CN105277927B - Aircraft formation Transient Electromagnetic characteristic time domain exponent number step-by-step analysis method - Google Patents
Aircraft formation Transient Electromagnetic characteristic time domain exponent number step-by-step analysis method Download PDFInfo
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Abstract
The invention discloses a kind of aircraft formation Transient Electromagnetic characteristic time domain exponent number step-by-step analysis methods.This method is using wide band time domain electromagnetic pulse as excitation, it is established that the time-domain analysis model of aircraft formation；Each aircraft is set as a solution subregion, will be on the equivalent equivalent face to the encirclement subregion of the scattering current of subregion；The equivalent scattering electromagnetic current on its surface is constantly updated until stablizing by the effect of intercoupling between each equivalent face；Radar Cross Section is solved by the final equivalent scattering electromagnetic current on equivalent face.The present invention can carry out quick Electromagnetic Simulation to multiple targets, it can be used for analyzing the Transient Electromagnetic characteristic of target, in-field expansion, equivalent face interaction and the calculating of radar cross section have been all made of rotationally symmetric body moment method during it is realized, accelerate also substantially to save memory consumption while calculating speed, stability when time domain exponent number step-by-step analysis method has rear has very strong practical engineering application value.
Description
Technical field
The invention belongs to electromagnetic characteristic of scattering numerical computation technology field, especially a kind of aircraft formation transient state electricity
Magnetic characteristic time domain exponent number step-by-step analysis method.
Background technology
The electromagnetic scattering problems of how accurate, efficient analysis target are always as the important mission of Computational electromagnetics, quilt
The method of solution is also varied.In practical engineering application, more and more need to all kinds of complex targets, multiple target or
The Electromagnetic Scattering Characteristics that person's period repeats the target complex that target is formed are analyzed, therefore high-precision and efficient electromagnetic field
Numerical algorithm also seem more important.Traditional such as moment method of the method based on integral equation (MoM) is extensive
Scattering for analyzing various targets and radiation problem.However, traditional frequency domain method is a kind of steady-state analysis method, primary
Target can be analyzed in the Electromagnetic Scattering Characteristics of single frequency point, excitation waveform can only also use the sinusoidal waveform of single-frequency, with very big
Limitation.
Invention content
The purpose of the present invention is to provide a kind of aircraft formation Transient Electromagnetic characteristic time domain exponent number steppings efficiently, stable
Analysis method can quickly obtain wide band Electromagnetic Scattering Characteristics parameter by a numerical computations.
Realize that the technical solution of the object of the invention is：A kind of aircraft formation Transient Electromagnetic characteristic time domain exponent number stepping
Analysis method, steps are as follows：
Aircraft formation is divided into multiple subregions by step 1, is solved scattering subregion and is surrounded the equivalent of the subregion
Interaction between face is encouraged using being used as with wide band Time Domain Planar wave impulse, and in-field generates on equivalent face etc.
Incoming electromagnetic stream is imitated, which generates induction field on the Scattering Targets of subregion and generate corresponding dissipate
Radio magnetic current, the scattering electromagnetic current in target induce corresponding equivalent scattering electromagnetic current on equivalent face；
Step 2 solves interaction between equivalent face and equivalent face, and the equivalent scattering electromagnetic current on an equivalent face exists
Corresponding equivalent scattering electromagnetic current is induced on other equivalent faces, is constantly updated by the effect of intercoupling between each equivalent face
The equivalent scattering electromagnetic current on its surface, until reaching stable state；
Step 3, according between step 1 Scattering Targets acquired and the equivalent face for surrounding the target interaction relationship and
Interaction relationship between step 2 gained equivalent face and equivalent face is gone out using solution by iterative method on equivalent face final equivalent
Scatter electromagnetic current；
Step 4, by the final equivalent scattering electromagnetic current on the equivalent face of each sub-regions, thunder is solved according to reciprocal theorem
Up to scattering resonance state.
