Antenna optimal working surface fitting method and system based on Latin hypercube sampling

Abstract

The present invention discloses an antenna optimal working surface fitting method and system based on Latin hypercube sampling, the method comprising: constructing a least squares conditional equation of the initial optimal working surface equation of the reflector antenna; calculating the partial derivative of the least squares conditional equation of the initial optimal working surface equation of the reflector antenna to obtain a normal equation group of the reflector antenna; sampling the panel of the reflector antenna by the Latin hypercube sampling method to construct a reflector antenna panel sampling point set; solving the normal equation group of the reflector antenna according to the reflector antenna panel sampling point set to obtain the optimal working surface equation of the reflector antenna and the optimal design variables of the reflector antenna. The present invention can effectively reduce the root mean square error of the reflector antenna surface and improve the pointing accuracy and antenna gain of the reflector antenna. As an antenna optimal working surface fitting method and system based on Latin hypercube sampling, the present invention can be widely used in the technical field of large-caliber reflector antennas.

Description

Technical Field

[0001] The invention relates to the technical field of large-aperture reflector antennas, and in particular to an antenna optimal working surface fitting method and system based on Latin hypercube sampling. Background Art

[0002] Microwave antennas, with reflector antennas as a typical representative, are widely used and play an important role in accurately receiving target information or accurately tracking target positions in the fields of radio astronomy, target detection, remote sensing and telemetry. Single-aperture reflector antennas have strong signal collection capabilities and high signal-to-noise ratio, and can effectively collect weak signals, making them indispensable in the field of radio astronomy. Their simple structure and ease of use also made them occupy a place in the detection field in the early days. However, with the increasing requirements for antenna performance, the requirements for antenna pointing accuracy have also become more stringent.

[0003] In the traditional antenna fitting surface calculation process based on the least squares method, six design variables are introduced, including the coordinate system of the main reflector surface when the reflector surface is torsionally deformed. Axis and Amount of rotation of the axis and , due to these two rotation variables, the pointing of the best fit surface may deviate from the ideal pointing. For radio telescopes, the final pointing accuracy of the antenna is very important. A small difference can lead to a big error. Take Mars exploration as an example. The closest distance between the Earth and Mars is about 50 million kilometers. When the pointing deviation of the reflector antenna is 10 arc seconds, the pointing deviation of the telescope can reach nearly 5,000 kilometers. Therefore, the servo system is used to control the azimuth and pitch movement of the antenna. and The stepping accuracy of the servo system cannot meet the requirements. Summary of the invention

[0004] In order to solve the above technical problems, the purpose of the present invention is to provide an antenna optimal working surface fitting method and system based on Latin hypercube sampling, which can effectively reduce the surface root mean square error of the reflector antenna and improve the pointing accuracy and antenna gain of the reflector antenna.

[0005] The first technical solution adopted by the present invention is: an antenna optimal working surface fitting method based on Latin hypercube sampling, comprising the following steps:

[0006] According to the structural parameters of the reflector antenna and the working frequency of the reflector antenna, a least square method condition equation of the initial optimal working surface equation of the reflector antenna is constructed;

[0007] The least square method condition equation of the initial optimal working surface equation of the reflector antenna is calculated by partial derivative calculation to obtain the normal equation group of the reflector antenna;

[0008] The panel of the reflector antenna is sampled by the Latin hypercube sampling method to construct a sampling point set of the reflector antenna panel;

[0009] The normal equations of the reflector antenna are solved according to the sampling point set of the reflector antenna panel, and the optimal working surface equation of the reflector antenna and the optimal design variables of the reflector antenna are obtained.

[0010] Furthermore, the step of constructing a least squares condition equation of an initial optimal working surface equation of the reflector antenna according to the structural parameters of the reflector antenna and the working frequency of the reflector antenna specifically includes:

[0011] When the reflector antenna is in an ideal position, a geodetic coordinate system is established with the vertex of the reflector antenna as the origin;

[0012] Based on the geodetic coordinate system, the structural parameters of the reflector antenna and the operating frequency of the reflector antenna are obtained, and the ideal reflector equation of the reflector antenna is determined;

[0013] According to the ideal reflector equation of the reflector antenna, the ideal node coordinates of the panel actuator of the reflector antenna are determined;

[0014] When the reflector antenna is in a deformed position, obtaining the coordinates of the deformation nodes of the panel actuator of the reflector antenna;

[0015] Determine the deformation displacement of the vertex of the main parabola of the reflector antenna and the deformation displacement of the focus of the main parabola of the reflector antenna according to the ideal node coordinates of the panel actuator of the reflector antenna and the deformation node coordinates of the panel actuator of the reflector antenna;

[0016] Combining the deformation displacement of the vertex of the main parabola of the reflector antenna and the deformation displacement of the focus of the main parabola of the reflector antenna, the initial optimal working surface equation of the reflector antenna is constructed;

[0017] The initial optimal working surface equation of the reflector antenna is expanded, and the least square condition equation of the initial optimal working surface equation of the reflector antenna is constructed.

