CN110196961A - Non- cooperation does not know the rebecca echo prediction method of shape - Google Patents

Non- cooperation does not know the rebecca echo prediction method of shape Download PDF

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CN110196961A
CN110196961A CN201810160600.2A CN201810160600A CN110196961A CN 110196961 A CN110196961 A CN 110196961A CN 201810160600 A CN201810160600 A CN 201810160600A CN 110196961 A CN110196961 A CN 110196961A
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control point
nurbs
coordinate
dough sheet
shape
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CN110196961B (en
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陈如山
何姿
丁大志
樊振宏
王珂琛
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Nanjing University of Science and Technology
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Abstract

The invention discloses a kind of rebecca echo prediction methods that non-cooperation does not know shape.Model aircraft is established by using non-Rational B-Spline surface modeling technique, the coordinate of arbitrary point can be indicated with corresponding control point coordinates on the face NURBS, the uncertain control point coordinates by the face NURBS of target geometric shape control, and are relatively independent between each control point coordinates；Coordinate on control point in all directions (direction x, y, z) is respectively set to stochastic variable for describing the uncertainty of target shape, and then the geological information of basic function RWG basic function is indicated with corresponding stochastic variable on the face NURBS；The uncertainty of target geometrical model has been introduced into the matrix equation of integral Equation Methods by stochastic variable, and then has the radar return size of uncertain shape aircraft can be by method of perturbation effectively quantitative description.

