Rocket projectile launching end point intensity influence factor analysis method, system, equipment and medium

Abstract

The invention discloses a rocket projectile launching end point intensity influence factor analysis method, system and device and a medium. The method comprises the following steps: establishing a six-degree-of-freedom rigid in-vitro ballistic equation of the variable mass rocket projectile in a matrix form; the method comprises the following steps: generating a parameter sample based on a Monte Carlo random simulation principle by comprehensively considering three types of influence parameters of rocket projectile processing errors, initial disturbance and meteorological conditions, performing external trajectory equation numerical integration by combining a fourth-order Runge-Kutta method, and calculating a rocket projectile launching end point coordinate; three uncertainty sensitivity analysis methods are adopted, the influence degree of various parameters on the emission end point is quantified, results of the three methods are compared, and the influence degree of each factor is determined. According to the method, the influence degree of each factor on the rocket projectile launching terminal point is compared and analyzed by using multiple uncertainty sensitivity analysis methods, and the accuracy is relatively high.

Description

Technical Field

[0001] The present invention belongs to the technical field of weapon system engineering and trajectory simulation analysis, and in particular, relates to a method, system, equipment and medium for analyzing factors affecting the density of a rocket launch endpoint. Background Art

[0002] Multiple rocket launchers are widely deployed due to their wide firepower coverage, but the large dispersion of the landing points of unguided rockets is a key issue that restricts performance improvement. The trajectory of the rocket is affected by the rocket processing error (mass eccentricity L m1 、L m2 , dynamic imbalance angle β D1 , β D2 , thrust eccentric angle β p1 , β p2 , thrust eccentricity L1, L2), initial disturbance (launch position x, y, z; initial velocity v x 、v y 、v z ,; Initial pitch angle Initial deflection angle Initial roll angle γ; initial angular velocity ), meteorological conditions (wind speed w v ) and other factors. At present, the traditional rocket ballistic parameter analysis methods mainly include two categories:

[0003] 1. Test launch method: Acquiring data through multiple launch tests of real missiles requires the consumption of large amounts of ammunition, fuel, and measurement and control resources. A single test cycle usually lasts from several weeks to several months.

[0004] 2. Single analysis methods based on local sensitivity: A six-degree-of-freedom trajectory model for a rocket is established, parameters are set, and a simulated launch is conducted. After statistical analysis, sensitivity analysis using a single method, such as the Morris method, the Sobol index method, or the EFAST method, is performed to identify the impact of each factor. While single analysis methods based on local sensitivity can identify key influencing factors, they still have significant limitations. These methods inherently only reflect the linear response of parameters near their nominal values, fail to capture global nonlinear characteristics, and inadequately assess the interactions of strongly coupled parameters. While computationally efficient, the Morris method only provides a qualitative ranking and cannot quantify the impact, while also ignoring higher-order interactions between parameters. While the Sobol index method can account for the interaction effects between parameters, calculating the overall sensitivity index requires a sample size on the order of 10^4, making it computationally expensive. The EFAST method is sensitive to the probability distribution assumptions of the parameters, and its periodic sampling characteristics can lead to uneven coverage of the parameter space. Furthermore, the analysis results of single methods are often biased. Summary of the Invention

[0005] The present invention aims to provide a method for analyzing factors affecting the density of a rocket launch endpoint and a simulation system.

[0006] The technical solution for achieving the purpose of the present invention is: a method for analyzing factors affecting the density of a rocket launch endpoint, comprising:

[0007] (1) Exoballistic flight dynamics modeling: Establishing a matrix-based set of six-degree-of-freedom rigid body ballistic equations for a variable-mass rocket. The equations represent three types of factors that affect the rocket launch endpoint in matrix form.

[0008] (2) Using the Monte Carlo method, random parameter samples are generated based on the statistical characteristics of the three types of parameters that affect the rocket launch endpoint. Each set of samples corresponds to a complete launch parameter set of a rocket.

