Array antenna deformation prediction method based on improved modal-DBOBP algorithm

Abstract

The invention discloses an array antenna deformation prediction method based on an improved modal-DBOBP algorithm, and the method comprises the steps: building an array antenna finite element model, exerting a constraint and a load, and extracting a strain and displacement modal and an ideal displacement sequence; performing normalization processing on the array antenna estimation displacement sequence, and dividing the array antenna estimation displacement sequence into a displacement sequence training set and a displacement sequence test set; adopting a DBO algorithm population to initialize behaviors and positions of dung beetles; defining and calculating a fitness function of an array antenna shape minimization reconstruction error; performing repeated iteration, updating and optimization on behaviors and positions of dung beetles in the original DBO algorithm; determining that an iteration termination condition is satisfied, and training the BP neural network after assignment; obtaining a normalized displacement prediction value; and carrying out reverse normalization on a displacement sequence result output by the BP neural network model to obtain a predicted displacement sequence. Effective displacement prediction is realized through the modal method and the BP neural network, and the problem of low precision of array antenna reconstruction is effectively solved.

Description

Technical Field

[0001] The invention belongs to the technical field of array antennas, and in particular to an array antenna deformation prediction method based on an improved mode-DBOBP algorithm. Background Art

[0002] Modern array antenna systems are usually composed of a large number of antenna elements, and their overall structure is complex and precise. Array antennas usually work under various complex environmental conditions, such as high temperature, wind load and vibration. These environmental factors will cause different degrees of deformation to the antenna structure. For example, the antenna structure will expand and contract in a high temperature environment, and will produce mechanical deformation under strong wind loads. Any slight displacement change may cause beam deviation, increase side lobes, and have a significant impact on the electrical performance of the entire array antenna.

[0003] In the field of structural deformation reconstruction research, modal method and modal transformation theory (MTT) are typical and efficient reconstruction methods. Chen-Jung LI, Ulsoy AG. High-precision Measurement of Tool-tip Displacement Using Strain Gauges in Precision Flexible Line Boring [J]. Mechanical Systems and Signal Processing, 1999, 13 (4): 531-546 derived the conversion relationship between strain and displacement based on modal theory, and proposed a new displacement measurement method, which measures the strain of linear boring by placing multiple sets of strain gauges and converts it into displacement information, thereby achieving precise displacement measurement. Experimental results show that this method is suitable for high-precision flexible line boring. Kang LH, Kim DK, Han JH. Estimation of dynamic structural displacements using fiber Bragg grating strain sensors[J]. Journal of Sound and Vibration, 2007, 305(3): 534-542 used the strain-displacement conversion relationship of the modal method and measured the strain data through FBG sensors to successfully reconstruct the dynamic deformation of the structure, and carried out a reconstruction experiment using a beam structure as an example. Rapp S, Kang LH, Han JH, et al. Displacement field estimation for a two-dimensional structure using fiber Bragg grating sensors[J]. Smart Material Structures, 2009, 18(2): 025006 used the displacement-strain conversion matrix based on the modal method to monitor the surface deformation of a large, high-precision spatial reflector by integrating a FBG sensor network, and reconstructed the displacement field of the structure surface using the measured strain data.Kim HI, Kang LH, Han J H. Shape estimation with distributed fiber Bragg grating sensors for rotating structures [J]. Smart Materials and Structures, 2013, 20 (3): 035011, applied the modal method to a rotating beam structure, optimized the sensor position by minimizing the condition number of the transformation matrix, performed transient and steady-state analysis, and compared the high-speed camera photography results to verify the effectiveness of the modal method. Bang HJ, Ko SW, Jang MS, et al. Shape estimation and health monitoring of wind turbine tower using a FBG sensor array [C]. Conference Record-IEEE Instrumentation and Measurement Technology Conference, 2012 applied the modal method reconstruction theory to the wind turbine tower, reconstructed its operating state through a high-speed fiber Bragg grating system, and verified the reliability of the FBG system. Most of the existing dynamic reconstruction studies are completed in step-by-step static conditions, but in dynamic conditions, due to the high-order modal aliasing phenomenon, the signal-to-noise ratio of the measurement system increases significantly, resulting in a decrease in reconstruction accuracy. Lively PS, Atalla MJ, Hagood N W. Investigation of filtering techniques applied to the dynamic shapeestimation problem [J]. Smart Materials and Structures, 2004, 10 (2): 264-272. Combining Kalman filtering technology with the modal method, a dynamic deformation reconstruction technology is proposed. The required low-frequency modes are screened out through the Kalman filter, and the measurement error is considered and the aliasing effect of the high-frequency mode is reduced. The numerical example results show that this method improves the accuracy of dynamic reconstruction. Although the modal method is relatively stable, it is overly dependent on the modal vibration shape. Once the model error is large, the reconstruction accuracy will be greatly affected.Ko WL, Richards WL, Fleischer VT, Displacement Theories for In-flight Deformed Shape Predictions of Aerospace Structures[J], 2007, NASA / TP-2007-214612 proposed a KO displacement theory, which is based on the classical beam equation. By integrating the measured discrete strains, the rotation angle and deflection are obtained. The deformation sensing theory developed by Ko and his colleagues is applicable to beams and plates. The core idea is to obtain the deflection of beam-like structures by double integration of the measured strain information. Jutte CV, Ko WL, Stephens CA, et al. Deformed Shape Calculation of a Full-Scale Wing Using Fiber Optic Strain Data from a Ground Loads Test[J]. 2011, NASA / TP-2011-215975 The KO displacement theory was used to conduct bending and torsion deformation experiments on aircraft wings. The experimental results verified the effectiveness of the theory. Since the KO displacement method has great limitations in application and the reconstruction position is affected by the position of the sensor, Pak, Chan-gi. Wing Shape Sensing from Measured Strain [J]. AIAA Journal, 2016, 54 (3): 1068-1077 proposed a two-step reconstruction method combining the KO displacement theory and the modal method: the first step is to determine the strain and deflection of the key FOSS segment by the KO method, and the second step is to expand these deformation information to the entire array based on the modal method to obtain the displacement information of all nodes. Tessler A, Spangler J L. Aleast-squares variational method for full-field reconstruction of elastic deformations in shear-deformable plates and shells [J]. Computer Methods in Applied Mechanics and Engineering, 2005, 194 (2-5): 327-339 proposed an inverse finite element (IFE) method and established a variational principle for inverting the displacement field of three-dimensional plates and shells from the experimentally measured surface strain field. The reconstruction formula is based on the minimization of a least squares functional that uses strain measurements that conform to the linear first-order shear deformation theory, takes into account the transverse shear deformation, and is suitable for deformation reconstruction of thin plates and moderately thick plate and shell structures.However, it is difficult to construct unit shape functions for complex structures. Therefore, this method is more practical for simple structures such as plates and shells that are easy to construct shape functions. Summary of the invention

