CN111539143A - Strain electromagnetic coupling-based electrical property compensation method for active phased array antenna - Google Patents

Strain electromagnetic coupling-based electrical property compensation method for active phased array antenna Download PDF

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CN111539143A
CN111539143A CN202010313795.7A CN202010313795A CN111539143A CN 111539143 A CN111539143 A CN 111539143A CN 202010313795 A CN202010313795 A CN 202010313795A CN 111539143 A CN111539143 A CN 111539143A
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strain
antenna
array
electromagnetic coupling
displacement
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CN111539143B (en
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王艳
王从思
王志海
时海涛
闵志先
任恒
徐鹏颖
许谦
王璐
郑元鹏
王飞朝
彭雪林
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Xian University of Architecture and Technology
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Abstract

The invention discloses an electrical property compensation method of an active phased array antenna based on strain electromagnetic coupling, which comprises the steps of determining the structural parameters and the material properties of the active phased array antenna; establishing an antenna finite element model, carrying out modal analysis, extracting a displacement mode and a strain mode, determining the order of a main mode, establishing a strain displacement conversion matrix, and determining the position offset of an array element; establishing a strain electromagnetic coupling model and decomposing the strain electromagnetic coupling model into an ideal electrical property item and an electrical property change item; performing two-dimensional fast Fourier transform, introducing an ideal and strain information excitation current Fourier series into the electrical property of the antenna, and performing two-dimensional fast Fourier inverse transformation; and comparing the initial excitation current to obtain the amplitude and phase compensation quantity of the array element excitation current based on the strain information. The method can directly evaluate the electrical property of the active phased array antenna based on the strain measurement information, can quickly determine the amplitude and the phase compensation quantity of the excitation current according to the strain information, and effectively ensures the reliable service performance of the antenna with limited carrier space.

Description

Strain electromagnetic coupling-based electrical property compensation method for active phased array antenna
Technical Field
The invention belongs to the technical field of antennas, and particularly relates to an electrical property compensation method of an active phased array antenna based on strain electromagnetic coupling.
Background
The active phased array antenna has the advantages of high reliability, multiple functions, strong detection and tracking capabilities and the like, and is widely applied to various radar systems such as airborne, shipborne, spaceborne and the like. With the increasing demand of radar, the performance requirements of the antenna are more stringent. However, in the service process of the antenna, the complex working environment of the radar, such as vibration, sea waves, wind load, space heat sink, high-temperature heat power consumption and the like, can cause structural deformation of the antenna, and deteriorate the electrical performance of the antenna. Therefore, in order to ensure reliable service of the antenna, a compensation technology is urgently needed to ensure the electrical performance of the antenna.
One of the characteristics of the active phased array antenna is that an antenna directional diagram can be controlled by changing the excitation current of an antenna array element, so that the electrical property deterioration caused by structural deformation is compensated by adopting a mode of adjusting the excitation current of the antenna array element, and the active phased array antenna is the most main method applied to the current active phased array antenna, wherein the determination of the excitation current compensation quantity is a key problem. At present, the determination method for studying the excitation current compensation amount is mainly performed from three aspects, namely, measuring an antenna directional diagram and reversely deducing the compensation amount of the excitation current of an array element. However, the directional pattern of the active phased array antenna in service is difficult to measure; and secondly, measuring the phase difference of the antenna array elements and determining the phase adjustment quantity of the excitation current. Schippers H, Van Tongren J H, Knott P, et al, simulation and compensation techniques research in NATO/RTO/SET 087/RTG 50[ C ]. Aerospace Conference,2007 IEEE,2007:1-13, each antenna array element is provided with an analog integrated circuit, and the phase difference change in the array element is measured to give the phase adjustment amount of the excitation current. The method is applied to a service stage, however, the method is only effective to the phase difference in the array of the antenna, and cannot compensate the spatial phase error caused by structural deformation; and thirdly, measuring the deformation of the antenna structure, and calculating the adjustment quantity of the exciting current according to the deformation quantity of the array elements. Lesueur G, Merlet T, Queguiner M, equivalent. management of a deformable active antenna [ C ]. radio Conference-Surveillance for a Safer World,2009.RADAR. International. IEEE,2009:1-5, by optical probe acquisition antenna array surface structure deformation, according to the space phase change caused by the deformation, calculating the adjustment amount of array element excitation. The antenna structure deformation is measured by a laser camera, a laser polarization device and the like during working, and the influence of the structure deformation on the electrical property of the antenna is compensated. When the antenna structure deformation is measured, the adopted measurement equipment such as an optical probe, laser photography and the like can be strictly limited by the carrier platform of the antenna, for airborne, satellite-borne and other antenna systems, the carrier space is very limited, and the antenna structure deformation measurement device is difficult to assemble, so that the measurement of the antenna structure deformation cannot be realized. The strain sensor is convenient to install, low in cost and capable of overcoming the limitation of a carrier platform, strain information of a structure in the service process of the antenna can be collected in real time, structural deformation information of the antenna can be represented indirectly, however, how to evaluate electrical property change of the antenna and provide corresponding array element excitation current compensation quantity based on the strain information is still lack of relevant research work at present.
