CN110375705B - Antenna reflector and profile deformation measuring method and contrast measuring method thereof - Google Patents
Antenna reflector and profile deformation measuring method and contrast measuring method thereof Download PDFInfo
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Abstract
An antenna reflector and a profile deformation measuring method and a contrast measuring method thereof belong to the field of integral deformation measurement, and aim to solve the problems of large deviation, complex operation, time and labor waste of the existing grid reflector profile deformation measurement, the key points are that a plurality of target points are arranged on the reflector profile, the three-dimensional coordinates of the target points are measured, and the deformation displacement of the target points of the reflector profile is measured by a sensor at a single time; dividing the reflector profile into a plurality of fitting regions; respectively fitting the coordinate information of the target points in different fitting areas by adopting a polynomial to correspond to the deformation displacement of the target points, and solving polynomial coefficients by using a least square method to obtain a fitting function corresponding to each fitting area; and substituting the coordinate information of the target points in different regions into the fitting function of the corresponding region, updating and obtaining the deformation displacement of the corresponding target point.
Description
Technical Field
The invention belongs to the field of integral deformation measurement, and relates to a method for measuring the profile deformation of an antenna reflector.
Background
High-precision fixed-surface antenna reflectors such as grid reflectors are widely applied to the fields of satellite communication, earth observation, deep space exploration and the like. The high profile precision is required to be kept under the working state, the requirement of the working frequency can be met, however, the profile of the reflector is deformed under the influence of factors such as space heat load, structure relaxation, material creep and the like, the profile precision is reduced, and the profile deformation is required to be measured for adjustment.
At present, the method of taking an average value by single measurement or multiple measurements by using a sensor such as photogrammetry is often adopted to determine the deformation of the profile of the reflector, but the method is limited by the measurement precision of the sensor, the value of the single measurement always has certain deviation, and the method of taking the average value by multiple repeated measurements can improve the measurement precision, but the method is complicated in specific operation, wastes time and labor, and particularly does not have the condition of taking the average value by multiple measurements under the condition of dynamic deformation of the profile of the reflector.
Disclosure of Invention
The invention provides an antenna reflector profile deformation measuring method, aiming at solving the problems of large deviation, complex operation, time and labor consumption of the existing antenna reflector profile deformation measurement.
In order to achieve the purpose, the invention provides the following technical scheme: an antenna reflector profile deformation measuring method comprises the following steps:
s1, arranging a plurality of target points on a molded surface of a reflector, measuring three-dimensional coordinates of the target points, arranging an origin of a coordinate system at the center of the molded surface of the reflector, enabling a Z axis to be parallel to the out-of-plane deformation direction of the reflector, enabling an XY plane to be vertical to the Z axis, and carrying out single measurement on the Z axis direction deformation displacement dz of the target points of the molded surface of the reflector by using a sensor;
s2, dividing the profile of the reflector into a plurality of fitting areas according to the profile characteristics of the reflector and the number of target points required by fitting;
s3, respectively fitting X, Y-axis coordinate information of target points in different fitting areas with polynomial fitting corresponding to Z-axis direction deformation displacement dz of the target points, and solving polynomial coefficients by using a least square method to obtain a fitting function corresponding to each fitting area;
and S4, substituting the X, Y-axis coordinate information of the target points in different areas into the fitting function of the corresponding area, and updating to obtain the Z-axis direction deformation displacement dz of the corresponding target point.
Furthermore, taking the grating reflector as an example, the grating reflector is a regular hexagon, the back is provided with a plurality of grooves for mounting the PZT piezoelectric actuators, and the grooves on the back of the grating reflector influence the continuity of the whole profile of the grating reflector, so the grating reflector is divided into a plurality of small triangular areas according to the distribution of the grooves, and a plurality of adjacent small triangles are integrated into a triangular fitting area, so that the regular hexagon grating reflector has six triangular fitting areas with basically the same shape, each fitting area has an intersected vertex, the fitting areas are distributed in an inverted triangle manner by the vertex, and the number of target points in each fitting area exceeds 10.
