Carrier rocket injection precision identification method
By simulated target shooting, supplementary samples were generated and confidence interval estimation and covariance matrix method were used, the problem of orbital entry accuracy identification under small sample conditions was solved, and efficient orbital entry accuracy evaluation and optimization were achieved.
Patent Information
- Application Number
- CN202411512729.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-28
- Publication Date
- 2025-02-18
AI Technical Summary
The identification of orbital accuracy of the launch vehicle under small sample conditions is difficult, and the existing methods fail to make full use of pre-test information and actual flight samples, resulting in poor identification results.
The supplementary samples were generated by simulated target shooting, and the confidence interval estimation and covariance matrix method were used to identify and evaluate the entry accuracy and correlation.
The accuracy identification of launch vehicle entry into orbit under small sample conditions is achieved, providing reasonable evaluation and optimization basis, and reducing the test cost and development cycle.
Smart Images
Figure CN119475570A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the field of overall design of launch vehicles and relates to an orbital accuracy identification method suitable for launch vehicles. Background Art
[0002] Orbital insertion accuracy refers to the accuracy with which a launch vehicle sends its payload into orbit. It is an important evaluation indicator for measuring the overall performance of a launch vehicle. It is very important to scientifically and effectively evaluate the orbital insertion accuracy of a launch vehicle.
[0003] At present, the orbital accuracy identification of my country's launch vehicles mainly adopts the method of mathematical simulation, that is, only using simulation samples, without making full use of the useful information of actual flight samples, which will inevitably affect the identification effect. However, the launch mission of the launch vehicle is expensive and the number of tests is limited. Therefore, the samples used for orbital accuracy identification are small samples. If the orbital accuracy identification is only based on the flight test results, it is difficult to obtain a high confidence identification result. In response to such problems, it is necessary to study how to fully exploit and utilize the prior information (such as ground tests, simulation tests, etc.), expand the actual flight samples, and obtain the most reliable identification results. At present, the accuracy identification methods for small samples include the Bayes accuracy identification method based on multi-source information of the prior information credibility, the bootstrap method, the substitution point estimation method, the confidence upper bound estimation and confidence interval estimation method based on the parameter bootstrap method, and the Monte Carlo method. The above-mentioned missile hit accuracy identification methods can be fully used for reference, but they need to be combined with the correlation characteristics between the orbital parameters to form an effective method for orbital accuracy identification. However, the correlation research between the orbital parameters is affected by many complex factors, and an accurate and reliable correlation research method has not yet been formed. Summary of the invention
[0004] The purpose of the present invention is to overcome the above-mentioned defects and provide a method for evaluating the orbital accuracy of a launch vehicle, which solves the problem of high difficulty in evaluating the orbital accuracy of a launch vehicle under the condition of a small sample. The present invention generates supplementary samples by simulating target shooting, and uses confidence interval estimation and covariance matrix method to evaluate and assess the orbital accuracy and its correlation, which provides an important basis for reasonably evaluating and optimizing the overall performance of the launch vehicle under the condition of a small sample and making scientific decisions on subsequent mission plans, and has very important engineering application value.
[0005] In order to achieve the above-mentioned object of the invention, the present invention provides the following technical solutions:
[0006] A method for evaluating the accuracy of a launch vehicle entering orbit, comprising:
[0007] S1 generates supplementary samples of deviations of various orbital parameters;
[0008] S2 performs compatibility test and normality test on the supplementary samples and flight samples of each orbital parameter deviation, and takes the supplementary samples and flight samples that pass the compatibility test and normality test as the comprehensive samples;
[0009] S3 uses the confidence interval estimation method based on comprehensive samples to obtain the accuracy interval of each orbital parameter deviation;
[0010] S4 calculates the covariance matrix between the deviations of each orbital parameter based on the comprehensive samples;
[0011] The correlation between the orbital parameter deviations is obtained according to the covariance matrix between the orbital parameter deviations;
[0012] S5 completes the orbital accuracy assessment of the launch vehicle based on the accuracy range of each orbital parameter deviation and the correlation between each orbital parameter deviation.
