CN115906657A - RCS (radar cross section) reduction method for straight rod type metal structure - Google Patents
RCS (radar cross section) reduction method for straight rod type metal structure Download PDFInfo
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Abstract
The invention discloses an RCS (Radar Cross section) reduction method of a straight rod type metal structure, which comprises the following steps of: s1, setting parameters of an incident plane wave and the length of a straight rod type metal: the incident plane wave parameters comprise incident wave frequency f, incident wave wavelength lambda and incoming wave direction of incident waves; s2, constructing a traveling wave current model based on the first Bessel function and the length of the straight rod type metal; and S3, current regulation and control are carried out by using impedance loading, and the impedance loading value of the surface of the metal straight rod structure is determined by a moment method and a GA genetic algorithm. According to the invention, an impedance loading mode is adopted, the regulation and control of the surface current of the metal structure can be realized through the moment method calculation, the current distribution is optimized through a genetic algorithm, the required current distribution is finally realized physically, and the efficiency of RCS reduction design can be effectively improved.
Description
Technical Field
The invention relates to RCS reduction of a metal structure, in particular to a RCS reduction method of a straight rod type metal structure.
Background
The RCS reduction means of the metal structure is of great significance to the electromagnetic stealth design. For metallic structures, the main sources of RCS can be divided into two categories, one is structural term scattering due to electromagnetic wave reflection, and the other is mode term scattering due to induced current secondary radiation resulting from plane wave incident excitation. The increase of RCS can cause serious damage to the stealth performance of the metal structure. For an electrically large metal structure with a size larger than the wavelength of an incident plane wave, a traveling wave current distribution is formed on the excited lower surface of the plane wave, and the traveling wave current may be seriously reflected at the end of the metal structure, thereby causing the promotion of back scattering and causing the serious deterioration of RCS. A plurality of metal straight rod structures with large electrical size are distributed on platforms with high stealth performance requirements, such as airplanes, ships and the like, so that stealth design is necessary.
In order to solve the above problems, a common method at present is to suppress the traveling wave current on the surface of the metal structure by loading a wave-absorbing material, so as to achieve the RCS reduction effect. However, the daily maintenance cost caused by the loading of the wave-absorbing material is high, and most of the loading modes of the wave-absorbing material at present are completed according to experience and a large number of optimization designs, so that the time cost is high and a specific theoretical reference is lacked.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide an RCS (radar cross section) reduction method of a straight-bar metal structure, wherein the method adopts an impedance loading mode, can realize the regulation and control of the surface current of the metal structure through the moment method, optimizes the current distribution through a genetic algorithm, finally physically realizes the required current distribution, and can effectively improve the RCS reduction design efficiency.
The purpose of the invention is realized by the following technical scheme: a method of RCS reduction of a straight bar type metal structure comprising the steps of:
s1, setting parameters of incident plane waves and the length of a straight rod type metal:
the incident plane wave parameters comprise incident wave frequency f, incident wave wavelength lambda and incoming wave direction theta of incident waves;
s2, constructing a traveling wave current model based on the first Bessel function and the length of the straight rod type metal;
s201, determining the distance l from the midpoint of the straight metal rod structure to the starting endpoint according to the length of the straight metal rod structure 0 ：l 0 Is half of the length L of the straight-bar type metal structure, i.e. L 0 ＝L/2；
S202, selecting a zero-order Bessel function J of a first kind 0 Constructing a current amplitude distribution of a traveling wave current model：
For the point of the straight-bar type metal structure which is at a distance of l from the metal end, the current amplitude is A (l)
A(l)＝J 0 (αk×|l-l 0 |)
Wherein, J 0 Expressing a zero order Bessel function of the first kind, k expressing a wave number and taking the value of 2 pi/lambda, alpha expressing a zero point adjustment factor for regulating and controlling current distribution and taking the value of 0.3-1, and l 0 The distance between the middle point of the metal straight rod structure and the starting end point is shown, wherein l is in the value range of [0]The current amplitudes at different values in the traveling wave current model form the current amplitude distribution of the straight rod metal structure;
s203, constructing a traveling wave current model, namely determining the current distribution of the straight rod metal:
for a point on the straight-bar type metal structure with a distance of l from the end of the metal bar, the current I (l) is:
I(l)＝A 0 A(l)×e -jβl
A 0 represents the peak value of the current, and is constant, e -jβl The current phase factor of a point which is on the straight rod type metal structure and has a distance of l from the tail end of the metal rod is represented, beta represents a propagation constant and is equal to 2 pi/lambda; l is in the range of [0]The current at different values in the structure forms the current distribution of the straight rod metal structure.