Compared with prior art, the present invention its remarkable advantage is：(1) few to the consumption of computing resource：Rotationally symmetric body square
The unknown quantity that amount method generates is few, and memory consumption is also substantially saved while accelerating calculating speed；(2) matrix condition is good：Base
In the Domain Decomposition Method of the principle of equal effects, it can be that several sub-regions are solved by one big PROBLEM DECOMPOSITION, improve matrix
Conditional number；(3) afterwards stability is good when：Exponent number stepping time-domain integration method is unconditional stability, overcomes time step progradation
Unstable weakness when equation being divided to obtain rear；(4) the wide band Electromagnetic Scattering Characteristics of target can be analyzed：Using with broadband spy
Property time domain waveform as excitation, carry out time-domain-simulation, the wide band Electromagnetic Scattering Characteristics of target can be obtained, it can also be used to wink
State is analyzed.
Present invention is further described in detail below in conjunction with the accompanying drawings.
Description of the drawings
Fig. 1 is null field principle of equal effects schematic diagram of the present invention.
Fig. 2 is the effect schematic diagram of equivalent face of the present invention and Scattering Targets in equivalent face.
Fig. 3 is the effect schematic diagram between equivalent face and equivalent face of the present invention.
Fig. 4 is the schematic diagram of calculation result under different frequent points in the embodiment of the present invention 1, wherein when (a) frequency is 50MHz
Dual station RCS, dual station RCS when (b) frequency is 100MHz, dual station RCS when (c) frequency is 150MHz, (d) frequency is 200MHz
When dual station RCS, (e) frequency be 250MHz when dual station RCS.
Specific implementation mode
Present invention is further described in detail below in conjunction with the accompanying drawings.
In conjunction with attached drawing 1~3, aircraft formation Transient Electromagnetic characteristic time domain exponent number step-by-step analysis method of the present invention, step is such as
Under：
Aircraft formation is divided into multiple subregions by step 1, and an imaginary spherical surface is all established around all subregion and is made
For equivalent face, the interaction between scattering subregion and the equivalent face for surrounding the target is solved, using with wide band time domain
As excitation, typical plane wave source mainly has modulation Gauss plane-wave and Gaussian-pulsed planewave, in-field for plane wave impulse
Equivalent incoming electromagnetic stream is generated on equivalent face, which generates inductive electromagnetic on the Scattering Targets of subregion
Field simultaneously generates corresponding scattering electromagnetic current, and the scattering electromagnetic current in target induces corresponding equivalent scattering electromagnetism on equivalent face
Stream, wherein the test of in-field is as follows using the test mode of rotationally symmetric body moment method：
(1.1) the equivalent incoming electromagnetic stream that incident electromagnetic field incudes generation on equivalent face is solved, by the null field principle of equal effects
It is found that incident electromagnetic field is irradiated on equivalent face, equivalent incoming electromagnetic stream is produced on equivalent face, outside equivalent face
Source, equivalent incoming electromagnetic stream on equivalent face enters radio, magnetic field what equivalent face internal excitation had gone out most original, and is waiting
Field outside effect face then becomes zero, and incident electric fields and incident magnetic are irradiated on equivalent face, produced on equivalent face it is equivalent enter
Radio stream and equivalent incident magnetic current：
Wherein, Hi(r, τ) indicates the incident magnetic at r point τ moment, Ei(r, τ) indicates the incident electric fields at r point τ moment,For
The outer normal vector of equivalent face,Indicate the equivalent incident current at r point τ moment on equivalent face,Indicate equivalent
The equivalent incident magnetic current at r points τ moment on face；
It is with MOD-BOR base function expansions by the electromagnetism current density of time domain：
In formula, J and M indicate that current coefficient and magnetic current coefficient, subscript t indicate that the coefficient corresponds to the BOR skies in the directions t respectively
Between basic function,Indicate that the coefficient corresponds toThe spaces the BOR basic function in direction, subscript α indicate that Fourier's pattern, n indicate the spaces BOR
The serial number of basic function, v are the exponent numbers of time basic function Laguerre polynomials,Intermediate scheme is α, the BOR in n-th of direction t is empty
Between basic function,Intermediate scheme be α, n-thThe spaces the BOR basic function in direction, NBFor the number of BOR basic functions,Table
Show the Laguerre polynomials of v ranks weighting.
