CN106156431A - Target conductor electromagnetic scattering emulation mode based on nurbs surface modeling - Google Patents

Abstract

The invention discloses a kind of target conductor electromagnetic scattering emulation mode based on nurbs surface modeling, mainly solve the problem that existing method simulation efficiency is low and high to calculator memory demand.Its scheme is: 1. modeled Scattering Targets by business software Rhino nurbs surface；2. the parameter region of pair Scattering Targets model decomposes, and derives the coordinate formula of nurbs surface, and then obtains target conductor physical optics scattering integral and edge diffraction field integral formula；3. Computational Physics optical scattering integration and edge diffraction field principal value of integral；4. utilize physical optics scattering integral and edge diffraction field principal value of integral, obtain the Monostatic RCS RCS of target conductor.The present invention, on the premise of ensureing precision, improves simulation efficiency, reduces the emulation experiment demand to calculator memory, can be used for obtaining the Monostatic RCS RCS of Scattering Targets.

Description

Target conductor electromagnetic scattering emulation mode based on nurbs surface modeling

Technical field

The invention belongs to radar electromagnetic simulation technique field, relate generally to electromagnetic scattering numerical simulation, specifically a kind of base In the target conductor electromagnetic scattering emulation mode of non-uniform rational B-spline nurbs surface modeling, for obtaining the list of Scattering Targets Stand RCS RCS.

Background technology

Along with the fast development of information technology, modern war is developed into IT-based warfare by mechanized warfare.Modern spy Measurement equipment and armament systems to intelligent, in high precision, develop at a distance, the electromagnetic scattering research of complex target theory analysis with Actual application has great importance.When airborne or spaceborne radar carry out electromagnetic surveying to the complex target such as aircraft, guided missile Time, by echo-signal analysis, and then certain forewarning function can be played.The electric size of Scattering Targets is defined as scattering mesh Target physical size and the ratio of incidence wave wavelength.When the physical size of Scattering Targets is far longer than incident wavelength, scatter mesh Being designated as Electrically large size object, its electromagnetic scattering problems is TV university scattering problems.Owing to radar system is operated in microwave frequency band, common The huge unknown quantity that the contour structures of the target complexity of military target such as aircraft, guided missile, naval vessel etc. and electrically large sizes are caused is asked Topic, adds the complexity that target radar scattering cross-section RCS estimates.Therefore, the thunder of this type of target is calculated the most quickly and efficiently Reach scattering section and become numerous scholars problem of interest.Thus, the research of complex target scattering properties in national defence and Civil area has significant learning value and is widely applied prospect.

Along with developing rapidly of computer technology, particularly hardware technology, RCS is with its good real-time And interactivity so that understand its Electromagnetic Scattering Characteristics at the development initial stage of weaponry and be possibly realized, become the high-end force of control Device design cost and the important means of design cycle.When having come into TV university target due to the research of present stage Electromagnetic Scattering Characteristics In generation, huge unknown quantity causes the calculating of RCS very time-consumingly, and tradition full-wave simulation method, such as moment method, time domain The simulation efficiency of the method such as finite difference method, finite element can not meet engineer applied requirement the most completely.

Summary of the invention

Present invention aims to current TV university scattering problems, it is proposed that a kind of based on leading that nurbs surface models Body Electromagnetic Scattering of Target emulation mode, with while ensureing simulation accuracy, improves the efficiency of electromagnetic scattering emulation, reduces emulation The experiment demand to calculator memory, meets engineer applied requirement.

For achieving the above object, technical scheme includes the following:

(1) opening business software Rhino, click on " control point coordinate sets up curved surface " in surface model option, input dissipates Penetrate target control point coordinates, obtain the non-uniform rational B-spline nurbs surface model of Scattering Targets, and with " iges " tray Formula derives institute's established model；

(2) the nurbs surface bin information included in " iges " file is read, and by the parameter region of nurbs surface It is decomposed into multiple subparameter region, derives the coordinate formula of NURBS subsurface corresponding to each subparameter region:Wherein τ=3i+j+1, α_τAnd β_τFor multinomial coefficient；

(3) according to physics diffraction theory, obtaining target conductor scattering electric field integration, this integration includes that physical optics scattering is long-pending Divide and edge diffraction field integration；

(4) Computational Physics optical scattering integration, including step:

4.1) coordinate of three class key points of Computational Physics optical scattering integration, i.e. first kind key point coordinate (u_s,v_s), Equations of The Second Kind key point coordinate (u_c,v_c), the 3rd class key point coordinate (u_V,v_V)；

4.2) the above-mentioned three class key points contribution margin I to physical optics scattering integral is calculated respectively_s, I_c, I_V；

4.3) according to 4.2) result, obtain value E of physical optics scattering integral^PO=I_s+I_c+I_V；

(5) edge diffraction field integration is calculated, including step:

5.1) calculate edge diffraction field integration in phase point (u_d,v_d)；

5.2) calculate in phase point (u_d,v_d) contribution margin I to diffraction field, edge integration_d；

5.3) according to 5.2) result, obtain edge diffraction field principal value of integral E^d=I_d；

(6) target conductor scattering electric field principal value of integral: E is calculated_s=E^PO+E^d；

(7) target conductor scattering electric field integrated value E is utilized_s, obtain the Monostatic RCS RCS of target conductor.

Compared with prior art, present invention have the advantage that

1. improve the efficiency of electromagnetic scattering emulation

Due to the fact that and use technical scheme nurbs surface being modeled and key point being calculated, not only increase The efficiency of electromagnetic scattering emulation, and simulation time is unrelated with the electric size of Scattering Targets, can realize electrically large sizes mesh Target electromagnetic scattering emulates；

2. reduce the emulation experiment demand to calculator memory

Due to the fact that the method in phase bit of use calculates the scattered field of target conductor, thus emulation experiment is in computer The demand deposited is far smaller than the quick multistage submethod MLFMM of existing multilamellar and Gordon integration method.