[0004] In order to solve the above-mentioned defects existing in the prior art, the purpose of the present invention is to establish an array antenna deformation prediction method based on an improved modal-DBOBP algorithm. Through the modal superposition principle, strain-displacement conversion relationship, and neural network model, the displacement sequence of the array antenna structure deformation is predicted, which effectively solves the low-precision problem of array antenna structure deformation reconstruction.

[0005] The present invention is achieved through the following technical solutions.

[0006] The present invention provides an array antenna deformation prediction method based on an improved modal DBO-BP algorithm, comprising the following steps:

[0007] Establish a finite element model of the array antenna, apply constraints and loads to the array antenna, extract the strain and displacement modes under different working conditions, and the ideal displacement sequence;

[0008] Based on the modal superposition principle and the strain-displacement conversion relationship, the estimated displacement sequence of the array antenna is obtained;

[0009] The array antenna estimated displacement sequence is normalized and divided into a training set and a test set of the estimated displacement sequence;

[0010] The DBO algorithm population is used to initialize the behavior and position of dung beetles;

[0011] Define and calculate the fitness function of the array antenna shape to minimize the reconstruction error;

[0012] Repeatedly iterate and update the behavior and position of dung beetles in the original DBO algorithm;

[0013] Optimize the behavior and position of dung beetles in the iterated and updated DBO algorithm;

[0014] The number of iterations is defined, and the iteration termination condition is determined to be satisfied, so as to obtain the optimal position of the dung beetle in the DBO algorithm, and the initial weight and threshold of the BP neural network are assigned to the optimal position;

[0015] Input the estimated displacement sequence training set into the BP neural network model, and train the assigned BP neural network;

[0016] The estimated displacement sequence test set is input into the trained BP neural network model to obtain the normalized displacement prediction value; the displacement sequence result output by the BP neural network model is denormalized to obtain the predicted displacement sequence.

