A Fast Calculation Method for the Electromagnetic Scattering Characteristics of Isomorphic Swarm Targets

Abstract

The present invention discloses a fast calculation method for the electromagnetic scattering characteristics of homogeneous swarm targets, which can save memory, reduce the number of iterations, and improve the simulation efficiency. First, obtain the triangular mesh information of target t1 in the homogeneous swarm structure and the geometric center coordinates of other targets; establish an octree structure of the multi-level fast multipole for target t1, and extend the multi-level fast multipole data structure to the top layer; determine the layer where the coupling transfer between two targets in the homogeneous swarm is located according to the distance between the targets; perform the filling of the coupling transfer matrix; perform the filling of the excitation term matrix for all targets in the target group; according to the multi-level fast multipole algorithm, obtain the initial solution of the equivalent current of each target in the homogeneous swarm; on the basis of the initial solution, calculate the plane wave of the coupling effect between the targets according to the determined layer where the coupling transfer is located and the coupling transfer matrix, and use GMRES iteration to solve the equivalent current of the entire target group and then calculate the scattering field.

Description

Technical Field

[0001] The present invention belongs to the technical field of electromagnetic simulation calculation, and particularly relates to a fast calculation method for the electromagnetic scattering characteristics of a homogeneous swarm target. Background Art

[0002] As an important equipment in the future aviation equipment system, the swarm has attracted much attention from researchers in recent years because of its strong situation awareness and the ability to suppress or destroy the enemy's air defense system. For such a combat system with a large number of targets, how to quickly and accurately calculate the electromagnetic scattering characteristics of the aircraft group is of great significance to the management of unmanned aerial vehicles and the combat system.

[0003] The homogeneous swarm target has the characteristics of a large number of targets but the same geometric structure and electrical parameters. For solving the electromagnetic scattering characteristics of similar large-scale targets, a currently widely used and relatively effective method is the MLFMA (Multilevel Fast Multipole Algorithm). The multilevel fast multipole algorithm regards the target to be calculated as a whole, uses a single cubic box to enclose the entire target group, and then recursively divides the box layer by layer using the binary rule until the size of the lowest layer box is less than half a wavelength. After all the boxes are divided, the unknowns are arranged to establish the octree structure of the MLFMA, and then the near-far interaction matrix is filled and calculated. Finally, the equivalent current and field values are solved by iteration, as Figure 1 shown.

[0004] As the number of targets increases, the number of iterations and the memory requirement of the multilevel fast multipole algorithm will continuously increase, which is unacceptable in terms of simulation efficiency and computational resource requirements. Summary of the Invention

[0005] In view of this, the present invention provides a fast calculation method for the electromagnetic scattering characteristics of a homogeneous swarm target, which can save memory, reduce the number of iterations, and improve the simulation efficiency.

[0006] The inventive method is compatible with the MLFMA algorithm, and the two are organically combined to form a new MLFMA technology applicable to homogeneous swarm targets. The invention only needs to independently calculate the data structure of the MLFMA for a single target in the group, construct a small-scale electromagnetic coupling transfer matrix according to the relative spatial position relationship between the targets in the group, and the electromagnetic coupling between two targets in the group can be quickly calculated through the existing single-target aggregation, divergence, and transfer between targets, which can greatly save memory. At the same time, the initial solution of the iteration is solved and calculated, and both the number of iterations and the iteration time consumption are effectively reduced.

[0007] In order to solve the above technical problems, the present invention is implemented as follows.

[0008] A fast calculation method for the electromagnetic scattering characteristics of a homogeneous swarm target includes:

[0009] Step 1: Obtain the triangular grid information of target t1 in the isomorphic swarm structure and the geometric center coordinates of other targets;

[0010] Step 2: Establish an octree structure with multi-level fast multipole sub-division for target t1 and fill the near-far interaction matrix; when recording the octree structure, extend the multi-level fast multipole data structure to the top layer;

[0011] Step 3: Determine the layer where the coupling transfer between two targets in the isomorphic swarm is located according to the distance between the targets, which is used to characterize the coupling scattering effect between the targets; obtain the center coordinates of each non-empty box in the layer where the coupling transfer is located and higher layers;