Therefore, in order to compensate the limited service performance of the active phased array antenna, especially an antenna with a limited carrier platform such as an airborne carrier platform and a satellite-borne carrier platform, and further ensure the reliable work of the antenna under the load of a complex environment, it is necessary to analyze the influence relationship between the strain information of the active phased array antenna and the electromagnetic performance of the antenna, establish a strain electromagnetic coupling model of the active phased array antenna, and calculate the array element excitation current adjustment quantity containing strain measurement information based on the strain electromagnetic coupling model.
Disclosure of Invention
Based on the problems, the influence relation between the strain information of the active phased array antenna and the electromagnetic performance of the antenna is researched, a strain electromagnetic coupling model of the active phased array antenna is established, and the electrical property change of the antenna can be directly estimated according to the strain information; on the basis, the amplitude and the phase adjustment quantity of the array element excitation current containing strain measurement information are calculated, theoretical guidance is provided for the electrical property compensation of the active phased array antenna, and the reliable work of the active phased array antenna under the load of a complex service environment is guaranteed.
In order to achieve the above object, the compensation method provided by the present invention comprises the following steps:
(1) determining the structural parameters and material properties of the active phased array antenna;
(2) establishing a finite element model of the active phased array antenna, performing modal analysis, and extracting a displacement mode and a strain mode of the antenna;
(3) determining the main mode order of the antenna according to the effective mass fraction corresponding to the displacement mode of the antenna in the step (2);
(4) combining the order of the main mode in the step (3) and the mode shape distribution of the strain mode in the step (2), and arranging a strain sensor on the antenna array surface;
(5) establishing a strain displacement conversion matrix, and determining the position offset of an array element based on strain acquisition information;
(6) determining a strain electromagnetic coupling factor matrix according to the phase change of the space radiation field of the active phased array antenna caused by the position offset of the array element, and establishing a strain electromagnetic coupling model;
(7) performing first-order Taylor series expansion on the strain electromagnetic coupling model in the step (6) and decomposing the strain electromagnetic coupling model into an ideal electrical property item and an antenna electrical property change item containing strain information;
(8) performing two-dimensional fast Fourier transform on the array element initial excitation current in the ideal electrical property item in the step (7) and the excitation current containing strain information in the electrical property change item;
(9) introducing the Fourier series of the ideal array element initial excitation current and the excitation current containing strain information into the electrical performance of the antenna;
(10) discretizing the direction cosine of the target observation direction, and performing two-dimensional fast Fourier inverse transformation on the Fourier series of the excitation current containing strain information in the antenna electrical performance in the step (9);
(11) and comparing the ideal excitation current to obtain the amplitude and phase compensation quantity of the antenna array element excitation current based on the strain information.
The structural parameters of the active phased array antenna in the step (1) comprise the number M of rows of antenna array elements, the number H of columns of the antenna array elements and the spacing d of the array elementsxAnd dyThe antenna array element, the array antenna, the antenna array surface, the actuator and the structure parameters of the array surface back frame structure; the material properties of the antenna include modulus of elasticity, poisson's ratio, and density.
Establishing an active phased array antenna finite element model in the step (2), determining the constraint position of the antenna, performing modal analysis, extracting the displacement mode and the strain mode of the antenna, and respectively expressing the displacement mode and the strain mode as
Figure BDA0002458802140000041
And
Figure BDA0002458802140000042
wherein N isdAnd S is the number of nodes and the degree of freedom of the finite element model of the antenna respectively.
In the step (3), according to the effective mass fractions corresponding to the displacement modalities extracted in the step (2), under the condition of ensuring the calculation accuracy, the effective mass fractions of the displacement modalities of all orders are arranged according to a descending order, the effective mass fractions of the displacement modalities of all orders are accumulated, and when the accumulation reaches 95%, a modality order which mainly contributes to the displacement response is obtained and is set as an order r.
And (4) combining the main mode order and the strain mode distribution in the step (3), and arranging strain sensors on the antenna array surface, wherein the number of the strain sensors is not less than the intercepted main mode order, and in addition, the position of the sensor is selected at a place with a larger strain number in the strain mode so as to effectively acquire the strain information of the deformed structure.
The step (5) comprises the following specific steps:
(5a) according to the modal superposition method, the displacement response of the antenna structure can be represented by linear combination of modal shapes;
(5b) the strain distribution corresponding to the displacement mode is the strain mode
Figure BDA0002458802140000043
The strain of the antenna structure under the influence of service loads can be expressed as a linear combination of strain modes,
(5c) when the antenna structure is deformed, the information collected by the p strain sensors arranged on the antenna array surface isp×1＝[1 2…p]TFrom strain mode
Figure BDA0002458802140000044
Method for extracting strain mode psi of node at installation position of strain sensorp×r。
Calculating the distance Ψ in Euclidean space using the 2-normp×rqr×1Andp×1modal coordinate q with minimum distance between themr×1Obtaining the optimal generalized modal coordinate;
(5c) when the total number of the antenna array elements is N, the displacement of the deformed antenna array elements can be obtained
(5d) Using the components of the displacement mode in the x, y, z directions, respectively, i.e.
Figure BDA0002458802140000051
And calculating to obtain the position offset of the antenna element node in the x, y and z directions.
The step (6) comprises the following specific steps:
(6a) the antenna array element position deviation can cause the phase distribution of the array antenna space radiation field to change, so that the space phase error caused by the array element position deviation is obtained, and further a strain electromagnetic coupling factor matrix is obtained;
(6b)according to the superposition principle of the directional diagram of the array antenna, under the condition of not considering mutual coupling, the directional diagram function of the array antenna is expressed as the product of the directional diagram of the array element and the array factor, and the directional diagram of the antenna array element is set as feAnd after the antenna structure is deformed, introducing the strain electromagnetic coupling factor matrix into the array factor directional diagram, and establishing a strain electromagnetic coupling model of the array antenna.
