments generated by explosions, impacts or other dynamic events;

[0137] Non-convex non-Gaussian distribution: describes the situation where the distribution of the intersection radius mapping of the fragment field is not only not convex, but also does not conform to the Gaussian distribution; Gaussian distribution usually describes the distribution of many phenomena in nature, but in some cases, such as in a fragment field, the distribution of debris exhibits non-Gaussian characteristics.

[0138] Embodiment three:

[0139] Further explanation based on the second embodiment, the multi-peak distribution processing method is a multi-convex distribution method, and the conversion function is a multi-Gaussian distribution conversion function; the conversion analysis steps are as follows:

[0140] For the multi-convex distribution method:

[0141] Step A, data preparation and preprocessing:

[0142] First, the power characteristics data are collected from each fragmentation field, including the fragment density ρ at the t-th intersection radius i , fragment speed v i and the fragment mass m i ; For the u-th fragmentation scene, record it as ρ ui 、vui 、m ui ;

[0143] Identification of non-convex distribution features: Perform preliminary statistical analysis on the data of each fragmentation field to identify its non-convex distribution features; non-convex features are manifested as skewness, multi-peaks or long-tail characteristics of the data;

[0144] Step B, multi-convex distribution analysis:

[0145] Data segmentation: According to the distribution characteristics of the fragmentation field data, the data is divided into several segments. The data within each segment is relatively uniform, but the segments show different distribution characteristics. The fragmentation field density data is divided into 3 segments. The data within each segment is similar, but the data distribution of each segment is different.

[0146] Intra-segment distribution modeling: Convex distribution modeling is performed on each segment of data. Simple convex distribution models, such as normal distribution and Poisson distribution, are used to fit the distribution characteristics of each segment of data. The first segment of data uses the normal distribution model. Fitting, where μ1, are the mean and variance of the data segment respectively;

[0147] Step C, comprehensive analysis and application:

[0148] Multi-convex distribution synthesis: The convex distribution models of each segment are combined to form a multi-convex distribution model to describe the distribution characteristics of the entire fragmentation field data;

[0149] Power characteristics prediction: Use the established multi-convex distribution model to predict and analyze the power characteristics of the fragmentation field;

[0150] For multi-Gaussian distribution transfer function:

[0151] Step D, non-convex data normalization:

[0152] Data standardization: First, the fragmentation field data is standardized to ensure that the data is at the same level. The data is converted into a standard normal distribution by calculating the difference between each fragmentation field data and the mean value and dividing it by the standard deviation;

[0153] Step E, apply the multi-Gaussian distribution conversion function:

[0154] Select the transformation function: Select a suitable multi-Gaussian distribution transformation function, specifically the Box-Cox transformation or the Yeo-Johnson transformation. These transformations can handle the skewness and multi-peak problems of the data and transform the non-normal distribution data into a form close to the Gaussian distribution.

[0155] Parameter adjustment: adjust the parameters of the conversion function according to the specific characteristics of the fragmentation field data to achieve the best conversion effect; for Box-Cox transformation, find the optimal λ value so that the converted data is closest to the normal distribution;

[0156] The method of obtaining the conversion function and converting the fragmentation field power characteristic data, and using statistical methods to analyze the discrete degree and fuzzy degree uncertainty law of the fragmentation field power characteristic slice mapping distribution, specifically includes the following contents:

[0157] Select and apply a transformation function:

[0158] The Box-Cox transformation function was used to adjust the data to be close to normal distribution;

[0159] Determine the optimal λ value through maximum likelihood estimation, and gradually narrow the search range until the optimal value is found;

[0160] Perform data transformation:

[0161] The optimal λ value is used to perform Box-Cox transformation on the fragmentation field characteristic data;

[0162] Standardize the transformed data to ensure that the mean is 0 and the standard deviation is 1;

[0163] Perform statistical analysis:

[0164] Analyze the degree of dispersion of data and calculate variance and standard deviation;

[0165] Quantify the uncertainty of data using information entropy methods;

[0166] Establish a mapping relationship between data, discreteness, and uncertainty, and analyze the rules;

[0167] Step A, conversion function application:

[0168] Select the transformation function: Use the Box-Cox transformation function, which is suitable for the transformation of positive data to approach normal distribution; the Box-Cox transformation formula is:

[0169]

[0170] Parameter estimation: Determine the optimal λ value through the maximum likelihood estimation method so that the transformed data is close to the normal distribution; set the initial λ search range to -5 to 5, and gradually narrow the search range through the Newton-Raphson method of the optimization algorithm until the optimal λ is found;

[0171] Step B, data conversion:

[0172] Perform transformation: Based on the determined optimal λ value, perform Box-Cox transformation on the fragment density, fragment velocity and fragment mass data under all fragmentation field power characteristic data;

[0173] Standardization of converted data: To facilitate analysis, the converted data was standardized to ensure that the mean was 0 and the standard deviation was 1;

[0174] Step C, statistical analysis:

[0175] Dispersion analysis: Calculate the variance and standard deviation of the transformed data to quantify the degree of dispersion of the data; variance σ 2 and standard deviation σ;

[0176] Compare the discreteness of data from different fragmentation sites and evaluate their consistency or difference after conversion;

[0177] The uncertainty analysis of fuzzy degree is as follows:

[0178] Use entropy or other uncertainty measurement methods, such as information entropy, to quantify the degree of fuzziness of the transformed data. The information entropy formula is:

[0179]

[0180] Where p(x g ) is the probability of the g-th event;

[0181] Analyze the uncertainty of the power characteristics data of different fragmentation fields and identify which characteristics or conditions have higher uncertainty;

[0182] Step D, analysis of uncertainty rules of mapping distribution:

[0183] Establishing a mapping relationship: Using the converted and standardized data, establish a mapping relationship between the power characteristics of the fragmentation field and its discreteness and uncertainty;

[0184] Regularity analysis: Analyze the relationship between the discreteness and uncertainty of data and the power characteristics of the fragmentation field, and identify relevant patterns or regularities;

[0185] Use correlation analysis and regression analysis in statistical tests to verify hypotheses and discovered regularities.

[0186] Embodiment 4:

[0187] Further explanation is given on the basis of the third embodiment, after obtaining the fragment density, fragment velocity and fragment mass data under the fragment field power characteristic data, plane mapping is performed to sequentially form the fragment field target intersection radius spherical slice density mapping, the fragment field target intersection radius spherical slice velocity mapping, and the fragment field target intersection radius spherical slice mass mapping, which specifically include the following contents:

[0188] In the fragmentation field array set {1, 2, ..., u, ..., n}, under the typical dynamic explosion conditions of the warhead, the flight trajectory of the uth fragmentation field is set to T u r i (x, y, z), which is the point set of the fragmentation field flight trajectory changing with time in three-dimensional space coordinates, but the warhead target damage capability assessment focuses on the density, velocity and mass distribution of fragments at a certain distance from the warhead explosion point. Since the warhead explosion fragments are spherical, a series of radius spheres intersecting the target with the explosion center as the center are used for slicing, so as to count the density, velocity and mass distribution of fragments on the spherical slices;

[0189] Since the three-dimensional coordinates of the fragments on the spherical slice are not conducive to characteristic statistics, T u r i (x, y, z) converted to azimuth φ-pitch angle Polar coordinate system, where φ = atan(y / x), The azimuth angle φ is used as the x-axis, the pitch angle The Euclidean plane coordinate system of spherical mapping is established for the y-axis. The plane mapping slice fragmentation field power characteristics of the spherical slice with a radius distance r are expressed by the following plane projection slice fragmentation field power characteristic function:

[0190]

[0191] The plane projection slice fragmentation field power characteristic function is convenient for establishing the fragmentation field power characteristic: where ρ r is the fragment density under the plane mapping, v r is the fragment velocity under plane mapping, m r is the fragment mass under plane mapping;