[0012] Step 4: Fill the coupling transfer matrix: the distance vector in the coupling transfer matrix is represented by the distance between the center coordinates of the boxes in the layer where the coupling transfer is located;

[0013] Step 5: Fill the excitation term matrix for all targets in the isomorphic swarm;

[0014] Step 6: Obtain the initial solution of the equivalent current of each target in the isomorphic swarm according to the multi-level fast multipole algorithm;

[0015] Step 7: On the basis of the initial solution, consider the influence of the coupling scattering effect described in Step 3 on the scattering characteristics of the isomorphic swarm, calculate the plane wave of the coupling effect between the targets according to the layer where the coupling transfer is located and the coupling transfer matrix, and then use the excitation term matrix as the right-hand side term, and adopt GMRES iterative solution to obtain the equivalent current of the entire target group, and then perform scattering field calculation.

[0016] Preferably, the determination of the layer where the coupling transfer between two targets in the isomorphic swarm is located according to the distance between the targets is as follows:

[0017] When the distance between the geometric centers of two targets exceeds twice the maximum size of the target, the layer where the coupling transfer is located is the 0th layer;

[0018] When the distance between the geometric centers of the targets is greater than the maximum scale of the target and less than the sum of the maximum size of the target and the maximum size of the target At this time, the transfer occurs in the Cth layer of the box, and C takes values of 1, 2, 3...

[0019] Preferably, Step 6 is as follows: First, calculate the accurate solution of the equivalent current of target t1 based on MLFMA as the initial solution of target t1; then, according to the initial solution of target t1, use the relative positions of the two targets to obtain the equivalent currents of other targets as the respective initial solutions of other targets, so as to obtain the initial solution of the entire iteration.

[0020] Preferably, the obtaining of the equivalent currents of other targets by using the relative positions of the two targets according to the initial solution of target t1 is as follows:

[0021] Let the equivalent current of target t1 be I t1 , then the equivalent current of other target t2 is:

[0022]

[0023] where j represents the imaginary number, and k i represents the wave number of the incident wave, and r ct2 -r ct1 is the relative position vector between the two targets.

[0024] Preferably, the calculation of the plane wave of the coupling effect between targets according to the determined layer where the coupling transfer is located and the coupling transfer matrix is as follows:

[0025] Let the two targets be t1 and t2 respectively, and the plane wave of the coupling effect between target t1 and t2 is:

[0026]

[0027] where is the plane wave of the coupling effect from target t2, is the expression of the plane wave of target t2 aggregated from the bottom layer to the layer where the coupling transfer is located; is the center of the box of target t1 and target t2, is the interpolation matrix of the target plane wave, is the coupling transfer matrix between the two targets.

[0028] Preferably, the multi-level fast multipole data structure described in step two includes: the number of plane wave modes, the total number of plane waves, the starting position of plane waves in each layer, the box size, the non-empty box number, and the weight factor of Gaussian sampling points.

[0029] Beneficial effects:

[0030] (1) The method of the present invention is compatible with the MLFMA algorithm, and the two are organically combined to form a new MLFMA technology applicable to homogeneous swarm targets. The invention only needs to independently calculate the data structure of MLFMA for a single target in the swarm, and then can construct a small-scale electromagnetic coupling transfer matrix according to the relative spatial position relationship between the targets in the swarm. The electromagnetic coupling between two targets in the swarm can be quickly calculated through the existing single-target aggregation, divergence, and transfer between targets, which can greatly save memory.

[0031] (2) The present invention takes into account that the coupled scattering effect may exist in the 0th and 1st layers. Therefore, when establishing the octree structure, the corresponding data structure is extended to the top layer of the octree structure, that is, a multi-layer fast multipole data structure that records all levels starting from the 0th layer. When determining the layer where the transfer is located, it is determined according to the target distance. The layer where the transfer is located may be in any layer of the octree. This method is more in line with the actual situation, without sacrificing calculation accuracy and efficiency.

