CN104933213A - Large-scale phased antenna array wide-angle scanning optimization method based on space mapping - Google Patents

Abstract

The present invention discloses a large-scale phased antenna array wide-angle scanning optimization method based on space mapping. The large-scale phased antenna array wide-angle scanning optimization method based on space mapping comprises the following steps of: establishing an array antenna model; under the condition of not considering mutual coupling, obtaining a directional diagram of an array by multiplying directional diagrams of array elements by an array factor so as to establish a rough mode of array antenna space mapping, optimizing the rough model and determining the optimal design parameter of the rough model; processing a fine model by adopting a full-wave analysis moment method, enabling response of the rough model to approach to response of the fine model by parameter extraction and establishing a mapping relation between the rough model parameter and a fine model parameter; and obtaining the predicted parameter of the fine model by utilizing the optimal design parameter of the rough model and inverse mapping of the established mapping relation and if the predicted parameter of the fine model does not meet the design requirement, carrying out iterative updating on the mapping relation until the predicted parameter of the fine model meets the design requirement. According to the method, the designed parameter is integrally optimized and on the premise of ensuring accuracy, calculating time is saved.

Description

Based on the extensive phased array col width angle sweep optimization method of spatial mappings

Technical field

The invention belongs to phased array antenna technical field, particularly a kind of extensive phased array col width angle sweep optimization method based on spatial mappings.

Background technology

Phased array antenna has many peculiar functions, as to sky search, identify and follow the tracks of, and the ability etc. of high-power, High Data Rate and opposing severe environmental conditions.Be mainly used in Space Object Detection, airborne radar, the vehicle-mounted early warning radar of business, RFID RFID tag etc.To control flexibly large-scale array aerial direction figure, strong electromagnetism Scattering Calculation method must be relied on.In the past for the research work of array antenna radiation characteristic, over-borrowing helped the numerical algorithms such as method of moment or the business software based on numerical algorithm, but when array antenna scale is excessive, and these class methods will the computational resource of at substantial and time.

Apply the optimization Challenge of traditional method to the angle sweep of extensive phased array col width, first be difficult to obtain design initial value, even if obtained the initial value of closely optimal value, if only apply electromagnetic simulation software (to suppose that parameter is n) be optimized to many reference amounts, very consuming time, because consuming time with 2 ⁿbe directly proportional, this array antenna optimization larger for design parameters is difficult to realize.Space mapping method is the new optimization method of combined circuit emulation rapidity and Electromagnetic Simulation accuracy, and it is that solution is complicated, high cost Electromagnetic Simulation optimization problem brings brand-new thought as a kind of optimization method.But for the target of complicated structure, there is not analytical expression due to roughcast type or equivalent electrical circuit is not easy to describe, traditional space mapping method will no longer be restrained, and cannot realize the optimization of large phased-array large-angle scanning.

Summary of the invention

The object of the present invention is to provide a kind of quick, stable extensive phased array col width angle sweep optimization method based on spatial mappings, the method memory consumption is low and simple.

The technical solution realizing the object of the invention is:

Based on an extensive phased array col width angle sweep optimization method for spatial mappings, step is as follows:

1st step, sets up array antenna model, determines the built-up radiation field of array antenna when not considering mutual coupling;

2nd step, by the built-up radiation field of the 1st step gained array antenna, derives the antenna pattern formula of array antenna according to directional diagram product method, set up array antenna spatial mappings roughcast type, optimizes roughcast type and determines the optimal design parameter of roughcast type;

3rd step, thin model adopts full wave analysis method of moment, is extracted and makes the response of roughcast type approach the response of thin model, set up the mapping relations of thick model parameter and thin model parameter by parameter;

4th step, to utilize in the optimal design parameter of roughcast type in the 2nd step and the 3rd step set up mapping relations inverse mapping obtain the prediction parameter of thin model, simulating, verifying is carried out to the prediction parameter of thin model, judge whether gained response meets design requirement, if do not met, iteration renewal is carried out to the mapping relations of set up thick model parameter and thin model parameter, constantly obtains the new prediction parameter of thin model simultaneously and carry out simulating, verifying, until gained response meets design requirement.