The step (7) is carried out according to the following steps when the first-order Taylor series expansion is carried out on the corresponding electromagnetic coupling model:
(7a) for a rectangular grid active phased array antenna commonly applied in engineering, an M × H array element is arranged along the x and y directions according to the distance dx,dyArranging to obtain a strain electromagnetic coupling model;
(7b) and performing first-order Taylor series expansion on the strain electromagnetic coupling model of the rectangular grid active phased array antenna.
The step (8) comprises the following specific steps:
(8a) a plurality of αgqIs an ideal excitation current ImnThe ideal excitation current is represented by Fourier series when the two-dimensional fast Fourier transform series is obtained;
(8b) separately make a plurality of βgq、γgq、ζgqAnd obtaining the excitation current containing the strain information by the two-dimensional fast Fourier transform series of the excitation current term containing the strain information of the antenna array element.
Compared with the prior art, the invention has the following characteristics:
1. the invention clears the quantitative influence relation between the strain information and the electromagnetic performance of the antenna structure, establishes the strain electromagnetic coupling model of the active phased array antenna, can directly evaluate the electrical property change of the active phased array antenna according to the strain measurement information when the antenna structure deforms, and provides theoretical guidance for the structural design of the active phased array antenna.
2. The invention provides an active phased array antenna array element excitation current amplitude and phase compensation quantity calculation model based on strain measurement information, corresponding excitation current amplitude and phase adjustment quantity can be quickly obtained according to the strain measurement information, a theoretical basis is provided for real-time compensation of a serving active phased array antenna, particularly an antenna with limited carrier platforms such as an airborne carrier platform and a satellite carrier platform, and reliable service performance of the active phased array antenna is guaranteed.
Drawings
FIG. 1 is a flow chart of the strain electromagnetic coupling based method for compensating the electrical performance of an active phased array antenna;
FIG. 2 is a diagram of an active phased array antenna structure;
FIG. 3 is an active phased array antenna array finite element model;
FIG. 4 is an active phased array antenna array surface strain information measurement system;
FIG. 5 shows the compensation amount (unit: dB) of the excitation current amplitude of the active phased array antenna element;
FIG. 6 shows phase compensation of excitation current of an active phased array antenna element (unit:);
fig. 7 is an electrical performance of an ideal, deformed, compensated active phased array antenna when phi is 0 deg.;
fig. 8 shows the electrical performance of an ideal, deformed, compensated active phased array antenna when phi is 90 deg..
Detailed Description
The invention will be further explained with reference to the drawings and the embodiments
Referring to fig. 1, the invention relates to an electrical property compensation method of an active phased array antenna based on strain electromagnetic coupling, which comprises the following specific steps:
step 1, determining the structural parameters and material properties of the active phased array antenna.
As shown in fig. 2, the structural parameters of the active phased array antenna include the number of rows M, the number of columns H, and the spacing d of the antenna elementsxAnd dyThe antenna array element 1, the array antenna 2, the antenna array surface 3, the actuator 4 and the array surface back frame structure 5; the material properties of the antenna include modulus of elasticity, poisson's ratio, and density.
And 2, establishing a finite element model of the active phased array antenna, performing modal analysis, and extracting a displacement mode and a strain mode of the antenna.
Establishing a finite element model of an active phased array antenna array structure, as shown in fig. 3, considering that an antenna array element and the antenna array structure are in full-constraint connection, and the deformation of the array structure can reflect the position deviation of the antenna array element, so that the finite element model of the antenna array is established on the premise of ensuring the calculation precision, the constraint position of the antenna array structure is determined, modal analysis is carried out, and the displacement mode and the strain mode of the antenna structure are extracted.
And 3, determining the main mode order of the antenna according to the effective mass fraction corresponding to the displacement mode of the antenna structure.
Extracting effective mass fractions corresponding to the displacement modes of the antenna structure in ANSYS, arranging the effective mass fractions of the displacement modes of all orders according to a descending order under the condition of ensuring the calculation accuracy, accumulating the effective mass fractions of the displacement modes of all orders, obtaining a mode order which mainly contributes to displacement response when the accumulation reaches 95%, and setting the mode order as an order r.
And 4, arranging a strain sensor on the antenna array surface according to the main mode order and the strain mode distribution of the antenna structure.
According to the main mode order and the strain mode distribution of the antenna structure, strain sensors are arranged on an antenna array surface, wherein the number of the strain sensors is not less than the intercepted main mode order, and a constructed strain measurement system is shown in fig. 4, wherein 1 is an active phased array antenna structure, 2 is a single fiber bragg grating strain sensor on the antenna array surface, 3 is the layout of the strain sensors on the antenna array surface, 4 is a fiber bragg grating demodulator, and 5 is an upper computer for displaying a strain measurement result.
And 5, establishing a strain displacement conversion matrix, and determining the position offset of the array element based on strain acquisition information.
5.1 according to the modal superposition method, the displacement response of the antenna structure can be expressed by the linear combination of modal modes
Figure BDA0002458802140000081
In the formula (I), the compound is shown in the specification,
Figure BDA0002458802140000082
in the displacement mode, qS×1＝[q1,q2,…,qS]TIs a generalized modal coordinate.
