Stealth aircraft dynamic RCS sequence prediction method based on AVMD-BiLSTM model

Abstract

The application provides a stealth aircraft dynamic RCS sequence prediction method based on an AVMD-BiLSTM model, and relates to the technical field of aircraft radar stealth. The application establishes a 3D model of a stealth aircraft, solves a full-space static RCS database of the stealth aircraft under HH and VV polarization modes, and obtains a dynamic RCS sequence of the stealth aircraft under a steady circling flight path; an adaptive variational mode decomposition method AVMD is proposed, the dynamic RCS sequence is decomposed, an optimal decomposition scale K is obtained, and each mode component after decomposition is obtained; each mode component obtained through decomposition is input into a bidirectional long short-term memory network BiLSTM, K BiLSTM network prediction models are finally obtained, and the obtained prediction results are added and reconstructed to obtain the final prediction result of the dynamic RCS.

Description

TECHNICAL FIELD

[0001] The application relates to the field of aircraft radar stealth technology, and in particular to a stealth aircraft dynamic RCS sequence prediction method based on an AVMD-BiLSTM model. BACKGROUND

[0002] The dynamic RCS of an aircraft is affected by the frequency, polarization mode and attitude angle change of a radar incident wave, which leads to the complex fluctuation characteristics of the dynamic RCS of the aircraft, and the traditional dynamic RCS estimation method can only roughly estimate the change trend of the RCS and cannot accurately estimate the dynamic RCS value.

[0003] In summary, in order to more effectively evaluate the dynamic RCS of a stealth aircraft, a more accurate method needs to be proposed to accurately estimate the dynamic RCS sequence of the stealth aircraft. SUMMARY

[0004] In view of the deficiencies of the prior art, the application provides a stealth aircraft dynamic RCS sequence prediction method based on an AVMD-BiLSTM model, so as to accurately estimate the dynamic RCS sequence of the stealth aircraft and more effectively analyze the radar stealth characteristics of the stealth aircraft.

[0005] A stealth aircraft dynamic RCS sequence prediction method based on an AVMD-BiLSTM model comprises the following steps:

[0006] Step 1: modeling software is used to model the stealth aircraft, and a 3D model of the stealth aircraft is established;

[0007] Step 2: electromagnetic needle software is used to solve the full-space static RCS database of the stealth aircraft under HH and VV polarization modes;

[0008] Step 3: based on the full-space static RCS database in step 2, the dynamic RCS sequence of the stealth aircraft under the constant circling flight path is obtained;

[0009] Step 4: the VMD (Variational Modal Decomposition) method is improved, and the AVMD (Adaptive Variational Modal Decomposition) method is proposed;

[0010] The mathematical expression of the VMD (Variational Modal Decomposition) method is as follows:

[0011]

[0012] In the formula, K is the number of modes to be decomposed, that is, the decomposition scale, K is a positive integer, and σ t represents Gaussian smoothing calculation, j is a symbol of an imaginary number, t is a time axis, {u k} and {ω k} are the sets of modal components and central frequencies after decomposition respectively, u k is the modal component after decomposition, ω k is the central frequency, x is the original signal, δ(t) is the unit impulse function, u k (t) is the sequence after modal decomposition, s represents the Fourier transform;

[0013] In the VMD method, the ratio of residual energy to original signal energy is introduced as a decomposition scale criterion, which can set the decomposition scale according to the signal itself, and the criterion is as follows.

[0014]

[0015] In the formula, f is the original sequence, N is the sequence length, and MAPE is the evaluation index. When MAPE≤1%, the final modal decomposition number is determined.

