A method for predicting wind force coefficient of a reflector antenna based on a proxy model

Abstract

This invention discloses a method for predicting the wind force coefficient of a reflector antenna based on a surrogate model. The method includes: acquiring the structural parameters of the reflector antenna and establishing a simulation model; determining the sampling points for the reflector's azimuth and elevation variables and performing numerical simulation calculations; extracting the drag, lateral force, and lift values ​​of the reflector at different sampling points; calculating the reflector wind force coefficient and storing it in a sample point database; constructing a surrogate model with regularized minimum energy tensor product splines and checking the fitting accuracy; generating the predicted reflector wind force coefficient for new sample points; calculating the error between the predicted and simulated values ​​of the reflector wind force coefficient at the new sample points; if the accuracy requirement is not met, adding the simulated value to the sample point database and reconstructing the surrogate model until the accuracy requirement is met. This invention saves time in simulating and calculating the reflector wind force coefficient under different poses while ensuring accuracy.

Description

Technical Field

[0001] This invention belongs to the field of antenna technology, specifically relating to a method for predicting the wind force coefficient of a reflector antenna based on a surrogate model. Background Technology

[0002] Reflector antennas are widely used in detection, communication, and radio astronomy due to their advantages of high gain and long detection and communication distances. In radio astronomy, to detect nano-Hertz gravitational waves generated by galactic-scale supermassive binary black hole systems, reflector antennas require extremely high sensitivity and stability, necessitating large-aperture and robust antenna structures. However, large-aperture antennas operating outdoors (hundreds of meters in diameter) are inevitably affected by time-varying wind loads, leading to reduced pointing accuracy, efficiency, and gain, thus significantly impacting the reflector antenna's sensitivity and stable observation duration. Therefore, conducting wind load characteristic analysis of reflectors under different azimuths and elevations to provide more technical data on the wind force coefficients of the reflectors in different orientations is of significant engineering application value for antenna structure design and wind resistance research.

[0003] Currently, the main methods for obtaining the wind force coefficient of a reflector surface are wind tunnel experiments and numerical simulation. For wind tunnel experiments, because the thickness of the reflector surface is several orders of magnitude smaller than its aperture size, the reflector surface in the experimental model is relatively thin, making the placement and routing of pressure gauges inconvenient. This inevitably leads to an increase in the model thickness, resulting in size effects and errors. Furthermore, wind tunnel experiments are extremely expensive and are generally only used to verify the results of numerical simulations. Thanks to advancements in computer technology, numerical simulation offers numerous advantages, including low cost, repeatability, ease of control, comprehensive result acquisition, and the provision of visualized flow field information.

[0004] Due to the blunt body structure of the reflector antenna, the flow field changes of the reflector under different azimuth and elevation angles are extremely complex. It is necessary to consider phenomena such as impact, separation, backflow, circulation and eddies. Even though the CFD (Computational Fluid Dynamics) numerical simulation method can obtain the wind force of the reflector at a low cost, obtaining the wind force coefficient will be extremely time-consuming when facing the reflector attitude under various combinations of azimuth angles of 0-180° and elevation angles of 0-90°, which is difficult to meet engineering requirements. Summary of the Invention

[0005] To address the aforementioned problems in the existing technology, this invention provides a method for predicting the wind force coefficient of a reflector antenna based on a surrogate model.

[0006] The technical problem to be solved by this invention is achieved through the following technical solution:

[0007] A method for predicting the wind force coefficient of a reflector antenna based on a surrogate model, the prediction method comprising:

[0008] Step 1: Obtain the structural parameters of the radio telescope's reflecting surface;

[0009] Step 2: Under different reflector pose conditions, establish CFD models of the reflector corresponding to different sampling points based on the structural parameters of the reflector.

[0010] Step 3: Process the CFD model of the reflecting surface using the SSTk-ω turbulence model to obtain the simulation results of the CFD model of different reflecting surfaces, where the inlet is velocity and the outlet is zero pressure.

[0011] Step 4: Extract the drag, lateral force, and lift of the reflecting surface from the simulation results of the CFD models of the different reflecting surfaces;

[0012] Step 5: Obtain the wind force coefficient of the reflector based on the drag, lateral force, and lift of the reflector, and store the wind force coefficient of the reflector in a sample point database. The sample point database includes several sample points, each of which represents a pose state. The wind force coefficient includes the drag coefficient, lateral force coefficient, lift coefficient, and resultant force coefficient obtained based on the drag coefficient, lateral force coefficient, and lift coefficient.