[0009] (3) Calculate the launch endpoint coordinates corresponding to each group of samples; use the matrix-formed six-degree-of-freedom rigid body trajectory equations of the variable mass rocket as deterministic equations, bring the samples generated by step (2) into the equations, and calculate to obtain the launch endpoint coordinates corresponding to each group of samples;

[0010] (4) Use three uncertainty sensitivity analysis methods to calculate the impact of each factor and rank them from large to small;

[0011] (5) Compare the rankings of the influence of factors calculated by each method; if the ranking results of the three methods are completely consistent, then this consistent ranking is adopted as the basis for determining the influence of each factor on the launch endpoint coordinates. The higher the ranking, the greater the influence; if the results are inconsistent, return to step (2), increase the number of simulation samples and recalculate until the ranking is consistent.

[0012] Furthermore, the three types of factors affecting the end point of rocket launch include rocket processing errors, initial disturbances, and meteorological conditions.

[0013] Furthermore, the matrix form of the variable mass rocket six-degree-of-freedom rigid body flight dynamics equations is:

[0014]

[0015] Where Y is the generalized velocity matrix of the rocket:

[0016]

[0017] M is the mass matrix:

[0018]

[0019] B is the generalized force and moment matrix:

[0020]

[0021] In the above formula, is the first-order derivative of the coordinate array of the rocket's geometric center O4 in the ground system with respect to time; G ω GB is the projection of the absolute angular velocity of the missile system in the ground system; m is the mass of the rocket; A GB is the direction cosine matrix of the missile system relative to the missile axis system; is the coordinate array of the rocket's center of mass C in the missile system; is the projection of the rocket's moment of inertia tensor about point O4 in the missile system; is the coordinate array of the rocket's center of mass C in the ground system; G f a K is the main arrow received by the rocket on the ground G The coordinate array of K is the main moment of the rocket in the ground system G The coordinate array of .

[0022] Furthermore, each set of random parameter samples is substituted into the matrix form of the variable mass rocket six-degree-of-freedom rigid body ballistic equations Solve the problem; for one input sample of each influencing factor, perform numerical integration of the ballistic equations based on the fourth-order Runge-Kutta method to calculate the corresponding launch endpoint ballistic parameters; repeat the flight dynamics simulation and calculate the launch endpoint ballistic parameters for other input samples of the influencing factors according to this method to form a ballistic dispersion data set and obtain the corresponding launch endpoint coordinates.

[0023] Furthermore, using each set of parameter samples as the independent variable and the launch endpoint coordinates as the dependent variable, the correlation analysis method, the Sobol sensitivity analysis method, and the EFAST method are used to calculate the sensitivity index of each influencing factor, and the ranking is performed accordingly. 5. A rocket launch endpoint density influencing factor analysis system, characterized by comprising:

[0024] The exterior ballistic flight dynamics modeling module is used to establish a matrix-based system of six-degree-of-freedom rigid body ballistic equations for variable-mass rockets. The system of equations represents three types of factors that affect the rocket launch endpoint in matrix form.

[0025] The simulation module generates random parameter samples based on the statistical characteristics of three types of parameters that affect the rocket launch endpoint. Each set of samples corresponds to a complete set of launch parameters for a rocket, and calculates the launch endpoint coordinates corresponding to each set of samples.

[0026] The analysis module is used to calculate the impact of each factor using three uncertainty sensitivity analysis methods and rank them from large to small;

[0027] The comparison module is used to compare the influence rankings of factors calculated by each method and determine the key influencing factors.

[0028] Compared with existing technologies, this invention has the following significant advantages: 1. It uses Monte Carlo random sampling combined with multi-method sensitivity analysis (Sobol / EFAST / correlation analysis) to overcome the large error problem of traditional single methods in high-dimensional nonlinear ballistic systems, significantly improves the accuracy of sensitivity analysis, and can quantify the impact of interactions between parameters. 2. It replaces physical testing with numerical simulation (fourth-order Runge-Kutta method), batch-calculates ballistic dispersions through a matrixed six-degree-of-freedom ballistic model, significantly reducing testing costs and cycles, and addressing the drawbacks of traditional testing methods, such as high resource consumption and long cycles (several weeks to several months). BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a schematic diagram of the coordinate system of the rocket's six-degree-of-freedom trajectory model and its transformation relationship.

[0030] Figure 2 It is a flow chart for solving the rocket flight dynamics.

[0031] Figure 3 It is the flow chart of Monte Carlo simulation system.