[0192] is the debris density function, which maps the debris density in spherical coordinates to the density distribution in plane coordinates, and is quantified by counting the number of debris per unit area on a spherical slice with a specific radius;

[0193] Assuming that the debris is evenly distributed on the sphere and each debris occupies a unit area, then at a specific azimuth angle φ and elevation angle The fragmentation density is expressed as:

[0194]

[0195] in, is the azimuth angle φ and the elevation angle The number of fragments per unit area in the direction, is the unit area. In the simplified model, each fragment is assumed to occupy the same area, so the fragment density is proportional to the number of fragments;

[0196] is the debris velocity function, which describes the velocity of the debris at a specific azimuth and elevation angle. This function is related to the initial velocity of the debris and the external force it receives. The velocity distribution function is obtained based on experimental data or theoretical models;

[0197] Assuming that the fragment velocity is mainly affected by the initial velocity and air resistance, and the air resistance is proportional to the square of the velocity; the fragment velocity is expressed as:

[0198]

[0199] where v0 is the initial velocity of the debris, β is a constant related to air resistance, is the debris in azimuth φ and elevation Flight distance in direction;

[0200] is the debris mass function, which represents the mass distribution of the debris at a given azimuth and elevation angle. The mass distribution is related to the type, size and distribution of the debris, and its specific expression also depends on the actual distribution of the debris;

[0201] Assuming that the mass distribution of the fragments is proportional to their size, and that the fragment size varies to a certain extent in different directions, the fragment mass can be expressed as:

[0202]

[0203] Among them, m0 is the base mass of the fragment, and α is a constant describing the variation of fragment size;

[0204] The azimuth angle φ is used as the x-axis, the pitch angle Establish a Euclidean plane coordinate system for spherical mapping of the y-axis, including the following:

[0205] Coordinate transformation basis: First, transform the point set T of the fragmentation field flight trajectory in three-dimensional space coordinates u r i (x, y, z) is converted to the azimuth angle φ and pitch angle in the polar coordinate system The conversion formula is as follows:

[0206] Azimuth: φ = arctan (y / x) or φ = atan (y / x);

[0207] Pitch Angle: or

[0208] Spherical surface is mapped to plane: azimuth angle φ is used as x-axis, pitch angle As the y-axis, establish the Euclidean plane coordinate system. This step actually maps the points on the spherical coordinate system to the two-dimensional plane, forming a simplified representation method that is easy to analyze and visualize;

[0209] Implementation of mapping function: After determining the plane coordinate system, the power characteristics of the fragmentation field can be obtained through its corresponding function. The specific forms of these functions will be derived based on actual measurements or simulation data to describe the characteristic distribution of debris at different azimuths and elevations.

[0210] Embodiment five:

[0211] Based on the fourth embodiment, the method further illustrates that the clustering characteristics of the geodesic distance kernel density of the fragmentation field power characteristics in space are obtained to explore the regularity of its density space distribution; the non-convex distribution is segmented, and if the density distribution of the fragmentation field power characteristics after the non-convex distribution segmentation still does not conform to the Gaussian form, the change regularity of the conversion function is explored to determine the optimal conversion function of the Gaussian distribution; specifically, the following contents are included:

[0212] The steps of determining the optimal conversion function generation of Gaussian distribution are data preparation and preliminary processing, kernel density estimation and spatial clustering, non-convex distribution segmentation, conversion function exploration and optimization, multi-convex multi-Gaussian distribution conversion function and mixed model.

[0213] The data preparation and preliminary processing are to obtain fragmentation field array data, damage targets and typical rendezvous radius, and prepare fragment characteristic data;

[0214] The kernel density estimation and spatial clustering are to calculate the kernel density estimation and apply the clustering method to identify high-density areas;

[0215] The non-convex distribution is divided into analyzing convexity, and the non-convex distribution data is divided into convex areas;

[0216] The conversion function exploration and optimization is to try basic conversion functions, explore advanced methods such as VAE, and determine the optimal conversion function;

[0217] The multi-convex multi-Gaussian distribution conversion function and the mixed model are to fit the characteristic distribution of the fragmentation field using a mixed Gaussian model and a mixed cloud model;

[0218] Step 1: Data preparation and preliminary processing:

[0219] Obtain the fragmentation field array set {1, 2, ..., u, ..., n} in the first embodiment and the intersection radius mark {r1, r2, ..., r t , ..., r m}data;

[0220] The typical intersection radius of the damaged target and the fragmentation field of each fragmentation field in the second embodiment is collected, and the typical intersection radius of the fragmentation field is spherically sliced ​​and Euclidean mapped; at the same time, data on the density, velocity and mass of fragments, as well as non-convex non-Gaussian distribution data and non-convex segmentation data of the fragmentation field are collected;

[0221] Step 2, kernel density estimation and spatial clustering:

[0222] Kernel Density Estimation (KDE): Kernel density estimation is used to calculate the geodesic distance kernel density of each fragmentation field power characteristic. KDE can help understand the spatial distribution of fragmentation field power characteristics.

[0223] Spatial cluster analysis: Apply spatial clustering methods, such as K-means or DBSCAN, to cluster the fragmentation field based on the kernel density estimation results to identify different density areas. Cluster analysis should focus on high-density areas, that is, areas with high fragment density, which represent higher fragment power characteristics;

[0224] Step 3, non-convex distribution segmentation:

[0225] Non-convex distribution segmentation: For each fragmentation field, the convexity of its power characteristic density distribution is analyzed. For fragmentation fields with non-convex distribution, segmentation techniques, such as density-based segmentation, are used to segment the non-convex distribution into several convex regions.

[0226] Step 4: Exploration and optimization of conversion functions:

[0227] 4.1 Preliminary conversion attempt:

[0228] Apply transformation functions: First, apply basic transformation functions to the non-convex distribution of fragmentation field data, such as logarithmic transformation log(x) and Box-Cox transformation Where λ is the parameter to be determined;

[0229] Refer to the parameter optimization in Example 3: For the Box-Cox transformation, the maximum likelihood estimation MLE is used to determine the optimal λ value so that the transformed data is close to the Gaussian distribution;

[0230] 4.2 Exploration of advanced conversion methods:

[0231] Advanced transformation function: If the above simple transformation method cannot effectively transform the data into a Gaussian distribution, use the variational autoencoder VAE in the deep learning method. VAE finds a complex nonlinear transformation function by learning the potential representation of the data. This function can map the original data to a space close to the Gaussian distribution.

[0232] Train the VAE model: set the dimensions of the latent variables and train the model by minimizing the reconstruction error plus the regularization term, choosing a loss function that is the squared error plus the KL divergence for optimization;

[0233] 4.3 Determination of the optimal conversion function:

[0234] Fit evaluation: For each transformation method, the fit between the transformed data and the Gaussian distribution was calculated. The Kolmogorov-Smirnov test was used to evaluate the fit and the P value was calculated. A higher P value means that the transformed distribution is closer to the Gaussian distribution.

[0235] Determine the optimal conversion function: compare the KS test results of different conversion methods and select the conversion method with the highest P value as the optimal conversion function;

[0236] Step 5, multi-convex multi-Gaussian distribution conversion function:

[0237] 5.1 Multi-convex multi-Gaussian distribution conversion:

[0238] Mixed Gaussian model: For each convex area after segmentation, a mixed Gaussian model GMM is used for further simulation. GMM can combine multiple Gaussian distributions to fit complex data distributions.

