Aerospace test danger area calculation method based on principal component analysis

Abstract

The invention relates to an aerospace test danger area calculation method based on principal component analysis, and belongs to the technical field of aerospace tests. The method comprises the following steps that a scattering result of target shooting drop points is regarded as a two-dimensional population, a two-dimensional scattering point data set is constructed according to the two-dimensional population, and the two-dimensional scattering point data set comprises a plurality of target shooting drop points; calculating the expectation of the two-dimensional population, and calculating the covariance matrix of the two-dimensional population according to the expectation; deriving a main direction of the two-dimensional scatter data set according to the covariance matrix; and determining the actual range of the aerospace test danger area according to the main direction. According to the method, the range of the aerospace test dangerous area can be accurately determined, and the safety of the aerospace test is improved.

Description

Technical Field

[0001] The present application relates to the field of aerospace test technology, and in particular to a method for calculating aerospace test danger zones based on principal component analysis. Background Art

[0002] The space test danger zone refers to the possible landing area of ​​rocket booster stage debris, re-entry spacecraft and other targets. The establishment of the space test danger zone is a factor that needs to be considered in the space test design process. In the process of space test preparation, the safety control of the space test danger zone is indispensable. Relevant departments are required to survey the space test danger zone, understand the personnel, roads and facilities in the space test danger zone, evacuate the personnel and important property in the space test danger zone, and seal off the space test danger zone to ensure the safety of personnel and property during the implementation of the mission.

[0003] Targets such as rocket booster stage debris have characteristics such as unstable reentry attitude, difficult to obtain aerodynamic characteristics, and are greatly affected by high-altitude winds. This brings great difficulties to how to accurately estimate the danger zone of space tests. In order to ensure the safety of space tests, relevant departments generally combine the position error and velocity error of the separation point of the debris target, the reentry aerodynamic coefficient of the debris target and high-altitude wind and other factors, use trajectory prediction algorithms, and calculate the landing point distribution area of ​​the debris target based on the shooting results of the separation point of the main debris target. When demarcating the danger zone of space tests, a rectangular area is usually demarcated, namely the theoretical landing point area, so that it covers the landing point distribution area of ​​the debris target, but the actual landing point area of ​​the wreckage target and the theoretical landing point area often have the following problems:

[0004] The active phase of the spacecraft generally performs guidance and attitude adjustment. After reentry, the spacecraft is affected by high-altitude winds, so the debris target may not fly in the direction of launch, and the lateral deviation and longitudinal deviation of the actual landing point of the debris target cannot meet the normal distribution, resulting in the actual landing area of ​​the debris target being asymmetric with respect to the theoretical landing area, and the main direction of the actual landing area of ​​the debris target deviates from the launch direction. This situation makes it impossible to accurately delineate the dangerous area of ​​space experiments, which poses a great safety hazard to the landing area, especially in densely populated areas.

[0005] Therefore, it is necessary to propose a solution to improve one or more problems existing in the above-mentioned related technical solutions.

[0006] It should be noted that the information disclosed in the above background technology section is only used to enhance the understanding of the background of the present application, and therefore may include information that does not constitute the prior art known to ordinary technicians in the field. Summary of the invention

[0007] The present application embodiment provides a method for calculating aerospace test danger zone based on principal component analysis, comprising the following steps:

[0008] The scatter results of the target shooting points are regarded as a two-dimensional population, and a two-dimensional scattered point data set is constructed according to the two-dimensional population, wherein the two-dimensional scattered point data set includes a plurality of target shooting points;

[0009] Calculating the expectation of the two-dimensional population, and calculating the covariance matrix of the two-dimensional population based on the expectation;

[0010] Derived the main direction of the two-dimensional scattered point data set according to the covariance matrix;

[0011] The actual scope of the space test danger zone is determined based on the main direction.

[0012] In an exemplary embodiment of the present application, the step of regarding the distribution results of the target shooting points as a two-dimensional population and constructing a two-dimensional scattered point data set according to the two-dimensional population includes:

[0013] Consider the distribution results of the target shooting points as the two-dimensional population;

[0014] The distribution center of all the target shooting points in the two-dimensional scattered point data set is taken as the coordinate origin, the shooting direction is taken as the x-axis, the direction passing through the coordinate origin and perpendicular to the shooting direction is taken as the y-axis, and the z-axis direction is determined according to the right-hand rule, so as to construct a rectangular coordinate system including all the target shooting points, wherein each target shooting point includes a longitude coordinate and a latitude coordinate;

[0015] In the rectangular coordinate system, a sample set is selected from the two-dimensional population according to the number of the target shooting points to construct the two-dimensional scattered point data set.

[0016] In an exemplary embodiment of the present application, the expression of the two-dimensional population is:

[0017] M=(L,B)' (1)

[0018] Wherein, M represents a two-dimensional population, L represents the set of coordinates of all target shooting points in the x-axis direction of the rectangular coordinate system, B represents the set of coordinates of all target shooting points in the z-axis direction of the rectangular coordinate system, and (·)' represents the transpose of (·).

[0019] In an exemplary embodiment of the present application, the expression of the two-dimensional scattered point data set is:

[0020]

[0021] Where X represents a two-dimensional scattered point data set, m represents the number of target shooting points, i = 1, 2, ..., m, L m represents the coordinate of the mth target's landing point in the x-axis direction of the rectangular coordinate system, B m Represents the coordinate of the mth target's landing point in the z-axis direction of the rectangular coordinate system.

