CN110287549A - Aircraft RCS prediction technique is applied in many places scumbling with uncertain source - Google Patents

Aircraft RCS prediction technique is applied in many places scumbling with uncertain source Download PDF

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CN110287549A
CN110287549A CN201910482898.3A CN201910482898A CN110287549A CN 110287549 A CN110287549 A CN 110287549A CN 201910482898 A CN201910482898 A CN 201910482898A CN 110287549 A CN110287549 A CN 110287549A
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aircraft
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CN110287549B (en
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何姿
陈如山
丁大志
樊振宏
万军
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Nanjing University of Science and Technology
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Abstract

The invention discloses a kind of many places scumblings with uncertain source to apply aircraft RCS prediction technique, comprising the following steps: establishes MTDS improved Electric Field Integral Equation；Establish the geometrical model that there is many places scumbling of shape uncertainty to apply aircraft；It extracts many places scumbling and applies aircraft shape uncertain parameter；Analyze the Electromagnetic Scattering Characteristics that there is many places scumbling of shape uncertainty to apply aircraft.Many places scumbling is applied the uncertain of aircraft geometric shape and is introduced into the matrix equation of MTDS integral Equation Methods by the basic function with stochastic variable by the present invention, and then there is many places scumbling of uncertain shape to apply the RCS of aircraft can be by method of perturbation effectively quantitative forecast, this method can preferable simulation the metal object that there is multimedium piece scumbling in many places to apply.

Description

Aircraft RCS prediction technique is applied in many places scumbling with uncertain source
Technical field
The invention belongs to electromagnetic characteristic of scattering numerical computation technology fields, and in particular to a kind of with uncertain source Aircraft RCS prediction technique is applied in many places scumbling.
Background technique
The asymmetric strategic thought gesture of swift and violent epoch " the short of son is attacked with oneself length " is changed in nowadays this military technology Mainstream must be become.The asymmetric war of zero contact, which must strive, will become the important feature of future war.However only technical equipment Absolute predominance is just able to achieve zero contact, therefore seems in the stealthy field of military operations for the research of stealth technology and be even more important.Hidden The strong reflection spot of body target has become achievable important stealth technology to entire Stealthy Target coating absorbing material, Since the easy to operate of the technology, simple process, application parameters are convenient for adjusting, it has been widely used in military field.
But in actual life and practical engineering application, due to the influence of manufacturing process and human factor, electromagnetic field system The uncertainty of system is generally existing.This uncertain uncertainty including realistic objective geometry, material properties Uncertainty, load lamped element performance uncertainty, the uncertainty etc. of incidence wave polarization mode.In order to measure Change and assesses these probabilistic influences, in recent decades, many scholars are dedicated to studying effective analysis method of stochastic problem, Propose the method for many analysis stochastic problems.In numerous stochastic problem analysis methods, monte carlo method (Monte Carlo, MC) it is to solve the most classical and mature method of uncertain problem.Monte carlo method is also known as statistical simulation method, random Sampling techniques is a kind of Method of Stochastic, based on probability and statistical methods, is come using random number (pseudo random number) Solving practical problems.The problem of it will be solved is associated with certain probabilistic model, realizes statistical simulation or pumping with computer Sample, to obtain the Statistical Solutions of problem.The cardinal principle of the method is repeatedly certainty to be called to ask on a series of sampled point Topic solver obtains the result on different sampled points and for statistical analysis, and this method has easy to operate and Noninvasive (Nonintrusive) the characteristics of, almost can be suitably used for all uncertain problems, but monte carlo method is by low constringent shadow It rings and needs to obtain enough sample datas by repeatedly repeatedly testing or emulating, therefore the ability of its problem analysis will receive The limitation of computing resource.Although being suggested to improve its convergence there are many improved monte carlo method, such as quasi- Monte Carlo Method (quasi-MC method) uses the different method of samplings to accelerate the convergence of monte carlo method, such as stratified sampling (Stratified Sampling), Latin hypercube sampler body (Latin Hypercube Sampling), importance sampling (Importance Sampling), low diversity sequence (Low-discrepancy Sequences) etc. and Marko's love chain Monte carlo method (Markov Chain MC method) generates the sample under certain distribution using Marko's love chain.So And these methods only for low dimensional the problem of there is effect, compared to two dimension target, for three-dimensional target shape description more For complexity, there is irregular shape mostly especially close to the target in actual conditions, the information of geometric shape can not be simple Ground description, and if the subdivision grid according to target goes to describe, required information is too many, can seriously affect computational efficiency and essence Degree, and it is very complicated to operate, therefore is difficult to easily and effectively describe outside three-dimensional realistic objective using current research method The variation of shape simultaneously carries out analysis of uncertainty.
