A method for reconstructing displacement of antenna array elements under wind load

Abstract

The application discloses a kind of antenna array element displacement real-time reconstruction methods based on limited strain information, it is suitable for the electric performance compensation after phased array radar array surface deformation.This method uses data-driven mode, by combining numerical simulation and multilayer perception machine network, according to the strain value of limited monitoring point, the displacement of all target points is reconstructed.By introducing the loss function based on the assumption of Gaussian distribution and homoscedasticity uncertainty, the network architecture is optimized to improve the reconstruction accuracy.Using the data set generated by finite element analysis, the efficient reconstruction of multi-target point displacement on four-edge hinged plate is realized.Discrete strain data as input features, array element displacement data as output target values, are used to train and verify the deformation perception model based on MLP.The results show that sparse arrangement of monitoring points can realize synchronous and accurate reconstruction of displacement of multiple measuring points.It can be widely used in the field of deformation perception and performance compensation of complex structures.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of structural deformation sensing measurement, and particularly relates to an antenna array element displacement reconstruction method under wind load. BACKGROUND

[0002] Phased array radar is a high-performance electronic device, and slight deformation of the antenna array surface can have a significant impact on electrical performance, such as beam pointing accuracy, gain, and sidelobe level, especially in complex or extreme service environments. Therefore, accurate monitoring and real-time compensation of antenna array element displacement are crucial for maintaining the electrical performance of phased array radar. Traditional antenna array surface displacement monitoring and compensation methods usually rely on a large number of high-precision sensor arrangements or complex measurement equipment, which not only increases system cost and complexity, but also may be affected by environmental noise and measurement blind areas. In addition, analytical methods based on full-field displacement measurement often have difficulty meeting real-time requirements, and limited strain information has technical bottlenecks in the trade-off between reconstruction accuracy and computational efficiency.

[0003] Currently, there is little research on practical engineering applications for such problems. Existing deformation reconstruction methods mainly include curvature recursion method, KO displacement theory, modal method, and inverse finite element method, etc. For radar array surface systems, the transmission path between the strain measurement position and the array center is very complex. Whether it is the modal method or the inverse finite element method, their physical models follow certain mechanical simplification principles, and there are initial modeling errors, making it difficult to fit the mapping relationship between strain information at different positions and the displacement at the center of the antenna array element. Using physical-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. A very detailed modeling requires a greater cost and sacrifices 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 perceptron (MLP) have shown superiority in handling nonlinear relationships and complex high-dimensional data. However, existing technologies lack efficient and accurate displacement reconstruction methods for the special application scenario of phased array antenna arrays, making it difficult to meet the needs of sparse sensor arrangement, real-time performance, and reconstruction accuracy. Based on the above background, the present application proposes a real-time antenna array element displacement reconstruction method combining finite element analysis (FEA) and multi-layer perceptron network, providing a new technical solution for antenna array deformation monitoring and compensation. SUMMARY

[0005] In order to overcome the defects of the prior art, the application provides a reconstruction method for antenna array element displacement under wind load, aiming at solving the problems of precision and efficiency in phased array radar antenna array surface deformation monitoring and compensation.

[0006] The technical scheme adopted by the application to solve the technical problems is:

[0007] The method uses data-driven technology, builds a multi-layer perception (MLP) network, and combines the collected high-precision strain-displacement data set to realize efficient reconstruction of the target point displacement, and is suitable for antenna array surface deformation perception and electrical performance compensation in complex service environments. In order to achieve the above goal, the application proposes the following technical scheme:

[0008] Step 1: Determine the installation position and number of sensors.

[0009] After determining the pasting method of the strain sensor, the fiber Bragg grating (FBG) strain sensor is installed on the measured antenna reflector panel at a suitable position. Through the arranged strain sensing system, the strain distribution on the structure surface is measured and obtained, and the strain values at different positions are recorded as ε i , wherein i (1, 2,..., n) represents the strain gauge serial number.

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

[0011]

[0012] , wherein y (n) is the effective value of the n-th sliding window filtering output, N is the size of the sliding window, that is, the number of data points participating in calculation each time. y max is the maximum value of each data point participating in calculation. min is the minimum value of each data point participating in calculation.

[0013] Step 2: Data set construction.

