CN116956472B - RCS surface sensitivity calculation method for MLFMA concomitant solution - Google Patents
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Abstract
The invention relates to the field of stealth design of appearance of aircrafts, and discloses an RCS surface sensitivity calculation method for MLFMA concomitant solution. The method is characterized by comprising the following steps: a multipole expansion method of the impedance matrix with respect to the surface mesh partial derivative matrix; partial derivative calculation and index storage methods of near field impedance with respect to a surface grid; a calculation method and an index storage method of aggregation factors, configuration factor relations and excitation vectors and radar cross sections related to partial derivatives of surface grids in far interaction; a calculation method for multiplying the matrix of the partial derivative of the impedance by the matrix-vector of the surface current and the accompanying variable in the far interaction solution; the invention solves the problems that the classical design variable gradient solving based on the accompanying method needs to be repeatedly filled with an impedance matrix and the surface sensitivity calculating method based on the moment method is not suitable for the optimal design of the electric large and super-electric large outline low radar scattering cross section, and realizes the efficient and high-precision solving of the electric large and super-electric large outline surface sensitivity.
Description
Technical Field
The invention relates to the field of stealth design of aircraft appearance, in particular to a radar cross section surface (RCS) sensitivity calculation method based on an accompanying equation.
Background
Radar stealth technology is a technology that improves target survivability, and low detectable features are one of the important features that future military aircraft should possess. The aircraft appearance stealth technology avoids the main scattering energy of radar waves to several non-main threat orientations by changing the layout or appearance surface characteristics of the aircraft, and reduces the RCS in a specific angle range. The appearance stealth is the foundation and root of stealth design, is the primary factor for determining the stealth performance of the aircraft, and the high-efficiency and high-precision appearance stealth design means is the key of the fine design of the appearance stealth of the aircraft.
The surface sensitivity can reflect the influence of the surface grid change on the objective function, and has a guiding effect on the optimization design; meanwhile, as the gradient of the design variable can be directly obtained according to the surface sensitivity, the surface sensitivity can provide a basis for realizing efficient gradient optimization. The multi-layer fast multipole algorithm is a fast algorithm of a moment method, and by expanding a green function by adopting an addition theorem, the calculated amount and the storage amount required for solving a Max Wei Jifen equation are calculated from O (N 2 ) The method is reduced to the order of O (Nlog N), and is the basis for solving the electromagnetic scattering problem of the large-size and super-large-size targets based on an integral equation numerical solution of accurate modeling.
Therefore, the development of the surface sensitivity calculation method based on the multilayer rapid multipole sub-algorithm is a key for realizing gradient optimization of the electric large and super-electric large-size appearance, and is also a problem to be solved in the future in the advanced military machine fine design.
Disclosure of Invention
The invention aims to provide an RCS surface sensitivity calculation method for MLFMA concomitant solution, which solves the problems of calculated amount and storage amount faced in calculation of electric large and super-electric large appearance of surface sensitivity based on a moment method, and realizes high-efficiency and high-precision solution of electric large and super-electric large appearance of surface sensitivity.
In order to achieve the above purpose, the present invention provides the following technical solutions:
a discrete adjoint method and a multilayer fast multipole sub-algorithm-based surface sensitivity calculation method of a Radar Cross Section (RCS) suitable for optimizing design of an electric large and ultra-electric large outline low, is characterized by comprising the following steps:
s1, a multipole unfolding method of an impedance matrix relative to a surface grid partial derivative matrix;
s2, partial derivative calculation and index storage methods of near interaction impedance elements with respect to the surface grid;
s3, calculating a partial derivative of an aggregation factor and a configuration factor with respect to a surface grid in far interaction and storing an index;
s4, calculating a partial derivative of the excitation vector and the radar cross section with respect to the surface grid and storing an index;
s5, calculating a matrix-vector multiplication method of the partial derivative matrix of the impedance and the surface current and the accompanying variable in far interaction solution;
the RCS surface sensitivity calculation method based on discrete accompanying method and multilayer fast multipole sub-algorithm suitable for the electric large and super-electric large shapes is characterized in that: the multi-pole expansion method of the impedance matrix relative to the surface grid partial derivative matrix adopts a multi-layer rapid multi-pole algorithm to solve the surface sensitivity of the target appearance by combining with an accompanying equation, and performs multi-pole expansion on the impedance matrix relative to the surface grid partial derivative matrix to form a matrix-vector product calculation method between the impedance partial derivative matrix and the induced current and accompanying variables suitable for far interaction.
