A short-term evolution method in continuum disassembly fragments based on numerical method

Abstract

This invention relates to the field of space debris environment modeling technology, specifically to a short-term evolution method for continuum disintegration debris based on numerical methods. The method includes: Step 1, establishing an initial distribution model of disintegration debris, including a disintegration debris velocity increment model and a numerical model of the initial distribution of disintegration debris; Step 2, sampling feature points of the continuum using a gradient-based sampling method, selecting the top N samples with the highest L2 norm scores of the gradient vectors as feature points of the continuum to be evolved; Step 3, processing the continuum equations using numerical solutions, considering the six orbital roots and four perturbation factors to perform short-term evolution of feature points; Step 4, reconstructing the final state distribution of disintegration debris using a Student's t-mix model. This invention fills the gap in previous research in this field, which only focused on ultra-short-term and long-term evolution, and has the beneficial technical effects of requiring fewer samples, having lower computational costs, shorter computation time, higher result accuracy, and stronger robustness.

Description

Technical Field

[0001] This invention relates to the field of space debris environment modeling technology, specifically to a short-term evolution method for continuum disintegration debris based on numerical methods. Background Technology

[0002] As human exploration of the space environment deepens, the amount of space debris is increasing year by year, and disintegration events are one of the main sources of space debris. Existing research largely focuses on the long-term evolution and mitigation strategies of the debris environment, while relatively little attention is paid to the short- to medium-term dynamics of debris evolution after a disintegration event. After a sudden disintegration event, the resulting debris cloud initially exhibits a sharp increase in spatial density and a highly concentrated yet uneven distribution. This high-density, non-uniform debris cloud forms a rapidly expanding "danger zone," posing an immediate and extremely high collision risk to nearby spacecraft in orbit. Therefore, in-depth research into the short- to medium-term evolution of space debris under sudden disintegration events has significant theoretical and engineering application value.

[0003] Current methods for assessing the evolution and risk of space debris generated by short-term, sudden disintegration events have the following limitations:

[0004] (1) In terms of evolution, the traditional Monte Carlo discretization method is weak in capturing low-probability events. Even with a large number of samples, it is still difficult to accurately reflect the overall distribution and evolution trend of the debris swarm. Therefore, a continuity method needs to be introduced to describe the debris evolution through a distribution function. However, existing analytical continuum-like methods usually only establish the initial distribution based on the orbital semi-major axis, eccentricity, and inclination. In short-term evolution, due to the limited time, the orbital parameters have not reached a statistical equilibrium state, and the distribution is difficult to become uniform. Therefore, it is necessary to include all orbital parameters in the initial modeling to more accurately characterize the initial state of the debris after disintegration.

[0005] (2) In terms of dynamic modeling, perturbation effects in short-term evolution cannot be adequately averaged over time, and the impact of instantaneous disturbances is significant. Higher-precision perturbation equations are needed to characterize complex short-term orbital dynamics. In this case, analytical solutions to the continuum equations are often difficult to obtain, making numerical solutions more suitable. This involves representing the continuum through finite feature points and indirectly reflecting the overall evolutionary pattern through the evolution of these feature points. Therefore, solving the continuum equations becomes a problem of selecting, evolving, and reconstructing feature points.

[0006] (3) In terms of collision risk assessment, the assessment method based on environmental engineering models has low computational efficiency and is difficult to meet the needs of rapid response to short-term emergencies; while the method based on analytical flux models is more efficient, its effective coverage period is usually short (several hours to several days), and it fails to fully cover the critical risk period of several days to several months after disintegration. Therefore, it is urgent to develop a collision risk analysis model that takes into account both computational efficiency and assessment accuracy and can cover the time window of several days to several months after disintegration. Summary of the Invention

[0007] To address the technical problems existing in the prior art, this invention proposes a short-term evolution method for fragments in continuum disintegration based on numerical methods, which is used to establish a fragment evolution model with high computational efficiency and accuracy.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] This invention provides a short-term evolution method for continuum disintegration fragments based on numerical methods, which is carried out according to the following steps:

[0010] Step S1: Establish an initial distribution model for the disintegration fragments, which includes a velocity increment model for the disintegration fragments and a numerical model for the initial distribution of the disintegration fragments.