[0013] Furthermore, in step S1, the method for generating a supplementary sample includes:
[0014] S1.1 Establish a rocket flight dynamics model;
[0015] S1.2 Determine the distribution law and mathematical model of each interference source that affects the orbital accuracy of the launch vehicle, add the distribution law and mathematical model of each interference source to the rocket flight dynamics model to perform Monte Carlo simulation shooting, and obtain supplementary samples.
[0016] Furthermore, the orbital parameter deviations of the launch vehicle include the perigee height deviation △H p , orbit period deviation △T, orbit inclination deviation △i, perigee argument deviation △ω, ascending node longitude deviation △Ω e Or latitude argument deviation △u.
[0017] Furthermore, in step S2, the compatibility test method includes:
[0018] Let X = (X 1 ,…X k ,...X m )′ is an m-dimensional random vector composed of the orbital parameter deviations of the launch vehicle, 1<m≤6;
[0019] For any orbital parameter deviation, let is a complementary sample with capacity n1, is a flight sample with capacity n2;
[0020] X 0 and X are combined into a sample with a capacity of n = n1 + n2, and the sample data in the sample are sorted from small to large to obtain a new sample sequence: z 1 ≤z 2≤…≤z n ;
[0021] According to X 0 the ranks of the sample data are obtained according to their order in the new sample sequence, and then the rank sum R of X 0 is obtained;
[0022] At the preset significance level α, the upper and lower limits Cu(α / 2) and CL(α / 2) of the rank sum are obtained. When Cu(α / 2) < R < CL(α / 2), the supplementary samples and the on-site samples are considered to belong to the same population through the compatibility test; otherwise, the supplementary samples and the on-site samples are considered to belong to different populations.
[0023] Furthermore, in step S2, the methods of normality test include:
[0024] Based on the new sample sequence, calculate the b value of each orbit injection parameter deviation;
[0025] Calculate the statistic W according to the b value: where S 2 is the sample variance of the orbit injection parameter deviation;
[0026] According to the significance level α and the sample size n, obtain the critical value Wα(n) of W;
[0027] If for each orbit injection parameter deviation, it can satisfy W ≥ Wα(n), then the normality test is passed, indicating that each orbit injection parameter deviation follows a normal distribution population; otherwise, it does not follow a normal distribution.
[0028] Furthermore, in step S3, the method of obtaining the precision interval of each orbit injection parameter deviation includes:
[0029] Assume that the orbit injection parameter deviations are independent of each other, and the mean μ and variance σ are unknown. Then, at the confidence level of 1 - α, 0 < α < 1, there is:
[0030]
[0031] where P represents probability, represents the chi-square distribution at the confidence level of 1 - α and sample size n;
[0032] Then, at the confidence level of 1 - α, the upper confidence bound 2 of the variance σ is:
[0033]
[0034] Furthermore, the upper confidence bound of 3σ is:
[0035]
[0036] Furthermore, in step S4, the covariance matrix P′ between the orbit entry parameter deviations is:
[0037]
[0038] Among them, c ij = cov(X i ,X j ), for different orbital parameter deviations X i , X j The covariance coefficient between .