[0013] Step 6: Construct a regularized minimum energy tensor product spline surrogate model based on the sample point database and test the fitting accuracy of the minimum energy tensor product spline surrogate model, wherein the fitting accuracy is characterized by the correction coefficient of determination.

[0014] Step 7: Randomly generate new sample points and use the regularized minimum energy tensor product spline surrogate model to predict the wind force coefficient of the reflecting surface of the new sample point;

[0015] Step 8: Perform numerical simulation on the new sample points generated in Step 7 and extract the wind force coefficient of the reflective surface of the new sample points;

[0016] Step 9: Calculate the error between the wind force coefficient of the reflector surface of the new sample point predicted by the regularized minimum energy tensor product spline surrogate model described in Step 7 and the wind force coefficient of the reflector surface of the new sample point obtained through numerical simulation in Step 8. If the error meets the preset accuracy requirements, the wind force coefficient of the reflector surface is predicted using the regularized minimum energy tensor product spline surrogate model, and the predicted wind force coefficient is obtained. If the error does not meet the preset accuracy requirements, the wind force coefficient of the reflector surface obtained from the numerical simulation of the new sample point is added to the sample point database, the regularized minimum energy tensor product spline surrogate model is reconstructed, and steps 6 to 9 are repeated until the error between the model prediction value and the numerical simulation value of the wind force coefficient of the reflector surface meets the preset accuracy requirements.

[0017] Optionally, the structural parameters include the aperture and focal diameter ratio of the reflecting surface, wherein the focal diameter ratio is the ratio of the focal length to the aperture of the reflecting surface.

[0018] Optionally, the pose of the reflector is determined by two variables: azimuth and pitch.

[0019] Optionally, the CFD model of the reflecting surface is:

[0020] x=Δ×u×u

[0021] y=Δ×usinv

[0022] z = Δ × ucosv

[0023] Where (x, y, z) are the coordinates of each sampling point on the reflective surface in the 3D modeling, x = h, y = h. 2 +z 2 =(D / 2) 2 The range of u is The range of v is (0, 2π), and Δ is the scaling factor. h is the depth of the reflecting surface, D is the aperture of the reflecting surface, and f is the focal length of the reflecting surface.

[0024] Optionally, the drag coefficient is:

[0025]

[0026] The lateral force coefficient is:

[0027]

[0028] The lift coefficient is:

[0029]

[0030] The resultant force coefficient is:

[0031]

[0032] Among them, CF D F is the drag coefficient. D For the drag of the reflecting surface, CF S F is the lateral force coefficient. S For the lateral force of the reflecting surface, CF L F is the lift coefficient. L For the lift of the reflecting surface, CF T The resultant force coefficient is ρ, where ρ is the air density and u is the resultant force coefficient. ref Let A be the velocity at the inlet and A be the characteristic area of ​​the reflecting surface.

[0033] Optionally, the regularized minimum-energy tensor-product spline surrogate model is:

[0034] y=F(x)w

[0035] Where x is the prediction input vector, y is the prediction output vector, w is the spline coefficient vector, and F(x) maps the spline coefficient vector to the prediction output vector.

[0036] Optionally, the spline coefficient vector is solved by an energy minimum optimization problem, which is:

[0037]

[0038] in, Let i be the input vector for the i-th sample point. Let H be the output vector of the i-th sample point, and let H be the second derivative matrix. To map the spline coefficients to the output vector of the i-th sample point, β is the vector norm of the degrees of freedom, α is the norm of the Lagrange multiplier, T is the transpose, and n t This represents the number of sample points.

[0039] Optionally, the correction determination coefficient is:

[0040]

[0041]

[0042] Among them, R 2 _adjusted is the adjusted coefficient of determination, R0 2 n is the coefficient of determination. t The number of sample points. Let i be the numerical simulation value of the i-th sample point. Let p be the model prediction value for the i-th sample point, and p be the number of model features.

[0043] Optionally, the error is:

[0044]

[0045] in, The numerical simulation value is for the wind force coefficient of the reflective surface at the new sample point. The model prediction value for the wind force coefficient of the reflective surface of the new sample point.