Further, taking a grating reflector as an example, the area of the molded surface of the grating reflector is 0.311 square meter, 30 PZT piezoelectric actuators are installed in a U-shaped groove at the back of the reflector, 178 target points with the diameter of 1.6 centimeters are arranged on the front surface of the grating reflector, coordinates of the target points are measured by using DIC, the grating reflector is divided into 24 small triangular areas according to the distribution of grooves, four adjacent small triangles are integrated into 1 fitting area, the regular hexagonal grating reflector is provided with six triangular fitting areas with basically the same shape, each fitting area is provided with an intersected vertex, the fitting areas are distributed in an inverted triangle mode by the vertex, and the number of the target points in each fitting area is 28-32.
Furthermore, the fitting adopts quadratic polynomial fitting, and the Z-axis direction deformation displacement dz of any target point in a certain fitting area is seti＝f(xi,yi) Writing into:
when there are n target points in a certain area, the following n equations:
in the above formula a20、a02、a11、a10、a01、a00For the fitting coefficient to be solved for, (x)i,yi) Is a two-dimensional coordinate of the target point in the XY plane, dziDeformation displacement along the Z-axis direction as a target point, RiFor the residual, select the appropriate fitting coefficient aijSum the squares of the residuals
After the minimum value is reached and a polynomial fitting function is obtained, (x) of n target points is obtainedi,yi) Substituting the coordinates into a fitting function to update the Z-axis direction deformation displacement dz of the corresponding target pointi。
Further, the selection of the proper fitting coefficient aijSum the squares of the residuals
To a minimum by separately solving
And for the partial derivatives of all the fitting coefficients, solving the coefficient to be fitted when all the partial derivatives are 0.
The invention also relates to a grid reflector which is a regular hexagon grid reflector, the projection caliber of the grid reflector is 0.6 meter, the area of the grid reflector is 0.311 square meter, 30 PZT piezoelectric actuators are installed in a U-shaped groove at the back of the reflector, 178 target points with the diameter of 1.6 cm are arranged on the front surface of the grid reflector, coordinates of the target points are measured by DIC, the grid reflector is divided into 24 small triangular areas according to the distribution of the grooves, four adjacent small triangles are integrated into 1 fitting area, so that the regular hexagon grid reflector has six triangular fitting areas with basically the same shape, each fitting area has an intersected vertex, the fitting areas are distributed in an inverted triangle with the vertex, the number of the target points in each fitting area is 30, and the number of the target points with one or two fitting areas is less than 30.
The invention also relates to a method for comparing and measuring the deformation of the molded surface of an antenna reflector, which uses a regular hexagon grating reflector, the projection caliber of which is 0.6 meter, 30 PZT piezoelectric actuators are arranged in a U-shaped groove at the back of the reflector, 178 target points with the diameter of 1.6 cm are arranged on the grating reflector, the coordinates of the target points are measured by adopting a DIC system, the measurement precision of the DIC system is 20um +10um/m, the grating reflector is divided into 24 small triangular areas according to the distribution of grooves, four adjacent small triangles are integrated into 1 fitting area, so that the regular hexagon grating reflector has six triangular fitting areas with basically the same shape, each fitting area has an intersected vertex, the fitting areas are distributed in an inverted triangle by the vertex, the number of the target points in each fitting area is 30, and the number of the target points in one or two fitting areas is less than 30, arranging a plurality of target points on the molded surface of the reflector, measuring the three-dimensional coordinates of the target points, arranging the origin of a coordinate system at the center of the molded surface of the reflector, enabling the Z axis to be parallel to the out-of-plane deformation direction of the reflector, and enabling the XY plane to be vertical to the Z axis;
repeatedly measuring by a DIC system for 50 times in an initial state, recording target point data, locating an origin o of a coordinate system at the center of the reflector, enabling a Z axis to be vertical to the plane of the reflector along the out-of-plane deformation direction of the reflector, and numbering the PZT piezoelectric actuators;
randomly extracting 2 target points from 178 target points, repeatedly measuring the Z-axis coordinate for 50 times in the initial state, and observing the difference value between the Z-axis coordinate obtained by 49 times of measurement and the Z-axis coordinate obtained by the first time of measurement; taking the average value of Z-axis coordinates of 50 times of measurements as a measurement value in the current state;
