CN109408967B - Antenna housing system structure integrated optimization algorithm - Google Patents
Antenna housing system structure integrated optimization algorithm Download PDFInfo
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- CN109408967B CN109408967B CN201811262042.7A CN201811262042A CN109408967B CN 109408967 B CN109408967 B CN 109408967B CN 201811262042 A CN201811262042 A CN 201811262042A CN 109408967 B CN109408967 B CN 109408967B
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
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- H01Q—ANTENNAS, i.e. RADIO AERIALS
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- H01Q1/42—Housings not intimately mechanically associated with radiating elements, e.g. radome
Abstract
The invention provides an antenna housing system structure integrated optimization algorithm, which belongs to the technical field of antenna housing design and comprises the following steps: acquiring parameters of an antenna housing and an antenna through far field calculation, establishing a space model of the antenna system with the housing, and calculating excitation current of a phased array antenna unit; by means of the idea of operator separation, different optimization strategies are adopted for antenna housing structure parameters and antenna radiation parameters; the antenna housing structure parameters are optimized by using a variable-thickness antenna housing optimization method, and antenna radiation parameters are optimized by using a particle swarm optimization, so that the integrated optimization of the antenna housing system structure is realized. Experimental results show that compared with a traditional variable-thickness antenna housing optimization algorithm, the algorithm is lower in aiming error and higher in wave transmission rate, and the overall design difficulty of the antenna housing is reduced.
Description
Technical Field
The invention belongs to the technical field of antenna housing design, and particularly relates to an antenna housing system structure integrated optimization algorithm.
Background
The antenna housing is used as an important component of an airborne radar system, and can protect the antenna from the influence of external harsh environment. Because the mounting position of the antenna cover is close to the antenna, the antenna can radiate radio waves to be refracted and reflected, and the performance of the antenna is further influenced. The main parameters of the antenna housing affecting the antenna performance include: aiming error (BSE) and Transmission Coefficient (TC), the former reflects the degree of influence of the antenna housing on the pointing accuracy of the antenna, and the latter reflects the degree of attenuation of the antenna housing on the operating distance of the antenna.
In the optimization design of the antenna housing, a design method based on a variable-thickness cover body is widely used, and particularly for an airborne or missile-borne cover with a special structure, the design method is favorable for realizing the optimal wave-transmitting characteristic of each space position of the cover body. The most basic variable thickness design method is to solve the local thickness of the position according to the transmission characteristics of the flat medium by calculating the local ray incidence angle of the antenna shield wall. However, this method does not consider the far-field characteristic of the antenna with the cover, and has a limited calculation accuracy. The radome design method based on the evolutionary algorithm is more accurate, for example, aiming errors of a single-layer radome are optimized by adopting a simulated annealing method in Hsu, a particle swarm algorithm based on a substitution model is researched by Carlin, and the calculation efficiency of aiming error optimization is improved. And the Meng and the Cheng respectively use a genetic algorithm and an immune clone algorithm to optimize the aiming error and the wave transmission rate of the antenna housing. Xu optimizes the aiming error and transmission loss of the antenna housing by means of a multi-target particle swarm algorithm, and further optimizes the variance of the thickness of the housing. The literature relies on the adjustment of the excitation of the array elements to achieve optimization of the radome aiming error. The above researches only individually optimize the antenna cover body or the antenna array unit, and respectively realize optimization of the aiming error and the wave-transparent rate. In practice, the antenna and the cover are taken as an integrated system, and the antenna and the cover should not be separated from each other, and the integrated optimization design of the antenna and the cover should be considered.
Therefore, optimization of the structure of the antenna cover wall is an effective method for designing the electrical performance of the antenna cover, and the traditional variable-thickness antenna cover optimization algorithm only optimizes the antenna cover, so that the integrated optimization of the antenna and the cover cannot be realized. Aiming at a phased array antenna-cover system, the application provides an antenna cover system structure integrated optimization algorithm, and the combined optimization of aiming error and wave transmittance is realized.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention provides an antenna housing system structure integrated optimization algorithm.
In order to achieve the above purpose, the invention provides the following technical scheme:
an antenna housing system structure integrated optimization algorithm comprises the following steps:
evaluating the performance of the designed antenna housing by utilizing the aiming error and the wave-transmitting rate of the antenna housing, wherein the two parameters are obtained on the premise of calculating the far field of an antenna-housing system; determining basic parameters of the antenna housing and the antenna according to design indexes, wherein the parameters comprise the shape of the housing body, the external contour size of the housing, the housing wall structure and the number of array units, and establishing a phased array antenna-housing system model, which specifically comprises the following steps:
the array antenna in the cover is represented by a group of infinite-length current sources, and the current of each array element antenna cover array unit is as follows:
wherein M is the serial number of the array element, A and phi respectively represent the amplitude and phase of the current, M is the number of the array elements, e is a natural constant, and j is an imaginary unit;
step 2, radiation field calculation
Step 2.1, radiation field in cover
The radiation electric field of the antenna array only has a component in the z direction, and the incident electric field at the p-th subdivision unit on the inner surface of the antenna cover is as follows:
where d is the total number of subdivision elements within the housing, ω is the electromagnetic angular frequency, μ 0 Is free space magnetic permeability, H 0 (2) For the second class of zeroth-order Hankel functions, k is the free-space wavenumber, ρ pn Is the distance between the source point n and the field point p; the x-component of the incident magnetic field at the inner surface of the shield is:
wherein, y n And y p Respectively the y-coordinates of the source point n and the field point p,
is a first class zero-order hank function, j is an imaginary unit;
the y-component of the incident magnetic field at the inner surface of the shield is:
wherein x is n And x p X coordinates of a source point n and a field point d, respectively;
the current excitation source, the incident electric field on the inner surface of the cover, and the x-component and y-component of the incident magnetic field are respectively expressed by matrix, i.e.