Accompanying drawing explanation

Fig. 1 is the flowchart of the present invention；

Fig. 2 is the decomposing schematic representation in the present invention to nurbs surface parameter region；

Fig. 3 is physical optics scattering integral three class key point coordinate position view in parameter region in the present invention；

Fig. 4 is the nurbs surface model of convex surface Scattering Targets；

Fig. 5 is the nurbs surface model of saddle camber Scattering Targets；

Fig. 6 is under the conditions of different angle of incidence, by the present invention and existing multilevel fast multipole method MLFMM and Gordon integration method carries out electromagnetic scattering and emulates the mono-static RCS correlation curve figure obtained model in Fig. 4；

Fig. 7 is under the conditions of different angle of incidence, by the present invention and existing multilevel fast multipole method MLFMM and Gordon integration method carries out electromagnetic scattering and emulates the mono-static RCS correlation curve figure obtained model in Fig. 5；

Fig. 8 is under different incidence wave frequency conditions, by the present invention and Gordon integration method, model in Fig. 4 is carried out electricity The simulation time correlation curve figure of magnetic scattering emulation；

Fig. 9 is under different incidence wave frequency conditions, by the present invention and Gordon integration method, model in Fig. 5 is carried out electricity The simulation time correlation curve figure of magnetic scattering emulation.

Detailed description of the invention

Below in conjunction with the accompanying drawings embodiments of the invention and effect are described in further detail.

With reference to Fig. 1, the present invention to realize step as follows:

Step 1: obtain Scattering Targets model.

(1a) opening business software Rhino, click on " control point coordinate sets up curved surface " in surface model option, input dissipates Penetrate the control point coordinate of target, obtain the nurbs surface model of Scattering Targets.

(1b) built Scattering Targets model is derived with " iges " file format.

Step 2: calculate the coordinate of point on nurbs surface, comprise the steps.

(2a) reading the bin information of nurbs surface in " iges " file, this bin information includes nurbs surface u direction Knot vector U=[0.0 ..., 1.0], v direction knot vector V=[0.0 ..., 1.0], control point coordinate d_i,jWith weights ω_i,j, Wherein, i=0 ..., m, j=0 ..., n, m and n are respectively u direction and v direction controlling point sum；

(2b) Fig. 2 is combined, according to u direction knot vector U and v direction knot vector V, by the parameter region of nurbs surface Ω=[0.0,1.0] × [0.0,1.0] is decomposed into multiple subparameter region Ω '=[u_I,u_I+1]×[v_J,v_J+1], each subparameter The corresponding NURBS subsurface in region, wherein, u_IAnd u_I+1The i-th of respectively u direction knot vector U and the I+1 node, v_JAnd v_J+1The j-th of respectively v direction knot vector V and the J+1 node, wherein, I=1 ..., umax-1, J=1 ..., Vmax-1, umax and vmax are respectively u direction knot vector U and the node total number of v direction knot vector V；

(2c) subparameter region Ω '=[u is calculated_I,u_I+1]×[v_J,v_J+1] point on corresponding NURBS subsurface (u, v) Coordinate formula r (u, v) formula is:

$r(u,v)=\frac{p(u,v)}{\mathrm{\&omega;}(u,v)}---<1>$

Wherein, (u, v) is the first intermediate variable to p, and (u, v) is the second intermediate variable to ω, and (u, v) with ω (u, calculating v) for p Formula is:

$p(u,v)=\underset{i=0}{\overset{2}{\&Sigma;}}\underset{j=0}{\overset{2}{\&Sigma;}}{\mathrm{\&alpha;}}_{\mathrm{\&tau;}}{u}^i{v}^j---<2>$

$\mathrm{\&omega;}(u,v)=\underset{i=0}{\overset{2}{\&Sigma;}}\underset{j=0}{\overset{2}{\&Sigma;}}{\mathrm{\&beta;}}_{\mathrm{\&tau;}}{u}^i{v}^j---<3>$

Wherein, τ=3i+j+1, α_τIt is the first intermediate variable p (u, multinomial coefficient v), β_τIt is the second intermediate variable ω (u, multinomial coefficient v), τ ∈ [1,9].

(2d) the first intermediate variable p (u, multinomial coefficient α v) are calculated respectively_τWith the second intermediate variable ω (u, v) many Binomial coefficient β_τ:

$\left[\begin{array}{c}{\mathrm{\&alpha;}}_1\\ {\mathrm{\&alpha;}}_2\\ {\mathrm{\&alpha;}}_3\\ {\mathrm{\&alpha;}}_4\\ {\mathrm{\&alpha;}}_5\\ {\mathrm{\&alpha;}}_6\\ {\mathrm{\&alpha;}}_7\\ {\mathrm{\&alpha;}}_8\\ {\mathrm{\&alpha;}}_9\end{array}\right]=A^{-1}\left[\begin{array}{c}{p}^{\&prime;}(u_1,v_1)\\ p^{\&prime;}(u_2,v_1)\\ p^{\&prime;}(u_3,v_1)\\ p^{\&prime;}(u_1,v_2)\\ p^{\&prime;}(u_2,v_2)\\ p^{\&prime;}(u_3,v_2)\\ p^{\&prime;}(u_1,v_3)\\ p^{\&prime;}(u_2,v_3)\\ p^{\&prime;}(u_3,v_3)\end{array}\right]---<4>$