Compared with prior art, its remarkable advantage is in the present invention: (1) is to the parameter global optimization of design: for space mapping algorithm, only need find the mapping relations in roughcast type and thin model parameter space; (2) the optimization time is saved: due to many Optimization Works are put in roughcast type, obtain satisfied effect of optimization with minimum high cost thin model emulation number of times, so this method greatly saves the time under the prerequisite ensureing result accuracy; (3) simple to operate: to constantly update the mapping relations between two set up parameter spaces, improve, the continuous predictive designs parameter new to thin model is verified simultaneously, meets the demands until obtain optimal design value.

Below in conjunction with accompanying drawing, the present invention is described in further detail.

Accompanying drawing explanation

Fig. 1 is the array antenna structure schematic diagram of the extensive phased antenna array that the present invention is based on spatial mappings.

Fig. 2 is the array antenna coordinate system schematic diagram of the extensive phased antenna array that the present invention is based on spatial mappings.

Fig. 3 is the array antenna structure figure based on the extensive phased antenna array of spatial mappings in embodiment 1.

Fig. 4 is the optimum results based on the extensive phased-array antenna array large-angle scanning of spatial mappings in embodiment 1.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described in further detail.

Composition graphs 1 ~ 2, the present invention is based on the extensive phased array col width angle sweep optimization method of spatial mappings, step is as follows:

1st step, sets up array antenna model, and determine the built-up radiation field of array antenna when not considering mutual coupling, concrete steps are as follows:

Step 1.1, sets up array antenna model, sets up N element array antenna, and the spacing often in row between adjacent cells is d _x, the longitudinal pitch between adjacent rows unit is d _y, with the 0th antenna element for true origin, with the 0th array antenna unit for x-axis, with the 0th array antenna unit for y-axis, with perpendicular to array antenna upward direction for z-axis sets up coordinate system xyz, if the angle of pitch of any point is θ in coordinate system xyz, horizontal angle is in Fig. 1, the coordinate position of i-th unit is (d _ix, d _iy, 0), i-th unit added excitation A _ibe expressed as:

$A_i=I_i{e}^{-j({\mathrm{\α}}_x+{\mathrm{\α}}_y)}---\left(1\right)$

Wherein, I _ibe the excitation amplitude of i-th unit, α _xfor encouraging horizontal phase place, α _yfor encouraging longitudinal phase place;

Step 1.2, ignores the mutual coupling between each antenna element in array antenna, and determine the built-up radiation field of array antenna, concrete steps are as follows:

(1.2.1) radiation field of antenna element is first determined, then the radiation field E of i-th antenna element _ias follows:

$E_i=A_i\frac{e^{-\mathrm{jk}{r}_i}}{r_i}=I_i\frac{e^{-\mathrm{jkr}}}{r}{e}^{-j({\mathrm{\α}}_x+{\mathrm{\α}}_y)}{e}^{-\mathrm{jk}(r_i-r)}---\left(2\right)$

Wherein, k is wave number and k=2 π/λ _g, r represents the 0th distance vector that antenna element is shown up a little, r _irepresent the distance vector that i-th antenna element is shown up a little, wave path-difference is:

(1.2.2) formula (3) is substituted into formula (2), then the radiation field E of i-th antenna element _ibe expressed as:

(1.2.3) when not considering antenna element mutual coupling, the built-up radiation field E of array antenna _tsuperposition for each antenna element radiation field:

Wherein, for pattern function, and and:

Formula (6) is substituted into (5), is not considered the radiation field E of the array antenna of mutual coupling _tfor:

Wherein, N is the number of antenna element in aerial array.

2nd step, by the built-up radiation field of the 1st step gained array antenna, derives the antenna pattern formula of array antenna according to directional diagram product method, set up array antenna spatial mappings roughcast type, optimizes roughcast type and determines the optimal design parameter of roughcast type; Wherein the roughcast type of spatial mappings is the built-up radiation field of the array antenna ignoring mutual coupling, and adopts this roughcast type of genetic algorithm optimization, and parameter to be optimized is the horizontal phase place α of excitation of each antenna element _xwith the longitudinal phase place α of excitation _y, then fitness function fitness is:

fitness＝w ₁|SLL_max-SLVL|+w ₂|Ge(i)-Gain| (8)

In formula, SLVL is optimization aim secondary lobe; Gain is target gain; w ₁, w ₂for weight coefficient and w ₁=1.0, w ₂=4.0, w ₁, w ₂value just indicate both proportionate relationship; Ge (i) represents Antenna Array Pattern gain; SLL_max is overall maximum secondary lobe.

