Reconstruction method of antenna array element displacement under wind load effect

Abstract

The invention discloses an antenna array element displacement real-time reconstruction method based on finite strain information. The method is suitable for electrical performance compensation after array plane deformation of a phased array radar. According to the method, a data driving mode is adopted, numerical simulation is combined with a multi-layer perceptron network, and displacement of all target points is reconstructed according to strain values of a limited number of monitoring points. By introducing a loss function based on Gaussian distribution hypothesis and same variance uncertainty, the network architecture is optimized to improve the reconstruction precision. And a data set generated by finite element analysis is utilized to realize efficient reconstruction of multi-target-point displacement on the four-side hinged support plate. Discrete strain data is used as an input feature, array element displacement data is used as an output target value, and an MLP-based deformation sensing model is trained and verified. The result shows that the sparsely arranged monitoring points can realize synchronous and accurate reconstruction of multi-measurement-point displacement. The method can be widely applied to the field of deformation sensing and performance compensation of complex structures.

Description

Technical Field

[0001] The present invention belongs to the technical field of structural deformation perception measurement, and particularly relates to a method for reconstructing the displacement of an antenna element under wind load. Background Art

[0002] A phased array radar is a high-performance electronic device. A slight deformation of the shape of its antenna array surface may have a significant impact on electrical performance (such as beam pointing accuracy, gain, and sidelobe level), especially in complex or extreme service environments. Therefore, accurately monitoring and compensating the displacement of antenna elements in real time is crucial for maintaining the electrical performance of the phased array radar. Traditional methods for monitoring and compensating the displacement of the antenna array surface usually rely on the arrangement of a large number of high-precision sensors or complex measurement devices, which not only increases the system cost and complexity but may also be affected by environmental noise and measurement blind spots. In addition, analytical methods based on full-field displacement measurement often fail to meet the real-time requirements, and there are technical bottlenecks in the trade-off between reconstruction accuracy and computational efficiency for limited strain information.

[0003] Currently, there is little research on the practical engineering application of such problems. Existing deformation reconstruction methods mainly include the curvature recurrence method, KO displacement theory, modal method, inverse finite element method, etc. For the radar array surface system, since the transmission path between the strain measurement position and the center of the array surface is very complex. Whether it is the modal method or the inverse finite element method, their physical models follow certain mechanical simplification principles, there are initial modeling errors, and it is difficult to fit the mapping relationship between the strain information at different positions and the displacement at the center of the antenna element of interest. Using physics-based methods, error accumulation is inevitable. When the composition of the target structure and its boundary conditions are complex, this model error will be more significant. And very refined modeling requires a greater cost and will sacrifice efficiency.

[0004] In recent years, with the development of artificial intelligence and data-driven methods, using limited strain information to predict structural displacement has become a potential technical path. In particular, deep learning models such as multi-layer perceptrons (MLPs) have shown superiority in dealing with nonlinear relationships and complex high-dimensional data. However, the existing technology lacks an efficient and accurate displacement reconstruction method for the special application scenario of the phased array antenna surface, and it is difficult to simultaneously meet the requirements of sparse sensor arrangement, real-time performance, and reconstruction accuracy. Based on the above background, the present invention proposes a real-time antenna element displacement reconstruction method combining finite element analysis (FEA) and multi-layer perceptron network, providing a new technical solution for the monitoring and compensation of antenna array surface deformation. Summary of the Invention

[0005] To overcome the deficiencies of the prior art, the present invention provides a method for reconstructing the displacement of an antenna element under wind load, aiming to solve problems such as accuracy and efficiency in the deformation monitoring and compensation of a phased array radar antenna surface.

[0006] The technical solution adopted by the present invention to solve its technical problems is as follows:

[0007] This method utilizes data-driven technology. By constructing a multi-layer perceptron (MLP) network and combining the collected high-precision strain-displacement data set, it realizes the efficient reconstruction of the displacement of the target point, and is applicable to the deformation perception and electrical performance compensation of the antenna surface under complex service environments. To achieve the above objectives, the present invention proposes the following technical solutions:

[0008] Step 1: Determine the installation positions and quantities of the sensors.

[0009] After determining the pasting method of the strain sensors, select appropriate positions on the measured antenna reflector panel to install fiber Bragg grating (FBG) strain sensors. Through the arranged strain sensing system, the strain distribution on the surface of the structure is actually measured, measurement data is obtained, and the strain values at different positions are recorded as ε i , where i (1, 2, ···, n) represents the strain gauge serial number.

