A method for calculating the pointing accuracy of radio telescopes under structural deformation

Abstract

The present invention relates to the field of pointing accuracy of radio telescopes, and discloses a method for calculating the pointing accuracy of radio telescopes under structural deformation. The method calculates the pointing accuracy by the following formula: , wherein, , and are the pointing accuracy in the horizontal state, the sky-pointing state and the reference state, respectively, is the temperature influence coefficient of the pointing accuracy in the VW plane under the effect of temperature, is the temperature influence coefficient of the pointing accuracy in the UW plane under the effect of temperature, and is the temperature change of the i-th component. By applying the technical solution of the present invention, the influence of gravity and temperature on the pointing error can be accurately identified and separated according to the corresponding gravity model and temperature model.

Description

Technical Field

[0001] The invention relates to the technical field of pointing accuracy of radio telescopes, and in particular to a method for calculating the pointing accuracy of a radio telescope under the action of structural deformation. Background Art

[0002] Radio telescopes are basic equipment for observing and studying radio waves from celestial bodies. In order to observe farther, darker, and more subtle celestial structures, it is usually necessary to increase the aperture of the radio telescope. However, as the aperture of the radio telescope increases and the detection frequency increases, the requirements for the pointing accuracy of the radio telescope are becoming more and more stringent. In addition to the effect of gravity, large-aperture radio telescopes are also very susceptible to the influence of the surrounding environment. Deformations caused by wind, sunlight, temperature, etc. can cause a sharp drop in pointing accuracy.

[0003] At present, in order to evaluate the impact of external loads such as gravity and temperature on pointing accuracy, a multi-parameter antenna pointing model is often used. Through the parameter model, the non-orthogonality between the axis systems, encoder errors and other error terms with fixed change rules can be eliminated in theory. However, the pointing error caused by temperature gradient is highly random and cannot be completely eliminated using the parameter model. Summary of the invention

[0004] In view of the above problems, an object of the present invention is to provide a method for calculating the pointing accuracy of a radio telescope, so as to solve the problem in the prior art that the influence of the combined effects of gravity and temperature on the pointing accuracy cannot be eliminated by the antenna pointing model.

[0005] In order to solve the above problems, the present invention provides a method for calculating the pointing accuracy of a radio telescope under the action of structural deformation. The calculation formula is:

[0006] , among which, among which, , and are the pointing accuracy in the horizontal state, the sky-pointing state and the reference state, is the temperature influence coefficient of pointing accuracy in the VW plane under the effect of temperature, is the temperature influence coefficient of pointing accuracy in the UW plane under the effect of temperature, is the temperature change displacement of the ith component.

[0007] In an optional manner, the The formula represents the VW plane pointing accuracy under gravity , the specific calculation steps include:

[0008] Step 1: Obtain the structural deformation in the flat state under the action of gravity only , structural deformation in the sky-pointing state And pre-adjustment angle Lower structure deformation ; According to the structural deformation, the pointing accuracy of the antenna in the horizontal state, the sky-pointing state and the pre-adjusted angle state is calculated respectively , as well as ;

[0009] Step 2: The antenna is in an elastic state when working. According to the principle of antenna structure deformation superposition, calculate any pitch angle Lower structure deformation : , It is the structural deformation after removing the reference state pre-adjustment angle at any pitch angle;

[0010] Step 3: Based on the fact that the pointing accuracy in a single plane is a linear combination of external loads, the pointing accuracy under gravity is obtained. The calculation formula is: .

[0011] In an optional manner, the antenna has any elevation angle. Lower structure deformation The calculation steps include:

[0012] Step (1): The antenna can be vector-decomposed under the action of gravity P, and decomposed into , Two items, , , where y refers to the horizontal state direction, and z refers to the vertical state direction;

[0013] Step (2): When the antenna is in an elastic state under working conditions, the displacement of each point on the reflection surface is described in matrix form as: ,in is the reflection surface node displacement matrix, is the antenna structure stiffness matrix, is the load matrix;

[0014] The displacement of the antenna in the horizontal state is: ;

[0015] The displacement of the antenna in the sky-pointing state is: ;

[0016] Step (3): According to the principle of antenna structure deformation superposition, the structural deformation can be written as: .

