Fast control algorithm for the reflector of the five-hundred-meter aperture spherical telescope based on BP neural network

Abstract

The application discloses a FAST reflector control algorithm based on a BP neural network, which comprises two stages of data set division design and training of a BP neural network model (hereinafter referred to as a BP model); wherein training samples for training the BP model are continuously updated along with the development of the calibration parabolic surface work, so as to update the BP model. The control algorithm provided by the application has flexibility and accuracy, and the flexibility comprises: 1) the BP model structure design for the elongation of 2225 actuators improves the training accuracy and convergence speed; 2) the BP model is convenient for updating the BP model at any time by increasing the measured samples. The accuracy comprises: 1) taking the existing FAST reflector control database as the sample, the FAST reflector control requirement is met (the surface type accuracy is slightly improved, within 5 mm, and the prediction time is within 500 ms); 2) the BP model has a deep learning ability, and is convenient for updating at any time by increasing the measured samples, so as to continuously improve the actual control accuracy of the reflector.

Description

Technical Field

[0001] This invention relates to the field of control algorithms for telescope reflectors, and in particular to a FAST reflector control algorithm based on a BP neural network. Background Technology

[0002] The Five-hundred-meter Aperture Spherical radio Telescope (FAST), a major national science and technology infrastructure project, is currently the world's largest single-dish radio telescope with the highest sensitivity. Its active reflector system allows FAST to create parabolic surfaces with a diameter of 300 meters in different regions of its 500-meter diameter dome-shaped reflector. FAST's active reflector uses a cable net as its support structure. Rigid panels are connected to nodes in the flexible cable net structure via connecting mechanisms. The cable net structure consists of 6,670 main cables and pull cables at 2,225 nodes on the main cables. The other end of the pull cables is fixed to the foundation on the ground via actuators. The edges of the cable net structure are fixed to tension plates on a ring beam via 150 main cables. During observations, FAST controls the position of the main cable nodes by moving the pull cables through the actuators, thus shifting the reflector in different regions to create the parabolic surfaces required for current astronomical observations.

[0003] The FAST active reflector is characterized by its large span and high precision. To perform tracking observations, FAST requires the reflector control algorithm to calculate the elongation of 2225 actuators under the current operating conditions within a specified time (within 500ms) and send the calculations to the actuator PLCs in real time for execution. This controls the reflector to continuously form the parabolic surface required for observation at the current moment, thus tracking and observing celestial bodies.

[0004] Currently, the FAST reflector control adopts a cable-net node control scheme based on a mechanical model. This scheme (CN201811382149.5) obtains the actuator elongation data of any parabolic surface by performing real-time interpolation calculations on the reflector control database, enabling real-time tensioning of the parabolic surface. This scheme solves the problem that closed-loop control schemes based on real-time measurements cannot achieve all-weather, real-time feedback for FAST. However, this scheme requires sample data at discrete spatial and temperature points, making it impossible to use more accurate field-measured samples, which limits the potential for further improvement in the accuracy of FAST reflector control. Moreover, while finer meshing might improve the reflector control accuracy, re-meshing requires establishing a new calibration database, which is time-consuming. Furthermore, since simulation-generated sample data cannot match the accuracy of measured samples, the potential for improvement is also limited.

[0005] The information disclosed in this background section is intended only to enhance the understanding of the general background of the invention and should not be construed as an admission or in any way implying that the information constitutes prior art known to those skilled in the art. Summary of the Invention

[0006] The purpose of this invention is to provide a FAST reflective surface control algorithm based on BP neural network to solve the problems in the prior art that cannot make full use of measured data and that it is difficult to further improve the surface accuracy.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] This invention provides a FAST reflector control algorithm based on a BP neural network. The method includes two stages: dataset partitioning and training a BP neural network model (hereinafter referred to as the BP model). Its steps are as follows:

[0009] 1) Correlation analysis was performed on the experimental data, i.e., the reflector control database (see CN201811382149.5), to determine that the input indicators of the BP model are ambient temperature and the spatial position of the vertex of the displacement parabola (azimuth angle, zenith angle, coordinates x, y, z), and the output indicator is the total elongation of the actuator (the elongation of the actuator's reference spherical surface plus the elongation from the reference spherical surface to the theoretical parabola).