[0016] Step 5: using the adaptive VMD method AVMD to decompose the dynamic RCS sequence obtained in step 3, to obtain the optimal decomposition scale K, and to obtain the decomposed modal components;

[0017] Step 6: inputting each modal component obtained by decomposition into a bidirectional long short-term memory network BiLSTM, and dividing the training set and the test set according to the input sequence length setting ratio, wherein the training set is used for data samples for model fitting, and the training error is gradient descended in the training process, learning, and the weight parameters can be trained, the test set is used to evaluate the generalization ability of the final model, and finally K BiLSTM network prediction models are obtained;

[0018] The bidirectional long short-term memory network BiLSTM is stacked by two LSTM networks, which are forward propagation layer and backward propagation layer, and the output result is determined by the two LSTM networks together;

[0019] In the forward propagation layer, the output H′ t of the current memory cell is determined by the current input X t and the output H′ t-1 of the t-1 time step, and after calculation, the output is stored for the calculation of the next time step and the calculation of the output layer.

[0020] H′ t =LSTM forw (X t ,H′ t-1 ,C′ t-1 ) (3)

[0021] In the formula, LSTM forw () represents forward propagation calculation, C′ t-1denotes the state of the memory cell at the previous time step.

[0022] At the backward propagation layer, the output H t of the current memory cell is determined by the current input X t and the output H t+1 at the t+1 time step.

[0023] H t = LSTM back (X t ,H t+1 ,C t+1 ) (4)

[0024] where LSTM back () denotes the backward propagation calculation, and C t+1 denotes the state of the memory cell at the next time step.

[0025] The output Yt of the final model is determined by the output results of the forward propagation layer and the backward propagation layer, i.e.

[0026] Y t = Sig(W s ·H′ t +W o ·H t ) (5)

[0027] where Sig() is a logistic S (Sigmoid) function, W s denotes the weight of the forward propagation hidden layer to the output layer, and W o denotes the weight of the backward propagation hidden layer to the output layer.

[0028] Step 7: Finally, the prediction results of the K BiLSTM network prediction models are summed and reconstructed to obtain the final prediction result of the dynamic RCS.

[0029] The beneficial effects produced by the above technical scheme are as follows:

[0030] The application provides a stealth aircraft dynamic RCS sequence prediction method based on an AVMD-BiLSTM model, which decomposes the original dynamic RCS sequence of the stealth aircraft in the frequency domain through AVMD to obtain signals of different frequencies, predicts the decomposed signals through a BiLSTM network, sums and reconstructs the prediction results to obtain the final dynamic RCS sequence prediction result. The method can effectively improve the prediction accuracy of the dynamic RCS sequence of the stealth aircraft, so as to better analyze the stealth characteristics of the aircraft.

[0031] The method can be applied to dynamic RCS prediction of different types of aircraft under different incident radar wave frequencies and different flight paths. BRIEF DESCRIPTION OF DRAWINGS

[0032] Figure 1 is a flowchart of a dynamic RCS sequence prediction method of a stealth aircraft provided by an embodiment of the present application;

[0033] Figure 2 is a dynamic RCS sequence of an F-22 aircraft in VV and HH polarization modes in a VHF frequency band provided by an embodiment of the present application;

[0034] wherein Fig. (a) is a dynamic RCS sequence in a VV polarization mode, and Fig. (b) is a dynamic RCS sequence in a HH polarization mode;

[0035] Figure 3 is a dynamic RCS sequence of an FA-XX aircraft in VV and HH polarization modes in a VHF frequency band provided by an embodiment of the present application;

[0036] wherein Fig. (a) is a dynamic RCS sequence in a VV polarization mode, and Fig. (b) is a dynamic RCS sequence in a HH polarization mode;

[0037] Figure 4 is a dynamic RCS sequence of an F-35 aircraft in VV and HH polarization modes in a VHF frequency band provided by an embodiment of the present application;

[0038] wherein Fig. (a) is a dynamic RCS sequence in a VV polarization mode, and Fig. (b) is a dynamic RCS sequence in a HH polarization mode;

[0039] Figure 5 is a prediction result of an AVMD-BiLSTM model on a dynamic RCS sequence of an F-22 aircraft in a HH polarization provided by an embodiment of the present application;