And S3, current regulation and control are carried out by using impedance loading, and the impedance loading value of the surface of the metal straight rod structure is determined by a moment method and a GA genetic algorithm.
S301, dividing the straight rod type metal structure into N sections, wherein N +1 end points are provided, the end points are respectively 0-N, and the coordinate of each end point is expressed as [ x [ ] 0 ,x 1 ,…,x N-1 ,x N ]Wherein x is 0 As the starting endpoint coordinate, x N Is the coordinate of the end point, and the corresponding coordinate of the end point of the nth segment is [ x ] n-1 ,x n ]；
In the method of moments the current is spread by a basis function defined over two adjacent segments, for the end point n (coordinate x) n ) In other words, the basis functions f on two adjacent segments n (x) Expressed as:
wherein x represents the coordinate value of any point between the (n-1) th endpoint and the (n + 1) th endpoint, i.e. the value range (x) of x n-1 ，x n+1 )，n＝1,2,…N-1；
Representing the current distribution of the surface of the straight-bar type metal structure by the weighted sum of the basis functions; the surface current of the straight-bar type metal structure is represented by the following formula
Wherein alpha is n As a basis function f n (x) The weighting coefficients of (a);
s302, obtaining an impedance matrix of the straight rod type metal structure by using an operator obtained by an electric field integral equation;
integral equation of electric field of
Wherein E s Is a scattered field, G is a Green function, and L is the length of the straight-bar metal structure; dL' is a vector line element on the straight-bar type metal structure; omega is the angular frequency of the scattered field, mu is the free space magnetic conductivity and is a constant, r is the direct distance vector between a certain point on the straight-bar metal structure and a far-field observation point, and r' is the position vector of a certain point on the straight-bar metal structure;
according to the electric field boundary condition of the metal surface
Wherein E i An incident field that is a plane wave;
the electric field integral equation can be discretized by a moment method, and the current is represented by the form in step S301 of the basis function, i.e.
Expressed as [ I ] by the form of a vector]＝[α 1 f 1 ,α 2 f 2 ,…,α N-1 f N-1 ] T ；
E i Is the known incident field of a plane wave, E i The electric field at each segment of the straight-bar type metal structure is expressed as an N-1 dimensional excitation vector V]The mapping of the current of the integral equation to the electric field is represented by an operator Z written in the form of a matrix of order N-1, i.e. an impedance matrix of order N-1 [ Z ]]；
S303, current regulation and control of the surface of the straight rod type metal structure are achieved in a resistance loading mode;
the straight bar type metal structure is divided into N sections, and the coordinate of the corresponding end point in each section is [ [ 2 ] ] x1 ,x 2 ,…,x N-2 ,x N-1 ]Is loaded in series, N-1 resistive loads are represented by a diagonal matrix of order N-1, denoted as
The resistance loading can achieve a regulating effect, i.e., change the current distribution on the surface of the straight-bar metal structure.
According to the moment equation, after impedance loading, the loading matrix can regulate and control the impedance matrix in the step S302, and meanwhile, because the incident wave is unchanged, the excitation matrix [ V ] is unchanged, so that the current distribution on the surface of the straight-bar metal structure after impedance loading regulation and control can be obtained through moment calculation:
the current distribution on the surface of the straight-bar type metal structure is represented by the following formula [ I l ]＝[Z+R L ] -1 [V]Here [ I ] l ]Showing the current distribution on the surface of the straight-bar type metal structure after the regulation by the load, [ I l ]Is a vector with N-1 dimension, and each vector element corresponds to the position of the straight rod type metal structure;
s304, determining a traveling wave current model based on the Bessel function of the first type according to the step S2
Current sampling is carried out on N-1 points to obtain travelling wave current distribution [ I ] with the dimension of N-1 based on the Bessel function of the first kind]＝[I 1 ,I 2 ,…,I N-1 ] T Wherein->
Determining an optimized objective function, i.e. F obj ＝[I l ]-[I]＝[Z+R L ] -1 [V]-[I]The optimized variable is [ R ] L ]In order to approximate the current distribution after which to the traveling wave current distribution based on the Bessel function of the first kind with the dimension N-1, the variable [ R ] is optimized L ]It is necessary to make the two-norm F of the objective function obj || 2 Small enough, ideal | | | F obj || 2 Near 0,GA genetic algorithm will automatically converge to the objective function F obj ＝[I l ]-[I]＝[Z+R L ] -1 [V]-[I]Two norms F obj || 2 When the optimization is considered to be completed, and outputs an optimization variable [ R ] at that time L ]；
On a straight-bar type metal structure, according to [ R ] L ]And (3) carrying out resistance loading to realize approaching to the traveling wave current model proposed in the step (S2), thereby realizing RCS reduction.