Formula (3) and formula (4) are substituted into formula (1) and formula (2) respectively, and using the gold test of gal the Liao Dynasty, obtained：
In formula, NmFor Fourier's pattern count, NτFor the exponent number of the Laguerre polynomials of required calculating.In derivation, use
The orthogonality of Fourier's pattern, only as α=β, there is nonzero value on the equation left side, and has：
In addition, also applying the property of Laguerre polynomials：
Obviously, the coefficient matrix on formula (5) and formula (6) equal sign left side is not with Fourier's pattern count and Laguerre polynomials rank
Several variation and change.
It is as follows that formula (5) and formula (6) can be written as matrix form：
In formula, UBBIndicate that the temporal current density of the test function test MOD-BOR base function expansions with MOD-BOR generates
Coefficient matrix；I indicates that electromagnetic current coefficient vector, the D in subscript indicate that it is current coefficient, and B indicates that it is magnetic current coefficient,
Its subscript t indicates that the coefficient corresponds to the spaces the BOR basic function in the directions t,Indicate that the coefficient corresponds toThe spaces the BOR base letter in direction
Number, i then indicate that it is incoming electromagnetic stream, and the B in subscript is then used for indicating that it is the corresponding electromagnetic current system of MOD-BOR basic functions
Number, ES indicate that it is the electromagnetic current coefficient on equivalent face；V is the test vector of in-field, and the t in subscript indicates the test knot
Fruit corresponds to the BOR test functions in the directions t,Indicate that the test result corresponds toThe BOR test functions in direction, E expression tests are
What electric field and H then indicated test is magnetic field.
(1.2) the corresponding incoming electromagnetic stream coefficient of MOD-BOR basic functions on equivalent face can be converted to by following formula
The corresponding incoming electromagnetic stream coefficient of MOD-RWG basic functions：
In formula, URBIndicate that the temporal current density of the test function test MOD-BOR base function expansions with MOD-RWG generates
Coefficient matrix；URRIndicate that the temporal current density with the test function test MOD-RWG base function expansions of MOD-RWG generates
Coefficient matrix；I indicates that electromagnetic current coefficient vector, subscript B indicate that it is the corresponding electromagnetic current coefficient of MOD-BOR basic functions, R tables
Show that it is the corresponding electromagnetic current coefficient of MOD-RWG basic functions, ES indicates that it is the electromagnetic current coefficient on equivalent face.
(1.3) the equivalent incident electric fields incuded on Scattering Targets are solved by the equivalent incoming electromagnetic stream on equivalent face, it is as follows：
The inside and outside electric field of any one closing face and magnetic field can be by the tangential electromagnetism on this closing face surface
Place decision, presented above to be released by Maxwell equation, time domain electric field on target surfaceExpression formula be：
In formula, r is the position vector of source point, and τ is time variable, and r' is the position vector of source point, and τ '=τ-R/c are electromagnetism
Wave from source point at the time of, R=| r-r'|, c indicate the light velocity, operator Le,KmIt is defined as follows：
In formula, J indicates that electric current, M indicate that magnetic current, A indicate that vector magnetic potential, Φ indicate electric scalar potential.
Target surface is used in combination by the electromagnetism current density MOD-RWG base function expansions of time domain on equivalent face for formula (13)
MOD-RWG test functions test the formula, you can obtain the test result of equivalent incident electric fields incuded in target, process is whole
Reason, the formula can be written as matrix form：
In formula,It indicates to use the test function of target surface to test again with base function expansion the electromagnetic current on equivalent face
Obtained coefficient of zero order matrix,Indicate that coefficient matrix of the v ranks by recombination, subscript oi indicate source field on equivalent face
In target surface, VuIt is the test vector of the in-field of u ranks.