[0032] (3) When determining the initial value, the present invention first calculates the exact solution of the equivalent current of target t1 based on MLFMA, and then obtains the approximate solutions of other targets based on the exact solution of t1, and uses them together as the initial value of the iteration, so that the initial value of the iteration is closer to the solution, and the number of iterations and the iteration time are effectively reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a flow chart of MLFMA implementation in the prior art;

[0034] Figure 2 It is a schematic diagram of target coupling transfer at different distances;

[0035] Figure 3 It is a comparison diagram of the inventive method of one-layer transfer when the distance between two ball targets satisfies one-layer transfer, top-layer transfer and multi-layer fast multi-level sub-method;

[0036] Figure 4 It is the flow chart for solving the initial solution of current;

[0037] Figure 5 It is a schematic diagram of the warhead aircraft model;

[0038] Figure 6 It is a formation of ten warhead aircraft;

[0039] Figure 7 yes Figure 6 Comparison of the scattering cross sections calculated by the invented method and MLFMA in the form of formation;

[0040] Figure 8 yes Figure 7 Comparison chart of the relationship between the number of MLFMA iterations and residuals of the invention under the example;

[0041] Figure 9 It is the memory / time / iteration number comparison between MLFMA and the invented method;

[0042] Figure 10 It is a flowchart of the new MLFMA implementation suitable for homogeneous bee colony structure proposed by the inventive method. DETAILED DESCRIPTION

[0043] The present invention provides a fast calculation method for the electromagnetic scattering characteristics of a homogeneous swarm target, which is a new type of MLFMA technology applicable to homogeneous swarm targets. Considering the homogeneity of each target in the homogeneous swarm (see Figure 2 , 5 , 6), that is, the number of targets in the homogeneous swarm is large but the geometric structure and electrical parameters are the same. This method only needs to independently calculate the data structure of MLFMA for a single target within the homogeneous swarm, and construct a small-scale electromagnetic coupling transfer matrix according to the relative spatial position relationship between the targets within the swarm to characterize the coupled scattering effect between the targets. Then, the electromagnetic coupling between two targets within the swarm can be quickly calculated through the existing single-target aggregation, divergence, and transfer between targets, which can greatly save memory.

[0044] Furthermore, the present invention solves the calculation of the initial solution of the iteration, and both the number of iterations and the iteration time consumption are effectively reduced.

[0045] The present invention effectively solves the problem that as the number of targets increases, the number of iterations and the memory requirements of the multi-level fast multi-pole sub-algorithm will continuously increase, which is unacceptable in terms of simulation efficiency and computing resource requirements.

[0046] The following combines the accompanying drawings and gives embodiments to describe the present invention in detail.

[0047] See Figure 10 , the fast calculation method for the electromagnetic scattering characteristics of the homogeneous swarm target provided by this embodiment includes the following steps:

[0048] Step 1: Obtain the triangulation grid information of a target t1 in the homogeneous swarm structure and the geometric center coordinates of other targets.

[0049] The target t1 can be arbitrarily selected. For example, the first target in the homogeneous swarm can be selected. The triangulation grid information can be read from the pre-stored information in the database, or the target can be triangulated to obtain the triangulation grid information.

[0050] Step 2: Establish an octree structure of the multi-level fast multi-pole for the target t1. In the present invention, the multi-level fast multi-pole octree structure of the target t1 needs to be established starting from the top layer.

[0051] The present invention only needs to establish an octree structure for one target and does not need to establish octree structures for all targets.

[0052] In this step, the maximum size of the target is calculated according to the target grid information, so as to obtain the maximum box size of a single target. Then, the binary method is used to recursively divide the box layer by layer until the size of the lowest-layer box is less than half the wavelength, and a multi-level fast multi-pole octree structure is established. Different from the existing MLFMA technology, the aggregation and transfer operations of the existing MLFMA technology start from the second layer. Therefore, the existing MLFMA technology only stores the multi-level fast multi-pole data structure starting from the second layer, while the coupling transfer of the present invention may occur at any layer including the top layer. Therefore, it is necessary to further expand the corresponding data structure to the top layer of the octree structure, that is, record the multi-level fast multi-pole data structure of all levels starting from the 0th layer.

[0053] This data structure includes: the number of plane wave modes, the total number of plane waves, the starting positions of plane waves at each layer, the box size, the non-empty box number, the weight factor of the Gaussian sampling point, etc.

[0054] Step 3: Fill the far and near interaction matrix.