Further, in step S2, the partial derivative calculation and index storage method of the near-interaction impedance element with respect to the surface grid comprises deriving the partial derivative of the near-field impedance matrixIs an expression of (2); combination->Adopts a sparse matrix storage method to establish the dimension as +.>Is stored with an index, and is established +.>Personal (S)Complex partial derivative matrix storage->Is a value of (2). Wherein->For the number of basis functions>For the near field sparse impedance matrix number, +.>Is the sparse impedance matrix rank size.
Further, in step S3, the method for calculating partial derivatives of aggregation factors and configuration factors with respect to the surface grid in the far interaction and the index storage method comprise the steps ofIs needed to calculate the partial derivative of the aggregation factor +.>Partial derivative of the configuration factor->And an integral term and product term of the angular spectrum vector, vector and the like. Manual derivation->And->The development form of the matrix is stored by adopting a sparse matrix storage method;
wherein the method comprises the steps ofZIs an impedance matrix,rIs a grid coordinate of the surface of the object,and->Aggregation factor and configuration factor, respectively, +.>And->The aggregate factor, the configuration factor, and the partial derivative of the surface mesh, respectively.
Further, in step S4, the excitation vector, the method for calculating the partial derivatives of the radar cross section with respect to the surface grid, and the index storage method include deriving the partial derivatives of the excitation vectorPartial derivative of radar cross sectionAnd stored by adopting a sparse matrix storage method.
Further, in step S5, the far-field interaction is calculated by multiplying the matrix of the partial derivative of the impedance with the matrix-vector of the surface current and the accompanying variableThe calculation of (2) is divided into two parts, wherein the first part adopts a matrix-vector multiplier when solving a control equation, and the second part adopts a matrix-vector multiplier when solving an accompanying equation.
Wherein,matrix of the concomitant variable with distant interactions->And induction current->Is a product of (a) and (b).
By adopting the technical scheme, the invention has the following beneficial effects: the method can efficiently calculate the surface sensitivity of the RCS with the electric large and ultra-electric large appearance, and realize the visualization of the surface sensitivity of the RCS. For any number of design variables and incidence angles, solving a primary control equation, solving a primary accompanying equation and solving a primary surface sensitivity equation, and obtaining the sensitivity of the RCS on the surface grid. The method comprises the steps of solving a surface sensitivity equation, namely solving and integrating radar scattering cross section partial derivatives, accompanying variable and excitation partial derivatives, accompanying variable and near interaction impedance matrix partial derivatives and surface current calculation, and accompanying variable, impedance and surface current in far interaction in a polymerization-transfer configuration process, and integrating to obtain an RCS gradient on the basis, so that the RCS gradient calculation time is independent of the number of design variables.
Detailed Description
In order that those skilled in the art will better understand the present invention, a further detailed description of embodiments of the present invention will be provided below, with the understanding that the present invention is described in some, but not all, embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, shall fall within the scope of the present invention.
It should be noted that, without conflict, the embodiments of the present invention and features of the embodiments may be combined with each other. The present invention will be described in detail with reference to examples.