[0039] Furthermore, in step S4, the correlation coefficient matrix R′ between the orbital parameter deviations is obtained according to the covariance matrix between the orbital parameter deviations:
[0040]
[0041] Among them, ρ ij is the orbital parameter deviation X i , X j The correlation coefficient of ij ≤1;
[0042]
[0043] Compared with the prior art, the present invention has at least one of the following beneficial effects:
[0044] (1) The present invention creatively proposes a method for evaluating the orbital accuracy of a launch vehicle, which makes full use of simulation methods to make up for the shortage of on-site samples, reduces the test cost, and shortens the development cycle;
[0045] (2) The present invention solves the problem of high difficulty in orbital precision identification under small sample conditions of launch vehicles, and at the same time realizes quantitative evaluation of the correlation between various orbital parameters of launch vehicles through the covariance matrix method, which provides an important basis for the overall performance identification of launch vehicles and closed-loop optimization of precision indicators. BRIEF DESCRIPTION OF THE DRAWINGS
[0046] Figure 1 The present invention is a flow chart of a method for evaluating the orbital accuracy of a launch vehicle. DETAILED DESCRIPTION
[0047] The following detailed description of the present invention will make the features and advantages of the present invention more clear and explicit.
[0048] The word "exemplary" is used exclusively herein to mean "serving as an example, embodiment, or illustration." Any embodiment described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments. Although various aspects of the embodiments are shown in the drawings, the drawings are not necessarily drawn to scale unless otherwise noted.
[0049] In view of the small sample situation and the characteristics of the orbital insertion parameters themselves, the present invention proposes an orbital insertion accuracy identification method suitable for launch vehicles. Supplementary samples are generated by simulated target shooting, and confidence interval estimation and covariance matrix calculation are used to realize the identification of the orbital insertion accuracy and its correlation of the launch vehicle, which provides an important basis for the reasonable evaluation and optimization of the overall performance of the launch vehicle and the scientific decision-making of the subsequent mission plan.
[0050] The steps of a method for evaluating the orbital accuracy of a carrier rocket of the present invention include:
[0051] Generate supplementary samples through Monte Carlo simulation of target shooting;
[0052] Compatibility test and normality test are performed on the supplementary sample and flight sample of each orbital parameter deviation;
[0053] Ensure that they all come from the same normal distribution population, so as to obtain a comprehensive sample for orbital accuracy assessment;
[0054] The confidence interval estimation method is used to obtain the orbital accuracy assessment values of each launch vehicle;
[0055] Calculate the covariance matrix between various orbital parameters and quantitatively evaluate the correlation between the deviations of various orbital parameters;
[0056] The above results are combined to complete the assessment of the launch vehicle's orbital accuracy.
[0057] Example:
[0058] like Figure 1 The present invention provides a method for evaluating the accuracy of a launch vehicle entering orbit, comprising the following steps:
[0059] The first step is to generate supplementary samples.
[0060] Refer to GJB 2106-94 "Test Methods for Hit Accuracy Evaluation of Ground-to-Ground Strategic Missile Weapon Systems" for the selection principle of the number of test rounds, that is, the number of flight test rounds used to evaluate hit accuracy should comprehensively consider my country's economic, human, material, development progress and other constraints, and should also consider the following factors: 1) The minimum number of rounds required to evaluate hit accuracy, and the proportion of newly developed systems and equipment. The number of rounds used as evaluation samples is usually not less than 6 for new models and not less than 3 for improved models. If the accuracy evaluation requirements are met, the number of rounds can be reduced; 2) The adequacy of ground tests, the pre-test information that has been mastered and can be obtained before the flight test, including information obtained from historical data, theoretical and engineering analysis, simulation and sufficient ground tests.
[0061] According to the above regulations, for the small sample identification of the launch vehicle orbital accuracy, when the number of flight test samples (i.e., field samples) does not meet the accuracy identification requirements, it is necessary to generate supplementary samples. The method is as follows: establish a set of dynamic models describing the launch vehicle flight, and fully verify the model through flight tests, semi-physical simulation tests, and other ground tests to ensure the correctness of the model. At the same time, determine the distribution law and mathematical model of each interference source that affects the launch vehicle orbital accuracy, and add it to the rocket flight dynamics model for Monte Carlo simulation shooting, so as to generate supplementary samples. Taking a certain type of launch vehicle as an example, the field samples (i.e., flight samples) and the supplementary samples generated by the above method are shown in Table 1.