[0040] Figure 6 is a prediction result of an AVMD-BiLSTM model on a dynamic RCS sequence of an FA-XX aircraft in a HH polarization provided by an embodiment of the present application;

[0041] Figure 7 is a prediction result of an AVMD-BiLSTM model on a dynamic RCS sequence of an F-35 aircraft in a HH polarization provided by an embodiment of the present application;

[0042] Figure 8 is a prediction result of an AVMD-BiLSTM model on a dynamic RCS sequence of an F-22 aircraft in a VV polarization provided by an embodiment of the present application;

[0043] Figure 9 is a prediction result of an AVMD-BiLSTM model on a dynamic RCS sequence of an FA-XX aircraft in a VV polarization provided by an embodiment of the present application;

[0044] Figure 10This is the prediction result of the AVMD-BiLSTM model provided in an embodiment of the present invention for the dynamic RCS sequence of the F-35 aircraft under VV polarization. DETAILED DESCRIPTION

[0045] The following embodiments of the present invention are described in further detail with reference to the accompanying drawings and examples. The following examples are used to illustrate the present invention but are not intended to limit the scope of the present invention.

[0046] A stealth aircraft dynamic RCS sequence prediction method based on AVMD-BiLSTM model, such as Figure 1 As shown, the following steps are included:

[0047] Step 1: Use modeling software to model the stealth aircraft and create a 3D model of the stealth aircraft. In this embodiment, the modeling software uses CATIA software, and the stealth aircraft are F-22, F-35 and FA-XX.

[0048] For complex, large-scale targets like aircraft, their RCS is largely determined by their external structure. During the modeling process, specialized modeling software can more accurately reflect the detailed structure of the target model, thereby improving the accuracy of the RCS simulation data. CATIA software, recognized for its powerful surface design capabilities, was used to build the target model. CATIA's freeform surface and generative shape design modules are highly specialized in surface modeling. Data for target modeling was sourced from the internet and publicly available literature. During modeling, the aircraft's three-view drawing was first imported into the freeform surface design module, and key feature lines for each component were drawn based on these three views. The feature lines were then filled and swept using the generative shape design module to complete the aircraft's 3D model.

[0049] Step 2: Use FEKO electromagnetic simulation software to solve the full airspace static RCS database of the stealth aircraft in both HH and VV polarization modes;

[0050] FEKO software is easier to use, with multiple built-in solvers suitable for electromagnetic simulation calculations in various frequency bands. FEKO also features script editing capabilities, allowing scripts to be written as needed. It also supports CPU multi-core parallelism and GPU acceleration, greatly improving computational efficiency. In FEKO, the signal source is set to a plane wave, the incident wave frequency is set to 300MHz, the pitch angle is set to 0-180°, the azimuth angle is set to 0-360°, the step angle is set to 1°, and the ray tracing geometric optics method (RL-GO) is selected as the solver to solve for the full-space static RCS.

[0051] Step 3: Based on the full airspace static RCS database in step 2, obtain the dynamic RCS sequence of the stealth aircraft under the steady circling trajectory;

[0052] The steady spiral flight path is commonly used for testing the dynamic RCS of an aircraft. First, the maneuvering flight path of a stealth aircraft is established, the coordinate system is converted, and the attitude angle of the radar line of sight in the body coordinate system is solved. In space, let any point P be the position of the radar, which is represented by rectangular coordinates in the radar coordinate system as (x p ,y p ,z p ), and the target is regarded as a particle. Then the flight path coordinates of the aircraft in the radar coordinate system are represented by rectangular coordinates as (x b (t),y b (t),z b (t)). Then the coordinates of point P in the target body coordinate system are represented by (x1(t),y1(t),z1(t)). According to the principle of coordinate transformation, the position coordinates of the radar in the radar coordinate system (x p (t),y p (t),z p (t)) are converted to the body coordinate system, and the converted coordinates are represented as (x1(t),y1(t),z1(t)). The conversion matrix of the radar coordinate system to the body coordinate system is as shown in the following formula.