[0010] Filter the original data collected by the strain sensors. The extreme value removal sliding average filtering algorithm is used to remove data burrs and ensure real-time performance.

[0011]

[0012] Among them, y(n) is the effective value of the nth sliding window filtering output, N is the size of the sliding window, that is, the number of data points participating in the calculation each time. y max is the maximum value among the data points participating in the calculation each time, and y min is the minimum value among the data points participating in the calculation each time.

[0013] Step 2: Construct the data set.

[0014] Place the antenna surface in a wind tunnel under laboratory conditions, and apply wind loads with different speeds and directions to the antenna surface. Use distributed strain sensors to collect the strain of limited measurement points on the antenna surface structure, and at the same time use high-precision vision measurement equipment to collect the element displacement response under the corresponding strain response, so as to establish a high-precision strain-displacement data set and provide reliable data support for the training of the deep learning model.

[0015] Step 3: Data-driven displacement reconstruction model.

[0016] Build a displacement reconstruction model, and optimize the network architecture based on the Gaussian distribution assumption and the loss function of homoscedastic uncertainty, so that it has an efficient strain-to-displacement mapping ability and realizes the accurate reconstruction of the target point displacement. This model takes the in-situ strain measurement values as input and the displacements of all array elements on the array surface as output.

[0017] For the input feature data, first use the Embedding layer to achieve feature embedding, mapping all features from the low-dimensional space to the high-dimensional space.

[0018] x emb = φ(x)

[0019] Among them, is the low-dimensional feature vector, representing the measurement value input features of each strain measurement point, is the embedding mapping function, is the high-dimensional sparse feature vector, representing the embedding result of the corresponding feature.

[0020] To enhance the input feature expression of the model, absolute position encoding is performed on all input features. By assigning a unique identifier to the recording order of each strain measurement, the position encoding is directly incorporated into the input feature vector. This encoding process does not change the strain data, but enriches the strain data with metadata, where the metadata represents the sequence of the sensor in the array. The representation of each position is defined as a learnable vector, and this process can be expressed by the following mathematical formula:

[0021]

[0022] In the above formula, is the k-th input feature, and PE k is the encoding of the k-th position. Through this method, the model can better understand and utilize the position information of the input features, thereby improving the prediction performance.

[0023] Input the processed feature data into the multi-layer perceptron, and the calculation process can be mathematically represented as follows:

[0024]

[0025] where r (l) ~ N(1, p(1 - p)), is a random variable generated for each neuron in the l-th layer, following the Gaussian distribution. f represents the activation function, which performs a non-linear transformation on each element. Specifically, in this model, it refers to the Tanh activation function, which is used to add non-linearity to the network to improve the model's ability to express non-linear behaviors.

[0026] To maintain the dimensional consistency between the error and the true value for a more intuitive interpretation of the error magnitude, based on the Gaussian distribution assumption, this model uses the root mean square error (RMSE) as the loss calculation method for each task. The calculation formula is as follows:

[0027]

[0028] For the processing of the learning losses of multiple subtasks, homoscedastic uncertainty is interpreted as task-related weights, and homoscedastic uncertainty is used to combine the losses of multiple subtasks to achieve simultaneous learning of multiple objectives. Based on the above theory and the Gaussian loss distribution assumption, the minimized objective loss function of the multi-output model is obtained:

[0029]

[0030] where m is the number of subtasks, and L j (W) represents the losses of each subtask that depend on the model parameters W, and σ j represents the noise level of each task.

[0031] Step 4: Model training and optimization.

[0032] The MLP network is trained in a supervised learning manner. By adjusting the network structure and hyperparameters, the accuracy and generalization ability of displacement prediction are improved to ensure its applicability under different boundary conditions.

[0033] Step 5: Online displacement prediction and compensation.

[0034] Using the trained MLP network, the displacement of the antenna array elements is calculated based on the strain data collected in real time and provided as input to the electrical performance compensation system to achieve intelligent adjustment of the phased array radar and reduce the electrical performance error caused by deformation.

[0035] The real-time reconstruction of the displacement of the antenna array elements based on limited strain information is crucial for the electrical performance compensation after the deformation of the phased array radar antenna surface. The present invention can achieve high-precision real-time perception and reconstruction of the deformation of the antenna surface under the condition of sparsely arranged sensors, and has the advantages of high computational efficiency, strong adaptability, low cost, etc., providing a reliable technical solution for the high-performance application of phased array radars. This method can not only be used for the deformation monitoring of radar antennas, but also be extended to other fields involving structural health monitoring, intelligent manufacturing, and high-precision displacement measurement.

