CN105161860B - Deformation planar array electrical performance compensation method based on mechanical-electric coupling and Fourier transformation - Google Patents

Abstract

The invention discloses a method for compensating electrical properties of deformed area array antennas based on electromechanical coupling and Fourier transform, including: 1) determining the parameters of the area array antennas, that is, M linear array antennas; 2) obtaining the vibration environment below by finite element analysis 3) Using the linear array antenna electromechanical coupling model to calculate the electrical performance of the i-th linear array antenna after deformation; 4) Decomposing the electrical performance into ideal linear array electrical performance and linear array electrical performance change items; 5) Perform fast Fourier transform on 4) respectively to obtain the adjustment amount of the excitation current amplitude and phase for compensating the antenna spatial phase error; 6) judge whether the adjustment amount of all excitation current amplitudes and phases has been calculated; 7) convert the excitation current Adjust the amplitude and phase into the electromechanical coupling model to calculate the electrical performance of the deformed area array antenna; 8) judge whether the electrical performance of the deformed area array antenna after compensation meets the index requirements. The invention can ensure good electrical performance for the area array antenna in service.

Description

Electrical Performance Compensation Method of Deformed Area Array Antenna Based on Electromechanical Coupling and Fourier Transform

technical field

The invention belongs to the technical field of antennas, and in particular relates to a method for compensating the electric properties of deformed area array antennas based on electromechanical coupling and Fourier transform.

Background technique

Antennas are widely used in radio systems such as communications, broadcasting, television, radar, and navigation. They can radiate and receive radio waves and are an indispensable device in radio communications. Compared with a single antenna, the area array antenna has high radiation intensity, high reliability, multiple functions, strong detection and tracking capabilities, and good stealth performance, so it is widely used in various radar systems, navigation systems, and electronic countermeasures.

The antenna is the core component of the radar system, and the performance of the radar system largely depends on the electrical performance of the antenna. The antenna structure is the carrier for the realization of the electrical performance of the antenna, and the change of the displacement field of the antenna directly affects the amplitude and phase distribution of the electromagnetic field of the antenna in space. When the antenna is in service, the working environment loads such as self-weight, rain and snow, sunlight, vibration, impact, etc. will change the structural performance of the antenna, causing structural errors in the antenna, and random errors in the structure of the antenna during processing and assembly. All of these will cause position error of the antenna radiating unit, which will eventually lead to a decrease in antenna gain, elevation of side lobes, and pointing deviation. The reduction of the electrical performance of the antenna will directly lead to the reduction of the performance of the radar system, or even cannot be realized. Therefore, in order to reduce the impact of structural errors on the electrical performance of the area array antenna and ensure the normal operation of the radar system, the electrical performance of the antenna must be compensated.

The active compensation method is the main way to compensate the electrical performance of the antenna. The active compensation of the electrical performance of the antenna is to compensate the change of the electrical performance of the antenna by adjusting the excitation current of the antenna radiating unit. Therefore, in the active compensation method, the deformation The compensation amount of the antenna excitation current improves the electrical performance of the deformable antenna, which is the key to the effectiveness of the compensation method. Scholars at home and abroad have done a lot of work on using active compensation methods to compensate the electrical properties of deformed antennas, such as in Svensson B, Lanne M, Wingard J, et al.Element position error compensation inactive phased array antennas[C]//2010 In the Proceedings of the Fourth European Conference on Antennas and Propagation.2010, the unit position error of the antenna was compensated by adjusting the excitation current of the antenna. However, the position error of the unit is assumed to obey the Gaussian distribution, not the structural error of the antenna under actual working conditions. Therefore, the excitation current compensation obtained by this method does not compensate the electrical performance change caused by the actual structural error of the antenna. In addition, in Tsao J.Adaptive phase compensation for distorted phased array by minimum sidelobe response criteria[C]//Antennas and Propagation Society International Symposium.Merging Technologies for the 90's.Digest.IEEE,1990:1466-1469, the deformation phase control The compensation of the electrical performance of the array antenna can only be achieved by adjusting the phase of the excitation current of the antenna unit. However, adjusting the phase of the excitation current can only compensate the beam pointing of the antenna, and the sidelobe level of the antenna will not be effectively compensated, while the excitation The magnitude of the current is directly related to the antenna gain and the sidelobe level. Therefore, the phase and magnitude of the excitation current should be adjusted at the same time to make the electrical performance of the antenna meet the requirements.