two working conditions are set, and the working conditions are set,
working condition 1: selecting two actuators to apply 150V voltage respectively, and repeating the current state measurement for 50 times to obtain an average value;
working condition 2: selecting four actuators to apply 150V voltage respectively, and repeating the current state measurement for 50 times to obtain an average value;
subtracting the average value of the Z-axis coordinate measured for 50 times in the initial state to obtain profile standard deformation data under two working conditions in the current state, and drawing a cloud picture;
randomly selecting a certain Z-axis coordinate measurement value from the working conditions 1 and 2 to subtract the first Z-axis coordinate measurement value in the initial state to obtain profile deformation data of the grating reflector measured at one time, and drawing a cloud picture;
comparing the standard phenotype cloud pictures of the reflector profiles under the working conditions 1 and 2 with the single-measurement reflector profile deformation cloud pictures, and recording the difference between the single-measurement reflector profile deformation and the mean value of the multiple measurements of the reflector profile deformation;
dividing the profile of the reflector into a plurality of fitting areas according to the profile characteristics of the reflector and the number of target points required by fitting, fitting X, Y-axis coordinate information of the target points in different fitting areas to the Z-axis direction deformation displacement dz of the corresponding target point by adopting a polynomial, and solving a polynomial coefficient by using a least square method to obtain a fitting function corresponding to each fitting area;
respectively adopting quadratic polynomial to perform surface fitting on the target point coordinates in each region through the data measured in single working condition 1 and working condition 2, and setting the Z-axis direction deformation displacement dz of any target point in a certain fitting regioni＝f(xi,yi) Writing into:
when there are n target points in a certain area, the following n equations:
in the above formula a20、a02、a11、a10、a01、a00For the fitting coefficient to be solved for, (x)i,yi) Is a two-dimensional coordinate of the target point in the XY plane, dziDeformation displacement along the Z-axis direction as a target point, RiFor the residual, select the appropriate fitting coefficient aijSum the squares of the residuals
After the minimum value is reached and a polynomial fitting function is obtained, (x) of n target points is obtainedi,yi) Substituting the coordinates into a fitting function to update the Z-axis direction deformation displacement dz of the corresponding target pointi；
Drawing an error value of the Z-axis direction deformation displacement of the corresponding target points before and after fitting and the Z-axis direction deformation displacement which is obtained by means of multiple times of measurement and averaging;
calculating the average error under the condition of averaging the Z-axis direction deformation displacement of all target points measured in a single time and the Z-axis direction deformation displacement measured in multiple times in the working condition 1, and the average error under the condition of averaging the Z-axis direction deformation displacement of all target points subjected to single-time measurement fitting and the Z-axis direction deformation displacement measured in multiple times;
calculating the average error under the condition of averaging the Z-axis direction deformation displacement of all target points measured in a single time and the Z-axis direction deformation displacement measured in multiple times in the working condition 2, and the average error under the condition of averaging the Z-axis direction deformation displacement of all target points subjected to single-time measurement fitting and the Z-axis direction deformation displacement measured in multiple times;
drawing a reflector profile deformation cloud picture by the fitted data;
the fitted reflector profile deformation cloud picture is measured once under the working conditions 1 and 2, and is closer to a standard deformation cloud picture which is obtained by measuring and averaging the working conditions 1 and 2 for multiple times compared with the reflector profile deformation cloud picture measured once;
subtracting the standard deformation cloud picture which is obtained by taking the average value of multiple measurements from the single-measurement reflector profile deformation cloud pictures and the single-measurement fitted reflector profile deformation cloud pictures under the working conditions 1 and 2 respectively to obtain profile deformation error cloud pictures; and comparing the single-measurement reflector profile error of the working condition 1 and the working condition 2 with the single-measurement reflector profile error after fitting.