For all d discrete points in the cover, the incident electric field and the incident magnetic field on the inner surface of the cover are expressed in a matrix form:
E＝W 1 I (9)
H x ＝W 2 I (10)
H y ＝W 3 I (11)
wherein, the first and the second end of the pipe are connected with each other,
when the radiation field in the antenna housing is calculated, a matrix W is calculated in advance 1 、W 2 And W 3 And storing;
step 2.2, covering the external radiation field
Tangential electric field E on the outer surface of the radome t And tangential magnetic field H t Respectively as follows:
E t ＝[(b·E i )b]T ⊥ +[(t·E i )t]T // (15)
H t ＝[(b·H i )b]T // +[(t·H i )t]T ⊥ (16)
wherein E is i Is the incident electric field on the inner surface of the radome, H i Is an incident magnetic field on the inner surface of the radome, T // For parallel polarization transmission coefficient, T ⊥ B is a unit vector of a vertical polarization direction of an incident plane, and t is a unit vector of a parallel polarization direction; based on local flat plate approximation principle, T is obtained by a transmission line matrix method according to the incident angle, the cover thickness and the cover dielectric constant epsilon // And T ⊥ ；
The equivalent electromagnetic flow on the outer surface of the shroud can be expressed as:
J＝a×H t (17)
M'＝E t ×a (18)
wherein J is equivalent current, M' is equivalent magnetic current, and a is unit external normal vector of the equivalent surface;
the radiation field of the equivalent electromagnetic flow in two-dimensional space is:
wherein rho is a distance vector between the outer surface point of the cover and the far field point, and l is the outer surface profile of the cover; when ρ → ∞, the equation (19) is simplified by progressive expansion using a hank function and expressed in scalar form:
wherein pi is the circumferential rate, e is a natural constant,
is a far field unit direction vector, rho 'is a position vector of a surface point outside the cover, n' is an external normal direction vector of the surface point outside the cover, and eta is the intrinsic impedance of the unconsumed medium;
converting equation (20) to numerical integration, and obtaining the far field at the q-th surface point outside the hood:
wherein d is the number of the cover outer surface subdivision unit,
is the far field unit direction vector of the d-th cell, n p Is the outer normal direction vector of the d-th cell, M p Is an equivalent magnetic current of the d unit, J p Is the equivalent current of the d-th cell, p p Is the position vector of the d-th element, l p The length of the subdivision zone of the unit d on the outer surface of the cover;
assuming a total of Q far-field points outside the enclosure, the far-field radiation field is represented in matrix form:
the out-of-shield radiation far field is represented in matrix form:
Ef ar ＝wW 4 M-wW 5 J (23)
and is provided with
When the antenna and the antenna housing are determined, the shape and the position of the antenna housing are not changed, and the coefficient W and the matrix W 4 、W 5 Can be counted in advanceCalculating and storing;
step 3, antenna housing system structure integrated optimization algorithm
Step 3.1, antenna housing system structure integrated optimization model
X for setting structural parameters of radome r The thickness of the core layer with variable thickness at a limited station position on the antenna cover is represented by X pairs r Spline interpolation is carried out; x for setting antenna radiation parameters a Representing excitation change on each antenna housing array unit of the antenna, including phase compensation and amplitude adjustment, wherein the dimension of the excitation change is determined by the number of the antenna housing array units; setting G as index parameters including aiming error G of the antenna array with the cover 1 And wave transmittance G 2 ；
According to the antenna housing structural parameter X r And antenna radiation parameter X a Calculating far field radiation intensity of the antenna with the cover in all directions in space, drawing a difference directional diagram, finding a zero-depth direction of the difference directional diagram, wherein the deviation of the direction from the expected direction of the antenna is called aiming error and G is used 1 ＝B(X r ，X a θ), where θ represents the antenna scan angle, i.e. the desired pointing angle of the antenna; the wave transmittance is the ratio of far field intensity in the maximum radiation direction before and after covering, and is G 2 ＝P(X r ，X a And theta) is represented;
aiming errors and wave-transparent rates under all scanning angles are used as an integral target to be optimized, and an established antenna housing system structure integrated optimization model is as follows:
where F is the overall evaluation of the shrouded antenna system, S is the total number of scan angles, s is the number of the scanning angle and, U the total number of index parameters of the shrouded antenna array, u is the number of the index parameter, v (θ) s ) Is corresponding to the scan angle theta s The weight function of (a) is selected, wu representing the index parameter Gu Right of (1)Heavy factor, D r And D a Is X r And X a The value space of (a);
in the integrated optimization model represented by equation (27), the shroud parameter X is adjusted r And antenna parameter X a So as to make the aiming error G under a plurality of scanning angles 1 And wave transmittance G 2 The optimization is achieved;
step 3.2, implementation process of integrated optimization algorithm
Solving the optimization model by using an operator separation idea, and adopting a two-step optimization strategy;
