Method and device for accelerating multi-angle single-station RCS iterative solution and storage medium

Abstract

The invention discloses a method and equipment for accelerating multi-angle single-station RCS (Radar Cross Section) iterative solution and a storage medium, and aims to relieve the problem that iterative solution consumes too long time when a moment method is used for multi-angle RCS simulation. The method comprises the following steps: firstly, acquiring a group of historical convergence current solution sequences corresponding to initial incidence angles, preprocessing the historical convergence current solution sequences, and constructing an initial observation sequence of an autoregression model; secondly, aiming at a new incident angle, estimating an autoregression coefficient by utilizing a Burg algorithm based on an observation sequence, and predicting an iteration initial value of a current angle; finally, the initial value is applied to an iterative solver to accelerate convergence. Compared with a traditional phase correction initial value guessing method, the predicted initial value is closer to an iterative convergence solution, and therefore the number of iterations and the solving time are remarkably reduced. In addition, the additional calculation complexity introduced for predicting each initial value is only low, and the compatibility is good.

Description

Technical Field

[0001] This invention relates to the field of radar cross section (RCS) analysis technology, and in particular to a method for accelerating multi-angle single-station RCS iterative solution based on initial value prediction using an autoregressive (AR) model. Background Technology

[0002] Multi-angle monostatic RCS simulation is an essential step in analyzing target scattering characteristics and conducting stealth design. The Method of Moments (MoM) is widely used as an effective means of accurately analyzing the electromagnetic scattering characteristics of targets. However, when using MoM in conjunction with an iterative solver to solve monostatic RCS, the iterative solution process of the matrix equations needs to be restarted for each incident angle when the incident angle changes. Therefore, when dense angular scanning of the target is required, the overall computational cost becomes very high.

[0003] Existing techniques for accelerating iterative solutions can be mainly categorized into several types: (1) preprocessing techniques, such as incomplete LU (ILU) decomposition and sparse approximate inverse (SAI) preprocessing; (2) fast algorithms, such as the multilevel fast-multipole algorithm (MLFMA); and (3) macro-basis function methods, such as the characteristic basis function method (CBFM). Another acceleration strategy that complements the above techniques is to improve the quality of the initial value of the iterative solver so that it is as close as possible to the final converged solution. However, existing research in this direction is relatively limited, and the most commonly used method is the phase correction initial value guessing method (reference to the phase correction initial value guessing method: J. Song, et al. Multilevel fast multipolealgorithm for electromagnetic scattering by large complex objects. IEEETraps. Antennas Propag. 1997, Vol. 45 (No. 10), pp. 1488-1493). While this method is effective, there is still considerable room for improvement, and it warrants further research.

[0004] Autoregressive (AR) models are statistical tools and a classic method for analyzing time series data. They use a linear combination of historical values ​​from several previous points to describe the current value. AR models have been successfully applied in various fields, including price forecasting, noise observation, biomedical signal processing, disease prediction, and environmental forecasting. The Burg algorithm is an effective method for estimating AR model parameters. The Burg algorithm is more suitable for short data series and ensures model stability (Reference for the Burg algorithm: JP Burg, Maximum Entropy Spectral Analysis, Stanford, CA, USA: Stanford Univ., 1975.). Summary of the Invention

[0005] This invention addresses the problem of accelerating the iterative solution of multi-angle single-station RCS by proposing a method based on the prediction of initial values ​​using an autoregressive (AR) model.

[0006] The core idea of ​​this invention lies in utilizing an important characteristic in multi-angle RCS simulation: the strong sequential correlation between solutions (current coefficients) of adjacent incident angles. This invention constructs a time series of converged current solutions for calculated angles and establishes an autoregressive (AR) model based on this time series to dynamically predict the initial values ​​for the current angle to be analyzed. The initial values ​​predicted by this invention are closer to the final converged solution, thus reducing the initial iteration error and effectively reducing the number of iterations required for convergence, ultimately reducing the time consumption for iterative solution.