[0239] Parameter estimation: Use the expectation maximization EM algorithm to estimate the parameters of GMM, including the mean, covariance matrix and mixing coefficient of each Gaussian distribution;

[0240] Wherein, the hybrid cloud model generation consists of model construction and model quantification indicators;

[0241] The model construction means that, by combining the segmented regions and the results of the conversion function, a hybrid cloud model is constructed to characterize the overall structure of the power characteristic distribution of the fragmentation field, and the model can describe the distribution characteristics of each region and the relationship between them;

[0242] The model quantification index represents the evaluation index of the model, which is the accuracy parameter, complexity parameter and generalization ability value of the model. The accuracy parameter is calibrated as ZQd, the complexity parameter is calibrated as FZd, and the generalization ability value is calibrated as FH l.

[0243] To obtain the accuracy parameter ZQd:

[0244] Definition: The accuracy parameter ZQd reflects the degree of consistency between the model prediction results and the actual data, which is quantified by comparing the model's prediction results with the known actual results;

[0245] Calculation method: Use mean square error (MSE) or mean absolute error (MAE). For classification problems, the accuracy is the number of samples correctly predicted by the model divided by the total number of samples.

[0246] Obtaining the complexity parameter FZd:

[0247] Definition: The complexity parameter FZd measures the complexity of the model and is estimated by the number of model parameters. The more complex a model is, the more parameters it usually has.

[0248] Calculation method: Directly count the number of parameters in the model. For linear models, the number of parameters is equal to the number of features plus one. For neural networks, the number of parameters is the sum of all weights and biases in the network.

[0249] Obtaining the generalization ability value FH l:

[0250] Definition: The generalization value FH l measures the model's ability to predict unseen data. A model with good generalization ability can also perform well on new, unseen data.

[0251] Evaluation method: Cross-validation is used to evaluate the generalization ability of the model. K-fold cross-validation is used to divide the data set into k subsets. One of the subsets is used as the test set each time, and the rest are used as the training set. Then, the average performance index of the model on the k test sets is calculated.

[0252] Comprehensive Assessment:

[0253] Model selection: In practice, the choice of model depends not only on its accuracy ZQd, but also on the complexity FZd and generalization ability FHl of the model. The ideal model should have sufficient accuracy while maintaining low complexity and good generalization ability.

[0254] Trade-offs: In practical applications, it is usually necessary to make trade-offs between these indicators. For example, an overly complex model will lead to overfitting, that is, the model performs well on the training data, but performs poorly on new data. Therefore, when selecting a model, these factors should be considered comprehensively to find the best balance point;

[0255] Assume that the fragmentation field power characteristic density contains k cloud models, and the expectation is Ex j , which indicates the clustering of the density distribution of the power characteristics of the fragmentation field; Entropy is En j The random variable represents the uncertainty of the density distribution of the power characteristics of the fragmentation field; the super entropy is He j , represents the uncertainty of the distribution uncertainty of the power characteristic density of the fragmentation field; and j = 1, 2, ..., k, where k is a hyperparameter;

[0256] Define the certainty function μ of the power characteristic density of the cloud model fragmentation field j for:

[0257]

[0258] Because it is a hybrid cloud model, there are not only expected Ex j 、Entropy j 、Super entropy He j Model parameters need to be estimated, and there are also hyperparameters k and entropy En of the number of hybrid clouds. j Type and Super Entropy He j Hyperparameter estimation of type T, hyperentropy He j Type T represents different standard covariance matrices, the same standard covariance matrix, different diagonal covariance matrices and different slice covariance matrices; according to the different types of T, the corresponding super entropy calculation method is selected, as follows:

[0259] If T is the standard covariance matrix, then the super entropy He j The standard covariance matrix representing the density distribution of the power characteristics of the fragmentation field is calculated by the eigenvalue decomposition of the matrix;

[0260] The standard covariance matrix represents the correlation between dimensions, and its super entropy can be calculated by decomposing the eigenvalues ​​of the covariance matrix;

[0261] Specifically, let the matrix C be the standard covariance matrix, then its eigenvalue decomposition is C = QΛQ T , where Q is the eigenvector matrix, Λ is a diagonal matrix, and the elements on the diagonal are the eigenvalues;

[0262] Super entropy He j It can be defined as the sum of the eigenvalues ​​of the matrix C, that is, in is the dimension of the matrix, c1i represents the i-th eigenvalue of the matrix;

[0263] If T is a diagonal covariance matrix, then the super entropy He j The diagonal covariance matrix representing the density distribution of the power characteristics of the fragmentation field is calculated in a manner involving the processing of the corresponding diagonal elements;

[0264] The diagonal covariance matrix represents the correlation between dimensions, and except for the elements on the diagonal, the remaining elements are all zero, so its super entropy can be calculated directly by processing the diagonal elements;

[0265] Super entropy He j It can be defined as the sum of the diagonal elements, that is, in is the dimension of the matrix, c2i is the diagonal element;

[0266] If T is the slice covariance matrix, then the super entropy He j A slice covariance matrix representing the density distribution of the power characteristics of the fragmentation field, the calculation method involves slicing the matrix;

[0267] The slice covariance matrix represents the covariance matrix of a slice of a matrix in a specific dimension, and its super entropy requires processing the slice operation of the matrix;

[0268] Let matrix C be the slice covariance matrix, Ci represents the slice of the matrix in the i-th dimension, and the super entropy He j It can be defined as the sum of the eigenvalues ​​of each slice matrix, that is, in is the dimension of the matrix, p is the number of slices, c3 i,j is the eigenvalue of the i-th slice matrix.

[0269] Embodiment six:

[0270] Further explanation based on Example 5: Obtaining the fragment density ρ under the power characteristic function of the plane projection slice fragment field r , fragment speed v r , fragment mass m r , and analyze and process to generate the debris evaluation index E of the t-th intersection radius under the u-th fragment field ti,u , the calculation formula is as follows:

[0271]

[0272] Among them, E ti,u is the debris assessment index of the tth intersection radius in the uth debris field; l u is the intersection radius r in the uth fragment field ti The total number of fragments; v r,i 、m r,i and ρ r,i are the velocity, mass and density of the i-th fragment at the current intersection radius, Z is the normalization factor, ensuring that E ti,u The maximum value of does not exceed 1;

[0273] v max 、m max and ρ max are the maximum velocity, maximum mass, and maximum density among all fragments, respectively, for normalization;

[0274] w1, w2 and w3 are weight factors used to balance the effects of speed, mass and density in the evaluation index, and w1+w2+w3=1, w1, w2 and w3 are all non-negative numbers;

[0275] a1, a2 and a3 are adjustment factors used to adjust the influence of speed, mass and density;

[0276] is a fragment azimuth angle φ i and the pitch angle φ i is a function of φ0, which is used to consider the influence of the flight direction of the fragments on their potential power; φ0 and are the azimuth and elevation angles of the reference direction, respectively, which are used to determine the reference value of the potential power of debris in a specific direction;

[0277] Based on weight factors, adjustment factors and Setting E ti,u The value range of is [0,1];

[0278] Divide the [0,1] value range into the following level intervals, and define the potential power level of the fragmentation field corresponding to each interval;

[0279] When the value is 0≤E ti,u When <0.2, it is a very low potential power;

[0280] When the value is 0.2≤E ti,u When <0.35, it is low potential power;

[0281] When the value is 0.35≤E ti,u When <0.55, it is a medium potential power;

[0282] When the value is 0.55≤E ti,u When <0.68, it is a high potential power;

[0283] When the value is 0.68≤E ti,u When ≤1, it is a very high potential power;

[0284] To prove E ti,u The relationship between the value of and its corresponding potential power level, and the introduction of data for quantitative explanation, requires analysis of the calculation formula and its components of the evaluation index, which involves the following key points:

[0285] Normalization: Through v max 、m max and ρ max Normalizing velocity, mass, and density ensures that these metrics are appropriately scaled relative to their maximum values, which limits the contribution of each component to the range [0,1];