[0062] Table 1 Field samples and supplementary samples
[0063]
[0064] Among them, △H p , △T, △i, △ω, △Ω e , △u are the perigee altitude deviation, orbital period deviation, orbital inclination deviation, perigee argument deviation, ascending node longitude deviation, and latitude argument deviation respectively.
[0065] The second step is sample testing.
[0066] The rank sum test method is used to carry out compatibility test and normality test on the supplementary sample and the field sample of each orbital parameter deviation to ensure that they all come from the same normal distribution population, so as to obtain a comprehensive sample for orbital accuracy evaluation.
[0067] Let X = (X 1 ,…X k ,...X m )′ is an m-dimensional random vector composed of the orbital parameter deviations of the launch vehicle, generally m≤6. Taking Table 1 as an example, m=6. For any orbital parameter deviation, let is a supplementary sample with a capacity of n1, is a field sample with a capacity of n2. Usually, n1 ≤ n2. Taking Table 1 as an example, n1 = n2 = 5. For the orbit injection parameter deviation △H p , are 0.011, 0.036, 0.022, 0.035, 0.004 respectively, x 1 , x 2 ,… x 5 are -0.302, -0.086, -0.064, -0.049, 0.161 respectively; Combine the two samples into a sample with a capacity of n = n1 + n2, and sort it from small to large to obtain a new sample sequence
[0068] z 1 ≤ z 2 ≤ … ≤ z n (1)
[0069] If that is, the i-th sample data in X 0 is ranked as j in the new sample sequence, and j is the rank of x i 0 i , denoted as r i (X 0 ) = j.
[0070] Add up the ranks of all sample data in X 0 , that is
[0071]
[0072] where R is called the sum of ranks of the supplementary sample X 0 .
[0073] When the significance level is α, look up the sum-of-ranks critical value table (n1, n2) to obtain the upper and lower limits of the sum of ranks Cu(α / 2) and CL(α / 2). If for each orbit injection parameter deviation, Cu(α / 2) < R < CL(α / 2) can be satisfied, it can be considered that the supplementary sample and the field sample belong to the same population, otherwise they belong to different populations. For samples belonging to different populations, they can be剔除 and new samples can be re-added.
[0074] For the field sample and the supplementary sample in Table 1, under the condition of a confidence level of 0.9, look up the sum-of-ranks critical value table to obtain the upper limit of the sum of ranks R, CL(α / 2) = 19, and the lower limit, Cu(α / 2) = 36. Calculate the sum of ranks of each orbit injection parameter using the above test method as shown in Table 2:
[0075] Table 2 Sum of ranks R
[0076] It should be noted that the term "剔除" in the original text seems to be a Chinese character that may not be recognized in a standard English context. You may need to check if there is a more appropriate English expression for this operation. If it is a specific technical term in Chinese, it may need to be accurately translated or explained according to the relevant field. Here, I have left it in Chinese for now.
[0077] According to the calculation results of the rank sum, the rank sums of the supplementary samples of the deviations of each orbit injection parameter all satisfy Cu(α / 2) < R < CL(α / 2). Therefore, it is considered that the supplementary samples and the on-site samples belong to the same population and can be used for orbit injection accuracy identification.
[0078] Based on the sample sequence constructed in Equation (1), the W-test method is used to calculate the b value of the deviation of the orbit injection parameter:
[0079]
[0080]
[0081] Among them, when n is even, m = n / 2; when n is odd, let m = (n - 1) / 2, and the coefficient a n-i+1 can be obtained by looking up the table of numbers.
[0082] Calculate the statistic W
[0083]
[0084] In the formula, S 2 is the sample variance of the deviation of the orbit injection parameter.
[0085] According to the sample size n and the significance level α of the test, by looking up the quantile table of the statistic W, the critical value Wα(n) can be obtained. If for each deviation of the orbit injection parameter, W ≥ Wα(n) can be satisfied, then each deviation of the orbit injection parameter follows a normal distribution population; otherwise, it does not follow a normal distribution.