Therefore, in order to ensure the normal operation of the array antenna in the service environment, how to compensate the electrical performance of the deformed area array antenna under actual working conditions by adjusting the amplitude and phase of the excitation current has become an urgent technical problem in this field.

Contents of the invention

Based on the above problems, in order to compensate for the decline of the electrical performance of the area array antenna in the actual working environment, the present invention uses the electromechanical coupling model of the array antenna to obtain the variation of the electrical performance of the antenna under the load of the working environment, and combines the FFT method for all the area array antennas The excitation current amplitude and phase of the radiating unit are adjusted to compensate the electrical performance of the deformed array antenna, ensuring that the array antenna can work normally under the service environment. This method can effectively solve the problem of the deterioration of the electrical performance of the area array antenna caused by the working load, and ensure the normal operation of the area array antenna in the service environment. Electrical properties provide theoretical guidance.

The technical solution for realizing the present invention is to determine the structural parameters and electromagnetic parameters of the area array antennas of M rows and N columns, that is, M line array antennas; according to the area array antenna structure parameters, set up the area array antenna structure finite element model, analyze and obtain the area The amount of structural deformation of the array antenna; extract the i-th (1≤i≤M) line array antenna, use the electromechanical coupling model of the line array antenna, and calculate the electrical performance of the i-th line array antenna after deformation in the loading environment; the i-th deformation The electrical performance of the linear array antenna is decomposed into the electrical performance of the ideal linear array and the change item of the electrical performance of the linear array caused by structural deformation, and the Fast Fourier Transform (FFT) is performed on the electrical performance of the ideal linear array and the change item of the electrical performance of the linear array respectively. ), to get the adjustment of excitation current amplitude and phase to compensate antenna space phase error; to judge whether the adjustment of excitation current amplitude and phase has been calculated for all linear array antennas, and if it is satisfied, the excitation current amplitude and phase array antenna unit are obtained Phase adjustment, otherwise extract the next linear array antenna for calculation; bring the obtained excitation current amplitude and phase adjustment of the area array antenna unit into the electromechanical coupling model of the area array antenna to calculate the electrical performance of the deformed area array antenna; judge Whether the electrical performance of the deformed area array antenna after compensation meets the index requirements, if so, it indicates that the excitation current amplitude and phase adjustment with the best electrical performance of the compensated deformed area array antenna are obtained, so that the area array antenna can reach the optimum in the service environment work performance; otherwise, modify the structural parameters of the area array antenna and repeat the above steps until the requirements are met.

The present invention is achieved through the following technical solutions:

The electrical performance compensation method of deformed area array antenna based on electromechanical coupling and Fourier transform includes the following process:

(1) According to the structural parameters of the area array antennas in M rows and N columns, that is, M line array antennas, determine the geometric model parameters and material properties of the area array antenna, and determine the operating parameters of the area array antenna;

(2) Establish the structure finite element model of the area array antenna according to the geometric model parameters and material properties of the area array antenna; determine the constraints of the antenna finite element model according to the installation form of the area array antenna; apply the airborne random vibration power to the area array antenna finite element model spectrum, calculate the structural deformation of the area array antenna, and extract the position offset of the central node of the area array antenna radiating element in the x, y, and z directions;

(3) Extract the position offset of the i-th (1≤i≤M) line-array antenna and the central node of its radiating element among the M line-array antennas, and use the electromechanical coupling model of the line-array antenna to calculate the i-th line array antenna in the upload environment The electrical performance of the linear array antenna after deformation;

(4) Decompose the electrical performance of the ith deformed linear array antenna into the electrical performance of the ideal linear array and the change item of the electrical performance of the linear array caused by structural deformation, where the electrical performance change item of the linear array consists of the excitation current and Composition of antenna spatial phase error caused by structural deformation;