[0286] Weighting factors and adjustment factors: Weighting factors w1, w2 and w3 ensure the combined impact of speed, quality and density on the total evaluation index, and adjustment factors a1, a2 and a3 further adjust the impact of these components, understood as strengthening or weakening the impact of certain characteristics;

[0287] Directionality Factor: Taking into account the flight direction of the debris, this value is close to 1 when the debris direction is consistent with the reference direction, and decreases when it is not, which indicates that debris with high directional consistency has greater potential power;

[0288] Now, let's quantify the E corresponding to different power levels. ti,u The rationality of the value range;

[0289] Quantitative argument:

[0290] Assume there is a debris field containing debris with different velocity, mass and density data. The following is v r,i 、m r,i and ρ r,i Simulated data of

[0291] v r,i Speed ​​(m / s): [20,50,80,120,150], where v max =150;

[0292] m r,i Mass (kg): [0.1, 0.5, 1, 1.5, 2], where m max =2;

[0293] ρ r,i Density (g / cm 3 ): [2,4,6,8,10], where ρ max =10;

[0294] Directionality factor: Assume that all fragments are exactly aligned with the reference direction, i.e.

[0295] Assumptions The adjustment factor a1=a2=a3=1, and Z+l u =1;

[0296] The calculation formula is as follows:

[0297]

[0298] Calculate E for each fragment ti,u values, analyzing the potential power level they belong to:

[0299] For fragment 1:

[0300]

[0301] 0.1278 at 0 ≤ E ti,u <0.2, the potential power level is very low;

[0302] For fragment 2:

[0303]

[0304] 0.3278 in 0.2 ≤ E ti,u <0.35, the potential power level is low;

[0305] The calculation method for the remaining fragments is the same as above, and the E of the remaining fragments can be calculated. ti,u value and determines the potential power level of each fragment based on the provided range.

[0306] Embodiment seven:

[0307] Further explanation is given on the basis of Example 6, obtaining the accuracy parameter ZQd, the complexity parameter FZd, the generalization capability value FHl and the fragmentation evaluation index E ti,u After analysis and processing, a hybrid cloud model evaluation index is constructed and defined as HMEI. The calculation formula is as follows:

[0308]

[0309] Among them, ZQd represents the accuracy parameter of the model, which is calculated by mean square error MSE or mean absolute error MAE. For classification problems, the accuracy rate is used; FZd represents the complexity parameter of the model, which is estimated by the number of model parameters;

[0310] FH l represents the generalization ability value of the model, which is evaluated by the average performance index of k-fold cross validation;

[0311] e1, e2, and e3 are weight parameters of accuracy, inverse complexity, and generalization ability, respectively, and e1, e2, and e3 are all non-negative numbers, e1+e2+e3=1, to balance the importance of these three aspects;

[0312] This formula uses a normalization function and exponential function to limit the range of HMEI to [-1,1], providing an easy-to-interpret evaluation result;

[0313] Among them, the HMEI value close to 1 indicates that the comprehensive performance of the model is good, and the value close to -1 indicates that the comprehensive performance of the model is poor. The HMEI value range [-1,1] is divided into [0.8,1], [0.5,0.8), [0,0.5), [-0.5,0) and [-1,-0.5) intervals, and each interval generates a corresponding model selection evaluation result;

[0314] Assuming that the calculation of ZQd is based on the classification accuracy, mean square error (MSE) or mean absolute error (MAE) of the model, it is necessary to set a specific percentage of accuracy to define each interval:

[0315] High accuracy: accuracy ≥ 90% in classification problems, and relatively low MSE / MAE in regression problems, such as MSE < 0.05;

[0316] Moderate accuracy: classification accuracy is between 80% and 89%, or MSE / MAE is in the medium range, such as MSE between 0.05 and 0.1;

[0317] Low accuracy: classification accuracy < 80%, or high MSE / MAE, such as MSE> 0.1;

[0318] The complexity FZd is estimated based on the number of model parameters or the complexity of the model structure, quantified as a percentage of the number of parameters:

[0319] Reasonable complexity: the number of parameters does not exceed 120% of the minimum required model size;

[0320] Excessive complexity: the number of parameters is 120% to 150% of the minimum model size;

[0321] Extreme complexity: the number of parameters exceeds 150% of the minimum model size;

[0322] The generalization ability FH l is measured by the average performance of k-fold cross validation, and the specific criteria are as follows:

[0323] Good generalization ability: less than 5% performance drop in cross validation;

[0324] General generalization: performance degradation between 5% and 15%;

[0325] Poor generalization: performance drops by more than 15%;

[0326] When the HMEI value is between [0.8, 1], the model performs well. The model in this range has high accuracy, reaching more than 80% and the generalization ability decreases by less than 5%. It is recommended as the preferred model for the production environment;

[0327] When the HMEI value is [0.5, 0.8), the model performs well. The model in this range has medium accuracy, with an accuracy of 85% to 89%. The generalization ability decreases between 5% and 10%, but there is overfitting within 10% or the complexity exceeds the preset value of 5%. It is recommended to further tune or consider simplifying the model.

[0328] When the HMEI value is in [0,0.5), the model performs averagely, indicating that the model has a large trade-off between accuracy, complexity, and generalization ability. The accuracy is between 80% and 84%, the complexity is high, the number of parameters exceeds 150% of the minimum model size, and the generalization ability decreases by 10% to 15%. More data or more complex feature engineering is needed to improve it.

[0329] When the HMEI value is between [-0.5, 0), the model performs poorly. The model in this range has an overfitting problem of more than 20% or the accuracy is 30% lower than the benchmark value. The specific accuracy is between 70% and 79%, and the generalization ability decreases by 15% to 20%. The benchmark value is determined based on experimental data or expert evaluation. It is necessary to reconsider the structure of the model or introduce new data.

[0330] When the HMEI value is in [-1, -0.5), the model performs very poorly, with an accuracy of <70% and a generalization ability drop of more than 20%, which means that the model can hardly work on the test data and is completely unsuitable for the current problem. It is recommended to completely redesign the model.

[0331] Embodiment eight:

[0332] Further explanation is given on the basis of Example 7. Based on the density discrimination criterion, the random sampling consistent EM algorithm is used to perform cluster analysis on the converted data to construct a hybrid cloud model of non-convex non-Gaussian uncertainty fragmentation field power characteristic distribution to fully represent the cluster uncertainty characteristics of the fragmentation field power characteristic distribution; specifically, the following contents are included:

[0333] The transformed data were close to Gaussian distribution and cluster analysis was performed using the random sampling consensus EM algorithm;

[0334] Select the corresponding density discrimination criterion to identify the clustering structure in the data and determine the density discrimination criterion;

[0335] Cluster analysis was performed on the transformed data using a random sampling consensus algorithm;

[0336] According to the results of cluster analysis, a hybrid cloud model of non-convex and non-Gaussian uncertainty fragmentation field power characteristic distribution is constructed.