Description

Non- cooperation does not know the rebecca echo prediction method of shape
Technical field
The invention belongs to electromagnetic characteristic of scattering numerical computation technology fields, specifically, being one kind for non-cooperation The rebecca echo prediction method of uncertain shape.
Background technique
In actual life and practical engineering application, due to the influence of manufacturing process and human factor, electromagnetism field system Uncertainty is generally existing.This uncertain uncertain including geometry, material properties are uncertain, load collection The uncertainty etc. of total element function.In order to assess these probabilistic influences, scholars have researched and proposed many The method for analyzing stochastic problem.In numerous stochastic problem analysis methods, most widely used is exactly monte carlo method (Monte Carlo,MC)(G.Fishman and M.Carlo,Concepts,Algorithms,and Applications.New York,NY,USA:Springer-Verlag,1996.).The groundwork of monte carlo method is former Reason is to carry out stochastical sampling according to the probability distribution of uncertain factor, is then carried out using Deterministic Methods to each sample parameter Deterministic parsing finally obtains the statistical property of uncertain problem.Monte carlo method is simply easily achieved, therefore application is non- Often extensively.However Monte Carlo have the shortcomings that convergence it is slow, although have scholar propose some improved monte carlo methods with Improve its convergence, but appearance problem is not known for the objective with various dimensions uncertain variables, this method is still It cannot achieve effective analysis.Therefore need a kind of effective emi analysis method analysis that there are various dimensions not know outer deformation quantity Objective electromagnetic scattering problems.
Summary of the invention
The purpose of the present invention is to provide a kind of rebecca echo prediction method that non-cooperation does not know shape, Ke Yigao The noncooperative radar return size with uncertain shape aircraft of effect ground analysis prediction.
The technical solution for realizing the aim of the invention is as follows: a kind of non-cooperation does not know the rebecca echo prediction of shape Method, steps are as follows:
Step 1, by computer software using non-Rational B-splines (Non-uniform Rational B-spline, NURBS analysis of aircraft model needed for) surface modeling technique is established, extracts the information of NURBS dough sheet, i.e., each NURBS dough sheet The number and coordinate of order and Control point；
Step 2 carries out NURBS dough sheet with the triangular element based on Rao-Wilton-Glisson (RWG) basic function Subdivision, obtains the subdivision information of each NURBS dough sheet, i.e. triangular element number and each node coordinate, and by each node coordinate It is indicated with the control point coordinates on corresponding NURBS dough sheet；
Step 3 can indicate according to each node coordinate of step 2 intermediate cam shape with the control point coordinates on NURBS dough sheet, into And the geological information for describing RWG basic function can be come out with the coordinate representation at corresponding control point；
Step 4 changes related control point coordinates according to step 3, setting and aircraft configuration as stochastic variable, passes through RWG The information of stochastic variable is introduced into the matrix equation of integral Equation Methods by basic function；
Step 5 combines method of perturbation according to step 4, obtains the corresponding current coefficient of each basic function of aircraft surfaces with target The variation range of uncertain shape, and then the radar return size with uncertain shape aircraft can be calculated.
Compared with prior art, the present invention its remarkable advantage are as follows: (1) stochastic variable quantity is few and irrelevant.We Method establishes object module using non-Rational B-Spline surface modeling technique, and the shape of aircraft can be by that can control NURBS dough sheet The control point coordinates of shape control, and seldom control point can control the shape of target, and be between each control point coordinates Relatively independent.The coordinate at control point, which is arranged, can easily describe the uncertainty of target shape for stochastic variable.(2) it counts It is fast to calculate speed.It, can after the uncertainty of aircraft configuration is introduced into the matrix equation of integral Equation Methods by stochastic variable With the radar return size for using method of perturbation analysis to quantify to have uncertain shape aircraft, the calculating time repeatedly adopts much smaller than needs The monte carlo method of sample analysis.
Detailed description of the invention
Fig. 1 is the NURBS dough sheet schematic diagram containing 6 control points.
Fig. 2 is RWG basic function fn(r) schematic diagram.
Fig. 3 is that the present invention utilizes non-Rational B-Spline surface modeling technique to establish certain model aircraft.
Fig. 4 is model aircraft wing section model and control point schematic diagram in example of the present invention.
Fig. 5 is certain model aircraft dual station RCS result (mean value and the change in the embodiment of the present invention with uncertain wing length Change) curve graph.
Specific embodiment
The invention will be further described below in conjunction with the accompanying drawings.
Step 1, by computer software using non-Rational B-splines (Non-uniform Rational B-spline, NURBS analysis of aircraft model needed for) surface modeling technique is established, extracts the information of NURBS dough sheet, i.e., each NURBS dough sheet The number and coordinate of order and Control point；
Step 2 carries out NURBS dough sheet with the triangular element based on Rao-Wilton-Glisson (RWG) basic function Subdivision, obtains the subdivision information of each NURBS dough sheet, i.e. triangular element number and each node coordinate, and by each node coordinate It is indicated with the control point coordinates on corresponding NURBS dough sheet；Specific step is as follows:
NURBS dough sheet schematic diagram containing 6 control points is as shown in Figure 1.Any NURBS dough sheet is mapped to a side length For on 1 regular square dough sheet, it is flat that orthogonal two sides of facing on piece, which are divided equally and are combined with each other, respectively Then consecutive points are attached to form uniform triangular mesh, each discrete nodes by equally distributed discrete nodes on face It can be mapped to by mapping equation on corresponding NURBS dough sheet, and then triangular mesh is also mapped on the face NURBS.Node Mapping equation can indicate are as follows:
What wherein S (u, v) was indicated is that the node of facing on piece is mapped to the coordinate put on the face NURBS.Ri,j(u,v) Indicate the bivariate Piecewise Rational function on the description surface NURBS, U and V are illustrated respectively in along two side u of NURBS dough sheet, the side v The number at upward control point.Pij=[Pijx,Pijy,Pijz] it is illustrated respectively in x, y, the coordinate at control point on the direction z.
Step 3 can indicate according to each node coordinate of step 2 intermediate cam shape with the control point coordinates on NURBS dough sheet, into And the geological information for describing RWG basic function can be come out with the coordinate representation at corresponding control point；Specific step is as follows:
RWG basic function fn(r) schematic diagram is as shown in Figure 2.Wherein, lnIndicate the side length of common edge,It respectively indicates up and down The area of triangle, r are representedWithIn arbitrary some points of observation, base vectorWith With Respectively represent triangleWith lower triangleThe corresponding free vertex of middle common edge, i.e., in addition except common edge two-end-point Two o'clock.Know that the apex coordinate of the triangular mesh on NURBS dough sheet can be indicated with corresponding control point coordinates by (1) formula, table It is as follows up to formula:
Sx, Sy, SzThat respectively indicate is the x of the coordinate of triangular apex, and y, z-component, control point coordinates can be used by distinguishing X, y, z components indicate.And then the geological information (side length l, area A etc.) of RWG basic function can be used by apex coordinate and be controlled Point coordinate representation comes out, expression formula are as follows:
l1, l2, l3The side length on Atria side is respectively indicated, the node serial number in the triangles of the digital representation in subscript Or node serial number corresponding to side.
Step 4 changes related control point coordinates according to step 3, setting and aircraft configuration as stochastic variable, passes through RWG The information of stochastic variable is introduced into the matrix equation of integral Equation Methods by basic function；Specific step is as follows:
The all directions coordinate that control point is arranged is stochastic variable α=[α1,α2,…αt], the geological information of RWG basic function It can be indicated with stochastic variable, therefore with after RWG basic function discrete integration equation, stochastic variable has just been introduced into the square of moment method In battle array equation, it is shown below:
Z (α) I (α)=b (α) (5)
Z (α) and b (α) respectively indicate moment method impedance matrix and excitation vector with stochastic variable.For field integral The impedance matrix elements and excitation vector element of equation (EFIE) can indicate are as follows:
Wherein m and n respectively indicates the line number and row number of matrix element, EincWhat is indicated is incident electric fields, and k is wave number, η table Show free space wave impedance.Similarly for magnetic field integral equation (MFIE), corresponding impedance matrix elements and excitation vector Element can indicate are as follows:
Wherein HincWhat is indicated is incident magnetic,What is indicated is the normal vector by target internal outside.
Step 5 combines method of perturbation according to step 4, obtains the corresponding current coefficient of each basic function of aircraft surfaces with aircraft The variation range of uncertain shape, and then the radar return size with uncertain shape aircraft can be calculated.Specific steps It is as follows:
It can be obtained by formula (7), when stochastic variable is imported into moment method matrix equation by RWG basic function, aircraft configuration Uncertainty be just introduced into matrix equation.For the uncertainty of aircraft configuration, corresponding random change can be expressed as Measure αiIn a sectionInterior random variation.According to interval theory,With Δ αi It is respectively defined as the intermediate value and radius in section, as follows:
ThereforeIt can be expressed asFor all stochastic variables, intermediate value and radius It can be expressed as vectorWith Δ α=[Δ α1,Δα2…Δαt]。
According to the principle of method of perturbation, impedance matrix and excitation vector in formula (5) can be in αcPlace's first order Taylor grade Number expansion, as follows:
WithWhat is respectively indicated is impedance matrix Z (α) and excitation vector b (α) in αcPlace is to stochastic variable αiPartial derivative.
Then formula (5) can indicate are as follows:
[Z(αc)+ΔZ](Ic+ Δ I)=b (αc)+Δb (14)
Wherein Z (αc), b (αc) and IcCorrespond to impedance matrix when stochastic variable takes intermediate value, the right vector and induced electricity Coefficient is flowed, following relationship is met:
Z(αc)Ic=b (αc) (15)
Therefore pass through the disturbance of induced current coefficient caused by formula (14) available uncertainty due to aircraft configuration Radius Δ I 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 Provide the radar return size of uncertain shape aircraft.
Embodiment
The present embodiment has carried out the exemplary simulation of the Electromagnetic Scattering Characteristics to the model aircraft with uncertain wing length, Emulation is inside saved as and is realized in the computing platform of 512GB in DELL Intel Xeon E7-4850CPU 2.0GHz, model aircraft As shown in figure 3,56 NURBS dough sheet structures can be used in this model aircraft by using non-Rational B-Spline surface modeling method At mould shapes are controlled by 100 control points.The head of aircraft is placed along the direction-y, the intermediate value on x, tri- directions y, z Size is respectively the λ of λ × 0.83 of 10.47 λ × 4.2, and the variation of wing length is [- 0.5 λ, 0.5 λ].In model aircraft, wing Length only by the x at 8 control points as shown in Figure 4, the direction y coordinate control.It therefore, only need to be by the x at this 8 control points, y Direction coordinate is set as stochastic variable, i.e. totally 16 stochastic variables.Plane wave incidence angle is θi=90 °,Along machine Head is incident, and viewing angle is0°≤θo≤180°.The method of the present invention and sampling 1000 times monte carlo methods analyze tool There are dual station RCS mean value and the statistics variations result of the model aircraft of uncertain wing length as shown in Figure 5, it can be seen that two songs Line coincide fine.The memory requirements of two methods and the comparison for calculating the time are as shown in table 1.
1 present invention of table is compared with monte carlo method memory requirements and calculating are temporal
The memory requirements of the method for the present invention is less times greater than 1000 MC methods of sampling it can be seen from table.However it asks The solution time is far smaller than sampling 1000 times MC methods.This embodies high efficiency of the method for the present invention compared to MC method.