[0018] Furthermore, it also includes:

[0019] Calculate the surface root mean square error of the reflector antenna according to the ideal node coordinates of the panel actuator of the reflector antenna and the deformed node coordinates of the panel actuator of the reflector antenna;

[0020] Set the threshold requirement range of the surface root mean square error of the reflector antenna;

[0021] If the surface root mean square error of the reflector antenna meets the threshold requirement range of the surface root mean square error of the reflector antenna, the initial optimal working surface equation of the reflector antenna is the optimal working surface equation of the reflector antenna;

[0022] If the surface root mean square error of the reflector antenna does not meet the threshold requirement range of the surface root mean square error of the reflector antenna, return to the step of determining the deformation displacement of the vertex of the main parabola of the reflector antenna and the deformation displacement of the focus of the main parabola of the reflector antenna.

[0023] Furthermore, the initial optimal working surface equation of the reflector antenna is specifically expressed as follows:

[0024] ;

[0025] In the above formula, and Represents the deformation displacement of the vertex of the main parabola of the reflector antenna, Indicates the deformation displacement of the focus of the main parabola of the reflector antenna, The point representing the optimal working surface equation, Represents the focal length of the antenna's main parabola equation.

[0026] Furthermore, the expression of the least squares condition equation of the initial optimal working surface equation of the reflector antenna is specifically as follows:

[0027] ;

[0028] In the above formula, represents the least squares conditional equation, and Represents the deformation displacement of the vertex of the main parabola of the reflector antenna, Indicates the deformation displacement of the focus of the main parabola of the reflector antenna, Indicates the number of sampling points, Indicates sampling points, The point representing the optimal working surface equation, represents the focal length of the antenna main parabola equation, represents the parabola equation of the original antenna design, Represents the deviation between the original antenna parabola equation and the optimal working surface.

[0029] Furthermore, the step of calculating partial derivatives of the least squares condition equation of the initial optimal working surface equation of the reflector antenna to obtain the normal equation group of the reflector antenna specifically includes:

[0030] The deformation displacement of the vertex of the main parabola of the reflector antenna and the deformation displacement of the focus of the main parabola of the reflector antenna are calculated by the least square method condition equation of the initial optimal working surface equation of the reflector antenna, and the partial derivative calculation result is obtained;

[0031] The partial derivative calculation results are sorted and simplified to obtain the normal equations of the reflector antenna.

[0032] Furthermore, the step of sampling the panel of the reflector antenna by the Latin hypercube sampling method to construct a sampling point set of the reflector antenna panel specifically includes:

[0033] Classifying the sampling points of the panel of the reflector antenna to obtain reflector antenna panel sampling key points and reflector antenna panel sampling non-key points, wherein the reflector antenna panel sampling key points represent the corresponding nodes of the panel actuator, and the reflector antenna panel sampling non-key points represent the corresponding nodes of the non-panel actuator;

[0034] The non-critical sampling points of the reflector antenna panel are evenly sampled by equidistant division using the Latin hypercube sampling method to obtain the sampled non-critical sampling points of the reflector antenna panel;

[0035] The reflector antenna panel sampling key points and the sampled reflector antenna panel sampling non-key points are integrated to construct a reflector antenna panel sampling point set.

[0036] Further, the step of solving the normal equations of the reflector antenna according to the sampling point set of the reflector antenna panel to obtain the optimal working surface equation of the reflector antenna and the optimal design variables of the reflector antenna specifically includes:

[0037] Substitute the sampling point set of the reflector antenna panel into the normal equation group of the reflector antenna to solve it, and obtain the deformed reflector equation of the reflector antenna;

[0038] Determining the coordinates of deformation nodes of the panel actuator of the sampled reflector antenna according to the deformation reflector equation of the reflector antenna;

[0039] Determine the deformation displacement of the vertex of the main parabola of the reflector antenna after sampling and the deformation displacement of the focus of the main parabola of the reflector antenna after sampling according to the ideal node coordinates of the panel actuator of the reflector antenna and the deformation node coordinates of the panel actuator of the reflector antenna after sampling;

[0040] Calculate the surface root mean square error of the sampled reflector antenna according to the panel actuator deformation node coordinates of the reflector antenna and the sampled panel actuator deformation node coordinates of the reflector antenna;

[0041] If the surface root mean square error of the reflector antenna after sampling does not meet the threshold requirement range of the surface root mean square error of the reflector antenna, then return to the step of sampling the panel of the reflector antenna through the Latin hypercube sampling method to construct a reflector antenna panel sampling point set;

[0042] If the surface root mean square error of the reflector antenna after sampling meets the threshold requirement range of the surface root mean square error of the reflector antenna, then the deformed reflector surface equation of the reflector antenna is the optimal working surface equation of the reflector antenna, and the deformation displacement of the vertex of the main parabola of the reflector antenna after sampling and the deformation displacement of the focus of the main parabola of the reflector antenna after sampling are the optimal design variables of the reflector antenna.

[0043] Furthermore, the calculation expression of the surface root mean square error of the reflector antenna is specifically as follows:

[0044] ;

[0045] In the above formula, represents the surface RMS error of the reflector antenna, represents a set of sampling points, Indicates sampling points, and Represents the coordinates of the deformation nodes of the panel actuator of the reflector antenna, and Panel actuator deformation node coordinates representing the sampled reflector antenna.