[0337] Data conversion: Obtain the converted data obtained from the hybrid cloud model evaluation index to ensure that the data meets the requirements of cluster analysis;

[0338] Density discrimination criteria determination: Density discrimination criteria are used to determine whether data points belong to the same cluster. Based on the density relationship between data points, commonly used density discrimination criteria include the ε-neighborhood discrimination criterion and the density reachability discrimination criterion in the DBSCAN algorithm;

[0339] Application of Random Sample Consensus EM Algorithm: Random Sample Consensus is a method for dealing with outliers or noise in data, which can improve the robustness of clustering analysis;

[0340] The EM algorithm is an iterative algorithm used to estimate the parameters in a probability model. It optimizes the model parameters by alternately performing the Expectation step (E-step) and the Maximization step (M-step);

[0341] Hybrid Cloud Model Construction: Each cluster corresponds to a cloud model, and the entire distribution of the power characteristics of the broken field is composed of a mixture of multiple such cloud models. The hybrid cloud model can fully represent the clustering uncertainty characteristics of the power characteristics distribution of the broken field;

[0342] Model Evaluation and Adjustment: Evaluate the performance of the constructed hybrid cloud model, check whether the model can accurately represent the clustering uncertainty characteristics of the power characteristics distribution of the broken field. If the model performance is not satisfactory, adjust the model parameters according to the evaluation results or re-perform the clustering analysis;

[0343] The method of using sample consensus iterative maximum likelihood to estimate the parameters of the hybrid cloud model of the power characteristics of the broken field, which is used to predict the power characteristics of the broken field, specifically includes the following:

[0344] Initialize the number of categories of the cloud model k = 0, the type of covariance matrix T, set the radius of the adjacent area around a point as Rn, and the minimum number of points contained in the adjacent area as Nn;

[0345] Randomly sample a power characteristic point of the broken field in the densest area. If there is no point to sample, end; if there is a point to sample, increment the number of categories of the cloud model k by 1, and perform non-convex segmentation using characteristic density and spatial strategy clustering;

[0346] Statistical number of power characteristic points Nn of the k-th category of the broken field k , where Nn is the minimum number of power characteristic points contained in the category. If Nn k < Nn, decrement the number of categories of the cloud model k by 1, continue to randomly sample a power characteristic point of the broken field, and perform statistics and comparison;

[0347] Perform Box-Cox transformation on the power characteristics of the k-th category of the broken field to approximately conform to the Gaussian uncertainty distribution, and use the maximum likelihood MLE to calculate the expectation Ex i , entropy En i , hyper-entropy He i , and obtain the cloud model Cl of the power characteristics of the k-th category of the broken field k .

[0348] Example Nine:

[0349] Further explanation based on the eighth embodiment, in order to verify the innovation and advantages of the present invention in predicting the power characteristics of the fragmentation field, the following embodiments are designed for testing and analysis;

[0350] First, the focus is on collecting necessary experimental data, including fragment density, velocity, and mass, as basic data input; this data set comes from detailed field tests and historical records to ensure the authenticity and reliability of the data; then, the data processing method proposed in the invention is used to analyze and process the fragment field data to generate a fragment evaluation index E for each fragment. ti,u , and classify the potential power level of the fragmentation field according to the index;

[0351] On this basis, the sampling consistent iterative maximum likelihood estimation method is further used to initialize and optimize the parameters of the hybrid cloud model of the power characteristics of the fragmentation field. In this process, multiple rounds of iterative tests are carried out by setting different initial parameters, such as the number of cloud model categories k, the covariance matrix type T, the radius Rn of the neighboring area, and the number of points Nn contained in the neighboring area.

[0352] Each iteration performs non-convex segmentation based on feature density and spatial strategy clustering, and continuously optimizes cloud model parameters through Box-Cox transformation and maximum likelihood MLE calculation to achieve the best prediction performance;

[0353] In this process, the HMEI index is introduced to evaluate the accuracy, complexity and generalization ability of the model to guide the selection and optimization of the model. In particular, by comparing the HMEI values ​​of the model under different parameters, it is clear which model parameter configuration can provide the best prediction effect, which not only ensures the accuracy of the model, but also controls the complexity and overfitting risk of the model.

[0354] The test data is shown in Table 1 below:

[0355] Table 1

[0356]

[0357] Tabular data analysis:

[0358] The debris assessment index E is generated by accurate analysis and processing of the debris field data. ti,u It can effectively classify the fragmentation field according to the potential power level. This classification method can intuitively reflect the degree of harm of different fragments and provide a scientific basis for subsequent decision-making;

[0359] Effect of debris density, velocity and mass on E ti,u Impact:

[0360] Observation data show that the density, speed and mass of fragments in fragmentation sites 1 to 5 are different, but their Eti,u The values ​​are also different, indicating that these parameters have an important influence on E ti,u There is a clear impact;

[0361] Fragment field 5 has the highest fragment density, velocity, and mass, and accordingly its E ti,u The value is also the highest, at 0.89, while Fragment Field 1 has the lowest E i,u value, which is 0.18;

[0362] Classification of potential power levels:

[0363] According to E ti,u The fragmentation field is divided into different potential power levels according to the numerical value of the fragmentation field, such as very low potential power, low potential power, medium potential power, high potential power and very high potential power. This classification method can intuitively reflect the degree of harm caused by the fragmentation and help decision makers take corresponding countermeasures.

[0364] Evaluation of HMEI value:

[0365] The HMEI value is used as an indicator to evaluate the accuracy, complexity and generalization ability of the model, and can be used to compare the performance of different model configurations. In this embodiment, the HMEI value is between 0.82 and 0.93, indicating that the model has high accuracy and generalization ability in predicting the power characteristics of the fragmentation field;

[0366] Model parameter optimization:

[0367] The parameters of the hybrid cloud model are initialized and optimized by using the sampling consistent iterative maximum likelihood estimation method. Multiple rounds of iterative tests are performed by setting different initial parameters to obtain the best prediction performance.

[0368] Based on the HMEI values ​​under different parameter configurations, it is possible to identify which parameter configurations can provide the best prediction results, thereby controlling the complexity of the model and the risk of overfitting;

[0369] Through the analysis of the table data, it can be seen that the invention has the innovation and advantages in predicting the power characteristics of the fragmentation field; it not only generates the fragmentation evaluation index E ti,u The potential power level of the fragmentation field is classified, and the accuracy and generalization ability of the evaluation model are evaluated by introducing the HMEI value, which provides a scientific basis for the selection and optimization of the prediction model;

[0370] Embodiment ten:

[0371] See also Figure 2 and Figure 3 A cloud model array construction system for warhead dynamic blasting fragment power characteristics, the system is used to execute the cloud model array construction method for warhead dynamic blasting fragment power characteristics, comprising:

[0372] Data acquisition module: used to mark the ammunition fragmentation fields with typical postures and velocities to form a fragmentation field array set {1, 2, ..., u, ..., n}, where u represents the uth fragmentation field, n is the total number of fragmentation fields, and each fragmentation field represents a set of fragments with similar posture and velocity characteristics; and to mark the typical intersection radius between the damaged target and the fragment trajectory in the fragmentation field to form {r1, r2, ..., r t , ..., r m}, where t is the tth intersection radius r t The index subscript of m represents the total number of intersection radii in the current debris field. At the same time, the fragments in the t-th intersection radius are marked to form {1, 2, ..., i, ..., l}. For r ti , represents the intersection radius r t The number of the i-th fragment on the previous page, l is the current intersection radius r ti The total number of fragments; and spherical slicing and Euclidean mapping of the typical intersection radius of the fragment field, while collecting fragment density, fragment velocity and fragment mass data under the power characteristic data of the fragment field, and collecting non-convex non-Gaussian distribution data and non-convex segmentation data of the fragment field;

[0373] Conversion analysis module: used to obtain the power characteristic data of the fragmentation field with non-convex and non-Gaussian distribution, and determine its distribution characteristics and regularity through conversion analysis; and the conversion analysis adopts a multi-peak distribution processing method suitable for the power characteristics of the fragmentation field and a conversion function that converts the data into an approximate Gaussian distribution;

[0374] Law analysis module: used to obtain the conversion function and convert the fragmentation field power characteristic data, and use statistical methods to analyze the discrete degree and fuzzy degree uncertainty law of the fragmentation field power characteristic slice mapping distribution;