Has the advantages that: according to the invention, firstly, according to the profile characteristics of the reflector and the requirement of polynomial fitting on the number of target points, the profile is divided into areas with proper size, then the coordinate information of the target points in different areas is fitted with the deformation displacement of the corresponding target points by adopting the polynomial fitting to obtain corresponding fitting functions, then the coordinates of the target points in different areas are substituted into the corresponding fitting functions to update the deformation displacement of the corresponding target points, the deviation of single measurement of the sensor can be effectively reduced by a data processing mode, the overall deformation measurement precision of the profile of the reflector is improved, namely, the overall deformation measurement precision of the profile of the reflector is improved by utilizing the spatial continuity characteristics of deformation, and the method is simple to operate, time-saving and labor-saving. The invention also relates to a method for measuring the profile precision of the reflector in the dynamic deformation process, which solves the problems of complex operation, time and labor waste and low single measurement precision caused by repeated measurement, and is also suitable for the profile precision measurement in the dynamic deformation process of the reflector. The invention can also be popularized and applied to the profile measurement of the surface deformation of a general structure.
Drawings
FIG. 1 is a schematic view of the back of a grille reflector
FIG. 2 Grating Reflector Profile area partition
FIG. 3 is a schematic view of a coordinate system
FIG. 4 PZT piezoelectric actuator distribution diagram
FIG. 5 is a graph of the difference between random point 1 and multiple measurements
FIG. 6 is a graph of the difference between random point 2 and multiple measurements
FIG. 7 Standard deformation diagram of Reflector Profile under working Condition 1
FIG. 8 Standard deformation diagram of Reflector surface under working Condition 2
FIG. 9 working condition 1 single measurement reflector profile deformation diagram
FIG. 10 working condition 2 single measurement reflector profile deformation diagram
FIG. 11 error plot of mean values of the first 89 targets before and after fitting and multiple measurements under condition 1
FIG. 12 error plot of mean values of 89 target points before and after fitting under condition 1 and multiple measurements
FIG. 13 error plot of mean values of the first 89 targets before and after fitting and multiple measurements under condition 2
FIG. 14 error plot of mean values of 89 target points before and after fitting and multiple measurements after operating condition 2
FIG. 15 working condition 1 single measurement fitted reflector profile deformation diagram
FIG. 16 working condition 2 single measurement fitted reflector profile deformation diagram
FIG. 17 Condition 1 Single measurement Reflector Profile error map
FIG. 18 Condition 1 Reflector Profile error map after single measurement fitting
FIG. 19 operating mode 2 Single measurement Reflector Profile error
Figure 20 condition 2 reflector profile error after single measurement fit.
Detailed Description
Example 1: the embodiment describes a grating reflector-based profile deformation measurement method, which can improve the overall deformation measurement accuracy for spatial continuity characteristics, and comprises the following steps:
s1: a plurality of target points are arranged on the molded surface of the reflector, the density of the target points in a unit area is improved as much as possible, the three-dimensional coordinates of the target points are measured by using a sensor, the origin of a coordinate system is arranged at the center of the molded surface of the structure, the Z axis is parallel to the large deformation direction of the molded surface, the large deformation direction has uniqueness, the XY plane is perpendicular to the Z axis, and the small deformation occurring in the XY plane has weak influence on the performance of the grid reflector, so the embodiment is not considered.
S2: according to the profile characteristics of the structure and the requirement of polynomial fitting on the number of target points, the profile is divided into six triangular fitting areas. The grating reflector is regular hexagon, the area is 0.311 square meter, it has 178 target points to paste in the front, the back sets up 30 recess installation PZT piezoelectric actuator, because grating reflector back recess has influenced the continuity of its whole profile, so divide the grating reflector into 24 little triangle-shaped regions according to the distribution of recess, nevertheless consider that little triangle-shaped region interior target point quantity is less than 10 and is difficult to satisfy the data demand of polynomial fitting, so integrate four little triangles into 1 fitting region, every fitting region interior target point quantity is about 30 left and right sides, specifically as shown in fig. 1, 2.
S3: and respectively fitting X, Y-axis coordinate information of target points in different areas with polynomial to correspond to the Z-axis direction deformation displacement dz of the target points, and solving polynomial coefficients based on a least square method to obtain a fitting function corresponding to each area.
S4: and substituting the X, Y axis coordinates of the target points in different areas in the S2 into the corresponding fitting functions, and updating the Z-axis direction deformation displacement dz of the target points.