(1.4) the scattering current coefficient in target is solved, establishes following improved Electric Field Integral Equation on the target surface：
[Es(r,τ)+Ei(r,τ)]tan=0 (17)
Assuming that target is perfact conductor, the scattered field on surface can indicate as follows：
By the temporal current density MOD-RWG base function expansions on target surface, the gold test of gal the Liao Dynasty is used in combination, by time domain rank
Number stepping moment method obtains the scattering current on Scattering Targets：
Wherein, Z0,PECIt indicates that the temporal current density in target is spatially directly used RWG base function expansions, in the time
On be unfolded with Laguerre polynomials, the obtained zeroth order impedance matrix of gal the Liao Dynasty gold test is used in combination；Zv,PECIndicate v ranks by recombination
Impedance matrix；I indicates that current coefficient vector, subscript s indicate that it is scattering current coefficient, and the u and u-v in subscript indicate its institute
Corresponding Laguerre polynomials exponent number；PEC is for indicating that I is the current coefficient in target, NτIt is total rank of Laguerre polynomials
Number；
(1.5) the equivalent scattering field generated on corresponding equivalent face by the scattering current on Scattering Targets is solved：
Scattering electromagnetic current on equivalent face in equivalent face internal excitation is null field, has been gone out in equivalent face external excitation original
Scattering field, this is also the null field principle of equal effects.According to the null field principle of equal effects, the equivalent scattering electromagnetic current on equivalent face can table
It is shown as：
For formula (20) and formula (21), by the time domain scattering current MOD-RWG base function expansions on equivalent face and target,
It is used in combination the MOD-RWG test functions on equivalent face to test, after arrangement, it is as follows matrix form can be written as：
In formula,It indicates to use the test function of target surface to test again with base function expansion the electromagnetic current on equivalent face
Obtained coefficient of zero order matrix,Indicate that coefficient matrix of the v ranks by recombination, subscript io indicate source field on equivalent face
In target surface,Indicate the corresponding scattering current system of MOD-RWG basic functions on equivalent face,It indicates on equivalent face
The corresponding scattering magnetic current system of MOD-RWG basic functions.
(1.6) the corresponding scattering electromagnetic current coefficient of MOD-RWG basic functions on equivalent face is converted into MOD-BOR basic functions
The process of corresponding scattering electromagnetic current coefficient is shown below：
In formula, UBBIndicate that the temporal current density of the test function test MOD-BOR base function expansions with MOD-BOR generates
Coefficient matrix；UBRIndicate that the temporal current density with the test function test MOD-RWG base function expansions of MOD-BOR generates
Coefficient matrix；I indicates that electromagnetic current coefficient vector, the D in subscript indicate that it is current coefficient, and B indicates that it is magnetic current coefficient,
Subscript t indicates that the coefficient corresponds to the spaces the BOR basic function in the directions t,Indicate that the coefficient corresponds toThe spaces the BOR basic function in direction,
S then indicates that it is scattering electromagnetic current, and the B in subscript is used for indicating that it is the corresponding electromagnetic current coefficient of MOD-BOR basic functions, R
For indicating that it is the corresponding electromagnetic current coefficient of MOD-RWG basic functions, ES indicates that it is the electromagnetic current coefficient on equivalent face.
Thus the equivalent scattering electromagnetic current coefficient that MOD-BOR basic functions are corresponded on each equivalent face is acquired, as shown in Figure 2.
In conclusion S can be definedESInteraction between operator representation equivalent face and its target surrounded：
Step 2 solves interaction between equivalent face and equivalent face, and the equivalent scattering electromagnetic current on an equivalent face exists
Corresponding equivalent scattering electromagnetic current is induced on other equivalent faces, the equivalent incident electromagnetic field induced can be superimposed upon original flat
On the incident electromagnetic field of surface wave, the Scattering Targets in equivalent face are acted on, between each equivalent face not by the effect of intercoupling
It is disconnected to update the equivalent scattering electromagnetic current on its surface, no longer change until reaching stable state i.e. numerical value, as shown in Figure 3.