[0032] Figure 4 This is a histogram of the Spearman coefficient and Pearson coefficient of each factor in the X direction at a 20° angle.

[0033] Figure 5 is the S of each factor in the X direction at a 20° angle i and ST i Bar chart (Sobol).

[0034] Figure 6 is the S of each factor in the X direction at a 20° angle i and ST i Histogram (EFAST). DETAILED DESCRIPTION

[0035] A method for analyzing factors affecting the density of a rocket launch endpoint according to the present invention specifically comprises the following steps:

[0036] (1) Exoballistic flight dynamics modeling: A matrix-based set of six-degree-of-freedom rigid body ballistic equations for a variable-mass rocket is established. The matrix-based set of equations represents three factors that affect the rocket launch endpoint, namely, rocket manufacturing errors, initial disturbances, and meteorological conditions.

[0037] (2) Random flight dynamics simulation system based on Monte Carlo random principle: Random sampling of three types of uncertainty factors is performed to generate multiple groups of input samples; for one input sample of each influencing factor, the ballistic equation group is numerically integrated based on the fourth-order Runge-Kutta method to calculate the corresponding launch endpoint ballistic parameters; according to this method, the flight dynamics simulation is repeated for other input samples of the influencing factors and the launch endpoint ballistic parameters are calculated to form a ballistic dispersion data set.

[0038] (3) Uncertainty sensitivity analysis method to calculate the influence of each factor: The following methods are used to evaluate the influence of each factor on the launch endpoint coordinates:

[0039] 1. Correlation analysis method: calculate the Pearson correlation coefficient and Spearman correlation coefficient between each parameter and the emission endpoint coordinate;

[0040] 2. Sobol sensitivity analysis method: quantify the impact of single parameters and interactions between parameters through variance decomposition;

[0041] 3.EFAST method: It performs efficient sampling based on Fourier transform and then calculates the global sensitivity index through variance decomposition.

[0042] (4) Comparative analysis of the calculation results of the three methods: Compare the analysis results of the three methods and identify the key influencing factors.

[0043] The present invention will be further described below with reference to the accompanying drawings.

[0044] A specific implementation method adopted by the present invention is to establish a ballistic dynamics equation for a variable mass six-degree-of-freedom rigid body. Figure 1 It is a schematic diagram of the coordinate system of the six-degree-of-freedom trajectory model of the rocket and its conversion relationship; according to the rocket processing error (such as mass eccentricity L m1 , L m2 , dynamic imbalance angle β D1 , β D2 , thrust eccentric angle β p1 , β p2 , thrust eccentricity L1, L2), initial disturbance (launch position x, y, z; initial velocity v x 、v y 、v z ,; Initial pitch angle Initial deflection angle Initial roll angle γ; initial angular velocity ), meteorological conditions (wind speed w v)'s statistical characteristics (such as mean and mean square error), the corresponding random variable sequence is generated by the random simulation principle, and the ballistic dynamics equation of the variable mass six-degree-of-freedom rigid body is used as a deterministic equation to perform n deterministic calculations. In each calculation, the relevant random variables take a set of deterministic values ​​in the random variable sequence generated above. By counting the results of these n calculations, the statistical characteristics of the relevant parameters during the random flight process and the launch endpoint coordinates of each rocket are obtained. Figure 2 It is a flow chart for solving the rocket flight dynamics; calculate the influence of various factors on the launch endpoint coordinates according to different uncertainty sensitivity analysis methods; compare and analyze the calculation results of three methods to identify the key influencing factors, Figure 3 This is the flow chart of the Monte Carlo simulation system. The specific process includes the following 4 steps:

[0045] (1) Exoballistic flight dynamics modeling: A matrix-based set of six-degree-of-freedom rigid body ballistic equations for a variable-mass rocket is established. The matrix-based set of equations represents three factors that affect the rocket launch endpoint, namely, rocket manufacturing errors, initial disturbances, and meteorological conditions.

[0046] (2) Random flight dynamics simulation system based on Monte Carlo random principle: Random sampling of three types of uncertainty factors is performed to generate multiple groups of input samples; for one input sample of each influencing factor, the ballistic equation group is numerically integrated based on the fourth-order Runge-Kutta method to calculate the corresponding launch endpoint ballistic parameters; according to this method, the flight dynamics simulation is repeated for other input samples of the influencing factors and the launch endpoint ballistic parameters are calculated to form a ballistic dispersion data set.