[0011] Step S2: Based on the initial distribution model of the disintegration fragments established in Step S1, a gradient-based sampling method is used to sample the feature points of the continuum, selecting the points with the highest L2 norm score of the gradient vector. Each sample is used as a feature point of the continuum to be evolved;

[0012] Step S3: Based on the continuum feature points selected in step S2, the continuum equation is processed using a numerical solution method. The six orbital roots and four perturbation forces are considered to carry out the short- and medium-term evolution of the feature points, and the continuum feature points and their distribution after the short- and medium-term evolution are obtained.

[0013] Step S4: Based on the short-to-medium-term evolution continuum feature points obtained in Step S3, the final state distribution of the disintegration fragments is reconstructed using the Student's t-mix model.

[0014] Furthermore, step S1 specifically includes the following steps:

[0015] Step S11: Velocity increment distribution modeling, determining the actual fragment velocity increment distribution based on the standard disintegration model. ,pass The probability density of the velocity increment vector of the disintegration fragments and the probability density of the velocity vector of the disintegration fragments are obtained;

[0016] Step S12, Numerical modeling of the initial distribution of disintegration fragments: The model of the fragment velocity increment... enter And combined with the transformation matrix, based on the spacecraft position vector Inverse solution of possible orbital parameter vectors A numerical model of the initial distribution of disintegration fragments was established.

[0017] Further, in step S11, the method of... The probability density of the velocity increment vector of the disintegration fragments and the probability density of the velocity vector of the disintegration fragments are obtained by the following formulas:

[0018] The modulus of fragment velocity increment The probability density function is shown in equation (7):

[0019] (7)

[0020] In the formula, Let be the probability density function of the fragment velocity increment. Let log be the probability density function of the fragment velocity increment. The modulus of the fragment velocity increment;

[0021] Disintegration fragment velocity increment vector The probability density function is as shown in the formula. As shown:

[0022] (8)

[0023] In the formula, Let be the probability density function of the velocity increment vector of the disintegration fragments;

[0024] The probability density function of the velocity vector of the disintegration fragments is shown in the formula. As shown:

[0025] (9)

[0026] In the formula, Let be the probability density function of the velocity vector of the disintegration fragments. and These are the velocity vectors before and after the spacecraft disintegrates, respectively.

[0027] Furthermore, in step S12, the numerical modeling of the initial distribution of the disintegration fragments is divided into four parts:

[0028] First, determine the coordinate transformation matrix. and orbital parameter probability density function Secondly, the discrete semi-major axis, eccentricity, and right ascension of the ascending node. Space and considering the semi-major axis eccentricity Constraints are given for each fragment ,according to and spacecraft position vector Determine the possible orbital parameter vectors of the disintegration fragments. Then, using Find the velocity vector of the fragment. and the spacecraft velocity vector The modulus of velocity increment obtained by subtraction Finally, Input orbital parameter probability density function The initial distribution of disintegration fragments is obtained by combining the transformation matrix. .

[0029] Furthermore, step S2 specifically includes the following steps:

[0030] Step S21: Perform forward propagation for each sample and calculate the loss;

[0031] Step S22: Obtain the gradient vector through backpropagation and calculate its L2 norm as the score of the sample;

[0032] Step S23: Sort all samples in descending order according to gradient magnitude, and select the top-scoring samples. Each sample is a feature point of a continuum, and the sampling result is output.

[0033] Furthermore, in step S22, the formulas for the gradient vector and its L2 norm are as follows:

[0034] (15)

[0035] In the formula, Represents the orbital parameter vector of the disintegration fragments Compared to gradient vector, This represents the probability density function of the orbital parameters of the disintegration debris. ,in The orbital number is a six-element number;

[0036] The L2 norm is defined as follows:

[0037] (twenty two)

[0038] In the formula, Represents the gradient vector The L2 norm.