[0022] In an exemplary embodiment of the present application, the expression for calculating the expectation of the two-dimensional population is:

[0023]

[0024] Among them, E(M) represents the expectation of the two-dimensional population, L i represents the coordinate of the target point of the ith target in the x-axis direction of the rectangular coordinate system, B i represents the coordinate of the target point of the ith target in the z-axis direction of the rectangular coordinate system, It represents the average value of the coordinates of all target landing points in the x-axis direction of the rectangular coordinate system. It represents the average value of the coordinates of all target landing points in the z-axis direction of the rectangular coordinate system.

[0025] In an exemplary embodiment of the present application, the expression for calculating the covariance matrix of the two-dimensional population is:

[0026]

[0027] Where C represents the covariance matrix of the two-dimensional population, var(x) represents the variance of the two-dimensional population, and (ME(M))' represents the transpose of (ME(M)).

[0028] In an exemplary embodiment of the present application, the step of deriving the main direction of the two-dimensional scattered point data set according to the covariance matrix includes:

[0029] Performing linear transformation on the variables L and B in the two-dimensional population respectively to obtain a linear equation system;

[0030] Determine the coefficients of the linear equations using a covariance matrix, wherein a first eigenvalue of the covariance matrix corresponds to a first orthogonal unit eigenvector, and a second eigenvalue of the covariance matrix corresponds to a second orthogonal unit eigenvector; the direction where the first orthogonal unit eigenvector is located is a direction with a maximum variance, and the direction where the second orthogonal unit eigenvector is located is a direction with a minimum variance;

[0031] Using the first orthogonal unit eigenvector with the maximum variance direction as the principal component of the two-dimensional scattered point data set; Using the direction of the first orthogonal unit eigenvector with the maximum variance direction as the principal direction of the two-dimensional scattered point data set;

[0032] The first eigenvalue is represented by λ1, the second eigenvalue is represented by λ2, λ1≥λ2≥0, the first orthogonal unit eigenvector is represented by α1, the second orthogonal unit eigenvector is represented by α2; the direction of the first orthogonal unit vector is perpendicular to the direction of the second orthogonal unit eigenvector.

[0033] In an exemplary embodiment of the present application, the step of determining the actual range of the space test danger zone according to the main direction includes:

[0034] The two-dimensional scattered point data set is projected onto the main direction to obtain a first projection set, where the expression of the first projection set is:

[0035] l=α1'X (5)

[0036] Where l represents the first projection set, α1' represents the projection of the first orthogonal unit eigenvector;

[0037] The two-dimensional scattered point data set is projected to the direction of the second orthogonal unit vector to obtain a second projection set, where the expression of the second projection set is:

[0038] w=α2'X (6)

[0039] Wherein, w represents the second projection set, and α2' represents the projection of the second orthogonal unit eigenvector.

[0040] extracting the extreme values ​​of the first projection set and the second projection set respectively as the initial range of the space test danger zone;

[0041] According to actual needs, the initial range of the space test danger zone is enlarged or reduced, and the actual range of the space test danger zone is determined based on the result of the enlargement or reduction.

[0042] In an exemplary embodiment of the present application, the expression of the initial range of the aerospace test danger zone is:

[0043]

[0044] Among them, Y0 represents the coordinates of each vertex in the initial range of the space test danger zone, l max represents the maximum value of the first projection set, l max =max(l),l min represents the minimum value of the first projection set, l min =min(l),w max represents the maximum value of the second projection set, w max=max(w),w min represents the minimum value of the second projection set, w min =min(w).

[0045] In an exemplary embodiment of the present application, the step of enlarging or reducing the initial range of the space test danger zone according to actual needs, and determining the actual range of the space test danger zone according to the result of the enlarging or reducing process includes:

[0046] Let l 极值差 = l max -l min , w 极值差 =w max -w min , l 极值差 represents the first extreme value difference between the maximum value of the first projection set and the minimum value of the first projection set, w 极值差 A second extreme value difference between a maximum value of the second projection set and a minimum value of the second projection set is represented, and a proportional coefficient is defined, wherein the proportional coefficient is represented by k, k>0 represents a magnification process, and k<0 represents a reduction process;

[0047] According to the first extreme value difference, the second extreme value difference and the proportional coefficient, the initial range of the space test danger zone is enlarged or reduced;

[0048] The expression for performing the enlargement process or the reduction process on the initial range is:

[0049]

[0050] Among them, Y k Indicates the result of enlarging or reducing the initial range;

[0051] The actual range is expressed as:

[0052] X k =AY k (9)

[0053] Among them, X k The coordinates of each vertex representing the actual range of the space test danger zone, X k =(x1,x2)', x1 represents the coordinates of each vertex of the actual range of the space test danger zone in the rectangular coordinate system on the x-axis, x2 represents the coordinates of each vertex of the actual range of the space test danger zone in the rectangular coordinate system on the z-axis, (x1,x2)' represents the transpose of (x1,x2), A represents the orthogonal matrix, A = (α1,α2).