[0046] The second technical solution adopted by the present invention is: an antenna optimal working surface fitting system based on Latin hypercube sampling, comprising:

[0047] The first module is used to construct a least squares condition equation of the initial optimal working surface equation of the reflector antenna according to the structural parameters of the reflector antenna and the working frequency of the reflector antenna;

[0048] The second module is used to calculate the partial derivative of the least squares condition equation of the initial optimal working surface equation of the reflector antenna to obtain the normal equation group of the reflector antenna;

[0049] The third module is used to sample the panel of the reflector antenna by using the Latin hypercube sampling method to construct a sampling point set of the reflector antenna panel;

[0050] The fourth module is used to solve the normal equations of the reflector antenna according to the sampling point set of the reflector antenna panel to obtain the optimal working surface equation of the reflector antenna and the optimal design variables of the reflector antenna.

[0051] The beneficial effects of the method and system of the present invention are as follows: the present invention constructs a least squares conditional equation of the initial optimal working surface equation of the reflector antenna; then performs partial derivative calculation on the least squares conditional equation of the initial optimal working surface equation of the reflector antenna to obtain a normal equation group of the reflector antenna; further samples the panel of the reflector antenna through the Latin hypercube sampling method to construct a reflector antenna panel sampling point set, improves the effectiveness of the antenna optimal working surface fitting method through the Latin hypercube sampling method based on non-critical nodes, and finally solves the normal equation group of the reflector antenna according to the reflector antenna panel sampling point set to obtain the optimal working surface equation of the reflector antenna and the optimal design variables of the reflector antenna, which can effectively reduce the surface root mean square error of the reflector antenna and improve the pointing accuracy and antenna gain of the reflector antenna. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 It is a flowchart of the steps of the antenna optimal working surface fitting method based on Latin hypercube sampling of the present invention;

[0053] Figure 2 It is a structural block diagram of the antenna optimal working surface fitting system based on Latin hypercube sampling of the present invention;

[0054] Figure 3 is a schematic diagram of optimal working surface fitting provided by a specific embodiment of the present invention;

[0055] Figure 4 It is a schematic diagram of the partitioning of the QTT antenna panel provided by a specific embodiment of the present invention;

[0056] Figure 5 is a schematic diagram of numbering of panels in region 11 provided in a specific embodiment of the present invention;

[0057] Figure 6 It is a QTT main reflection surface calculation node displacement cloud map provided by a specific embodiment of the present invention;

[0058] Figure 7 It is a schematic diagram of the directions corresponding to the surfaces of the QTT simulation and calculation results provided by a specific embodiment of the present invention;

[0059] Figure 8 is a schematic diagram of node distribution after secondary sampling provided by a specific embodiment of the present invention;

[0060] Fig. 9 is a schematic diagram of sampling point uniformity provided by a specific embodiment of the present invention;

[0061] Fig.10 It is a schematic diagram comparing directional diagrams before and after fitting provided by a specific embodiment of the present invention. DETAILED DESCRIPTION

[0062] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. The step numbers in the following embodiments are only provided for the convenience of explanation and description, and the order between the steps is not limited in any way. The execution order of each step in the embodiment can be adaptively adjusted according to the understanding of those skilled in the art.

[0063] Reference Figure 1 The present invention provides an antenna optimal working surface fitting method based on Latin hypercube sampling, the method comprising the following steps:

[0064] S100, constructing a least squares condition equation of an initial optimal working surface equation of the reflector antenna according to the structural parameters of the reflector antenna and the working frequency of the reflector antenna;

[0065] Specifically, when the reflector antenna is in an ideal position, a geodetic coordinate system is established with the vertex of the reflector antenna as the origin; based on the geodetic coordinate system, the structural parameters of the reflector antenna and the operating frequency of the reflector antenna are obtained, and the ideal reflector surface equation of the reflector antenna is determined; based on the ideal reflector surface equation of the reflector antenna, the ideal node coordinates of the panel actuator of the reflector antenna are determined.

[0066] In this embodiment, according to the structural parameters and operating frequency of the large parabolic antenna, a geodetic coordinate system is established with the vertex of the reflector antenna as the origin. When the reflector antenna panel is in an ideal position, the coordinates of any point on the panel satisfy the equation ;in, is the focal length; and determines the initial node information of the panel actuator.

[0067] When the reflector antenna is in a deformed position, the coordinates of the deformation nodes of the panel actuator of the reflector antenna are obtained; the deformation displacement of the vertex of the main parabola of the reflector antenna and the deformation displacement of the focus of the main parabola of the reflector antenna are determined according to the ideal node coordinates of the panel actuator of the reflector antenna and the deformation node coordinates of the panel actuator of the reflector antenna; the initial optimal working surface equation of the reflector antenna is constructed by combining the deformation displacement of the vertex of the main parabola of the reflector antenna and the deformation displacement of the focus of the main parabola of the reflector antenna; the initial optimal working surface equation of the reflector antenna is expanded to construct the least squares conditional equation of the initial optimal working surface equation of the reflector antenna.