[0036] This method has the following advantages:

[0037] (1) The present invention can directly infer the displacements of all target points based on the strain values of a limited number of monitoring points, and can be used to efficiently and accurately reconstruct the displacements of the antenna array elements. Sparse arrangement of monitoring points can achieve synchronous and accurate reconstruction of the displacements of multiple measurement points.

[0038] (2) The operation of the present invention is simple and convenient, with a fast calculation speed and high solution accuracy, and it is easy to be popularized and applied to the radar array structure.

[0039] (3) The deformation reconstruction model established by the neural network method is independent of the material properties, structural parameters of the object to be measured, and the distribution form of environmental loads, so it has strong versatility. Description of the Drawings

[0040] The following further elaborates on the technical solution of the present invention in conjunction with the drawings and specific implementation methods.

[0041] Figure 1 is a schematic diagram of the structure to be measured (viewing angle perpendicular to the array surface);

[0042] Figure 2 is a schematic diagram of the simulation loading conditions;

[0043] Figure 3 is a schematic diagram of the simulated working conditions;

[0044] Figure 4 is a schematic diagram of the loss curve;

[0045] Figure 5 is a schematic diagram of the comparison of prediction results on the test set:

[0046] Figure 6 is a schematic diagram of the computational domain and mesh division;

[0047] Figure 7 is a schematic diagram of the wind pressure distribution on the windward side at a certain moment;

[0048] Figure 8 is a test result graph of calculating the displacement of the antenna array element based on the strain data collected in real time;

[0049] Figure 9 is a flowchart of a method for reconstructing the displacement of the antenna array element under wind load. Detailed Implementation Manner

[0050] The following is for the radar antenna reflector panel structure, and a deformation real-time prediction system with the structure shown in Figure 1 is built. A square aluminum alloy plate is used to simulate the radar antenna reflector panel. The size of the square plate is 1200mm×1200mm, and 16 displacement measurement points (D-1 to D-16) are evenly distributed on it to represent the installation positions of the antenna array elements. The interval between the displacement measurement points is 300mm, and the coordinate of D-1 is (150mm, 150mm). The technical solution of the present invention is elaborated in conjunction with the description of the drawings and corresponding examples. To reduce the solution complexity of this embodiment, only the deformation in the direction perpendicular to the array surface (Z direction) is reconstructed.

[0051] Step 1: Determine the installation location and quantity of the sensors.

[0052] Adopt the FBG strain sensor layout scheme as Figure 1 shown on the right, divide the square plate into 9 uniform grids, and determine the strain acquisition positions at the centroids of each grid. Install strain rosettes at each strain acquisition position to extract the strain on the upper surface at the center point of the grid as the input feature of the model.

[0053] Step 2: Dataset construction

[0054] To verify the reconstruction ability of the proposed model without being restricted by hardware or experimental complexity, use ANSYS simulation software to conduct a simulation study on the proposed experimental device. Establish a finite element simulation model to replace the actual structural deformation and extract the strain and displacement responses. First, establish a simulation model of an aluminum alloy square plate in the software, and its material properties are shown in Table 1. The simulation loading conditions are as Figure 2 shown. Apply two concentrated loads on the square plate to simulate the effect of wind load. The magnitude and position of each load are randomly generated within the specified range by a pseudo-random number generator. Subsequently, import the load information into ANSYS through the written command script, conduct a large number of simulation calculations, and export the simulation result data. This method can more clearly distinguish various loading conditions, thus obtaining a more diverse strain response distribution, promoting the creation of a more comprehensive dataset. This helps to avoid excessive similarity between training data and ensure that the model captures a wider range of structural deformation scenarios.

[0055] Table 1: Material property table

[0056]

[0057] For the working condition of a simply supported plate with four edges, as Figure 3 , use ANSYS simulation software to establish a finite element model of an aluminum alloy square plate with dimensions of 1200×1200×4mm. Fix the four edges with simply supported constraints, and it is necessary to restrict the translational degrees of freedom, that is, make UX, UY, and UZ always 0, and allow the rotational degrees of freedom ROTX, ROTY, and ROTZ. Figure 3 The boundary conditions and finite element mesh division settings of the simulation model are shown in. The model is discretized using SOLID186 elements with a size of 10mm. Its loading conditions are shown in Table 2. Through a large number of simulations, 10,000 groups of data samples are accumulated.