first, the antenna radiation parameter X is maintained a Unchanged, the traditional variable-thickness radome optimization method is utilized to carry out antenna radome structural parameter X r Optimizing; then, keeping the structural parameter X of the antenna housing r Invariably, the particle swarm algorithm is utilized to radiate the parameter X of the antenna a Optimizing;
the optimization of the antenna radiation parameters by using the particle swarm optimization is realized as follows;
each particle represents a potential optimal solution of the optimization problem, and the particle characteristics are represented by three indexes of position, speed and fitness value;
assuming that the dimension of the search space is L, M particles constitute a population Z = (Z) 1 ,Z 2 ,...,Z i ,...,Z M ) Wherein the position of the ith particle is represented as a vector Z i ＝(z i1 ,z i2 ,...,z il ,...,z iL ) The velocity is represented as V i ＝(v i1 ,v i2 ,...,v il ,...,v iL ) L =1,2,. Major, L; the particle Z can be calculated according to the fitness function i Corresponding fitness value with individual extreme value of P besti ＝(P i1 ,P i2 ,...,P il ,...,P iL ) The population extremum of the population is G best ＝(G 1 ,G 2 ,...,G l ,...,G L ) (ii) a Particle tracking individual extremum P best And group extremum G best Updating the speed and position of the self, namely:
wherein c is the inertia weight, iter is the iteration number; c. C 1 And c 2 A non-negative constant, called the acceleration factor; r is a radical of hydrogen 1 And r 2 Is distributed over [0,1 ]]A random number of intervals;
the implementation process for realizing the optimization of the antenna radiation parameters by utilizing the particle swarm optimization comprises three aspects: particle position and fitness, particle initialization and particle update;
(1) Particle position and fitness
When the number of the antenna cover array units is M ', the search space is L =2M', the front M 'dimension is the phase of the current of the antenna cover array unit, and the rear M' dimension is the amplitude of the current of the antenna cover array unit; defining the particle as a 2M' vector, the value range of vector element is D a (ii) a To optimize both the collimation error and the wave-transparent rate, a fitness function is defined as:
wherein, w 1 And w 2 Is the aiming error B (X) r ，X a ，θ s ) And wave transmittance P (X) r ，X a ，θ s ) The weight coefficient of (2) determines the priority of two optimization targets; v (theta) s ) Is corresponding to the scan angle theta s A weighting function of; b max Is the maximum aiming error, P, at each scan angle before optimization max And P min Maximum and minimum wave-transparent rates before optimization;
(2) Particle initialization
The initial position of the ith particle is
Initial populationIs->
Calculating the fitness of each particle, and setting the optimal position of the ith particle as->
Initial population extremum set to
Setting the initial speed of each particle, wherein the speed range of each variable is half of the corresponding position range;
(3) Particle renewal
In the iterative process, the speed of each particle is updated according to the formula (28), after the updating, whether the speed of the particle is in the speed range needs to be checked, if not, the speed of the particle is replaced by a boundary value, and then the position of each particle is updated according to the formula (29); calculating the fitness of the updated particle, if the fitness of the particle is less than the individual extreme value thereof, namely
The individual extremum position is updated>
Otherwise, keeping the state unchanged; meanwhile, updating the position G of the group extreme value according to the updated individual extreme value best ；
Through continuous iteration, the antenna radiation parameter X with the minimum fitness value can be searched a And the phase and amplitude of the antenna housing array unit current are adjusted, so that the minimum aiming error and the highest wave transmission rate can be ensured, and the integrated optimization design of the antenna system with the housing is realized.
The antenna housing system structure integrated optimization algorithm provided by the invention establishes an optimization model of the antenna housing system structure design by analyzing the influence of antenna housing structure parameters and antenna radiation parameters on aiming errors and wave-transparent rates; by means of the idea of operator separation, different optimization strategies are adopted for antenna housing structure parameters and antenna radiation parameters; the antenna housing structural parameters are optimized by using a variable-thickness antenna housing optimization method, and antenna radiation parameters are optimized by using a particle swarm optimization, so that the integrated optimization of the antenna housing system structure is realized. The experimental result shows that compared with the traditional variable-thickness antenna housing optimization algorithm, the algorithm provided by the embodiment has the advantages of lower aiming error and higher wave transmittance, and the effectiveness of the algorithm provided by the embodiment is fully shown.
Drawings
Fig. 1 is a phased array antenna-radome system model of the radome system structure integration optimization algorithm provided in this embodiment;
FIG. 2 is a plot of pointing error versus scan angle;
FIG. 3 is a graph of wave transmissivity as a function of scan angle;
fig. 4 is a core layer thickness distribution curve of the interlayer radome a after optimization;
FIG. 5 is a compensated phase versus current amplitude curve obtained by IO-RPA optimization.