[0007] To achieve the above-mentioned objectives, this application first provides a method for accelerating multi-angle single-station RCS iterative solution based on initial value prediction using an autoregressive model, characterized by the following steps: Initialization phase: For the first [period] in a continuous sequence of incident angles From each angle, an iterative solver is used to calculate the corresponding convergent current solution, wherein the initial value of the iterative solver is set to 0, or obtained through a traditional initial value guessing method, and It is the preset minimum initial data length; the convergence current is deconstructed into a time series, and the time series is preprocessed to generate an initial observation sequence suitable for the autoregressive model; Prediction and Solution Phase: For the first... An angle of incidence, : a) Discretize the problem of predicting the initial value vector into the problem of predicting the current coefficient of each basis function; b) For each basis function, the autoregressive coefficients are estimated using the Burg algorithm based on the historical data corresponding to it in the initial observation sequence; c) Use an autoregressive model to generate preprocessed domain predicted values; d) Reconstruct the predicted values ​​in the preprocessed domain: perform inverse first-order difference and correct the phase factor to obtain the predicted current coefficients on the corresponding basis functions; e) Repeat steps a) to d) until the predicted current coefficients on all basis functions are obtained, and combine them into a vector as the final predicted initial value vector for the iteration. ; f) The predicted initial value vector As input to the iterative solver, the calculation of the... Converging current solution for each incident angle; Update phase: The first The convergent current solutions of each incident angle are used for data preprocessing to obtain new observations, which are then added to the initial observation sequence for prediction of subsequent initial angle values.

[0008] RCS calculation: Calculate the RCS based on the convergence current solution.

[0009] To achieve the above-mentioned objectives, this application also provides an electronic device, including a processor and a memory, wherein the memory stores a program that can run on the processor, characterized in that when the program is executed by the processor, it implements the steps of the method for accelerating multi-angle single-station RCS iterative solution based on autoregressive model prediction of initial values.

[0010] To achieve the above-mentioned objectives, this application also provides a computer-readable storage medium storing at least one program that can be executed by at least one processor to implement the steps of the method for accelerating multi-angle single-station RCS iterative solution based on autoregressive model prediction of initial values.

[0011] This invention fully utilizes the correlation between solutions at adjacent incident angles and proposes the aforementioned method for accelerating multi-angle single-station RCS iterative solution based on the prediction of initial values ​​using an autoregressive model. First, a set of historical converged current solution sequences corresponding to an initial incident angle is obtained and preprocessed to construct the initial observation sequence of the autoregressive model. Second, for a new incident angle, based on the observation sequence, the Burg algorithm is used to estimate the autoregressive coefficients and predict the initial value of the current angle for iteration. Finally, this initial value is applied to the iterative solver to accelerate convergence.

[0012] Compared with the prior art, the present invention has the following beneficial effects: 1. Reduce the number of iterations and shorten the iteration solution time: Compared with the phase correction initial value guessing method, the initial value predicted by the autoregressive model in this invention is closer to the convergent solution, thereby making the initial relative residual of the iterative solver (such as GMRES) lower, effectively reducing the number of iterations required to achieve convergence, and ultimately achieving the goal of reducing the iteration solution time.

[0013] 2. Extremely low prediction overhead: The computational complexity required to predict each initial vector is only a fraction of the total computational cost. ,here The number of unknowns has little impact on the total computation time.

[0014] 3. Strong compatibility: This invention is not limited to the type of integral equation or the type of iterative solver. It does not change the original impedance matrix, does not affect the final solution accuracy, and can be easily integrated with other acceleration technologies such as fast algorithms (such as MLFMA) and preprocessing techniques (such as SAI). Attached Figure Description

[0015] Figure 1 This is a basic flowchart of the present invention; Figure 2 This is an aircraft model analyzed in an embodiment of the present invention; Figure 3 This is a curve showing the change of the iterative relative residual with the number of iterations in an embodiment of the present invention; Figure 4 This is a comparison of the number of iterations in the embodiments of the present invention; Figure 5 This is an RCS result diagram of an embodiment of the present invention. Detailed Implementation

[0016] To more clearly illustrate the technical features of this patent, the following detailed description is provided through specific embodiments and in conjunction with the accompanying drawings.