[0039] Furthermore, step S3 specifically includes the following steps:

[0040] Step S31: Determine the orbital parameter vectors under the four perturbation forces. The derivative with respect to time ;

[0041] Step S32 The orbital parameter vector for each sampled feature point. For each sampled feature point, the probability density function of the fragment orbital parameters is given. Calculate the impact of each perturbation force on the debris at the current moment. Impact ;

[0042] Step S33: Repeat step S32, using numerical methods to iterate continuously, and finally obtain the evolved debris orbit parameters. ;

[0043] Step S34 Mapped to ;

[0044] Step S35: Repeat steps S32 to S34 until all feature fragments have been traversed, and finally determine the evolved feature fragment distribution. .

[0045] Furthermore, step S4 specifically includes the following steps:

[0046] Step S41: Establish a Student t-mixture model representing the final state distribution of the disintegration fragments;

[0047] Step S42: Use the expectation-maximization algorithm to solve for the parameters in the student t-mixed model.

[0048] Further, in step S42, the method of using the expectation-maximization algorithm to solve for the parameters in the student t-mix model specifically involves: first, initializing the parameters in the TMM model, and then using the expectation-maximization algorithm to solve for the parameters in the TMM; through alternating expectation and maximization steps, converging to a threshold to solve for the above parameters; the parameters are the mean, covariance, and weighting coefficients.

[0049] The present invention also provides a computer-readable storage medium storing a program that, when executed by a processor, implements the above-described method for short-term evolution of continuum fragments based on numerical methods.

[0050] Compared with the prior art, the present invention has the following beneficial technical effects:

[0051] 1. Compared with the traditional Monte Carlo method, the method proposed in this invention has a smaller sample size, lower computational cost, and shorter computation time by dividing the grid and sampling based on gradient.

[0052] 2. This invention mainly studies the evolution of spacecraft debris over a period of several days to several months after the disintegration of the spacecraft. This is a short-to-medium-term evolution, which fills the gap in the past research in this field, which only focused on ultra-short-term (within a few hours) and long-term (several years and more) evolution.

[0053] 3. Compared with the prior art, the spatial density result of the disintegration fragments obtained by the present invention has higher accuracy. The reasons are as follows: on the one hand, the iterative method based on numerical methods is used when performing fragment evolution, which takes into account all orbital parameters and four perturbation forces, and can more accurately characterize the state of the fragments after evolution; on the other hand, the Student's t-mixture model is used when performing final state distribution, which is more robust than the traditional Gaussian mixture model. Attached Figure Description

[0054] Figure 1 This is a flowchart of the short-term evolution method for continuum disintegration fragments based on numerical methods according to the present invention;

[0055] Figure 2 This is a flowchart of the short-term evolution modeling of continuum disintegration fragments based on numerical methods according to the present invention;

[0056] Figure 3 This is a schematic diagram illustrating the short-term evolution of fragments in a continuum disintegration based on numerical methods, as presented in this invention.

[0057] in Figure 3 (a) is a schematic diagram of the initial distribution. Figure 3 (b) is a sampling diagram.

[0058] Figure 3 (c) is a schematic diagram of short- to medium-term evolution. Figure 3 (d) is a schematic diagram of the final state distribution reconstruction;

[0059] Figure 4 This is a schematic diagram of the spacecraft's orbital coordinate system according to the present invention;

[0060] Figure 5 This is a comparison chart of the reconstructed spatial density result of the final state distribution and the actual spatial density result in the example.

[0061] in Figure 5 (a) is a spatial density diagram of the final state distribution reconstruction using the method of the present invention.

[0062] Figure 5 (b) is a map showing the actual spatial density reconstructed using the Monte Carlo method. Detailed Implementation

[0063] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to the accompanying drawings. Specific Implementation Method 1

[0065] This invention provides a numerical method for the short-term evolution of fragments in the disintegration of a continuum. See [link to relevant documentation]. Figures 1 to 3 It is done in the following steps:

[0066] Step S1: Establish the initial distribution model of the disintegration debris. The initial distribution model of the disintegration debris includes the velocity increment model of the disintegration debris and the numerical model of the initial distribution of the disintegration debris, which specifically includes the following steps:

[0067] Step S11: Velocity increment distribution modeling, determining the actual fragment velocity increment distribution based on the standard disintegration model. ,pass The probability density of the velocity increment vector of the disintegration fragments and the probability density of the velocity vector of the disintegration fragments are obtained.