Assuming that there are two Scattering Targets to be surrounded respectively by a corresponding equivalent face；Electric current on first equivalent face will be right
Second equivalent face generates side effect, to generate additional incident current and additional incident magnetic current on the second equivalent face, the
The process of two equivalent faces is similar.It is introduced by taking the effect of first the second equivalent face of equivalent face pair as an example below mutual between equivalent face
Effect, the mechanism of first the second equivalent face of equivalent face pair are as follows：
(2.1) it if the line of centres of two equivalent faces (spherical surface) and the z-axis (shaft) of global coordinate system are not parallel, builds
A local coordinate system is found, z-axis rotation is allowed to parallel with the line of centres of two equivalent faces, is directed toward source equivalent face (i.e. first
Equivalent face), and convert the scattering electromagnetic current coefficient on the first equivalent face to the scattering electromagnetic current coefficient under local coordinate system.Its
In, the method for rotating coordinate system is：First determine azimuth of the z' axis of local coordinate system relative to global coordinate systemThen
Coordinate system is rotated clockwise around z-axisObtain a new coordinate system (x', y', z)；Again by new coordinate system around x' axis
- θ is rotated clockwise, the local coordinate system (x', y', z') needed for us is obtained.
Arbitrary electromagnetic current coefficient of the single order MOD-BOR basic functions under global coordinate system of certain known equivalent face (spherical surface), is asked
The method of electromagnetic current coefficient of the equivalent face under local coordinate system is as follows：First the electromagnetic current coefficient under global coordinate system is substituted into
In the expansion of the spaces BOR basic function, the electromagnetic current of arbitrary point on equivalent face is obtained；Then empty with the BOR under local coordinate system
Between basic function on equivalent face electromagnetic current carry out space test (taking inner product), obtain a series of test results；U is used againBBIt is inverse
The test result of premultiplication electric current and magnetic current vector respectively, you can obtain the electromagnetic current coefficient under local coordinate system.
What the scattering field of the scattering electromagnetic current excitation of (2.2) first equivalent faces generated on the second equivalent face additionally enters
Radio magnetic current indicates as follows：
In formula,Indicate the additional incident current of the second equivalent face,Indicate the additional scattering magnetic current of the second equivalent face,Indicate the scattering electric field of the scattering electromagnetic current excitation of the first equivalent face,Indicate the scattering electromagnetic current excitation of the first equivalent face
Fringe magnetic field, r is the position vector of certain point on second equivalent face, and τ is time variable,For the outer method of the second equivalent face
Vector,Indicate the scattering current of the first equivalent face,Indicate the scattering magnetic current of the first equivalent face, operator Le、Ke、Lm、KmIt is fixed
Justice is as follows：
Wherein, A indicates that vector magnetic potential, Φ indicate electric scalar potential, AmIndicate vector current potential, ΦmIndicate that scalar magnetic potential, η are certainly
By the wave impedance in space.
For formula (27) and formula (28), by the respective MOD-BOR base function expansions of the electromagnetic current on two equivalent faces, then
It is tested on peer-to-peer both sides simultaneously with the MOD-BOR test functions on the second equivalent face, can arrange to obtain following matrix equation：
In formula, T0,21It indicates to use the test function of equivalent face 2 to test again with base function expansion the electromagnetic current on equivalent face 1
Obtained coefficient of zero order matrix, Tv,21Indicate that coefficient matrix of the v ranks by recombination, I indicate electromagnetic current coefficient vector, subscript
In D and B for distinguishing it be current coefficient or magnetic current coefficient, the i and s in subscript for distinguish it be incoming electromagnetic stream also
It is scattering electromagnetic current, the B in subscript is then used for indicating that it is the corresponding electromagnetic current coefficient of MOD-BOR basic functions.
(2.3) the additional incoming electromagnetic stream coefficient at this time on the second equivalent face be under local coordinate system, need to be by its turn
Turn to the electromagnetic current coefficient under global coordinate system.