[0014] In the laboratory environment, the array surface is placed in the wind tunnel, and wind load with different speed and direction is applied to the array surface. The distributed strain sensor is used to collect strain at the limited measurement points of the antenna array surface structure, and the high-precision visual measurement equipment is used to collect the array 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] A displacement reconstruction model is constructed, and the network architecture is optimized based on the loss function of Gaussian distribution assumption and homoscedastic uncertainty, so that it has efficient strain-to-displacement mapping capability, and realizes accurate reconstruction of target point displacement. The model takes in-situ strain measurement values as input and the displacement of all array elements on the array surface as output.

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

[0018] x emb = φ(x)

[0019] where, is a low-dimensional feature vector, representing the measured value input feature of each strain cloth point, is an embedding mapping function, is a high-dimensional sparse feature vector, representing the embedding result of the corresponding feature.

[0020] In order to enhance the input feature expression of the model, the absolute position coding is carried out for all input features, and a unique identifier is assigned to the recording order of each strain measurement, so that the position coding is directly included in the input feature vector. This coding process does not change the strain data, but enriches the strain data with metadata, which 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 represented by the following mathematical formula:

[0021]

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

[0023] The processed feature data is input into the multilayer 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 layer, following a Gaussian distribution. f represents the activation function, which performs a nonlinear transformation on each element. In this model, it specifically refers to the Tanh activation function, which is used to add a nonlinear factor to the network to improve the model's expression ability for nonlinear behavior.

[0026] In order to keep the dimension consistency between error and true value, so as to more intuitively explain the error size, the model adopts root mean square error (RMSE) as the loss calculation method of each task on the basis of Gaussian distribution assumption. The calculation formula is as follows:

[0027]

[0028] For the learning loss processing of multiple subtasks, the homoscedastic uncertainty is explained as a task-related weight, and the homoscedastic uncertainty is used to combine the losses of multiple subtasks to realize the simultaneous learning of multiple targets. Based on the above theory and Gaussian loss distribution assumption, the minimum target loss function of the multi-output model is obtained:

[0029]

[0030] Wherein, m is the number of subtasks, L j (W) represents the loss of each subtask depending on the model parameters W, 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, and the network structure and hyperparameters are adjusted to improve the accuracy and generalization ability of displacement prediction, and to ensure its applicability under different boundary conditions.

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

[0034] The trained MLP network is used to calculate the displacement of the antenna array element based on the real-time collected strain data, and the displacement is provided as input to the electrical performance compensation system to realize intelligent adjustment of the phased array radar to reduce the electrical performance error caused by deformation.

[0035] The real-time reconstruction of the displacement of the antenna array element based on the limited strain information is crucial for the electrical performance compensation of the phased array radar after the array surface deformation. The present application can realize high-precision real-time perception and reconstruction of the antenna array surface deformation under the condition of sparse arrangement of sensors, has the advantages of high calculation efficiency, strong adaptability, low cost and the like, and provides a reliable technical scheme for high-performance application of the phased array radar. The method can not only be used for deformation monitoring of the radar antenna, but also can be popularized to other fields involving structural health monitoring, intelligent manufacturing and high-precision displacement measurement.

[0036] The method has the following advantages:

[0037] (1) The present application can directly infer the displacement of all target points according to the strain values of a limited number of monitoring points, and can be used for efficient and accurate reconstruction of the displacement of the antenna array element. Sparse arrangement of monitoring points can realize synchronous and accurate reconstruction of the displacement of multiple measurement points.

[0038] (2) The present invention is simple and convenient to operate, fast to calculate, and has high solution accuracy, making it easy to promote and apply in radar array structures.

[0039] (3) The deformation reconstruction model established by the neural network method is independent of the material properties, structural parameters and environmental load distribution of the tested object, so it has strong versatility. Attached Figure Description

[0040] The present invention will now be described in further detail with reference to the accompanying drawings and specific implementation methods.

[0041] Figure 1 This is a schematic diagram of the structure under test (view perpendicular to the array surface);

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

[0043] Figure 3 This is a schematic diagram simulating the working conditions;

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

[0045] Figure 5 A diagram illustrating the comparison of prediction results on the test set:

[0046] Figure 6 A schematic diagram of the computational domain and mesh partitioning;

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

[0048] Figure 8 The test results are shown in the figure, which calculates the displacement of the antenna array elements based on the strain data acquired in real time.