[0068] This method uses NASA's standard disintegration model, in which the equivalent diameter of the disintegration fragments is... , flour quality ratio Speed ​​increment The distribution is shown in formulas (1) to (3):

[0069] (1)

[0070] In the formula, The probability density function of the equivalent diameter of the disintegration fragments; It is a dimensionless parameter that depends on the type of disintegration and the physical properties of the disintegrated objects; The total number of fragments; ; ; The equivalent diameter (m) of the disintegrated fragments; This is the lower bound of the equivalent diameter; This is the upper bound of the equivalent diameter.

[0071] (2)

[0072] In the formula, The conditional probability density of the surface-to-mass ratio of the disintegration fragments is based on the equivalent diameter; The interval number is used to divide the data. ; The surface-to-mass ratio of the disintegrated fragments; ;function Let be the weight coefficient for the i-th interval. , These are the expected value and variance of each normal distribution interval for the surface-to-mass ratio, respectively. These three functions depend on the type of disintegration and the type of disintegrating object. This represents a normal distribution.

[0073] (3)

[0074] In the formula, The conditional probability density of the velocity increment of disintegration fragments based on the surface-to-mass ratio; ; The modulus (m / s) of the velocity increment of the disintegration fragments; function , These are the expected value and variance of the normal distribution of velocity increments, respectively, which depend on the type of disintegration and the type of disintegrating object.

[0075] From the formula To the formula Fragments can be obtained , and The joint probability density function is as shown in the formula. As shown:

[0076] (4)

[0077] In the formula, Let be the joint probability density function of the fragment's equivalent diameter, surface-to-mass ratio, and velocity increment.

[0078] fragments and The joint probability density function is shown in equation (5):

[0079] (5)

[0080] In the formula, Let be the joint probability density function of surface-to-mass ratio and velocity increment; ; .

[0081] The logarithmic probability density function of the fragment velocity increment is shown in Equation (6):

[0082] (6)

[0083] In the formula, Let log be the probability density function of the fragment velocity increment; It represents the set of real numbers.

[0084] The modulus of fragment velocity increment The probability density function is shown in equation (7):

[0085] (7)

[0086] In the formula, Let be the probability density function of the fragment velocity increment.

[0087] According to the formula To the formula In a given fragment , and When the range is defined, the velocity increment distribution of the disintegration fragments can be obtained through numerical fitting.

[0088] The disintegration model assumes that the velocity increment of the disintegrating debris relative to the disintegrating spacecraft has the same probability in any direction in three-dimensional space. Therefore, the velocity increment vector of the disintegrating debris... The probability density function is as shown in the formula. As shown:

[0089] (8)

[0090] In the formula, Let be the probability density function of the velocity increment vector of the disintegration fragments.

[0091] The probability density function of the velocity vector of the disintegration fragments is shown in the formula. As shown:

[0092] (9)

[0093] In the formula, Let be the probability density function of the velocity vector of the disintegration fragments. and These are the velocity vectors before and after the spacecraft disintegrates, respectively. Since the velocity increment of the disintegrated fragments has the same probability in any direction, the coordinate system can be freely chosen.

[0094] Step S12, Numerical modeling of the initial distribution of disintegration fragments: The model of the fragment velocity increment... enter And combined with the transformation matrix, based on the spacecraft position vector Inverse solution of possible orbital parameter vectors A numerical model of the initial distribution of disintegration fragments was established.