[0010] 2) The experimental data were redistributed according to the principle of randomness;

[0011] 3) Preprocess the experimental data, that is, standardize the experimental data using the min-max normalization method;

[0012] 4) Based on the above experimental data, design the dataset partitioning for the training set, validation set, and test set;

[0013] 5) For the above dataset, design the BP model structure (including the network nodes and hyperparameter settings of the BP model), and use the BP algorithm to construct BP models for the total elongation of 2225 actuators respectively;

[0014] 6) For the above 2225 BP models, in the test samples, the predicted values ​​of the BP models are compared with the actual calibration values ​​of the test samples. A root mean square error threshold is set, and BP models with root mean square errors exceeding the threshold are put into iterative training. The BP model with the best training effect is selected to optimize the parameters.

[0015] 7) Extract the weight (threshold) matrices of the above 2225 BP models, write the weight (threshold) matrix corresponding to the hidden layer of each BP model into a large matrix in ascending order of numbering, and further split it into 10 sub-matrices;

[0016] 8) Input the actual ambient temperature and the spatial position information of the vertex of the parabolic surface (azimuth, zenith angle, coordinates x, y, z). Calculate the final actuator elongation using the weights, threshold matrices, and activation functions of each hidden layer in step 7). After inverse normalization, the final actuator elongation is obtained.

[0017] 9) Subtract the old spherical actuator elongation from the final actuator elongation, and add the most recently updated spherical actuator elongation to obtain the final parabolic actuator elongation, which is then sent to the controller for execution.

[0018] 10) As the subsequent calibration work is carried out, some actuator elongation data of artificially calibrated parabolic surfaces will be saved and filled into the training samples of the BP model to update the BP model and improve the prediction accuracy of the BP model.

[0019] As a further technical solution, the correlation analysis method described in step 1) is Pearson correlation analysis, which performs correlation analysis on the elongation of the actuator and the actual ambient temperature, the azimuth angle of the parabolic vertex, the zenith angle, and the coordinates x, y, and z based on experimental data.

[0020] As a further technical solution, the experimental data described in step 2) is redistributed according to the principle of randomness, that is, all experimental data are randomly sorted by columns (each column of data includes the elongation of 2225 actuators corresponding to the calibrated parabola, ambient temperature, azimuth angle of the vertex of the parabola, zenith angle, coordinates x, y, z).

[0021] As a further technical solution, the calculation formula for the min-max normalization method described in step 3) is as follows:

[0022]

[0023] Among them, y max =1, y min =-1, x max Let x be the maximum value of the metric represented by x in the training samples. min Let x be the minimum value of the metric represented by x in the training samples, where x is the metric value before standardization. * These are the standardized indicator values.

[0024] As a further technical solution, the dataset partitioning design in step 4) includes extracting 25% of the total database as test samples and the remaining 75% as training samples. The specific ratio of each dataset partition during the training process is training set: validation set: test set = 70%: 15%: 15%.

[0025] As a further technical solution, the network node configuration in the BP model structure design described in step 5) is one input layer, three hidden layers, and one output layer. The input layer contains 6 neurons, and the three hidden layers contain 12, 6, and 3 neurons respectively. All hidden layers use the hyperbolic tangent function (Tanh function, see Equation 2) as the activation function. The output layer contains 1 neuron and uses the linear transfer function (Purelin function, see Equation 3).

[0026]

[0027] y = x (3)

[0028] Where x represents the input to the neuron in this layer of the neural network, and tanh(x) and y represent the output values ​​of different activation functions that map the input to the output.

[0029] As a further technical solution, in the BP model structure design described in step 5), the hyperparameters are set as follows: learning rate is 0.01, validation checks are 20, maximum number of training iterations is 2000, target accuracy is 1e-7, and the training algorithm is the Levenberg-Marquardt algorithm.