[0046] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0047] The wind force coefficient prediction method for reflector antennas of the present invention saves time in simulating and calculating the wind force coefficient of the reflector under different orientations while ensuring accuracy. Furthermore, this invention can be combined with wind prediction to provide timely feedback of wind force information to the reflector antenna control system, avoiding the performance degradation caused by the time-varying nature of wind speed and the time lag of the antenna control system, thus greatly ensuring the performance of the reflector antenna in complex wind environments.

[0048] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0049] Figure 1 This is a flowchart illustrating a method for predicting the wind force coefficient of a reflector antenna based on a surrogate model, provided in an embodiment of the present invention.

[0050] Figure 2 This is a flowchart illustrating another method for predicting the wind force coefficient of a reflector antenna based on a surrogate model, provided in an embodiment of the present invention.

[0051] Figure 3 This is a schematic diagram of the structural parameters of a reflective surface provided in an embodiment of the present invention;

[0052] Figure 4 This is a schematic diagram illustrating the pitch and azimuth changes of a reflector provided in an embodiment of the present invention;

[0053] Figure 5 This is a comparative schematic diagram of the wind force coefficient calculation values ​​of a reflector surface provided by an embodiment of the present invention;

[0054] Figure 6 This is an embodiment of the present invention that provides a fitting accuracy diagram of constructing a proxy model to predict the wind force coefficient of the reflector surface and simulating the wind force coefficient. Detailed Implementation

[0055] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0056] Example 1

[0057] Please see Figure 1 and Figure 2 , Figure 1 This is a flowchart illustrating a method for predicting the wind force coefficient of a reflector antenna based on a surrogate model, provided in an embodiment of the present invention. Figure 2 This is a flowchart illustrating another method for predicting the wind force coefficient of a reflector antenna based on a surrogate model, provided by an embodiment of the present invention. The embodiment of the present invention provides a method for predicting the wind force coefficient of a reflector antenna based on a surrogate model, which includes:

[0058] Step 1: Obtain the structural parameters of the radio telescope's reflector.

[0059] In this embodiment, the parameters of the reflective surface are as follows: Figure 3 As shown, the structural parameters include the aperture and focal diameter ratio of the reflector. The focal diameter ratio is the ratio of the focal length to the aperture of the reflector, and it is a commonly used parameter in reflector design. The parameters required for modeling are the depth and aperture of the reflector, which involves the conversion between the focal diameter ratio and the depth-to-diameter ratio, as shown in the following formula:

[0060]

[0061] Where h is the depth of the reflecting surface, D is the aperture of the reflecting surface, f is the focal length of the reflecting surface, h / D is the depth-to-diameter ratio, and f / D is the focal length-to-diameter ratio.

[0062] Step 2: Under different reflector pose conditions, establish CFD models of the reflector corresponding to different sampling points based on the structural parameters of the reflector.

[0063] Specifically, the pose of a reflector corresponds to a CFD model of that reflector. Therefore, by using the poses of multiple reflectors, CFD models of multiple reflectors can be established. The pose of a reflector can be determined by two variables: azimuth and pitch. The azimuth of a reflector is 0-180°, and the pitch is 0-90°. Therefore, CFD models of reflectors with different poses can be established based on sampling points of different azimuths and pitches.

[0064] In this embodiment, the CFD model of the reflecting surface is:

[0065] x=Δ×u×u

[0066] y=Δ×usinv

[0067] z = Δ × ucosv

[0068] Where (x, y, z) are the coordinates of each sampling point on the reflective surface in the 3D modeling, x = h, y = h. 2 +z 2 =(D / 2) 2 Solving the above equations simultaneously, we can determine the range of u as follows: The range of v is (0, 2π), and Δ is the scaling factor. This decision establishes a correlation between the CFD model parameters of the reflecting surface and the aperture and focal length ratio.

[0069] Step 3: Use the SSTk-ω turbulence model to process the CFD model of the reflecting surface and obtain the simulation results of the CFD model of different reflecting surfaces. The inlet is the velocity and the outlet is zero pressure.

[0070] Specifically, the SSTk-ω turbulence model is used to simulate the CFD model of the reflecting surface to obtain the simulation results corresponding to the CFD model of each reflecting surface, and the velocity inlet and zero pressure outlet are used as the boundary conditions of the SSTk-ω turbulence model.

[0071] Step 4: Extract the drag, lateral force, and lift of the reflector from the simulation results of CFD models of different reflectors.

[0072] Specifically, the simulation results obtained by simulating the CFD model of the reflector using the SSTk-ω turbulence model include all the data from the CFD model of the reflector. Therefore, the drag, lateral force, and lift of the reflector can be directly extracted from these data.