In roughcast type, find the response meeting radiation pattern design objective, corresponding parameter is the optimum solution of roughcast type, the optimum parameter value of roughcast type be expressed as:

$x_c^{*}=\left[\begin{array}{cccccccc}{\mathrm{\α}}_{x0}& {\mathrm{\α}}_{x1}& \·\·\·& {\mathrm{\α}}_{\mathrm{xN}-1}& {\mathrm{\α}}_{y0}& {\mathrm{\α}}_{y1}& \·\·\·& {\mathrm{\α}}_{\mathrm{yN}-1}\end{array}\right]---\left(9\right)$

3rd step, thin model adopts full wave analysis method of moment, is extracted and makes the response of roughcast type approach the response of thin model, set up the mapping relations of thick model parameter and thin model parameter by parameter, specific as follows:

Step 3.1, verifies the antenna pattern of array antenna in thin model, and adopt full wave analysis method of moment to realize, optimization design problem to be solved is defined as:

$x_f^{*}=\arg \underset{x_f}{\min }U\left(R_f\left(x\right)\right)---\left(10\right)$

Wherein, x is design variable, R _fbe the response about design variable, U is suitable targets function, the optimum solution value of consult volume of tried to achieve optimization problem, x _frepresent thin model parameter value;

Step 3.2, carries out parameter extraction, in roughcast type Variational Design space, obtain parameter x _c, make:

$x_c=\underset{x_c}{\min }\left|\right|R_f\left(x_f\right)-R_c\left(x_c\right)\left|\right|---\left(11\right)$

Wherein, R _f(x _f) represent that thin model responds, R _c(x _c) represent the response of roughcast type, expression makes || R _f(x _f)-R _c(x _c) || minimum x _cvalue of consult volume, known by formula (11), for one group of design parameters x of thin model _f, the design parameter x of the corresponding thick model space _cjust can try to achieve, after parameter has extracted, obtain the mapping relations of thick model parameter and thin model parameter:

x _c＝P(x _f) (12)

In formula, P is thick model parameter x _cwith thin model parameter x _fmapping relations.

4th step, to utilize in the optimal design parameter of roughcast type in the 2nd step and the 3rd step set up mapping relations inverse mapping obtain the prediction parameter of thin model, simulating, verifying is carried out to the prediction parameter of thin model, judge whether gained response meets design requirement, if do not met, iteration renewal is carried out to the mapping relations of set up thick model parameter and thin model parameter, constantly obtain the new prediction parameter of thin model simultaneously and carry out simulating, verifying, until gained response meets design requirement, concrete steps are as follows:

Step 4.1, makes the primary value of consult volume x of thin model _f ⁽¹⁾equal the optimum parameter value of roughcast type that is:

${x_f}^{\left(\text{1}\right)}=x_c^{*}---\left(13\right)$

Step 4.2, when (14) formula is set up, algorithm convergence:

$\left|\right|x_c-x_c^{*}\left|\right|=\left|\right|P\left(x_f\right)-x_c^{*}\left|\right|\≤\mathrm{\ϵ}---\left(14\right)$

Wherein, ε is the margin of error;

Step 4.3, now remaining vector f is:

$f=f\left(x_f\right)\stackrel{\mathrm{\Δ}}{=}P\left(x_f\right)-x_c^{*}\≈0---\left(15\right)$

Step 4.4, progressive space mapping algorithm solves the root x of following nonlinear equation in quasi-Newton iteration method mode _f:

f＝f(x _f)＝0 (16)

Step 4.5, if the value of consult volume of the thin model in i-th iteration is its parameter extraction of values is remaining vector f then in i-th iteration ⁽ⁱ⁾for:

$f^{\left(i\right)}=P\left(x_f^{\left(i\right)}\right)-x_c^{*}---\left(17\right)$