[0058] Table 2: Loading conditions

[0059]

[0060] Collect 10,000 samples through simulation. Each sample has 27 input features, corresponding to three strain measurement values (0°, 45°, 90°) at nine strain measurement points from S1 to S9. Using the displacement of the selected measurement points on the structure as the target value, construct the comprehensive dataset required for training the model, and divide the dataset into a training set, a validation set, and a test set according to the ratio of 6:2:2. Analyzing the dataset shows that there are significant differences in the numerical scale and distribution range of the feature values. Since features with larger value ranges will dominate the calculation of the Euclidean distance between samples, it is necessary to preprocess the samples to normalize the features of each dimension to the same numerical interval to obtain the best results. Use the maximum normalization method to standardize the final data, and its formula is as follows:

[0061]

[0062] Step 3: Data-driven displacement reconstruction model

[0063] Construct a displacement reconstruction model, and optimize the network architecture based on the Gaussian distribution assumption and the loss function of homoscedastic uncertainty to enable it to have an efficient strain-to-displacement mapping ability and achieve accurate reconstruction of the target point displacement. This model takes the in-situ strain measurement values as input and the displacements of all array elements on the array as output.

[0064] Step 4: Model training and optimization

[0065] Use the comprehensive dataset obtained from a large number of simulation experiments to train and validate the proposed network model. The loading conditions in the simulation experiments are randomly generated within the specified range by a pseudo-random number generator, meeting the randomness requirements such as uniform distribution and independence. Use the supervised learning method to train the model network, and by adjusting the network structure and hyperparameters, improve the accuracy and generalization ability of displacement prediction to ensure its applicability. After adjustment, the hyperparameter values used in model training are shown in Table 3, and its training loss curve is as follows Figure 4 。

[0066] Table 3: Model hyperparameter values

[0067]

[0068]

[0069] Select four representative displacement measurement points (D-1, D-6, D-11, D-16), and compare the prediction results of the trained model on the test set. The predicted mean absolute errors of the four measurement points are 0.01093mm, 0.09343mm, 0.13226mm, and 0.04228mm respectively. To visually display the prediction performance of the proposed model, the prediction results of the test set are visualized. From Figure 5It can be seen that the predicted displacement values in blue can cover the actual displacement values in red to a large extent, and achieve an almost overlapping effect in multiple test samples. This indicates that the prediction deviation of the model is small and the prediction effect is good.

[0070] Step 5: Online displacement prediction

[0071] To more accurately reflect the actual situation, a fluid-structure interaction (FSI) multi-physics simulation model was developed using Fluent. This model takes into account a more realistic wind field distribution and reflects the specific impact of strong winds on antenna deformation. The FSI-based simulation can effectively capture the dynamic coupling between aerodynamic loads and structural responses under strong wind conditions. As Figure 6 shown, the antenna structure was simplified to a flat plate with dimensions of 1200mm × 1200mm × 20m, the angle θ between the panel and the ground was 70°, the size of the computational domain was 3000mm × 3000mm × 2100mm, the velocity inlet boundary condition was adopted for the inlet boundary of the flow domain, the pressure outlet boundary condition was adopted for the outlet boundary, and the symmetric boundary condition was adopted for the four sides of the computational domain. The time history of the simulated wind speed was generated by the harmonic superposition method, in which the Kaimal spectrum and Cholesky decomposition were used. The panel was placed at 1 / 2 of the distance from the velocity inlet boundary. The wind pressure distribution on the windward side caused by the wind speed at a certain moment is as Figure 7 shown.

[0072] Using the trained network model, the displacement of the antenna elements was calculated based on the real-time collected strain data. The test results are as Figure 8 shown. Under the wind load condition, the maximum deformation of the four-sided hinged plate does not exceed 6mm, and the absolute error predicted by the model does not exceed 0.5mm. The deformation reconstruction effect is good.

Claims

1. A method for reconstructing the displacement of an antenna element under wind load, characterized in that, It includes the following steps: Step 1: Determine the installation positions and quantities of sensors; Step 2: Construct a data set; Step 3: A data-driven displacement reconstruction model; Step 4: Model training and optimization; Step 5: Online displacement prediction and compensation.

2. A method for reconstructing the displacement of an antenna element under wind load according to claim 1, characterized in that: In Step 1, after determining the pasting method of the strain sensor, select appropriate positions on the measured antenna reflector panel to install Fiber Bragg Grating (FBG) strain sensors; through the arranged strain sensing system, actually measure the strain distribution on the surface of the structure, obtain measurement data, and record the strain values at different positions as, where i(1,2,···,n) represents the strain gauge serial number.