[0017] Preferably, a finite element model of the array antenna is established using finite element analysis software ANSYS, constraints are imposed on the short sides of the antenna at both ends, and a load is applied along the negative direction of the Z axis to perform modal analysis and extract strain values, displacement modes, strain modes and ideal displacement sequences.

[0018] Preferably, the array antenna estimated displacement sequence is normalized, the data value range of the array antenna estimated displacement sequence is mapped to the range of [0,1], and the mapminmax function in MATLAB is used to perform data normalization operation.

[0019] As a preferred method, the DBO algorithm population is used to initialize the behavior and position of dung beetles, including:

[0020] Assume the solution space is H-dimensional and define the population size G;

[0021] For each dimension j (1≤j≤H), the upper and lower bounds of the solution space are defined as lower d and upper d , divide the interval into U equally spaced subintervals and determine the length of each subinterval;

[0022] For each pair of sample points, calculate the Euclidean distance between them;

[0023] Find the minimum distance between all sample points;

[0024] Set the number of iterations, randomly select two sample points for each iteration, exchange their values ​​at a randomly selected dimension, recalculate the minimum distance between all samples, and if it is larger than the current one, accept the exchange and update d min , after reaching the maximum number of iterations T, the population initialization ends.

[0025] As a preferred method, the behavior and position of the dung beetle in the original DBO algorithm are repeatedly iterated and updated according to the value of the fitness function, and the steps are as follows:

[0026] In the rolling ball behavior in DBO, the variable spiral update mechanism is introduced into the rolling ball behavior of dung beetles;

[0027] The boundary selection strategy is simulated by the way that female dung beetles lay eggs in their areas;

[0028] Determine the location of the chicks, the best foraging areas for baby dung beetles, baby dung beetle location updates, and thieving dung beetle location updates.

[0029] Preferably, the estimated displacement sequence training set is input into the BP neural network model, and the assigned BP neural network is trained, including:

[0030] Input the training set data and get its corresponding target output;

[0031] For the input data x i , the forward propagation process of the BP neural network calculates the output;

[0032] Calculate the prediction error and adjust the weights and thresholds through the error back propagation algorithm.

[0033] The present invention adopts the above technical solution, which has the following beneficial effects:

[0034] The present invention reconstructs a low-precision preliminary estimated displacement sequence of an array antenna through the principle of modal superposition, optimizes the weights and thresholds of a BP neural network using the dung beetle algorithm, and uses the preliminary estimated displacement sequence of the array antenna to train the neural network, thereby obtaining a displacement sequence prediction model that can predict the deformation of the array antenna structure based on the measured strain value. The low-precision problem of nonlinear deformation reconstruction of the array antenna structure is effectively solved, and effective deformation prediction is achieved through the principle of modal superposition and neural networks. The present invention can be applied to the prediction of deformation of the array antenna structure, so that compensation and control strategies can be made in advance for the electrical performance according to the antenna deformation results, providing a guarantee for the performance index requirements of the array antenna during service and operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] The drawings described herein are used to provide a further understanding of the present invention, constitute a part of the present application, and do not constitute an improper limitation of the present invention. In the drawings:

[0036] Figure 1 It is a flow chart of the array antenna deformation prediction method based on the improved mode-DBOBP algorithm of the present invention;

[0037] Figure 2 is the finite element model of the array antenna;

[0038] Figure 3 It is a diagram of the specific steps of the modal method;

[0039] Figure 4 It is the cumulative modal contribution diagram of the first 20 orders;

[0040] Figure 5 It is a variable spiral strategy diagram;

[0041] Figure 6 It is a comparison chart of iteration curves;

[0042] Figure 7 It is a three-dimensional comparison chart of predicted value and true value;

[0043] Figure 8 It is a comparison chart between the improved mode-DBOBP predicted samples and the real samples. DETAILED DESCRIPTION

[0044] The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments. The exemplary embodiments and descriptions of the present invention are used to explain the present invention but are not intended to limit the present invention.

[0045] Reference Figure 1 The present invention is an array antenna deformation prediction method based on an improved modal-DBOBP algorithm, and the specific steps are as follows:

[0046] Step 1: Establish a finite element model of the array antenna, apply constraints and loads to the array antenna, and extract the strain and displacement modes and ideal displacement sequences under different working conditions.