[0054] Beneficial effects:

[0055] The present application provides a method for calculating the danger zone of aerospace experiments based on principal component analysis, which has at least the following beneficial effects:

[0056] (1) The present application uses the principal component analysis method to analyze the main direction of the target shooting point, determines the longitudinal direction and lateral direction of the initial range of the space test danger zone, and adjusts the size of the space test danger zone according to the dispersion of the target shooting point, thereby achieving accurate positioning of the space test danger zone and improving the safety of the space test;

[0057] (2) In view of the situation where the calculated space test danger zone is a non-standard rectangle due to the nonlinear correlation between the longitude and latitude of the earth's surface, the present application takes the scattered center of the target shooting point as the coordinate origin, the shooting direction as the x-axis, the direction perpendicular to the coordinate origin and the shooting direction as the y-axis, and determines the z-axis direction according to the right-hand rule to construct a rectangular coordinate system for the target shooting point, wherein each target shooting point includes longitude coordinates and latitude coordinates, thereby making the calculation result more accurate and further increasing the positioning accuracy of the space test danger zone. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] The drawings herein are incorporated into the specification and constitute a part of the specification, illustrate embodiments consistent with the present application, and together with the specification are used to explain the principles of the present application. Obviously, the drawings described below are only some embodiments of the present application, and for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0059] Figure 1 A schematic diagram showing the division of existing hazardous areas for aerospace testing;

[0060] Figure 2 A comparison chart showing the actual landing point distribution area and the theoretical landing point area of ​​a certain type of rocket second-stage debris target;

[0061] Figure 3 A schematic diagram showing the steps of a method for calculating a dangerous area of ​​aerospace testing based on principal component analysis in an exemplary embodiment of the present application is shown;

[0062] Figure 4 A schematic flow chart showing a method for calculating a dangerous area of ​​aerospace testing based on principal component analysis in an exemplary embodiment of the present application is shown;

[0063] Figure 5 A schematic diagram showing the distribution of the target landing points and the main directions of the second stage debris target of a certain type of rocket in an exemplary embodiment of the present application in a rectangular coordinate system;

[0064] Figure 6A schematic diagram showing the distribution of the target landing points of a certain type of rocket secondary debris target in an exemplary embodiment of the present application in a rectangular coordinate system, and the corresponding initial range of the space test danger zone determined in the rectangular coordinate system;

[0065] Figure 7 A schematic diagram showing the distribution of the target landing points of a certain type of rocket second-stage debris target in an exemplary embodiment of the present application in a rectangular coordinate system, and the corresponding actual range of the aerospace test danger zone determined in the rectangular coordinate system. DETAILED DESCRIPTION

[0066] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be implemented in a variety of forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this application will be more comprehensive and complete and fully convey the concepts of the example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0067] In addition, the accompanying drawings are only schematic illustrations of the present application and are not necessarily drawn to scale. The same reference numerals in the figures represent the same or similar parts, and thus their repeated description will be omitted. Some of the block diagrams shown in the accompanying drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software form, or implemented in one or more hardware modules or integrated circuits, or implemented in different networks and / or processor devices and / or microcontroller devices.

[0068] After analysis and research, the factors that affect the dangerous area of ​​space tests mainly include the position error and speed error of the wreckage separation point, the wreckage reentry aerodynamic coefficient and high-altitude wind, etc. Using these factors and the trajectory prediction algorithm, and based on the shooting results of the development department at the separation point (i.e. the position and speed of the wreckage target), the landing point distribution area of ​​the wreckage target can be calculated.

[0069] In the past, when demarcating dangerous areas for space experiments, Figure 1 As shown, a rectangular area is usually defined, which refers to the scattered area covering the debris target. The long side of the rectangle is the launch direction of the spacecraft, the wide side of the rectangle is the direction perpendicular to the launch direction, and the center of the rectangle is the theoretical landing point of the debris target. The size of the rectangle can be determined as follows:

[0070] Depend on Figure 1It can be seen that, first, any landing point p is projected to the emission direction to obtain p', then |op'| is the longitudinal deviation of point p, and |pp'| is the lateral deviation of point p; then, the longitudinal deviation and lateral deviation of all landing points are counted, and the long side and wide side of rectangle ABCD are determined according to the Sigma criterion (also known as the Laida criterion).

[0071] The premise of this method is to assume that the debris target still flies in the direction of ejection after stage separation or head-body separation, and the lateral deviation and longitudinal deviation of the actual landing point of the debris target satisfy the normal distribution, and the actual landing area of ​​the debris target is symmetrical with respect to the theoretical landing area. However, the actual situation is that the spacecraft generally performs guidance and attitude adjustment during the active phase of flight, and then when the debris target of the spacecraft separates from the main body of the spacecraft, it is no longer affected by the active force, but is completely in the passive phase of flight, and will be affected by the high-altitude wind after reentry. Therefore, the debris target does not necessarily fly in the direction of ejection, and the lateral deviation and longitudinal deviation of the actual landing point of the debris target cannot satisfy the normal distribution, which leads to the actual landing area of ​​the debris target being asymmetric with respect to the theoretical landing area, and the main direction of the actual landing area of ​​the debris target deviates from the ejection direction.

[0072] like Figure 2 As shown, Figure 2 The figure shows the comparison between the actual landing point distribution area and the theoretical landing point area of ​​the second stage debris target of a certain type of rocket. Figure 2 It can be clearly seen that the actual impact area of ​​the debris target is not symmetrical with respect to the theoretical impact area. Many impact points at the front longitudinal end are outside the theoretical impact area, while the theoretical impact area is too wide in the transverse direction. Therefore, the theoretical impact area defined in this way is unreasonable.