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

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

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

[0052] The FBG strain sensor distribution scheme as shown in Fig. 1 is used to divide the square plate into 9 uniform grids, and the strain collection position is determined at the center of each grid. A strain gauge is installed at each strain collection position to extract the strain on the upper surface of the grid center as the input feature of the model. Figure 1

[0053] Step 2: Data set construction

[0054] To verify the reconstruction ability of the proposed model without being limited by hardware constraints or experimental complexity, a simulation study is conducted on the proposed experimental device using ANSYS simulation software. A finite element simulation model is established to replace the actual structure deformation, and strain and displacement responses are extracted. First, a simulation model of an aluminum alloy square plate is established in the software, and the material properties are shown in Table 1. The simulation loading conditions are shown in Fig. 2, two concentrated loads are applied on the square plate to simulate the wind load effect, and the size and position of each load are randomly generated within the specified range by a pseudo-random number generator. Subsequently, the load information is imported into ANSYS through the command script written, and a large number of simulation calculations are performed to export the simulation result data. This method can more clearly distinguish various loading conditions, thereby obtaining more diverse strain response distribution, promoting the creation of a more comprehensive data set. This helps to avoid excessive similarity between training data and ensures that the model captures a wider range of structural deformation scenarios. Figure 2

[0055] Table 1: Material properties table

[0056]

[0057] For the working conditions of the four-edge hinged plate, as shown in Fig. 3, a finite element model of an aluminum alloy square plate with dimensions of 1200x1200x4mm is established using ANSYS simulation software. The four edges are hinged and constrained, and the translation freedom degrees UX, UY, and UZ are set to 0, and the rotation freedom degrees ROTX, ROTY, and ROTZ are allowed. Figure 3 Figure 3 The boundary conditions and finite element meshing settings of the simulation model are shown in Fig. 4. The model is discretized using 10mm-sized SOLID186 elements. The loading conditions are shown in Table 2. Through a large number of simulations, 10000 data samples are accumulated.

[0058] Table 2: Loading conditions

[0059]

[0060] ​​​10000 samples are collected by simulation, each sample has 27 input features, which correspond to three strain measurement values (0°, 45°, 90°) at nine strain measurement points S1 to S9 respectively. The displacement of the selected measurement points on the structure is taken as the target value to construct the comprehensive data set required for training the model, and the data set is divided into training set, validation set and test set according to the ratio of 6:2:2. Analysis of the data set shows that there is a large difference in the numerical scale and distribution range of the feature values. Since the features with a large value range will dominate the calculation of the Euclidean distance between samples, it is necessary to preprocess the samples and normalize the features of each dimension to the same numerical interval to obtain the best results. The maximum normalization method is used to standardize the final data, and the formula is as follows:

[0061]

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

[0063] The displacement reconstruction model is constructed, and the network architecture is optimized based on the loss function of Gaussian distribution assumption and homoscedastic uncertainty, so that it has efficient strain-to-displacement mapping capability and realizes accurate reconstruction of the target point displacement. The model takes in-situ strain measurement values as input and the displacement of all array elements on the array surface as output.

[0064] Step 4: Model training and optimization

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

[0066] Table 3: Model hyperparameter values

[0067]

[0068]

[0069] Four representative displacement measurement points (D-1, D-6, D-11, D-16) are selected, and the prediction results of the trained model on the test set are compared. The average absolute error of the four measurement points is 0.01093 mm, 0.09343 mm, 0.13226 mm and 0.04228 mm respectively. In order to visually display the prediction performance of the proposed model, the test set prediction results are visualized. From the Figure 5As can be seen, the predicted displacement value of blue can cover the real displacement value of red quite a lot, and achieves the effect of close coincidence in multiple test samples. This shows that the prediction deviation of the model is small, and the prediction effect is good.

[0070] Step 5: Online displacement prediction

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

[0072] Using the trained network model, the displacement of the antenna array element is calculated based on the real-time collected strain data, and the test results are shown in Figure 8 . Under the wind load condition, the maximum deformation of the four-edge hinged plate is not more than 6mm, the absolute error of the model prediction is not more than 0.5mm, and the deformation reconstruction effect is good.