[0047] (3) Uncertainty sensitivity analysis method to calculate the influence of each factor: The following methods are used to evaluate the influence of each factor on the emission endpoint:

[0048] 1. Correlation analysis method: calculate the Pearson correlation coefficient and Spearman correlation coefficient between each parameter and the emission endpoint coordinate;

[0049] 2. Sobol sensitivity analysis method: quantify the impact of single parameters and interactions between parameters through variance decomposition;

[0050] 3.EFAST method: It performs efficient sampling based on Fourier transform and then calculates the global sensitivity index through variance decomposition.

[0051] (4) Comparative analysis of the calculation results of three uncertainty sensitivity analysis methods: Compare the analysis results of the three methods and identify the key influencing factors.

[0052] In step (1), the matrix form of the variable mass rocket six-degree-of-freedom rigid body flight dynamics equations is:

[0053]

[0054] Where Y is the generalized velocity matrix of the rocket:

[0055]

[0056] M is the mass matrix:

[0057]

[0058] B is the generalized force and moment matrix:

[0059]

[0060] is the first-order derivative of the coordinate array of the rocket's geometric center O4 in the ground system with respect to time; G ω GB is the projection of the absolute angular velocity of the missile system in the ground system; m is the mass of the rocket; A GB is the direction cosine matrix of the missile system relative to the missile axis system; is the coordinate array of the rocket's center of mass C in the missile system; is the projection of the rocket's moment of inertia tensor about point O4 in the missile system; is the coordinate array of the rocket's center of mass C in the ground system; G f a K is the main arrow received by the rocket on the ground G The coordinate array of K is the main moment of the rocket in the ground system G The coordinate array of .

[0061] The law of weight change of rocket in flight

[0062]

[0063] f p∑ (t) is the total thrust at time t; μ eff is the effective exhaust velocity.

[0064] In step (2), according to the random variables (such as mass eccentricity L m1 、L m2 , dynamic imbalance angle β D1 , β D2 , thrust eccentric angle β p1 , β p2 , thrust eccentricity L1, L2), initial disturbance (launch position x, y, z; initial velocity v x 、v y 、v z ; Initial pitch angle Initial deflection angle Initial roll angle γ; initial angular velocity ) and meteorological conditions (wind speed w v ) statistical properties (such as mean and mean square error). Using the principle of random simulation, a corresponding sequence of random variables is generated. The ballistic dynamics equation for a variable-mass, six-degree-of-freedom rigid body is treated as a deterministic equation and subjected to n deterministic calculations. In each calculation, the relevant random variables sequentially take on a set of deterministic values ​​within the generated sequence of random variables. By summarizing these n calculations, the statistical properties of the relevant parameters during random flight and the launch endpoint of each rocket are obtained.

[0065] In step (3), the algorithms of the three uncertainty sensitivity analysis methods are 1. Pearson correlation coefficient and Spearman correlation coefficient

[0066] Pearson correlation coefficient r

[0067]

[0068] In the formula, n is the total number of samples, X i is the ith independent variable, Y i is the i-th dependent variable, is the mean value of each variable, σ X , σ Y is the standard deviation.

[0069] Spearman correlation coefficient r s

[0070]

[0071] n is the total sample size, d i is the rank difference between the independent variable and the dependent variable.

[0072] 2. Sobol global sensitivity analysis method

[0073] Assume that the mathematical model f(X) under study is in the input variable space I n ={X|0≤x i ≤1; i=1,……,n} square integrable, I n is an n-dimensional unit hypercube. In order to obtain the output function f(X), the input parameters X=(x1,x2…x n ) changes, expanding f(X) to 2 n The sum of increasing terms:

[0074]

[0075] Where f0 is a constant term, f i is a first-order term, fij is a second-order term, etc. Assume that in equation (9), except for f0, the results of each term when integrated with respect to each parameter it contains are all zero. Then:

[0076]

[0077] Where, 1≤i1<…<i s ≤n, in this case, it can be proved that the decomposition form of expression (9) is unique, and this decomposition form is called variance decomposition.