$\left[\begin{array}{c}{\mathrm{\&beta;}}_1\\ {\mathrm{\&beta;}}_2\\ {\mathrm{\&beta;}}_3\\ {\mathrm{\&beta;}}_4\\ {\mathrm{\&beta;}}_5\\ {\mathrm{\&beta;}}_6\\ {\mathrm{\&beta;}}_7\\ {\mathrm{\&beta;}}_8\\ {\mathrm{\&beta;}}_9\end{array}\right]=A^{-1}\left[\begin{array}{c}{\mathrm{\&omega;}}^{\&prime;}(u_1,v_1)\\ {\mathrm{\&omega;}}^{\&prime;}(u_2,v_1)\\ {\mathrm{\&omega;}}^{\&prime;}(u_3,v_1)\\ {\mathrm{\&omega;}}^{\&prime;}(u_1,v_2)\\ {\mathrm{\&omega;}}^{\&prime;}(u_2,v_2)\\ {\mathrm{\&omega;}}^{\&prime;}(u_3,v_2)\\ {\mathrm{\&omega;}}^{\&prime;}(u_1,v_3)\\ {\mathrm{\&omega;}}^{\&prime;}(u_2,v_3)\\ {\mathrm{\&omega;}}^{\&prime;}(u_3,v_3)\end{array}\right]---<5>$

Wherein, matrix A^-1For the inverse matrix of matrix A, (u, v) is control point function to p ', and (u v) is weight function, square to ω ' The expression formula of battle array A is:

$A=\left[\begin{array}{ccccccccc}1& u_1& u_1^2& v_1& u_1{v}_1& u_1{v}_1^2& v_1^2& u_1{v}_1^2& u_1^2{v}_1^2\\ 1& u_2& u_2^2& v_2& u_2{v}_1& u_2{v}_1^2& v_1^2& u_2{v}_1^2& u_2^2{v}_1^2\\ 1& u_3& u_3^2& v_3& u_3{v}_1& u_3{v}_1^2& v_1^2& u_3{v}_1^2& u_3^2{v}_1^2\\ 1& u_1& u_1^2& v_1& u_1{v}_2& u_1{v}_2^2& v_2^2& u_1{v}_2^2& u_1^2{v}_2^2\\ 1& u_2& u_2^2& v_2& u_2{v}_2& u_2{v}_2^2& v_2^2& u_2{v}_2^2& u_2^2{v}_2^2\\ 1& u_3& u_3^2& v_3& u_3{v}_2& u_3{v}_2^2& v_2^2& u_3{v}_2^2& u_3^2{v}_2^2\\ 1& u_1& u_1^2& v_1& u_1{v}_3& u_1{v}_3^2& v_3^2& u_1{v}_3^2& u_1^2{v}_3^2\\ 1& u_2& u_2^2& v_2& u_2{v}_3& u_2{v}_3^2& v_3^2& u_2{v}_3^2& u_2^2{v}_3^2\\ 1& u_3& u_3^2& v_3& u_3{v}_3& u_3{v}_3^2& v_3^2& u_3{v}_3^2& u_3^2{v}_3^2\end{array}\right]---<6>$

Wherein, u₁, u₂, u₃It is respectively the nurbs surface coordinate at first, second and third sampled point of u direction, u₁=u_I,u₃=u_I+1；v₁, v₂, v₃It is respectively the nurbs surface coordinate at first, second and third sampled point in v direction, v₁ =v_J,v₃=v_J+1；Control point function p ' (u, v) and weight function ω ' (u, v) computing formula is:

$p^{\&prime;}(u,v)=\underset{i=I-2}{\overset{I}{\&Sigma;}}\underset{j=J-2}{\overset{J}{\&Sigma;}}{\mathrm{\&omega;}}_{i,j}{d}_{i,j}{N}_{i,2}\left(u\right)N_{j,2}\left(v\right)---<7>$

${\mathrm{\&omega;}}^{\&prime;}(u,v)=\underset{i=I-2}{\overset{I}{\&Sigma;}}\underset{j=J-2}{\overset{J}{\&Sigma;}}{\mathrm{\&omega;}}_{i,j}{N}_{i,2}\left(u\right)N_{j,2}\left(v\right)---<8>$

Wherein, N_i,2(u) and N_j,2V () is respectively nurbs surface u direction and the Quadric Spline basic function in v direction, NURBS The Quadric Spline basic function N of curved surface u direction_i,2U () computing formula is:

$N_{i,2}\left(u\right)=\frac{u-u_i}{u_{i+2}-u_i}\frac{u-u_i}{u_{i+1}-u_i}---<9>$

Wherein, u_i, u_i+1, u_i+2Respectively the i-th of nurbs surface u direction knot vector U, i+1, i+2 node, NURBS The Quadric Spline basic function N in curved surface v direction_j,2V () computing formula is:

$N_{j,2}\left(v\right)=\frac{v-v_j}{v_{j+2}-v_j}\frac{v-v_j}{v_{j+1}-v_j}---<10>$

Wherein, v_j, v_j+1, v_j+2For the jth of nurbs surface v direction knot vector V, j+1, j+2 node

Step 3: build target conductor scattering electric field integral expression.