[0086] For the samples in Table 1, the W values of each orbit injection parameter are calculated as shown in Table 3:
[0087] Table 3 Statistic W values for normality test
[0088]
[0089] According to the calculation results of the normality test statistic, the statistic W values of the samples of the deviations of each orbit injection parameter all satisfy W ≥ Wα(n). Therefore, it is considered that the deviations of each orbit injection parameter all follow a normal distribution.
[0090] The third step is the interval estimation of the orbit injection accuracy.
[0091] For the samples of the launch vehicle orbit injection accuracy identification that pass the rank sum test and the normality test, assuming that the deviations of each orbit injection parameter are independent of each other, and the mean μ and variance σ are both unknown, then at the confidence level of 1 - α (0 < α < 1), there is
[0092]
[0093] Then at the confidence level of 1 - α, the variance σ2 The confidence upper bound of for
[0094]
[0095] Generally, users require that the accuracy of each orbit insertion can meet the index requirements at the 3σ probability level. The confidence upper bound of 3σ can be further calculated by formula (7): for
[0096]
[0097] When the confidence level is 0.8, the above method is used for the samples in Table 1 to obtain the 3σ confidence upper bound estimates of the deviations of each orbital parameter as shown in Table 4.
[0098] Table 4 3σ confidence upper bound estimation
[0099]
[0100] The fourth step is to estimate the correlation of orbit insertion accuracy.
[0101] Considering that the orbital parameter deviations of the launch vehicle are not independent of each other, but have certain correlations with each other, the covariance matrix method is used to evaluate the correlation between them. For the m-dimensional random vector X composed of the orbital parameter deviations of the launch vehicle, its covariance matrix P′ is
[0102]
[0103] Among them, c ij = cov(X i ,X j ), is the orbital parameter deviation X i , X j The covariance coefficient between .
[0104] make
[0105]
[0106] Among them, ρ ij is the orbital parameter deviation X i , X j The correlation coefficient of ij ≤1. When ρ ij =1, indicating that X i , X j Perfectly positive correlation; when ρ ij = -1, indicating that X i , X j Completely negative correlation; when ρ ij =0, indicating that X i , X jThe correlation coefficients between the orbital parameters can be used to form the correlation coefficient matrix R′:
[0107]
[0108] The correlation coefficient matrix of each orbital accuracy of a certain type of launch vehicle calculated based on the Monte Carlo shooting results is shown in Table 5:
[0109] Table 5 Orbital insertion accuracy correlation coefficient matrix
[0110]
[0111] According to the obtained orbital accuracy range and the correlation coefficient between each orbital parameters, a correlation coefficient matrix can be constructed to obtain the orbital accuracy identification result of the launch vehicle.
[0112] The present invention has been described in detail above in conjunction with specific implementations and exemplary examples, but these descriptions cannot be understood as limiting the present invention. Those skilled in the art understand that, without departing from the spirit and scope of the present invention, a variety of equivalent substitutions, modifications or improvements may be made to the technical solution of the present invention and its implementation methods, all of which fall within the scope of the present invention. The scope of protection of the present invention shall be subject to the attached claims.
[0113] The contents not described in detail in the specification of the present invention belong to the common knowledge of those skilled in the art.
Claims
1. A method for evaluating the orbital accuracy of a launch vehicle, characterized in that: Including: S1 Generate supplementary samples of various orbit injection parameter deviations; S2 Respectively conduct compatibility tests and normality tests on the supplementary samples and flight samples of each orbit injection parameter deviation, and use the supplementary samples and flight samples that pass the compatibility tests and normality tests as comprehensive samples; S3 Based on the comprehensive samples, use the confidence interval estimation method to obtain the accuracy intervals of various orbit injection parameter deviations; S4 Based on the comprehensive samples, calculate the covariance matrix between various orbit injection parameter deviations; Obtain the correlation between various orbit injection parameter deviations according to the covariance matrix between various orbit injection parameter deviations; S5 Complete the orbit injection accuracy identification of the launch vehicle based on the accuracy intervals of various orbit injection parameter deviations and the correlation between various orbit injection parameter deviations.