[0017] In an optional manner, the antenna has any elevation angle. Lower structure deformation The calculation step also includes: when performing finite element calculation, obtaining the pitch angle Displacement in posture When ,Right now .

[0018] In an optional manner, the displacement of the reflecting surface in step (2) includes displacement of a main reflecting surface and displacement of a sub-reflecting surface.

[0019] In an optional manner, the pointing accuracy under the temperature effect and The calculation steps include:

[0020] Step 1: Control the temperature of a single component to rise by 1°C, and keep the temperature of other components unchanged, and calculate the displacement of the upper node of the main reflector and the corresponding node displacement of the secondary reflector;

[0021] Step 2: Based on the node displacement in step 1, obtain the change in pointing accuracy of the radio telescope in a single plane when a single component rises by 1°C ;

[0022] Step 3: Calculate the change in pointing accuracy in the VW and UW planes of the radio telescope when all rods rise by 1°C, and obtain the temperature change coefficients of pointing accuracy in the two planes respectively. , ;

[0023] Step 4: According to the fact that the pointing accuracy in a single plane is a linear combination of the external loads, the pointing accuracy in the VW plane and the UW plane is obtained. and The formula is: .

[0024] In an optional manner, step 1 controls a single component to increase in temperature by 1° C. and keeps the temperatures of other components unchanged, thereby quantifying the impact of temperature changes of each component on the pointing accuracy.

[0025] The invention has the following advantages: the influence of the displacement of the structural nodes of the radio telescope on the pointing accuracy can be quantified, and the influence of gravity and temperature gradient on the pointing error can be accurately identified and separated; according to the fact that the pointing accuracy in a single plane is a linear combination of external loads, and according to various models affecting the pointing error, the complex load effect can be decomposed into calculable independent factors, the pointing error influence can be corrected in a targeted manner, and data processing and error correction are simplified; the deformation of each point on the reflection surface when the antenna is working is calculated by a vector decomposition method, and the deformation of the antenna structure when it rotates around the pitch axis to any pitch angle can be obtained by vector decomposing and combining the deformations when the antenna is in the sky-pointing state and the antenna is in the horizontal state, thereby avoiding the rotation operation of the antenna structure in each calculation and reducing the calculation workload.

[0026] The above description is only an overview of the technical solution of the present invention. In order to more clearly understand the technical means of the present invention, it can be implemented according to the contents of the specification. In order to make the above and other purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are listed below. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] The accompanying drawings are only used to illustrate the embodiments and are not to be considered as limiting the present invention. In addition, the same reference symbols are used to represent the same components throughout the accompanying drawings. In the accompanying drawings:

[0028] Figure 1 A schematic flow chart of an embodiment of a method for calculating the pointing accuracy of a radio telescope under the action of structural deformation provided by the present invention is shown.

[0029] Figure 2 A schematic diagram of the beam pointing deflection angle caused by the deformation of the main reflecting surface of the radio telescope of the present invention is shown.

[0030] Figure 3 A schematic diagram of the beam pointing deflection angle caused by the lateral movement of the feed source of the radio telescope of the present invention is shown.

[0031] Figure 4 A schematic diagram of the beam pointing deflection angle caused by the lateral movement of the sub-reflecting surface of the radio telescope of the present invention is shown.

[0032] Figure 5 A schematic diagram of the deflection angle of the beam pointing of the radio telescope caused by the rotation of the sub-reflecting surface of the radio telescope of the present invention is shown.

[0033] Figure 6 A schematic plan view of the displacement analysis of the radio telescope of the present invention is shown.

[0034] Figure 7 A schematic diagram showing the deformation of the radio telescope of the present invention at any pitch angle is shown.

[0035] Figure 8 A schematic diagram showing the stress condition of the reflector of the radio telescope of the present invention under its own weight is shown.

[0036] Fig. 9 A schematic diagram showing the pointing accuracy of the radio telescope of the present invention at different pitch attitudes under the action of its own weight is shown.