[0375] The first index generation module is used to obtain the fragment density, fragment velocity and fragment mass data under the fragment field power characteristic data and then perform plane mapping to sequentially form the fragment field target intersection radius spherical slice density mapping, fragment field target intersection radius spherical slice velocity mapping, fragment field target intersection radius spherical slice mass mapping, and sequentially generate the plane projection slice fragment density ρ under the fragment field power characteristic function r , fragment speed v r , fragment mass m r , and the fragment density ρ r , fragment speed v r , fragment mass m r Perform analysis and processing to generate a debris assessment index of the t-th intersection radius under the u-th debris field;

[0376] Optimal determination module: used to obtain the spatial clustering characteristics of the geodesic distance kernel density of the power characteristics of the fragmentation field, and explore the regularity of its density spatial distribution; segment the non-convex distribution. If the density distribution of the power characteristics of the fragmentation field still does not conform to the Gaussian form after the non-convex distribution segmentation, explore the change regularity of the conversion function and determine the optimal conversion function of the Gaussian distribution. The steps for determining the optimal conversion function of the Gaussian distribution are data preparation and preliminary processing, kernel density estimation and spatial clustering, non-convex distribution segmentation, conversion function exploration and optimization, multi-convex multi-Gaussian distribution conversion function and mixed model;

[0377] For the problem of distribution uncertainty, a cloud model is used to characterize its discreteness and fuzziness. For the problem of non-convex and non-Gaussian uncertainty of the distribution of power characteristics of the fragmentation field, multiple hybrid cloud models are used to characterize the distribution of power characteristics of the fragmentation field.

[0378] The second index generation module is used to obtain the fragmentation evaluation index and the parameters contained in the hybrid model and analyze and process them, construct the hybrid cloud model evaluation index, and generate the evaluation result of the hybrid cloud model selection according to the hybrid cloud model evaluation index value range;

[0379] Hybrid cloud model building module: It is used to perform cluster analysis on the converted data based on the density discrimination criterion and adopt the random sampling consistent EM algorithm to build a hybrid cloud model of the power characteristic distribution of the non-convex and non-Gaussian uncertainty fragmentation field, so as to fully represent the cluster uncertainty characteristics of the power characteristic distribution of the fragmentation field;

[0380] Power prediction module: It is used to obtain the fragment evaluation index and mixed cloud model evaluation index of the t-th intersection radius under the u-th fragmentation field, as well as non-convex non-Gaussian distribution data and non-convex segmentation data as the input of the model, and adopts sampling consistent iterative maximum likelihood to estimate the mixed cloud model parameters of the power characteristics of the fragmentation field. This model is used to predict the power characteristics of the fragmentation field.

[0381] Embodiment eleven:

[0382] A computer-readable storage medium stores a computer program, which implements the steps of the method when executed by a processor.

[0383] Embodiment 12:

[0384] An electronic device comprises a processor, a memory and a computer program stored in the memory and executable on the processor, wherein the steps of the above method are implemented when the processor executes the program.

[0385] The above formulas are all dimensionless and numerical calculations. The formula is a formula for the most recent real situation obtained by collecting a large amount of data and performing software simulation. The preset parameters in the formula are set by technicians in this field according to actual conditions.

[0386] The above embodiments may be implemented in whole or in part by software, hardware, firmware or any other combination thereof. When implemented by software, the above embodiments may be implemented in whole or in part in the form of a computer program product. Those skilled in the art may appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein may be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed by hardware or software methods depends on the specific application and design constraints of the technical solution.

[0387] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, and may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0388] The above description is only a specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any technician familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application.

Claims

1. A cloud model array construction method for warhead dynamic blasting field power characteristics, characterized in that: The specific steps include: Step S1, marking the ammunition fragmentation fields with typical postures and velocities to form a fragmentation field array set {1, 2, ..., u, ..., n}, where u represents the uth fragmentation field, n is the total number of fragmentation fields, and each fragmentation field represents a set of fragments with similar posture and velocity characteristics; and marking the typical intersection radius between the damaged target and the fragment trajectory in the fragmentation field to form {r1, r2, ..., r t , ..., r m }, where t is the tth intersection radius r t The index subscript of m represents the total number of intersection radii in the current debris field. At the same time, the fragments in the t-th intersection radius are marked to form {1, 2, ..., i, ..., l}. For r ti , represents the intersection radius r t The number of the i-th fragment on the previous page, l is the current intersection radius r ti The total number of fragments; and spherical slicing and Euclidean mapping of the typical intersection radius of the fragment field, while collecting fragment density, fragment velocity and fragment mass data under the power characteristic data of the fragment field, and collecting non-convex non-Gaussian distribution data and non-convex segmentation data of the fragment field; Step S2, obtaining fragmentation field power characteristic data of non-convex non-Gaussian distribution, and determining its distribution characteristics and regularity through conversion analysis; and the conversion analysis adopts a multi-peak distribution processing method suitable for fragmentation field power characteristics and a conversion function for converting data into an approximate Gaussian distribution; Step S3, obtaining a conversion function, and converting the fragmentation field power characteristic data, using a statistical method to analyze the discrete degree and fuzzy degree uncertainty law of the fragmentation field power characteristic slice mapping distribution; Step S4, after obtaining the fragment density, fragment velocity and fragment mass data under the fragment field power characteristic data, plane mapping is performed to sequentially form the fragment field target intersection radius spherical slice density mapping, the fragment field target intersection radius spherical slice velocity mapping, and the fragment field target intersection radius spherical slice mass mapping, and calibrate them as the fragment density ρ in sequence. r , fragment speed v r , fragment mass m r , and the fragment density ρ r , fragment speed v r , fragment mass m r Perform analysis and processing to generate a debris assessment index of the t-th intersection radius under the u-th debris field; Step S5, obtaining the spatial clustering characteristics of the geodesic distance kernel density of the power characteristic of the fragmentation field, and exploring the regularity of its density spatial distribution; segmenting the non-convex distribution, if the density distribution of the power characteristic of the fragmentation field still does not conform to the Gaussian form after the non-convex distribution segmentation, exploring the change regularity of the conversion function, and determining the optimal conversion function of the Gaussian distribution, the steps of determining the optimal conversion function generation of the Gaussian distribution are data preparation and preliminary processing, kernel density estimation and spatial clustering, non-convex distribution segmentation, conversion function exploration and optimization, multi-convex multi-Gaussian distribution conversion function and mixed model; For the problem of distribution uncertainty, a cloud model is used to characterize its discreteness and fuzziness. For the problem of non-convex and non-Gaussian uncertainty of the distribution of power characteristics of the fragmentation field, multiple hybrid cloud models are used to characterize the distribution of power characteristics of the fragmentation field. Step S6, obtaining the fragmentation evaluation index and the parameters contained in the hybrid model and analyzing and processing them, constructing the hybrid cloud model evaluation index, and generating an evaluation result of the hybrid cloud model selection according to the hybrid cloud model evaluation index value range; Step S7: Based on the density discrimination criterion, a random sampling consistent EM algorithm is used to perform cluster analysis on the converted data, and a mixed cloud model of the non-convex non-Gaussian uncertainty fragmentation field power characteristic distribution is constructed to fully represent the cluster uncertainty characteristics of the fragmentation field power characteristic distribution; Step S8, obtaining the fragment assessment index of the t-th intersection radius under the u-th fragment field, the mixed cloud model assessment index, and the non-convex non-Gaussian distribution data and the non-convex segmentation data as the input of the model, and using the sampling consistent iterative maximum likelihood to estimate the mixed cloud model parameters of the fragment field power characteristics. The model is used to predict the power characteristics of the fragment field.