[0053]

[0054] The position coordinates of the radar coordinate system converted to the position coordinates of the body coordinate system are

[0055]

[0056] where α, γ and η are the yaw angle, pitch angle and roll angle, respectively.

[0057] According to the converted real-time position coordinates of the target, the azimuth angle and the pitch angle θ(t) of the radar line of sight in the target body coordinate system are solved.

[0058]

[0059] The solved attitude angles are combined with the full-space RCS database to obtain the dynamic RCS sequence of the three-type aircraft, as shown in Figure 2 , Figure 3 , Figure 4 . The statistical characteristics of the dynamic RCS of the three-type aircraft are shown in the following table.

[0060] Table 1 Statistical characteristics of the dynamic RCS of the three-type aircraft

[0061]

[0062] Step 4: On the basis of the variational mode decomposition method VMD, an adaptive variational mode decomposition method AVMD is proposed, which overcomes the shortcoming of signal loss in the decomposition process of VMD;

[0063] Variational mode decomposition (VMD) is an adaptive, completely non-recursive mode variational and signal processing method. This technology has good adaptability, can determine the number of mode decomposition of the given sequence according to the actual situation, and can adaptively match the best center frequency and limited bandwidth of each mode in the subsequent search and solution process, and can realize effective separation of intrinsic mode function (IMF) and division of signal frequency domain, and then obtain the effective decomposition components of the given signal, and finally obtain the optimal solution of the variational problem.

[0064] The mathematical expression of the variational mode decomposition method VMD is as follows:

[0065]

[0066] In the formula, K is the number of modes to be decomposed, that is, the decomposition scale, K is a positive integer, and σ t represents Gaussian smoothing calculation, j is a symbol of imaginary number, t is a time axis, {u k} and {ω k} are the sets of decomposed modal components and center frequencies respectively, u k is the decomposed modal component, ω k is the center frequency, x is the original signal, δ(t) is the unit impulse function, u k (t) is the sequence after modal decomposition, and s represents Fourier transform.

[0067] VMD needs to manually set the number of modal decomposition K in the decomposition process. At present, the number of decomposition K is mainly judged according to whether the center frequency of modal decomposition is stable. This behavior of setting the decomposition scale according to experience seriously limits the adaptability of the VMD method, because a large deviation of the number of modal decomposition will lead to signal loss or modal confusion, and cannot be well applied to signal analysis of dynamic RCS sequence. In the variational mode decomposition method VMD, the ratio of residual energy to original signal energy is introduced as a decomposition scale criterion, which can set the decomposition scale autonomously according to the signal itself, and the criterion is as follows.

[0068]

[0069] In the formula, f is the original sequence, N is the length of the sequence, and MAPE is an evaluation index. When MAPE≤1%, the final number of modal decomposition is determined.

[0070] Step 5: Use the adaptive variational mode decomposition method AVMD to decompose the dynamic RCS sequence obtained in step 3 to obtain the optimal decomposition scale K, thereby obtaining the decomposed modal components;

[0071] Step 6: Input each modal component obtained by decomposition into the bidirectional long short-term memory network BiLSTM, and divide the training set and test set into a ratio of 7:3 according to the input sequence length. The training set is used as the data sample for model fitting. During the training process, the training error is gradient-decreased to learn the trainable weight parameters. The test set is used to evaluate the generalization ability of the final model, and finally obtain K BiLSTM network prediction models.

[0072] The bidirectional long short-term memory network BiLSTM is composed of two LSTM networks superimposed, namely the forward propagation layer and the reverse propagation layer, and the output result is jointly determined by the two LSTM networks;

[0073] In the forward propagation layer, the output H′ of the current memory cell t By the current input X t and the output H′ at time step t-1 t-1 After the calculation, the output is stored and used for the calculation of the next time step and the calculation of the output layer.