Detailed Description
The following description of the embodiments of the present invention will be made with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
Example 1
The invention provides an antenna housing system structure integrated optimization algorithm, which utilizes the aiming error and wave-transparent rate of an antenna housing to evaluate the performance of a designed antenna housing, and the two parameters are obtained on the premise of calculating the far field of an antenna-housing system; firstly, a phased array antenna-cover system model is given, then a far-field radiation field is calculated by adopting an AI-SI method, and a basis is provided for the calculation of aiming error and wave transmittance, and the method specifically comprises the following steps:
the array antenna in the cover is represented by a group of infinite-length current sources, and the current of each array element antenna cover array unit is as follows:
the phased array antenna-cover system model is shown in fig. 1, wherein N is an array element serial number, a and phi respectively represent the amplitude and phase of current, N is an array element number, e is a natural constant, and j is an imaginary unit;
step 2, radiation field calculation
Step 2.1, radiation field in cover
The radiation electric field of the antenna array only has a component in the z direction, and the incident electric field at the p-th subdivision unit on the inner surface of the antenna cover is as follows:
where d is the total number of subdivision elements within the housing, ω is the electromagnetic angular frequency, μ 0 Is the magnetic permeability of the free space and is,
for the second class of zeroth-order Hankel functions, k is the free-space wavenumber, ρ pn Is the distance between the source point n and the field point p; the x-component of the incident magnetic field at the inner surface of the shield is: />
Wherein, y n And y p Respectively the y-coordinates of the source point n and the field point p,
is a first class zeroth-order Hankel function, and j is an imaginary number unit;
the y-component of the incident magnetic field at the inner surface of the shield is:
wherein x is n And x p X coordinates of a source point n and a field point d, respectively;
the current excitation source, the incident electric field on the inner surface of the cover, and the x-component and y-component of the incident magnetic field are respectively expressed by matrix, i.e.
For all d discrete points in the cover, the incident electric field and the incident magnetic field on the inner surface of the cover are expressed in a matrix form:
E＝W 1 I (9)
H x ＝W 2 I (10)
H y ＝W 3 I (11)
wherein the content of the first and second substances,
analysis matrix W 1 、W 2 And W 3 Find each element generationThe table shows the spatial position relationship between the radiation field and the source point, which is independent of the source current characteristics; when the radiation field in the antenna housing is calculated, the matrix W can be calculated in advance 1 、W 2 And W 3 Storing the radiation field to improve the solving speed of the radiation field;
step 2.2, covering the external radiation field
Tangential electric field E on the outer surface of the radome t And tangential magnetic field H t Respectively as follows:
Et＝[(b·E i )b]T ⊥ +[(t·E i )t]T // (15)
H t ＝[(b·H i )b]T // +[(t·H i )t]T ⊥ (16)
wherein, E i Is the incident electric field on the inner surface of the radome, H i Is an incident magnetic field, T, on the inner surface of the radome // For parallel polarization transmission coefficient, T ⊥ Is a vertical polarization transmission coefficient, b is a unit vector of the vertical polarization direction of the incident plane, and t is a unit vector of the parallel polarization direction; based on local flat plate approximation principle, T is obtained by a transmission line matrix method according to the incident angle, the cover thickness and the cover dielectric constant epsilon // And T ⊥ ；
The equivalent electromagnetic flow on the outer surface of the shroud can be expressed as:
J＝a×H t (17)
M'＝E t ×a (18)
wherein J is equivalent current, M' is equivalent magnetic current, and a is unit external normal vector of the equivalent surface;
the radiation field of the equivalent electromagnetic flow in two-dimensional space is:
wherein rho is a distance vector between the outer surface point of the cover and the far field point, and l is the outer surface profile of the cover; when ρ → ∞, the equation (19) is simplified by progressive expansion using a hank function and expressed in scalar form:
wherein pi is the circumferential rate, e is a natural constant,
is a far-field unit direction vector, rho 'is a position vector of a surface point outside the cover, n' is an external normal direction vector of the surface point outside the cover, and eta is a lossless medium intrinsic impedance;
converting equation (20) to numerical integration to obtain the far field at the qth surface point outside the mask:
wherein d is the number of the cover outer surface subdivision unit,
is the far field unit direction vector of the d-th cell,
n p is the outer normal direction vector of the d-th cell, M p Is an equivalent magnetic current of the d unit, J p Is the equivalent current of the d-th cell, p p Is the position vector of the d-th element, l p The length of the subdivision zone of the unit d on the outer surface of the cover;
assuming a total of Q far-field points outside the enclosure, the far-field radiation field is represented in matrix form:
the out-of-shield radiation far field is represented in matrix form:
E far ＝wW 4 M-wW 5 J (23)
and is
When the antenna and the antenna housing are determined, the shape and the position of the antenna housing are not changed, and the coefficient W and the matrix W are 4 、W 5 The calculation can be carried out in advance and stored so as to improve the efficiency of the calculation of the far field of the radiation outside the cover;
step 3, antenna housing system structure integrated optimization algorithm
Analyzing the relation between the aiming error and the wave-transparent rate and the antenna housing structural parameters and the antenna radiation parameters, and establishing an optimization model of the antenna housing system structural design; on the basis of an operator separation idea, aiming errors and wave-transparent rates are used as optimization targets, a two-step optimization strategy is designed, the antenna housing structure parameters are optimized by adopting a traditional variable thickness optimization method, antenna radiation parameters are optimized by utilizing a particle swarm optimization, and the implementation process of an integrated optimization algorithm is given;
step 3.1, antenna housing system structure integrated optimization model
X for setting structural parameters of radome r The thickness of the core layer with variable thickness at a limited station position on the antenna cover is represented by X pairs r Spline interpolation is carried out; x for setting antenna radiation parameters a Representing excitation change on each antenna housing array unit of the antenna, including phase compensation and amplitude adjustment, wherein the dimension of the excitation change is determined by the number of the antenna housing array units; setting G as index parameters including aiming error G of the antenna array with the cover 1 And wave transmittance G 2 ；