5.2 the strain distribution corresponding to the displacement mode is the strain mode, i.e.
Figure BDA0002458802140000083
The strain of the antenna structure under the influence of service load can be expressed as a linear combination of strain modes
Figure BDA0002458802140000084
Namely, it is
Figure BDA0002458802140000085
Wherein q isr×1Generalized modal coordinates of the intercepted r-order mode;
5.3 the antenna structure is deformed, and the information collected by the p strain sensors arranged on the antenna array surface isp×1＝[1 2…p]TFrom strain mode
Figure BDA0002458802140000086
Extracting the strain mode of the node at the installation position of the strain sensor, and expressing the mode as psip×r. In order to avoid the generation of singularity in the generalized modal coordinate matrix in the formula (2), the strain measurement information should be not less than the number of the intercepted main modes, namely p is not less than r.
Calculating the distance Ψ in Euclidean space using the 2-normp×rqr×1Andp×1modal coordinate q with minimum distance between themr×1I.e. by
min||Ψp×rqr×1-p×1||2(3)
Mode coordinate q for minimizing distance in formula (3)r×1The square of the distance can also be minimized, i.e.
Figure BDA0002458802140000091
In order to satisfy the minimum distance square of the formula (4), the formula (4) is added to qr×1Conducting derivation to obtain
Figure BDA0002458802140000092
The optimal generalized modal coordinate obtained according to equation (5) is
Figure BDA0002458802140000093
5.4 when the total number of antenna array elements is N, the displacement of the deformed antenna array element obtained by bringing the formula (6) into the formula (1) is N
Figure BDA0002458802140000094
In the formula (I), the compound is shown in the specification,
Figure BDA0002458802140000095
is a strain displacement transformation matrix.
The above formula (7) can also be written as
N×1＝ΦN×r r×p p×1(8)
In the formula (I), the compound is shown in the specification,
Figure BDA0002458802140000096
strain mode factor, Φ, representing a strain sensor position nodeN×rFor the displacement mode of the antenna element node, the components of the displacement mode in the x, y and z directions are respectively used, namely
Figure BDA0002458802140000097
Calculating to obtain the position offset of the antenna element node in the x, y and z directions, namely
[x,y,z]T＝[Φx,Φy,Φz]T(9)
In the formula (I)r×pThe strain mode factor of the position node of the strain sensor is expressed asAnd changing information collected by the sensor.
And 6, determining a strain electromagnetic coupling factor matrix according to the phase change of the space radiation field of the active phased array antenna caused by the position offset of the array element, and establishing a strain electromagnetic coupling model.
6.1 the position deviation of the antenna element can cause the phase distribution of the space radiation field of the array antenna to change, and the space phase error caused by the position deviation of the antenna element is
Figure BDA0002458802140000098
Wherein k is 2 pi/lambda is a wave constant, and lambda is an electromagnetic wave wavelength;
Figure BDA0002458802140000101
n is 1-N and represents displacement matrixes of all array elements in the x, y and z directions;
Figure BDA0002458802140000102
wherein
Figure BDA0002458802140000103
Representing the displacement matrix of the 1 st array element in the x, y and z directions; u ═ sin θ cos φ, sin θ sin φ, cos θ]TThe cosine of the direction (theta, phi) of the target relative to the coordinate system is observed for the far zone.
By bringing formula (9) into formula (10), a strain electromagnetic coupling factor matrix can be obtained as shown below
Figure BDA0002458802140000104
In the formula (I), the compound is shown in the specification,
Figure BDA0002458802140000105
respectively are component matrixes of all array elements in the x direction, the y direction and the z direction relative to the displacement mode; wherein
Figure BDA0002458802140000106
Φ1＝[Φ1,1,Φ1,2,…,Φ1,r]1×rIs a displacement mode matrix of the 1 st array element,
Figure BDA0002458802140000107
are respectively a matrix phiAComponent matrices in x, y, z directions.
6.2 according to the superposition principle of the directional diagrams of the array antennas, under the condition of not considering mutual coupling, the directional diagram function of the array antennas is expressed as the product of the directional diagrams of the array elements and the array factors, and the directional diagram of the antenna array elements is set as feAfter the antenna structure is deformed, the strain electromagnetic coupling factor matrix is introduced into the array factor directional diagram, and a strain electromagnetic coupling model of the array antenna is established as
E()＝feΙ1×N[expjk([RU]n+[C]n)]N×1(12)
In the formula, N is 1-N and is the number of array elements; i ═ Anexp(jζn)]1×NRepresenting the excitation current vector of an array element in an array antenna, AnAnd ζnRespectively the amplitude and the phase of the exciting current of the nth array element,
Figure BDA0002458802140000108
an ideal displacement matrix representing N array elements,
Figure BDA0002458802140000109
the initial displacement of the strain sensor in the x direction and the y direction is the information collected by the strain sensor, and j is an imaginary unit.
And 7, performing first-order Taylor series expansion on the corresponding electromagnetic coupling model, and decomposing the first-order Taylor series expansion into an ideal electrical property item and an antenna electrical property change item containing strain information.