[0095] Numerical modeling of the initial distribution of disintegration fragments consists of four parts: First, determining the coordinate transformation matrix. and orbital parameter probability density function Secondly, the discrete semi-major axis, eccentricity, and right ascension of the ascending node. Space and considering the semi-major axis eccentricity Constraints are given for each fragment ,according to and spacecraft position vector Determine the possible orbital parameter vectors of the disintegration fragments. Then, using Find the velocity vector of the fragment. and the spacecraft velocity vector The modulus of velocity increment obtained by subtraction Finally, Input orbital parameter probability density function The initial distribution of disintegration fragments is obtained by combining the transformation matrix. The specific details are as follows:

[0096] The inertial coordinate system and spacecraft orbital coordinate system used in this paper are as follows: Figure 4 As shown, the x, y, and z axes belong to the inertial coordinate system, with the origin at the Earth's center of mass. The z-axis is parallel to the Earth's axis and points towards the North Pole. The x-axis points towards the intersection of the Prime Meridian and the equator. The y-axis, x-axis, and z-axis form a right-handed coordinate system. The t, h, and n axes belong to the spacecraft's orbital coordinate system, with the origin at the spacecraft's center of mass. The t-axis is along the direction of the spacecraft's velocity vector. The h-axis is perpendicular to the orbital plane. The n-axis, t-axis, and h-axis form a right-handed coordinate system.

[0097] In this coordinate system, the formula can be used Obtain the probability density function of the orbital parameters of the disintegration fragments. .

[0098] (10)

[0099] In the formula, ; .

[0100] The probability density function of the orbital parameters of the disintegration debris. Let be the probability density function of the location and velocity of the disintegration fragments; The orbital parameter vector of the disintegration debris (hereinafter referred to as the orbital parameter vector); The six orbital elements correspond to the semi-major axis, eccentricity, orbital inclination, right ascension of the ascending node, argument of the pericenter, and true anomaly of the debris orbit, respectively. The position of the disintegration debris in the spacecraft's orbital coordinate system ( ) and velocity vector ( The joint vector of ). This indicates that the matrix is ​​transformed into a determinant; The basis vector set transition matrix represents the transition from the inertial coordinate system to the spacecraft orbital coordinate system; Let be the coordinate transformation matrix, defined as shown in formula (11):

[0101] (11)

[0102] In the formula, For the latitude argument of the fragment, It is a positive half-focal string. Let ω be the angular momentum, and r be the distance from the debris to the Earth's center (km). ; ; ;

[0103] ;

[0104] ;

[0105] ;

[0106] ;

[0107] .

[0108] Through formula To the formula The vector probability density function of the disintegration fragment orbital parameters can be obtained. The expression is shown in formula (12):

[0109] (12)

[0110] This represents the probability density function of the orbital parameters of the disintegration fragments.

[0111] because The function is complex, so an inverse solution method is used to determine the orbital parameter vectors of the disintegration fragments. To further determine the velocity of the fragments and speed increment Finally, based on the formula Obtain the initial distribution of disintegration fragments .

[0112] See Figure 4 Given a point on the trajectory of the disintegrating debris, its coordinates in an inertial frame are... That is, the spacecraft disintegration point, given the disintegration debris. At this point, there are exactly two possible orbital parameters for the disintegrating fragments, denoted as . and ,in , .

[0113] Furthermore, given the disintegration fragments hour, and There are constraints between them, as shown in formulas (13) and (14):

[0114] (13)

[0115] In the formula, The radius of the Earth (km); The radius of the debris pericenter (km); The radius (km) is the centroid of the debris.

[0116] After sorting, we can obtain:

[0117] (14)

[0118] Step S2: Based on the initial distribution model of the disintegration fragments established in Step S1, a gradient-based sampling method is used to sample the feature points of the continuum, selecting the points with the highest L2 norm score of the gradient vector. Each sample is used as a feature point of the continuum to be evolved.

[0119] This sampling method evaluates the importance of each sample in the fragmented dataset obtained from the initial modeling by calculating the gradient magnitude. The specific process is as follows:

[0120] Step S21: Perform forward propagation for each sample and calculate the loss.

[0121] Step S22: Obtain the gradient vector through backpropagation and calculate its L2 norm as the score of the sample.

[0122] For the probability density function of the orbital parameters of the disintegration fragments in this method Define the orbital parameter vector of the disintegration fragments. Compared to gradient vector As shown in formulas (15) to (21):

[0123] (15)

[0124] (16)

[0125] (17)

[0126] (18)

[0127] (19)

[0128] (20)

[0129] (twenty one)

[0130] The L2 norm is defined as follows:

[0131] (twenty two)

[0132] In the formula, Represents the gradient vector The L2 norm.