In conclusion defining TmnEffects of the operator representation equivalent face n to equivalent face m：
Step 3, according between step 1 Scattering Targets acquired and the equivalent face for surrounding the target interaction relationship and
Interaction relationship between step 2 gained equivalent face and equivalent face is gone out using solution by iterative method on equivalent face final equivalent
Electromagnetic current is scattered, detailed process is as follows：
Assuming that shared NESA subregion to be asked uses corresponding equivalent face by this N respectivelyESA subregion to be asked surrounds, then
It is as follows equation group can be established to all subregion：
Wherein, I indicates electromagnetic current coefficient vector, and the D in subscript indicates that I is current coefficient, and B indicates that I is magnetic current coefficient, on
I in mark indicates that I is incoming electromagnetic stream coefficient, and s indicates that I is scattering electromagnetic current coefficient, and the B in subscript then indicates that I is MOD-BOR
The corresponding electromagnetic current coefficient of basic function, m, n in subscript represent the number of subregion；
SmOperator and TmnOperator is defined as follows：
Define SmOperator representation indicates the interaction between m-th of equivalent face and its target surrounded：
TmnEffects of the operator representation equivalent face n to equivalent face m, as shown in formula (34).
To NESSub-regions establish equation group, simultaneous N respectivelyESThe equation group of sub-regions, continuous iteration update are each equivalent
Scattering electromagnetic current coefficient on face solves final scattering electromagnetic current coefficient until reaching stable state.
Step 4, by the final equivalent scattering electromagnetic current on the equivalent face of each sub-regions, thunder is solved according to reciprocal theorem
Up to scattering resonance state, wherein far field scattered field is acquired by reciprocal theorem：
∫∫∫(Es·J2-Hs·M2) dV=∫ ∫S(J·E2-M·H2)dS (37)
Wherein, EsFor the scattering electric field at the arbitrary point of space, HsFor the fringe magnetic field at the arbitrary point of space, J is to generate scattering
The current source of field, M are the magnetic current source for generating scattered field, E2For incidence wave electric field, H2For incidence wave magnetic field, J2To generate in-field
Current source, M2To generate the magnetic current source of in-field；
Under three-dimensional system of coordinate, the dual station RCS in the direction (θ, φ) is：
Embodiment 1
The present embodiment has carried out the Electromagnetic Scattering Characteristics emulation of multiple metal targets, emulates in dominant frequency 2.83GHz, memory
Realized on the personal computer of 3.5GB, the cube that three length of sides are 0.3 meter, centre coordinate be respectively (0,0,0), (0,0,
1.6), (1.2,0,0), equivalent face are the spherical surface of 0.4 meter of radius.Using modulation Gaussian plane wave excitation, maximum frequency is set as
300MHz, centre frequency 150MHz, incident direction θ,The subdivision size of metal cuboid is 0.1 meter, equivalent
Two kinds of mesh generations of face triangle and annulus, wherein the subdivision size of triangle be 0.12 meter, busbar be averaged subdivision be 16 sections,
Using 3 Fourier's patterns, calculate to 50 ranks.For the correctness and efficiency of proving program, this patent result and commercialization are soft
Part FEKO compares.Fig. 4 gives the dual station RCS values of different frequency, wherein dual station RCS when (a) frequency is 50MHz, (b)
Dual station RCS when frequency is 100MHz, dual station RCS when (c) frequency is 150MHz, dual station when (d) frequency is 200MHz
RCS, dual station RCS when (e) frequency is 250MHz, viewing angle existPlane.It can be seen that the result of the present invention
It coincide with FEKO fine, wide band electromagnetic property can be obtained by a numerical computations, held using the program of this method
Row total time is：174.4s, peak memory consumption are：256,124KB, and it is total directly to use the program of MOD-EPA methods to execute
Time is：284.1s, peak memory consumption are：1,301,828KB, it is clear that this method computational efficiency higher, the consumption to resource
Less.
In conclusion the present invention is repeated for the TV university period or the target comprising fine structure, based on the principle of equal effects whole
A solution domain is divided into several and solves subdomain, each solves subdomain and is surrounded by the equivalent face of spherical surface by a shape,
Unknown quantity is transferred to from internal object on equivalent face, it is equivalent to which the scattering electromagnetic current for calculating each region is converted to calculating
Equivalent scattering electromagnetic current on face, the phase coupling effect between zoning are converted into the phase calculated between the equivalent face for surrounding each region
Interaction.Because the shape of equivalent face is all very regular, larger subdivision size can be taken, so that unknown on equivalent face
Amount greatly reduces for the unknown quantity on internal fine structural object surface, so when iterative solution matrix, formation
Matrix condition to be asked is excellent, and iterative steps are substantially reduced, and has significantly saved the iterative solution time.