7.1 for the rectangular grid active phased array antenna commonly used in engineering, the number of rows M and the number of columns H of the antenna are set, M × H array elements are arranged along the x direction and the y direction according to the distance dx,dyAlignment, the strain electromagnetic coupling model of equation (12) is written as follows
Figure BDA0002458802140000111
In the formula (I), the compound is shown in the specification,
Figure BDA0002458802140000112
for ideal excitation current of antenna elements, the real part AmnAnd imaginary part
Figure BDA0002458802140000113
Amplitude and phase of the excitation current respectively; m and n are the number of the array elements,x_mn、y_mn、z_mnrespectively displacement of the (m, n) th array element in the x, y and z directions,x_1,1、y_1,1、z_1,1the displacement of the (1,1) th array element in the x, y and z directions respectively, u is sin theta cos phi, and v is sin theta sin phi which is the direction cosine of the target relative to the x and y axes respectively;
7.2 the strain electromagnetic coupling model of the rectangular grid active phased array antenna of the formula (13) is expanded by the first-order Taylor series
Figure BDA0002458802140000114
In the formula, E0(u, v) is a physical electrical property term, Es(u, v,) is the electrical property change term that contains strain information.
And 8, respectively carrying out two-dimensional fast Fourier transform on the array element initial excitation current in the ideal electrical property item and the excitation current containing strain information in the electrical property change item.
8.1 order complex αgqIs an ideal excitation current ImnThe ideal excitation current can be represented as a Fourier series by a two-dimensional fast Fourier transform series of
Figure BDA0002458802140000115
In the formula, g and q are coefficients corresponding to all dimensions in two-dimensional fast Fourier transform respectively;
8.2 respectively making a plurality of βgq、γgq、ζgqExcitation current item k I containing strain information for antenna array elementmn(x_mn()-x_1,1())、kΙmn(y_mn()-y_1,1() And k Imn(z_mn()-z_1,1() In a two-dimensional fast fourier transform series), the excitation current containing strain information can be represented as
Figure BDA0002458802140000121
Figure BDA0002458802140000122
Figure BDA0002458802140000123
Wherein k is 2 pi/lambda is a wave constant, and lambda is an electromagnetic wave wavelength;
and 9, introducing an ideal excitation current Fourier series containing strain information into the electrical property of the antenna.
The electrical properties of the modified antenna can be obtained by bringing the formulas (15) to (18) into the formula (14)
Figure BDA0002458802140000124
And 10, dispersing the direction cosine of the target observation direction, and performing two-dimensional fast Fourier inverse transformation on the Fourier series of the array element excitation current in the electrical property of the antenna.
10.1 array element exciting current term in formula (19)
Figure BDA0002458802140000125
The directional cosines u and v continuity functions are respectively dispersed into a series of directional cosines u of orthogonal observation directionsg＝-(g-1)λ/MdxAnd vq＝-(q-1)λ/HdyAnd then:
Figure BDA0002458802140000126
in the formula ugIs in a direction of orthogonal observationCorresponding cosine of direction in x-direction, vqThe direction cosine along the y direction corresponding to the orthogonal viewing direction;
10.2 the two-dimensional fast Fourier transform of the array element exciting current item in the formula (20) can be obtained
Figure BDA0002458802140000131
In the formula
Figure BDA0002458802140000132
After the antenna structure is deformed, the array element exciting current is adjusted for compensating the electrical property of the antenna, i.e.
Figure BDA0002458802140000133
And 11, calculating the amplitude and the phase compensation quantity of the excitation current of the antenna array element based on the strain information.
Comparing the ideal excitation current to obtain the amplitude and phase compensation of the antenna array element excitation current based on the strain information, as shown below
Figure BDA0002458802140000134
In the formula,. DELTA.Amn() And
Figure BDA0002458802140000135
the amplitude and phase adjustment of the antenna element exciting current based on the strain measurement information are shown in fig. 5 and fig. 6, respectively.
The ideal antenna electrical performance, the antenna electrical performance after deformation, and the antenna electrical performance after adjusting the excitation current amplitude and phase using equation (23) are compared, and the compensation effect of the electrical performance is determined, where antenna patterns with phi 0 ° and phi 90 ° are compared, respectively, and the results are shown in fig. 7 and 8.
The advantages of the present invention can be further illustrated by the following experimental tests:
1. determining the structural parameters and material properties of the active phased array antenna, establishing a finite element model of the antenna, performing modal analysis to extract the displacement mode and strain mode of the antenna, and determining the main mode order of the antenna
As shown in fig. 2, the X-band active phased array antenna experimental platform mainly includes an antenna array element 1, an array element array 2, a front panel 3, an actuator 4, and a front back frame 5, the arrangement form of the antenna array element is 24 × 32, and the array element pitch is 0.65 λ. The antenna array elements are arranged in a rectangular grid and are arranged on the array surface panel, the array surface panel is connected with the array surface back frame through 9 actuators, the 9 actuators are independently controlled and are used for simulating different types of array deformation in a service environment, and the maximum stroke of the array deformation is 32 mm. The T/R assembly is arranged in the back frame and is connected with the horn antenna through a cable. Array element initial excitation current adopts a Taylor weighted amplitude distribution and equal phase distribution mode. Table 1 lists the structural dimensions and major material properties of the antenna experimental platform.