[0017] Example 1 This embodiment provides a method for accelerating multi-angle single-station RCS iterative solution based on initial value prediction using an autoregressive model, such as... Figure 1 As shown, it includes the following steps: Initialization phase: For the front of a series of incident angles From each angle, the corresponding convergent current solution is calculated using an iterative solver (with initial values ​​of 0 or using the traditional initial value guessing method). ,in It is the minimum initial data length; The convergence current corresponding to continuous incident angles is deconstructed into a time series, and the... Data preprocessing is performed on historical convergent current solutions: 1) Remove phase factor : (1) in, This represents the value after removing the phase factor. It is the first The incident wave vector at each incident angle, It is the location of the venue.

[0018] 2) Perform a first-order difference on the value after removing the phase factor: (2) This is the initial observation sequence used in the autoregressive model.

[0019] Prediction and Solution Phase: Regarding the first An angle of incidence, : a) Discretize the problem of predicting the initial value vector into the problem of predicting the current coefficient of each basis function, with N basis functions; b) Regarding the first One Rao-Wilton-Glisson (RWG) basis function, based on the corresponding historical data in the initial observation sequence. ,here It is a vector The corresponding number in the middle The elements of the basis functions are used to estimate the autoregressive coefficients using the Burg algorithm. ,in It is the order of the preset AR model; c) Use an autoregressive model to generate preprocessed domain predicted values : (3) d) Predicting values ​​for the preprocessed domain Perform data reconstruction: 1) Inverse first-order difference: (4) in It is an intermediate quantity obtained by the inverse first-order difference.

[0020] 2) Correction phase factor: (5) here That is, the first Predicted current coefficients on each basis function.

[0021] e) Repeat steps a) to d) until the predicted current coefficients on all basis functions are obtained, and combine them into a vector as the final predicted initial value vector for the iteration. : (6) in This indicates transpose.

[0022] f) The predicted initial value vector As input to the iterative solver, the calculation of the... Converging current solution at each incident angle ; Update phase: The first Converging current solution at each incident angle The data is preprocessed according to the aforementioned method to obtain new observations, which are then added to the initial observation sequence for subsequent angle prediction. When the observation sequence is too long, it affects the computational efficiency of the autoregressive model. To maintain computational efficiency, a sliding window mechanism is used: once the accumulated observation sequence length exceeds a preset window size D, the oldest observation sequence is systematically discarded. .

[0023] RCS calculation: Calculate the RCS based on the convergent current solution.

[0024] The invention will be further illustrated by a specific example below: Non-uniform meshes typically increase the system matrix condition number, negatively impacting convergence. This invention uses an ideal conductor aircraft model with a length of 14.6 m (see attached diagram). Figure 2 The advantages of this invention will be illustrated by an example.

[0025] The frequency to be analyzed is 100 MHz. The model is non-uniformly divided into triangular meshes with mesh sizes starting from 0.03. Up to 0.1 The inconsistency resulted in 16113 RWG basis functions. It is a wavelength of 100MHz in free space. The incident angle of the incident wave is... angular interval The polarization mode is Polarization. The GMRES iterative solver was used, with a convergence threshold set to 10. -5 The integral equation used is the Combined Field Integral Equation (CFIE), with a mixing coefficient of 0.5. The order of the autoregressive model is set to 4 (an empirical value). The sliding window size is set to 20.

[0026] The relative iterative residual is used to measure iterative performance. The expression for the relative residual is: (7) in, It is an activation vector. It is an impedance matrix. It is the solution after the s-th iteration in the iterative solver. It represents the 2-norm. Figure 3 Showing some incident angles ( When using phase-corrected initial values ​​and the convergence performance of the initial values ​​predicted by this invention, it can be seen that the initial relative residual of the initial values ​​predicted by this invention is approximately... The initial relative residual is more than an order of magnitude lower than that of the initial value of the phase correction.