[0074] H′ t =LSTM forw (X t ,H′ t-1 ,C′ t-1 )

[0075] Where, LSTM forw () represents the forward propagation calculation, C′ t-1 Indicates the state of the memory cell at the previous moment.

[0076] In the back propagation layer, the output H of the current memory cell t By the current input X t and the output H at time step t+1 t+1 Decide.

[0077] H t =LSTM back (X t ,H t+1 ,C t+1 )

[0078] Where, LSTM back () indicates the back propagation calculation, C t+1 Indicates the state of the memory cell at the next moment.

[0079] The output Yt of the final model is determined by the output results of the forward propagation layer and the back propagation layer, that is

[0080] Y t = Sig(W s ·H′ t +W o ·H t )

[0081] In the formula, Sig() is a logical S (Sigmoid) function, W s represents the weight value of the forward propagation hidden layer to the output layer, and W o represents the weight value of the back propagation hidden layer to the output layer.

[0082] Step 7: Finally, the prediction results of the K BiLSTM network prediction models are summed and reconstructed to obtain the final prediction result of the dynamic RCS.

[0083] In the embodiment, four prediction models of BiLSTM, VMD-BiLSTM and AVMD-BiLSTM are applied to predict the dynamic RCS sequence, and the prediction results are analyzed by using model evaluation indexes. The final prediction results of the dynamic RCS sequence of the stealth aircraft are shown in Figure 5 、 6 , 7, 8, 9 and 10.

[0084] The model evaluation indexes MAE, MAPE, RMSE and R 2 The prediction accuracy of the three prediction models is evaluated, and the error statistics are shown in the following table.

[0085] Table 2 MAE, MAPE and RMSE error statistics

[0086]

[0087]

[0088] R 2 The statistical table is shown as follows.

[0089] Table 3 R 2 statistics table of three models

[0090]

[0091] According to the prediction error and the coefficient of determination statistical table of the three models for different data sets, it can be seen that the error of the AVMD-BiLSTM dynamic RCS prediction model proposed in the application is greatly reduced compared with the single BiLSTM model and the VMD-BiLSTM model, and the R 2The value is closer to 1. In order to more intuitively reflect the prediction accuracy of the AVMD-BiLSTM model compared with the other two models, the error reduction ratios of MAE, MAPE and RMSE under different data sets are calculated and compared in this paper. As shown in Tables 4 and 5.

[0092]

[0093] According to the above table, taking the Case1 data as an example, the MAE of the proposed AVMD-BiLSTM model is reduced by 74.86% and 56.74% compared with the single BiLSTM model and the VMD-BiLSTM model respectively; the MAPE is reduced by 84.43% and 71.66% respectively; and the RMSE is reduced by 42.91% and 7.95% respectively. The other five groups of data also have a large error reduction. According to the calculation, the average MAE reduction ratio of AVMD-BiLSTM compared with the single BiLSTM model and the VMD-BiLSTM model is 79.54% and 56.59% respectively, the average MAPE reduction ratio is 77.85% and 58.00% respectively, and the average RMSE reduction ratio is 63.24% and 24.37% respectively. From the above data, it can be seen that after introducing VMD based on the BiLSTM model, the prediction accuracy compared with the single BiLSTM network model has been improved, and the AVMD-BiLSTM model further improves the prediction accuracy on the basis of the two.

[0094] The above description is only the preferred embodiments of the present disclosure and the explanation of the applied technical principles. Those skilled in the art should understand that the scope of the application involved in the embodiments of the present disclosure is not limited to the technical solutions formed by the specific combinations of the above technical features, and should also cover other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the above inventive concept. For example, the above features are replaced with the technical features disclosed in the embodiments of the present disclosure (but not limited to) having similar functions to form technical solutions.