[0068] In this embodiment, four design variables for determining the optimal working surface are , , and ,in, , and is the deformation displacement of the vertex of the main parabola of the reflecting surface, is the parabola focus deformation displacement, and the initial optimal working surface equation is constructed, which is expressed as follows:

[0069] ;

[0070] In the above formula, , and Represents the deformation displacement of the vertex of the main parabola of the reflector antenna, Indicates the deformation displacement of the focus of the main parabola of the reflector antenna, The point representing the optimal working surface equation, Represents the focal length of the antenna's main parabola equation.

[0071] Expand the initial optimal working surface equation and multiply the fractions above and below by , and ignoring the high-order terms of small variables, we can get:

[0072] ;

[0073] The least squares condition equation can be constructed, and its expression is:

[0074] ;

[0075] Make

[0076] ;

[0077] In the above formula, represents the least squares conditional equation, , and Represents the deformation displacement of the vertex of the main parabola of the reflector antenna, Indicates the deformation displacement of the focus of the main parabola of the reflector antenna, Indicates the number of sampling points, Indicates sampling points, The point representing the optimal working surface equation, represents the focal length of the antenna main parabola equation, represents the parabola equation of the original antenna design, Represents the deviation between the original antenna parabola equation and the optimal working surface.

[0078] It should also be noted that the surface root mean square error of the reflector antenna is calculated based on the ideal node coordinates of the panel actuator of the reflector antenna and the deformation node coordinates of the panel actuator of the reflector antenna; the threshold requirement range of the surface root mean square error of the reflector antenna is set; if the surface root mean square error of the reflector antenna meets the threshold requirement range of the surface root mean square error of the reflector antenna, then the initial optimal working surface equation of the reflector antenna is the optimal working surface equation of the reflector antenna; if the surface root mean square error of the reflector antenna does not meet the threshold requirement range of the surface root mean square error of the reflector antenna, then return to the step of determining the deformation displacement of the vertex of the main parabola of the reflector antenna and the deformation displacement of the focus of the main parabola of the reflector antenna.

[0079] It should be noted that according to the initial node information of the panel actuator , combined with the extracted deformation node coordinates of the deformed reflective surface , the surface root mean square error of the reflecting surface can be calculated, and its expression is:

[0080] ;

[0081] Determine whether the surface root mean square error of the antenna panel meets the requirements. If so, output the optimal working surface equation and design variables. If not, construct the optimal working surface equation and the least squares condition equation.

[0082] Furthermore, it should be noted that the embodiment of the present invention is designed for the panel accuracy of large-aperture reflector antennas. Through the optimization process of finding an optimal set of design variables, the root mean square error between the point on the optimal working surface corresponding to the sampling point and the ideal point is minimized. The optimal working surface of the reflector panel under the influence of the antenna service environment can be obtained more accurately, the gain loss of the smaller antenna can be reduced, and the pointing accuracy of the antenna can be significantly improved.

[0083] S200, performing partial derivative calculation on the least squares condition equation of the initial optimal working surface equation of the reflector antenna to obtain a normal equation group of the reflector antenna;

[0084] Specifically, the deformation displacement of the vertex of the main parabola of the reflector antenna and the deformation displacement of the focus of the main parabola of the reflector antenna are calculated by the least squares condition equation of the initial optimal working surface equation of the reflector antenna to obtain the partial derivative calculation result;

[0085] In this embodiment, the least squares condition equation is The partial derivatives of the four design variables are calculated respectively, and the expressions are:

[0086] ;

[0087] The partial derivative calculation results are sorted and simplified to obtain the normal equations of the reflector antenna.

[0088] In this embodiment, the normal equations can be obtained by arranging and simplifying, and the expression is:

[0089] ;

[0090] In the above formula, is the coefficient matrix, is the column vector of design variables, is a constant column vector.

[0091] Among them, the expression of the coefficient matrix is:

[0092] ;

[0093] The expression of the design variable column vector is:

[0094] ;

[0095] The expression for the constant column vector is:

[0096] ;

[0097] In the above formula, Indicates the initial node information of the panel actuator.

[0098] S300, sampling the panel of the reflector antenna by using a Latin hypercube sampling method to construct a sampling point set of the reflector antenna panel;

[0099] Specifically, the sampling points of the panel of the reflector antenna are classified to obtain the reflector antenna panel sampling key points and the reflector antenna panel sampling non-key points, wherein the reflector antenna panel sampling key points represent the corresponding nodes of the panel actuator, and the reflector antenna panel sampling non-key points represent the corresponding nodes of the non-panel actuator;

[0100] In this embodiment, the sampling points of the reflection surface are classified into key points and non-key points, the nodes where the actuators are located are classified as key points, and the other nodes are classified as non-key points, that is, , is the sampling times.

[0101] The Latin hypercube sampling method is used to equidistantly divide and uniformly sample the non-critical sampling points of the reflector antenna panel to obtain the sampled non-critical sampling points of the reflector antenna panel; the reflector antenna panel sampling key points and the sampled non-critical sampling points of the reflector antenna panel are integrated to construct a reflector antenna panel sampling point set.