[0078] According to formula (10), all the terms in formula (9) are orthogonal to each other and can be expressed by integrating f(X):

[0079]

[0080] This orthogonality and integral representation ensure the uniqueness and accuracy of the decomposition. By analogy, each term in (9) can be obtained.

[0081] The total variance of the function f(X) is defined as:

[0082]

[0083] Indicates the influence of all parameters on the model output.

[0084] The partial variance of function f(X) is defined as:

[0085] D i =∫f i 2 (x i )dx i (15)

[0086]

[0087] In the model, a single parameter x i The impact on output is usually measured through methods such as sensitivity analysis.

[0088] This type of analysis assesses the contribution of each parameter to the model output at different times or under different conditions. Furthermore, the interactions between multiple parameters can be characterized through corresponding interaction terms, which collectively contribute to changes in the model output. These interactions are often analyzed by constructing interaction effect models or using statistical methods to more accurately understand the overall impact of complex relationships between parameters on the output.

[0089] Square both sides of Equation (9) and add them into the input variable space I n Integrating above, we can get:

[0090]

[0091] Arranging equations (14), (15), (16), and (17) yields:

[0092]

[0093] The global sensitivity index is defined as the ratio of partial variance to total variance:

[0094]

[0095] 3.EFAST global sensitivity analysis method

[0096] Let y = f(x1, x2, ..., x m ), after Fourier transform, it becomes y = f(s), and the function becomes

[0097]

[0098] Where,

[0099]

[0100] ω i is the parameter x i Oscillation frequency, i = 1, 2, ..., m; For each parameter x i The random initial phase is [0,2π]; p is the Fourier transform parameter; s is a scalar variable, with a value of [-π,π]; A p ,B p is the Fourier amplitude. Variance V i With X i The relationship is

[0101]

[0102] Where: p∈Z={-∞,…,-1,1,…,+∞}.

[0103] The total variance of the function is

[0104]

[0105] Fourier amplitude A p ,B p The approximate calculation formula is

[0106]

[0107] Where, The sampling range of s is [-π,π].

[0108] The total variance of the function can be decomposed into

[0109]

[0110] After normalization, the variable x i The first-order sensitivity index S i It can be expressed as the contribution to the total variance of the function:

[0111]

[0112] The total sensitivity index can be expressed as:

[0113]

[0114] Where: V i is the variable x i Variance caused by changes; V ij is the variable x i By variable x j Variance of contribution; V ～i Divide the variable x i The sum of the variances of all other variables.

[0115] In step (4), the influence of the factors is determined by comparative analysis based on the results calculated by the three methods obtained in step 3.

[0116] The following is a further explanation through the following simulation calculation example in conjunction with the accompanying drawings.

[0117] The influencing factors considered in the simulation are rocket parameters (mass eccentricity L m1 、L m2 , dynamic imbalance angle β D1 , β D2 , thrust eccentric angle β p1 , β p2 , thrust eccentricity L1, L2, initial mass m0), initial disturbance (launch position x, y, z; initial velocity v x 、v y 、v z ,; Initial pitch angle Initial deflection angle Initial roll angle γ; initial angular velocity ), wind speed w v (To simulate the impact of random wind on the landing point, a wind speed influence factor ω is set according to the normal distribution f ~N(1,0.1). After interpolating the current wind speed w0 and wind direction of the rocket in the function, the actual wind speed is w v =w0×ω f ), the parameter data are shown in Table 1 and Table 2.

[0118] Table 1 Rocket manufacturing process random parameters

[0119]

[0120] Table 2 Random parameters of initial disturbance of rocket launch

[0121]

[0122]

[0123] The stochastic flight dynamics simulation program compiled by this invention simulates a certain type of multiple rocket launcher firing 1000 rounds, totaling 18,000 rounds, to ensure a sufficiently large sample size and to calculate the rocket impact points. The 22 parameter data listed above are used as independent variables, and the two coordinates of the rocket impact points are used as dependent variables to calculate the Spearman coefficient and Pearson coefficient, respectively. Tables 3 and 4 show the results of different firing angles α. L The Spearman correlation coefficient and Pearson correlation coefficient in the X and Z directions are shown. Figure 4 This is a histogram of the Spearman coefficient and Pearson coefficient of each factor in the X direction at a 20° angle.

