CN115859483A - Material distribution position optimization design method based on Maxwell Wei Fangfa adjoint equation - Google Patents

Material distribution position optimization design method based on Maxwell Wei Fangfa adjoint equation Download PDF

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CN115859483A
CN115859483A CN202310123977.1A CN202310123977A CN115859483A CN 115859483 A CN115859483 A CN 115859483A CN 202310123977 A CN202310123977 A CN 202310123977A CN 115859483 A CN115859483 A CN 115859483A
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equation
wei
jifen
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CN115859483B (en
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周琳
黄江涛
陈宪
邓俊
钟世东
阙肖峰
刘刚
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Institute of Aerospace Technology of China Aerodynamics Research and Development Center
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Abstract

The invention discloses a material distribution position optimization design method based on Maxwell Wei Fangfa adjoint equation, which relates to the technical field of aircraft dielectric coating stealth, and adopts the technical scheme that: the method specifically comprises the following steps: s1: dividing and numbering the aircraft surface areas; s2: constructing a continuous design variable D and a coating area constraint C; s3: solving a target and a constraint value by combining a Max Wei Jifen equation of the impedance boundary condition; s4: solving a Maxs Wei Jifen equation discrete adjoint equation to obtain the gradient of the design variable relative to the target and the constraint; s5: inputting the obtained target, the constraint value and the gradient into a sequence quadratic programming algorithm to obtain a design variable variation; s6: steps S3-S5 are repeated until the optimization converges. The method finds a wave-absorbing material distribution position scheme capable of reducing the scattering cross section of the target radar most effectively under the condition of meeting weight (total coating area) constraint.