[0037] Fig.10 A schematic diagram showing the deviation of the deformed parabola from the best matching parabola of the present invention is shown. DETAILED DESCRIPTION

[0038] Exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be limited to the embodiments set forth herein.

[0039] For card antennas, the pointing deviation caused by the deformation of the antenna structure can ultimately reflect the displacement and local deformation of the reflector in absolute coordinates. The pointing error can be attributed to the following aspects: deformation of the main reflector, lateral movement of the feed source, movement and rotation of the sub-reflector. The following is the calculation process of the UW plane pointing accuracy. The calculation process of the VW plane (pitch plane) and the UW plane (perpendicular to the pitch plane) is the same.

[0040] As attached Figure 2 As shown in Figure 2, the deflection angle of the radio telescope beam caused by the deformation of the main reflector for

[0041] (1)

[0042] In the formula, is the beam deviation factor; is the deflection angle of the best matching parabola axis; The distance to move the vertex of the best-fit parabola; is the focal length.

[0043] As attached Figure 3 As shown in the figure, the deflection angle of the radio telescope beam caused by the lateral movement of the feed source is for

[0044] (2)

[0045] In the formula, is the lateral movement distance of the feed phase center; is the magnification factor.

[0046] As attached Figure 4 As shown in the figure, the deflection angle of the radio telescope beam caused by the lateral movement of the sub-reflector for

[0047] (3)

[0048] In the formula, is the focal length of the secondary reflector, is the lateral movement distance of the sub-reflector.

[0049] As attached Figure 5 As shown in the figure, the deflection angle of the radio telescope beam caused by the rotation of the sub-reflector is for

[0050] (4)

[0051] In the formula, is the sub-reflector angle.

[0052] The above formula assumes that all displacements occur in the same plane. Figure 6 As shown, the definition The pointing accuracy in the plane (pitch plane) is and The pointing accuracy in the plane (perpendicular to the pitch plane) is In the analysis of this paper, the pointing accuracy in two planes is calculated separately and the pointing accuracy is synthesized. . After deduction, the synthesis formula is:

[0053] (5)

[0054] From the above, it can be concluded that the influence of the displacement of each point on the reflection surface on the deflection and movement of the best matching parabola is linearly superimposable. The lateral movement distance of the feed source is obtained according to the displacement of the relevant nodes in the back frame structure, and the lateral movement and rotation angle of the sub-reflector are obtained according to the displacement of the relevant nodes of the sub-reflector. If it is proved that the best matching parabola is affected by the displacement of the structural nodes independently and superimposable, it can be considered that the pointing accuracy is affected by the displacement of the structural nodes independently and superimposable.

[0055] The best fitting parabola is affected by the displacement of the structural nodes independently and can be superimposed. The proof is as follows:

[0056] Given the displacement of each node of the main reflector, a set of best-fit paraboloids can be found. The best-fit paraboloid can be represented by six parameters: and ,here is the vertex displacement of the designed parabola, is the rotation angle, It is the focal axis change.

[0057] To design the parabolic coordinate system, is the best fitting parabola coordinate system. In the coordinate system, Represents the displacement of the reflection surface node in this coordinate system. middle, Represents the node displacement of the reflection surface node in this coordinate system. The relationship between the two is:

[0058]

[0059] In the design parabola coordinate system, the best fitting parabola formula is:

[0060]

[0061] The least square method is used to fit the best fitting parabola. The deviation of the deformed parabola from the best fitting parabola is as follows: Fig.10 As shown in the figure, the normal deviation expression of the deformed parabola relative to the best matching parabola is:

[0062]

[0063] make , , , , , , , , , , , :

[0064] ,

[0065] The best matching parabola of the antenna is the The initial coordinates of each point are , which is transformed into When the least squares method is used to fit the best fitting parabola, the basis function can be obtained as:

[0066] , , , , , ;

[0067] The coefficient matrix is:

[0068]

[0069] Undetermined parameter vector:

[0070] Offset vector:

[0071] Then the residual term is:

[0072] According to the definition of the least squares method, we now need to find a set of coefficients , so that the inner product of the residual vector and itself is minimized, that is, .