Claims (2)
1. a kind of aircraft formation Transient Electromagnetic characteristic time domain exponent number step-by-step analysis method, which is characterized in that steps are as follows：
Aircraft formation is divided into multiple subregions by step 1, is solved between scattering subregion and the equivalent face for surrounding the subregion
Interaction, using with wide band Time Domain Planar wave impulse as encourage, in-field generated on equivalent face it is equivalent enter
Radio magnetic current, the equivalent incoming electromagnetic stream generate induction field on the Scattering Targets of subregion and generate corresponding scattering electricity
Magnetic current, the scattering electromagnetic current in target induce corresponding equivalent scattering electromagnetic current on equivalent face；
Step 2 solves interaction between equivalent face and equivalent face, and the equivalent scattering electromagnetic current on an equivalent face is at other
It induces corresponding equivalent scattering electromagnetic current on equivalent face, its table is constantly updated by the effect of intercoupling between each equivalent face
The equivalent scattering electromagnetic current in face, until reaching stable state；
Step 3, according to the interaction relationship and step between step 1 Scattering Targets acquired and the equivalent face for surrounding the target
Interaction relationship between 2 gained equivalent faces and equivalent face goes out equivalent scattering final on equivalent face using solution by iterative method
Electromagnetic current；
Step 4, by the final equivalent scattering electromagnetic current on the equivalent face of each sub-regions, radar is solved according to reciprocal theorem and is dissipated
Penetrate sectional area；
The interaction between Scattering Targets and the equivalent face for surrounding the target is solved described in step 1, specifically includes following steps：
(1.1) the equivalent incoming electromagnetic stream that incident electromagnetic field incudes generation on equivalent face, incident electric fields and incident magnetic are solved
It is irradiated on equivalent face, equivalent incident current and equivalent incident magnetic current is produced on equivalent face：
Wherein, Hi(r, τ) indicates the incident magnetic at r point τ moment, Ei(r, τ) indicates the incident electric fields at r point τ moment,For equivalent face
Outer normal vector,Indicate the equivalent incident current at r point τ moment on equivalent face,Indicate r points τ on equivalent face
The equivalent incident magnetic current at moment；
(1.2) the equivalent incident electric fields incuded on Scattering Targets, target surface are solved by the equivalent incoming electromagnetic stream on equivalent face
The expression formula of upper time domain electric field is：
In formula,Indicate time domain electric field on target surface, r is the position vector of source point, and τ is time variable, and r' is source point
Position vector, τ '=τ-R/c be electromagnetic wave from source point at the time of, R=| r-r'|, c indicate the light velocity, operator Le,KmDefinition is such as
Under：
In formula, J indicates that electric current, M indicate that magnetic current, A indicate that vector magnetic potential, Φ indicate electric scalar potential；
(1.3) the scattering electromagnetic current on Scattering Targets is solved, the electricity of the scattering on Scattering Targets is obtained by time domain exponent number stepping moment method
Stream：
Wherein, Z0,PECIt indicates that the temporal current density in target is spatially directly used RWG base function expansions, uses in time
Laguerre polynomials are unfolded, the zeroth order impedance matrix for being used in combination the gold test of gal the Liao Dynasty to obtain；Zv,PECIndicate impedance of the v ranks by recombination
Matrix；I indicates that current coefficient vector, subscript s indicate that it is scattering current coefficient, and the u and u-v in subscript are indicated corresponding to it
Laguerre polynomials exponent number；PEC is for indicating that I is the current coefficient in target, NτIt is total exponent number of Laguerre polynomials；
(1.4) the equivalent scattering field generated on corresponding equivalent face by the scattering current on Scattering Targets is solved：
It enablesIndicate the scattering electric field that the scattering current on target surface inspires,Indicate the scattering electricity on target surface
The fringe magnetic field that stream inspires, then have：
Wherein,Indicate the scattering current on target surface, operator KeIt is defined as follows：
Then the equivalent scattering electromagnetic current on equivalent face is expressed as：
In formula,Equivalent scattering current on equivalent face,Equivalent scattering magnetic current on equivalent face；
The interaction between equivalent face and equivalent face is solved described in step 2, specially：
Assuming that there are two Scattering Targets to be surrounded respectively by a corresponding equivalent face；Electric current on first equivalent face will be to second
Equivalent face generates side effect, so that additional incident current and additional incident magnetic current are generated on the second equivalent face, second etc.