Step 4.6, then the increment step-length h of new thin model parameter value ⁽ⁱ⁾obtained by following formula:

B ⁽ⁱ⁾h ⁽ⁱ⁾＝-f ⁽ⁱ⁾(18)

In above formula, B ⁽ⁱ⁾the Jacobian matrix J about mapping relations P _papproximate, J _pfor:

$J_P\stackrel{\mathrm{\Δ}}{=}{J}_P\left(x_f\right)={\left(\frac{{\∂P}^T}{{\∂x}_f}\right)}^T={\left(\frac{\∂\left(x_c^T\right)}{{\∂x}_f}\right)}^T---\left(19\right)$

Step 4.7, through type (18), obtains the increment step-length h of new thin model parameter value ⁽ⁱ⁾, then the value of consult volume of the thin model in the i-th+1 time iteration of thin model for:

$x_f^{(i+1)}=x_f^{\left(i\right)}+h^{\left(i\right)}---\left(20\right)$

Step 4.8, through type (20) obtains the prediction parameter of thin model next iteration, simulating, verifying is carried out to the prediction parameter of thin model, judge whether gained response meets design requirement, if do not met, return step 4.2, iteration renewal is carried out to the mapping relations of set up thick model parameter and thin model parameter, obtain the new prediction parameter of thin model simultaneously and carry out simulating, verifying, until gained response meets design requirement.

Embodiment 1

In order to verify correctness and the validity of context of methods, analyze below array antenna choose as Fig. 3 arrangement 568 yuan of planar arraies, antenna element is chosen and is of a size of 10.668mm × 3.0mm, length is the rectangular waveguide unit of 1 wavelength, frequency of operation is 22.587GHz, and array element distance is 8mm × 6.8mm.

Figure 4 shows that scanning (θ=60 °, ) time, antenna array pattern result, as seen from the figure, the main lobe position of directional diagram achieves the sweep length of 60 degree at 60 degree, and minor level is also less than design objective 6.5dB simultaneously.This also sufficient proof based on the validity of the extensive phased array large-angle scanning optimization method of space mapping algorithm.

In sum, the basic procedure that the present invention is based on the extensive phased array col width angle sweep optimization method of spatial mappings is as follows: optimize in rough model, obtain rough model optimum solution; Verify in refined model; Set up the mapping relations in rough model design variable space and refined model design variable space by parameter extraction process, upgrade the agent model of refined model namely corrected by mapping relations after rough model; Thin modelling value is made a prediction.The method is to the parameter global optimization of design, the mapping relations in roughcast type and thin model parameter space only need be found for space mapping algorithm, in addition, Optimization Work is put in roughcast type, obtain satisfied effect of optimization with minimum high cost thin model emulation number of times, under the prerequisite ensureing result accuracy, greatly save computing time.

Claims (5)

1., based on an extensive phased array col width angle sweep optimization method for spatial mappings, it is characterized in that, step is as follows:

1st step, sets up array antenna model, determines the built-up radiation field of array antenna when not considering mutual coupling;

2nd step, by the built-up radiation field of the 1st step gained array antenna, derives the antenna pattern formula of array antenna according to directional diagram product method, set up array antenna spatial mappings roughcast type, optimizes roughcast type and determines the optimal design parameter of roughcast type;

3rd step, thin model adopts full wave analysis method of moment, is extracted and makes the response of roughcast type approach the response of thin model, set up the mapping relations of thick model parameter and thin model parameter by parameter;

4th step, to utilize in the optimal design parameter of roughcast type in the 2nd step and the 3rd step set up mapping relations inverse mapping obtain the prediction parameter of thin model, simulating, verifying is carried out to the prediction parameter of thin model, judge whether gained response meets design requirement, if do not met, iteration renewal is carried out to the mapping relations of set up thick model parameter and thin model parameter, constantly obtains the new prediction parameter of thin model simultaneously and carry out simulating, verifying, until gained response meets design requirement.