[0073] Can be seen as a vector is a quadratic continuous function of the independent variable, so there exists a set of parameters , so that To reach the minimum, only :

[0074] Using matrix operations we can get:

[0075]

[0076] It can be seen that Each of the items is based on The result is given, so the coefficient matrix is ​​given It can be considered as a constant matrix under the premise of These dependent variables are only present in the offset vector , and the other parameters in the offset vector can also be considered as known constants. are all first-order terms in the offset vector, then the elements in the undetermined parameter vector can be expressed as Linear combination of variables, or undetermined parameter vector Each term in Linearly related, therefore, each parameter in the unknown parameter vector is affected by the displacement of each point The effects are independent and linearly additive.

[0077] The displacement of the antenna back frame structure nodes is calculated by the finite element method with the help of large-scale general finite element software, such as ANSYS software. Without considering geometric nonlinearity and material nonlinearity, according to Hooke's law, the displacement of each node on the antenna satisfies:

[0078] (6)

[0079] In the formula, ——antenna node displacement matrix; ——antenna stiffness matrix; ——Antenna loading matrix.

[0080] Because the stiffness matrix of the structure is a known quantity, the node displacement is a linear combination of the external loads. It can be concluded that the deformation of the main reflector, the lateral movement of the feed source, the movement and rotation of the sub-reflector are linear combinations of the external loads. Finally, it can be concluded that the pointing accuracy in a single plane is a linear combination of the external loads.

[0081] According to the conclusion that the pointing accuracy in a single plane is a linear combination of external loads, the present invention performs vector decomposition and combination on the pointing accuracy in a single plane to obtain a calculation, thereby simplifying data processing and error correction, while also avoiding the need to rotate the antenna structure each time the calculation is performed, thereby reducing the workload of the calculation.

[0082] A method for calculating the pointing accuracy of a radio telescope under structural deformation, the method comprising:

[0083] S1: Calculate the pointing accuracy under gravity ;

[0084] This step specifically includes:

[0085] Step S11: Obtaining the structural deformation in the flat state under the action of gravity only , structural deformation in the sky-pointing state And pre-adjustment angle Lower structure deformation ; and according to formulas (1)-(4), the pointing accuracy of the radio telescope in the horizontal state, the sky-pointing state and the pre-adjusted angle state is calculated respectively. , as well as .

[0086] Step S121: The antenna can be vector decomposed under the action of gravity P, such as Figure 8 As shown, it is decomposed into , Two items, , , where y refers to the horizontal state direction and z refers to the vertical state direction. Figure 7 Force analysis of the antenna reflector in working posture;

[0087] Calculate the different pitch angles of the antenna under its own weight The accuracy of the reflecting surface (main reflecting surface and sub-reflecting surface) under the condition of antenna needs to take into account the deformation of the antenna reflecting surface under various angles. The complexity of the antenna structure lies in the fact that the calculation of the deformation of the reflecting surface requires the rotation of the antenna's pitch mechanism and azimuth mount. Since the working conditions of the antenna are diverse, the model must be rotated for each calculation, which is a huge workload. However, when the antenna structure is working, the various components of the structure are in an elastic state. Therefore, the vector decomposition method can be used to calculate the deformation of each point on the reflecting surface when the antenna is working. Specifically, the deformation of the antenna structure when it is rotated around the pitch axis to any pitch angle can be obtained by vector decomposing and combining the deformations when the antenna is pointing to the sky and the antenna is pointing horizontally, thereby avoiding the rotation of the antenna structure for each calculation and reducing the workload of the calculation. Figure 7 When the back frame rotates around the pitch axis, vector decomposition is required in space.

[0088] It is usually considered that the antenna is in an elastic state under working conditions, and the displacement of each point on the reflection surface is described in matrix form as: ,in is the reflection surface node displacement matrix, is the antenna structure stiffness matrix, is the load matrix.

[0089] Figure 7 This is the force analysis of the antenna reflector in the working posture. It can be seen that the antenna Under the action, vector decomposition can be performed and decomposed into , Two items, , , where y refers to the horizontal state direction and z refers to the vertical state direction.