Claims

1. A method for reconstructing displacement of an antenna array element under wind loading, characterized in that, The method comprises the following steps: Step one: determine the installation position and quantity of the sensor; Step two: data set construction; Step three: data-driven displacement reconstruction model; Step four: model training and optimization; Step five: online displacement prediction and compensation; In step one, after determining the pasting mode of the strain sensor, a fiber Bragg grating (FBG) strain sensor is installed at a suitable position on the measured antenna reflector panel; the strain distribution on the structure surface is obtained by the arranged strain sensing system, and measurement data are obtained; the strain values at different positions are recorded as ε i, where i (1, 2,..., n) represents the strain gauge serial number; In step two, the array is placed in a wind tunnel in a laboratory environment, and wind loads with different speeds and directions are applied to the array; the distributed strain sensor is used to collect the strain of the limited measurement points of the antenna array structure, and the high-precision visual measurement equipment is used to collect the displacement response of the array element 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; In step three, the displacement reconstruction model is constructed, and the network architecture is optimized based on the Gaussian distribution assumption and the loss function of the same variance uncertainty, so that the model has efficient strain-to-displacement mapping capability and can accurately reconstruct the displacement of the target point; the model takes the in-situ strain measurement value as the input and the displacement of all array elements on the array as the output; In step four, the MLP network is trained in a supervised learning manner, the network structure and hyperparameters are adjusted, the accuracy and generalization ability of displacement prediction are improved, and the applicability of the model under different boundary conditions is ensured; In step five, the trained MLP network is used to calculate the displacement of the antenna array element based on the real-time collected strain data, and the displacement is provided as input to the electrical performance compensation system to realize intelligent adjustment of the phased array radar and reduce the electrical performance error caused by deformation.

2. The method of claim 1, wherein: In step one, the original data collected by the strain sensor is filtered; The de-extreme moving average filtering algorithm is used to remove data burrs and ensure real-time performance; wherein is the effective value of the n th sliding window filtering output, N is the size of the sliding window, that is, the number of data points participating in calculation each time; is the maximum value of each data point participating in calculation, and is the minimum value of each data point participating in calculation.

3. The method of claim 1, wherein the wind load is determined by: ###0002### where: ###0003### and ###0004### are the wind speed and direction, respectively, at the antenna site; and ###0005### is the wind speed and direction, respectively, at the reference site. In step three, for the input feature data, first, the Embedding layer is used to realize feature embedding, and all features are mapped from a low-dimensional space to a high-dimensional space; wherein is a low-dimensional feature vector, represents the measurement value input feature of each strain distribution, is an embedding mapping function, and is a high-dimensional sparse feature vector, representing the embedding result of the corresponding feature.

4. The method of claim 3, wherein: In step three, in order to enhance the input feature expression of the model, the absolute position coding is performed on all input features, a unique identifier is assigned to the recording order of each strain measurement, and the position coding is directly incorporated into the input feature vector; This coding process does not change the strain data, but enriches the strain data with metadata, which 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 represented by the following mathematical formula: In the above formula, is the kth input feature, is the encoding of the kth position; in this way, the model can better understand and utilize the position information of the input features, thereby improving the prediction performance; The processed feature data is input into a multilayer perceptron, and the calculation process can be mathematically represented as follows: wherein, , is a random variable generated for each neuron in the 1th layer, following a Gaussian distribution; represents an activation function, which performs a non-linear transformation on each element; In the present model, the Tanh activation function is specifically referred to, which is used to add a nonlinear factor to the network to improve the model's expression ability for nonlinear behavior.

5. The method of claim 4, wherein: In step three, in order to keep the dimension consistency between error and true value, so as to more intuitively explain the error size, on the basis of Gaussian distribution assumption, the root mean square error (RMSE) is used as the loss calculation method of each task; the calculation formula is as follows: For the learning loss processing of multiple subtasks, the homoscedastic uncertainty is explained as a task-related weight, and the homoscedastic uncertainty is used to combine the losses of multiple subtasks to realize the simultaneous learning of multiple objectives; based on the above theory and Gaussian loss distribution assumption, the minimum target loss function of the multi-output model is obtained: wherein m is the number of sub-tasks, represents the loss of each sub-task depending on the model parameters , represents the noise level of each task.

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