Examples: a discrete companion method and multilayer fast multipole sub-algorithm-based surface sensitivity calculation method of Radar Cross Section (RCS) suitable for optimization design of electric large and ultra-electric large outline low-Radar Cross Section (RCS) is shown in tables 1-2, and specifically comprises the following steps:
s1: the method of multipole expansion of an impedance matrix with respect to a surface mesh partial derivative matrix. In this example, the surface sensitivity calculation method based on the accompanying equation is as follows:
wherein:is radar cross section;Zan impedance matrix for the equation of maxwell Wei Jifen;Vis an excitation vector;ris the surface grid coordinates;Ifor induced current, the method is obtained by solving a Maxwell Wei Jifen equation; />As the accompanying variables, the accompanying equations are obtained by solving the maxwell Wei Jifen equation, and the accompanying equations are as follows:
calculating partial derivative matrix of far-phase acting impedance matrix relative to surface grid by adopting multilayer fast multipole sub-algorithmIn the form of multipole expansion:
wherein,
wherein:is the basis function in far interaction->And base function->Is a resistance element of (a); />Is the angular frequency of the incident wave; />Is magnetic permeability;kis the wave number of the incident wave; />Is the unit direction vector of the incident wave; />Is a configuration factor;to be from->Group center to->Sagittal diameter of group center; />Is a transfer factor; />Is an aggregation factor;
in surface sensitivity solvingThe calculation of (2) is divided into two parts of an in-interaction and a far-interaction, wherein +.>Sparse matrix vector multiplication, far field part->In the form of a aggregation-transfer-configuration.
S2: partial derivative calculation and index storage methods of near field impedance with respect to a surface grid. In this example, the near field impedance elementPartial derivative with respect to the surface grid->At most, only four triangles connected to the basis function m and the basis function n are related to the positions of 8 surface grid points in total. Calculating the partial derivative of the near-field impedance element>When RWG basis function is used, will +.>Is expressed as a combination of the integral terms int1, int2 and their partial derivatives and res1, res2, res3 and their partial derivatives. Wherein the expressions of the integral terms int1 and int2 are as follows:
the expressions of the product terms res1, res2, and res3 are as follows:
wherein:；/>the vector diameter of the basis function; />As a basis functionmIs a length of (2); />Is triangular in shapenIs a part of the area of (2);
thenFor linear combinations of res1, res2 and res3 and their partial derivatives,the calculation form is as follows: to the boxmAnd boxnAll triangle pairs in (1) are looped for the triangle by (b)pAnd triangle shapeqTriangle pairs formed, calculate trianglespMiddle Gaussian integral pointiAnd triangle shapeqGaussian integral in (a)jCorresponding integral amounts int1 and int2; triangle is then calculated from int1 and int2pEdges of (2)mAnd triangle shapeqEdges of (2)nCorresponding impedance matrix elementZ mn With respect to surface grid pointsrIs a partial derivative of (c). Manually deriving the partial derivatives of the product term and the product term with respect to the surface mesh, combining to obtain +.>。
Storage by sparse matrix storage technologyEstablishing a dimension of +.>Is indirectly stored with near field +.>The number of the associated 8 grid points, build +.>Personal->Complex partial derivative matrix storage->Wherein N is e For the number of basis functions>For the near field sparse impedance matrix number, +.>Compressed access pattern for sparse impedance matrix rank sizeThe formula is shown in Table 1.
Table 1: RWG basis function-based impedance matrix partial derivative sparse matrix storage and access method schematic table
Note that: localNum means "position number", put to means "put in", where localNum1 is T + Points in the triangle that do not include the vertices of the basis functions; localNum2 is T - Points in the triangle that do not include the vertices of the basis functions; the number of localNum increases in the right hand direction.
S3: far-interacting aggregation factors, configuration factors, partial derivative calculation methods and index storage methods. Polymerization factorAnd configuration factor->The expression is as follows:
wherein:is of->Group global number->The number in the group is->Is a basis function of (2);is of->Group global numbering of/>The number in the group is->Is a basis function of (2); />A unit normal vector which is a basis function; />Is a mixing factor of an electric field integral equation and a magnetic field integral equation in the mixed field integral equation.
Manual derivationAnd->Is an expression of (2). Polymerization factor->And a configuration factorAt most, only two triangles connected with the basis function m are related to four grid points, and the numbers of the 4 grid points related according to the column number index are adopted during storage, and the compression access form is shown in the table 2.