[0090] Step S122: The antenna is in an elastic state under working conditions, and the displacement of each point on the reflection surface is described in matrix form as follows: ,in is the reflection surface node displacement matrix, is the antenna structure stiffness matrix, is the load matrix.

[0091] The displacement of the antenna in the horizontal state is: (7)

[0092] The displacement of the antenna in the sky-pointing state is: (8)

[0093] Step S123: The structural deformation satisfies the superposition principle, such as Figure 6 As shown, the structural deformation can be written as: (9)

[0094] At this time, the effect of the pre-adjustment angle on the deformation still needs to be considered. The antenna usually selects a certain pitch angle The installation of the reflector is called the reference state. In the reference state, when no adjustment is made, its displacement is Obviously, for the installed telescope structure, when the pitch angle is rotated to other When the angle is greater than 0.03, the shape of the reflecting surface will form a new deviation from the ideal parabola. Therefore, when performing finite element calculation, the pitch angle is Displacement in posture When ,Right now , It is the structural deformation after removing the reference pre-adjustment angle at any pitch angle.

[0095] Step S13: According to the fact that the pointing accuracy in a single plane is a linear combination of the external loads, the pointing accuracy under gravity is obtained. The calculation formula is: (11).

[0096] In this step, since the radio telescope is a symmetrical structure, Pointing accuracy in plane (vertical pitch plane) The pointing accuracy of the antenna under the action of gravity at any elevation angle can be obtained by combining the pointing direction of the antenna when pointing to the sky and the pointing direction when pointing to the horizon. The pointing accuracy of the radio telescope under any elevation condition without the reference state displacement is .

[0097] S2: Calculate the pointing accuracy under temperature.

[0098] In this step, the pointing accuracy in a single plane is concluded to be a linear combination of external loads, and the impact of temperature changes of each component on the radio telescope is quantified.

[0099] This step specifically includes:

[0100] Step S21: Control the temperature of a single component to rise by 1°C, and keep the temperatures of other components unchanged, and calculate the displacement of the upper surface nodes of the main reflector and the corresponding node displacements of the secondary reflector.

[0101] Step S22: Obtain the change in pointing accuracy of the radio telescope in a single plane when a single component rises by 1°C according to the node displacement in step 1 .

[0102] Step S23: Calculate the change in pointing accuracy in the VW plane and UW plane of the radio telescope when all rods rise by 1°C, and obtain the temperature change coefficients of pointing accuracy in the two planes respectively. , .

[0103] Step S24: According to the fact that the pointing accuracy in a single plane is a linear combination of the external loads, the pointing accuracy in the VW plane and the UW plane is obtained. and The formula is: (12), where is the temperature change of the ith component.

[0104] S3: Calculate the pointing accuracy under the combined effects of temperature and gravity

[0105] (13).

[0106] Fig. 9 The figure shows a schematic diagram of the pointing accuracy of the radio telescope of the present invention at different pitch attitudes under the action of its own weight. When only under the action of gravity, the influence of gravity on the pointing error can be corrected according to the relationship between the pointing accuracy and the pitch angle in this figure. By quantifying the influence of the displacement of the structural nodes of the radio telescope on the pointing accuracy, the corresponding pointing error can be corrected individually and quickly.

[0107] The method for calculating the pointing accuracy of a radio telescope under the combined action of multiple factors provided by the present invention has the following advantages: the influence of the displacement of the structural nodes of the radio telescope on the pointing accuracy can be quantified; the error source separation: through the decoupling mechanism, the influence of gravity and temperature on the pointing error can be accurately identified and separated; the pointing accuracy is quickly calculated: according to each model, the complex load effect can be decomposed into calculable independent factors, simplifying data processing and error correction.

[0108] In the description provided herein, numerous specific details are described. However, it is understood that embodiments of the present invention may be practiced without these specific details. Similarly, in order to streamline the present invention and aid in understanding one or more of the various inventive aspects, in the above description of exemplary embodiments of the present invention, various features of embodiments of the present invention are sometimes grouped together into a single embodiment, figure, or description thereof. Wherein, the claims that follow the specific embodiments are hereby expressly incorporated into the specific embodiments, wherein each claim itself serves as a separate embodiment of the present invention.