Further, firstly, a sensor is used for carrying out single measurement on a target point on the profile of the reflector, then the profile is divided into small enough areas according to the profile characteristics and the requirement of polynomial fitting on the number of the target points, and X, Y-axis coordinate information of the target points in different areas is fitted to correspond to the Z-axis direction deformation displacement dz of the target points by the polynomial fitting.
Taking quadratic polynomial fitting as an example, the Z-axis direction deformation displacement dz of any target point in a certain area is seti＝f(xi,yi) Can be written as:
when there are n target points in a region, the following n equations can be used:
in the above formula a20、a02、a11、a10、a01、a00For the fitting coefficient to be solved for, (x)i,yi) Is a two-dimensional coordinate of the target point in the XY plane, dziDeformation displacement along the Z-axis direction as a target point, RiFor the residual, select the appropriate fitting coefficient aijSum the squares of the residuals
To a minimum by separately solving
And for the partial derivatives of all the fitting coefficients, solving the coefficient to be fitted when all the partial derivatives are 0. After obtaining the polynomial fitting function, (x) of n target pointsi,yi) Substituting the coordinates into a fitting function to update the Z-axis direction deformation displacement dz of the corresponding target pointi。
The measuring method of the embodiment has the following effects: (1) in the prior art, when a sensor is used for repeatedly measuring a target point on a molded surface of a reflector for multiple times in the same state, a measured value of the same target point fluctuates in a range near a certain value, the value is an average value of the repeated measurement for multiple times, and the specific deviation condition depends on the measurement precision of the sensor. The method for taking the average value by repeated measurement is undoubtedly the most accurate, but the specific operation is complicated, time and labor are wasted, and the repeated measurement of the structure in the same state cannot be carried out under the condition that the structural profile is deformed. According to the embodiment, data which are measured in a single time in advance are processed, the target points on the molded surface are subjected to region division, and the target point data in each region are subjected to polynomial fitting to update new data, so that the deviation of the single measurement can be effectively reduced, and the measurement precision of the integral deformation of the molded surface of the reflector is improved. The problems that the operation is complicated and time and labor are wasted due to repeated measurement for many times under the condition that the reflector is static, and the problem that the single measurement has certain deviation due to the limitation of the measurement precision of the sensor are thoroughly solved. (2) The method is particularly suitable for the problem of profile accuracy measurement in the dynamic deformation process of the reflector, under the condition, the average value of repeated degree measurement cannot be obtained for many times, and only single measurement is carried out.
Example 2: in the embodiment, a method for averaging single measurement and multiple measurements of the sensor is used as a comparative example, and compared with the measurement method disclosed by the invention, experimental results show that the method disclosed by the invention can effectively reduce the deviation of the single measurement of the sensor and improve the measurement precision of the integral deformation of the profile of the reflector, namely the measurement precision of the integral deformation of the reflector is improved by utilizing the space continuity characteristic, and the method is simple to operate, time-saving and labor-saving.
Taking a regular hexagon grid reflector as an example, the projection caliber of the regular hexagon grid reflector is 0.6 m, 30 PZT piezoelectric actuators are arranged in a U-shaped groove at the back of the reflector, and 178 target points with the diameter of 1.6 cm are arranged on the grid reflector. DIC (three-dimensional optical speckle system) is adopted to measure the coordinates of the target point, and the measurement precision of the system is 20um +10 um/m. According to the method, as shown in figure 1, a grid reflector is divided into 24 small triangular areas according to the distribution of grooves, as shown in figure 2, four adjacent small triangles are integrated into 1 fitting area, so that the regular hexagonal grid reflector is provided with six triangular fitting areas with basically the same shape, each fitting area is provided with an intersected vertex, the fitting areas are distributed in an inverted triangle mode through the vertexes, the number of target points in each fitting area is 30, and one fitting area is selected and allocated with 28 target points.
Arranging a plurality of target points on the molded surface of the reflector, measuring the three-dimensional coordinates of the target points, repeatedly measuring 50 times by a DIC system in an initial state, recording data of the target points, establishing a coordinate system as shown in the following figure 3, wherein the origin o of the coordinate system is positioned at the center of the reflector, the Z axis is perpendicular to the plane of the reflector along the out-of-plane deformation direction of the reflector, and simultaneously giving the number distribution of the PZT piezoelectric actuators, as shown in figure 4.