(3a) scatter basic theories according to physical optics, obtain physical optics scattering integral E^POExpression formula:

$E^{\mathrm{PO}}=A^{\mathrm{PO}}{\&Integral;}_{\mathrm{\&Omega;}}g(u,v)e^{j_0\mathrm{kf}(u,v)}\mathrm{dudv}---<1>$

Wherein,j₀For imaginary unit, λ is incidence wave wavelength, and k is the wave number of electromagnetic wave, and r is emulation Position is from the distance of zero；Ω is the integral domain of physical optics scattering integral；(u, v) (u v) is respectively physics to g with f The amplitude function of optical scattering integration and phase function；

Amplitude function g (u, v) expression formula is:

$g(u,v)={\hat{k}}_s\&times;\{{\hat{k}}_s\&times;\&lsqb;(r_u\&times;r_v)\&times;({\hat{k}}_i\&times;E_0)\&rsqb;\}---<12>$

Wherein,For electromagnetic wave incident direction unit vector,For electromagnetic scattering direction unit vector, r_uFor scattering mesh Put on point coordinates r (u, v) partial derivative to u, r_vFor point coordinates parameter r on Scattering Targets (u, v) partial derivative to v, E₀For coordinate The electric field component of incidence wave at initial point；

Phase function f (u, v) expression formula is:

$f(u,v)=\frac{\mathrm{\&xi;}(u,v)}{\mathrm{\&omega;}(u,v)}---<13>$

Wherein, ξ (u, v) is the 3rd intermediate variable, and its computing formula is:

Wherein,For electromagnetic scattering direction unit vector,For electromagnetic wave incident direction unit vector, ζ_τIt is in the 3rd Between the coefficient of variable,Computing formula be

(3b) according to edge diffraction basic theories, edge diffraction integration E is obtained^dExpression formula is:

Wherein,Z₀For free space natural impedance, λ is incidence wave wavelength, and r is that emulation location is from initial point Distance, integral domainFor the integral domain of edge diffraction integration, g^d(u v) is amplitude function, f^d(u, v) is phase function, Its computing formula is:

$g^d(u,v)={\hat{k}}_s\&times;({\hat{k}}_s\&times;I_l)+\frac{({\hat{k}}_s\&times;M_l)}{Z_0}---<16>$

Wherein, I_lAnd M_lIt is respectively the equivalent current on diffraction edge and equivalent magnetic current；

(3c) according to physics diffraction theory, target conductor scattering electric field integration E_sFor physical optics integration E^POAnd edge Diffraction field integration E^dSum, thus, obtain target conductor scattering electric field integration E_sExpression formula E_s=E^PO+E^d。

Step 4: three class key points of Computational Physics optical scattering integration.

4.1) the first kind key point (u of Computational Physics optical integration_s,v_s):

(4.1a) according to the basic theories of method in phase bit, build and solve first kind key point coordinate (u_s,v_s) equation Group:

$\begin{array}{c}{f}_u(u,v)=\frac{{\mathrm{\&xi;}}_u(u,v)\mathrm{\&omega;}(u,v)-\mathrm{\&xi;}(u,v){\mathrm{\&omega;}}_u(u,v)}{{\&lsqb;\mathrm{\&omega;}(u,v)\&rsqb;}^2}=0\\ f_v(u,v)=\frac{{\mathrm{\&xi;}}_v(u,v)\mathrm{\&omega;}(u,v)-\mathrm{\&xi;}(u,v){\mathrm{\&omega;}}_v(u,v)}{{\&lsqb;\mathrm{\&omega;}(u,v)\&rsqb;}^2}=0\end{array}---<18>$

Wherein, f_u(u v) is physical optics scattering integral phase function f (u, v) partial derivative to u, f_v(u v) is physics Optical scattering integration phase function f (u, v) partial derivative to v, ξ_u(u, v) be the 3rd intermediate variable ξ (u, v) partial derivative to u, ω_u(u v) is the second intermediate variable ω (u, v) partial derivative to u, ξ_v(u, (u, v) to v's v) to be respectively the 3rd intermediate variable ξ Partial derivative, ω_v(u, v) be the second intermediate variable ω (u, v) partial derivative to v, its computing formula is:

ω_u(u, v)=(β₄+β₅v+β₆v²)+2(β₇+β₈v+β₉v²)u <20>

ω_v(u, v)=(β₂+β₅u+β₈u²)+2(β₃+β₆u+β₉u²)v <22>

By in formula<3>ω (u, v), ξ in formula<14>(u, ξ v), in formula<19>-<22>_u(u, v), ω_u(u, V), ξ_v(u, v), ω_v(u, v) substitutes into formula<18>abbreviation, obtains equation below group:

$\begin{array}{c}{c}_0\left(v\right)u^2+c_1\left(v\right)u+c_2\left(v\right)=0\\ d_0\left(u\right)v^2+d_1\left(u\right)v+d_2\left(u\right)=0\end{array}---<23>$

Wherein, c₀V () is secondary u coefficient function, c₁V () is a u coefficient function, c₂V () is zero degree u coefficient function, d₀ U () is secondary v coefficient function, d₁U () is a v coefficient function, d₂U () is zero degree v coefficient function, its computing formula is:

(4.1b) to the solving equations in formula<23>, first kind key point coordinate (u is obtained_s,v_s)。

4.2) the Equations of The Second Kind key point (u of Computational Physics optical integration_c,v_c):

Understand in conjunction with Fig. 3, the Equations of The Second Kind key point (u of physical optics scattering integral_c,v_c) it is positioned at nurbs surface parameter region Four edges circle on, four edges circle is respectively u=0, u=1, v=0 and v=1 border, accordingly to Equations of The Second Kind key point (u_c,v_c) Be specifically calculated as follows:

4.2a) set Equations of The Second Kind key point (u on u=0 border_c,v_c) coordinate isSubstantially manage according to method in phase bit Opinion, builds Equations of The Second Kind key point v direction coordinate on u=0 borderEquation:

d₀(0)v²+d₁(0)v+d₂(0)=0<30>

To the equation solution in above formula, obtain Equations of The Second Kind key point on u=0 borderCoordinate；

4.2b) set Equations of The Second Kind key point (u on u=1 border_c,v_c) coordinate isSubstantially manage according to method in phase bit Opinion, builds Equations of The Second Kind key point v direction coordinate on u=1 borderEquation:

d₀(1)v²+d₁(1)v+d₂(1)=0<31>

To the equation solution in above formula, obtain Equations of The Second Kind key point on u=0 borderCoordinate；