Description

Material distribution position optimization design method based on Maxwell Wei Fangfa adjoint equation
Technical Field
The invention relates to the technical field of aircraft dielectric coating stealth, in particular to a material distribution position optimization design method based on Maxwell equation adjoint equations.
Background
The aircraft stealth design mainly works to reduce the radar scattering cross section as much as possible by means of appearance design, coating materials and the like. The appearance stealth design is the basis of stealth design, but the appearance stealth has certain limitation, and when the appearance of the low RCS that the appearance stealth obtained reaches certain order of magnitude, can't further reduce RCS. The material stealth technology is not limited by appearance conditions, so that the damage to the pneumatic characteristic caused by stealth design can be reduced, the defect of the appearance stealth can be overcome, and the material stealth technology is an important component of the stealth design. However, the design of the stealth material has a series of disadvantages, and for the coating type wave-absorbing material, the coating thickness and the wavelength meet certain conditions, the weight is increased when the coating type wave-absorbing material is used, so the weight increasing condition must be considered when the coating type wave-absorbing material is applied. The traditional stealth material coating is generally carried out on the whole aircraft, so that the weight of the material is large, and in order to reduce RCS of the aircraft as far as possible and control the total weight of the aircraft, the most effective wave-absorbing material distribution mode on the target surface needs to be found.
The adjoint method is an important method for the fine design of a high-dimensional design problem based on the gradient, by deducing the adjoint equation of the control equation, the gradient of the target function can be accurately and efficiently obtained through the first-time control equation solution and the first-time adjoint equation solution. How to apply the accompanying method to find the most effective wave-absorbing material distribution mode on the target surface is an important problem to be solved by improving the design efficiency of the material coating position.
Disclosure of Invention
The invention aims to provide a material distribution position optimization design method based on an accompanied equation of Max Wei Fangfa, and the method finds a wave-absorbing material distribution position scheme capable of reducing the scattering cross section of a target radar most effectively under the condition of meeting weight (total coating area) constraint.
The technical purpose of the invention is realized by the following technical scheme: the material distribution position optimization design method based on the Maxwell Wei Fangfa adjoint equation specifically comprises the following steps:
s1: dividing and numbering the surface area of the aircraft based on a K-means clustering method;
s2: constructing a continuous design variable D and a coating area constraint C based on an improved Sigmoid function;
s3: solving a target and a constraint value by combining an Max Wei Jifen equation of impedance boundary conditions;
s4: solving a Maxs Wei Jifen equation discrete adjoint equation to obtain the gradient of the design variable relative to the target and the constraint;
s5: inputting the obtained target, the constraint value and the gradient into a sequence quadratic programming algorithm to obtain a design variable variation;
s6: steps S3-S5 are repeated until the optimization converges.
Further, the specific steps of S1 are:
s1-1: dividing the surface required by given optimization into the number of regions;
s1-2: and taking the number of the divided areas as the number of clustering centers of the K-means clustering, clustering the physical coordinates of the grid points, and taking the same cluster obtained by clustering as an area surface grid area.
Further, the improved Sigmoid function in S2 is:
Figure SMS_1
wherein the content of the first and second substances,
Figure SMS_2
relative surface impedance of the wave-absorbing material; />
Figure SMS_3
For the design variables of the region or regions, device for selecting or keeping>
Figure SMS_4
；/>
Figure SMS_5
For the relative surface impedance of the area in the design process, <' >>
Figure SMS_6
；
The constraint form of the coating area in S2 is as follows:
Figure SMS_7
wherein the content of the first and second substances,
Figure SMS_8
is a region->
Figure SMS_9
C is a given constant constraint.
Further, the equation of Max Wei Jifen in S3 is:
Figure SMS_10
wherein the content of the first and second substances,
Figure SMS_11
an impedance matrix of Max Wei Jifen equations, <' >>
Figure SMS_12
，/>
Figure SMS_13
Is an induced current>
Figure SMS_14
Is responsive to a magnetic flow>
Figure SMS_15
The excitation vector is the equation for Max Wei Jifen.
Further, the max Wei Jifen equation discretization adjoint equation in S4 is:
Figure SMS_16
wherein the content of the first and second substances,
Figure SMS_17
an impedance matrix of Max Wei Jifen equations, <' >>
Figure SMS_18
For accompanying variable to be evaluated>
Figure SMS_19
In order to be a radar cross-section,
Figure SMS_20
，/>
Figure SMS_21
for inducing current to combine>
Figure SMS_22
Is induced magnetic current; the discrete adjoint variable solution adopts a multilayer fast multipole algorithm.
Further, the solution results of the max Wei Jifen equation and the adjoint equation in S4 are used to calculate the design variable gradient, and the calculation equation is:
Figure SMS_23
。
in conclusion, the invention has the following beneficial effects: the method can automatically divide the surface grid of the aircraft into a plurality of areas, quickly and accurately find the RCS inhibition effect of the wave-absorbing material coated on each area, thereby obtaining the most effective wave-absorbing material distribution mode and effectively reducing the total weight of the required wave-absorbing material on the basis of having good RCS reduction characteristics.
Drawings
FIG. 1 is a flow chart of a material distribution position optimization design method based on Maxwell's equations in an embodiment of the invention;
fig. 2 is a schematic diagram of an improved Sigmoid function form in the embodiment of the present invention.
Detailed Description
The present invention is described in further detail below with reference to FIGS. 1-2.
Example (b): the material distribution position optimization design method based on the maxwell equation adjoint equation specifically comprises the following steps as shown in fig. 1 and fig. 2:
s1: dividing and numbering the surface area of the aircraft based on a K-means clustering method;
in this embodiment, the number N of surface divided regions required for optimization is given, the number of another clustering centers is N, the geometric coordinates of the aircraft surface mesh are clustered, and the surface mesh is classified into N classes, so as to obtain N surface divided regions.
S2: constructing a continuous design variable D and a coating area constraint C based on an improved Sigmoid function;
in this example, the design variables of the coating design
Figure SMS_26
Indicates a region->
Figure SMS_27
Whether or not a material coating is carried out and, if so, the area is electromagnetically evaluated->
Figure SMS_29
Otherwise the area is->
Figure SMS_24
Otherwise the area is->
Figure SMS_28
(metal conductor). Introducing a design variable->
Figure SMS_30
Indicates the material application on the surface, when applied->
Figure SMS_31
Otherwise->
Figure SMS_25
. Since the gradient optimization based on the adjoint equation requires that the variables are designed to be continuous functions and the discrete variables 0 and 1 of 'whether to coat' need to be changed into continuous variables, the invention introduces an improved Sigmoid function to realize the continuity of the variables, and records that:
Figure SMS_32
where k is used to adjust the variable from 1 to
Figure SMS_33
In fig. 2 shows>
Figure SMS_34
=10, 20 and 40 {>
Figure SMS_35
The value of (a). The coating area constraint adopted by the configuration optimization requires that the total coating area is smaller than a given constraint requirement C, namely:
Figure SMS_36
wherein
Figure SMS_37
Is the area of each surface region.
S3: solving a target and a constraint value by combining a Max Wei Jifen equation of the impedance boundary condition;
establishing a Maxwell Wei Jifen equation radar scattering cross section (RCS) evaluation method based on impedance boundary conditions, and giving parameters of the wave-absorbing material to be adopted, including the relative dielectric constant of the material
Figure SMS_38
Relative magnetic permeability->
Figure SMS_39
The coating thickness d, from which the relative surface resistance of the material is calculated->
Figure SMS_40
Will input>
Figure SMS_41
The radar cross section evaluation program for impedance boundary conditions completes the RCS evaluation. Wherein the radar scattering cross section estimator solves the discrete form of the integral equation:
Figure SMS_42
wherein
Figure SMS_43
Equation impedance matrix for Max Wei Jifen; />
Figure SMS_44
J is induction current and M is induction magnetic current; v is the excitation vector of Max Wei Jifen equation.
S4: solving a Maxs Wei Jifen equation discrete adjoint equation to obtain the gradient of the design variable relative to the target and the constraint;
in this embodiment, the discrete adjoint equation is:
Figure SMS_45
wherein
Figure SMS_46
Is the accompanying variable to be solved; />
Figure SMS_47
Is a radar cross section. And calculating the gradient of the design variable according to the Max Wei Jifen equation and the solution result of the adjoint equation, wherein the calculation method is as follows:
Figure SMS_48
。
s5: inputting the obtained target, the constraint value and the gradient into a sequence quadratic programming algorithm to obtain a design variable variation;
in this embodiment, a sequence quadratic programming algorithm based on slslsrqp is used to solve the design variables for a new iteration.
S6: and repeating the steps S3-S5 until the optimization converges, and finally obtaining the optimization result of the material distribution position.
The present embodiment is only for explaining the present invention, and it is not limited to the present invention, and those skilled in the art can make modifications of the present embodiment without inventive contribution as needed after reading the present specification, but all of them are protected by patent law within the scope of the claims of the present invention.