[0030] As a further technical solution, the 2225 BP models mentioned in step 5) have the same structural design, and their formulas are as follows;

[0031] a 4 =f 4 (W 4 f 3 (W 3 f 2 (W 2 f 1 (W 1 p+b 1 )+b 2 )+b 3 )+b 4 (4)

[0032] Where p is the input of the input layer, W 1 W 2 W 3 The connection weights W for hidden layer 1, hidden layer 2, and hidden layer 3 are respectively.4 b represents the connection weights of the output layer. 1 b 2 b 3 These are the connection thresholds for hidden layer 1, hidden layer 2, and hidden layer 3, respectively, b 4 f is the connection threshold of the output layer. 1 ~f 3 Here are the activation functions f for hidden layer 1, hidden layer 2, and hidden layer 3, respectively. 4 Let a be the activation function of the output layer. 4 This is the total elongation of the actuator.

[0033] As a further technical solution, the large matrix mentioned in step 7) can be represented as a weight matrix:

[0034]

[0035] And threshold matrix:

[0036]

[0037] Where m takes values ​​of 1, 2, 3, and 4, corresponding to hidden layer 1, hidden layer 2, hidden layer 3, and output layer, respectively, and n represents the actuator number (in actual engineering, the actuator number is n+1). This represents the weight matrix of the m-th layer of the neural network in the BP model, where the actuator elongation is represented by the number n. This represents the threshold matrix of the m-th layer of the neural network in the BP model, where the actuator elongation is numbered n.

[0038] As a further technical solution, the step 7) of splitting a large matrix into submatrices can be represented as a weight matrix:

[0039]

[0040] And threshold matrix:

[0041]

[0042] in, These represent the 1st to 10th weight submatrices, These represent the 1st to 10th threshold submatrices, respectively.

[0043] As a further technical solution, the most recently updated reference spherical actuator elongation in step 9) is consistent with the reference spherical actuator elongation used in the field.

[0044] Using the above technical solution, the control algorithm provided by this invention has both flexibility and accuracy. Its flexibility includes: 1) The BP model structure design for the elongation of 2225 actuators improves training accuracy and convergence speed, saves training time, and reduces modeling time (approximately 2-3 days). Based on this, the BP model can be easily updated at any time by adding measured samples; 2) The BP model can be easily updated at any time by adding measured samples, without requiring sample points to fall on the vertices (or the midpoints of any edge) of the triangular mesh divided in the discrete domain of the reflector surface. This solves the problem that existing interpolation algorithms can only update the model by first re-dividing the mesh and establishing a new calibration database, which is inflexible and time-consuming. Its accuracy includes: 1) Using the existing FAST reflector surface control database as samples, the trained BP model can accurately predict the elongation of 2225 actuators under arbitrary parabolic surface conditions of FAST, and its accuracy is improved compared to existing interpolation algorithms. In addition, by combining and further dividing the weight and threshold matrices of 2225 BP models, the BP model can simultaneously predict the elongation of 2225 actuators. The average time to generate the elongation of 2225 actuators each time is about 34.3ms, which meets the FAST reflector control requirements (within 500ms); 2) The BP model has deep learning capabilities, which can be easily updated at any time by adding measured samples to continuously improve the actual control accuracy of the reflector. Attached Figure Description

[0045] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0046] Figure 1 A flowchart of the FAST reflector control algorithm based on BP neural network provided in an embodiment of the present invention.

[0047] Figure 2 The diagram shows the actuator neural network structure numbered n, provided for an embodiment of the present invention.

[0048] Figure 3 The simulation results of the BP model training for actuator elongation (numbered 1383) provided in this embodiment of the invention are shown in the figure.

[0049] Figure 4 The goodness-of-fit diagram of the BP model for actuator elongation (numbered 1383) provided in this embodiment of the invention.

[0050] Figure 5A comparison chart of the predicted and actual values ​​of the BP model for actuator elongation (number 1383) provided in the embodiment of the present invention in the test sample.

[0051] Figure 6 A statistical chart showing the time required for the BP model to complete 9 operations as provided in this embodiment of the invention.