Table 2: sparse matrix storage and access method schematic table of partial derivatives such as excitation, radar scattering cross section and the like based on RWG basis functions
S4: excitation vector, partial derivative calculation method of radar cross section and index storage method. Manually derived excitation vector V and radar cross sectionPartial derivatives with respect to the surface grid coordinates>And->In the form of an expression of (a). The numbers of the relevant 4 grid points are indexed according to the column numbers during storage, and the compressed access form is shown in table 2.
S5: a calculation method for matrix-vector multiplication of partial derivative matrix and surface current and accompanying variable in far interaction solution. The method will be far fieldThe calculation of (2) is divided into two parts, wherein the first part adopts a matrix-vector multiplier when solving a control equation, and the second part adopts a matrix-vector multiplier when solving an accompanying equation; partial derivative matrix of impedance with respect to surface grid and matrix-vector multiplication of the concomitant variable and surface induced current +.>The calculation shape is as follows:
the calculation time is carried out in two steps Step1 and Step 2:
wherein Step1 adopts an Ax matrix-vector multiplier when solving a control equation; step2 employs A when solving the accompanying equation T x matrix-vector multiplier.
The present embodiment is only for explanation of the present invention and is not to be construed as limiting the present invention, and modifications to the present embodiment, which may not creatively contribute to the present invention as required by those skilled in the art after reading the present specification, are all protected by patent laws within the scope of claims of the present invention.
Claims (6)
1. An RCS surface sensitivity calculation method for MLFMA concomitant solution, comprising:
s1, a multipole unfolding method of an impedance matrix relative to a surface grid partial derivative matrix; the surface sensitivity calculation method based on the accompanying equation is as follows:
wherein: sigma radar cross section, Z is Maxwell Wei Jifen equation impedance matrix; v is an excitation vector; r is the surface grid coordinates; i is an induced current, which is obtained by solving a Maxwell Wei Jifen equation; Λ is a companion variable derived from solving the companion equation of the maxwell Wei Jifen equation, which takes the form of:
calculating partial derivative matrix of far-phase acting impedance matrix relative to surface grid by adopting multilayer fast multipole sub-algorithmIn the form of multipole expansion:
wherein:impedance elements for the basis functions n and n' in the far interaction; omega is the ingressAngular frequency of the wave; mu is magnetic permeability; k is the wave number of the incident wave; />Is the unit direction vector of the incident wave; />Is a configuration factor; />Is from m G-1 Group center to m G Sagittal diameter of group center; t (T) L Is a transfer factor; />Is an aggregation factor;
in surface sensitivity solvingThe calculation of (2) is divided into two parts of an in-interaction and a far-interaction, whereinSparse matrix vector multiplication, far field part->In the form of a aggregation-transfer-configuration;
s2, calculating partial derivatives of near interaction impedance elements on the surface grids and storing indexes; near field impedance element Z mn Partial derivatives with respect to surface meshesFour triangles connected to the basis function m and the basis function n, the positions of 8 surface grid points in total being related; calculating the partial derivative of the near-field impedance element>When RWG basis function is used, will +.>Expressed as a combination of integral terms int1, int2 and their partial derivatives and res1, res2, res3 and their partial derivatives; wherein the expressions of the integral terms int1 and int2 are as follows:
the expressions of the product terms res1, res2, and res3 are as follows:
wherein: r= |r m -r′ n |；The vector diameter of the basis function; l (L) m Length as basis function m; />Is the area of triangle n;
thenFor linear combinations of res1, res2 and res3 and their partial derivatives, the form of calculation is as follows: circulation is performed for all triangle pairs in box m and box n, for triangles consisting of triangle p and triangle qShape pairs, calculating the impedance matrix element Z corresponding to Gao Siji point i in triangle p and edge n in triangle q mn Partial derivatives about surface grid points r; manually deriving the partial derivatives of the product term and the product term with respect to the surface mesh, combining to obtain +.>
Storage by sparse matrix storage technologyEstablishing dimension N based on base function number e X 4 integer node index, line number index according to impedance matrix partial derivative indirectly stores and near field Z mn The number of the related 8 grid points establishes N sparse N number n,i ×N n,j 8 Complex partial derivative matrix storage ∈8>Wherein N is e As the number of basis functions, N sparse For the near field sparse impedance matrix number, (N) n,i ,N n,j ) Is the size of a sparse impedance matrix row and column;