According to the antenna housing structure parameter X r And antenna radiation parameter X a Calculating far field radiation intensity of the antenna with the cover in each direction in space, drawing a difference directional diagram, and finding the difference directional diagramThe direction of zero depth, the deviation of this direction from the desired orientation of the antenna, called the pointing error, by G 1 ＝B(X r ，X a And θ), where θ represents the antenna scan angle, i.e., the desired pointing angle of the antenna; the wave transmittance is the ratio of far field intensity in the maximum radiation direction before and after covering, and is G 2 ＝P(X r ，X a And theta) is represented;
aiming errors and wave-transparent rates under all scanning angles are used as an integral target to be optimized, and an established antenna housing system structure integrated optimization model is as follows:
where F is the overall evaluation of the shrouded antenna system, S is the total number of scan angles, s is the number of the scanning angle and, U the total number of index parameters of the antenna array with the cover, u is the number of the index parameter, v (θ) s ) Is corresponding to the scan angle theta s The weight function of (a) is selected, wu representing the index parameter Gu Weight factor of, D r And D a Is X r And X a The value space of (a);
in the integrated optimization model represented by equation (27), the shroud parameter X is adjusted r And antenna parameter X a So as to make the aiming error G under a plurality of scanning angles 1 And wave transmittance G 2 The optimization is achieved; the method is a multivariable multi-target optimization problem, and how to ensure the optimization precision and efficiency is the key for realizing the integrated optimization of the antenna housing structure;
step 3.2, implementation process of integrated optimization algorithm
The integrated optimization model is a typical multi-objective optimization problem and can be solved by adopting an evolutionary algorithm; however, the variable parameters in the model are too much, and the calculation load is heavy, so that the optimal solution is difficult to be solved; considering that the thickness of the cover body does not have severe fluctuation, the incident angle of incoming radiation waves at any position in the cover can be considered not to be changed due to the adjustment of the thickness of the cover body and the excitation of the array unit of the antenna cover, and X is r And X a There is no coupling relationship; therefore, the optimization model is solved by utilizing the operator separation idea, and a two-step optimization strategy is adopted;
first, the antenna radiation parameter X is maintained a Unchanged, the traditional variable-thickness radome optimization method is utilized to carry out antenna radome structural parameter X r Optimizing; then, keeping the antenna housing structure parameter X r Invariably, the particle swarm algorithm is utilized to radiate the parameter X of the antenna a Optimizing; the traditional variable-thickness antenna housing optimization method is not repeated herein, and the implementation process of optimizing the antenna radiation parameters by using a particle swarm algorithm is analyzed below;
each particle represents a potential optimal solution of the optimization problem, and the particle characteristics are represented by three indexes of position, speed and fitness value;
assuming that the dimension of the search space is L, M' particles constitute a population Z = (Z) 1 ,Z 2 ,...,Z i ,...,Z M ) Wherein the position of the ith particle is represented as a vector Z i ＝(z i1 ,z i2 ,...,z il ,...,z iL ) The velocity is represented as V i ＝(v i1 ,v i2 ,...,v il ,...,v iL ) L =1,2,. Major, L; the particle Z can be calculated according to the fitness function i Corresponding fitness value with individual extreme value of P besti ＝(P i1 ,P i2 ,...,P il ,...,P iL ) The population extremum of the population is G best ＝(G 1 ,G 2 ,...,G l ,...,G L ) (ii) a Particle tracking individual extremum P best And group extremum G best Updating the speed and position of the self, namely:
wherein c is the inertial weight, iter is the number of iterations; c. C 1 And c 2 A non-negative constant, called the acceleration factor; r is a radical of hydrogen 1 And r 2 Is distributed over [0,1 ]]A random number of intervals;
the optimization model needs to take two parameters of aiming error and wave-transparent rate into consideration, and if the optimization is realized by using the traditional multi-target particle swarm algorithm, the calculation efficiency is low; by designing a reasonable fitness function, the optimization process can be realized by using a single-target particle swarm algorithm, and the optimization efficiency can be greatly improved; the implementation process for realizing the optimization of the antenna radiation parameters by utilizing the particle swarm optimization comprises three aspects: particle position and fitness, particle initialization and particle update;
(1) Particle position and fitness
When the number of the antenna cover array units is M ', the search space is L =2M', the front M 'dimension is the phase of the current of the antenna cover array unit, and the rear M' dimension is the amplitude of the current of the antenna cover array unit; defining the particle as a 2M' vector, the value range of vector element is D a (ii) a To optimize both the collimation error and the wave-transparent rate, a fitness function is defined as:
wherein, w 1 And w 2 Is the aiming error B (X) r ，X a ，θ s ) And wave transmittance P (X) r ，X a ，θ s ) The weight coefficient of (2) determines the priority of two optimization targets; v (theta) s ) Is corresponding to the scan angle theta s A weighting function of (a); b is max Is the maximum aiming error, P, at each scan angle before optimization max And P min Maximum and minimum wave-transparent rates before optimization;
(2) Particle initialization
The initial position of the ith particle is
The initial population is->
Calculating fitness of each particle, and setting optimal position of ith particle as->
Initial population extremum set to
Setting the initial speed of each particle, wherein the speed range of each variable is half of the corresponding position range;
(3) Particle renewal
In the iterative process, the speed of each particle is updated according to the formula (28), after the updating, whether the speed of the particle is in the speed range needs to be checked, if not, the speed of the particle is replaced by a boundary value, and then the position of each particle is updated according to the formula (29); calculating the fitness of the updated particle, if the fitness of the particle is less than the individual extreme value thereof, namely
The individual extremum position is updated>
Otherwise, keeping the state unchanged; meanwhile, updating the group extreme value position G according to the updated individual extreme value best ；
Through continuous iteration, the antenna radiation parameter X with the minimum fitness value can be searched a And the phase and amplitude of the current of the antenna housing array unit are adjusted, so that the minimum aiming error and the highest wave transmission rate can be ensured, and the integrated optimization design of the antenna system with the housing is realized.