4.2c) set Equations of The Second Kind key point (u on v=0 border_c,v_c) coordinate isSubstantially manage according to method in phase bit Opinion, builds Equations of The Second Kind key point u direction coordinate on v=0 borderEquation:

c₀(0)u²+c₁(0)u+c₂(0)=0<32>

To the equation solution in above formula, obtain Equations of The Second Kind key point u direction coordinate on v=0 border

4.2d) set Equations of The Second Kind key point (u on v=1 border_c,v_c) coordinate is (u_c, 1), basic according to method in phase bit Theory, builds Equations of The Second Kind key point u direction coordinate on v=1 borderEquation:

c₀(1)u²+c₁(1)u+c₂(1)=0<33>

To the equation solution in above formula, obtain Equations of The Second Kind key point u direction coordinate on v=1 border

4.3) the 3rd class key point (u of Computational Physics optical integration_V,v_V)

Understand in conjunction with Fig. 3, four angles that the 3rd class key point is nurbs surface parameter region of physical optics scattering integral Point, therefore, the 3rd class key point (u_V,v_V) it is (0,0), (1,0), (0,1), (1,1).

Step 5: Computational Physics optical scattering principal value of integral E^PO。

5.1) according to method in phase bit, first kind key point (u is calculated_s,v_s) contribution margin to physical optics scattering integral I_s；

5.2) according to method in phase bit, Equations of The Second Kind key point (u is calculated_c,v_c) contribution margin to physical optics scattering integral I_c；

5.3) according to method in phase bit, the 3rd class key point (u is calculated_V,v_V) contribution margin to physical optics scattering integral I_V；

5.4) according to 5.1), 5.2), 5.3) result of calculation, the value obtaining physical optics scattering integral is E^PO=I_s+I_c+ I_V。

Step 6: calculate edge diffraction principal value of integral E^d

6.1) point coordinates in phase of calculating edge diffraction integration:

By formula<13>and<17>, and the phase function f of edge diffraction integration (u, v) and the phase of physical optics integration Bit function f^d(u, v) equal, the therefore (u of point coordinates in phase of edge diffraction integration_d,v_d) it is physical optics integration Equations of The Second Kind pass Key point coordinates (u_c,v_c)；

6.2) according to the basic theories of method in phase bit, calculate and stay phase point (u_d,v_d) contribution margin to diffraction field, edge integration I_d；

6.3) according to 6.2) result, obtain edge diffraction field principal value of integral E^d=I_d。

Step 7: according to physics diffraction theory, calculates target conductor scattering electric field integrated value E_sFor: E_s=E^PO+E^d, wherein E^POFor physical optics integrated value, E^dFor edge diffraction field integrated value.

Step 8: obtain the Monostatic RCS RCS of Scattering Targets.

According to target conductor scattering electric field integrated value E_s, utilize radar scattering coefficient equation, obtain the list station of Scattering Targets RCS RCS:

$RCS=10log\left(4{\mathrm{\&pi;r}}^2\right|\frac{E_s}{E^{inc}}{|}^2)---<34>$

Wherein, r is the emulation location distance from zero, E^incElectric vector for incidence wave.

The effect of the present invention can be further illustrated by following instance:

1. simulated conditions

Radar incident frequencies f=3.0GHz, the incidence wave wavelength X=0.1m used in emulation experiment, incidence wave is plane Electromagnetic wave, the electric vector of incidence wave isE₀For the electric field intensity of zero, r ' is on Scattering Targets The coordinate of point, polarization of electromagnetic wave mode is vertical polarization.

Emulation experiment is Intel (R) Core (TM) i3 at CPU, dominant frequency 3.3GHz, and free memory is the Windows of 3.5GB Complete with Intel Fortran 2010 software programming in 7 systems.

2. test simulation example and interpretation of result

Emulation experiment 1:

If incidence angle θ_i∈ [0 °, 90 °], incident orientation angleLong-pending by the inventive method and existing MLFMM, Gordon Point method is scattered emulation to the convex surface target shown in Fig. 4, obtains mono-static RCS result, such as Fig. 6.Can from Fig. 6 Going out, in all of angle of incidence, the inventive method emulates the mono-static RCS result and existing MLFMM and Gordon integration side obtained The mono-static RCS result that obtains of method emulation is basically identical, it was demonstrated that the accuracy of emulation mode of the present invention.

Emulation experiment 2, by the inventive method and existing MLFMM method and Gordon integration method to the convex song shown in Fig. 4 Area Objects is scattered emulation, its simulation time and memory requirements such as table 1.

Table 1 distinct methods is scattered simulation time and the memory requirements of emulation to Fig. 4 model

Emulation mode	Simulation time (second)	Memory requirements (MB)
			The inventive method	0.018	0.003
MLFMM	61124.208	52793
			Gordon integration method	7.379	65.92

From table 1 it follows that model in Fig. 4 is scattered the simulation time of emulation and memory requirements all by the present invention It is far smaller than existing MLFMM and Gordon integration method.As can be seen here, the present invention improves the emulation effect of electromagnetic scattering emulation Rate, provides one emulation mode fast and effectively for scattering Electromagnetic Scattering of Target.

Emulation experiment 3

If incidence angle θ_i=90 °, incident orientation angleWith the inventive method and existing MLFMM, Gordon Integration method is scattered emulation to the saddle camber target shown in Fig. 5, obtains mono-static RCS, result such as Fig. 7.

It can be seen from figure 7 that in all of angle of incidence, the mono-static RCS result 7 that the inventive method emulation obtains is with existing There is the mono-static RCS result that obtains of MLFMM and Gordon integration method emulation basically identical, it was demonstrated that the standard of emulation mode of the present invention Really property.