Summary of the invention
The purpose of the present invention is to provide a kind of many places scumblings with uncertain source to apply aircraft RCS prediction technique.
The technical solution for realizing the aim of the invention is as follows: a kind of deposited aircraft RCS of many places scumbling with uncertain source Prediction technique, steps are as follows:
Step 1 establishes MTDS improved Electric Field Integral Equation；Flight is applied when uniform plane wave is irradiated to many places scumbling from either direction When device, the scattered field in entire space will be applied induction surface current, the surface charge, thin-medium body pole of aircraft surface by many places scumbling Galvanic current and the polarization charge of upper and lower surface generate, and all sources are transformed into the induction surface current of metal surface to indicate, Finally set up MTDS improved Electric Field Integral Equation；
Step 2 establishes the geometrical model that there is many places scumbling of shape uncertainty to apply aircraft；It is used by rhinoceros software Non- Rational B-Spline surface modeling technique leads to for extracting NURBS dough sheet information with shape uncertainty target Geometric Modeling Cross the control of dominating pair of vertices target geometric shape；
Step 3 extracts the deposited aircraft shape uncertain parameter of many places scumbling；Using conformal triangular mesh to the face NURBS Piece carries out subdivision and forms RWG basic function, and the coordinate representation at corresponding control point is used for the geological information of RWG basic function；It will be more Place's scumbling applies the related control point coordinates of aircraft profile variation and is set as stochastic variable, by RWG basic function by stochastic variable Information be introduced into MTDS integral equation；
The Electromagnetic Scattering Characteristics that there is many places scumbling of shape uncertainty to apply aircraft for step 4, analysis；It will according to step 3 After stochastic variable is extracted and is introduced into the matrix equation of MTDS integral Equation Methods, the random change information of mode shape is introduced into In matrix equation；In conjunction with method of perturbation, obtains many places scumbling and apply the corresponding current coefficient of each basic function of aircraft surface with many places Scumbling applies aircraft and does not know the variation range of shape, and then calculates many places scumbling with uncertain source and apply aircraft RCS Size.
Compared with prior art, the present invention its remarkable advantage are as follows: (1) MTDS (Multiple Thin Dielectric Sheets) it only will appear a unknown quantity in entire integral equation；Numerical result shows that this method can preferably simulation have The metal object for having many places multimedium piece scumbling deposited；In addition, the lamellated dielectric parameter of institute and thickness can be directly arranged in program, Convenient for the multiple simulation in optimization design；(2) present invention is based on non-Rational B-splines (Non-uniform by rhinoceros software Rational B-spline, NURBS) surface modeling technique is established with shape uncertainty target, then extracts NURBS dough sheet Information can realize the description to the variation of complex three-dimensional target shape, and seldom control only by the variation at control point System point can control target geometric shape deformation；It solves conventional method to be difficult to describe the difficulty of complex target irregular shape Topic；Between each control point be also it is relatively independent, be arranged control point coordinate be stochastic variable can easily describe it is more Locate the uncertainty that aircraft shape is applied in scumbling；(3) prediction technique computational efficiency of the present invention is high；It is by stochastic variable that many places are thin The uncertainty of coating aircraft shape is introduced into the integral equation side MTDS (Multiple Thin Dielectric Sheets) After in the matrix equation of method, there can be many places scumbling in uncertain source to apply aircraft RCS size using method of perturbation analysis quantization, The time is calculated much smaller than the monte carlo method for needing multiple repairing weld to analyze.
Detailed description of the invention
Fig. 1 is many places coating object module figure not of the same race for being closed metal.