[0102] In this embodiment, Latin hypercube sampling is performed on non-key points on the basis of including key points. ; and the key point group, there are , for The number of nodes in the middle, the obtained nodes and the key nodes form a node set, and Latin hypercube sampling can be used to evenly sample the non-key points in the entire main surface of the reflection surface by equidistant division, thereby achieving uniform traversal of the non-key points.

[0103] Furthermore, it should be explained that the optimal working surface fitting method for the reflector antenna based on Latin hypercube sampling of non-critical nodes is achieved by classifying all sampling points on the main surface of the reflector antenna, wherein the critical points are the nodes where the actuators are located, and the other points are non-critical points; all sampling points on the main surface of the reflector antenna are then resampled, and Latin hypercube sampling is performed on the non-critical points on the basis of including the critical points, and then a series of optimal working surface families are obtained according to each sampling node set, and the surface that minimizes the surface root mean square error of all nodes is found in the optimal working surface family, and the design variables corresponding to the surface are the optimal design variables, thereby achieving the fitting of the optimal working surface of the reflector antenna.

[0104] S400, solving the normal equations of the reflector antenna according to the sampling point set of the reflector antenna panel to obtain the optimal working surface equation of the reflector antenna and the optimal design variables of the reflector antenna.

[0105] Specifically, the sampling point set of the reflector antenna panel is substituted into the normal equation group of the reflector antenna for solving, so as to obtain the deformed reflector surface equation of the reflector antenna; the deformation node coordinates of the panel actuator of the sampled reflector antenna are determined according to the deformed reflector surface equation of the reflector antenna; the deformation displacement of the vertex of the main parabola of the reflector antenna after sampling and the deformation displacement of the focus of the main parabola of the reflector antenna after sampling are determined according to the ideal node coordinates of the panel actuator of the reflector antenna and the deformation node coordinates of the panel actuator of the sampled reflector antenna; the reflector after sampling is calculated according to the deformation node coordinates of the panel actuator of the reflector antenna and the deformation node coordinates of the panel actuator of the sampled reflector antenna. the surface root mean square error of the reflector antenna; if the surface root mean square error of the sampled reflector antenna does not meet the threshold requirement range of the surface root mean square error of the reflector antenna, then return to the step of sampling the panel of the reflector antenna through the Latin hypercube sampling method to construct a reflector antenna panel sampling point set; if the surface root mean square error of the sampled reflector antenna meets the threshold requirement range of the surface root mean square error of the reflector antenna, then the deformed reflector surface equation of the reflector antenna is the optimal working surface equation of the reflector antenna, and the deformation displacement of the vertex of the main parabola of the reflector antenna after sampling and the deformation displacement of the focus of the main parabola of the reflector antenna after sampling are the optimal design variables of the reflector antenna.

[0106] In this embodiment, according to The node data in the equations are solved to obtain , get the optimal working surface of the main surface of the deformable reflector antenna in this round, and use the deformation node Nodes on the corresponding optimal working surface The surface root mean square error of the reflection surface is calculated based on the coordinates of the reflection surface. When the surface root mean square error is not satisfied, the Latin hypercube sampling points of this round are eliminated.

[0107] Among them, through the deformation node Nodes on the corresponding optimal working surface The expression for calculating the surface root mean square error of the reflection surface is as follows:

[0108] ;

[0109] In the above formula, represents the surface RMS error of the reflector antenna, represents a set of sampling points, Indicates sampling points, and Represents the coordinates of the deformation nodes of the panel actuator of the reflector antenna, and Panel actuator deformation node coordinates representing the sampled reflector antenna.

[0110] In summary, the embodiments of the present invention are further explained through specific simulation experimental values:

[0111] 1) Determine the ideal reflection surface equation of the antenna and the initial node information of the actuator on the reflection surface.

[0112] Taking QTT as the research object, assuming that the antenna works in the 10GHz frequency band, the correctness and effectiveness of the proposed method are demonstrated by studying the shape of the antenna under gravity deformation when it is facing upward. The vertex of the reflector antenna is taken as the origin to establish a geodetic coordinate system. When the reflector antenna panel is in an ideal position, the coordinates of any point on the panel satisfy the equation ; Then partition the QTT antenna panel, such as Figure 4 As shown, the panel of area 11 is selected. The number of panels to be calculated is 25 in total, divided into 5 rings and 5 columns, and each actuator and panel is numbered, as shown in Figure 5 As shown, the initial node information of the actuator is obtained.

[0113] 2) Calculate the surface RMS error of the reflecting surface.

[0114] The initial node information of the panel actuator is ; Extract the coordinates of the deformation nodes of the deformed reflective surface , as shown in Table 1.