(5) Fast Fourier Transform (FFT) is performed on the ideal linear array electrical performance and the linear array electrical performance change item respectively to obtain the adjustment amount of the excitation current amplitude and phase for compensating the spatial phase error of the antenna;

(6) Judging whether the adjustments of excitation current amplitude and phase have been calculated for all M linear array antennas, if yes, the adjustments of excitation current amplitude and phase of M linear array antennas are obtained, otherwise extract the next line array Antenna, and repeat step (3) to step (6);

(7) Bring the obtained M linear array antennas, i.e. the adjustments of the excitation current amplitude and phase of all the area array antennas, into the electromechanical coupling model of the area array antenna, and calculate the electrical performance of the deformed area array antenna;

(8) Determine whether the electrical performance of the deformed area array antenna after compensation meets the index requirements. If it meets the requirements, it indicates that the excitation current amplitude and phase adjustment with the best electrical performance of the compensated deformed area array antenna have been obtained, so that the area array antenna can be used in the service environment. The optimal performance is achieved; otherwise, modify the structural parameters of the area array antenna, and repeat steps (1) to (7) until the requirements are met.

In the step (1), the geometric model parameters of the area array antenna include the position distribution, number, size, and unit spacing of the area array antenna radiation elements, the size parameters of the T/R assembly, cold plate and stiffener; The material properties of the area array antenna include density ρ, elastic modulus E and Poisson's ratio μ; the electromagnetic working parameters of the area array antenna include the central operating frequency f of the area array antenna, the amplitude and phase of the excitation current.

In the step (2), the structural deformation of the area array antenna is calculated, according to the structural parameters and material properties of the area array antenna, the structure finite element model of the area array antenna is established, and the finite element model of the area array antenna is determined according to the actual installation of the area array antenna Constraint conditions, load the airborne random vibration power spectrum, and calculate the position offset of the center node of the radiation element of the area array antenna in the x, y, and z directions.

In the step (3), using the electromechanical coupling model of the linear array antenna, the electric performance of the ith deformed linear array antenna calculated is realized by the following formula:

In the formula, d is the distance between the radiating elements, I _in is the excitation current of the ideal linear array electrical performance of the nth radiating element in the ith linear array antenna, where A _in is the amplitude of the excitation current, is the excitation current phase, k is the wave constant, j is the imaginary number unit; k=2π/λ, λ is the working wavelength of the area array antenna, θ is the pitch angle of the line array antenna, Δy _in and Δz _in are the , the position error along the y-direction and z-direction generated by the nth radiation unit, Δy _i0 and Δz _i0 are the position errors of the 0th radiation unit, that is, the initial radiation unit in the y-direction and z-direction, respectively, in the i-th line array .

In the step (4), the electric performance of the i deformed linear array antenna is decomposed into the ideal linear array electric performance and the linear array electric performance change item caused by structural deformation, and is carried out according to the following process:

When the structural deformation of the radiating element of the linear array antenna is not greater than 0.06λ/πcos(λ/2d), according to the nature of the exponential function Decompose the array factor pattern of the deformed linear array antenna:

in, Indicates the electrical performance change item caused by the structural deformation of the i-th linear array antenna; f _ia (θ) indicates the ideal electrical performance of the i-th linear array antenna.

In order to perform subsequent fast Fourier transform on the ideal electrical properties and electrical properties change items of the linear array, u is used to represent sinθ, then f _ia (θ) and f _iae (θ) are expressed as:

In the described step (5), FFT transformation is carried out to the ideal linear array electrical performance and the electrical performance change item of the ith deformed linear array antenna respectively, as follows:

(5a) Perform FFT transformation on the excitation current I _in of the ideal linear array electrical performance of the ith deformed linear array antenna:

Among them, _αim is the Fourier series of the excitation current, and m represents the serial number of the current signal after the fast Fourier transform;

In the ideal linear array antenna main beam direction In the above, the Fourier transform relationship between the electrical performance of the antenna and the excitation current I _in of the ideal linear array electrical performance is established, and the FFT transformation is performed on the ideal linear array electrical performance f _ia (u) of the ith deformed linear array antenna:

Among them, u=sinθ; Indicates the spatial phase generated by the radiating element of the linear array antenna under ideal conditions; Indicates the main beam direction of the linear array antenna;

(5b) For the electrical performance disturbance term f _iae (θ) of the linear array antenna, establish its Fourier series expression. Using FFT transformation, make β _im =FFT[kI _in (Δy _in -Δy _i0 )], γ _im =FFT[kI _in (Δz _in -Δz _i0 )], because discrete Fourier transform satisfies linear superposition, so f _iae The Fourier series form of (θ) can be expressed as:

The influence of the structural deformation on the direction u is converted into the influence on the main beam of the linear array antenna to u _m , then the adjustment of the excitation current is calculated on the main beam of the linear array antenna, and the above formula F _iae (u) becomes:

At this time, the Fourier series form of the antenna array factor pattern f _ias (θ) with structural errors is

(5c) FFT inverse transform is carried out to the Fourier series F _ias (u) of the array factor pattern of the deformed linear array antenna, and the array factor pattern of the deformed linear array antenna is obtained as follows:

in, Indicates the excitation current containing structural errors in the i-th deformed linear array antenna, usually adjusting the current can compensate for the influence of structural deformation on the electrical performance of the linear array;

(5d) The main beam pointing of the line array antenna On, the adjustment amount of excitation current amplitude and phase is calculated. On the main beam pointing u _m , the excitation current I _ins including the structure error is:

The relationship between this current and the excitation current I _in of the ideal linear array electrical performance is as follows:

in, Indicates the amplitude disturbance coefficient caused by structural errors in the excitation current of the deformed area array antenna; Indicates the phase disturbance caused by structural errors in the excitation current of the deformed area array antenna, and Im represents the imaginary part of the imaginary number;

(5e) The amplitude disturbance coefficient ΔA _n and phase disturbance of the excitation current caused by the structural deformation of the linear array antenna A correction is made to compensate for the effect of structural deformation on the electrical performance of the linear array antenna. Introduce the amplitude coefficient adjustment amount of the excitation current ΔA _inc = -ΔA _in , the phase adjustment amount of the excitation current Then the adjusted excitation current becomes:

Using the adjusted excitation current I _inc to replace the excitation current I _in of the ideal linear array electrical performance in the deformed linear array antenna array factor f _ias (θ), the electrical performance of the deformed linear array antenna after compensation can be obtained as:

In the formula, Indicates the amplitude coefficient adjustment amount of the excitation current; Indicates the adjustment amount of the phase of the excitation current.

In the step (6), it is judged whether the adjustments of excitation current amplitude and phase have been calculated for all linear array antennas, if satisfied, the excitation current amplitude and phase adjustment of the area array unit are obtained, if not satisfied, the next line array antenna, and repeat steps (3) to (6).

In the described step (7), the M linear array antennas obtained, i.e. the adjustments of the excitation current amplitude and the phase of all the area array antennas, are brought into the area array antenna electromechanical coupling model, which is:

In the step (7), the electrical performance of the deformed linear array antenna after compensation is calculated, and the electrical performance parameters of the antenna including antenna gain, sidelobe level and beam pointing are obtained. Judging whether the electrical performance of the deformed area array antenna after compensation meets the index requirements, if it meets the requirements, it indicates that the excitation current amplitude and phase adjustment with the best electrical performance of the compensated deformed area array antenna have been obtained, so that the area array antenna can achieve the best performance in the service environment. Otherwise, modify the structural parameters of the area array antenna, including enhancing the structural stiffness of the antenna, modifying the constraint position of the area array antenna, etc., and repeat steps (1) to (8) until the requirements are met.

In the step (8), modifying the structural parameters of the area array antenna includes enhancing the structural rigidity of the area array antenna and modifying the constraint position of the area array antenna.