[0073] Step 5: Obtain the wind force coefficient of the reflector based on the drag, lateral force, and lift of the reflector, and store the wind force coefficient of the reflector in the sample point database. The sample point database includes several sample points, each of which represents a pose state. The wind force coefficient includes the drag coefficient, lateral force coefficient, lift coefficient, and the resultant force coefficient obtained based on the drag coefficient, the lateral force coefficient, and the lift coefficient.

[0074] In this embodiment, the drag coefficient is:

[0075]

[0076] The lateral force coefficient is:

[0077]

[0078] The lift coefficient is:

[0079]

[0080] The resultant force coefficient is:

[0081]

[0082] Among them, CF D F is the drag coefficient. D For the drag of the reflecting surface, CF S F is the lateral force coefficient. S For the lateral force of the reflecting surface, CF L F is the lift coefficient. L For the lift of the reflecting surface, CF T The resultant force coefficient is ρ, where ρ is the air density, ρ = 1.225 kg / m³. 3 u ref Let A be the characteristic area of ​​the reflecting surface and D be the aperture of the reflecting surface, representing the velocity at the entrance of the computational domain.

[0083] Step 6: Construct a regularized minimum energy tensor product spline surrogate model based on the sample point database and test the fitting accuracy of the minimum energy tensor product spline surrogate model. The fitting accuracy is characterized by the correction determination coefficient. The closer the correction determination coefficient is to 1, the higher the fitting accuracy.

[0084] The regularized minimum-energy tensor product spline surrogate model is:

[0085] y=F(x)w

[0086] Where x is the prediction input vector, x is the matrix composed of wind coefficients corresponding to different poses, y is the prediction output vector, i.e. the predicted wind coefficients, w is the spline coefficient vector, and F(x) maps the spline coefficient vector to the prediction output vector.

[0087] The regularized minimum energy tensor product spline surrogate model calculates the spline coefficients w by solving the energy minimization problem under the condition that the spline curve passes through the sample points.

[0088] For convenience, let H denote the discrete matrix of the continuous energy functional. Thus, the energy minimization optimization problem constrained by sample points is:

[0089]

[0090] sty=F(x)w

[0091] Regularization is used to ensure the linear system matrix is ​​invertible. The norm of the degree-of-freedom vector with coefficient β is added to the Lagrange multiplier, and the norm of the Lagrange multiplier with coefficient α is subtracted from it. This is formulated as an unconstrained optimization problem, where the objective function consists of a term with the second derivative of the splines, a term representing the approximation error of the sample points, and another term for regularization. Therefore, the regularized energy minimization optimization problem constrained by sample points can be written as:

[0092]

[0093] in, Let be the input vector for the i-th sample point, i.e., the wind force coefficient for the i-th sample point. Let H be the output vector of the i-th sample point, which is the predicted wind force coefficient of the i-th sample point. H is the second derivative matrix, which also represents the discrete matrix of the energy functional. To map the spline coefficients to the output vector of the i-th sample point, β is the vector norm of the degrees of freedom, α is the norm of the Lagrange multiplier, T is the transpose, and n t This represents the number of sample points.

[0094] In this embodiment, the correction determination coefficient is used to detect the fitting accuracy of the regularized minimum energy tensor product spline surrogate model. The correction determination coefficient can offset the influence of the sample size. The larger the correction determination coefficient, the better the performance of the regularized minimum energy tensor product spline model. The formula is as follows:

[0095]

[0096]

[0097] Among them, R 2 _adjusted is the adjusted coefficient of determination, R0 2 n is the coefficient of determination. t The number of sample points. This represents the numerical simulation value for the i-th sample point, i.e., the simulated value of the wind force coefficient. Let p be the model prediction value for the i-th sample point, i.e., the predicted value of the wind force coefficient, and p be the number of model features.

[0098] Step 7: Randomly generate new sample points and use a regularized minimum energy tensor product spline surrogate model to predict the wind force coefficient of the reflector surface of the new sample points.

[0099] Step 8: Perform numerical simulation on the new sample points generated in Step 7 and extract the wind force coefficient of the reflective surface of the new sample points.

[0100] Specifically, the CFD model of the reflector surface of the new sample point is simulated using the SSTk-ω turbulence model to obtain simulation results, and the wind force coefficient of the reflector surface of the new sample point is extracted from the simulation results.