2. according to claim 1 based on the extensive phased array col width angle sweep optimization method of spatial mappings, it is characterized in that, set up array antenna model described in 1st step, determine the built-up radiation field of array antenna when not considering mutual coupling, concrete steps are as follows:

Step 1.1, sets up array antenna model, sets up N element array antenna, and the spacing often in row between adjacent cells is d _x, the longitudinal pitch between adjacent rows unit is d _y, with the 0th antenna element for true origin, with the 0th array antenna unit for x-axis, with the 0th array antenna unit for y-axis, with perpendicular to array antenna upward direction for z-axis sets up coordinate system xyz, if the angle of pitch of any point is θ in coordinate system xyz, horizontal angle is in figure, the coordinate position of i-th unit is (d _ix, d _iy, 0), i-th unit added excitation A _ibe expressed as:

$A_i=I_i{e}^{-j({\mathrm{\α}}_x+{\mathrm{\α}}_y)}---\left(1\right)$

Wherein, I _ibe the amplitude of i-th element excitation, α _xfor encouraging horizontal phase place, α _yfor encouraging longitudinal phase place;

Step 1.2, ignores the mutual coupling between each antenna element in array antenna, and determine the built-up radiation field of array antenna, concrete steps are as follows:

(1.2.1) radiation field of antenna element is first determined, then the radiation field E of i-th antenna element _ias follows:

$E_i=A_i\frac{e^{-\mathrm{jk}{r}_i}}{r_i}=I_i\frac{e^{-\mathrm{jkr}}}{r}{e}^{-j({\mathrm{\α}}_x+{\mathrm{\α}}_y)}{e}^{-\mathrm{jk}(r_i-r)}---\left(2\right)$

Wherein, k is wave number and k=2 π/λ _g, r represents the 0th distance vector that antenna element is shown up a little, r _irepresent the distance vector that i-th antenna element is shown up a little, wave path-difference is:

(1.2.2) formula (3) is substituted into formula (2), then the radiation field E of i-th antenna element _ibe expressed as:

(1.2.3) when not considering antenna element mutual coupling, the built-up radiation field E of array antenna _tsuperposition for each antenna element radiation field:

Wherein, for pattern function, and and:

Formula (6) is substituted into (5), is not considered the built-up radiation field E of the array antenna of mutual coupling _tfor:

Wherein, N is the number of antenna element in aerial array.

3. according to claim 1 based on the extensive phased array col width angle sweep optimization method of spatial mappings, it is characterized in that, optimize roughcast type described in step 2 and determine the optimal design parameter of roughcast type, wherein the roughcast type of spatial mappings is the built-up radiation field of the array antenna ignoring mutual coupling, and adopting this roughcast type of genetic algorithm optimization, parameter to be optimized is the horizontal phase place α of excitation of each antenna element _xwith the longitudinal phase place α of excitation _y, then fitness function fitness is:

fitness＝w ₁|SLL_max-SLVL|+w ₂|Ge(i)-Gain| (8)

In formula, SLVL is optimization aim secondary lobe; Gain is target gain; w ₁, w ₂for weight coefficient and w ₁=1.0, w ₂=4.0; Ge (i) represents Antenna Array Pattern gain; SLL_max is overall maximum secondary lobe.

In roughcast type, find the response meeting radiation pattern design objective, corresponding parameter is the optimum solution of roughcast type, the optimum parameter value of roughcast type be expressed as:

$x_c^{*}=\left[\begin{array}{cccccccc}{\mathrm{\α}}_{x0}& {\mathrm{\α}}_{x1}& \·\·\·& {\mathrm{\α}}_{\mathrm{xN}-1}& {\mathrm{\α}}_{y0}& {\mathrm{\α}}_{y1}& \·\·\·& {\mathrm{\α}}_{\mathrm{yN}-1}\end{array}\right]---\left(9\right).$

4. according to claim 1 based on the extensive phased array col width angle sweep optimization method of spatial mappings, it is characterized in that, described in step 3, thin model adopts full wave analysis method of moment, being extracted by parameter makes the response of roughcast type approach the response of thin model, set up the mapping relations of thick model parameter and thin model parameter, specific as follows:

Step 3.1, verifies the antenna pattern of array antenna in thin model, and adopt full wave analysis method of moment to realize, optimization design problem to be solved is defined as:

$x_f^{*}=\arg \underset{x_f}{\min }U\left(R_f\left(x\right)\right)---\left(10\right)$

Wherein, x is design variable, R _fbe the response about design variable, U is suitable targets function, the optimum solution value of consult volume of tried to achieve optimization problem, x _frepresent thin model parameter value;

Step 3.2, carries out parameter extraction, in roughcast type Variational Design space, obtain parameter x _c, make:

$x_c=\underset{x_c}{\min }\left|\right|R_f\left(x_f\right)-R_c\left(x_c\right)\left|\right|---\left(11\right)$

Wherein, R _f(x _f) represent that thin model responds, R _c(x _c) represent the response of roughcast type, expression makes || R _f(x _f)-R _c(x _c) || minimum x _cvalue of consult volume, known by formula (11), after parameter has extracted, obtain the mapping relations of thick model parameter and thin model parameter:

x _c＝P(x _f) (12)

In formula, P is thick model parameter x _cwith thin model parameter x _fmapping relations.

5. according to claim 1 based on the extensive phased array col width angle sweep optimization method of spatial mappings, it is characterized in that, to utilize described in step 4 in the optimal design parameter of roughcast type in the 2nd step and the 3rd step set up mapping relations inverse mapping obtain the prediction parameter of thin model, simulating, verifying is carried out to the prediction parameter of thin model, judge whether gained response meets design requirement, if do not met, iteration renewal is carried out to the mapping relations of set up thick model parameter and thin model parameter, constantly obtain the new prediction parameter of thin model simultaneously and carry out simulating, verifying, until gained response meets design requirement, be specially:

Step 4.1, makes the primary value of consult volume x of thin model _f ⁽¹⁾equal the optimum parameter value of roughcast type that is:

${x_f}^{\left(\text{1}\right)}=x_c^{*}---\left(13\right)$

Step 4.2, when (14) formula is set up, algorithm convergence:

$\left|\right|x_c-x_c^{*}\left|\right|=\left|\right|P\left(x_f\right)-x_c^{*}\left|\right|\≤\mathrm{\ϵ}---\left(14\right)$

Wherein, ε is the margin of error;

Step 4.3, now remaining vector f is:

$f=f\left(x_f\right)\stackrel{\mathrm{\Δ}}{=}P\left(x_f\right)-x_c^{*}\≈0---\left(15\right)$

Step 4.4, progressive space mapping algorithm solves the root x of following nonlinear equation in quasi-Newton iteration method mode _f:

f＝f(x _f)＝0 (16)

Step 4.5, if the value of consult volume of the thin model in i-th iteration is its parameter extraction of values is remaining vector f then in i-th iteration ⁽ⁱ⁾for:

$f^{\left(i\right)}=P\left(x_f^{\left(i\right)}\right)-x_c^{*}---\left(17\right)$

Step 4.6, then the increment step-length h of new thin model parameter value ⁽ⁱ⁾obtained by following formula:

B ⁽ⁱ⁾h ⁽ⁱ⁾＝-f ⁽ⁱ⁾(18)

In above formula, B ⁽ⁱ⁾the Jacobian matrix J about mapping relations P _papproximate, J _pfor:

$J_P\stackrel{\mathrm{\Δ}}{=}{J}_P\left(x_f\right)={\left(\frac{{\∂P}^T}{{\∂x}_f}\right)}^T={\left(\frac{\∂\left(x_c^T\right)}{{\∂x}_f}\right)}^T---\left(19\right)$

Step 4.7, through type (18), obtains the increment step-length h of new thin model parameter value ⁽ⁱ⁾, then the value of consult volume of the thin model in the i-th+1 time iteration of thin model for:

$x_f^{(i+1)}=x_f^{\left(i\right)}+h^{\left(i\right)}---\left(20\right)$

Step 4.8, through type (20) obtains the prediction parameter of thin model next iteration, simulating, verifying is carried out to the prediction parameter of thin model, judge whether gained response meets design requirement, if do not met, return step 4.2, iteration renewal is carried out to the mapping relations of set up thick model parameter and thin model parameter, obtain the new prediction parameter of thin model simultaneously and carry out simulating, verifying, until gained response meets design requirement.