2. A method for evaluating the orbital accuracy of a launch vehicle according to claim 1, characterized in that: In step S1, the method for generating supplementary samples includes: S1.1 Establish a rocket flight dynamics model; S1.2 Determine the distribution laws and mathematical models of various interference sources affecting the orbit injection accuracy of the launch vehicle, and add the distribution laws and mathematical models of various interference sources to the rocket flight dynamics model for Monte Carlo simulation target shooting to obtain supplementary samples.
3. A method for evaluating the orbital accuracy of a launch vehicle according to claim 1, characterized in that: Deviations of various parameters of the launch vehicle into orbit, including the perigee height deviation △H of the orbital entry point p , orbit period deviation △T, orbit inclination deviation △i, perigee argument deviation △ω, ascending node longitude deviation △Ω e Or latitude argument deviation △u.
4. A method for evaluating the orbital accuracy of a launch vehicle according to claim 1, characterized in that: In step S2, the method for compatibility test includes: Let X=(X1,…X k ,…X m )′ is an m-dimensional random vector composed of the orbital parameter deviations of the launch vehicle, 1<m≤6; For any orbital parameter deviation, let is a complementary sample with capacity n1, is a flight sample with capacity n2; X 0 and X to form a sample with a capacity of n = n1 + n2, and sort the sample data in the sample from small to large to obtain a new sample sequence: z1≤z2≤…≤z n ; According to X 0 The order of each sample data in the new sample sequence is used to obtain the rank of each sample data, and then X is obtained. 0 The rank sum R; Under the preset significance level α, obtain the upper and lower limits Cu(α / 2) and CL(α / 2) of the rank sum. When Cu(α / 2) < R < CL(α / 2), the compatibility test is passed, and it is considered that the supplementary sample and the on-site sample belong to the same population, otherwise it is considered that the supplementary sample and the on-site sample belong to different populations.
5. A method for evaluating the orbital accuracy of a launch vehicle according to claim 4, characterized in that: In step S2, the method for normality test includes: Based on the new sample sequence, calculate the b value of each orbit injection parameter deviation; Calculate the statistic W based on the b value: Among them, S 2 is the sample variance of orbital parameter deviation; According to the significance level α and the sample size n, obtain the critical value Wα(n) of W; If for each orbit injection parameter deviation, it can be satisfied that W ≥ Wα(n), the normality test is passed, indicating that each orbit injection parameter deviation follows a normal distribution population, otherwise it does not follow a normal distribution.
6. A method for evaluating the orbital accuracy of a launch vehicle according to claim 1, characterized in that: In step S3, the method for obtaining the accuracy intervals of various orbit injection parameter deviations includes: Assume that various orbit injection parameter deviations are independent of each other, and the mean μ and variance σ are both unknown. Then at a confidence level of 1 - α, 0 < α < 1, there is: Where P represents probability, It represents the chi-square distribution with confidence level 1-α and sample size n; Then when the confidence level is 1-α, the variance σ 2 The confidence upper bound of for: We further obtain the confidence upper bound of 3σ for:
7. A method for evaluating the orbital accuracy of a launch vehicle according to claim 1, characterized in that: In step S4, the covariance matrix P′ between various orbit injection parameter deviations is: Among them, c ij = cov(X i ,X j ), for different orbital parameter deviations X i , X j The covariance coefficient between .
8. A method for evaluating the orbital accuracy of a launch vehicle according to claim 7, characterized in that: In step S4, obtain the correlation coefficient matrix R′ between various orbit injection parameter deviations according to the covariance matrix between various orbit injection parameter deviations: Among them, ρ ij is the orbital parameter deviation X i , X j The correlation coefficient of ij ≤1;