3. A method for reconstructing the displacement of an antenna element under wind load according to claim 2, characterized in that: In Step 1, filter the original data collected by the strain sensor; Adopt the extreme value removal sliding average filtering algorithm to remove data burrs and ensure real-time performance; Among them, is the effective value output by the nth sliding window filtering, N is the size of the sliding window, that is, the number of data points participating in the calculation each time; is the maximum value among the data points participating in the calculation each time, and is the minimum value among the data points participating in the calculation each time.

4. A method for reconstructing the displacement of an antenna element under wind load according to claim 1, characterized in that: In Step 2, place the array surface in a wind tunnel in a laboratory environment, apply wind loads with different speeds and directions to the array surface; use distributed strain sensors to collect the strain of finite measurement points on the antenna array surface structure, and at the same time use high-precision vision measurement equipment to collect the element displacement response under the corresponding strain response, so as to establish a high-precision strain-displacement data set and provide reliable data support for the training of the deep learning model.

5. A method for reconstructing the displacement of an antenna element under wind load according to claim 1, characterized in that: In Step 3, construct a displacement reconstruction model, and optimize the network architecture based on the Gaussian distribution hypothesis and the loss function of homoscedastic uncertainty, so that it has an efficient strain-to-displacement mapping ability to accurately reconstruct the displacement of the target point; this model takes the in-situ strain measurement value as the input and the displacements of all elements on the array surface as the output.

6. The reconstruction method of the displacement of the antenna array element under the action of wind load according to claim 5, characterized in that: In Step 3, for the input feature data, first use the Embedding layer to achieve feature embedding, and map all features from the low-dimensional space to the high-dimensional space; x emb = φ(x) Among them, is the low-dimensional feature vector, representing the measurement value input features of each strain layout point, is the embedding mapping function, is the high-dimensional sparse feature vector, representing the embedding result of the corresponding feature.

7. A method for reconstructing the displacement of an antenna element under wind load according to claim 6, characterized in that: In Step 3, in order to enhance the input feature expression of the model, perform absolute position encoding on all input features, and directly incorporate the position encoding into the input feature vector by assigning a unique identifier to the recording order of each strain measurement; This encoding process does not change the strain data, but enriches the strain data with metadata, where the metadata represents the sequence of the sensor in the array; the representation of each position is defined as a learnable vector, and this process can be expressed by the following mathematical formula: In the above formula, is the k-th input feature, and PE k is the encoding at the k-th position; by this method, the model can better understand and utilize the positional information of the input features, thereby improving the prediction performance; Input the processed feature data into a multi-layer perceptron, and the calculation process can be mathematically represented as follows: where r (l) ~ N(1, p(1 - p)) is a random variable generated for each neuron in the th layer and follows a Gaussian distribution; f represents the activation function that performs a non-linear transformation on each element; Specifically refers to the Tanh activation function in this model, which is used to add non-linearity to the network to improve the model's expression ability for non-linear behaviors.

8. A method for reconstructing the displacement of an antenna element under wind load according to claim 7, characterized in that: In step 3, in order to maintain the dimensional consistency between the error and the true value for a more intuitive explanation of the error magnitude, based on the Gaussian distribution assumption, this model uses the root mean square error (RMSE) as the loss calculation method for each task; the calculation formula is as follows: For the processing of the learning losses of multiple subtasks, homoscedastic uncertainty is interpreted as task-related weights, and homoscedastic uncertainty is used to combine the losses of multiple subtasks to achieve the simultaneous learning of multiple objectives; based on the above theory and the Gaussian loss distribution assumption, the minimized objective loss function of the multi-output model is obtained: where m is the number of subtasks, L j (W) represents the losses of individual subtasks that depend on the model parameter W, σ j represents the noise level of each task.

9. A method for reconstructing the displacement of an antenna element under wind load according to claim 1, characterized in that: In step 4, the MLP network is trained in a supervised learning manner. By adjusting the network structure and hyperparameters, the accuracy and generalization ability of displacement prediction are improved to ensure its applicability under different boundary conditions.

10. A method for reconstructing the displacement of an antenna element under wind load according to claim 1, characterized in that: In step 5, the trained MLP network is used to calculate the displacement of the antenna array elements based on the real-time collected strain data, and this is provided as an input to the electrical performance compensation system to achieve intelligent adjustment of the phased array radar, thereby reducing the electrical performance error caused by deformation.

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