Claims (6)

1. The material distribution position optimization design method based on the Maxwell Wei Fangfa adjoint equation is characterized in that: the method specifically comprises the following steps:
s1: dividing and numbering the surface area of the aircraft based on a K-means clustering method;
s2: constructing a continuous design variable D and a coating area constraint C based on an improved Sigmoid function;
s3: solving a target and a constraint value by combining a Max Wei Jifen equation of the impedance boundary condition;
s4: solving a Maxs Wei Jifen equation discrete adjoint equation to obtain the gradient of the design variable relative to the target and the constraint;
s5: inputting the obtained target, the constraint value and the gradient into a sequence quadratic programming algorithm to obtain a design variable variation;
s6: steps S3-S5 are repeated until the optimization converges.
2. The method for optimizing and designing the material distribution position based on the Max Wei Fangfa adjoint equation of claim 1, wherein: the specific steps of S1 are as follows:
s1-1: dividing the surface required by given optimization into the number of regions;
s1-2: and taking the number of the divided areas as the number of clustering centers of the K-means clustering, clustering the physical coordinates of the grid points, and taking the same class obtained by clustering as a surface grid area of the area.
3. The method of claim 1 for optimizing the design of material distribution positions based on max Wei Fangfa adjoint equation, wherein: the improved Sigmoid function in S2 is:
Figure QLYQS_1
；
wherein the content of the first and second substances,
Figure QLYQS_2
relative surface impedance of the wave-absorbing material; />
Figure QLYQS_3
Is a region->
Figure QLYQS_4
Is selected and/or selected>
Figure QLYQS_5
；/>
Figure QLYQS_6
For a region in the design process>
Figure QLYQS_7
Is relatively surface impedance, <' > is selected>
Figure QLYQS_8
；
The constraint form of the coating area in S2 is as follows:
Figure QLYQS_9
；
wherein, the first and the second end of the pipe are connected with each other,
Figure QLYQS_10
is a region->
Figure QLYQS_11
C is a given constant constraint.
4. The method for optimizing and designing the material distribution position based on the Max Wei Fangfa adjoint equation of claim 1, wherein: max Wei Jifen in S3 is the equation:
Figure QLYQS_12
；
wherein the content of the first and second substances,
Figure QLYQS_13
an impedance matrix of Max Wei Jifen equations, <' >>
Figure QLYQS_14
，/>
Figure QLYQS_15
Is an induced current>
Figure QLYQS_16
Is responsive to a magnetic flow>
Figure QLYQS_17
The excitation vector is the equation for Max Wei Jifen.
5. The method for optimizing and designing the material distribution position based on the Max Wei Fangfa adjoint equation of claim 1, wherein: max Wei Jifen equation discretization adjoint equation in S4 is:
Figure QLYQS_18
；
wherein the content of the first and second substances,
Figure QLYQS_19
an impedance matrix of Max Wei Jifen equations, <' >>
Figure QLYQS_20
For accompanying variable to be evaluated>
Figure QLYQS_21
In order to be a radar cross-section,
Figure QLYQS_22
，/>
Figure QLYQS_23
for inducing current to combine>
Figure QLYQS_24
Is induced magnetic current; the discrete adjoint variable solution adopts a multilayer fast multipole algorithm.
6. The method for optimizing and designing the material distribution position based on the Max Wei Fangfa adjoint equation of claim 1, wherein: in S4, the solution results of the Max Wei Jifen equation and the adjoint equation calculate the design variable gradient, and the calculation equation is as follows:
Figure QLYQS_25
；
wherein
Figure QLYQS_28
Is a radar cross section, is selected>
Figure QLYQS_30
An impedance matrix of Max Wei Jifen equations, <' >>
Figure QLYQS_32
Excitation vectors for the Max Wei Jifen equation>
Figure QLYQS_27
For accompanying variable to be evaluated>
Figure QLYQS_29
For design variables, <' >>
Figure QLYQS_31
，/>
Figure QLYQS_33
Is an induced current>
Figure QLYQS_26
Is an induced magnetic current. />
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