Fig. 2 is many places coating mesh equivalent model schematic diagram not of the same race for being closed metal.
Fig. 3 is certain guided missile model many places coating absorbing material schematic diagram.
Fig. 4 is that the present invention utilizes non-Rational B-Spline surface modeling technique to establish certain guided missile model schematic diagram.
Fig. 5 is that guided missile model body length changes schematic diagram in the embodiment of the present invention.
Fig. 6 is certain guided missile model dual station RCS result curve figure in the embodiment of the present invention with uncertain body length.
Specific embodiment
A kind of deposited aircraft RCS prediction technique of many places scumbling with uncertain source, comprising the following steps:
The foundation of step 1, MTDS (Multiple Thin Dielectric Sheets) improved Electric Field Integral Equation.When uniform When plane wave is irradiated to many places scumbling from either direction and applies aircraft, the scattered field in entire space will apply flight by many places scumbling The induction surface current J on device surfaceS, surface charge ρS, thin-medium body polarization current JpolWith the polarization charge ρ of upper and lower surfaceS,polIt generates , all sources are transformed into the induction surface current J of metal surfacesIt indicates, finally sets up MTDS (Multiple Thin Dielectric Sheets) improved Electric Field Integral Equation.Specific step is as follows:
When uniform plane wave coats target from many places thin-medium that either direction irradiates closure metal, as shown in Figure 1.By In closure metal inside electromagnetic field be 0, so the equivalent model of the coating target is such as according to the principle of equal effects and uniqueness theorem Shown in Fig. 2, the scattered field in entire space will be by the induction surface current J of the metal surfaces, surface charge ρS, thin-medium body polarization current Jpol,i,kWith the polarization charge ρ of upper and lower surfaceS,pol,i,kIt generates.When the thickness of thin-medium compare wavelength it is sufficiently thin when, thin-medium Body polarization current JpolIt is considered that being a constant on the thickness of entire dielectric layer.In addition to this, since thin-medium is with metal For substrate, so polarization current JpolTangential component be 0.It is tangential in metal surface according to the electric field boundary condition of perfact conductor Total electric field is 0, available:
[Esc+Einc]tan=0r ∈ S (1)
Wherein subscript tan indicates the tangential component of electric field, formula is done simple deformation, available expression formula below:
Then all sources are converted to the induction surface current J of metal surfacesIt indicates, converts as follows, i-th layer of body pole Galvanic current Jpol,i,kExpression formula are as follows:
The surface charge ρ of metal surfacesIt is converted to following expression-form:
The polarization charge densities ρ of interface between any two layers of thin-mediums,pol,i,kExpression formula are as follows:
The improved Electric Field Integral Equation that can must solve thin-medium coating target is updated in formula after all sources are converted:
Formula (1)~(8) are the foundation of MTDS improved Electric Field Integral Equation, wherein subscript tan is the tangential component of electric field, and S is to ask Region, r ' expression source point are solved, r indicates site；The corresponding normal vector of expression source triangle, EincThe in-field of representation space, Esc The scattered field of representation space；J is the opposite number of imaginary unit, and ω is corresponding angular frequency, μ0It is the magnetic conductivity of free space, ε0It is The dielectric constant of free space；G (r, r') is the Green's function of free space,It is the ladder of free space Green's function Degree；JsIt is the induction surface current of metal surface,It is the divergence of the induction surface current of metal surface, ρSIt is the sense of metal surface Answer surface charge, Jpol,i,kIt is thin-medium body polarization current, ρS,pol,i,kThe polarization charge of thin-medium upper and lower surface；I indicates i-th layer Number coating material, L indicate total coating number of plies, and k indicates that k-th of the area of application, N indicate the number of the total coating zone in metal surface That is sheet number, S1Indicate the interface element of metal and first layer thin-medium, Si,kRespectively indicate (i-1)-th layer of thin-medium and i layers The interface element of thin-medium, SL+1,kIndicate the interface element of the last layer thin-medium and air, Vi,kIndicate each layer thin The elementary volume, volume element of medium；εr,i+1,kFor the relative dielectric constant of thin-medium at i+1 layer kth.