The beneficial effects of the invention are: according to the invention, an impedance loading mode is adopted, the regulation and control of the surface current of the metal structure can be realized through the moment method calculation, the current distribution is optimized through a genetic algorithm, the required current distribution is finally realized physically, and the efficiency of RCS reduction design can be effectively improved.
Drawings
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a schematic view of a straight bar type metal structure;
FIG. 3 is a schematic diagram of a fringe field generated after a plane wave is incident on a straight-bar type metal structure;
FIG. 4 is a schematic diagram of the amplitude distribution of the traveling wave current under the irradiation of the plane wave;
FIG. 5 is an enhanced schematic diagram of backward scattering caused by the reflection of traveling wave current at the end of an electrically large metal straight rod structure;
FIG. 6 is a diagram illustrating a normalized current amplitude distribution according to an embodiment;
FIG. 7 is a diagram of normalized RCS generated from current distribution in an example;
FIG. 8 is an equivalent diagram of resistive loading;
fig. 9 is a schematic diagram showing a comparison of current distributions based on the first-type bessel function when the zero point adjustment factor α is 1;
FIG. 10 is an optimized loading matrix [ R ] L ]A diagonal element value diagram;
figure 11 is a diagram of normalized RCS for reference current generation.
Detailed Description
The technical solutions of the present invention are further described in detail below with reference to the accompanying drawings, but the scope of the present invention is not limited to the following.
As shown in fig. 1, a RCS reduction method of a straight bar type metal structure includes the steps of:
s1, setting parameters of incident plane waves and the length of a straight rod type metal:
in the embodiment of the present application, the frequency of the incident plane wave is 300MHz, and the wavelength is 1m. The incident angle of the incident plane wave is theta =150 degrees. The length of the metal structure of the electrically large straight rod is 4m, namely the length of four plane wave wavelengths, and a schematic diagram is shown in fig. 2. At this time, induced traveling wave current distribution is generated on the surface of the straight rod type metal structure, and a scattering field generated by the traveling wave current distribution is an object to be improved by the invention. When the traveling wave current is distributed at the tail end of the straight-bar type metal structure to be scattered, the backward scattering of the straight-bar type metal structure is enhanced, and therefore the RCS parameters are seriously deteriorated. After the plane wave is incident on the straight-bar type metal structure, the generated scattered field is as shown in fig. 3, and the backward scattered field can reach about 400mV at the incident angle θ =150 ° of the plane wave, and the RCS characteristic of the straight-bar type metal structure is poor.
S2, constructing a traveling wave current model based on the first Bessel function and the length of the straight rod type metal;
in the step S2, a traveling wave current distribution based on the bessel function of the first kind needs to be constructed on the surface of the straight-bar type metal structure, so as to realize RCS reduction of the electrically large-sized straight-bar type metal structure. The expression of the conventional traveling wave current model is as follows:
I(l)＝i(l)×e -jβl
wherein i (l) is the amplitude distribution of the traveling wave current, e -jβl Is the phase factor of the traveling wave current. In step S1, the amplitude distribution i (l) of the traveling wave current under the irradiation of the plane wave is as shown in fig. 4. As can be seen from the results of the fringe field calculation shown in fig. 3, the fringe field generated by the traveling wave current distribution at this time has a large amplitude of θ =150 °, which results in a large RCS value. This is because the traveling wave current is reflected at the end of the electrically large metal straight rod structure, resulting in an increase in backscattering, as shown schematically in fig. 5.