Emulation experiment 4, by the inventive method and existing MLFMM method and Gordon integration method to the saddle shown in Fig. 5 Area Objects is scattered emulation, its simulation time and memory requirements such as table 2.

Table 2 distinct methods is scattered simulation time and the memory requirements of emulation to Fig. 5 model

Emulation mode	Simulation time (second)	Memory requirements (MB)
			The inventive method	0.032	0.008
MLFMM	4954.478	31280
			Gordon integration method	5.023	37.07

From Table 2, it can be seen that with the present invention saddle camber target shown in Fig. 5 is scattered emulation simulation time and Memory requirements is all far smaller than existing MLFMM and Gordon integration method.As can be seen here, the present invention improves electromagnetic scattering emulation Simulation efficiency.

Emulation experiment 5

If incidence wave frequency f ∈ [1GHz, 20GHz], with convex to shown in Fig. 4 of this method and existing Gordon integration method Curved surface target is scattered emulation, its simulation time such as Fig. 8.

As can be seen from Figure 8, when the convex surface target shown in Fig. 4 being scattered emulation, simulation time of the present invention Keep constant along with the increase of incidence wave frequency, the simulation time of Gordon integration method along with incidence wave frequency increase and Increase, thus illustrate that the most existing method of the inventive method improves the efficiency of emulation.

Emulation experiment 6

If incidence wave frequency f ∈ [1GHz, 20GHz], by this method and existing Gordon integration method to the horse shown in Fig. 5 Saddle Area Objects is scattered emulation, its simulation time such as Fig. 9.

It can be seen in figure 9 that when the saddle camber target shown in Fig. 5 being scattered emulation, simulation time of the present invention Keep constant along with the increase of incidence wave frequency, the simulation time of Gordon integration method along with incidence wave frequency increase and Increase, again illustrate the simulation efficiency of the inventive method.

Claims (4)

1. a target conductor electromagnetic scattering emulation mode based on nurbs surface modeling, including step:

(1) open business software Rhino, click on " control point coordinate sets up curved surface " in surface model option, input scattering mesh Mark control point coordinate, obtains the non-uniform rational B-spline nurbs surface model of Scattering Targets, and leads with " iges " file format Go out institute's established model；

(2) read the nurbs surface bin information included in " iges " file, and the parameter region of nurbs surface is decomposed For multiple subparameter regions, derive the coordinate formula of NURBS subsurface corresponding to each subparameter region:Wherein τ=3i+j+1, α_τAnd β_τFor multinomial coefficient；

(3) according to physics diffraction theory, obtain target conductor scattering electric field integration, this integration include physical optics scattering integral and Edge diffraction field integration；

(4) Computational Physics optical scattering integration, including step:

4.1) coordinate of three class key points of Computational Physics optical scattering integration, i.e. first kind key point coordinate (u_s,v_s), second Class key point coordinate (u_c,v_c), the 3rd class key point coordinate (u_V,v_V)；

4.2) the above-mentioned three class key points contribution margin I to physical optics scattering integral is calculated respectively_s, I_c, I_V；

4.3) according to 4.2) result, obtain value E of physical optics scattering integral^PO=I_s+I_c+I_V；

(5) edge diffraction field integration is calculated, including step:

5.1) calculate edge diffraction field integration in phase point (u_d,v_d)；

5.2) calculate in phase point (u_d,v_d) contribution margin I to diffraction field, edge integration_d；

5.3) according to 5.2) result, obtain edge diffraction field principal value of integral E^d=I_d；

(6) target conductor scattering electric field principal value of integral: E is calculated_s=E^PO+E^d；

(7) target conductor scattering electric field integrated value E is utilized_s, obtain the Monostatic RCS RCS of target conductor.

2. according to the target conductor electromagnetic scattering emulation mode based on nurbs surface modeling described in claims 1, Qi Zhongbu Suddenly in (2) by be derived by NURBS subsurface corresponding to each subparameter region coordinate formula r (u, v), as follows Carry out:

(2a) reading the bin information of nurbs surface in " iges " file, this bin information includes nurbs surface u direction node Vector U=[0.0 ..., 1.0], v direction knot vector V=[0.0 ..., 1.0], control point coordinate d_i,jWith weights ω_i,j, its In, i=0 ..., m, j=0 ..., n, m and n are respectively u direction and v direction controlling point sum；

(2b) according to u direction knot vector U and v direction knot vector V, by the parameter region Ω of nurbs surface=[0.0,1.0] × [0.0,1.0] is decomposed into multiple subparameter region Ω '=[u_I,u_I+1]×[v_J,v_J+1], corresponding one of each subparameter region NURBS subsurface, wherein, u_IAnd u_I+1It is respectively i-th and the I+1 node, the v of u direction knot vector U_JAnd v_J+1It is respectively The j-th of v direction knot vector V and the J+1 node, I=1 ..., umax-1, J=1 ..., vmax-1, umax and vmax divide Wei u direction knot vector U and the node total number of v direction knot vector V；

(2c) subparameter region Ω '=[u_I,u_I+1]×[v_J,v_J+1] on corresponding NURBS subsurface point coordinate formula r (u, v) For:

$r(u,v)=\frac{p(u,v)}{\mathrm{\&omega;}(u,v)}---<1>$

Wherein, (u, v) is the first intermediate variable to p, and (u, v) is the second intermediate variable to ω, and (u, v) with ω (u, computing formula v) for p For:

$p(u,v)=\underset{i=0}{\overset{2}{\&Sigma;}}\underset{j=0}{\overset{2}{\&Sigma;}}{\mathrm{\&alpha;}}_{\mathrm{\&tau;}}{u}^i{v}^j---<2>$

$\mathrm{\&omega;}(u,v)=\underset{i=0}{\overset{2}{\&Sigma;}}\underset{j=0}{\overset{2}{\&Sigma;}}{\mathrm{\&beta;}}_{\mathrm{\&tau;}}{u}^i{v}^j---<3>$

Wherein, τ=3i+j+1, α_τIt is the first intermediate variable p (u, multinomial coefficient v), β_τBe the second intermediate variable ω (u, v) Multinomial coefficient, τ ∈ [1,9].