[0124] Table 3 Statistical values ​​of 20° shooting angle

[0125]

[0126] Table 4 50° shooting angle statistics

[0127]

[0128]

[0129] The random flight dynamics simulation program compiled by the present invention only needs to input the angle of fire α L and the number of Sobol samples N, the program will automatically output the first-order Sobol index S of each factor on the landing point in the X and Z directions under the shooting angle i and the total Sobol index ST i .

[0130] Set the angle of incidence α L =20, Sobol sample number N = 500, statistical calculation results are shown in Table 4.5; angle of incidence α L =50, Sobol sample number N=500, and the statistical calculation results are shown in Table 4.6. Figure 5 is the S of each factor in the X direction at a 20° angle i and ST i Bar chart.

[0131] Table 4.5 S in the X and Z directions for various factors at a 20° angle i and ST i Data (Sobol)

[0132]

[0133]

[0134] Table 4.6 S in the X and Z directions for various factors at a 50° angle i and ST i Data (Sobol)

[0135]

[0136] The random flight dynamics simulation program compiled by the present invention only needs to input the value of the angle of fire α L , the number of search curves N r , the number of samples N for each input parameter s The program will automatically output the first-order sensitivity index S of each factor to the landing point data in the X and Z directions under the shooting angle. i and total sensitivity index ST i .

[0137] The EFAST method stipulates that the number of samplings must be greater than or equal to 65 times the number of input parameters. The more samplings, the better the analysis results. Here, the sampling number is set to 200 times the input parameters, which means that 4400 rocket launches are simulated at two firing angles. L =20, the statistical calculation results are shown in Table 7; the angle of incidence α L =50The statistical calculation results are shown in Table 8. Figure 6 is the S of each factor in the X direction at a 20° angle i and ST i Histogram (EFAST).

[0138] Table 7 S in the X and Z directions for various factors at a 20° angle i and ST i Data (EFAST)

[0139]

[0140] Table 8 S in X and Z directions for various factors at 50° angle i and ST i Data (EFAST)

[0141]

[0142]

[0143] For the convenience of comparative analysis, the 20° angle is selected and the data in the X direction are plotted as a histogram. Figure 4 、 Figure 5 、 Figure 6 .according to Figure 4 It can be seen that: the initial pitch angular velocity The larger the value, the larger the range. The Spearman correlation coefficient and Pearson correlation coefficient between the two are close to 1, indicating that The size of the range X has the greatest impact on the size of the range, followed by the initial rocket mass m0, the thrust eccentricity L1, and the wind speed factor ω f .comprehensive Figure 5 、 Figure 6 It can be seen that the Sobol method and the EFAST method show high consistency in calculating the order sensitivity index and the total sensitivity index of each factor. Both methods can effectively reflect the degree of influence of the influencing factors on the output results. And it is observed that the ST of each random factor i Both are greater than S i , indicating that each factor is interactively coupled with other factors, jointly affecting the rocket's landing point. At a firing angle of 20°, the initial pitch angular velocity The impact on range is the greatest, with first-order sensitivity indices of 0.81 and 0.86 respectively; followed by the initial rocket mass m0 and wind speed factor ω f , but they are all less than 0.1, which has a certain degree of influence.

[0144] Based on the above results, the results of the analysis methods used here are highly consistent. The advantages of the Monte Carlo method and correlation analysis method are simple principles and ease of use. They can only analyze the degree of influence of a single independent variable on the output of the dependent variable, and cannot calculate the impact of interactions between variables on the output. The principles of the Sobol method and the EFAST method are both based on variance decomposition, and both can identify the sensitivity of each parameter by calculating the contribution ratio of each parameter to the output variance. However, in simulations, it was found that the Sobol method exhibited a negative exponential phenomenon when the sample selection was small. The results tended to stabilize after increasing the number of samples. In comparison, the EFAST method is more robust and efficient. Therefore, when the model has many parameters or the number of samples is small, the EFAST global sensitivity analysis method will be superior to the Sobol method.