[0133] Step S23: Sort all samples in descending order according to gradient magnitude, and select the top-scoring samples. Each sample is a feature point of a continuum, and the sampling result is output.

[0134] This method uses gradient information to select the samples that have the most significant impact on the model, thereby achieving importance-based data sampling.

[0135] Step S3: Based on the continuum feature points selected in step S2, the continuum equations are processed using a numerical solution method. The six orbital roots and four perturbation forces are considered to perform short- and medium-term evolution of the feature points, resulting in the continuum feature points and their distribution after short- and medium-term evolution.

[0136] The four perturbations take into account the gravitational perturbations of the Sun and Moon, the perturbations of the Earth's non-spherical shape, the perturbations of solar radiation pressure, and the perturbations of atmospheric drag.

[0137] The short-term evolution method for feature points specifically includes the following steps:

[0138] Step S31: Determine the orbital parameter vectors under the four perturbation forces. The derivative with respect to time .

[0139] Step S32 The orbital parameter vector for each sampled feature point. For each sampled feature point, the probability density function of the fragment orbital parameters is given. Calculate the impact of each perturbation force on the debris at the current moment. Impact .

[0140] Step S33: Repeat step S32, using numerical methods to iterate continuously, and finally obtain the evolved debris orbit parameters. .

[0141] Step S34 Mapped to The model considers the characteristics of feature fragments before and after evolution. The size remains unchanged.

[0142] Step S35: Repeat steps S32 to S34 until all feature fragments have been traversed, and finally determine the evolved feature fragment distribution. .

[0143] Step S4: Based on the short-to-medium-term evolution continuum feature points obtained in Step S3, the Student's t-mix model is used to reconstruct the final state distribution of the disintegration fragments.

[0144] Step S41: Establish a Student t-mixture model that represents the final state distribution of the disintegration fragments.

[0145] Compared to Gaussian mixture models, Student's t-mixture model (TMM) is insensitive to outliers and allows some data points far from the center. Therefore, this invention uses Student's t-mixture model for final state distribution reconstruction.

[0146] The fragment distribution obtained after evolution is divided into: The student t-distribution and t-mixture model are as follows:

[0147] (twenty three)

[0148] In the formula, It is the first The weighting coefficients of the t-distribution ( It must satisfy formula (24):

[0149] (twenty four)

[0150] It is the first The probability density of a t-distribution. Let represent the t-distribution of students, where For the first The mean of the t-distribution of a number of students. For the first The covariance matrix of the t-distribution of students. For the first The degrees of freedom of the t-distribution for each student; , , These are the parameters to be estimated.

[0151] Step S42: Use the expectation-maximization algorithm to solve for the parameters in the student t-mixed model.

[0152] First, the parameters in the TMM model are initialized, and then the expectation-maximization algorithm is used to solve for the parameters (including the mean) in the TMM. covariance and weighting coefficients By iteratively alternating between the expectation step and the maximization step, the solution converges to the threshold, and the above parameters are obtained. The iterative process is as follows:

[0153] (1) Expected steps

[0154] The posterior probability of each data point (i.e., the feature point of the continuum after short-term evolution) under each distribution is calculated as shown in Equation (25):

[0155] (25)

[0156] In the formula, These are characteristic points of the continuum after short- to medium-term evolution. for In the Degree of responsibility under each distribution Indicates the first A t-distribution.

[0157] Calculate the conditional expectation of the scaling variable:

[0158] (26)

[0159] (27)

[0160] In the formula, express In the Credibility weights under each distribution As an intermediate variable, For data dimensions.

[0161] (2) Maximization steps

[0162] The updated parameters are shown in formulas (23) to (25):

[0163] (28)

[0164] (29)

[0165] (30)

[0166] In the formula: It is the updated version of the first The weighting coefficients of a t-distribution. For the updated number The mean of the t-distribution of a number of students. For the updated number The covariance matrix of the t-distribution of students. The total number of sampling results (i.e., the first sampled in step S2) (sample). Specific Implementation Method Two

[0168] Based on the same inventive concept, the present invention also provides a computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the above-described method for short-term evolution of continuum fragments based on numerical methods.