The process in effect face is similar；The scattering field of the scattering electromagnetic current excitation of first equivalent face generates additional on the second equivalent face
Incoming electromagnetic flow table is shown as follows：
Wherein,Indicate the additional incident current of the second equivalent face,Indicate the additional scattering magnetic current of the second equivalent face,Table
Show the scattering electric field of the scattering electromagnetic current excitation of the first equivalent face,Indicate dissipating for the scattering electromagnetic current excitation of the first equivalent face
Magnetic field is penetrated, r is the position vector of certain point on second equivalent face, and τ is time variable,For the outer normal vector of the second equivalent face,Indicate the scattering current of the first equivalent face,Indicate the scattering magnetic current of the first equivalent face, operator Le、Ke、Lm、KmDefinition is such as
Under：
In formula, A indicates that vector magnetic potential, Φ indicate electric scalar potential, AmIndicate vector current potential, ΦmIndicate that scalar magnetic potential, η are freely empty
Between wave impedance；
Go out equivalent scattering electromagnetic current final on equivalent face described in step 3 using solution by iterative method, it is specific as follows：
Assuming that shared NESA subregion to be asked uses corresponding equivalent face by this N respectivelyESA subregion to be asked surrounds, then can be right
It is as follows that all subregion establishes equation group：
Wherein, I indicates electromagnetic current coefficient vector, and the D in subscript indicates that I is current coefficient, and B indicates that I is magnetic current coefficient, in subscript
I indicate that I is incoming electromagnetic stream coefficient, s indicates that I is scattering electromagnetic current coefficient, and the B in subscript then indicates that I is MOD-BOR base letters
Corresponding electromagnetic current coefficient is counted, m, n in subscript represent the number of subregion；
SmOperator and TmnOperator is defined as follows：
Define SmInteraction between m-th of equivalent face of operator representation and its target surrounded：
Define TmnEffects of the operator representation equivalent face n to equivalent face m：
To NESSub-regions establish equation group, simultaneous N respectivelyESThe equation group of sub-regions acquires NESOn a equivalent face finally
Equivalent scattering electromagnetic current.
2. aircraft formation Transient Electromagnetic characteristic time domain exponent number step-by-step analysis method according to claim 1, feature exist
In the expression formula of Radar Cross Section described in step 4 is：
Under three-dimensional system of coordinate, the dual station RCS in the direction (θ, φ) is：
Wherein, EsIndicate the electric field component of scattered field, EiThe electric field component of in-field is indicated respectively,π is
Pi.
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| CN105277927B true CN105277927B (en) | 2018-09-04 |
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| CN102129523A (en) * | 2011-03-23 | 2011-07-20 | 南京理工大学 | Method for analyzing electromagnetic scattering of complex target through MDA and MLSSM |
| CN103177193A (en) * | 2013-04-18 | 2013-06-26 | 南京理工大学 | Rotationally symmetric target electromagnetic scattering rapid calculation method of thin-medium-coated metal |
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| CN102129523A (en) * | 2011-03-23 | 2011-07-20 | 南京理工大学 | Method for analyzing electromagnetic scattering of complex target through MDA and MLSSM |
| CN103177193A (en) * | 2013-04-18 | 2013-06-26 | 南京理工大学 | Rotationally symmetric target electromagnetic scattering rapid calculation method of thin-medium-coated metal |
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