[0047] The finite element model of the array antenna was established using the finite element analysis software ANSYS. Constraints were imposed on the short sides of the antenna at both ends, and loads were applied along the negative direction of the Z axis. Modal analysis was performed to extract strain values, displacement modes, strain modes and ideal displacement sequences.

[0048] Step 2: Based on the modal superposition principle and the strain-displacement conversion relationship, the estimated displacement sequence v of the array antenna is obtained. N×1 for:

[0049] According to the modal superposition principle, the displacement ν at the N predicted target positions can be expressed as:

[0050]

[0051] Where {ε} is the strain value, [ψ] m×n is the strain modal matrix, is the displacement modal matrix, n is the number of sensors, m is the strain modal order, n>>m.

[0052] Step 3: normalize the array antenna estimated displacement sequence and divide it into a training set and a test set.

[0053] The normalized equation is:

[0054]

[0055] Where v(n) represents the estimated displacement sequence reconstructed by the modal method, v min (n) represents the minimum value in the estimated displacement sequence, v max (n) represents the maximum value in the estimated displacement sequence.

[0056] The array antenna estimated displacement sequence data value range is mapped to the range of [0,1] and normalized using the mapminmax function in MATLAB.

[0057] The training set and data set are divided into 7:3 for subsequent optimized BP neural network training and verification of prediction accuracy.

[0058] Step 4: Use the DBO algorithm population to initialize the behavior and position of dung beetles.

[0059] The DBO algorithm uses improved population initialization, that is, Latin hypercube sampling (LHS) based on the maximum and minimum idea to initialize the dung beetle population, which can ensure that the initial population is evenly distributed in the search space. The following are the detailed steps:

[0060] 4.1 Assume the solution space is H-dimensional and define the population size G;

[0061] 4.2 For each dimension j (1≤j≤H), define the upper and lower bounds of the solution space as lower and upper respectively, and divide the interval [lower, upper] into U equally spaced subintervals, each of which has a length of

[0062] 4.3 For each pair of sample points x i and x k (i≠k), calculate the Euclidean distance between them:

[0063]

[0064] Among them, x ij is the sample point x under dimension j i , x kj is the sample point x under dimension j k , find the minimum distance d between all sample points through Euclidean distance min ;

[0065] Find the minimum distance d between all sample points min ;

[0066] 4.4 Set the maximum number of iterations T c , randomly select two sample points x for each iteration i and x k (i≠k), swap their values ​​in a randomly selected dimension j, and recalculate the minimum distance between all samples if Than the current sample distance d min If it is large, accept the exchange and update d min , the population initialization ends after reaching the maximum number of iterations.

[0067] Step 5: define and calculate the fitness function for minimizing the reconstruction error of the array antenna deformation.

[0068] The array antenna deformation minimization reconstruction error uses the mean square error, and its function is:

[0069]

[0070] Among them, (x i ,y i ) is the sampling point coordinate of the displacement field, U c (x i ,y i ) is at the sampling point (x i ,y i ) is the deformation value predicted by the BP neural network, U r (x i ,y i ) is at the sampling point (x i ,y i ) is the actual deformation value at , and L is the total number of sampling points.

[0071] Step 6, repeatedly iterate and update the behavior and position of the dung beetle in the original DBO algorithm.

[0072] 6.1 In the rolling behavior of the original DBO algorithm, there is no clear target guidance. Although this is beneficial to global exploration, it may cause the algorithm to be too random and lack information exchange between individuals, which is not conducive to algorithm convergence in the later stage. Therefore, the variable spiral update mechanism is introduced into the rolling behavior of the dung beetle. The rolling behavior formula of the dung beetle is:

[0073]

[0074] β=e 5·cos(π·(1-t / T))

[0075] Where t is the current iteration number, is the position of the i-th dung beetle in the population at the t-th iteration, is the position of the i-th dung beetle in the population at the t-1th iteration, the constant k∈(0,0.2] is the perturbation coefficient, l is a random number, α∈{-1,1} is the deviation coefficient, 1 means no deviation, -1 means deviation from the original direction, is the optimal individual, X worse is the worst individual, D is the distance vector between the best individual and the current individual, β determines the shape of the spiral line of the individual's spiral advancement, b controls the shape of the spiral line when the individual advances, and usually takes a value of 1. As the iteration proceeds, β will become larger, making the spiral from large to small, and the algorithm will also transition from the early large-scale global exploration to the local development of small spirals.