[0055] Among them, the far interaction refers to aggregation, transfer, and divergence, and the near interaction refers to the interaction between adjacent boxes. Among them, the filling of the far and near interaction matrix is carried out based on the data structure of a single target, that is, only the data structures of the aggregation, transfer, divergence, and near interaction matrix of the MLFMA of a single target are established.

[0056] On the basis of having established the multi-level fast multi-pole data structure of a single target, the process of filling the far and near interaction matrix is a conventional technology and will not be elaborated here.

[0057] Step 4: Determine the layer where the coupling transfer between two targets in the isomorphic swarm is located according to the distance between the targets, so as to characterize the coupling scattering effect between the targets.

[0058] In a complex electromagnetic environment, there is an electromagnetic scattering coupling effect between the sub-targets of a large-scale swarm of targets.

[0059] In order to ensure calculation accuracy and take efficiency into account, the method of the present invention completes the coupling scattering effect between two targets through the coupling transfer of target plane waves. The layer where the coupling transfer occurs is determined by the distance between the two targets. Different distances between the targets result in different layers where the coupling transfer is located. Specifically:

[0060] 1) When the distance between the geometric centers of two targets exceeds twice the maximum scale of the target, the transfer operation is carried out at the top layer, as shown in the transfer operation between the upper left target and the lower right target in Figure 2 ;

[0061] 2) When the distance between the geometric centers of two targets is greater than the maximum target scale and less than the sum of the maximum target size and half of the box size, the transfer operation occurs only in the first layer of the two target MLFMA boxes; as shown in the transfer operation between the upper left target and the upper right target in Figure 2 ;

[0062] 3) When the distance between the geometric centers of two targets is greater than the maximum target scale and less than the sum of the maximum target size and one-fourth of the maximum target size, the transfer operation occurs in the second layer of the MLFMA boxes of the two targets. As shown in the transfer operation between the upper left target and the lower left target in Figure 2 ;

[0063] When the distance between the geometric centers of the targets is greater than the maximum target scale and less than the sum of the maximum target size and one-eighth of the maximum target size, the transfer occurs in the third layer of the box, and so on.

[0064] For example, the number of layers of a target coupling transfer is determined by the distance between it and the target with which it interacts. The incident wave frequency is 3 GHz, the radius of the sphere is 0.2 m, the number of unknowns for each sphere is 19626, the incident direction is θ = 90°, the receiving direction is θ = 0° - 180°, where θ is the elevation angle, and is the azimuth angle. The coordinates of the two targets are (0, 0, 0) and (0.6, 0, 0), that is, it satisfies the coupling transfer of the plane wave in the first layer. At this time, there is a large difference between the scattering cross-section values calculated by the top-layer transfer and the one-layer transfer, and the one-layer transfer fits well with the MLFMA, as shown in Figure 3 ;

[0065] The coupling transfer layer between each two targets needs to be determined and stored. The structure for recording this data can be in the form of an array: transl(l, t1, t2), where t1 and t2 represent any two different targets, and l is the layer where the coupling transfer occurs.

[0066] Step Six: Obtaining the box center coordinates. According to the layer where the coupling transfer is calculated in Step Five, obtain the center coordinates of each non-empty box in the layer where the coupling transfer occurs and non-empty boxes in higher layers. Because while looking for the layer where the coupling between two targets occurs in the previous step, the lower layers that need to be transferred will be recorded. In this way, the transfer will only occur in the recorded layer and higher layers, and the box center coordinates that may be needed will be stored.

[0067] Step 7: Fill in the coupling transfer matrix. The filling of the coupling transfer matrix is similar to that of the target internal sub-adjacent transfer matrix. The difference is that the distance vector in the coupling transfer matrix is represented by the distance between the center coordinates of the boxes at the layer where the transfer occurs between the targets determined in Step 6. Then, the plane wave calculation formula for the coupling effect between two targets can be expressed as:

[0068] Assume the targets are t1 and t2 respectively, and the plane wave of the coupling effect between target t1 and t2 is

[0069]

[0070] where is the plane wave of the coupling effect from target t2, is the expression of the plane wave of target t2 aggregated from the bottom layer to the transfer layer, which is the same as the MLFMA aggregation process. are the box centers of target t1 and target t2, is the interpolation matrix of the plane wave, which is the same as the MLFMA interpolation matrix. is the coupling transfer matrix between the targets.