When 2 target points are randomly extracted from 178 target points and the measurement is repeated 50 times in the initial state, the difference value of the Z-axis coordinate obtained by the latter 49 times of measurement and the first time of measurement is shown in the following graph.
It can be seen from fig. 5 and 6 that the measurement accuracy of the sensor is limited, and the repeated measurement values in the same state have a certain deviation, and it is the best choice to take the average value of 50 measurements as the measurement value in the current state.
Two working conditions are set, namely working condition 1: respectively applying 150V voltage to the A2 and B2 actuators, and repeating the current state for 50 times to obtain an average value; working condition 2: 150 voltages are applied to the A2, B2, A9, and B9 actuators, respectively, and the current state is averaged 50 times. And subtracting the average value measured for many times in the initial state to obtain the profile standard deformation data in the current state under two working conditions, as shown in fig. 7 and 8.
And randomly selecting a certain measured value from the working conditions 1 and 2 to subtract the first measured value in the initial state to obtain profile deformation data of a single measurement of the grating reflector, as shown in fig. 9 and 10.
By comparing the standard phenotype cloud pictures of the reflector profiles under the working conditions 1 and 2 with the single-measurement reflector profile deformation cloud pictures, the large difference between the single-measurement reflector profile deformation and the multiple-measurement averaging reflector profile deformation can be obviously seen.
Dividing the target points on the profile of the reflector into six areas according to the profile characteristics of the reflector, wherein the average number of the target points in each area is about 30. And based on the data of single measurement under the working conditions 1 and 2, respectively adopting quadratic polynomials to perform surface fitting on the target point coordinates in each block of area. Setting the Z-axis direction deformation displacement dz of any target point in a certain areai＝f(xi,yi) Can be written as:
when there are n target points in a region, the following n equations can be used:
scale RiFor the residual, select the appropriate fitting coefficient aijSum the squares of the residuals
A minimum value is reached. After obtaining the polynomial fitting function, (x) of n target pointsi,yi) Substituting the coordinates into a fitting function to update the Z-axis direction deformation displacement dz of the corresponding target pointi。
Fig. 11 and 12 show error values between the Z-axis deformation displacement of the corresponding target point before and after the fitting under condition 1 and the Z-axis deformation displacement averaged by multiple measurements.
TABLE 1 working conditions 1 target spot fitting front and back deformation error
Under the condition that the deformation displacement of all target points in the Z-axis direction of single measurement in the working condition 1 is averaged with multiple measurements, the average error is 11.762 micrometers, and the deformation displacement of all target points in the Z-axis direction of single measurement after fitting is averaged with multiple measurements, the average error is 7.112 micrometers.
TABLE 2 working conditions 2 target spot deformation error before and after fitting
Fig. 13 and 14 show error values of the Z-axis direction deformation displacement of the corresponding target point before and after the fitting of the working condition 1 and the Z-axis direction deformation displacement averaged by the multiple measurements.
In condition 2, the average error of all the Z-axis values of the target points measured in a single time and the average error of the Z-axis values of the target points measured in multiple times is 11.426 micrometers, and the average error of all the Z-axis values of the target points measured in a single time and the average error of the Z-axis values of the target points measured in multiple times is 6.861 micrometers.
The fitted data were plotted as deformed clouds, as shown in fig. 15, 16.
According to the reflector profile deformation cloud picture after the working condition 1 and the working condition 2 are subjected to single measurement fitting, it can be seen that compared with the reflector profile deformation cloud picture after single measurement, the standard deformation cloud picture is closer to the standard deformation cloud picture of the mean value of the working condition 1 and the working condition 2 which are subjected to multiple measurement. The profile deformation cloud charts of the reflectors under the working conditions 1 and 2 measured once and the fitted profile deformation cloud charts of the reflectors measured once are subtracted from the standard deformation cloud charts which are obtained by means of multiple measurements to obtain profile deformation error cloud charts respectively, and the profile deformation error cloud charts are compared with the standard deformation cloud charts, as shown in fig. 17-20. By comparing the errors of the reflector profiles measured in a single time and the errors of the reflector profiles subjected to fitting in a single time under the working conditions 1 and 2, the method provided by the invention can be obviously used for effectively reducing the deviation caused by the single measurement and effectively improving the measurement precision of the integral deformation of the structure.