[0169] The readable storage medium can be an internal storage unit of a device with data processing capabilities, such as a hard disk or memory; the readable storage medium can also be an external storage device, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc. equipped on the device.

[0170] Example:

[0171] The following simulation examples will further illustrate the specific implementation methods.

[0172] The simulation was performed according to the evolution method steps in Specific Implementation Method 1. In the simulation case, the initial orbital parameters of the disintegrated spacecraft are shown in the table below:

[0173]

[0174] Equivalent diameter of disintegration fragments The range is 10 -5 < <10 -1 m, surface-to-weight ratio The range is 10 -5 < <10 5 Speed ​​increment The range is 1 < <10 5 m / s.

[0175] Total number of sampling results in step S2 It is 135,000.

[0176] The evolution time in step S3 is 15 days, the initial evolution date is January 1, 2013, and the Earth's radius is... The distance is 6378 km, and the Earth's gravitational constant is 398600 km. 3 / s 2 The Moon's gravitational constant is 4887 km. 3 / s 2 The distance between the Earth and the Moon is 384,400 km.

[0177] Number of fragment distribution divisions in step S4 The degrees of freedom of all t-distributions are 15. All equal to 6, data dimensions The value is 4.

[0178] Figure 5 The diagram shows a comparison between the spatial density reconstructed based on the TMM final state distribution and the actual spatial density results from the direct evolution of all debris. The scatter points in the diagram correspond to the positions of the debris in the inertial coordinate system, and the color intensity represents spatial density; the closer to red, the greater the density, and the closer to blue, the smaller the density. Figure 5 The TMM reconstruction results in (a) show that high-density regions (red) are concentrated in the upper right and directly below the coordinate system, exhibiting a typical bimodal spatial structure. This distribution pattern is consistent with... Figure 5(b) The direct evolution distribution shows a high degree of agreement with the actual distribution, particularly exhibiting good consistency in the location, range, and trend of the main density peaks. The comparative results verify the reliability of the method of this invention in the short-term evolution of disintegration debris. The entire process of obtaining spatial density using this method takes less than 30 minutes, compared to the several hours required by the traditional Monte Carlo method, resulting in a shorter computation time.

[0179] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for short-term evolution of continuum disintegration fragments based on numerical methods, characterized in that... Follow these steps: Step S1: Establish an initial distribution model for the disintegration fragments, which includes a velocity increment model for the disintegration fragments and a numerical model for the initial distribution of the disintegration fragments. Step S2: Based on the initial distribution model of the disintegration fragments established in Step S1, a gradient-based sampling method is used to sample the feature points of the continuum, selecting the points with the highest L2 norm score of the gradient vector. Each sample is used as a feature point of the continuum to be evolved; Step S3: Based on the continuum feature points selected in step S2, the continuum equation is processed using a numerical solution method. The six orbital roots and four perturbation forces are considered to carry out the short- and medium-term evolution of the feature points, and the continuum feature points and their distribution after the short- and medium-term evolution are obtained. Step S4: Based on the short-to-medium-term evolution continuum feature points obtained in Step S3, the final state distribution of the disintegration fragments is reconstructed using the Student's t-mix model.

2. The short-term evolution method for continuum disintegration fragments based on numerical methods according to claim 1, characterized in that, Step S1 specifically includes the following steps: Step S11: Velocity increment distribution modeling, determining the actual fragment velocity increment distribution based on the standard disintegration model. ,pass The probability density of the velocity increment vector of the disintegration fragments and the probability density of the velocity vector of the disintegration fragments are obtained; Step S12, Numerical modeling of the initial distribution of disintegration fragments: The model of the fragment velocity increment... enter And combined with the transformation matrix, based on the spacecraft position vector Inverse solution of possible orbital parameter vectors A numerical model of the initial distribution of disintegration fragments was established.