Claims

1. A method for analyzing factors affecting the density of a rocket launch endpoint, characterized in that: include: (1) Exoballistic flight dynamics modeling: Establishing a matrix-based set of six-degree-of-freedom rigid body ballistic equations for a variable-mass rocket. The equations represent three types of factors that affect the rocket launch endpoint in matrix form. (2) Using the Monte Carlo method, random parameter samples are generated based on the statistical characteristics of the three types of parameters that affect the rocket launch endpoint. Each set of samples corresponds to a complete launch parameter set of a rocket. (3) Calculate the launch endpoint coordinates corresponding to each group of samples; use the matrix-formed six-degree-of-freedom rigid body trajectory equations of the variable mass rocket as deterministic equations, bring the samples generated by step (2) into the equations, and calculate to obtain the launch endpoint coordinates corresponding to each group of samples; (4) Use three uncertainty sensitivity analysis methods to calculate the impact of each factor and rank them from large to small; (5) Compare the rankings of the factors’ influence calculated by each method; if the ranking results of the three methods are completely consistent, then this consistent ranking is adopted as the basis for determining the influence of each factor on the launch endpoint coordinates. The higher the ranking, the greater the influence. If the results are inconsistent, return to step (2), increase the number of simulated samples and recalculate until the ranking is consistent.

2. The method for analyzing factors affecting the density of a rocket launch endpoint according to claim 1, wherein: The three types of factors that affect the end point of rocket launch include rocket processing errors, initial disturbances, and meteorological conditions.

3. The method for analyzing factors affecting the density of the rocket launch endpoint according to claim 2, wherein: The matrix form of the variable mass rocket's six-degree-of-freedom rigid body flight dynamics equations is: Where Y is the generalized velocity matrix of the rocket: M is the mass matrix: B is the generalized force and moment matrix: In the above formula, is the first-order derivative of the coordinate array of the rocket's geometric center O4 in the ground system with respect to time; G ω GB is the projection of the absolute angular velocity of the missile system in the ground system; m is the mass of the rocket; A GB is the direction cosine matrix of the missile system relative to the missile axis system; is the coordinate array of the rocket's center of mass C in the missile system; is the projection of the rocket's moment of inertia tensor about point O4 in the missile system; is the coordinate array of the rocket's center of mass C in the ground system; G f a K is the main arrow received by the rocket on the ground G The coordinate array of K is the main moment of the rocket in the ground system G The coordinate array of .

4. The method for analyzing factors affecting the density of the rocket launch endpoint according to claim 3, wherein: Substitute each set of random parameter samples into the matrix-formed six-degree-of-freedom rigid body ballistic equations of the variable mass rocket Solve the problem; for one input sample of each influencing factor, perform numerical integration of the ballistic equations based on the fourth-order Runge-Kutta method to calculate the corresponding launch endpoint ballistic parameters; repeat the flight dynamics simulation and calculate the launch endpoint ballistic parameters for other input samples of the influencing factors according to this method to form a ballistic dispersion data set and obtain the corresponding launch endpoint coordinates.

5. The method for analyzing factors affecting the density of the rocket launch endpoint according to claim 3, characterized in that: Taking each group of parameter samples as the independent variable and the launch endpoint coordinates as the dependent variable, the correlation analysis method, Sobol sensitivity analysis method and EFAST method were used to calculate respectively to obtain the sensitivity index of each influencing factor and rank them accordingly.

6. A rocket launch endpoint density influencing factor analysis system, characterized in that: include: The exterior ballistic flight dynamics modeling module is used to establish a matrix-based system of six-degree-of-freedom rigid body ballistic equations for variable-mass rockets. The system of equations represents three types of factors that affect the rocket launch endpoint in matrix form. The simulation module generates random parameter samples based on the statistical characteristics of three types of parameters that affect the rocket launch endpoint. Each set of samples corresponds to a complete set of launch parameters for a rocket, and calculates the launch endpoint coordinates corresponding to each set of samples. The analysis module is used to calculate the impact of each factor using three uncertainty sensitivity analysis methods and rank them from large to small; The comparison module is used to compare the influence rankings of factors calculated by each method and determine the key influencing factors.

7. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 5 are implemented.

8. A computer-readable 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 according to any one of claims 1 to 5 are implemented.

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