[0052] Figure 7 This invention provides the distribution of the radial error of the cable node within the parabolic aperture of the BP model under the conditions of a temperature of 13.5°C, an azimuth angle of 2°, and a zenith angle of 5°. Detailed Implementation

[0053] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0054] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0055] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0056] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0057] Combination Figure 1 As shown, this embodiment provides a FAST reflector control algorithm based on a BP neural network. The method includes two stages: dataset partitioning and design, and training of a BP neural network model (hereinafter referred to as the BP model). Its steps are as follows:

[0058] 1) Correlation analysis was performed on the experimental data, i.e., the reflector control database (see CN201811382149.5), to determine that the input indicators of the BP model are ambient temperature and the spatial position of the vertex of the displacement parabola (azimuth angle, zenith angle, coordinates x, y, z), and the output indicator is the total elongation of the actuator (the elongation of the actuator's reference spherical surface plus the elongation from the reference spherical surface to the theoretical parabola).

[0059] 2) The experimental data were redistributed according to the principle of randomness;

[0060] 3) Preprocess the experimental data, that is, standardize the experimental data using the min-max normalization method;

[0061] 4) Based on the above experimental data, design the dataset partitioning for the training set, validation set, and test set;

[0062] 5) For the above dataset, design the BP model structure (including the network nodes and hyperparameter settings of the BP model), and use the BP algorithm to construct BP models for the total elongation of 2225 actuators respectively;

[0063] 6) For the above 2225 BP models, in the test samples, the predicted values ​​of the BP models are compared with the actual calibration values ​​of the test samples. A root mean square error threshold is set, and BP models with root mean square errors exceeding the threshold are put into iterative training. The BP model with the best training effect is selected to optimize the parameters.

[0064] 7) Extract the weight (threshold) matrices of the above 2225 BP models, write the weight (threshold) matrix corresponding to the hidden layer of each BP model into a large matrix in ascending order of numbering, and further split it into 10 sub-matrices;

[0065] 8) Input the actual ambient temperature and the spatial position information of the vertex of the parabolic surface (azimuth, zenith angle, coordinates x, y, z). Calculate the final actuator elongation using the weights, threshold matrices, and activation functions of each hidden layer in step 7). After inverse normalization, the final actuator elongation is obtained.

[0066] 9) Subtract the old spherical actuator elongation from the final actuator elongation, and add the most recently updated spherical actuator elongation to obtain the final parabolic actuator elongation, which is then sent to the controller for execution.

[0067] 10) As the subsequent calibration work is carried out, some actuator elongation data of artificially calibrated parabolic surfaces will be saved and filled into the training samples of the BP model to update the BP model and improve the prediction accuracy of the BP model.

[0068] In this embodiment, as a further technical solution, the correlation analysis method described in step 1) is Pearson correlation analysis, which performs correlation analysis on the actuator elongation and actual ambient temperature, azimuth angle of the parabolic vertex, zenith angle, and coordinates x, y, z based on experimental data.

[0069] In this embodiment, as a further technical solution, the experimental data described in step 2) are redistributed according to the principle of randomness, that is, all experimental data are randomly sorted by columns (each column of data includes the elongation of 2225 actuators corresponding to the calibrated parabola, ambient temperature, azimuth angle of the vertex of the parabola, zenith angle, coordinates x, y, z).

[0070] In this embodiment, as a further technical solution, the calculation formula for the min-maxnormalization standardization method in step 3) is as follows:

[0071]

[0072] Among them, y max =1, y min =-1, x max Let x be the maximum value of the metric represented by x in the training samples. min Let x be the minimum value of the metric represented by x in the training samples, where x is the metric value before standardization. * These are the standardized indicator values.

[0073] In this embodiment, as a further technical solution, the dataset partitioning design described in step 4) is as shown in the attached figure. Figure 1 As shown, 25% of the total database is extracted as test samples, and the remaining 75% is used as training samples. The specific ratio of the training samples to each dataset during the training process is: training set: validation set: test set = 70%: 15%: 15%.