Based on the antenna electromechanical coupling model and Fourier transform, the invention can compensate the influence of environmental load on the electrical performance of the area array antenna in service, improve the electrical performance of the antenna, and do not increase the structural complexity and structural weight of the antenna, and can be used for To solve the problem of deterioration of the electrical performance of the array antenna caused by the service environment load, when the area array antenna is in service, the electrical performance of the deformed area array antenna can be compensated to ensure the normal operation of the antenna without increasing the structural complexity and weight of the antenna. At the same time, the compensated deformable area array antenna has strong anti-interference ability to the working environment. When the environmental load changes in a small range, the deformable area array antenna can be guaranteed to have good electrical performance without additional adjustments to the area array antenna. Therefore, this method provides an important technical guarantee for improving the electrical performance of the antenna, especially for large area array antennas.

Compared with the prior art, the present invention has the following characteristics:

1. The present invention analyzes the structural deformation of the array antenna under the actual airborne environment, and based on the coupling relationship between the structural deformation and electrical performance, combined with fast Fourier transform, the adjustment amount of the excitation current amplitude and phase of the area array antenna is solved , without increasing the structural complexity and structural weight of the antenna, the compensation of the electrical performance of the deformed area array antenna is realized, and the influence of the environmental load on the electrical performance of the antenna under actual working conditions is effectively reduced;

2. The deformed area array antenna after compensation has strong anti-interference ability to the working environment. When the environmental load changes in a small range, the deformed area array antenna can be guaranteed to have good electrical performance without additional adjustments to the area array antenna. Therefore, the method proposed by the present invention can be used to compensate the electrical performance of the area array antenna during service, and provides an important technical guarantee for improving the electrical performance of the antenna.

Description of drawings

Fig. 1 is the method for compensating electrical performance of deformed area array antenna based on electromechanical coupling and Fourier transform in the present invention;

Fig. 2 is a schematic diagram of arrangement of radiation elements of an area array antenna;

Fig. 3 is a spatial geometric relationship diagram of the observation point P relative to the coordinate system xyz;

Fig. 4 is a schematic diagram of a geometric structure model of an area array antenna;

Fig. 5 is a schematic diagram of the finite element model of the area array antenna in ANSYS software;

Fig. 6 is the airborne random vibration acceleration power spectrum;

Fig. 7 is the random vibration deformation cloud diagram of the area array antenna;

Figure 8 is a comparison diagram of the far-field pattern of the ideal and deformed rear array antennas;

Figure 9 is a comparison diagram of the far-field pattern of the ideal and compensated rear array antennas.

detailed description

The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

With reference to Fig. 1, the present invention is based on electromechanical coupling and Fourier transform method for electrical performance compensation of deformed area array antenna, the specific steps are as follows:

Step 1, determine the geometric model parameters, material properties and electromagnetic working parameters of the area array antenna

1.1 Determine the structural geometric model of the area array antenna based on the array shape, aperture size, type, number and arrangement of radiation elements in the array, and the structural parameters of the antenna frame;

1.2. Determine the material properties of the cold plate, T/R components, ribs, and radiation elements in the area array antenna system, including density ρ, elastic modulus E, and Poisson’s ratio μ.

1.3. Determine the electromagnetic working parameters of the area array antenna, including the central working frequency f of the antenna and the amplitude and phase of the excitation current.

Step 2, finite element analysis to obtain the front deformation

2.1 Construct the structural finite element model in ANSYS according to the geometric model parameters and material properties of the area array antenna, in which the element type of the cold plate, T/R component, and stiffener is the solid element SOLID92, and the element type of the radiation element is the surface element SHELL63 . Among them, there is no relative displacement between the cold plate and the rib, between the cold plate and the T/R component, between the T/R component and the radiation unit, and between the radiation unit and the rib.

2.2 According to the installation method of the antenna, impose constraints on the area array antenna, and apply the airborne random vibration acceleration power spectrum to the finite element model of the area array antenna structure, calculate the random vibration deformation of the array, and extract the position deviation of the radiation element caused by the vibration deformation. displacement, the position displacement of the nth radiation unit in the x, y, z directions is (Δx ₀ , Δy ₀ , Δz ₀ )······(Δx _N-1 ,Δy _N-1 ,Δz _N-1 ), where, (Δx _n , Δy _n , Δz _n ), n∈(0,N-1), n is a natural number between 0 and N-1, representing the N radiation elements in the area array antenna serial number.