[0101] Step 9: Calculate the error between the wind force coefficient of the reflector surface predicted by the regularized minimum energy tensor product spline surrogate model in Step 7 and the wind force coefficient of the reflector surface obtained by numerical simulation in Step 8. If the error meets the preset accuracy requirements, the wind force coefficient of the reflector surface is predicted using the regularized minimum energy tensor product spline surrogate model, and the predicted wind force coefficient is obtained. If the error does not meet the preset accuracy requirements, the wind force coefficient of the reflector surface obtained by numerical simulation of the new sample point is added to the sample point database, the regularized minimum energy tensor product spline surrogate model is reconstructed, and steps 6 to 9 are repeated until the error between the model prediction value and the numerical simulation value of the wind force coefficient of the reflector surface meets the preset accuracy requirements.

[0102] In other words, a threshold is first set, which can be set according to different application scenarios. Then, the obtained error is compared with the threshold. If the error is less than the set threshold, it means that the preset accuracy requirement has been met. If the error is greater than the set threshold, the regularized minimum energy tensor product spline surrogate model is adjusted until the preset accuracy requirement is met, and the final regularized minimum energy tensor product spline surrogate model is obtained to predict the wind force coefficient of the reflector surface, thus obtaining the wind force coefficient prediction result.

[0103] In this embodiment, the formula for calculating the error is:

[0104]

[0105] in, The numerical simulation value is for the wind force coefficient of the reflective surface at the new sample point. The model prediction value for the wind force coefficient of the reflective surface of the new sample point.

[0106] This invention provides a method for predicting the wind force coefficient of a reflector antenna based on a regularized minimum energy tensor product spline surrogate model. This method can meet the accuracy requirements of engineering applications and can be combined with wind prediction to provide timely feedback of wind force information to the reflector antenna control system. This avoids the time-delay problem caused by the time-varying nature of wind speed, and greatly ensures the performance of the reflector antenna in complex wind environments.

[0107] The wind force coefficient prediction method for reflector antennas of this invention can quickly and accurately predict the wind force coefficient of reflectors under different azimuth and elevation orientations, overcoming the problems of time-consuming reflector simulation and the inability to timely feed back wind force information to the reflector control system. It can guide the design of reflector antennas and replace CFD simulation, improving the real-time performance of wind force coefficient calculation. It provides information to the control system in a shorter time to compensate for reflector deformation, offsetting the impact of wind disturbance on reflector performance, and providing technical support for ensuring the observation performance of reflector antennas under complex wind loads.

[0108] Example 2

[0109] Based on Embodiment 1, the wind force coefficient prediction method for reflector antennas of the present invention will be described in detail with reference to the accompanying drawings and specific embodiments.

[0110] Please see Figure 2 The wind force coefficient prediction method for reflector antennas based on the surrogate model in this embodiment includes the following steps:

[0111] (1) Obtain structural parameters such as aperture and focal diameter ratio of the radio telescope reflector and establish a CFD model of the reflector based on the structural parameters of the reflector.

[0112] This example is based on the reflector parameters of the QiTai radio telescope (QTT) in Xinjiang. The reflector has an aperture of 110m and a focal diameter ratio of 0.33. The CFD model of the reflector is then obtained using the following formula:

[0113] x=Δ×u×u

[0114] y=Δ×usinv

[0115] z = Δ × ucosv

[0116] In this example, the range of u is (0, 0.3788), the range of v is (0, 2π), and Δ is the scaling factor, which is 145.195.

[0117] (2) Determine the sampling points for the two variables of azimuth and pitch of the reflector and perform numerical simulation calculations.

[0118] In this example, the azimuth angle of the reflecting surface is 0-180°, at every 10° position, and the elevation angle is 0-90°, at every 5° position. A total of 361 cases are modeled, with the azimuth angle rotating counter-clockwise and the elevation angle rotating clockwise, as shown in the attached diagram. Figure 4 As shown. The mesh is generated from an unstructured mesh. The calculation uses a velocity inlet and a zero-pressure outlet, and the simulation results are calculated using the SSTk-ω turbulence model.

[0119] (3) Extract the surface drag, lateral force and lift from the simulation results at different sampling points.

[0120] This example uses CFD simulation results of 361 reflective surfaces to extract drag, lateral force, and lift from the reflective surfaces using CFD-POST post-processing software and saves them into an Excel file.

[0121] (4) Calculate the wind force coefficient of the reflecting surface.