[0115] Table 1 Initial node information data table of panel actuator

[0116] serial number x / mm y / mm z / mm serial number x / mm y / mm z / mm serial number x / mm y / mm z / mm 1 5987.03 392.36 250.08 13 10647.02 697.83 839.39 25 15316.72 1003.88 1761.38 2 5884.69 1170.54 250.79 14 10464.82 2081.57 839.57 26 15054.61 2994.52 1761.54 3 5681.55 1928.63 250.92 15 10103.56 3429.69 839.76 27 14534.91 4933.92 1761.76 4 5381.19 2653.72 251.02 16 9569.44 4719.13 839.86 28 13766.54 6788.90 1761.78 5 4988.77 3333.40 251.10 17 8871.59 5927.83 839.95 29 12762.61 8527.72 1761.89 6 4510.98 3956.05 251.14 18 8021.92 7035.10 840.02 30 11540.27 10120.66 1761.97 7 8322.09 545.45 504.15 19 13011.82 852.82 1264.74 31 17596.64 1153.30 2332.33 8 8179.67 1627.04 504.38 20 12789.16 2543.91 1264.90 32 17295.47 3440.24 2332.67 9 7897.30 2680.78 504.56 21 12347.66 4191.46 1265.16 33 16698.49 5668.34 2332.56 10 7479.81 3688.65 504.71 22 11694.91 5767.29 1265.23 34 15815.77 7799.45 2332.48 11 6934.34 4633.41 504.80 23 10842.05 7244.45 1265.32 35 14662.37 9797.07 2332.77 12 6270.22 5498.88 504.86 24 9803.66 8597.67 1265.41 36 13258.09 11627.15 2332.77

[0117] Further, combined with and , the surface root mean square error of the reflecting surface can be calculated. In the embodiment of the present invention, the surface root mean square error rms is required to be less than or equal to , as shown in Table 2.

[0118] Table 2 Surface root mean square error data table of the reflective surface

[0119] / Calculation results Surface root mean square error / mm 7.13 Gain loss / dB -1.69

[0120] 3) Construct the optimal working surface equation and the least squares condition equation.

[0121] Four design variables to determine the optimal working surface , , and ,in, , and is the deformation displacement of the vertex of the main parabola of the reflecting surface, is the deformation displacement of the parabola focus, such as Figure 6 As shown, construct the optimal working surface equation:

[0122] ;

[0123] Then the least squares condition equation can be constructed:

[0124] ;

[0125] Make

[0126] ;

[0127] In the above formula, is the number of sampling points.

[0128] 4) Take partial derivatives of the design variables in the least squares conditional equation and simplify them to obtain the normal equation group.

[0129] Make function Calculate partial derivatives of the four design variables respectively:

[0130] ;

[0131] Simplifying the equations .

[0132] 5) Classify and Latin hypercube sample the sampling points on the reflector panel.

[0133] The sampling points of the reflection surface are classified into key points and non-key points, the nodes where the actuators are located are classified as key points, and the other nodes are classified as non-key points, that is, , sampling times ; Latin hypercube sampling is performed on non-key points on the basis that key points must be included. ; and the key point group, there are , for The number of midpoints.

[0134] 6) Substitute the node set including critical nodes and non-critical nodes into the normal equations to solve the design variables and the optimal working surface equation.

[0135] After obtaining the data of key points and secondary sampling points, the design variables and fitting surface equations of this round can be obtained, as shown below:

[0136] ;

[0137] According to the fitting equation, by deforming the nodes Nodes on the corresponding optimal working surface The coordinates of the reflection surface can be calculated to obtain the root mean square error of the fitting surface. .

[0138] 7) Analyze the results.

[0139] like Figure 7 As shown in , when the antenna works in the 10 GHz frequency band, it can be seen that the root mean square error of this round of fitting surface does not meet the requirements. Therefore, the sampling points of this round are removed and the non-critical points are resampled, as shown in Figure 8 According to the simulation calculation results, the optimal working surface that meets the root mean square error requirements is obtained in the sixth round of fitting. From then on, the optimal working surface fitting of the reflection surface based on the improved least squares method can be completed, and the directional diagram of the fitting surface can be obtained, as shown in Fig. 9 As shown. Fig.10 As shown in the figure, it can be seen that the directional pattern of the fitting surface is greatly improved compared with the deformed directional pattern. This example illustrates the effectiveness of the proposed antenna optimal working surface fitting method based on non-critical node Latin hypercube sampling, which can effectively reduce the antenna surface root mean square error, significantly improve the antenna pointing accuracy, and greatly improve the antenna gain.

[0140] Reference Figure 2, the antenna optimal working surface fitting system based on Latin hypercube sampling, including:

[0141] The first module 201 is used to construct a least squares condition equation of an initial optimal working surface equation of the reflector antenna according to the structural parameters of the reflector antenna and the working frequency of the reflector antenna;

[0142] The second module 202 is used to calculate the partial derivative of the least squares condition equation of the initial optimal working surface equation of the reflector antenna to obtain the normal equation group of the reflector antenna;

[0143] The third module 203 is used to sample the panel of the reflector antenna by using the Latin hypercube sampling method to construct a sampling point set of the reflector antenna panel;

[0144] The fourth module 204 is used to solve the normal equations of the reflector antenna according to the sampling point set of the reflector antenna panel to obtain the optimal working surface equation of the reflector antenna and the optimal design variables of the reflector antenna.