[0074] In this embodiment, as a further technical solution, the BP model structure design described in step 5) is as shown in the attached figure. Figure 2As shown, the network node configuration consists of one input layer, three hidden layers, and one output layer. The input layer contains 6 neurons, and the three hidden layers contain 12, 6, and 3 neurons respectively. All hidden layers use the hyperbolic tangent function (Tanh function, see Equation 2) as the activation function. The output layer contains 1 neuron and uses the linear transfer function (Purelin function, see Equation 3). Figure 2 In the table, x1 to x6 correspond to the input indicators mentioned above. f represents the weights from the i-th node in the input layer to the j-th node in hidden layer 1 of the BP neural network. 1 ~f 4 These are the activation functions for hidden layer 1, hidden layer 2, hidden layer 3, and the output layer, respectively.

[0075]

[0076] y = x (3)

[0077] Where x represents the input to the neuron in this layer of the neural network, and tanh(x) and y represent the output values ​​of different activation functions that map the input to the output.

[0078] In this embodiment, as a further technical solution, the hyperparameters in the BP model structure design described in step 5) are set as follows: learning rate of 0.01, validation checks of 20, maximum number of training iterations of 2000, target accuracy of 1e-7, and training algorithm of Levenberg-Marquardt algorithm.

[0079] In this embodiment, as a further technical solution, the 2225 BP models mentioned in step 5) have the same structural design, and their formulas are as follows;

[0080] a 4 =f 4 (W 4 f 3 (W 3 f 2 (W 2 f 1 (W 1 p+b 1 )+b 2 )+b 3 )+b 4 (4)

[0081] Where p is the input of the input layer, W 1 W 2 W 3 The connection weights W for hidden layer 1, hidden layer 2, and hidden layer 3 are respectively. 4b represents the connection weights of the output layer. 1 b 2 b 3 These are the connection thresholds for hidden layer 1, hidden layer 2, and hidden layer 3, respectively, b 4 f is the connection threshold of the output layer. 1 ~f 3 Here are the activation functions f for hidden layer 1, hidden layer 2, and hidden layer 3, respectively. 4 Let a be the activation function of the output layer. 4 This is the total elongation of the actuator.

[0082] In this embodiment, as a further technical solution, some training results of the BP model described in step 6) are shown in the attached figure, such as the simulation performance of the BP model training for actuator elongation numbered 1383. Figure 3 As shown, from Figure 3 The convergence results show that as the number of training iterations increases, the error between the training set and the test set gradually decreases, and the trends of the training set and the test set are consistent. When the network is trained 2000 times, the three curves basically become one, and the error gradually stabilizes.

[0083] In this embodiment, as a further technical solution, some training results of the BP model described in step 6) are shown in the attached figure, such as the goodness of fit of the BP model for actuator elongation numbered 1383. Figure 4 As shown, Y=T is the reference line, date is the actual data point, the horizontal and vertical axes represent the measured and predicted values, respectively, and FIT is the fitted line for date. The date points are basically distributed near the reference line. Figure 4 As can be seen, the goodness of fit of the training set, validation set, and test set are all above 0.9, which proves that the network training effect is excellent.

[0084] In this embodiment, as a further technical solution, a partial result comparing the predicted value of the actuator elongation BP model (numbered 1383) in step 6) with the actual calibration value of the test sample is attached. Figure 5 As shown, it can be seen that the predicted value and the actual calibration value of the test sample are not much different. The points representing the error values ​​are basically distributed around 0. Under 14853 working conditions, the distribution of these error points seems to be a straight line, which proves the accuracy of the BP model prediction of the actuator elongation of number 1383.

[0085] In this embodiment, as a further technical solution, the large matrix mentioned in step 7) can be represented as a weight matrix:

[0086]

[0087] And threshold matrix:

[0088]

[0089] Where m takes values ​​of 1, 2, 3, and 4, corresponding to hidden layer 1, hidden layer 2, hidden layer 3, and output layer, respectively, and n represents the actuator number (in actual engineering, the actuator number is n+1). This represents the weight matrix of the m-th layer of the neural network in the BP model, where the actuator elongation is represented by the number n. This represents the threshold matrix of the m-th layer of the neural network in the BP model, where the actuator elongation is numbered n.