Step 2, the geometrical Modeling Technology that aircraft is applied with many places scumbling of shape uncertainty.It is used by rhinoceros software Non- Rational B-splines (Non-uniform Rational B-spline, NURBS) surface modeling technique is not for true with shape Qualitative objective Geometric Modeling extracts NURBS dough sheet information, is controlled by dominating pair of vertices target geometric shape；Specific step is as follows:
The present invention uses the face NURBS by rhinoceros software proposed adoption non-uniform rational B-spline (NURBS) modeling technique To the Geometric Modeling of model, by changing corresponding control point variation description target geometric shape even variation feelings in a certain range Condition.
The shape in the face NURBS is controlled by several control points, and shape can be expressed as a binary rational function, thereon Any point coordinate can indicate are as follows:
M and n is illustrated respectively in u, the number at control point on the direction v.P and q is corresponding order.Pij=[Pijx,Pijy, Pijz] it is illustrated respectively in x, y, the coordinate at control point on the direction z.wijIt is corresponding weight.Ni,pIt (u) is p rank B-spline basic function.
By formula (10) it can be seen that the shape in the face NURBS can be determined by control point.Therefore change the coordinate at control point The shape in the i.e. changeable face NURBS, and then change the shape of model.
Step 3, many places scumbling apply the extractive technique of aircraft shape uncertain parameter.Using conformal triangular mesh pair NURBS dough sheet carries out subdivision and forms RWG basic function, for the geological information (side length l, area A and base vector ρ) of RWG basic function The coordinate representation at corresponding control point can be used.Many places scumbling apply the related control point coordinates of aircraft profile variation be set as with The information of stochastic variable is introduced into MTDS (Multiple Thin Dielectric by RWG basic function by machine variable Sheets) in integral equation；Specific step is as follows:
The related control point coordinates of aircraft profile variation are applied in many places scumbling and are set as stochastic variable α=[α1,α2,… αm], the geological information of each basic function can be indicated with stochastic variable, and basic function is updated to emi analysis equation In (MTDS integral equation), the matrix equation with stochastic variable can be expressed as
Z (α) I (α)=b (α) (9)
Z (α) and b (α) respectively indicates the impedance matrix and excitation vector of the equation with stochastic variable, and I (α) is wait ask Current coefficient.For the Impedance Moment of MTDS (Multiple Thin Dielectric Sheets) improved Electric Field Integral Equation (EFIE) Array element element and excitation vector element can indicate are as follows:
ZmnFor impedance matrix, wherein m and n respectively indicates the line number and row number of matrix element, and k is wave number, and η indicates freely empty Between wave impedance, EincThat indicate is incident electric fields, bmFor excitation vector, lmIt is expressed as the common edge of two triangles of a basic function Length,Indicate the area of corresponding triangle up and down.lnIt is expressed as the length of the common edge of two triangles of source basic function Degree,Indicate the area of corresponding triangle up and down.εr,i+1,kIt is thin at i+1 layer kth The relative dielectric constant of medium.
Step 4, the Analysis of Electromagnetic Scattering method that aircraft is applied with many places scumbling of shape uncertainty.It will according to step 3 After stochastic variable is extracted and is introduced into the matrix equation of integral Equation Methods, the random change information of mode shape is introduced into square In battle array equation.In conjunction with method of perturbation, obtains many places scumbling and apply the corresponding current coefficient of each basic function of aircraft surface as many places are thin It applies aircraft and does not know the variation range of shape, and then many places scumbling with uncertain source can be calculated and apply aircraft RCS size.Specific step is as follows:
As shown in (9) formula, after stochastic variable is extracted and is introduced into the matrix equations of integral Equation Methods, mode shape Random change information is introduced into matrix equation.For the uncertainty of mould shapes, stochastic variable αiIn sectionIn uniformly random variation.According to interval theory,WithIt is defined as the intermediate value and radius in section.This is answered, sectionIt can be expressed as For all stochastic variables, intermediate value and radius can be expressed as vector αcWith Δ α.Impedance according to method of perturbation, in formula (9) Matrix and excitation vector can be indicated with the method for first order Taylor series expansion are as follows:
M is stochastic variable number in formula,WithIndicate Z (α) and b (α) for stochastic variable αiIn αcIt is inclined Derivative, therefore the partial derivative of Z (α) and b (α) are easy to be derived out.It is as follows:
Zmn(α) and bm(α) respectively indicates the impedance matrix and excitation vector of the equation with stochastic variable, and ngo and ngs divide What is do not indicated is the Gauss point number for observing basic function and source basic function, and Linenum is the sample integration point number in height.lm It is expressed as the length of the common edge of two triangles of a basic function, lnIt is expressed as the length of the common edge of two triangles of source basic function Degree,It is expressed as the base vector of triangle on field, accordinglyIt is expressed as the base vector of triangle off field,It is expressed as on source The base vector of triangle, accordinglyIt is expressed as the base vector of triangle under source,The corresponding normal vector of expression source triangle.e-jkR/ 4 π R are the expansions of the Green's function of free space, and R indicates the distance between field source point, diFor the thickness for applying the corresponding number of plies Degree.Wl(iL)、Wo(Ko) and Ws(Ks) indicate the weight of corresponding Gauss point.Then the Z in above formulamn(α) and bm(α) is to stochastic variable αiLocal derviation can derive are as follows:
Then formula (9) can be expressed as
[Z(αc)+Δ Z] (Ic+ Δ I)=b (αc)+Δb (19)
Δ I is the disturbance radius of current coefficient to be asked, wherein Z (αc), b (αc) and IcIt corresponds to stochastic variable and takes intermediate value When impedance matrix, the right vector and induced current coefficient meet following relationship:
Z(αc)Ic=b (αc) (20)
And then many places scumbling applies the corresponding current coefficient of each basic function of aircraft surface as many places scumbling applies aircraft not Determine that the disturbance radius of profile variation can derive are as follows:
By the variation range of the disturbance available corresponding current coefficient of radius Δ I of current coefficient, and then can calculate Aircraft RCS is applied in many places scumbling for providing uncertain source.
The following describes the present invention in detail with reference to examples.
Embodiment
The present embodiment has carried out the Electromagnetic Scattering Characteristics to the coating dummy vehicle in many places with uncertain guided missile length Exemplary simulation, emulate in Inter (R) Core (TM) i7-4790K CPU 4.0GHz, inside save as in the computing platform of 16GB real Existing, for coating missile flight device model as shown in figure 3, by using non-Rational B-Spline surface modeling method, this guided missile model can be with It is constituted using 53 NURBS dough sheets, mould shapes are as shown in Figure 4 by 98 control point controls.The head of aircraft is along the direction+z It places, the median size on x, tri- directions y, z is respectively the λ of λ × 6.3 of 1.37 λ × 2.6, and the variation of body length is [- 0.5 λ, 0.5 λ], wherein for λ wavelength.In guided missile model, the length of body is only by the direction z at 9 control points as shown in Figure 5 Coordinate control.Therefore, only stochastic variable need to be set by the direction the z coordinate at this 9 control points, i.e. totally 9 stochastic variables.Plane Wave incident angle is θi=0 °,Along bullet incidence, viewing angle is0°≤θo≤180°.The method of the present invention With sampling 1000 times monte carlo method analyses have the coating guided missile model of uncertain body length dual station RCS mean value and Statistics variations result is as shown in Figure 6, it can be seen that two curves coincide fine.The memory requirements of two methods and calculating time Compare as shown in table 1.
Table 1
The memory requirements of the method for the present invention is less times greater than 1000 monte carlo methods of sampling it can be seen from table. However the solution time is far smaller than sampling 1000 times monte carlo methods.This embodies the method for the present invention compared to Monte Carlo The high efficiency of method.