TABLE 1 active phased array antenna Experimental model Material Properties
Figure BDA0002458802140000141
A finite element model of the active phased array antenna array structure was created using ANSYS, as shown in fig. 3, where the cell type was shell 63. And determining the constraint position of the antenna structure, performing modal analysis, and extracting the displacement mode and the strain mode of the antenna. And under the condition of ensuring the calculation accuracy, arranging the effective mass fractions of the displacement modes of all orders according to a descending order, accumulating the effective mass fractions of the displacement modes of all orders, and obtaining a mode order which mainly contributes to the displacement response and is 17 orders when the accumulation reaches 95%.
2. Arranging a strain sensor on an antenna array surface, collecting strain information of a deformed antenna, and calculating the electrical property of the antenna based on a strain electromagnetic coupling model
The fiber bragg grating sensor strain measurement system is built on the array surface panel to collect strain information of a deformed array surface in real time, as shown in fig. 4, wherein 1 is an active phased array antenna structure, 2 is a single fiber bragg grating strain sensor on the antenna array surface, 3 is the layout of the strain sensors on the antenna array surface, 4 is a fiber bragg grating demodulator, and 5 is an upper computer for displaying a strain measurement result. The sensor is a fiber grating sensor with the model of Acrylate SMF-28, and the precision of the optical wavelength can reach +/-0.25 nm. The number of the strain sensors is larger than the main mode order of the antenna array surface, meanwhile, the completeness of acquisition of array surface strain information can be improved by combining the strain mode shape distribution and considering the increase of the number of the antenna array surface sensors, the antenna array elements on the array surface are arranged in a rectangular grid mode, and the sensor can be arranged in a position near the rectangular grid, so that 9 rows and 13 columns of fiber bragg grating sensors are arranged on the antenna array surface in the rectangular grid mode, and the initial strain acquisition information of the fiber bragg grating sensors is calibrated.
The complex environment load can cause the structural deformation of the array surface, the simulation of the deformation of the array surface is carried out by adjusting 9 actuators behind the array surface, and the actuator structures are adjusted according to typical deformation conditions, wherein the adjustment amounts are 8mm, 3mm, 0mm, 3mm, 21mm, 22mm and 22mm respectively. Under this structural deformation, the values of wavefront strain acquired with the strain sensor are shown in table 2.
Table 2 deformation antenna wavefront strain measurements (× 10)-6)
Figure BDA0002458802140000151
Without considering mutual coupling, the electrical properties of the antenna after structural deformation can be calculated from the strain values measured on the antenna front in table 2, according to the strain electromagnetic coupling model of equation (12).
3. Calculating the amplitude and phase compensation of the antenna array element exciting current based on the strain information, and analyzing the compensation effect of the antenna electrical property
The amplitude and phase adjustment of the antenna element exciting current based on the strain measurement information are calculated according to equation (23), as shown in fig. 5 and fig. 6, respectively. Comparing the ideal antenna electrical performance, the antenna electrical performance after deformation, and the antenna electrical performance after adjusting the amplitude and phase of the excitation current, including the antenna patterns with phi 0 deg. and phi 90 deg., the results are shown in fig. 7 and 8, and specific pairs of antenna electrical performance parameters are shown in table 3.
TABLE 3 comparison of electrical parameters before and after compensation of antenna electrical properties
Figure BDA0002458802140000161
4. Analysis results
The antenna gain, the pointing accuracy, the side lobe level and the 3dB beam width can be simultaneously compensated by adopting an antenna excitation current amplitude-phase compensation method based on strain information. Wherein, the gain loss of the antenna is reduced from 3.72dB to 0.51 dB; the pointing accuracy of the plane phi of the antenna is 0 degrees, namely the pointing accuracy of the plane phi is 0.06 degrees, the pointing accuracy of the plane phi is 90 degrees, namely the pointing accuracy of the plane phi is 1.6 degrees, namely the pointing accuracy of the plane phi is 0.09 degrees, and complete compensation of beam pointing can be basically achieved; the 3dB wave beam width of the phi-0 degree surface and the phi-90 degree surface can be basically reached to the initial value through compensation; the same has a significant compensation effect for the first secondary lobe level, wherein the first secondary lobe levels of the 0 ° and 90 ° planes of the anamorphic antenna decrease from-27.23 dB to-33.89 dB and from-34.12 to-34.87 dB, respectively. Therefore, the strain electromagnetic coupling-based active phased array antenna electrical property compensation method has a good compensation effect on the electrical property of the whole observation area of the antenna, provides theoretical guidance for the active phased array antenna, particularly the guarantee of the service performance of the antenna with limited carrier platform, and has important academic significance and engineering application value.

Claims (10)

1. An electrical property compensation method for an active phased array antenna based on strain electromagnetic coupling is characterized by comprising the following steps:
(1) determining the structural parameters and material properties of the active phased array antenna;
(2) establishing a finite element model of the active phased array antenna, performing modal analysis, and extracting a displacement mode and a strain mode of the antenna;
(3) determining the main mode order of the antenna according to the effective mass fraction corresponding to the displacement mode of the antenna in the step (2);
(4) combining the order of the main mode in the step (3) and the mode shape distribution of the strain mode in the step (2), and arranging a strain sensor on the antenna array surface;
(5) establishing a strain displacement conversion matrix, and determining the position offset of an array element based on strain acquisition information;
(6) determining a strain electromagnetic coupling factor matrix according to the phase change of the space radiation field of the active phased array antenna caused by the position offset of the array element, and establishing a strain electromagnetic coupling model;
(7) performing first-order Taylor series expansion on the strain electromagnetic coupling model in the step (6) and decomposing the strain electromagnetic coupling model into an ideal electrical property item and an antenna electrical property change item containing strain information;
(8) performing two-dimensional fast Fourier transform on the array element initial excitation current in the ideal electrical property item in the step (7) and the excitation current containing strain information in the electrical property change item;
(9) introducing the Fourier series of the ideal array element initial excitation current and the excitation current containing strain information into the electrical performance of the antenna;
(10) discretizing the direction cosine of the target observation direction, and performing two-dimensional fast Fourier inverse transformation on the Fourier series of the excitation current containing strain information in the antenna electrical performance in the step (9);
(11) and comparing the ideal excitation current to obtain the amplitude and phase compensation quantity of the antenna array element excitation current based on the strain information.