[0073] In order to solve the above technical problems, this exemplary embodiment provides a method for calculating the danger zone of aerospace test based on principal component analysis, such as Figure 3 and Figure 4 As shown, the following steps may be included:

[0074] Step S101: treating the scatter results of target shooting points as a two-dimensional population, and constructing a two-dimensional scattered point data set according to the two-dimensional population, the two-dimensional scattered point data set including a plurality of target shooting points.

[0075] Step S102: Calculate the expectation of the two-dimensional population, and calculate the covariance matrix of the two-dimensional population according to the expectation.

[0076] Step S103: deriving the main direction of the two-dimensional scattered point data set according to the covariance matrix.

[0077] Step S104: Determine the actual range of the space test danger zone according to the main direction.

[0078] The embodiment of the present application proposes a method for calculating the danger zone of aerospace test based on principal component analysis (PCA), which has at least the following beneficial effects:

[0079] (1) The present application uses the principal component analysis method to analyze the main direction of the target shooting point, determines the longitudinal direction and lateral direction of the initial range of the space test danger zone, and adjusts the size of the space test danger zone according to the dispersion of the target shooting point, thereby achieving accurate positioning of the space test danger zone and improving the safety of the space test;

[0080] (2) In view of the situation where the calculated space test danger zone is a non-standard rectangle due to the nonlinear correlation between the longitude and latitude of the earth's surface, the present application takes the scattered center of the target shooting point as the coordinate origin, the shooting direction as the x-axis, the direction perpendicular to the coordinate origin and the shooting direction as the y-axis, and determines the z-axis direction according to the right-hand rule to construct a rectangular coordinate system for the target shooting point, wherein each target shooting point includes longitude coordinates and latitude coordinates, thereby making the calculation result more accurate and further increasing the positioning accuracy of the space test danger zone.

[0081] Next, a method for calculating the danger zone of aerospace tests based on principal component analysis proposed in this example embodiment will be described in more detail.

[0082] The purpose of this application is to solve the problem that the danger zone of aerospace testing cannot be accurately determined due to the asymmetry of the actual landing area of ​​the debris target with respect to the theoretical landing area and the deviation between the main direction of the landing area of ​​the debris target and the ejection direction.

[0083] The above problem can actually be simplified to: for a set of two-dimensional scattered points on a plane, how to calculate the minimum rectangular area that contains all the scattered points. Since the landing area of ​​the wreckage target is roughly a rectangular area, the key is to calculate the direction of the long side of the required rectangular area. Figure 1 and Figure 2 From the analysis, we can know that the direction of the long side of the rectangle is different from the shooting direction, which should be the main direction of the landing area of ​​the wreckage target. Mathematically, it can be described as projecting all the landing points onto this main direction, and the corresponding variance should also be the largest.

[0084] To this end, this application introduces the principal component analysis (PCA) method. The basic principle of this method is as follows:

[0085] PCA is a feature fusion algorithm, which is mainly used for data dimensionality reduction. Its purpose is to reduce the number of feature attributes under the premise of relatively less information loss. The main idea of ​​PCA is to map the s-dimensional features to the u-dimensional features. The u-dimensional features are new orthogonal features, also known as principal components. In this way, the u-dimensional features are reconstructed on the basis of the original s-dimensional features. PCA is to find a set of mutually orthogonal coordinate axes in order from the original space. The selection of new coordinate axes is closely related to the data itself. Among them, the selection of the first coordinate axis corresponds to the direction with the largest variance, the selection of the second coordinate axis corresponds to the direction with the largest variance in the plane orthogonal to the first coordinate axis, and the selection of the third coordinate axis corresponds to the direction with the largest variance in the plane orthogonal to the first two coordinate axes. By analogy, s such coordinate axes can be obtained. For all the new coordinate axes obtained in this way, most of the variance is contained in the first u coordinate axes, and the variance contained in the latter coordinate axes is almost 0. Therefore, the latter coordinate axes can be ignored, and only the first u coordinate axes containing most of the variance are retained. In fact, this is equivalent to retaining only the dimensional features that contain most of the variance and ignoring the feature dimensions that contain almost 0 variance, thereby achieving dimensionality reduction of data features.

[0086] This embodiment selects the calculation work of the landing point danger zone of the rocket sub-stage debris target in the space test, and uses 20,000 sets of target shooting parameters when the second-stage debris of a certain type of rocket is separated from the main rocket. The target shooting parameters include the position and speed of the target shooting. The method proposed in this application is used to accurately calculate the landing point danger zone of the second-stage debris target of this type of rocket.

[0087] In step S101 of this embodiment, the distribution results of the target shooting points are regarded as a two-dimensional population, and a two-dimensional scattered point data set is constructed based on the two-dimensional population. Step S101 of this embodiment may include the following sub-steps:

[0088] Sub-step S1011: Consider the distribution result of the target shooting points as a two-dimensional whole.

[0089] Furthermore, the expression of the two-dimensional population is:

[0090] M=(L,B)' (1)

[0091] Wherein, M represents a two-dimensional population, L represents the set of coordinates of all target shooting points in the x-axis direction of the rectangular coordinate system, B represents the set of coordinates of all target shooting points in the z-axis direction of the rectangular coordinate system, and (·)' represents the transpose of (·).