Next, the antenna housing system structure integrated optimization algorithm provided in this embodiment is verified and analyzed through an experiment:
a tangent oval A sandwich structure radome system containing 25 element linear arrays is established, and the system structure is optimized. The parameters of the antenna housing are as follows: the mask length is 40 λ, the base diameter is 20 λ, λ is the free space wavelength. Dielectric constant epsilon of two surface layers of A interlayer cover r =3.0, loss tangenttan δ =0.005. Core layer material epsilon r =1.1,tan δ =0.001. During the optimization, the thickness of the skin material was kept constant at 0.8mm and the thickness of the core material varied from 7mm to 12mm at 5 selected station points.
When the thickness of the core material was kept constant at 10mm, the collimation errors and wave transmission were obtained as a result when not optimized. And optimizing the structure of the radome system by adopting a variable-thickness radome optimization method and the algorithm provided by the embodiment. The variable thickness Radome Optimization method (RO) only optimizes the structural parameters of the Radome. The algorithm provided by the embodiment adopts a two-step optimization strategy, and the structural parameters of the antenna housing are optimized firstly, and then the radiation parameters of the antenna are optimized. The algorithm provided by the embodiment adjusts the Phase and amplitude of the current of the radome array unit at the same time, the variation range of the compensation Phase is-5 to 5 degrees, the variation range of the current amplitude is 4 to 6mA, and the algorithm provided by the embodiment is marked as IO-RPA (Integrated Optimization of antenna Phase and amplitude).
The aiming error and the wave-transparent rate after the antenna housing is optimized by using the two algorithms are shown in fig. 2 and fig. 3, wherein the scanning angle θ Is in the range of 0 to 50 deg. with a spacing of 5 deg.. The variable thickness optimization reduces the maximum BSE from 0.332 ° to 0.306 ° compared to a uniform thickness radome. The algorithm provided by this embodiment optimizes both the current amplitude and phase, further reducing the maximum BSE to 0.118 °. The variable thickness optimization increases the minimum wave-transparent rate from 86.5% to 92.0% compared to a uniform thickness radome. The algorithm provided by the embodiment jointly optimizes the current amplitude and the compensation phase, and the wave transmittance is close to 97.5%.
After the antenna housing system is optimized by using different algorithms, the average values of the obtained aiming error and the wave transmittance are shown in table 1. As can be seen from table 1, the average aiming error of the RO method is higher than the aiming error without optimization because the RO method can only make the aiming error at some scanning angles lower than the aiming error before optimization, while the algorithm IO-RPA provided by this embodiment can optimize the aiming error at all scanning angles, and the average aiming error is only 0.0196 °, which is an order of magnitude lower than the aiming error without optimization. The result of analyzing the wave transmittance shows that the RO method can improve the wave transmittance when the scanning angle is less than 20 degrees, but the wave transmittance of the RO method is lower than the non-optimized result after the scanning angle is more than 20 degrees, so the average wave transmittance is lower than the non-optimized result. The algorithm provided by the embodiment optimizes the wave transmission rate under all scanning angles as an integral target, the integral performance is improved, and the average wave transmission rate is as high as 97.5150%. Therefore, compared with non-optimization, the algorithm provided by the embodiment can improve the wave-transparent rate while reducing the aiming error.
TABLE 1 average sighting error and average wave-transparent rate of different algorithms
Fig. 4 shows the core thickness distribution along the radome axial station obtained by using a variable thickness radome optimization method. As can be seen from the figure, because only limited points are selected for optimization, the specific thickness of the cover body is determined according to spline interpolation, the thickness change is relatively gentle, and the process realization of the cover body is facilitated.
In the integrated optimization, an optimal radome array element excitation scheme corresponding to each scanning angle needs to be given, and when the scanning angle is 30 degrees, the current amplitude and the compensation phase obtained by using IO-RPA optimization are given in fig. 5. The antenna of the antenna housing array unit is adjusted by using the compensation phase and the current amplitude given in the diagram, the aiming error of the system is only 0.019 degrees, and the wave-transmitting rate reaches 97.5133 percent.