[0090] In this embodiment, as a further technical solution, the step 7) of splitting the large matrix into sub-matrices can be represented as a weight matrix:

[0091]

[0092] And threshold matrix:

[0093]

[0094] in, These represent the 1st to 10th weight submatrices, These represent the 1st to 10th threshold submatrices, respectively. Dividing the matrix avoids computationally intensive operations on large matrices, improving computational efficiency, as shown in the appendix. Figure 6 As shown, the final BP model calculated the elongation of 2225 actuators in 9 calculations, with an average time of only 0.0343 seconds.

[0095] In this embodiment, as a further technical solution, the most recently updated elongation of the reference spherical actuator in step 9) is consistent with the elongation of the reference spherical actuator used in the field. The final distribution of the cable node radial error within the parabolic aperture of the BP model under the conditions of a temperature of 13.5 degrees Celsius, an azimuth angle of 2°, and a zenith angle of 5° is shown in the attached figure. Figure 7 As shown, the surface accuracy is 1.6256mm (the existing interpolation algorithm has a surface accuracy of 1.8862mm).

[0096] In summary, the control algorithm provided by this invention possesses both flexibility and accuracy. Its flexibility includes: 1) The BP model structure design for the elongation of 2225 actuators improves training accuracy and convergence speed, saving training time and reducing modeling time (approximately 2-3 days). Based on this, the BP model can be easily updated at any time by adding measured samples; 2) The BP model can be easily updated at any time by adding measured samples, without requiring sample points to fall on the vertices (or the midpoints of any edge) of the triangular mesh divided in the discrete domain of the reflector surface. This solves the problem that existing interpolation algorithms require re-dividing the mesh and establishing a new calibration database to update the model, which is inflexible and time-consuming. Its accuracy includes: 1) Using the existing FAST reflector surface control database as samples, the trained BP model can accurately predict the elongation of 2225 actuators under arbitrary parabolic surface conditions in FAST, and its accuracy is improved compared to existing interpolation algorithms. In addition, by combining and further dividing the weight and threshold matrices of 2225 BP models, the BP model can simultaneously predict the elongation of 2225 actuators. The average time to generate the elongation of 2225 actuators each time is about 34.3ms, which meets the FAST reflector control requirements (within 500ms); 2) The BP model has deep learning capabilities, which can be easily updated at any time by adding measured samples to continuously improve the actual control accuracy of the reflector.

[0097] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for controlling a FAST reflector based on a BP neural network, characterized in that, The method comprises two stages of data set partition design and training of a BP neural network model, and the BP neural network model is referred to as a BP model. 1) Correlation analysis is performed on experimental data, i.e., a reflector control database, to determine that the input indicators of the BP neural network model are an environmental temperature, a spatial position of a vertex of a variable-position paraboloid, and the output indicator is a total elongation of an actuator; 2) The experimental data are redistributed according to a randomness principle; 3) The experimental data are preprocessed, i.e., the experimental data are standardized by using a min-max standardization processing method; 4) The data set partition design is performed on the experimental data regarding a training set, a verification set and a test set; 5) The BP model structure is designed for the data set, including network node and hyperparameter settings of the BP model, and 2225 BP models of total elongation of the actuator are respectively constructed by using a BP algorithm; 6) For the 2225 BP models, the predicted values of the BP models and the actual calibration values of the test samples are compared in the test samples, a root mean square error threshold is set, the BP models with the root mean square error exceeding the threshold are subjected to cyclic iterative training, the best BP model is selected, and thus the parameters are optimized; 7) The weight and threshold matrices of the 2225 BP models are extracted, the weight and threshold matrices corresponding to the hidden layers of each BP model are written into a large matrix in ascending order of the number, and the large matrix is further split into 10 sub-matrices; 8) The actual environmental temperature and the spatial position information of the vertex of the variable-position paraboloid are input, the weight, threshold matrix and activation function of each hidden layer in step 7) are used for calculation, and after inverse normalization processing, the final elongation of the actuator is obtained; 9) The final elongation of the actuator is subtracted from the elongation of the old spherical actuator, and the final paraboloid actuator elongation is obtained by adding the most recently updated spherical actuator elongation, and the controller is sent for execution; 10) As subsequent calibration work is carried out, some actuator elongation data of the artificially calibrated paraboloid are obtained and saved, and are filled into the training samples of the BP model, the BP model is updated, and the prediction accuracy of the BP model is improved; The large matrix in step 7) is represented as a weight matrix: and a threshold matrix: Wherein, m takes value 1, 2, 3, 4 respectively corresponding to implicit layer 1, implicit layer 2, implicit layer 3 and output layer, n represents the number of actuator, the number corresponding to the actuator in the actual engineering is n+1 BP model of the actuator numbered n, the weight matrix of the mth layer neural network, BP model of the actuator numbered n, the threshold matrix of the mth layer neural network; The large matrix in step 7) is split into a sub-matrix represented as a weight matrix: and a threshold matrix: wherein, respectively represent the 1st to 10th weight sub-matrices, respectively represent the 1st to 10th threshold sub-matrices; the most recently updated spherical actuator elongation in step 9) is consistent with the reference spherical actuator elongation in use.