[0092] In this embodiment, the re-entry aerodynamic coefficient of the second-stage debris target of this model of rocket and the high-altitude meteorological forecast data at the time of the test are queried, and the landing point prediction algorithm of the corresponding sub-stage debris target is substituted. The 20,000 sets of target shooting parameters are used as the landing point prediction extrapolation starting point, and the longitude, latitude and elevation of the 20,000 possible landing points of the second-stage debris target are extrapolated respectively. Then, these landing points (including longitude coordinates and latitude coordinates) are regarded as a two-dimensional whole.

[0093] Sub-step S1012: Take the scatter center of all target shooting points in the two-dimensional scattered point data set as the coordinate origin, the shooting direction as the x-axis, the direction passing through the coordinate origin and perpendicular to the shooting direction as the y-axis, the y-axis direction points outside the earth, and determine the z-axis direction according to the right-hand rule to construct a rectangular coordinate system including all target shooting points, wherein each target shooting point includes longitude coordinates and latitude coordinates.

[0094] Sub-step S1013: In a rectangular coordinate system, a sample set is selected from the two-dimensional population according to the number of target shooting points to construct a two-dimensional scattered point data set.

[0095] Furthermore, in this embodiment, the coordinate origin of the rectangular coordinate system is the scattering center of the 20,000 landing points. The launch direction of this model of rocket is the x-axis, the y-axis direction is consistent with the plumb line direction of the coordinate origin, pointing to the outside of the earth, and the z-axis, the x-axis and the y-axis form a right-handed coordinate system. Obviously, the x-axis and the z-axis are on the same horizontal plane. The converted landing point coordinates are expressed as: (x i ,y i ,z i ), 1≤i≤20000, the resulting landing plane data set is a two-dimensional scattered point data set.

[0096] Furthermore, assuming that there are m target shooting points, the expression of the obtained two-dimensional scattered point data set is:

[0097]

[0098] Where X represents the two-dimensional scattered point data set, m represents the number of target shooting points, i = (1, 2, ..., m), L m represents the coordinate of the mth target's landing point in the x-axis direction of the rectangular coordinate system, B m Represents the coordinate of the mth target's landing point in the z-axis direction of the rectangular coordinate system.

[0099] It can be seen that the two-dimensional scattered data set is the sample set of the two-dimensional population. The purpose here is to use the above principal component analysis method to calculate the main direction of the two-dimensional scattered data set, that is, to sequentially find a set of mutually orthogonal coordinate axes from the rectangular coordinate system, where the first coordinate axis is selected so that the variance of the two-dimensional scattered data set in the first coordinate axis is the largest, thereby finding the main direction of the two-dimensional scattered data set.

[0100] Specifically, in this embodiment, the landing point plane data set is:

[0101]

[0102] In step S102 of this embodiment, the expectation of the two-dimensional population is calculated, and the covariance matrix of the two-dimensional population is calculated based on the expectation.

[0103] Furthermore, in this embodiment, when calculating the expectation of a two-dimensional population, when there are enough samples, usually m>10000, and the number of points in this embodiment is 20000, the expectation of the two-dimensional population is approximately the average value of the samples. Therefore, the expression of the expectation of the two-dimensional population can be obtained as follows:

[0104]

[0105] Among them, E(M) represents the expectation of the two-dimensional population, L i represents the coordinate of the target point of the ith target in the x-axis direction of the rectangular coordinate system, B i represents the coordinate of the target point of the ith target in the z-axis direction of the rectangular coordinate system, It represents the average value of the coordinates of all target landing points in the x-axis direction of the rectangular coordinate system. It represents the average value of the coordinates of all target landing points in the z-axis direction of the rectangular coordinate system.

[0106] Furthermore, the expression of the covariance matrix of the two-dimensional population is:

[0107]

[0108] Among them, C represents the covariance matrix of the two-dimensional population, var(M) represents the variance of the two-dimensional population, and (ME(M))' represents the transpose of (ME(M)). Here, the divisor in the covariance matrix is ​​set to m-1 in order to obtain an unbiased estimate of the covariance matrix.

[0109] Specifically, using formula (4), the specific covariance matrix in this embodiment can be calculated:

[0110]

[0111] in,

[0112] In step S103 of this embodiment, the main direction of the two-dimensional scattered point data set is derived according to the covariance matrix. Specifically, the following sub-steps are included:

[0113] Sub-step S1031: performing linear transformation processing on the variables L and B in the two-dimensional population respectively to obtain a linear equation system;

[0114] The expression of this linear equation system is:

[0115]

[0116] Among them, a 11 、a 12 、a 21 and a 22 denote the coefficients of the linear equations, a1' denotes the transpose of a1, a1'=(a 11 ,a 12 ), a2' represents the transpose of a2, a2'=(a 21 ,a 22 ). Next, we need to calculate a1 so that the variance of y1 is maximized.

[0117] Sub-step S1032: Determine the first eigenvalue and the second eigenvalue of the covariance matrix according to the above-mentioned linear equation group, the first eigenvalue corresponds to the first orthogonal unit eigenvector, and the second eigenvalue corresponds to the second orthogonal unit eigenvector; the direction where the first orthogonal unit eigenvector is located is the direction of maximum variance, and the direction where the second orthogonal unit eigenvector is located is the direction of minimum variance.