The above description is only for the purpose of creating a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can substitute or change the technical solution and the inventive concept of the present invention within the technical scope of the present invention.
Claims (5)
1. A method for measuring the profile deformation of an antenna reflector is characterized by comprising the following steps:
s1, arranging a plurality of target points on a molded surface of a reflector, measuring three-dimensional coordinates of the target points, arranging an origin of a coordinate system at the center of the molded surface of the reflector, enabling a Z axis to be parallel to the out-of-plane deformation direction of the reflector, enabling an XY plane to be vertical to the Z axis, and carrying out single measurement on the Z axis direction deformation displacement dz of the target points of the molded surface of the reflector by using a sensor;
s2, dividing the profile of the reflector into a plurality of fitting areas according to the profile characteristics of the reflector and the number of target points required by fitting;
s3, respectively fitting X, Y-axis coordinate information of target points in different fitting areas with polynomial fitting corresponding to Z-axis direction deformation displacement dz of the target points, and solving polynomial coefficients by using a least square method to obtain a fitting function corresponding to each fitting area;
and S4, substituting the X, Y-axis coordinate information of the target points in different areas into the fitting function of the corresponding area, and updating to obtain the Z-axis direction deformation displacement dz of the corresponding target point.
2. The method for measuring the deformation of the profile of the antenna reflector according to claim 1, wherein the grating reflector is a regular hexagon, the back of the grating reflector is provided with a plurality of grooves for mounting the PZT piezoelectric actuators, the grooves on the back of the grating reflector influence the continuity of the overall profile of the grating reflector, so that the grating reflector is divided into a plurality of small triangular areas according to the distribution of the grooves, and adjacent small triangles are integrated into a triangular fitting area, so that the regular hexagon grating reflector has six triangular fitting areas with basically the same shape, each fitting area has an intersecting vertex, the fitting areas are distributed in an inverted triangle form by the vertex, and the number of target points in each fitting area exceeds 10.
3. The method for measuring the deformation of the profile of the antenna reflector according to claim 2, wherein the area of the profile of the grating reflector is 0.311 square meter, 30 PZT piezoelectric actuators are installed in a U-shaped groove at the back of the reflector, 178 target points with the diameter of 1.6 cm are arranged on the front surface of the grating reflector, coordinates of the target points are measured by using DIC, the grating reflector is divided into 24 small triangular areas according to the distribution of grooves, four adjacent small triangles are integrated into 1 fitting area, so that the regular hexagonal grating reflector has six triangular fitting areas with basically the same shape, each fitting area has an intersecting vertex, the fitting areas are distributed in an inverted triangle with the vertex, and the number of the target points in each fitting area is 28-32.
4. The method of claim 1, wherein the fitting is a quadratic polynomial fitting, and the Z-axis deformation displacement dz of any target point in a fitting region is determinedi＝f(xi,yi) Writing into:
when there are n target points in a certain area, the following n equations:
in the above formula a20、a02、a11、a10、a01、a00For the fitting coefficient to be solved for, (x)i,yi) Is a two-dimensional coordinate of the target point in the XY plane, dziDeformation displacement along the Z-axis direction as a target point, RiFor the residual, select the appropriate fitting coefficient aijSum the squares of the residuals
After the minimum value is reached and a polynomial fitting function is obtained, (x) of n target points is obtainedi,yi) Substituting the coordinates into a fitting function to update the Z-axis direction deformation displacement dz of the corresponding target pointi。
5. The method of claim 4, wherein the selecting of the appropriate fitting coefficient a is performed by a method of measuring the profile deformation of the antenna reflectorijSum the squares of the residuals
To a minimum by separately solving
And for the partial derivatives of all the fitting coefficients, solving the coefficient to be fitted when all the partial derivatives are 0.
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