Aiming at a phased array antenna housing system, a system structure integrated optimization algorithm is provided. The method comprises the steps of establishing an integrated optimization model of the antenna housing system structure by analyzing the influence of antenna housing structure parameters and antenna radiation parameters on aiming errors and wave-transparent rates. An operator separation idea is adopted, a two-step optimization strategy is formulated, and a thickness-variable method and a particle swarm optimization method are adopted to optimize the antenna housing structure parameters and the antenna radiation parameters respectively, so that the integrated optimization design of the antenna housing system structure is realized. The experimental result shows that compared with the variable-thickness radome optimization method only optimizing the radome, the algorithm provided by the embodiment has the advantages of small aiming error and high wave transmittance, and is favorable for reducing the overall design difficulty of the radome.
The above-mentioned embodiments are only preferred embodiments of the present invention, and the scope of the present invention is not limited thereto, and any simple modifications or equivalent substitutions of the technical solutions that can be obviously obtained by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.
Claims (1)
1. An antenna housing system structure integration optimization algorithm is characterized by comprising the following steps:
step 1, acquiring antenna housing and antenna parameters through far field calculation to obtain an antenna housing array unit, and calculating excitation current of the antenna housing array unit;
the array antenna in the cover is represented by a group of infinite-length current sources, and the current of each array element antenna cover array unit is as follows:
wherein M is the serial number of the array element, A and phi respectively represent the amplitude and phase of the current, M is the number of the array elements, e is a natural constant, and j is an imaginary unit;
step 2, radiation field calculation
Step 2.1, radiation field in cover
The radiation electric field of the antenna array only has a component in the z direction, and the incident electric field at the p-th subdivision unit on the inner surface of the antenna cover is as follows:
where d is the total number of subdivision elements within the housing, ω is the electromagnetic angular frequency, μ 0 Is the magnetic permeability of the free space and is,
for the second class of zeroth-order Hankel functions, k is the free-space wavenumber, ρ pn Is the distance between the source point n and the field point p; the x-component of the incident magnetic field at the inner surface of the shield is:
wherein, y n And y p Respectively the y-coordinates of the source point n and the field point p,
is a first class zeroth-order Hankel function, and j is an imaginary number unit;
the y-component of the incident magnetic field at the inner surface of the shield is:
wherein x is n And x p X coordinates of a source point n and a field point d, respectively;
the current excitation source, the incident electric field on the inner surface of the cover, and the x-component and y-component of the incident magnetic field are respectively expressed by matrix, i.e.
For all d discrete points in the cover, the incident electric field and the incident magnetic field on the inner surface of the cover are expressed in a matrix form:
E＝W 1 I (9)
H x ＝W 2 I (10)
H y ＝W 3 I (11)
wherein, the first and the second end of the pipe are connected with each other,
when the radiation field in the antenna housing is calculated, a matrix W is calculated in advance 1 、W 2 And W 3 And storing;
step 2.2, covering the external radiation field
Tangential electric field E on the outer surface of the radome t And tangential magnetic field H t Respectively as follows:
E t ＝[(b·E i )b]T ⊥ +[(t·E i )t]T // (15)
H t ＝[(b·H i )b]T // +[(t·H i )t]T ⊥ (16)
wherein E is i Is the incident electric field on the inner surface of the radome, H i Is an incident magnetic field on the inner surface of the radome, T // For parallel polarisation transmission coefficient, T ⊥ Is a vertical polarization transmission coefficient, b is a unit vector of the vertical polarization direction of the incident plane, and t is a unit vector of the parallel polarization direction; based on local plate approximation principle, according to incident angle, cover thickness and cover dielectric constant epsilon, by means of transmissionObtaining T by wire-transmission matrix method // And T ⊥ ；
The equivalent electromagnetic flow on the outer surface of the shroud can be expressed as:
J＝a×H t (17)
M'＝E t ×a (18)
wherein J is equivalent current, M' is equivalent magnetic current, and a is unit external normal vector of the equivalent surface;
the radiation field of the equivalent electromagnetic flow in two-dimensional space is:
wherein rho is a distance vector between the outer surface point of the cover and the far field point, and l is the outer surface profile of the cover; when ρ → ∞, the equation (19) is simplified by progressive expansion using a hank function and expressed in scalar form:
wherein pi is a circumference ratio, e is a natural constant,
is a far field unit direction vector, rho 'is a position vector of a surface point outside the cover, n' is an external normal direction vector of the surface point outside the cover, and eta is the intrinsic impedance of the unconsumed medium;
converting equation (20) to numerical integration to obtain the far field at the qth surface point outside the mask:
wherein d is the number of the subdivision unit on the outer surface of the cover,
is the far field unit direction vector of the d-th cell,
n p is the outer normal direction vector of the d-th cell, M p Is the equivalent magnetic current of unit d, J p Is the equivalent current of the d-th cell, p p Is the position vector of the d-th element, l p The length of the subdivision zone of the unit d on the outer surface of the cover;
assuming a total of Q far-field points outside the enclosure, the far-field radiation field is represented in matrix form:
the out-of-shield radiation far field is represented in matrix form:
E far ＝wW 4 M-wW 5 J (23)
and is
When the antenna and the antenna housing are determined, the shape and the position of the antenna housing are not changed, and the coefficient W and the matrix W are 4 、W 5 Can be calculated and stored in advance;
step 3, antenna housing system structure integrated optimization algorithm