Claims (4)

1. aircraft RCS prediction technique is applied in a kind of many places scumbling with uncertain source, which is characterized in that steps are as follows:
Step 1 establishes MTDS improved Electric Field Integral Equation；Aircraft is applied when uniform plane wave is irradiated to many places scumbling from either direction When, the scattered field in entire space polarizes the induction surface current that aircraft surface is applied by many places scumbling, surface charge, thin-medium body Electric current and the polarization charge of upper and lower surface generate, and all sources are transformed into the induction surface current of metal surface to indicate, most MTDS improved Electric Field Integral Equation is set up eventually；
Step 2 establishes the geometrical model that there is many places scumbling of shape uncertainty to apply aircraft；Had by rhinoceros software using non- B-spline surface modeling technique is managed for NURBS dough sheet information being extracted, passing through control with shape uncertainty target Geometric Modeling System point controls target geometric shape；
Step 3 extracts the deposited aircraft shape uncertain parameter of many places scumbling；Using conformal triangular mesh to NURBS dough sheet into Row subdivision forms RWG basic function, and the coordinate representation at corresponding control point is used for the geological information of RWG basic function；Many places are thin The related control point coordinates of coating aircraft profile variation are set as stochastic variable, by RWG basic function by the letter of stochastic variable Breath is introduced into MTDS integral equation；
The Electromagnetic Scattering Characteristics that there is many places scumbling of shape uncertainty to apply aircraft for step 4, analysis；It will be random according to step 3 After variable is extracted and is introduced into the matrix equation of MTDS integral Equation Methods, the random change information of mode shape is introduced into matrix In equation；In conjunction with method of perturbation, obtains many places scumbling and apply the corresponding current coefficient of each basic function of aircraft surface with many places scumbling It applies aircraft and does not know the variation range of shape, and then calculate many places scumbling with uncertain source and apply aircraft RCS size.
2. aircraft RCS prediction technique is applied in many places scumbling with uncertain source according to claim 1, feature exists In step 1 establishes MTDS improved Electric Field Integral Equation method particularly includes:
When uniform plane wave coats target from many places thin-medium that either direction irradiates closure metal, due to being closed metal inside Electromagnetic field be 0, according to the principle of equal effects and uniqueness theorem, the model of the coating target is carried out equivalent, entire space dissipates Penetrating field will be by the induction surface current J of the metal surfaceS, surface charge ρS, thin-medium body polarization current Jpol,i,kWith the pole of upper and lower surface Change charge ρS,pol,i,kIt generates；
According to the electric field boundary condition of perfact conductor, in metal surface, tangential total electric field is 0, available:
[Esc+Einc]tan=0 r ' ∈ S (1)
Formula is done into simple deformation, obtains expression formula below:
Then all sources are converted to the induction surface current J of metal surfacesIt indicates, convert as follows, i-th layer of body polarization is electric Flow Jpol,i,kExpression formula are as follows:
The surface charge ρ of metal surfacesIt is converted to following expression-form:
The polarization charge densities ρ of interface between any two layers of thin-mediums,pol,i,kExpression formula are as follows:
The improved Electric Field Integral Equation that can must solve thin-medium coating target is updated in formula after all sources are converted:
Wherein, subscript tan is the tangential component of electric field, and S is to solve for region, r ' expression source point, and r indicates site,Expression source triangle The corresponding normal vector of shape, EincThe in-field of representation space, EscThe scattered field of representation space, j are the opposite number of imaginary unit, ω It is corresponding angular frequency, μ0It is the magnetic conductivity of free space, ε0It is the dielectric constant of free space, g (r, r') is the lattice of free space Woods function,It is the gradient of free space Green's function, JsIt is the induction surface current of metal surface,It is metal watch The divergence of the induction surface current in face, ρSIt is the induction surface charge of metal surface, Jpol,i,kIt is thin-medium body polarization current, ρS,pol,i,k The polarization charge of thin-medium upper and lower surface, i indicate that the i-th number of plies coating material, L indicate total coating number of plies, and k indicates k-th of painting Region is applied, N indicates number, that is, sheet number of the total coating zone in metal surface, S1Indicate the boundary of metal and first layer thin-medium Face unit, Si,kRespectively indicate the interface element of (i-1)-th layer of thin-medium and i layers of thin-medium, SL+1,kIndicate the last layer thin-medium With the interface element of air, Vi,kIndicate the elementary volume, volume element of each layer of thin-medium；εr,i+1,kFor The relative dielectric constant of thin-medium at i+1 layer kth.