[0071] Step 8: Fill in the excitation term matrix for all targets in the target group.

[0072] The filling of the excitation term matrix is implemented for the entire target group structure. Based on the established data structure of target t1 and the position information of other targets relative to this target, the established grid information is obtained for other targets through translation operations. For example, the grid information of target t2 can be obtained by translating the grid information of target t1 by the distance vector r ct2 -r ct1 Then, according to the filling method of the MLFMA excitation term, the excitation term is filled for each target in turn, thus completing the filling of the excitation term matrix.

[0073] Step 9: Obtain the initial solution of the equivalent current for each target in the isomorphic swarm according to the multi-level fast multipole algorithm.

[0074] In the GMRES iterative solution process, the initial solution plays a crucial role throughout the iterative solution process. Usually, the initial value of the iteration is set to 0. In the iterative solution, as the number of targets in the target group increases, the vectors in its excitation term will continue to increase, resulting in an increase in the number of iterations and an increase in the calculation time.

[0075] According to the characteristics of the isomorphic aircraft swarm targets, such as Figure 4As shown in the figure, the present invention first calculates the exact solution of the equivalent current of target t1 according to MMFMA, and then, based on the solution of target t1 and using the relative position of the target, obtains the equivalent currents of other targets as the initial solutions of the respective other targets, thereby obtaining the initial solution for the entire iteration. The present invention uses the exact solution of one target to find the approximate solutions of other targets and uses them as the initial values, so that the initial solutions of the targets are close to the exact solutions, thereby reducing the number of iterations.

[0076] Specifically, taking two targets t1 and t2 as an example, it is introduced how to obtain the initial solutions of other targets based on the exact solution of target t1. Assume that the given target t1 is located at the origin of coordinates. For target t1, its incident wave can be expressed as:

[0077]

[0078] Then the incident wave of target t2 is:

[0079]

[0080] Therefore, we have:

[0081]

[0082] where E0 is the amplitude of the incident plane wave, r0 is the spatial distance from the incident wave to the target. j represents the imaginary number, k i is the incident wave beam, where θ i , is the incident elevation angle and the incident azimuth angle, is the unit vector of the rectangular coordinate system, r ct2 -r ct1 is the relative position vector between the two targets. I t1 represents the equivalent current of target t1, and I t2 represents the initial solution of the equivalent current of target t2 obtained based on I t1 . Then {I t1 , I t2} is used as the initial solution for the two target groups.

[0083] Step Ten: Solving the true solution of the equivalent current of the target group.

[0084] In this step, the solution result of Step Nine is used as the initial solution for GMRES iteration. According to the transfer layer and the coupling transfer matrix determined in Step Five and Step Seven, and using the plane wave calculation formula of the coupling effect expressed in formula (1) to calculate the scattering coupling effect between the targets, thereby obtaining the true solution of the equivalent current of the entire target group through GMRES iteration. During the GMRES iteration process, the excitation term matrix is used as the right-hand side term.

[0085] Step Eleven: Solving the scattered field.

[0086] Similar to the excitation term, the solution of the scattering field also needs to be calculated for the entire target group. Based on the established data structure of the target and the position information of other targets relative to this target, the grid information of other targets is calculated. According to the MLFMA scattering field calculation method, the scattering field of each target is solved in turn, so as to realize the solution of the scattering field of the entire target group.

[0087] Take Figure 5 the warhead model shown as an example to illustrate the effect of the method of the present invention. The maximum size of the target is 1.26 m, and the number of unknowns for each target is 5067. Take ten warhead models as examples, and their arrangement is as Figure 6 shown. The incident wave frequency is 1 GHz, the incident direction is θ = 0°, the receiving direction is θ = 0° - 180°, Figure 7 This is the comparison chart of the scattering cross-sections calculated by the method of the present invention and MLFMA, and the results show the accuracy of the method of the present invention. Figure 8 This is the comparison chart of the iteration times of the method of the present invention and MLFMA after adopting the iterative initial solution method described in step nine. Figure 9 The results show that the number of iterations has decreased from 113 times to 57 times. The iteration time of MLFMA is 45 s, and that of the method of the present invention is 32 s. The memory requirement of MLFMA is 904.2 MB, and the time for filling the matrix is 623 s; the memory requirement of the method of the present invention is 73.4 MB, and the time for filling the matrix is 7 s. In this embodiment, the speedup ratio is 17.128.