Step 3.1, antenna housing system structure integrated optimization model
X for setting structural parameters of radome r The thickness of the core layer with variable thickness at a limited station position on the antenna cover is represented by X pairs r Spline interpolation is carried out; x for setting antenna radiation parameters a Representing excitation change on each antenna housing array unit of the antenna, including phase compensation and amplitude adjustment, wherein the dimension of the excitation change is determined by the number of the antenna housing array units; setting G as index parameters including aiming error G of the antenna array with the cover 1 And wave transmittance G 2 ；
According to the antenna housing structure parameter X r And antenna radiation parameter X a Calculating far field radiation intensity of the antenna with the cover in all directions in space, drawing a difference directional diagram, finding a zero-depth direction of the difference directional diagram, wherein the deviation of the direction from the expected direction of the antenna is called aiming error and G is used 1 ＝B(X r ，X a And θ), where θ represents the antenna scan angle, i.e., the desired pointing angle of the antenna; the wave transmittance is the ratio of far field intensity in the maximum radiation direction before and after covering, and is G 2 ＝P(X r ，X a θ) represents;
aiming errors and wave-transparent rates under all scanning angles are used as an integral target to be optimized, and an established antenna housing system structure integrated optimization model is as follows:
wherein F is the overall evaluation of the antenna system with the cover, S is the total number of the scanning angles, S is the number of the scanning angles, U is the total number of index parameters of the antenna array with the cover, U is the number of the index parameters, and v (theta) s ) Is corresponding to the scan angle theta s Weight function of w u Representative index parameter G u Weight factor of D r And D a Is X r And X a A value space of (a);
in the integrated optimization model represented by equation (27), the shroud parameter X is adjusted r And antenna parameter X a So as to make the aiming error G under a plurality of scanning angles 1 And wave transmittance G 2 The optimization is achieved;
step 3.2, implementation process of integrated optimization algorithm
Solving the optimization model by using an operator separation idea, and adopting a two-step optimization strategy;
first, the antenna radiation parameter X is maintained a Unchanged, the traditional variable-thickness antenna housing optimization method is utilized to carry out optimization on the antenna housing structural parameter X r Optimizing; then, keeping the antenna housing structure parameter X r Invariably, the particle swarm algorithm is utilized to radiate the parameter X of the antenna a Optimizing;
the optimization of the antenna radiation parameters by using the particle swarm optimization is realized as follows;
each particle represents a potential optimal solution of the optimization problem, and the particle characteristics are represented by three indexes of position, speed and fitness value;
assuming that the dimension of the search space is L, M' particles constitute a population Z = (Z) 1 ,Z 2 ,...,Z i ,...,Z M ) Wherein the position of the ith particle is represented as a vector Z i ＝(z i1 ,z i2 ,...,z il ,...,z iL ) Velocity is shown as V i ＝(v i1 ,v i2 ,...,v il ,...,v iL ) L =1,2,. Major, L; the particle Z can be calculated according to the fitness function i Corresponding fitness value with individual extreme value of P besti ＝(P i1 ,P i2 ,...,P il ,...,P iL ) The population extremum of the population is G best ＝(G 1 ,G 2 ,...,G l ,...,G L ) (ii) a Particle tracking individual extremum P best And group extremum G best Updating the speed and position of the self, namely:
wherein c is the inertia weight, iter is the iteration number; c. C 1 And c 2 Is a nonnegative constantNumber, called acceleration factor; r is 1 And r 2 Is distributed over [0,1 ]]A random number of intervals;
the implementation process for realizing the optimization of the radiation parameters of the antenna by utilizing the particle swarm optimization comprises three aspects: particle position and fitness, particle initialization and particle update;
(1) Particle position and fitness
When the number of the antenna cover array units is M ', the search space is L =2M', the front M 'dimension is the phase of the current of the antenna cover array unit, and the rear M' dimension is the amplitude of the current of the antenna cover array unit; defining the particle as a 2M' dimensional vector, the value range of vector element is D a (ii) a To optimize both the collimation error and the wave-transparent rate, a fitness function is defined as:
wherein, w 1 And w 2 Is the aiming error B (X) r ，X a ，θ s ) And wave transmittance P (X) r ，X a ，θ s ) The weight coefficient of (2) determines the priority of two optimization targets; v (theta) s ) Is corresponding to the scan angle theta s A weighting function of; b is max Is the maximum aiming error, P, for each scan angle before optimization max And P min Maximum and minimum wave-transparent rates before optimization;
(2) Particle initialization
The initial position of the ith particle is
The initial population is->
Calculating the fitness of each particle, and setting the optimal position of the ith particle as->
Initial population extremum settingIs arranged as
Setting the initial speed of each particle, wherein the speed range of each variable is half of the corresponding position range;
(3) Particle renewal
In the iterative process, updating the speed of each particle according to formula (28), and checking whether the speed of the particles is in the speed range after updating, if not, replacing the speed with a boundary value, and then updating the position of each particle according to formula (29); calculating the fitness of the updated particle, if the fitness of the particle is less than the individual extreme value thereof, namely
Updating individual extremum positions>
Otherwise, keeping the state unchanged; meanwhile, updating the group extreme value position G according to the updated individual extreme value best ；
Through continuous iteration, the antenna radiation parameter X with the minimum fitness value can be searched a And adjusting the phase and amplitude of the current of the antenna housing array unit to realize the integrated optimization design of the antenna system with the housing.
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