[0118] In this embodiment, a1 is calculated according to the linear equation group so that the variance of y1 is maximized.

[0119] Here, the two eigenvalues ​​of the covariance matrix are set: λ1≥λ2≥0, α1 is the orthogonal unit eigenvector corresponding to λ1, and α2 is the orthogonal unit eigenvector corresponding to λ2, that is, Cα i =λ i α i , α i 'α i =1,α i 'α j =0, i≠j, i=1,2, j=1,2.

[0120] In this embodiment, the first eigenvalue of the covariance matrix is ​​λ1, the second eigenvalue is λ2, λ1≥λ2≥0. Accordingly, the first orthogonal unit eigenvector corresponding to the first eigenvalue λ1 is α1=(0.9997,0.0257), and the second orthogonal unit eigenvector corresponding to the second eigenvalue λ2 is α2=(0.0257,-0.9997). Obviously, α1 and α2 are perpendicular to each other.

[0121] Furthermore, since the covariance matrix is ​​a symmetric matrix, we can know from the correlation matrix theory that:

[0122]

[0123] Where A represents an orthogonal matrix, A = α1, α2, Λ represents a diagonal matrix with diagonal elements; A' = A -1 , A -1 Represents the inverse matrix of the orthogonal matrix, i = 1, 2, α i ' indicates α i The transpose of .

[0124] So we get the variance of y1:

[0125]

[0126] Sub-step S1033: taking the first orthogonal unit eigenvector with the maximum variance direction as the principal component of the two-dimensional scattered point data set; taking the direction of the first orthogonal unit eigenvector with the maximum variance direction as the principal direction of the two-dimensional scattered point data set.

[0127] In this embodiment, it can be known from the above formula that when a1=α1, the variance of the y1 axis is:

[0128] It reaches the maximum value, so y1=α1'x is the first principal component. Similarly, it can be proved that y2=α2'x is the second principal component.

[0129] In this embodiment, the direction where α1 is located is the direction with the largest variance, that is, the main direction of the dangerous area of ​​the aerospace test. In the initial coordinate system, the horizontal axis is the x-axis and the vertical axis is the z-axis. The equation of the straight line where α1 is located can be expressed as:

[0130] Translate it to the center point of the rectangular coordinate system like Figure 5 As shown by Figure 5 From the dotted line in the figure, we can see that the calculated main direction is consistent with the actual distribution of landing points, and the main direction of the dangerous area of ​​the aerospace test is not parallel to the x-axis.

[0131] like Figure 6 and Figure 7 As shown, in step S104, the actual range of the space test danger zone is determined according to the main direction. In this embodiment, step S104 may include the following sub-steps:

[0132] Sub-step S1041: Project the two-dimensional scattered point data set onto the main direction to obtain a first projection set.

[0133] Furthermore, the expression of the first projection set is:

[0134] l=α1'X (5)

[0135] Where l represents the first projection set, and α1' represents the projection of the first orthogonal unit eigenvector.

[0136] Sub-step S1042: Project the two-dimensional scattered point data set to the direction of the second orthogonal unit vector to obtain a second projection set.

[0137] Furthermore, the expression of the second projection set is:

[0138] w=α2'X (6)

[0139] Wherein, w represents the second projection set, and α2' represents the projection of the second orthogonal unit eigenvector.

[0140] Sub-step S1043: extracting the extreme values ​​of the first projection set and the second projection set respectively as the initial range of the space test danger zone.

[0141] Furthermore, the expression of the initial range of the space test danger zone is:

[0142]

[0143] Among them, Y0 represents the coordinates of each vertex in the initial range of the space test danger zone, l max represents the maximum value of the first projection set, l max =max(l),l min represents the minimum value of the first projection set, l min =min(l),w max represents the maximum value of the second projection set, w max =max(w),w min represents the minimum value of the second projection set, w min =min(w).

[0144] Sub-step S1044: According to actual needs, the initial range of the space test danger zone is enlarged or reduced, and the actual range of the space test danger zone is determined according to the result of the enlargement or reduction. Specifically:

[0145] The first step is to set l 极值差 = l max -l min , w 极值差 =w max -w min , l 极值差 represents the first extreme value difference between the maximum value of the first projection set and the minimum value of the first projection set, w极值差 The second extreme value difference between the maximum value of the second projection set and the minimum value of the second projection set is represented, and a proportional coefficient is defined. The proportional coefficient is represented by k, k>0 represents a magnification process, and k<0 represents a reduction process.

[0146] In the second step, the initial range of the space test danger zone is enlarged or reduced according to the first extreme value difference, the second extreme value difference and the proportional coefficient.

[0147] Furthermore, the expression for enlarging or reducing the initial range is:

[0148]

[0149] Among them, Y k Indicates the result of enlarging or reducing the initial range.

[0150] Note that Y k is the coordinate after the above projection (i.e. the above linear transformation). To obtain the coordinates of the aerospace test danger zone in the original rectangular coordinate system, the corresponding inverse transformation needs to be performed:

[0151] In this embodiment, the two variables in the rectangular coordinate system are X=(x1,x2)', (x1,x2)' represents the transpose of (x1,x2), the two variables in the new coordinate system are Y=(y1,y2)', (y1,y2)' represents the transpose of (y1,y2), and the orthogonal matrix is ​​A, A=(α1,α2).