[0145] The contents of the above method embodiments are all applicable to the present system embodiments. The functions specifically implemented by the present system embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0146] The above is a specific description of the preferred implementation of the present invention, but the invention is not limited to the embodiments. Those skilled in the art may make various equivalent modifications or substitutions without violating the spirit of the present invention. These equivalent modifications or substitutions are all included in the scope defined by the claims of this application.

Claims

1. The antenna optimal working surface fitting method based on Latin hypercube sampling is characterized by: The following steps are involved: According to the structural parameters of the reflector antenna and the working frequency of the reflector antenna, a least square method condition equation of the initial optimal working surface equation of the reflector antenna is constructed; The expression of the least squares condition equation of the initial optimal working surface equation of the reflector antenna is specifically as follows: ； In the above formula, represents the least squares conditional equation, and Represents the deformation displacement of the vertex of the main parabola of the reflector antenna, Indicates the deformation displacement of the focus of the main parabola of the reflector antenna, Indicates the number of sampling points, Indicates sampling points, The point representing the optimal working surface equation, represents the focal length of the antenna main parabola equation, represents the parabola equation of the original antenna design, Represents the deviation between the original antenna parabola equation and the optimal working surface; The least square method condition equation of the initial optimal working surface equation of the reflector antenna is calculated by partial derivative calculation to obtain the normal equation group of the reflector antenna; The panel of the reflector antenna is sampled by the Latin hypercube sampling method to construct a sampling point set of the reflector antenna panel; Substitute the sampling point set of the reflector antenna panel into the normal equation group of the reflector antenna to solve it, and obtain the deformed reflector equation of the reflector antenna; Determining the coordinates of deformation nodes of the panel actuator of the sampled reflector antenna according to the deformation reflector equation of the reflector antenna; Determine the deformation displacement of the vertex of the main parabola of the reflector antenna after sampling and the deformation displacement of the focus of the main parabola of the reflector antenna after sampling according to the ideal node coordinates of the panel actuator of the reflector antenna and the deformation node coordinates of the panel actuator of the reflector antenna after sampling; Calculate the surface root mean square error of the sampled reflector antenna according to the panel actuator deformation node coordinates of the reflector antenna and the sampled panel actuator deformation node coordinates of the reflector antenna; If the surface root mean square error of the reflector antenna after sampling does not meet the threshold requirement range of the surface root mean square error of the reflector antenna, then return to the step of sampling the panel of the reflector antenna through the Latin hypercube sampling method to construct a reflector antenna panel sampling point set; If the surface root mean square error of the reflector antenna after sampling meets the threshold requirement range of the surface root mean square error of the reflector antenna, then the deformed reflector surface equation of the reflector antenna is the optimal working surface equation of the reflector antenna, and the deformation displacement of the vertex of the main parabola of the reflector antenna after sampling and the deformation displacement of the focus of the main parabola of the reflector antenna after sampling are the optimal design variables of the reflector antenna.

2. The antenna optimal working surface fitting method based on Latin hypercube sampling according to claim 1 is characterized in that: The step of constructing a least squares condition equation of the initial optimal working surface equation of the reflector antenna according to the structural parameters of the reflector antenna and the working frequency of the reflector antenna specifically includes: When the reflector antenna is in an ideal position, a geodetic coordinate system is established with the vertex of the reflector antenna as the origin; Based on the geodetic coordinate system, the structural parameters of the reflector antenna and the operating frequency of the reflector antenna are obtained, and the ideal reflector equation of the reflector antenna is determined; According to the ideal reflector equation of the reflector antenna, the ideal node coordinates of the panel actuator of the reflector antenna are determined; When the reflector antenna is in a deformed position, obtaining the coordinates of the deformation nodes of the panel actuator of the reflector antenna; Determine the deformation displacement of the vertex of the main parabola of the reflector antenna and the deformation displacement of the focus of the main parabola of the reflector antenna according to the ideal node coordinates of the panel actuator of the reflector antenna and the deformation node coordinates of the panel actuator of the reflector antenna; Combining the deformation displacement of the vertex of the main parabola of the reflector antenna and the deformation displacement of the focus of the main parabola of the reflector antenna, the initial optimal working surface equation of the reflector antenna is constructed; The initial optimal working surface equation of the reflector antenna is expanded, and the least square condition equation of the initial optimal working surface equation of the reflector antenna is constructed.

3. The antenna optimal working surface fitting method based on Latin hypercube sampling according to claim 2 is characterized in that: Also includes: Calculate the surface root mean square error of the reflector antenna according to the ideal node coordinates of the panel actuator of the reflector antenna and the deformed node coordinates of the panel actuator of the reflector antenna; Set the threshold requirement range of the surface root mean square error of the reflector antenna; If the surface root mean square error of the reflector antenna meets the threshold requirement range of the surface root mean square error of the reflector antenna, the initial optimal working surface equation of the reflector antenna is the optimal working surface equation of the reflector antenna; If the surface root mean square error of the reflector antenna does not meet the threshold requirement range of the surface root mean square error of the reflector antenna, return to the step of determining the deformation displacement of the vertex of the main parabola of the reflector antenna and the deformation displacement of the focus of the main parabola of the reflector antenna.