[0076] 6.2 Dung beetles often roll the ball to a safe location suitable for laying eggs and hide it. The boundary selection strategy is to simulate the egg-laying area of ​​female dung beetles:

[0077]

[0078] In the formula, R = (1-t) / T is the linear factor, T is the maximum number of iterations, Lb and Ub are the lower and upper bounds of the optimization problem variables respectively; is the local optimal position of the current population, Lb * and Ub * Then are the lower and upper bounds of spawning;

[0079] When a female dung beetle determines the egg-laying area, it will lay eggs in that area. Each female dung beetle produces only one chick in each iteration. The position of the chick is determined by the egg-laying area, and the position formula is as follows:

[0080]

[0081] Among them, b1 and b2 are two independent D-dimensional random vectors that obey the normal distribution. is the position at the tth iteration;

[0082] 6.3 When the larvae produced by the female dung beetle hatch, the young dung beetles will go out to look for food. The mathematical expression of the optimal foraging area for the young dung beetles is as follows:

[0083]

[0084] in, is the global optimal position of the current population, Lb g and Ub g They represent the lower and upper bounds of the dung beetle's foraging area. The dung beetle's position is updated as follows:

[0085]

[0086] In the formula, C1 is a random number that obeys the normal distribution, and C2 is a 1×D random vector between (0,1);

[0087] 6.4 In a population, some dung beetles will steal the dung balls of other dung beetles in exchange for free money. When stealing, they usually choose the global optimal position to steal. The position of the stealing dung beetle is updated as follows:

[0088]

[0089] in, is the position of the i-th dung beetle in the population at the t-th iteration, S is a constant, usually taken as 0.5, and g is a D-dimensional random vector that obeys a normal distribution.

[0090] The behaviors and positions of the above-mentioned four types of dung beetles, namely, the rolling ball dung beetle, the small dung beetle, the stealing dung beetle and the brooding ball, are repeatedly iterated and updated to obtain the optimal positions of the current four types of dung beetle behaviors.

[0091] Step 7, optimizing the behavior and position of dung beetles in the iterated and updated DBO algorithm.

[0092] By introducing a elimination mechanism to eliminate and update some poor individuals according to certain rules during each iteration, the diversity of the population is enhanced, the overall fitness of the population is improved to improve the performance of the algorithm in complex problems, and the convergence speed is accelerated. In each iteration, the individuals with poor fitness will be defined as X w , then generate a new individual X based on the best individual and 1 randomly selected individual wnew :

[0093]

[0094] Among them, X wnew For the new individual, X w For poor individuals, X best is the optimal individual, r1 and r2 are random numbers between (0,1), a is the step factor, X rand It is a random individual, and its introduction provides a certain randomness for the generation of new individuals.

[0095] Step 8, define the number of iterations, make sure that the iteration termination condition is met, then get the optimal position of the dung beetle in the DBO algorithm, and assign the optimal position to the initial weight and threshold of the BP neural network.

[0096] The weights and thresholds of the 8.1BP neural network are initialized as and where represents the weight from the i-th node in the input layer to the j-th node in the hidden layer, Indicates the threshold value;

[0097] 8.2 Use the DBO algorithm to iterate and find the optimal solution. In each iteration, the position P of the dung beetle individual k Represents the candidate solution, including the network weight W ij and threshold b i :

[0098]

[0099] 8.3 After the iteration termination condition is met, the DBO algorithm returns the optimal solution Assign it as the initial weight and threshold of the BP neural network:

[0100]

[0101] Step 9, input the estimated displacement sequence training set into the BP neural network model, and train the assigned BP neural network.

[0102] 9.1 Input training set data X = {x1, x2, ..., x n}, and its corresponding target output is Y = {y1,y2,…,y n};

[0103] 9.2 For input data x i , the forward propagation process of the BP neural network calculates the output

[0104]

[0105] 9.3 Adjust the weights and thresholds through the error back propagation algorithm. The error back propagation formula is as follows:

[0106]

[0107] Step 10, input the estimated displacement sequence test set into the trained BP neural network model to obtain the normalized displacement prediction value; denormalize the displacement sequence result output by the BP neural network model to obtain the predicted displacement sequence.