[0027] Figure 4 The example demonstrates the number of iteration steps for three methods: setting the initial value to zero, using a traditional phase-corrected initial value, and predicting the initial value according to this invention. In this example, when the initial value is set to zero, the average number of iterations per angle is 252.0; when using a traditional phase-corrected initial value, the average number of iterations decreases to 143.0; while the method of this invention has an average of only 42.6 iterations. Accordingly, for the iterative solution process of this example, setting the initial value to zero takes 4185 seconds, using a traditional phase-corrected initial value takes 2384 seconds, and the method of this invention takes only 720 seconds. It is worth noting that although using the autoregressive model to predict the initial value takes an additional 2.8 seconds, compared with the traditional phase-corrected initial value guessing method, this invention still achieves a total time reduction of approximately 69.8%. Figure 5 The calculated RCS values ​​for a single station are shown, and the results from the three methods agree very well. This example verifies the efficiency and accuracy of the present invention.

[0028] Example 2 This embodiment provides an electronic device, including a processor and a memory, wherein the memory stores a program that can run on the processor, characterized in that when the program is executed by the processor, it implements the steps of the method for accelerating multi-angle single-station RCS iterative solution based on autoregressive model prediction of initial values ​​in Embodiment 1 described above.

[0029] Example 3 This embodiment provides a computer-readable storage medium storing at least one program that can be executed by at least one processor to implement the steps of the method for accelerating multi-angle single-station RCS iterative solution based on autoregressive model prediction of initial values ​​in Embodiment 1 described above.

Claims

1. A method for accelerating multi-angle single-station RCS iterative solution based on autoregressive model prediction of initial values, characterized in that, Includes the following steps: Initialization phase: For the first [period] in a continuous sequence of incident angles From each angle, an iterative solver is used to calculate the corresponding convergent current solution, wherein the initial value of the iterative solver is set to 0, or obtained through a traditional initial value guessing method, and It is the preset minimum initial data length; The convergence current is deconstructed into a time series, and the time series is preprocessed to generate an initial observation series suitable for the autoregressive model. Prediction and Solution Phase: For the first... An angle of incidence, : a) Discretize the problem of predicting the initial value vector into the problem of predicting the current coefficient of each basis function; b) For each basis function, the autoregressive coefficients are estimated using the Burg algorithm based on the historical data corresponding to it in the initial observation sequence; c) Use an autoregressive model to generate preprocessed domain predicted values; d) Reconstruct the predicted values ​​in the preprocessed domain to obtain the predicted current coefficients on the corresponding basis functions; e) Repeat steps a) to d) until the predicted current coefficients on all basis functions are obtained, and combine them into a vector as the final predicted initial value vector for the iteration. ; f) The predicted initial value vector As input to the iterative solver, the calculation of the... Converging current solution for each incident angle; Update phase: The first The convergent current solutions of each incident angle are used for the data preprocessing to obtain new observations, which are then added to the initial observation sequence for prediction of subsequent initial angle values. RCS calculation: Calculate the RCS based on the convergence current solution.

2. The method for accelerating multi-angle single-station RCS iterative solution based on autoregressive model prediction of initial values ​​as described in claim 1, characterized in that, The data preprocessing includes: removing the phase factor related to the incident angle from the convergent current solution, and performing a first-order difference operation on the data after removing the phase factor.

3. The method for accelerating multi-angle single-station RCS iterative solution based on autoregressive model prediction of initial values ​​as described in claim 1, characterized in that, The data reconstruction includes: performing an inverse first-order difference operation on the preprocessed domain prediction values ​​generated by the autoregressive model, and multiplying the inverse first-order difference data by a phase factor related to the current incident angle to correct the phase.

4. The method for accelerating multi-angle single-station RCS iterative solution based on autoregressive model prediction of initial values ​​as described in claim 1, characterized in that, A sliding window mechanism is used in the update phase: when the data length of the initial observation sequence exceeds the preset window size, the oldest observation data is systematically discarded.

5. An electronic device comprising a processor and a memory, wherein the memory stores a program executable on the processor, characterized in that... When the program is executed by the processor, it implements the steps of the method for accelerating multi-angle single-station RCS iterative solution based on the prediction of initial values ​​using an autoregressive model, as described in any one of claims 1-4.

6. A computer-readable storage medium, characterized in that, The storage medium stores at least one program, which can be executed by at least one processor to implement the steps of the method for accelerating multi-angle single-station RCS iterative solution based on the prediction of initial values ​​using an autoregressive model, as described in any one of claims 1-4.

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