[0152] According to the above linear transformation, we can get: Y = A'X, where A' = A -1 , then we get: X = AY;

[0153] Y k Substituting into the above formula, we can obtain the actual range of the dangerous area in aerospace testing.

[0154] Furthermore, the expression of the actual range of the danger zone is:

[0155] X k =AY k (9)

[0156] Among them, X k The coordinates of each vertex representing the actual range of the space test danger zone, X k =(x1,x2)', x1 represents the coordinates of each vertex of the actual range of the space test danger zone in the rectangular coordinate system on the x-axis, x2 represents the coordinates of each vertex of the actual range of the space test danger zone in the rectangular coordinate system on the z-axis, (x1,x2)' represents the transpose of (x1,x2), A represents the orthogonal matrix, A = (α1,α2).

[0157] The third step is that since the surface of the earth is a curved surface, as the latitude increases, the distance represented by the unit scale in the longitude direction gradually becomes smaller, and the change trend is nonlinear. Therefore, the calculated initial range is not a standard rectangle, especially in high-latitude areas. This has little effect on the smaller space test danger zone, but has a greater impact on the larger space test danger zone. In order to solve this problem, the target landing point can be first converted to a rectangular coordinate system, such as discussed in the above steps, so that the longitude and latitude values ​​of the space test danger zone are converted into specific coordinate values ​​in the rectangular coordinate system, thereby calculating a standard rectangular area;

[0158] Finally, the coordinates of the four vertices of the standard rectangle are converted into longitude and latitude coordinates in geodetic coordinates.

[0159] In view of the actual situation that the shooting direction was previously used as the longitudinal direction of the space test danger zone and the calculation of the danger zone size was inaccurate, this application proposes a method for calculating the space test danger zone based on principal component analysis. Among them, the principal component analysis method is used to calculate the "main direction" of the target landing point shooting scatter diagram, which is used as the longitudinal direction of the space test danger zone; the direction perpendicular to the "main direction" is the horizontal direction, the center point is the regional scatter center, and the size of the region is determined by the landing point scatter size. Furthermore, in view of the situation that the calculated space test danger zone is a non-standard rectangle due to the nonlinear correlation between the longitude and latitude of the earth's surface, it is proposed to convert the landing point shooting results into a rectangular coordinate system and then calculate the space test danger zone. Compared with the previous method for calculating the space test danger zone, the method of this application is more scientific and accurate, and is of great significance to the safety of space tests.

[0160] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the embodiments of the present application, the meaning of "multiple" is two or more, unless otherwise clearly and specifically defined.

[0161] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example" or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification.

[0162] The above description is only a specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any technician familiar with the technical field can easily think of various equivalent modifications or substitutions within the technical scope disclosed in the present application, and these modifications or substitutions should be included in the protection scope of the present application.

[0163] Those skilled in the art will readily appreciate other embodiments of the present application after considering the specification and practicing the invention disclosed herein. The present application is intended to cover any modification, use or adaptation of the present application, which follows the general principles of the present application and includes common knowledge or customary technical means in the art that are not disclosed in the present application.

Claims

1. A method for calculating the dangerous area of ​​aerospace experiments based on principal component analysis. It is characterized in that The following steps are involved: The scatter results of the target shooting points are regarded as a two-dimensional population, and a two-dimensional scattered point data set is constructed according to the two-dimensional population, wherein the two-dimensional scattered point data set includes a plurality of target shooting points; Calculating the expectation of the two-dimensional population, and calculating the covariance matrix of the two-dimensional population based on the expectation; Derived the main direction of the two-dimensional scattered point data set according to the covariance matrix; The actual scope of the space test danger zone is determined based on the main direction.

2. According to the method for calculating the danger zone of aerospace test based on principal component analysis according to claim 1, It is characterized in that The step of regarding the distribution results of the target shooting points as a two-dimensional population and constructing a two-dimensional scattered point data set according to the two-dimensional population includes: Consider the distribution results of the target shooting points as the two-dimensional population; The distribution center of all the target shooting points in the two-dimensional scattered point data set is used as the coordinate origin, the shooting direction is used as the x-axis, the direction passing through the coordinate origin and perpendicular to the shooting direction is used as the y-axis, and the z-axis direction is determined according to the right-hand rule to construct a rectangular coordinate system including all the target shooting points, wherein each target shooting point includes a longitude coordinate and a latitude coordinate; In the rectangular coordinate system, a sample set is selected from the two-dimensional population according to the number of the target shooting points to construct the two-dimensional scattered point data set.

3. According to the method for calculating the danger zone of aerospace test based on principal component analysis according to claim 2, It is characterized in that The expression of the two-dimensional population is: M=(L,B)' (1) Wherein, M represents a two-dimensional population, L represents the set of coordinates of all target shooting points in the x-axis direction of the rectangular coordinate system, B represents the set of coordinates of all target shooting points in the z-axis direction of the rectangular coordinate system, and (·)' represents the transpose of (·).

4. According to the method for calculating the danger zone of aerospace test based on principal component analysis as claimed in claim 3, It is characterized in that The expression of the two-dimensional scattered point data set is: Where X represents a two-dimensional scattered point data set, m represents the number of target shooting points, i = 1, 2, ..., m, L m represents the coordinate of the mth target's landing point in the x-axis direction of the rectangular coordinate system, B m Represents the coordinate of the mth target's landing point in the z-axis direction of the rectangular coordinate system.