2. The method for compensating the electrical performance of the active phased array antenna based on the strain electromagnetic coupling as claimed in claim 1, wherein in the step (1), the structural parameters of the active phased array antenna comprise the number M of rows of antenna elements, the number H of columns of antenna elements and the distance d between the antenna elementsxAnd dyThe antenna array element, the array antenna, the antenna array surface, the actuator and the structure parameters of the array surface back frame structure; the material properties of the active phased array antenna include modulus of elasticity, poisson's ratio, and density.
3. The strain electromagnetic coupling-based electrical property compensation method for the active phased array antenna according to claim 1, wherein in the step (3), according to the effective mass fractions corresponding to the displacement modes extracted in the step (2), under the condition of ensuring the calculation accuracy, the effective mass fractions of the displacement modes of the respective orders are arranged in a descending order, the effective mass fractions of the displacement modes of the respective orders are accumulated, and when the accumulation reaches 95%, a mode order having a main contribution to the displacement response is obtained.
4. The strain electromagnetic coupling-based electrical property compensation method for the active phased array antenna, according to claim 1, wherein in the step (4), the number of strain sensors arranged on the antenna array surface is not less than the truncated main mode order; the arrangement position of the sensor should be selected where the strain value is large in the strain mode shape.
5. The strain electromagnetic coupling-based electrical property compensation method for the active phased array antenna, according to claim 1, wherein the step (5) comprises the following steps:
(5a) according to the modal superposition method, the displacement response of the antenna structure is expressed by the linear combination of modal modes:
Figure FDA0002458802130000021
in the formula (I), the compound is shown in the specification,
Figure FDA0002458802130000022
in the displacement mode, qS×1＝[q1,q2,…,qS]TGeneralized modal coordinates;
(5b) the strain distribution corresponding to the displacement mode is the strain mode
Figure FDA0002458802130000023
Strain of antenna structure under influence of service load is expressed as linear combination of strain modes
Figure FDA0002458802130000024
Figure FDA0002458802130000025
Wherein q isr×1Generalized modal coordinates of the intercepted r-order mode;
(5c) when the antenna structure is deformed, the information collected by the p strain sensors arranged on the antenna array surface isp×1＝[1 2…p]TFrom strain mode
Figure FDA0002458802130000031
Method for extracting strain mode psi of node at installation position of strain sensorp×r(ii) a Wherein p is more than or equal to r;
calculating the distance Ψ in Euclidean space using the 2-normp×rqr×1Andp×1modal coordinate q with minimum distance between themr×1Obtaining the optimal generalized modal coordinate as
Figure FDA0002458802130000032
(5d) When the total number of the antenna array elements is N, the displacement of the deformed antenna array elements obtained by bringing the formula (6) into the formula (1) is N
Figure FDA0002458802130000033
In the formula (I), the compound is shown in the specification,
Figure FDA0002458802130000034
to the strain-displacement transformation matrix, transform it into:
N×1＝ΦN×r r×p p×1(8)
in the formula (I), the compound is shown in the specification,
Figure FDA0002458802130000035
strain mode factor, Φ, representing a strain sensor position nodeN×rAs bits of antenna element nodesMoving the mode;
(5e) using respective displacement modes phiN×rThe components in the x, y, z directions being
Figure FDA0002458802130000036
Calculating to obtain the position offset of the antenna element node in the x, y and z directionsx,y,z]T：
[x,y,z]T＝[Φx,Φy,Φz]T(9)
In the formula (I)r×pAnd the strain mode factors of the position nodes of the strain sensors are represented, and are information collected by the strain sensors.