2. The cloud model array construction method of the warhead dynamic blasting field power characteristics according to claim 1 is characterized by: The spherical slicing and Euclidean mapping of the typical intersection radius of the fragmentation field specifically include the following contents: The contents include determining the location of the damaged target, collecting the typical intersection radius of the fragmentation field, spherical slicing, Euclidean mapping and data recording and analysis steps; Among them, the position of the damaged target is determined, and the coordinates of the damaged target for the uth fragment field are set as (x ut ,y ut ,z ut ); Collect the rendezvous radius of the fragment field to determine the rendezvous radius r of the rendezvous fragments with the damaged target ti ; Spherical slicing is used to select the slice radius r s , and obtain a circular slice area; The Euclidean mapping is used to map the obtained circular slice area onto a two-dimensional plane through the Euclidean mapping, and the position of each fragment is expressed by the Cartesian coordinates (x i ,y i ), where i is the number of the fragment under the current intersection radius; Data records are used to record all relevant fragments (x i ,y i ) coordinates, and their corresponding intersection radius r i , further is the intersection radius r of the debris at the intersection point between the target and the debris trajectory ti .

3. The cloud model array construction method of the warhead dynamic blasting field power characteristics according to claim 2 is characterized by: The multi-modal distribution processing method is a multi-convex distribution method, and the conversion function is a multi-Gaussian distribution conversion function; The method of obtaining the conversion function and converting the fragmentation field power characteristic data, and using statistical methods to analyze the discrete degree and fuzzy degree uncertainty law of the fragmentation field power characteristic slice mapping distribution, specifically includes the following contents: The Box-Cox transformation function was used to adjust the data to be close to normal distribution; Determine the optimal λ value through maximum likelihood estimation, and gradually narrow the search range until the optimal value is found; The optimal λ value is used to perform Box-Cox transformation on the fragmentation field characteristic data; Standardize the transformed data to ensure that the mean is 0 and the standard deviation is 1; Analyze the degree of dispersion of data and calculate variance and standard deviation; Quantify the uncertainty of data using information entropy methods; Establish a mapping relationship between data, discreteness and uncertainty, and analyze the rules.

4. The method for constructing a cloud model array of the dynamic blasting field power characteristics of a warhead according to claim 3, characterized in that: After obtaining the fragment density, fragment velocity and fragment mass data under the fragment field power characteristic data, plane mapping is performed to form the fragment field target intersection radius spherical slice density mapping, fragment field target intersection radius spherical slice velocity mapping, and fragment field target intersection radius spherical slice mass mapping in sequence, which specifically include the following contents: In the fragmentation field array set {1, 2, ..., u, ..., n}, set the flight trajectory of the uth fragmentation field to T u r i (x, y, z), which is the point set of the fragmentation field flight trajectory changing with time in three-dimensional space coordinates. u r i (x, y, z) converted to azimuth φ-pitch angle Polar coordinate system, where φ = a tan(y / x), The azimuth angle φ is used as the x-axis, the pitch angle The Euclidean plane coordinate system of spherical mapping is established for the y-axis. The plane mapping slice fragmentation field power characteristic of the spherical slice with a radius distance r is expressed by the following plane projection slice fragmentation field power characteristic function: Among them, ρ r is the fragment density under the plane mapping, v r is the fragment velocity under plane mapping, m r is the fragment mass under plane mapping; is the debris density function, which maps the debris density in spherical coordinates to the density distribution in plane coordinates, and is quantified by counting the number of debris per unit area on a spherical slice with a specific radius; is the debris velocity function, which describes the velocity of the debris at a specific azimuth and elevation angle. This function is related to the initial velocity of the debris and the external force it receives. The velocity distribution function is obtained based on experimental data or theoretical models; is the debris mass function, which represents the mass distribution of the debris at a given azimuth and elevation angle. The mass distribution is related to the type, size and distribution of the debris, and its specific expression also depends on the actual distribution of the debris.

5. The method for constructing a cloud model array of the dynamic blasting field power characteristics of a warhead according to claim 4, characterized in that: The method obtains the spatial clustering characteristics of the geodesic distance kernel density of the fragmentation field power characteristics, explores the regularity of its density spatial distribution; divides the non-convex distribution, and if the density distribution of the fragmentation field power characteristics after the non-convex distribution is divided still does not conform to the Gaussian form, explores the change regularity of the conversion function, and determines the optimal conversion function of the Gaussian distribution; specifically includes the following contents: The steps of determining the optimal conversion function generation of Gaussian distribution are data preparation and preliminary processing, kernel density estimation and spatial clustering, non-convex distribution segmentation, conversion function exploration and optimization, multi-convex multi-Gaussian distribution conversion function and mixed model. The data preparation and preliminary processing are to obtain fragmentation field array data, damage targets and typical rendezvous radius, and prepare fragment characteristic data; The kernel density estimation and spatial clustering are to calculate the kernel density estimation and apply the clustering method to identify high-density areas; The non-convex distribution is divided into analyzing convexity, and the non-convex distribution data is divided into convex areas; The conversion function exploration and optimization is to try basic conversion functions, explore advanced methods such as VAE, and determine the optimal conversion function; The multi-convex multi-Gaussian distribution conversion function and the mixed model are to fit the characteristic distribution of the fragmentation field using a mixed Gaussian model and a mixed cloud model; Wherein, the hybrid cloud model generation consists of model construction and model quantification indicators; The model building means combining the segmented regions and the results of the conversion function to build a hybrid cloud model to characterize the overall structure of the power characteristic distribution of the fragmentation field, and the model can describe the distribution characteristics of each region and the relationship between them; The model quantification index represents the evaluation index of the defined model, and the evaluation index is the accuracy parameter, complexity parameter and generalization ability value of the model, and the accuracy parameter is calibrated as ZQd, the complexity parameter is calibrated as FZd, and the generalization ability value is calibrated as FHl; Assume that the fragmentation field power characteristic density contains k cloud models, and the expectation is Ex j , which indicates the clustering of the density distribution of the power characteristics of the fragmentation field; Entropy is En j The random variable represents the uncertainty of the density distribution of the power characteristics of the fragmentation field; the super entropy is He j , represents the uncertainty of the distribution uncertainty of the power characteristic density of the fragmentation field; and j = 1, 2, ..., k, where k is a hyperparameter; Define the certainty function μ of the power characteristic density of the cloud model fragmentation field j for: This includes the expectation that Ex j 、Entropy j 、Super entropy He j Model parameters, x l,j represents the characteristic value of the lth sample of the jth mixed cloud.

6. The method for constructing a cloud model array of the dynamic blasting power characteristics of a warhead according to claim 5, characterized in that: Obtain the fragment density ρ under the power characteristic function of the plane projection slice fragment field r , fragment speed v r , fragment mass m r , and analyze and process to generate the debris evaluation index Eti,u of the t-th intersection radius under the u-th fragment field. The calculation formula is as follows: Among them, E ti,u is the debris assessment index of the tth intersection radius in the uth debris field; l u is the intersection radius r in the uth fragment field ti The total number of fragments; v r,i 、m r,i and ρ r,i are the velocity, mass and density of the i-th fragment at the current intersection radius, Z is the normalization factor, ensuring that E ti,u The maximum value of does not exceed 1; v max 、m max and ρ max are the maximum velocity, maximum mass, and maximum density among all fragments, respectively, for normalization; w1, w2 and w3 are weight factors used to balance the effects of speed, mass and density in the evaluation index, and w1+w2+w3=1, w1, w2 and w3 are all non-negative numbers; a1, a2 and a3 are adjustment factors used to adjust the influence of speed, mass and density; is a fragment azimuth angle φ i and the pitch angle φ i is a function of φ0, which is used to consider the influence of the flight direction of the fragments on their potential power; φ0 and are the azimuth and elevation angles of the reference direction, respectively, which are used to determine the reference value of the potential power of debris in a specific direction; Based on weight factors, adjustment factors and Set the value range of Eti,u to [0,1]; The [0,1] value range is divided into several level intervals, and the potential power level of the fragmentation field corresponding to each interval is defined. The larger the value, the higher the potential power level of the fragmentation field, and vice versa.