Claims

1. A method for predicting dynamic RCS sequences of stealth aircraft based on the AVMD-BiLSTM model, characterized in that: The following steps are involved: Step 1: Use modeling software to model the stealth aircraft and establish a 3D model of the stealth aircraft; Step 2: Use electromagnetic guidance software to solve the full airspace static RCS database of the stealth aircraft in both HH and VV polarization modes; Step 3: Based on the full airspace static RCS database in step 2, obtain the dynamic RCS sequence of the stealth aircraft under the steady circling trajectory; Step 4: Based on the variational mode decomposition method VMD, an adaptive variational mode decomposition method AVMD is proposed; Step 5: Use the adaptive variational mode decomposition method AVMD to decompose the dynamic RCS sequence obtained in step 3 to obtain the optimal decomposition scale K, thereby obtaining the decomposed modal components; Step 6: Input each modal component obtained by decomposition into the bidirectional long short-term memory network BiLSTM, and divide the training set and test set into the ratio according to the input sequence length, and finally obtain K BiLSTM network prediction models; Step 7: Finally, the prediction results of the K BiLSTM network prediction models are added and reconstructed to obtain the final dynamic RCS prediction result.

2. The method for predicting dynamic RCS sequence of stealth aircraft based on AVMD-BiLSTM model according to claim 1 is characterized in that: The mathematical expression of the variational mode decomposition method VMD described in step 4 is as follows: Where K is the number of modes to be decomposed, that is, the decomposition scale, K is a positive integer, σ t Indicates Gaussian smoothing calculation, j is the symbol of imaginary number, t is the time axis, {u k } and {ω k } are the sets of modal components and center frequencies after decomposition, u k is the modal component after decomposition, ω k is the center frequency, x is the original signal, δ(t) is the unit pulse function, u k (t) is the sequence after modal decomposition, s represents Fourier transform; In the variational mode decomposition method VMD, the ratio of residual energy to original signal energy is introduced as the decomposition scale criterion, so that the decomposition scale can be set independently according to the signal itself. The criterion is shown in the following formula: Where f is the original sequence, N is the sequence length, MAPE is the evaluation index, and when MAPE ≤ 1%, the final modal decomposition number is determined.

3. The method for predicting dynamic RCS sequence of stealth aircraft based on AVMD-BiLSTM model according to claim 1, characterized in that: The bidirectional long short-term memory network BiLSTM described in step 6 is composed of two LSTM networks superimposed, one for the forward propagation layer and the other for the backward propagation layer. The output result is jointly determined by the two LSTM networks. In the forward propagation layer, the output H of the current memory cell t ′ is determined by the current input X t and the output H at time step t-1 t ' -1 After the calculation, the output is stored and used for the calculation of the next time step and the calculation of the output layer; H t ′=LSTM forw (X t ,H t ′ -1 ,C t ′ -1 ) (3) Where, LSTM forw () indicates forward propagation calculation, C t ' -1 Indicates the state of the memory cell at the previous moment; In the back propagation layer, the output H of the current memory cell t By the current input X t and the output H at time step t+1 t+1 Decide; H t =LSTM back (X t ,H t+1 ,C t+1 ) (4) Where, LSTM back () indicates the back propagation calculation, C t+1 Indicates the state of the memory cell at the next moment; The output Yt of the final model is determined by the output results of the forward propagation layer and the back propagation layer, that is, Y t =Sig(W s ·H t ′+W o ·H t ) (5) Where Sig() is the logistic sigmoid function, W s Represents the weight of the forward propagation from the hidden layer to the output layer, W o Represents the weights of backpropagation from the hidden layer to the output layer.

4. The method for predicting dynamic RCS sequence of stealth aircraft based on AVMD-BiLSTM model according to claim 1, characterized in that: The training set described in step 6 is used as a data sample for model fitting. During the training process, the training error is gradient-decreased to learn and train the weight parameters. The test set is used to evaluate the generalization ability of the final model.

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