Claims (3)

1. a kind of rebecca echo prediction method that non-cooperation does not know shape, it is characterised in that steps are as follows:
Step 1 establishes required analysis of aircraft model using non-Rational B-Spline surface modeling technique, extracts the letter of NURBS dough sheet Breath, i.e., the order of each NURBS dough sheet and the number and coordinate of Control point；
Step 2 carries out subdivision to NURBS dough sheet with the triangular element based on RWG basic function, obtains each NURBS dough sheet Subdivision information, i.e. triangular element number and each node coordinate, and by control point of each node coordinate on corresponding NURBS dough sheet Coordinate representation；
Step 3 is indicated according to each node coordinate of step 2 intermediate cam shape with the control point coordinates on NURBS dough sheet, will describe RWG The geological information of basic function is come out with the coordinate representation at corresponding control point；
It is stochastic variable that step 4, setting, which change related control point coordinates with aircraft configuration, will be become at random by RWG basic function The information of amount is introduced into the matrix equation of integral Equation Methods；
Step 5 combines method of perturbation according to step 4, obtains the corresponding current coefficient of each basic function of aircraft surfaces as aircraft is not true Determine the variation range of shape, and then calculates the radar return size with uncertain shape aircraft.
2. rebecca echo prediction method according to claim 1, it is characterised in that: with based on RWG base described in step 2 The triangular element of function carries out subdivision to NURBS dough sheet, and control point of each node coordinate on corresponding NURBS dough sheet is sat Mark indicates:
Any NURBS dough sheet is mapped on the regular square dough sheet that a side length is 1, respectively by the phase of facing on piece Mutually vertical two sides are divided equally and are combined with each other for discrete nodes equally distributed in plane, and consecutive points are then attached shape At uniform triangular mesh, each discrete nodes are mapped on the corresponding face NURBS by mapping equation, and then network of triangle Lattice are also mapped on the face NURBS；The mapping equation of node indicates are as follows:
Wherein, what S (u, v) was indicated is that the node of facing on piece is mapped to the coordinate put on the face NURBS, Ri,j(u, v) is indicated The bivariate Piecewise Rational function on the surface NURBS described, U and V are illustrated respectively in along two side u of NURBS dough sheet, on the direction v The number at control point, Pij=[Pijx,Pijy,Pijz] it is illustrated respectively in x, y, the coordinate at control point on the direction z.
3. rebecca echo prediction method according to claim 1, it is characterised in that: triangle described in step 3 respectively saves The corresponding control point of geological information that point coordinate is indicated with the control point coordinates on NURBS dough sheet, and then will describe RWG basic function Coordinate representation come out:
Show that the apex coordinate of the triangular mesh on NURBS dough sheet indicates that expression formula is such as with corresponding control point coordinates by (1) formula Under:
Sx, Sy, SzThat respectively indicate is the x of the coordinate of triangular apex, y, z-component, uses the x of control point coordinates respectively, y, z points Amount indicates, and then the geological information of RWG basic function is showed with control point coordinates by apex coordinate.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111414801A (en) * 2020-02-18 2020-07-14 南京理工大学 Classification and identification method for electrically large non-cooperative target with uncertain shape

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104076342A (en) * 2014-06-25 2014-10-01 西安电子科技大学 Method for predicting target RCS in radar tracking state
CN105717491A (en) * 2016-02-04 2016-06-29 象辑知源（武汉）科技有限公司 Prediction method and prediction device of weather radar echo image
CN106649900A (en) * 2015-10-29 2017-05-10 南京理工大学 Time domain analysis method for electromagnetic properties of non-uniform rotational symmetric body

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104076342A (en) * 2014-06-25 2014-10-01 西安电子科技大学 Method for predicting target RCS in radar tracking state
CN106649900A (en) * 2015-10-29 2017-05-10 南京理工大学 Time domain analysis method for electromagnetic properties of non-uniform rotational symmetric body
CN105717491A (en) * 2016-02-04 2016-06-29 象辑知源（武汉）科技有限公司 Prediction method and prediction device of weather radar echo image

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111414801A (en) * 2020-02-18 2020-07-14 南京理工大学 Classification and identification method for electrically large non-cooperative target with uncertain shape
CN111414801B (en) * 2020-02-18 2022-08-12 南京理工大学 Classification and identification method for electrically large non-cooperative target with uncertain shape

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