[0109] It should be noted that the above embodiments illustrate the present invention rather than limit it, and that those skilled in the art may devise alternative embodiments without departing from the scope of the appended claims. In the claims, any reference symbol between brackets shall not be construed as a limitation on the claims. The word "comprising" does not exclude the presence of elements or steps not listed in the claims. The word "one" or "an" preceding an element does not exclude the presence of a plurality of such elements. The present invention may be implemented by means of hardware comprising a number of different elements and by means of a suitably programmed computer. In a unit claim enumerating a number of devices, several of these devices may be embodied by the same hardware item. The use of the words first, second, and third, etc. does not indicate any order. These words may be interpreted as names. The steps in the above embodiments, unless otherwise specified, should not be understood as limitations on the order of execution.

Claims

1. A method for calculating the pointing accuracy of a radio telescope under structural deformation, characterized in that: Pointing accuracy Calculated by the following formula: ， in, , and are the pointing accuracy in the horizontal state, the sky-pointing state and the reference state, is the temperature influence coefficient of pointing accuracy in the VW plane under the effect of temperature, is the temperature influence coefficient of pointing accuracy in the UW plane under the effect of temperature, is the temperature change of the ith component; Said The formula represents the VW plane pointing accuracy under gravity , the specific calculation steps include: Step 1: Obtain the structural deformation in the flat state under the action of gravity only , structural deformation in the sky-pointing state And pre-adjustment angle Lower structure deformation ; According to the structural deformation, the pointing accuracy of the antenna in the horizontal state, the sky-pointing state and the pre-adjusted angle state is calculated respectively , as well as ; Step 2: The antenna is in an elastic state when in operation. According to the principle of deformation superposition of the antenna structure, calculate any pitch angle Lower structure deformation : , It is the structural deformation after removing the reference state pre-adjustment angle at any pitch angle; Step 3: Based on the fact that the pointing accuracy in a single plane is a linear combination of external loads, the pointing accuracy under gravity is obtained. The calculation formula is: ; Pointing accuracy under the temperature and The calculation steps include: Step 1: Control the temperature of a single component to rise by 1°C, and keep the temperature of other components unchanged, and calculate the displacement of the upper node of the main reflector and the corresponding node displacement of the secondary reflector; Step 2: Based on the node displacement in step 1, obtain the change in pointing accuracy of the radio telescope in a single plane when a single component rises by 1°C ； Step 3: Calculate the change in pointing accuracy in the VW and UW planes of the radio telescope when all rods rise by 1°C, and obtain the temperature change coefficients of pointing accuracy in the two planes respectively. , ; Step 4: According to the fact that the pointing accuracy in a single plane is a linear combination of the external loads, the pointing accuracy in the VW plane and the UW plane is obtained. and The formula is: 。 2. The method according to claim 1, characterized in that: Any elevation angle of the antenna Lower structure deformation The calculation steps include: Step (1): The antenna can be vector-decomposed under the action of gravity P, and decomposed into , Two items, , , where y refers to the horizontal state direction, and z refers to the vertical state direction; Step (2): When the antenna is in an elastic state under working conditions, the displacement of each point on the reflection surface is described in matrix form as follows: ,in is the reflection surface node displacement matrix, is the antenna structure stiffness matrix, is the load matrix; The displacement of the antenna in the horizontal state is: ; The displacement of the antenna in the sky-pointing state is: ; Step (3): According to the principle of antenna structure deformation superposition, the structural deformation can be written as: 。 3. The method according to claim 2, characterized in that Any elevation angle of the antenna Lower structure deformation The calculation step also includes: when performing finite element calculation, obtaining the pitch angle Displacement in posture When ,Right now .

4. The method according to claim 2, characterized in that: The displacement of the reflecting surface in step (2) includes the displacement of the main reflecting surface and the displacement of the sub-reflecting surface.

5. The method according to claim 1, characterized in that Also includes: The step 1 controls only a single component to increase in temperature by 1° C. and keeps the temperatures of other components unchanged, thereby quantifying the effect of the temperature change of each component on the pointing accuracy.

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