6. The strain electromagnetic coupling-based electrical property compensation method for the active phased array antenna according to claim 1, wherein the step (6) comprises the following steps:
(6a) according to the change of the phase distribution of the array antenna space radiation field caused by the position offset of the antenna array element, the space phase error caused by the position offset of the array element is as follows:
Figure FDA0002458802130000041
wherein k is 2 pi/lambda is a wave constant, and lambda is an electromagnetic wave wavelength;
Figure FDA0002458802130000042
representing x, y and z direction displacement matrixes of all array elements;
Figure FDA0002458802130000043
wherein
Figure FDA0002458802130000044
Representing the displacement matrix of the 1 st array element in the x, y and z directions; u ═ sin θ cos φ, sin θ sin φ, cos θ]TThe cosine of the direction (theta, phi) of the observation target in the far zone relative to the coordinate system;
by bringing formula (9) into formula (10), a strain electromagnetic coupling factor matrix can be obtained as shown below
Figure FDA0002458802130000045
In the formula (I), the compound is shown in the specification,
Figure FDA0002458802130000046
respectively are component matrixes of all array elements in the x direction, the y direction and the z direction relative to the displacement mode; wherein
Figure FDA0002458802130000047
Φ1＝[Φ1,1,Φ1,2,…,Φ1,r]1×rIs a displacement mode matrix of the 1 st array element,
Figure FDA0002458802130000048
are respectively a matrix phiAA matrix of components in the x, y, z directions;
(6b) the directional diagram function of the array antenna is expressed as the product of the directional diagram of the array element and the array factor, and the directional diagram of the antenna array element is set as feAfter the antenna structure is deformed, a strain electromagnetic coupling factor matrix is introduced into an array factor directional diagram, and a strain electromagnetic coupling model E () of the array antenna is established as
E()＝feΙ1×N[expjk([RU]n+[C]n)]N×1(12)
In the formula, N is 1-N and is the number of array elements; i ═ Anexp(jζn)]1×NRepresenting the excitation current vector of an array element in an array antenna, AnAnd ζnRespectively the amplitude and the phase of the exciting current of the nth array element,
Figure FDA0002458802130000049
an ideal displacement matrix representing N array elements,
Figure FDA00024588021300000410
the initial displacement of the strain sensor in the x direction and the y direction is the information collected by the strain sensor, and j is an imaginary unit.
7. The strain electromagnetic coupling-based electrical property compensation method for the active phased array antenna according to claim 1, wherein the step (7) is performed by performing a first-order Taylor series expansion on the strain electromagnetic coupling model according to the following steps:
(7a) setting the number of rows M and columns H of the rectangular grid active phased array antenna, M × H array elements are arranged at a distance d along the x and y directionsx,dyAlignment, the strain electromagnetic coupling model of equation (12) is written as follows
Figure FDA0002458802130000051
In the formula (I), the compound is shown in the specification,
Figure FDA0002458802130000052
for ideal excitation current of antenna elements, the real part AmnAnd imaginary part
Figure FDA0002458802130000053
Amplitude and phase of the excitation current respectively; m and n are the number of the array elements,x_mn、y_mn、z_mnrespectively displacement of the (m, n) th array element in the x, y and z directions,x_1,1、y_1,1、z_1,1the displacement of the (1,1) th array element in the x, y and z directions respectively, u is sin theta cos phi, and v is sin theta sin phi which is the direction cosine of the target relative to the x and y axes respectively;
(7b) the strain electromagnetic coupling model of the rectangular grid active phased array antenna of the formula (13) is expanded by a first-order Taylor series
Figure FDA0002458802130000054
In the formula, E0(u, v) is a physical electrical property term, Es(u, v,) is the electrical property variation term containing strain informationAnd j is an imaginary unit.
8. The strain electromagnetic coupling-based electrical property compensation method for the active phased array antenna according to claim 7, wherein the step (8) comprises the following steps:
(8a) a plurality of αgqIs an ideal excitation current ImnThe ideal excitation current can be represented as a Fourier series by a two-dimensional fast Fourier transform series of
Figure FDA0002458802130000055
In the formula, g and q are coefficients corresponding to all dimensions in two-dimensional fast Fourier transform respectively;
(8b) separately make a plurality of βgq、γgq、ζgqExcitation current item k I containing strain information for antenna array elementmn(x_mn()-x_1,1())、kΙmn(y_mn()-y_1,1() And k Imn(z_mn()-z_1,1() In a two-dimensional fast fourier transform series), the excitation current containing strain information can be represented as
Figure FDA0002458802130000061
Figure FDA0002458802130000062
Figure FDA0002458802130000063
Wherein k is 2 pi/lambda is a wave constant, and lambda is an electromagnetic wave wavelength;
in the step (9), the Fourier series of the excitation current which is ideal and contains strain information is introduced into the electrical property of the antenna, namely the equations (15) - (18) are brought into the equation (14), and the ideal excitation current can be obtained
Figure FDA0002458802130000064
9. The strain electromagnetic coupling based active phased array antenna electrical performance compensation method according to claim 8, wherein the step (10) is as follows:
(10a) exciting array element with current term
Figure FDA0002458802130000065
The directional cosines u and v continuity functions are respectively dispersed into a series of directional cosines u of orthogonal observation directionsg＝-(g-1)λ/MdxAnd vq＝-(q-1)λ/HdyAnd then:
Figure FDA0002458802130000066
in the formula ugCosine of direction in x direction corresponding to orthogonal viewing direction, vqThe direction cosine along the y direction corresponding to the orthogonal viewing direction;
(10b) the two-dimensional fast Fourier inverse transformation is carried out on the array element exciting current item in the formula (20) to obtain
Figure FDA0002458802130000071
In the formula
Figure FDA0002458802130000072
After the antenna structure is deformed, the array element exciting current is adjusted for compensating the electrical property of the antenna, i.e.
Figure FDA0002458802130000073
10. The strain electromagnetic coupling based electrical property compensation method for the active phased array antenna according to claim 7, wherein in the step (11), the ideal excitation currents are compared to obtain the amplitude and phase compensation amount of the excitation currents of the antenna elements based on strain information, as shown in the following
Figure FDA0002458802130000074
In the formula,. DELTA.Amn() And
Figure FDA0002458802130000075
respectively is the amplitude and the phase adjustment quantity of the antenna array element excitation current based on the strain measurement information.
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