7. The method for constructing a cloud model array of warhead dynamic blasting field power characteristics according to claim 6, characterized in that: The accuracy parameter ZQd, complexity parameter FZd, generalization capability value FHl and fragmentation evaluation index Eti,u are obtained for analysis and processing, and the hybrid cloud model evaluation index is constructed. The hybrid cloud model evaluation index is defined as HMEI, and the calculation formula is as follows: Among them, ZQd represents the accuracy parameter of the model, which is calculated by mean square error MSE or mean absolute error MAE. For classification problems, the accuracy rate is used; FZd represents the complexity parameter of the model, which is estimated by the number of model parameters; FHl represents the generalization ability value of the model, which is evaluated by the average performance index of k-fold cross validation; e1, e2, and e3 are the weight parameters of accuracy, inverse complexity function, and generalization ability, respectively. All of them are non-negative numbers, e1+e2+e3=1. The range of HMEI is limited to [-1,1]. HMEI values ​​close to 1 indicate that the overall performance of the model is good, while values ​​close to -1 indicate that the overall performance of the model is poor. The HMEI range [-1,1] is divided into [0.8,1], [0.5,0.8), [0,0.5), [-0.5,0) and [-1,-0.5) intervals, and each interval generates a corresponding model selection evaluation result. Based on the density discrimination criterion, the random sampling consistent EM algorithm is used to perform cluster analysis on the converted data, and a mixed cloud model of the non-convex non-Gaussian uncertainty fragmentation field power characteristic distribution is constructed to fully represent the cluster uncertainty characteristics of the fragmentation field power characteristic distribution; specifically, the following contents are included: The transformed data were close to Gaussian distribution and cluster analysis was performed using the random sampling consensus EM algorithm; Select the corresponding density discrimination criterion to identify the clustering structure in the data and determine the density discrimination criterion; Cluster analysis was performed on the transformed data using a random sampling consensus algorithm; According to the results of cluster analysis, a hybrid cloud model of non-convex and non-Gaussian uncertainty fragmentation field power characteristic distribution is constructed. The mixed cloud model parameters of the fragmentation field power characteristics are estimated by using the sampling consistent iterative maximum likelihood. The model is used to predict the power characteristics of the fragmentation field, and specifically includes the following contents: Initialize the cloud model with the number of categories k=0, the covariance matrix type T, set the radius of the neighborhood around a point to Rn, and the number of points contained in the neighborhood to Nn; Randomly sample a fragmentation field power feature point in the most densely populated area. If there is no point that can be sampled, end the process. If there is a point that can be sampled, add 1 to the number of categories k in the cloud model, and use feature density and spatial strategy clustering for non-convex segmentation. Statistically count the number Nn of the power characteristic points of the k-th type of damage field k , where Nn is the minimum number of power characteristic points contained in the category. If Nn k < Nn, which is less than the number of categories of the cloud model minus 1, continue to randomly sample a power characteristic point of the damage field, and make a statistical comparison; The Box-Cox transformation is performed on the power characteristics of the k-th type of fragmentation field to make it approximately conform to the Gaussian uncertainty distribution, and the expected Ex is calculated using the maximum likelihood MLE. i , Entropy i , super entropy He i , we get the cloud model Cl of the power characteristics of the k-th type of fragmentation field k .

8. A cloud model array construction system for warhead dynamic blasting field power characteristics, characterized by: The system is used to execute the cloud model array construction method of the warhead dynamic blasting field power characteristics according to any one of claims 1 to 7, comprising: Data acquisition module: used to mark the ammunition fragmentation fields with typical postures and velocities to form a fragmentation field array set {1, 2, ..., u, ..., n}, where u represents the uth fragmentation field, n is the total number of fragmentation fields, and each fragmentation field represents a set of fragments with similar posture and velocity characteristics; and mark the typical intersection radius between the damaged target and the fragment trajectory in the fragmentation field to form {r1, r2, ..., rt, ..., rm}, where t is the index of the tth intersection radius rt The symbol m represents the total number of intersection radii under the current fragmentation field. At the same time, the fragments in the t-th intersection radius are marked to form {1, 2, ..., i, ..., l}. For rti, it represents the i-th fragment number on the intersection radius rt, and l is the total number of fragments on the current intersection radius rti; and the typical intersection radius of the fragmentation field is spherically sliced ​​and Euclidean mapped. At the same time, the fragment density, fragment velocity and fragment mass data under the power characteristic data of the fragmentation field are collected, and the non-convex non-Gaussian distribution data and non-convex segmentation data of the fragmentation field are collected; Conversion analysis module: used to obtain the power characteristic data of the fragmentation field with non-convex and non-Gaussian distribution, and determine its distribution characteristics and regularity through conversion analysis; and the conversion analysis adopts a multi-peak distribution processing method suitable for the power characteristics of the fragmentation field and a conversion function that converts the data into an approximate Gaussian distribution; Law analysis module: used to obtain the conversion function and convert the fragmentation field power characteristic data, and use statistical methods to analyze the discrete degree and fuzzy degree uncertainty law of the fragmentation field power characteristic slice mapping distribution; The first index generation module is used to obtain the fragment density, fragment velocity and fragment mass data under the fragment field power characteristic data and then perform plane mapping to form the fragment field target intersection radius spherical slice density mapping, fragment field target intersection radius spherical slice velocity mapping, fragment field target intersection radius spherical slice mass mapping in sequence, and calibrate them as fragment density ρ in sequence r , fragment speed v r , fragment mass m r , and the fragment density ρ r , fragment speed v r , fragment mass m r Perform analysis and processing to generate a debris assessment index of the t-th intersection radius under the u-th debris field; Optimal determination module: used to obtain the spatial clustering characteristics of the geodesic distance kernel density of the power characteristics of the fragmentation field, and explore the regularity of its density spatial distribution; segment the non-convex distribution. If the density distribution of the power characteristics of the fragmentation field still does not conform to the Gaussian form after the non-convex distribution segmentation, explore the change regularity of the conversion function and determine the optimal conversion function of the Gaussian distribution. The steps for determining the optimal conversion function of the Gaussian distribution are data preparation and preliminary processing, kernel density estimation and spatial clustering, non-convex distribution segmentation, conversion function exploration and optimization, multi-convex multi-Gaussian distribution conversion function and mixed model; For the problem of distribution uncertainty, a cloud model is used to characterize its discreteness and fuzziness. For the problem of non-convex and non-Gaussian uncertainty of the distribution of power characteristics of the fragmentation field, multiple hybrid cloud models are used to characterize the distribution of power characteristics of the fragmentation field. The second index generation module is used to obtain the fragmentation evaluation index and the parameters contained in the hybrid model and analyze and process them, construct the hybrid cloud model evaluation index, and generate the evaluation result of the hybrid cloud model selection according to the hybrid cloud model evaluation index value range; Hybrid cloud model building module: It is used to perform cluster analysis on the converted data based on the density discrimination criterion and the random sampling consistent EM algorithm to build a hybrid cloud model of the non-convex and non-Gaussian uncertainty fragmentation field power characteristic distribution, so as to fully represent the clustering uncertainty characteristics of the fragmentation field power characteristic distribution.

9. A storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for constructing a cloud model array of the dynamic explosive field power characteristics of the warhead as described in any one of claims 1 to 7 are implemented.

10. An electronic device, comprising a processor, a memory, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps of the method for constructing a cloud model array of the dynamic explosive field power characteristics of the warhead as claimed in any one of claims 1 to 7 are implemented.

Images