In order to solve this problem, in step S2, the current distribution to be configured needs to ensure that the reflection of the traveling wave current generated on both sides of the electrically large straight rod type metal structure is sufficiently small. The length of the straight-bar-type metal structure is four wavelengths (4 lambda), the straight-bar-type metal structure is divided into 104 sections, wherein the starting point is the 1 st section, and the tail end is the 104 th section. In order to construct traveling wave current distribution without reflection at the tail end, the invention constructs a current distribution model of the surface of an electrically large straight rod type metal structure based on a zero-order Bessel function of the first class. The traveling wave current model expression based on the Bessel function of the first kind is as follows:
the symbolic meanings of the current model are shown in the following table
The traveling wave current model based on the Bessel function of the first kind is based on a typical traveling wave current model, and is constructed according to the amplitude distribution A (l) of the traveling wave current model. The current distribution based on the zero-order first-class Bessel function is characterized in that the current amplitude presents oscillation attenuation along with the distance, and the current amplitude is attenuated to be very small at the tail end of the straight-bar metal structure, so that the traveling wave current is ensured not to be reflected at the tail end on the surface of the electrically large-size straight-bar metal structure.
The length of the straight-bar metal structure is 4 lambda (4 m).
In the traveling wave current model based on the Bessel function of the first kind, the distance l from the midpoint of the metal straight rod structure to the starting endpoint 0 Is 2 lambda and the wave number k takes the value 2 pi/lambda.
In the traveling wave current model based on the bessel function of the first kind, the zero point adjustment factor α is used to adjust the zero point distribution of the current amplitude based on the bessel function of the first kind, α =1,0.7,0.43,0.3 is taken as an example, and the normalized current amplitude distribution is shown in fig. 6. In the current distribution, the peak value of the current amplitude is positioned in the center of the structure, and the current amplitudes at two ends of the structure are gradually attenuated, so that the effect that the tail end does not have reflection is achieved.
The zero point adjustment factor alpha can adjust the zero point distribution of the current amplitude, and the angular domain position of the peak value of the scattering field generated by the traveling wave current on the surface of the straight bar type metal structure is related to the zero point position distribution of the current amplitude, so that the angular domain distribution of the scattering field can be adjusted by adjusting the alpha. The current distribution when α =1,0.7,0.43,0.3 and the original current distribution shown in fig. 4 produce normalized RCS as shown in fig. 7. It can be seen that when the value of α is in the range of 0.3 to 1, the RCS generated at the incident angle θ =150 ° of the incident wave is effectively attenuated.
And S3, current regulation and control are carried out by using impedance loading, and the impedance loading value of the surface of the metal straight rod structure is determined by a moment method and a GA genetic algorithm.
In the step S3, the traveling wave current distribution based on the first-class bessel function in the step S2 is realized by performing impedance loading on the surface of the straight-bar metal structure, and an impedance loading value is optimized by combining a moment method and a GA genetic algorithm. The straight-bar type metal structure is divided into 104 sectionsThe starting point is the 1 st segment and the end point is the 104 th segment. An impedance matrix Z with 103 orders can be obtained by using a moment method]When the incident plane wave is determined, a 103-dimensional excitation vector [ V ] can be obtained according to a moment method and an electric field integral equation]. The current regulation and control of the surface of the straight rod type metal structure can be realized by utilizing a resistance loading mode, the equivalent schematic diagram of the resistance loading is shown in fig. 8, 103 resistance loadings can be represented by a diagonal matrix with 103 orders and are represented as
According to the equation of moment, the current distribution on the surface of the straight-bar metal structure after impedance loading can be represented by the following formula [ I l ]＝[Z+R L ] -1 [V]Here [ I ] l ]Showing the current distribution on the surface of the straight-bar metal structure after loading, [ I ] l ]Is a 103-dimensional vector, and each vector element corresponds to the position of the straight-bar type metal structure. Determining traveling wave current distribution [ I ] based on Bessel function of the first type according to the step S2]An optimized objective function, i.e. F, can be determined obj ＝[I l ]-[I]＝[Z+R L ] -1 [V]-[I]The optimized variable is [ R ] L ]. The target function and the optimization variable are brought into the GA genetic algorithm, the GA genetic algorithm can automatically complete the optimization process, and an optimized loading matrix [ R ] is output L ]And the optimized traveling wave current amplitude distribution [ I ] opt ]. The traveling wave current [ I ] realized after the optimization opt ]Fig. 9 shows a comparison between the zero point adjustment factor α and the current distribution based on the bezier function of the first type when the value of the zero point adjustment factor α is 1. The optimized loading matrix [ R ] L ]The element values of the diagonal are shown in fig. 10. The traveling wave current [ I ] realized after the optimization opt ]And the reference current generation normalized RCS shown in fig. 3 is shown in fig. 11. For the straight-bar type metal structure, when the current distribution on the surface of the structure obeys the traveling wave current realized after optimization, the RCS generated at the plane wave incidence angle is very small, and the excellent RCS reduction effect can be achieved. The flowchart for optimization using the moment method and the GA genetic algorithm is shown in fig. 11.