3. aircraft RCS prediction technique is applied in many places scumbling with uncertain source according to claim 2, feature exists In using conformal triangular mesh to NURBS dough sheet progress subdivision formation RWG basic function in step 3, for RWG basic function Geological information can include side length l, area A and base vector ρ with the coordinate representation at corresponding control point, geological information；Many places are thin The related control point coordinates of coating aircraft profile variation are set as stochastic variable, by RWG basic function by the letter of stochastic variable Breath is introduced into MTDS integral equation, specifically:
The related control point coordinates of aircraft profile variation are applied into many places scumbling and are set as stochastic variable α=[α1,α2,…αm], Middle m is the number of stochastic variable, and the geological information of each basic function can be indicated with stochastic variable, and basic function is updated to In MTDS integral equation, the matrix equation with stochastic variable is represented by
Z (α) I (α)=b (α) (9)
Z (α) and b (α) respectively indicates the impedance matrix and excitation vector of the equation with stochastic variable, and I (α) is electric current to be asked Coefficient；Impedance matrix elements and excitation vector element for MTDS improved Electric Field Integral Equation can indicate are as follows:
ZmnFor impedance matrix, wherein m and n respectively indicates the line number and row number of matrix element, and k is wave number, and η indicates free space wave Impedance, EincThat indicate is incident electric fields, bmFor excitation vector, lmIt is expressed as the length of the common edge of two triangles of a basic function Degree,Indicate the area of corresponding triangle up and down；lnIt is expressed as the length of the common edge of two triangles of source basic function Degree,Indicate the area of corresponding triangle up and down.
4. aircraft RCS prediction technique is applied in many places scumbling with uncertain source according to claim 3, feature exists In specific step is as follows for Analysis of Electromagnetic Scattering method of the step 4 with the deposited aircraft of shape uncertainty many places scumbling:
As shown in (9) formula, after stochastic variable is extracted and is introduced into the matrix equations of integral Equation Methods, mode shape it is random Change information is introduced into matrix equation；For the uncertainty of mould shapes, stochastic variable αiIn sectionIn uniformly random variation；According to interval theory,WithIt is defined as the intermediate value and radius in section；Therefore, sectionIt can be expressed as For all stochastic variables, intermediate value and radius are represented by vector αcWith Δ α；Impedance Moment according to method of perturbation, in formula (9) Battle array and excitation vector can be indicated with the method for first order Taylor series expansion are as follows:
M is stochastic variable number in formula,WithIndicate Z (α) and b (α) for stochastic variable αiIn αcPartial derivative, Therefore the partial derivative of Z (α) and b (α) is easy to be derived out, as follows:
Zmn(α) and bm(α) respectively indicates the impedance matrix and excitation vector of the equation with stochastic variable, and ngo and ngs distinguish table What is shown is the Gauss point number for observing basic function and source basic function, and Linenum is the sample integration point number in height；lmIt indicates For the length of the common edge of two triangles of field basic function, lnIt is expressed as the length of the common edge of two triangles of source basic function,It is expressed as the base vector of triangle on field, accordinglyIt is expressed as the base vector of triangle off field,It is expressed as triangle on source The base vector of shape, accordinglyIt is expressed as the base vector of triangle under source,The corresponding normal vector of expression source triangle；e-jkR/4 π R is the expansion of the Green's function of free space, and R indicates the distance between field source point, diFor the thickness for applying the corresponding number of plies；Wl (iL)、Wo(Ko) and Ws(Ks) indicate the weight of corresponding Gauss point；Z in above formulamn(α) and bm(α) is to stochastic variable αiLocal derviation It can derive are as follows:
Formula (9) is represented by
[Z(αc)+ΔZ](Ic+ Δ I)=b (αc)+Δb (19)
Δ I is the disturbance radius of current coefficient to be asked, wherein Z (αc), b (αc) and IcIt corresponds to when stochastic variable takes intermediate value Impedance matrix, the right vector and induced current coefficient, meet following relationship:
Z(αc)Ic=b (αc) (20)
And then many places scumbling applies the corresponding current coefficient of each basic function of aircraft surface as scumbling deposited aircraft in many places is uncertain The disturbance radius of profile variation can derive are as follows:
By the variation range of the disturbance available corresponding current coefficient of radius Δ I of current coefficient, and then it can calculate and have Aircraft RCS is applied in many places scumbling in uncertain source.
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