[0108] The anti-normalized equation is:

[0109] V'(n)=(Y[n]×(v max [n]-v min [n]))+v min [n]

[0110] Among them, Y(n) represents the displacement sequence predicted by BP neural network, x min (n) represents the minimum value in the estimated displacement sequence, x max (n) represents the maximum value in the estimated displacement sequence; the predicted data value range is mapped to the original data set range, and the mapminmax function in MATLAB is used for denormalization, and the value of V'(n) is the predicted value of the array antenna deformation prediction model.

[0111] The advantages of the present invention can be further illustrated by the following simulation experiments:

[0112] 1. Through finite element analysis of the array antenna structure model, the static analysis strain values ​​under different working conditions are extracted, and the displacement mode and strain mode of modal analysis are performed.

[0113] In this embodiment, the finite element analysis software ANSYS is used to establish the finite element model of the array antenna. The material properties are: elastic modulus 70GPa, Poisson's ratio 0.3, density 100.4kg / m 3 The unit type is shell63. The finite element model has 702 units and 385 nodes. Constraints are applied to the short sides of the antenna at both ends, and loads are applied along the negative direction of the Z axis to perform modal analysis. The finite element model of the array antenna is as follows: Figure 2 shown.

[0114] 2. Based on the modal superposition principle and the strain-displacement conversion relationship, the estimated displacement sequence of the array antenna is obtained.

[0115] The specific steps of the modal superposition principle and strain-displacement conversion relationship are as follows: Figure 3 As shown, Figure 4 The cumulative modal contributions of the first 20 orders are given, and it can be seen that the cumulative modal contributions of the first 16 orders have reached 90%, so the first 16 order modal information is selected for reconstructed displacement calculation.

[0116] 3. Repeatedly iterate and update the behavior and position of dung beetles in the original DBO algorithm.

[0117] This method selects a population size of 30, a number of rolling dung beetles of 6, a number of female dung beetles of 6, a number of small dung beetles of 7, a number of stealing dung beetles of 11, an upper limit of 3, a lower limit of -3, a maximum number of iterations of 50, and uses Latin hypercube based on the maximum and minimum idea to initialize the population. The array antenna displacement sequence obtained by the modal method is normalized; the BP neural network is trained using the normalized displacement sequence, and the weights and deviations of the training network are optimized by the dung beetle algorithm until the accuracy of the fitness function is met.

[0118] Table 1 Algorithm operations corresponding to dung beetle habits

[0119]

[0120] In the rolling behavior of the original DBO algorithm, there is no clear target guidance. Although this is beneficial to global exploration, it may cause the algorithm to be too random and lack information exchange between individuals, which is not conducive to algorithm convergence in the later stage. Therefore, a variable spiral update mechanism is introduced into the rolling behavior of dung beetles. The variable spiral search strategy is as follows Figure 5 As shown, the fitness curves of the improved mode-DBOBP model and the unimproved mode-DBOBP model are as follows Figure 6 As shown, it can be seen that the improved model works well in the iterative process.

[0121] 4. Optimize the behavior and position of dung beetles in the iterated and updated DBO algorithm.

[0122] By eliminating and updating some poor individuals according to certain rules during each iteration, the diversity of the population is enhanced, the overall fitness of the population is improved to improve the performance of the algorithm in complex problems and accelerate the convergence speed. In each iteration, the individuals with poor fitness will be defined as X w , then generate a new individual X based on the best individual and 1 randomly selected individual wnew .

[0123] 5. Assign the optimal position to the initial weight and threshold of the BP neural network, and input the normalized array antenna displacement estimation training set and test set to train and predict the BP neural network.

[0124] Normalization and denormalization can be processed using the mapminmax function, and the dung beetle algorithm is used to assign initial weights and thresholds to the BP neural network. The training set data is then used to train the mapping relationship, adjust the number of neurons and the number of hidden layers, and finally obtain a trained BP neural network prediction model. The true value, the improved modal-DBOBP model (abbreviated as ZYDBOBP), the unimproved modal-DBOBP model, and the BP model prediction value deformation results are plotted in the same coordinate system for comparison, such as Figure 7 and Figure 8 As shown in Table 2, it can be seen that the prediction effect is good. Further error analysis is performed on the true value and predicted value data.