2. The FAST reflector control method based on BP neural network according to claim 1, characterized in that, The correlation analysis method in step 1) is Pearson correlation analysis, and the elongation of the actuator and the actual environmental temperature, the azimuth angle, the zenith angle, the coordinates x, y and z of the vertex of the paraboloid are subjected to correlation analysis based on the experimental data.

3. The method of claim 1, wherein the BP neural network-based FAST reflector control method is characterized by, In step 2), the experimental data are redistributed according to the randomness principle, specifically: all the experimental data are randomly sorted by column; each column of data includes 2225 actuator elongations of the calibrated paraboloid, the environmental temperature, the azimuth angle, the zenith angle, the coordinates x, y and z of the vertex of the paraboloid.

4. The method of claim 1, wherein the BP neural network-based FAST reflector control method is characterized by, The calculation formula of the min-max standardization processing method in step 3) is: wherein y max = 1, y min = -1, x max is the maximum value of the index represented by x in the training sample, x min is the minimum value of the index represented by x in the training sample, x is the index value before normalization, and x * is the index value after normalization.

5. The method of claim 1, wherein the BP neural network-based FAST reflector control method is characterized by, The dataset partition design in step 4) includes extracting 25% of the total database as a test sample and the remaining 75% as a training sample. The training sample is divided into three datasets during the training process, with the proportions being training set: validation set: test set = 70%: 15%: 15%.

6. The method of claim 1, wherein the BP neural network-based FAST reflector control method is characterized by, In step 5), the network node configuration in the BP model structure design is one input layer, three hidden layers, and one output layer. The input layer contains 6 neuron nodes, the three hidden layers contain 12, 6, and 3 neuron nodes respectively, and the hyperbolic tangent function is used as the activation function for the hidden layers. The specific formula is shown in equation (2). The output layer contains 1 neuron node, and the linear transmission function is used. The specific formula is shown in equation (3): y = x (3) Where x represents the input on the neuron in the current layer of neural network, tanh(x) and y represent the output values of different activation functions mapping the input to the output.

7. The method of claim 1, wherein the BP neural network-based FAST reflector control method is characterized by, In step 5), the hyperparameter settings in the BP model structure design are as follows: learning rate is 0.01, Validation checks is 20, maximum training times is 2000, target precision is 1e-7, and training algorithm is Levenberg-Marquardt algorithm.

8. The method of claim 1, wherein the BP neural network-based FAST reflector control method is characterized by, The 2225 BP models in step 5) have the same structure design, and the formula is as follows: a 4 = f 4 (W 4 f 3 (W 3 f 2 (W 2 f 1 (W 1 p + b 1 ) + b 2 ) + b 3 ) + b 4 ) (4) wherein p is an input of an input layer, W 1 , W 2 , W 3 are connection weights of the hidden layer 1, the hidden layer 2, and the hidden layer 3, respectively, W 4 is a connection weight of an output layer, b 1 , b 2 , b 3 are connection thresholds of the hidden layer 1, the hidden layer 2, and the hidden layer 3, respectively, b 4 is a connection threshold of the output layer, f 1 ~ f 3 are activation functions of the hidden layer 1, the hidden layer 2, and the hidden layer 3, respectively, f 4 is an activation function of the output layer, and a 4 is a total elongation amount of the actuator.

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