[0122] In this example, Matlab is used to edit the following formulas into code to calculate the various wind force coefficients.

[0123]

[0124]

[0125]

[0126]

[0127] Among them, CF D F is the drag coefficient.D For the drag of the reflective surface; CF S F is the lateral force coefficient. S The lateral force on the reflecting surface; CF L F is the lift coefficient. L For the lift of the reflector surface; CF T This is the resultant force coefficient. ρ is the air density (ρ = 1.225 kg / m³). 3 ), u ref To calculate the domain inlet velocity, we take 12 m / s in this example, where A is the characteristic area of ​​the reflecting surface, calculated using the formula... The calculations are performed, where D is the diameter of the reflector; in this example, it is taken as 110m. The drag coefficient, lateral force coefficient, lift coefficient, and resultant force coefficient of the 361 sets of reflectors calculated based on simulation results are shown in the appendix. Figure 5 .

[0128] (5) Construct a regularized minimum energy tensor product spline surrogate model based on the sample point database and test the fitting accuracy of the surrogate model.

[0129] The surrogate model constructed in this example achieves a fitting accuracy of 0.9887 for the drag coefficient, 0.9929 for the lateral force coefficient, 0.9931 for the lift coefficient, and 0.9844 for the resultant force coefficient. The fitting accuracies are all very close to 1, demonstrating the good performance of the surrogate model. Detailed comparison charts of wind force coefficient simulation and prediction are attached. Figure 6 .

[0130] (6) Randomly generate new sample points and use the surrogate model to predict the wind force coefficient of the reflector surface under this sample point.

[0131] In this example, the drag coefficient, lateral force coefficient, lift coefficient, and resultant force coefficient for the reflector attitude (azimuth and pitch angles of 45°, which did not appear in the sample point database) predicted using the surrogate model are 0.828, 0.980, -1.397, and 1.896.

[0132] (7) Perform numerical simulation on the new sample points generated in (6) and extract and calculate the wind force coefficient of the reflector surface.

[0133] The CFD simulation results for this example are a drag coefficient of 0.848, a lateral force coefficient of 1.007, a lift coefficient of -1.429, and a resultant force coefficient of 1.942.

[0134] (8) Calculate the error of the wind force coefficient of the reflector in the surrogate model prediction and numerical simulation.

[0135] In this example, the errors in predicting the drag coefficient, lateral force coefficient, lift coefficient, and resultant force coefficient of the reflector at azimuth and pitch angles of 45° are 0.02, 0.027, 0.032, and 0.046, respectively. It can be seen that the errors are relatively small, and the predicted values ​​are conservative, allowing for some margin in engineering applications. This makes the reflector's observation performance safer and more reliable in complex wind environments.

[0136] It should be noted that the descriptions of the method / electronic device / storage medium / computer program product embodiments are relatively simple because they are basically similar to the system embodiments. For relevant details, please refer to the descriptions of the system embodiments.

[0137] It should be noted that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, features defined as "first" or "second" may explicitly or implicitly include one or more features. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0138] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0139] Although the invention has been described herein in conjunction with various embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings and the disclosure in carrying out the claimed invention. In this specification, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality. While certain measures are described in different embodiments, this does not mean that these measures cannot be combined to produce good results.