[0125] Table 2 Performance indicators of the prediction set

[0126]

[0127] 6. Results Analysis

[0128] From the above experiments, it can be seen that the application of the present invention to perform modal superposition and neural network prediction on the deformation of the array antenna has a good prediction effect on the deformation of the array antenna structure, and the four accuracy indicators of mean absolute error, root mean square error, mean square error and mean absolute percentage error are all within an acceptable range. Therefore, based on the improved modal-DBOBP model, the present invention can predict the deformation of the array antenna structure for antennas, radars, etc. working under various complex environmental conditions, and can then compensate and regulate the electrical performance of the entire array antenna in advance.

[0129] The present invention is not limited to the above-mentioned embodiments. On the basis of the technical solution disclosed in the present invention, technicians in this field can make some substitutions and deformations to some technical features therein according to the disclosed technical content without creative labor, and these substitutions and deformations are all within the protection scope of the present invention.

Claims

1. A method for predicting deformation of an array antenna based on an improved modal-DBOBP algorithm, characterized in that: include: Establish a finite element model of the array antenna, apply constraints and loads to the array antenna, extract the strain and displacement modes under different working conditions, and the ideal displacement sequence; Based on the modal superposition principle and the strain-displacement conversion relationship, the estimated displacement sequence of the array antenna is obtained; The array antenna estimated displacement sequence is normalized and divided into a training set and a test set of the estimated displacement sequence; The DBO algorithm population is used to initialize the behavior and position of dung beetles; Define and calculate the fitness function of the array antenna shape to minimize the reconstruction error; Repeatedly iterate and update the behavior and position of dung beetles in the original DBO algorithm; Optimize the behavior and position of dung beetles in the iterated and updated DBO algorithm; The number of iterations is defined, and the iteration termination condition is determined to be satisfied, so as to obtain the optimal position of the dung beetle in the DBO algorithm, and the initial weight and threshold of the BP neural network are assigned to the optimal position; Input the estimated displacement sequence training set into the BP neural network model, and train the assigned BP neural network; Input the estimated displacement sequence test set into the trained BP neural network model to obtain the normalized displacement prediction value; The displacement sequence results output by the BP neural network model are denormalized to obtain the predicted displacement sequence.

2. The array antenna deformation prediction method based on the improved modal-DBOBP algorithm according to claim 1, characterized in that: The finite element model of the array antenna was established using the finite element analysis software ANSYS. Constraints were imposed on the short sides of the antenna at both ends, and loads were applied along the negative direction of the Z axis. Modal analysis was performed to extract strain values, displacement modes, strain modes and ideal displacement sequences.

3. The array antenna deformation prediction method based on the improved modal-DBOBP algorithm according to claim 1, characterized in that: Based on the modal superposition principle and the strain-displacement conversion relationship, the estimated displacement sequence ν of the array antenna is obtained. N×1 for: Where {ε} is the strain value, [ψ] m×n is the strain modal matrix, is the displacement modal matrix, n is the number of sensors, m is the strain modal order, n>>m.

4. The method for predicting deformation of an array antenna based on an improved modal-DBOBP algorithm according to claim 1, characterized in that: The array antenna estimated displacement sequence is normalized, and the data value range of the array antenna estimated displacement sequence is mapped to the range of [0,1]. The mapminmax function in MATLAB is used to perform data normalization. The normalization equation is: Where v(n) represents the estimated displacement sequence of the array antenna reconstructed by the modal method, v min (n) represents the minimum value in the estimated displacement sequence, v max (n) represents the maximum value in the estimated displacement sequence.

5. The array antenna deformation prediction method based on the improved modal-DBOBP algorithm according to claim 1, characterized in that: The DBO algorithm population is used to initialize the behavior and position of dung beetles, including: (a) Assume the solution space is H-dimensional and define the population size G; (b) For each dimension j, 1≤j>H, define the upper and lower bounds of the solution space as lower and upper respectively, and divide the interval [lower,upper] into U equally spaced subintervals, each of which has a length of (c) For each pair of sample points x i and x k (i≠k), calculate the Euclidean distance d between them ik : Among them, x ij is the sample point x under dimension j i , x kj is the sample point x under dimension j k , find the minimum distance d between all sample points through Euclidean distance min ; (d) Set the number of iterations T and randomly select two sample points x for each iteration. i and x k , swap their values ​​in a randomly selected dimension j and recalculate the minimum distance between all samples if Than the current sample distance d min If it is large, accept the exchange and update d min , after reaching the maximum number of iterations T, the population initialization ends.