3. according to the target conductor electromagnetic scattering emulation mode based on nurbs surface modeling described in claims 2, wherein (2c) the first intermediate variable p (u, multinomial coefficient α v) in_τWith the second intermediate variable ω (u, multinomial coefficient β v)_τMeter Calculation formula is as follows:

$\left[\begin{array}{c}{\mathrm{\&alpha;}}_1\\ {\mathrm{\&alpha;}}_2\\ {\mathrm{\&alpha;}}_3\\ {\mathrm{\&alpha;}}_4\\ {\mathrm{\&alpha;}}_5\\ {\mathrm{\&alpha;}}_6\\ {\mathrm{\&alpha;}}_7\\ {\mathrm{\&alpha;}}_8\\ {\mathrm{\&alpha;}}_9\end{array}\right]=A^{-1}\left[\begin{array}{c}{p}^{\&prime;}(u_1,v_1)\\ p^{\&prime;}(u_2,v_1)\\ p^{\&prime;}(u_3,v_1)\\ p^{\&prime;}(u_1,v_2)\\ p^{\&prime;}(u_2,v_2)\\ p^{\&prime;}(u_3,v_2)\\ p^{\&prime;}(u_1,v_3)\\ p^{\&prime;}(u_2,v_3)\\ p^{\&prime;}(u_3,v_3)\end{array}\right]---<4>$

$\left[\begin{array}{c}{\mathrm{\&beta;}}_1\\ {\mathrm{\&beta;}}_2\\ {\mathrm{\&beta;}}_3\\ {\mathrm{\&beta;}}_4\\ {\mathrm{\&beta;}}_5\\ {\mathrm{\&beta;}}_6\\ {\mathrm{\&beta;}}_7\\ {\mathrm{\&beta;}}_8\\ {\mathrm{\&beta;}}_9\end{array}\right]=A^{-1}\left[\begin{array}{c}{\mathrm{\&omega;}}^{\&prime;}(u_1,v_1)\\ {\mathrm{\&omega;}}^{\&prime;}(u_2,v_1)\\ {\mathrm{\&omega;}}^{\&prime;}(u_3,v_1)\\ {\mathrm{\&omega;}}^{\&prime;}(u_1,v_2)\\ {\mathrm{\&omega;}}^{\&prime;}(u_2,v_2)\\ {\mathrm{\&omega;}}^{\&prime;}(u_3,v_2)\\ {\mathrm{\&omega;}}^{\&prime;}(u_1,v_3)\\ {\mathrm{\&omega;}}^{\&prime;}(u_2,v_3)\\ {\mathrm{\&omega;}}^{\&prime;}(u_3,v_3)\end{array}\right]---<5>$

Wherein, matrix A^-1For the inverse matrix of matrix A, (u, v) is control point function to p ', and (u, v) is weight function to ω ', matrix A Expression formula is:

$A=\left[\begin{array}{ccccccccc}1& u_1& u_1^2& v_1& u_1{v}_1& u_1{v}_1^2& v_1^2& u_1{v}_1^2& u_1^2{v}_1^2\\ 1& u_2& u_2^2& v_1& u_2{v}_1& u_2{v}_1^2& v_1^2& u_2{v}_1^2& u_2^2{v}_1^2\\ 1& u_3& u_3^2& v_1& u_3{v}_1& u_3{v}_1^2& v_1^2& u_3{v}_1^2& u_3^2{v}_1^2\\ 1& u_1& u_1^2& v_2& u_1{v}_2& u_1{v}_2^2& v_2^2& u_1{v}_2^2& u_1^2{v}_2^2\\ 1& u_2& u_2^2& v_2& u_2{v}_2& u_2{v}_2^2& v_2^2& u_2{v}_2^2& u_2^2{v}_2^2\\ 1& u_3& u_3^2& v_2& u_3{v}_2& u_3{v}_2^2& v_2^2& u_3{v}_2^2& u_3^2{v}_2^2\\ 1& u_1& u_1^2& v_3& u_1{v}_3& u_1{v}_3^2& v_3^2& u_1{v}_3^2& u_1^2{v}_3^2\\ 1& u_2& u_2^2& v_3& u_2{v}_3& u_2{v}_3^2& v_3^2& u_2{v}_3^2& u_2^2{v}_3^2\\ 1& u_3& u_3^2& v_3& u_3{v}_3& u_1{v}_3^2& v_3^2& u_3{v}_3^2& u_3^2{v}_3^2\end{array}\right]---<6>$

Wherein, u₁, u₂, u₃It is respectively the nurbs surface coordinate at first, second and third sampled point of u direction, u₁=u_I,u₃=u_I+1；v₁, v₂, v₃It is respectively the nurbs surface coordinate at first, second and third sampled point in v direction, v₁ =v_J,v₃=v_J+1；Control point function p ' (u, v) and weight function ω ' (u, v) computing formula is:

$p^{\&prime;}(u,v)=\underset{i=I-2}{\overset{I}{\&Sigma;}}\underset{i=J-2}{\overset{J}{\&Sigma;}}{\mathrm{\&omega;}}_{i,j}{d}_{i,j}{N}_{i,2}\left(u\right)N_{j,2}\left(v\right)---<7>$