5. According to the method for calculating the danger zone of aerospace test based on principal component analysis according to claim 4, It is characterized in that The expression for calculating the expectation of the two-dimensional population is: Among them, E(M) represents the expectation of the two-dimensional population, L i represents the coordinate of the target point of the ith target in the x-axis direction of the rectangular coordinate system, B i represents the coordinate of the target point of the ith target in the z-axis direction of the rectangular coordinate system, It represents the average value of the coordinates of all target landing points in the x-axis direction of the rectangular coordinate system. It represents the average value of the coordinates of all target landing points in the z-axis direction of the rectangular coordinate system.

6. According to the method for calculating the danger zone of aerospace test based on principal component analysis according to claim 5, It is characterized in that The expression for calculating the covariance matrix of the two-dimensional population is: Where C represents the covariance matrix of the two-dimensional population, var(M) represents the variance of the two-dimensional population, and (ME(M))' represents the transpose of (ME(M)).

7. According to the method for calculating the danger zone of aerospace test based on principal component analysis according to claim 6, It is characterized in that The step of deriving the main direction of the two-dimensional scattered point data set according to the covariance matrix comprises: Performing linear transformation processing on the variables L and B in the two-dimensional population respectively to obtain a linear equation system; Determine the coefficients of the linear equations using a covariance matrix, wherein a first eigenvalue of the covariance matrix corresponds to a first orthogonal unit eigenvector, and a second eigenvalue of the covariance matrix corresponds to a second orthogonal unit eigenvector; the direction where the first orthogonal unit eigenvector is located is a direction with a maximum variance, and the direction where the second orthogonal unit eigenvector is located is a direction with a minimum variance; Using the first orthogonal unit eigenvector with the maximum variance direction as the principal component of the two-dimensional scattered point data set; Using the direction of the first orthogonal unit eigenvector with the maximum variance direction as the principal direction of the two-dimensional scattered point data set; The first eigenvalue is λ 1 The second eigenvalue is represented by λ 2 To express, λ 1 ≥λ 2 ≥0, the first orthogonal unit eigenvector is α 1 To represent, the second orthogonal unit eigenvector is α 2 To indicate that the direction of the first orthogonal unit vector is perpendicular to the direction of the second orthogonal unit eigenvector.

8. According to the method for calculating the danger zone of aerospace test based on principal component analysis as claimed in claim 7, It is characterized in that The step of determining the actual range of the space test danger zone according to the main direction comprises: The two-dimensional scattered point data set is projected onto the main direction to obtain a first projection set, where the expression of the first projection set is: l＝α’ 1 X (5) Where l represents the first projection set, α' 1 represents the projection of the first orthogonal unit eigenvector; The two-dimensional scattered point data set is projected to the direction of the second orthogonal unit vector to obtain a second projection set, where the expression of the second projection set is: w=a' 2 X (6) Where w represents the second projection set, α' 2 represents the projection of the second orthogonal unit eigenvector; extracting the extreme values ​​of the first projection set and the second projection set respectively as the initial range of the space test danger zone; According to actual needs, the initial range of the space test danger zone is enlarged or reduced, and the actual range of the space test danger zone is determined based on the result of the enlargement or reduction.

9. According to the method for calculating the danger zone of aerospace test based on principal component analysis as claimed in claim 8, It is characterized in that The expression of the initial range of the space test danger zone is: Among them, Y 0 The coordinates of the vertices representing the initial range of the space test danger zone, l max represents the maximum value of the first projection set, l max =max(l),l min represents the minimum value of the first projection set, l min =min(l),w max represents the maximum value of the second projection set, w max =max(w),w min represents the minimum value of the second projection set, w min =min(w).

10. According to the method for calculating the danger zone of aerospace test based on principal component analysis according to claim 9, It is characterized in that The step of enlarging or reducing the initial range of the space test danger zone according to actual needs, and determining the actual range of the space test danger zone according to the result of the enlarging or reducing process comprises: Let l 极值差 = l max -l min , w 极值差 =w max -w min , l 极值差 represents the first extreme value difference between the maximum value of the first projection set and the minimum value of the first projection set, w 极值差 A second extreme value difference between the maximum value of the second projection set and the minimum value of the second projection set is represented, and a proportional coefficient is defined, wherein the proportional coefficient is represented by k, k>0 represents a magnification process, and k<0 represents a reduction process; According to the first extreme value difference, the second extreme value difference and the proportional coefficient, the initial range of the space test danger zone is enlarged or reduced; The expression for performing the enlargement process or the reduction process on the initial range is: Among them, Y k Indicates the result of enlarging or reducing the initial range; The actual range is expressed as: X k =YES k (9) Among them, X k The coordinates of each vertex representing the actual range of the space test danger zone, X k =(x 1 ,x 2 )',x 1 The coordinates of the vertices on the x-axis of the rectangular coordinate system represent the actual range of the space test danger zone. 2 The coordinates of the vertices of the actual range of the space test danger zone on the z-axis of the rectangular coordinate system, (x 1 ,x 2 )' means (x 1 ,x 2 ), A represents the orthogonal matrix, A=(α 1 ,α 2 ).

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