[0140] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for predicting wind force coefficients of a reflector antenna based on a proxy model, the method comprising: The prediction method includes: Step 1: Obtain the structural parameters of the radio telescope's reflecting surface; Step 2: Under different reflector pose conditions, establish CFD models of the reflector corresponding to different sampling points based on the structural parameters of the reflector. Step 3: Process the CFD model of the reflecting surface using the SSTk-ω turbulence model to obtain the simulation results of the CFD model of different reflecting surfaces, where the inlet is velocity and the outlet is zero pressure. Step 4: Extract the drag, lateral force, and lift of the reflecting surface from the simulation results of the CFD models of the different reflecting surfaces; Step 5: Obtain the wind force coefficient of the reflector based on the drag, lateral force, and lift of the reflector, and store the wind force coefficient of the reflector in a sample point database. The sample point database includes several sample points, each of which represents a pose state. The wind force coefficient includes the drag coefficient, lateral force coefficient, lift coefficient, and resultant force coefficient obtained based on the drag coefficient, lateral force coefficient, and lift coefficient. Step 6: Construct a regularized minimum energy tensor product spline surrogate model based on the sample point database and test the fitting accuracy of the minimum energy tensor product spline surrogate model, wherein the fitting accuracy is characterized by the correction coefficient of determination. Step 7: Randomly generate new sample points and use the regularized minimum energy tensor product spline surrogate model to predict the wind force coefficient of the reflecting surface of the new sample point; Step 8: Perform numerical simulation on the new sample points generated in Step 7 and extract the wind force coefficient of the reflective surface of the new sample points; Step 9: Calculate the error between the wind force coefficient of the reflector surface of the new sample point predicted by the regularized minimum energy tensor product spline surrogate model described in Step 7 and the wind force coefficient of the reflector surface of the new sample point obtained through numerical simulation in Step 8. If the error meets the preset accuracy requirements, the wind force coefficient of the reflector surface is predicted using the regularized minimum energy tensor product spline surrogate model, and the predicted wind force coefficient is obtained. If the error does not meet the preset accuracy requirements, the wind force coefficient of the reflector surface obtained from the numerical simulation of the new sample point is added to the sample point database, the regularized minimum energy tensor product spline surrogate model is reconstructed, and steps 6 to 9 are repeated until the error between the model prediction value and the numerical simulation value of the wind force coefficient of the reflector surface meets the preset accuracy requirements.

2. The method for predicting the wind force coefficient of a reflector antenna based on a surrogate model according to claim 1, characterized in that, The structural parameters include the aperture and focal diameter ratio of the reflecting surface, whereby the focal diameter ratio is the ratio of the focal length to the aperture of the reflecting surface.

3. The method for predicting the wind force coefficient of a reflector antenna based on a surrogate model according to claim 1, characterized in that, The orientation of the reflector is determined by two variables: azimuth and pitch.

4. The method for predicting the wind force coefficient of a reflector antenna based on a surrogate model according to claim 2, characterized in that, The CFD model of the reflecting surface is: x=Δ×u×u y=Δ×usinv z = Δ × ucosv Where (x, y, z) are the coordinates of each sampling point on the reflective surface in the 3D modeling, x = h, y = h. 2 +z 2 =(D / 2) 2 The range of u is The range of v is (0, 2π), and Δ is the scaling factor. h is the depth of the reflecting surface, D is the aperture of the reflecting surface, and f is the focal length of the reflecting surface.

5. The method for predicting the wind force coefficient of a reflector antenna based on a surrogate model according to claim 1, characterized in that, The drag coefficient is: The lateral force coefficient is: The lift coefficient is: The resultant force coefficient is: Among them, CF D F is the drag coefficient. D For the drag of the reflecting surface, CF S F is the lateral force coefficient. S For the lateral force of the reflecting surface, CF L F is the lift coefficient. L For the lift of the reflecting surface, CF T The resultant force coefficient is ρ, where ρ is the air density and u is the resultant force coefficient. ref Let A be the velocity at the inlet and A be the characteristic area of ​​the reflecting surface.

6. The method for predicting the wind force coefficient of a reflector antenna based on a surrogate model according to claim 1, characterized in that, The regularized minimum energy tensor product spline surrogate model is as follows: y=F(x)w Where x is the prediction input vector, y is the prediction output vector, w is the spline coefficient vector, and F(x) maps the spline coefficient vector to the prediction output vector.

7. The method for predicting the wind force coefficient of a reflector antenna based on a surrogate model according to claim 6, characterized in that, The spline coefficient vector is solved by an energy-minimum optimization problem, which is: in, Let i be the input vector for the i-th sample point. Let H be the output vector of the i-th sample point, and let H be the second derivative matrix. To map the spline coefficients to the output vector of the i-th sample point, β is the vector norm of the degrees of freedom, α is the norm of the Lagrange multiplier, T is the transpose, and n t This represents the number of sample points.

8. The method for predicting the wind force coefficient of a reflector antenna based on a surrogate model according to claim 6, characterized in that, The correction determination coefficient is: Among them, R 2 _adjusted is the adjusted coefficient of determination, R0 2 n is the coefficient of determination. t The number of sample points. Let i be the numerical simulation value of the i-th sample point. Let p be the model prediction value for the i-th sample point, and p be the number of model features.

9. The method for predicting the wind force coefficient of a reflector antenna based on a surrogate model according to claim 1, characterized in that, The error is: in, The numerical simulation value is for the wind force coefficient of the reflective surface at the new sample point. The model prediction value for the wind force coefficient of the reflective surface of the new sample point.

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