While the foregoing description shows and describes a preferred embodiment of the invention, it is to be understood, as noted above, that the invention is not limited to the form disclosed herein, but is not intended to be exhaustive or to exclude other embodiments and may be used in various other combinations, modifications, and environments and may be modified within the scope of the inventive concept described herein by the above teachings or the skill or knowledge of the relevant art. And that modifications and variations may be effected by those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (3)
1. A RCS (Radar Cross section) reduction method of a straight rod type metal structure is characterized in that: the method comprises the following steps:
s1, setting parameters of incident plane waves and the length of a straight rod type metal:
the incident plane wave parameters comprise incident wave frequency f, incident wave wavelength lambda and incoming wave direction theta of incident waves;
s2, constructing a traveling wave current model based on the first Bessel function and the length of the straight rod type metal;
and S3, current regulation and control are carried out by using impedance loading, and the impedance loading value of the surface of the metal straight rod structure is determined by a moment method and a GA genetic algorithm.
2. The RCS reduction method of a straight-bar metal structure according to claim 1, wherein: the step S2 includes:
s201, determining the distance l from the midpoint of the straight metal rod structure to the starting endpoint according to the length of the straight metal rod structure 0 ：l 0 Is half of the length L of the straight-bar type metal structure, i.e. L 0 ＝L/2；
S202, selecting a zero-order Bessel function J of a first kind 0 And constructing the current amplitude distribution of the traveling wave current model:
for the point of the straight-bar type metal structure which is at a distance of l from the metal end, the current amplitude is A (l)
A(l)＝J 0 (αk×|l-l 0 |)
Wherein, J 0 Representing zero-order Bessel of the first kindFunction, k represents wave number and takes 2 pi/lambda, alpha represents zero point adjustment factor for regulating current distribution and takes a value in the range of 0.3-1, l 0 The distance between the middle point of the metal straight rod structure and the starting end point is shown, wherein l is in the value range of [0]The current amplitudes at different values in the traveling wave current model form the current amplitude distribution of the straight rod metal structure;
s203, constructing a traveling wave current model, namely determining the current distribution of the straight rod metal:
for a point on the straight-bar type metal structure which is at a distance l from the end of the metal bar, the current I (l) is as follows:
I(l)＝A 0 A(l)×e -jβl
A 0 represents the peak current value, is constant, e -jβl The current phase factor of a point which is on the straight rod type metal structure and has a distance of l from the tail end of the metal rod is represented, and beta represents a propagation constant and is equal to 2 pi/lambda; l is in the range of [0]The current distribution of the straight rod metal structure is formed by the currents at different values in the straight rod metal structure.