3. The short-term evolution method for continuum disintegration fragments based on numerical methods according to claim 2, characterized in that, In step S11, the process of... The probability density of the velocity increment vector of the disintegration fragments and the probability density of the velocity vector of the disintegration fragments are obtained by the following formulas: The modulus of fragment velocity increment The probability density function is shown in equation (7): (7) In the formula, Let be the probability density function of the fragment velocity increment. Let log be the probability density function of the fragment velocity increment. The modulus of the fragment velocity increment; Disintegration fragment velocity increment vector The probability density function is as shown in the formula. As shown: (8) In the formula, Let be the probability density function of the velocity increment vector of the disintegration fragments; The probability density function of the velocity vector of the disintegration fragments is shown in the formula. As shown: (9) In the formula, Let be the probability density function of the velocity vector of the disintegration fragments. and These are the velocity vectors before and after the spacecraft disintegrates, respectively.

4. The short-term evolution method for continuum disintegration fragments based on numerical methods according to claim 2, characterized in that, In step S12, the numerical modeling of the initial distribution of disintegration fragments is divided into four parts: First, determine the coordinate transformation matrix. and orbital parameter probability density function Secondly, the discrete semi-major axis, eccentricity, and right ascension of the ascending node. Space and considering the semi-major axis eccentricity Constraints are given for each fragment ,according to and spacecraft position vector Determine the possible orbital parameter vectors of the disintegration fragments. Then, using Find the velocity vector of the fragment. and the spacecraft velocity vector The modulus of velocity increment obtained by subtraction Finally, Input orbital parameter probability density function The initial distribution of disintegration fragments is obtained by combining the transformation matrix. .

5. The short-term evolution method for continuum disintegration fragments based on numerical methods according to claim 1, characterized in that, Step S2 specifically includes the following steps: Step S21: Perform forward propagation for each sample and calculate the loss; Step S22: Obtain the gradient vector through backpropagation and calculate its L2 norm as the score of the sample; Step S23: Sort all samples in descending order according to gradient magnitude, and select the top-scoring samples. Each sample is a feature point of a continuum, and the sampling result is output.

6. The short-term evolution method for continuum disintegration fragments based on numerical methods according to claim 5, characterized in that, In step S22, the formulas for the gradient vector and its L2 norm are as follows: (15) In the formula, Represents the orbital parameter vector of the disintegration fragments Compared to gradient vector, This represents the probability density function of the orbital parameters of the disintegration debris. ,in The orbital number is a six-element number; The L2 norm is defined as follows: (22) In the formula, Represents the gradient vector The L2 norm.

7. The short-term evolution method for continuum disintegration fragments based on numerical methods according to claim 1, characterized in that, Step S3 specifically includes the following steps: Step S31: Determine the orbital parameter vectors under the four perturbation forces. The derivative with respect to time ; Step S32 The orbital parameter vector for each sampled feature point. For each sampled feature point, the probability density function of the fragment orbital parameters is given. Calculate the impact of each perturbation force on the debris at the current moment. Impact ; Step S33: Repeat step S32, using numerical methods to iterate continuously, and finally obtain the evolved debris orbit parameters. ; Step S34 Mapped to ; Step S35: Repeat steps S32 to S34 until all feature fragments have been traversed, and finally determine the evolved feature fragment distribution. .

8. The short-term evolution method for continuum disintegration fragments based on numerical methods according to claim 1, characterized in that, Step S4 specifically includes the following steps: Step S41: Establish a Student t-mixture model representing the final state distribution of the disintegration fragments; Step S42: Use the expectation-maximization algorithm to solve for the parameters in the student t-mixed model.

9. The short-term evolution method for continuum disintegration fragments based on numerical methods according to claim 8, characterized in that, In step S42, the method of using the expectation-maximization algorithm to solve for the parameters in the student t-mix model specifically involves: first, initializing the parameters in the TMM model, and then using the expectation-maximization algorithm to solve for the parameters in the TMM; through alternating expectation and maximization steps, converging to the threshold, and solving for the above parameters; the parameters are the mean, covariance, and weighting coefficients.

10. A computer-readable storage medium, characterized in that, The storage medium stores a program that, when executed by a processor, implements the short-term evolution method for continuum disintegration fragments based on numerical methods as described in any one of claims 1 to 9.

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