4. The antenna optimal working surface fitting method based on Latin hypercube sampling according to claim 3 is characterized in that: The expression of the initial optimal working surface equation of the reflector antenna is specifically as follows: ； In the above formula, and Represents the deformation displacement of the vertex of the main parabola of the reflector antenna, Indicates the deformation displacement of the focus of the main parabola of the reflector antenna, The point representing the optimal working surface equation, Represents the focal length of the antenna's main parabola equation.

5. The antenna optimal working surface fitting method based on Latin hypercube sampling according to claim 4 is characterized in that: The step of calculating partial derivatives of the least squares condition equation of the initial optimal working surface equation of the reflector antenna to obtain the normal equation group of the reflector antenna specifically includes: The deformation displacement of the vertex of the main parabola of the reflector antenna and the deformation displacement of the focus of the main parabola of the reflector antenna are calculated by the least square method condition equation of the initial optimal working surface equation of the reflector antenna, and the partial derivative calculation result is obtained; The partial derivative calculation results are sorted and simplified to obtain the normal equations of the reflector antenna.

6. The antenna optimal working surface fitting method based on Latin hypercube sampling according to claim 5 is characterized in that: The step of sampling the panel of the reflector antenna by the Latin hypercube sampling method to construct a sampling point set of the reflector antenna panel specifically includes: Classifying the sampling points of the panel of the reflector antenna to obtain reflector antenna panel sampling key points and reflector antenna panel sampling non-key points, wherein the reflector antenna panel sampling key points represent the corresponding nodes of the panel actuator, and the reflector antenna panel sampling non-key points represent the corresponding nodes of the non-panel actuator; The non-critical sampling points of the reflector antenna panel are evenly sampled by equidistant division using the Latin hypercube sampling method to obtain the sampled non-critical sampling points of the reflector antenna panel; The reflector antenna panel sampling key points and the sampled reflector antenna panel sampling non-key points are integrated to construct a reflector antenna panel sampling point set.

7. The antenna optimal working surface fitting method based on Latin hypercube sampling according to claim 6 is characterized in that: The calculation expression of the surface root mean square error of the reflector antenna is specifically as follows: ； In the above formula, represents the surface RMS error of the reflector antenna, represents a set of sampling points, Indicates sampling points, and represents the coordinates of the deformation nodes of the panel actuator of the reflector antenna, and Represents the sampled reflector antenna panel actuator deformation node coordinates. 8.An antenna optimal working surface fitting system based on Latin hypercube sampling, characterized in that: Includes the following modules: The first module is used to construct a least squares condition equation of the initial optimal working surface equation of the reflector antenna according to the structural parameters of the reflector antenna and the working frequency of the reflector antenna; The expression of the least squares condition equation of the initial optimal working surface equation of the reflector antenna is specifically as follows: ； In the above formula, represents the least squares conditional equation, and Represents the deformation displacement of the vertex of the main parabola of the reflector antenna, Indicates the deformation displacement of the focus of the main parabola of the reflector antenna, Indicates the number of sampling points, Indicates sampling points, The point representing the optimal working surface equation, represents the focal length of the antenna main parabola equation, represents the parabola equation of the original antenna design, Represents the deviation between the original antenna parabola equation and the optimal working surface; The second module is used to calculate the partial derivative of the least squares condition equation of the initial optimal working surface equation of the reflector antenna to obtain the normal equation group of the reflector antenna; The third module is used to sample the panel of the reflector antenna by using the Latin hypercube sampling method to construct a sampling point set of the reflector antenna panel; The fourth module is used to substitute the sampling point set of the reflector antenna panel into the normal equation group of the reflector antenna for solving, so as to obtain the deformed reflector equation of the reflector antenna; Determining the coordinates of deformation nodes of the panel actuator of the sampled reflector antenna according to the deformation reflector equation of the reflector antenna; Determine the deformation displacement of the vertex of the main parabola of the reflector antenna after sampling and the deformation displacement of the focus of the main parabola of the reflector antenna after sampling according to the ideal node coordinates of the panel actuator of the reflector antenna and the deformation node coordinates of the panel actuator of the reflector antenna after sampling; Calculate the surface root mean square error of the sampled reflector antenna according to the panel actuator deformation node coordinates of the reflector antenna and the sampled panel actuator deformation node coordinates of the reflector antenna; If the surface root mean square error of the reflector antenna after sampling does not meet the threshold requirement range of the surface root mean square error of the reflector antenna, then return to the step of sampling the panel of the reflector antenna through the Latin hypercube sampling method to construct a reflector antenna panel sampling point set; If the surface root mean square error of the reflector antenna after sampling meets the threshold requirement range of the surface root mean square error of the reflector antenna, then the deformed reflector surface equation of the reflector antenna is the optimal working surface equation of the reflector antenna, and the deformation displacement of the vertex of the main parabola of the reflector antenna after sampling and the deformation displacement of the focus of the main parabola of the reflector antenna after sampling are the optimal design variables of the reflector antenna.

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