s3, calculating a partial derivative of an aggregation factor and a configuration factor with respect to a surface grid in the far interaction and storing an index; polymerization factorAnd configuration factor->The expression is as follows:
wherein:to be m' G Global numbering n ' for the group and alpha ' for the intra-group ' G Is a basis function of (2); />Group global number n and group internal number alpha G Is a basis function of (2); />A unit normal vector which is a basis function; alpha is a mixing factor of an electric field integral equation and a magnetic field integral equation in the mixed field integral equation;
manual derivationAnd->Is an expression of (2); polymerization factor->And configuration factor->In the calculation of (a), at most, only two triangles connected with a basis function m are related to four grid points, and the serial numbers of the related 4 grid points are indexed according to the serial numbers during storage;
s4, calculating a partial derivative of the excitation vector and the radar cross section with respect to the surface grid and storing an index; manually derived excitation vector V and radar cross section σ with respect to the surfacePartial derivative of grid coordinatesAnd->Is the expression form of (a); the serial numbers of the related 4 grid points are indexed according to the serial numbers during storage;
s5, calculating a matrix-vector multiplication method of the partial derivative matrix of the medium impedance and the surface current and the accompanying variable through far interaction; the method will be far fieldThe calculation of (2) is divided into two parts, wherein the first part adopts a matrix-vector multiplier when solving a control equation, and the second part adopts a matrix-vector multiplier when solving an accompanying equation; partial derivative matrix of impedance with respect to surface grid and matrix-vector multiplication of the concomitant variable and surface induced current +.>The calculation shape is as follows:
the calculation time is carried out in two steps Step1 and Step 2:
wherein Step1 adopts an Ax matrix-vector multiplier when solving a control equation; step2 employs A when solving the accompanying equation T x matrix-vector multiplier.
2. The method for computing the RCS surface sensitivity of the MLFMA concomitant solution according to claim 1, wherein the method comprises the following steps: the multi-pole expansion method of the impedance matrix relative to the surface grid partial derivative matrix adopts a multi-layer rapid multi-pole algorithm to solve the surface sensitivity of the target appearance by combining with an accompanying equation, and performs multi-pole expansion on the impedance matrix relative to the surface grid partial derivative matrix to form a matrix-vector product calculation method between the impedance partial derivative matrix and the induced current and accompanying variables suitable for far interaction.
3. The method for computing the RCS surface sensitivity of the MLFMA concomitant solution according to claim 1, wherein the method comprises the following steps: method for calculating and index storage of partial derivatives of near field impedance with respect to surface grid, said method deriving near field impedance matrix partial derivativesIs an expression of (2); combination->The sparsity of (2) adopts a sparse matrix storage method to establish integer array storage indexes and complex array storage matrix elements.
4. The method for computing the RCS surface sensitivity of the MLFMA concomitant solution according to claim 1, wherein the method comprises the following steps: far-interacting aggregation factor, partial derivative calculation method of configuration factor and index storage method, said method being based onIs derived from multipole expansion results of (2)>And->And stored using a sparse matrix storage method.
5. The method for computing the RCS surface sensitivity of the MLFMA concomitant solution according to claim 1, wherein the method comprises the following steps: excitation vector, partial derivative calculation method and index storage method of radar scattering cross section, and excitation vector partial derivative is deducedDerivative ofRadar cross section partial derivative +.>And stored by adopting a sparse matrix storage method.
6. The method for computing the RCS surface sensitivity of the MLFMA concomitant solution according to claim 1, wherein the method comprises the following steps: method for calculating the matrix-vector multiplication of partial derivative matrix with surface current, concomitant variable in far-field interaction solution, said method involving far-fieldThe calculation of (2) is divided into two parts, wherein the first part adopts a matrix-vector multiplier when solving a control equation, and the second part adopts a matrix-vector multiplier when solving an accompanying equation.
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