3. The RCS reduction method of a straight-bar metal structure according to claim 1, wherein: the step S3 includes the following substeps:
s301, dividing a straight rod type metal structure into N sections, wherein the N sections have N +1 end points, namely an end point 0, an end point 1, \8230, and an end point N; the coordinates of each end point are denoted x 0 ,x 1 ,…,x N-1 ,x N ]Wherein x is 0 As the starting endpoint coordinate, x N Is the coordinate of the end point, and the coordinate corresponding to the end point of the nth segment is [ x ] n-1 ,x n ]；
In the method of moments, the current is expanded by the basis functions defined on two adjacent segments, and for the terminal n, the basis functions f on the two adjacent segments n (x) Expressed as:
wherein x represents the n-1 th endpoint and the n +1 th endpointThe coordinate value of any point between the endpoints, i.e. the value range (x) of x n-1 ，x n+1 )，n＝1,2,…N-1；
Representing the current distribution of the surface of the straight-bar type metal structure by the weighted sum of the basis functions; the surface current of the straight-bar type metal structure is represented by the following formula
Wherein alpha is n As a basis function f n (x) The weighting coefficient of (2); />
S302, obtaining an impedance matrix of the straight rod type metal structure by using an operator obtained by an electric field integral equation;
integral equation of electric field of
Wherein E s Is a scattered field, G is a Green function, and L is the length of the straight-bar metal structure; dL' is a vector line element on the straight-bar type metal structure; omega is the angular frequency of the scattered field, mu is the free space magnetic conductivity and is a constant, r is the direct distance vector between a certain point on the straight-bar metal structure and a far-field observation point, and r' is the position vector of a certain point on the straight-bar metal structure;
according to the electric field boundary condition of the metal surface
Wherein E i An incident field that is a plane wave;
the electric field integral equation can be discretized by a moment method, and the current is represented by the form in step S301 of the basis function, i.e.
Expressed by the form of a vector as [ I]＝[α 1 f 1 ,α 2 f 2 ,…,α N-1 f N-1 ] T ；
E i Is the known incident field of a plane wave, E i The electric field at each section of the straight-bar metal structure is expressed as an N-1 dimensional excitation vector V]Integral ofThe mapping of the equation current to the electric field is represented by an operator Z, which is written in the form of an N-1 order matrix, i.e. an N-1 order impedance matrix [ Z ]]；
S303, current regulation and control of the surface of the straight rod type metal structure are achieved in a resistance loading mode;
the straight-bar metal structure is divided into N sections, and the coordinate of the corresponding endpoint of each section is [ x ] 1 ,x 2 ,…,x N-2 ,x N-1 ]Is loaded in series, N-1 resistive loads are represented by a diagonal matrix of order N-1, denoted as
The resistance loading can achieve a regulating effect, namely, the current distribution on the surface of the straight rod type metal structure is changed.
According to the moment equation, after impedance loading, the loading matrix regulates and controls the impedance matrix in the step S302, and meanwhile, since the incident wave is unchanged, the excitation matrix [ V ] is unchanged, so that the current distribution on the surface of the straight-bar metal structure after impedance loading regulation and control can be obtained through moment calculation:
the current distribution on the surface of the straight-bar type metal structure is represented by the following formula [ I l ]＝[Z+R L ] -1 [V]Here [ I ] l ]Showing the current distribution on the surface of the straight-bar type metal structure after the regulation by the load, [ I l ]Is a vector with N-1 dimension, and each vector element corresponds to the position of the straight rod type metal structure;
s304, determining a traveling wave current model based on the Bessel function of the first type according to the step S2
Current sampling is carried out on N-1 points to obtain traveling wave current distribution [ I ] with the dimension of N-1 and based on Bessel function of the first kind]＝[I 1 ,I 2 ,…,I N-1 ] T Wherein->
Determining an optimized objective functionI.e. F obj ＝[I l ]-[I]＝[Z+R L ] -1 [V]-[I]The optimized variable is [ R ] L ]In order to approximate the current distribution after which to the traveling wave current distribution based on the Bessel function of the first kind with the dimension N-1, the variable [ R ] is optimized L ]It is necessary to make the two-norm F of the objective function obj || 2 Small enough, ideal | | | F obj || 2 Near 0,GA genetic algorithm will automatically converge to the objective function F obj ＝[I l ]-[I]＝[Z+R L ] -1 [V]-[I]Two norms F obj || 2 Is determined to be complete, and outputs an optimized variable [ R ] at that time L ]；
On a straight-bar metal structure according to [ R ] L ]And (3) carrying out resistance loading to realize approaching to the traveling wave current model provided in the step S2, thereby realizing RCS reduction.
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| CN116502524B (en) * | 2023-04-18 | 2024-01-30 | 北京航空航天大学 | RCS reduction method for metal structure under broadband scanning |
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