6. The method for predicting deformation of an array antenna based on an improved modal-DBOBP algorithm according to claim 1, characterized in that: The fitness function MSE of array antenna deformation minimizing weight error is: Among them, (x i ,y i ) is the sampling point coordinate of the displacement field, U c (x i ,y i ) is at the sampling point (x i ,y i ) is the deformation value predicted by the BP neural network, U r (x i ,y i ) is at the sampling point (x i ,y i ) is the actual deformation value at , and L is the total number of sampling points.

7. The method for predicting deformation of an array antenna based on an improved modal-DBOBP algorithm according to claim 1, characterized in that: According to the value of the fitness function, the behavior and position of the dung beetle in the original DBO algorithm are repeatedly iterated and updated. The steps are as follows: (a) In the rolling ball behavior in DBO, the variable spiral update mechanism is introduced into the rolling ball behavior of the dung beetle: in, is the position of the i-th dung beetle in the population at the t-th iteration, is the position of the i-th dung beetle in the population at the t-1th iteration, k is the perturbation coefficient, l is a random number, α is the deviation coefficient, is the optimal individual, X worse is the worst individual, D is the distance vector between the best individual and the current individual, and β is the shape of the spiral line of the individual's spiral progress; (b) The boundary selection strategy is to simulate the egg-laying area of ​​female dung beetles: Among them, R = (1-t) / T is the linear factor, T is the maximum number of iterations, Lb and Ub are the lower and upper bounds of the optimization problem variables respectively; is the local optimal position of the current population, Lb * and Ub * Then are the lower and upper bounds of spawning; Determine the location of the chicks: Among them, b1 and b2 are two independent D-dimensional random vectors that obey the normal distribution. is the position at the tth iteration; (c) Determine the best foraging areas for dung beetles: in, is the global optimal position of the current population, Lb g and Ub g They represent the lower and upper limits of the foraging area of ​​the small dung beetle, respectively; Determine the location update of the dung beetle: Among them, C1 is a random number that obeys the normal distribution, and C2 is a 1×D random vector between (0,1); (d) Determine the location update of the stealing dung beetle: in, is the position of the i-th dung beetle in the population at the t-th iteration, S is a constant, and g is a D-dimensional random vector that follows a normal distribution.

8. The array antenna deformation prediction method based on the improved modal-DBOBP algorithm according to claim 1, characterized in that: The behavior and position of dung beetles in the iterated and updated DBO algorithm are optimized, and a new individual X is generated based on the best individual and a randomly selected individual. wnew : Among them, X wnew For the new individual, X w For poor individuals, X best is the optimal individual, r1 and r2 are random numbers between (0,1), a is the step factor, X rand is a random individual, T is the maximum number of iterations, and t is the number of iterations.

9. The array antenna deformation prediction method based on the improved modal-DBOBP algorithm according to claim 1, characterized in that: Input the estimated displacement sequence training set into the BP neural network model, and train the assigned BP neural network, including: (a) Input training set data X = {x1, x2, ..., x n }, and its corresponding target output is Y = {y1,y2,…,y n }; (b) For input data x i , the forward propagation process of the BP neural network calculates the output Among them, h j represents the output of the jth neuron in the hidden layer, represents the predicted output of the kth output node, x i Represents the first i Features, and Corresponding to the jth and k The initial bias of the nodes, and represents the initial weights between different nodes, f(·) is the activation function, n is the number of sensors, and m is the strain modal order; (c) The weights and thresholds are adjusted through the error back propagation algorithm. The error back propagation formula is as follows: Where, ΔW ij represents the weight adjustment of η, Δb i represents the bias adjustment, η is the learning rate, and are the differentials of the error E with respect to the weight and bias, respectively.

10. The array antenna deformation prediction method based on the improved modal-DBOBP algorithm according to claim 1, characterized in that: Map the predicted data value range to the original data set range, and use the mapminmax function in MATLAB to denormalize it. The predicted value V'(n) of the array antenna deformation prediction model is: V'(n)=(Y[n]×(v max [n]-v min [n]))+v min [n] Among them, Y(n) represents the displacement sequence predicted by BP neural network, v min [n] represents the minimum value in the estimated displacement sequence, v max [n] represents the maximum value in the estimated displacement sequence.

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