[0088] The above specific embodiments only describe the design principle of the present invention. The shapes and names of the components in this description can be different and are not limited. Therefore, those skilled in the art of the present invention can modify or equivalently replace the technical solutions recorded in the foregoing embodiments; and these modifications and replacements do not depart from the gist and technical solutions of the present invention, and shall all fall within the protection scope of the present invention.

Claims

1. A fast calculation method for the electromagnetic scattering characteristics of an isomorphic bee colony target, characterized in that, Including: Step 1: Obtain the triangular grid information of target t1 and the geometric center coordinates of other targets in the isomorphic swarm structure; Step 2: Establish a multi-level fast multipole octree structure for target t1 and fill the near-far interaction matrix; when recording the octree structure, extend the multi-level fast multipole data structure to the top layer; Step 3: Determine the layer where the coupling transfer between two targets in the isomorphic swarm is located according to the distance between the targets, which is used to characterize the coupling scattering effect between the targets; Obtain the center coordinates of each non-empty box in the layer where the coupling transfer is located and higher layers; Step 4: Fill the coupling transfer matrix: the distance vector in the coupling transfer matrix is represented by the distance between the center coordinates of the boxes in the layer where the coupling transfer is located; Step 5: Fill the excitation term matrix for all targets in the isomorphic swarm; Step 6: Obtain the initial solution of the equivalent current of each target in the isomorphic swarm according to the multi-level fast multipole algorithm; Step 7: On the basis of the initial solution, consider the influence of the coupling scattering effect on the scattering characteristics of the isomorphic swarm, calculate the plane wave of the coupling effect between the targets according to the layer where the coupling transfer is located and the coupling transfer matrix, and then use the excitation term matrix as the right-hand side term, and adopt GMRES iterative solution to obtain the equivalent current of the entire target group, and then calculate the scattering field.

2. The method according to claim 1, characterized in that, The determination of the layer where the coupling transfer between two targets in the isomorphic swarm is located according to the distance between the targets is as follows: When the distance between the geometric centers of two targets exceeds twice the maximum size of the target, the layer where the coupling transfer is located is the 0th layer; When the target geometric center distance is greater than the target maximum scale and less than the target maximum size plus the target maximum size , the transfer occurs at the C-th layer of the box, where C takes values of 1, 2, 3, ….

3. The method according to claim 1, wherein Step 6 is: First, calculate the exact solution of the equivalent current of target t1 based on MLFMA as the initial solution of target t1; then, according to the initial solution of target t1, use the relative positions of the two targets to obtain the equivalent currents of other targets as the respective initial solutions of other targets, so as to obtain the initial solution of the entire iteration.

4. The method according to claim 3, wherein The obtaining of the equivalent currents of other targets by using the relative positions of the two targets according to the initial solution of target t1 is as follows: Let the equivalent current of target t1 be I t1 , then the equivalent current of other target t2 is: where j represents the imaginary number, and k i represents the wave number of the incident wave, and r ct2 -r ct1 is the relative position vector between the two targets.

5. The method according to claim 1, wherein The calculation of the plane wave of the coupling effect between the targets according to the determined layer where the coupling transfer is located and the coupling transfer matrix is as follows: Let the two targets be t1 and t2 respectively, and the plane wave of the coupling effect between target t1 and t2 is: Among them, is the plane wave of the coupling effect from the target t2, is the expression of the plane wave of the target t2 aggregated from the underlying layer to the layer where the coupling transfer is located; is the center of the boxes of the target t1 and the target t2, is the interpolation matrix of the target plane wave, which is the coupling transfer matrix between the two targets.

6. The method according to any one of claims 1-5, characterized in that, The multi-level fast multipole data structure described in Step 2 includes: the number of plane wave modes, the total number of plane waves, the starting positions of plane waves in each layer, the box size, the non-empty box number, and the weight factor of the Gaussian sampling points.

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