${\mathrm{\&omega;}}^{\&prime;}(u,v)=\underset{i=I-2}{\overset{I}{\&Sigma;}}\underset{i=J-2}{\overset{J}{\&Sigma;}}{\mathrm{\&omega;}}_{i,j}{N}_{i,2}\left(u\right)N_{j,2}\left(v\right)---<8>$

Wherein, N_i,2(u) and N_j,2V () is respectively nurbs surface u direction and the Quadric Spline basic function in v direction, nurbs surface The Quadric Spline basic function N of u direction_i,2U () computing formula is:

$N_{i,2}\left(u\right)=\frac{u-u_i}{u_{i+2}-u_i}\frac{u-u_i}{u_{i+1}-u_i}---<9>$

Wherein, u_i, u_i+1, u_i+2Respectively the i-th of nurbs surface u direction knot vector U, i+1, i+2 node, nurbs surface v The Quadric Spline basic function N in direction_j,2V () computing formula is:

$N_{j,2}\left(v\right)=\frac{v-v_j}{v_{j+2}-v_j}\frac{v-v_j}{v_{j+1}-v_j}---<10>$

Wherein, v_j, v_j+1, v_j+2For the jth of nurbs surface v direction knot vector V, j+1, j+2 node.

4. according to the target conductor electromagnetic scattering emulation mode based on nurbs surface modeling described in claims 1, Qi Zhongbu (4.1) calculate the first kind key point coordinate (u of physical optics scattering integral suddenly_s,v_s), carry out as follows:

4.1a) scatter basic theories according to physical optics, the phase function f of physical optics scattering integral (u, v) be:

$f(u,v)=({\hat{k}}_s-{\hat{k}}_i)\&CenterDot;r(u,v)=\frac{\mathrm{\&xi;}(u,v)}{\mathrm{\&omega;}(u,v)}---<11>$

Wherein, k_sScattering direction unit vector, k for electromagnetic wave_iFor the incident direction unit vector of electromagnetic wave, (u v) is r The coordinate of point on nurbs surface, ξ (u, v) is the 3rd intermediate variable, and its computing formula is:

Wherein,Be the 3rd intermediate variable ξ (u, multinomial coefficient v),

4.1b) Computational Physics optical scattering integration phase function f (u, v) the partial derivative f to u_u(u, v), its computing formula is:

$f_u(u,v)=\frac{{\mathrm{\&xi;}}_u(u,v)\mathrm{\&omega;}(u,v)-\mathrm{\&xi;}(u,v){\mathrm{\&omega;}}_u(u,v)}{{\&lsqb;\mathrm{\&omega;}(u,v)\&rsqb;}^2}---<13>$

Wherein, ω_u(u v) is the second intermediate variable ω (u, v) partial derivative to u, ξ_u(u v) is the 3rd intermediate variable

ξ (u, v) partial derivative to u, ω_u(u,v)、ξ_u(u, computing formula v) is:

ω_u(u, v)=(β₄+β₅v+β₆v²)+2(β₇+β₈v+β₉v²)u <14>

4.1c) Computational Physics optical scattering integration phase function f (u, v) the partial derivative f to v_v(u, v), its computing formula is:

$f_v(u,v)=\frac{{\mathrm{\&xi;}}_v(u,v)\mathrm{\&omega;}(u,v)-\mathrm{\&xi;}(u,v){\mathrm{\&omega;}}_v(u,v)}{{\&lsqb;\mathrm{\&omega;}(u,v)\&rsqb;}^2}---<16>$

Wherein, ω_v(u v) is the second intermediate variable ω (u, v) partial derivative to v, ξ_v(u v) is respectively the 3rd intermediate variable

ξ (u, v) partial derivative to v, ω_v(u,v)、ξ_v(u, computing formula v) is:

ω_v(u, v)=(β₂+β₅u+β₈u²)+2(β₃+β₆u+β₉u²)v <18>

4.1d) structure solves first kind key point coordinate (u_s,v_s) equation group:

$\begin{array}{c}{f}_u(u,v)=\frac{{\mathrm{\&xi;}}_u(u,v)\mathrm{\&omega;}(u,v)-\mathrm{\&xi;}(u,v){\mathrm{\&omega;}}_u(u,v)}{{\&lsqb;\mathrm{\&omega;}(u,v)\&rsqb;}^2}=0\\ f_v(u,v)=\frac{{\mathrm{\&xi;}}_v(u,v)\mathrm{\&omega;}(u,v)-\mathrm{\&xi;}(u,v){\mathrm{\&omega;}}_v(u,v)}{{\&lsqb;\mathrm{\&omega;}(u,v)\&rsqb;}^2}=0\end{array}---<19>$

4.1e) by ω in formula<3>, ((u, in expression formula v), formula<14>-<15>for u, ξ in expression formula v), formula<12> ω_u(u,v)、ξ_u(u, the ω in expression formula v),<17>-<18>_v(u,v)、ξ_v(u, expression formula v) substitutes into formula<19>and changes Letter, obtains equation below group:

$\begin{array}{c}{c}_0\left(v\right)u^2+c_1\left(v\right)u+c_2\left(v\right)=0\\ d_0\left(u\right)v^2+d_1\left(u\right)v+d_2\left(u\right)=0\end{array}---<20>$

Wherein, c₀V () is secondary u coefficient function, c₁V () is a u coefficient function, c₂V () is zero degree u coefficient function, d₀(u) be Secondary v coefficient function, d₁U () is a v coefficient function, d₂U () is zero degree v coefficient function, its computing formula is:

4.1f) to the solving equations in formula<20>, obtain first kind key point coordinate (u_s,v_s)。