Step 3, the linear array antenna electromechanical coupling model to calculate the electrical performance

Extract the i-th linear array antenna among the M linear array antennas, and use the electromechanical coupling model of the linear array antenna to calculate the electrical performance of the i-th deformed linear array antenna as follows:

In the formula, d is the distance between the radiating elements, I _in is the excitation current of the ideal linear array electrical performance of the nth radiating element in the ith linear array antenna, where A _in is the amplitude of the excitation current, is the excitation current phase, k is the wave constant, k=2π/λ, λ is the working wavelength of the area array antenna, θ is the pitch angle of the line array antenna, Δy _in and Δz _in are the i-th line array, the n-th radiation The position error along the y-direction and z-direction generated by the unit, Δy _i0 and Δz _i0 are the position errors of the 0th radiating unit, that is, the initial radiating unit in the y-direction and z-direction in the i-th line array, respectively.

Step 4, decompose the electrical performance of the i-th deformed linear array antenna

When the structural deformation of the radiating element of the linear array antenna is not greater than 0.06λ/πcos(λ/2d), the array factor pattern of the ith deformed linear array antenna is decomposed:

in, Indicates the electrical performance change item caused by the structural deformation of the i-th linear array antenna; f _ia (θ) indicates the ideal electrical performance of the i-th linear array antenna.

Step 5, perform FFT transformation on the i-th linear array ideal electrical performance and electrical performance change items respectively

(5a) Perform FFT transformation on the excitation current I _in the ideal linear array electrical performance of the ith deformed linear array antenna:

Among them, α _im is the Fourier series of the excitation current, and m represents the serial number of the current signal after fast Fourier transform.

In the ideal linear array antenna main beam direction Above, the Fourier transform relationship between the electrical performance of the antenna and the excitation current of the ideal linear array electrical performance is established, and the FFT transformation is performed on the ideal linear array electrical performance f _ia (u) of the ith deformed linear array antenna:

Among them, u=sinθ; Indicates the spatial phase generated by the radiating element of the linear array antenna under ideal conditions; Indicates the main beam direction of the linear array antenna;

(5b) For the electrical performance disturbance term f _iae (θ) of the linear array antenna, establish its Fourier series expression. Using FFT transformation, make β _im =FFT[kI _in (Δy _in -Δy _i0 )], γ _im =FFT[kI _in (Δz _in -Δz _i0 )], because discrete Fourier transform satisfies linear superposition, so f _iae The Fourier series form of (θ) can be expressed as:

The influence of the structural deformation on the direction u is converted into the influence on the main beam of the linear array antenna to u _m , then the adjustment of the excitation current is calculated on the main beam of the linear array antenna, and the above formula F _iae (u) becomes:

At this time, the Fourier series form of the antenna array factor pattern f _ias (θ) with structural errors is:

(5c) FFT inverse transform is carried out to the Fourier series F _ias (u) of the array factor pattern of the deformed linear array antenna, and the array factor pattern of the deformed linear array antenna is obtained as follows:

in, Indicates the excitation current that contains structural errors in the ith deformed linear array antenna. Usually, adjusting this current can compensate the influence of structural deformation on the electrical performance of the linear array.

(5d) The main beam pointing of the line array antenna On, the adjustment amount of excitation current amplitude and phase is calculated. On the main beam pointing u _m , the excitation current I _ins including the structure error is:

The relationship between this current and the excitation current I _in of the ideal linear array electrical performance is as follows:

in,

Indicates the amplitude disturbance coefficient caused by structural errors in the excitation current of the deformed area array antenna; Indicates the phase disturbance caused by structural errors in the excitation current of the deformed area array antenna, and Im represents the imaginary part of the imaginary number;

(5e) The amplitude disturbance coefficient ΔA _n and phase disturbance of the excitation current caused by the structural deformation of the linear array antenna A correction is made to compensate for the effect of structural deformation on the electrical performance of the linear array antenna. Introduce the amplitude coefficient adjustment amount of the excitation current ΔA _inc = -ΔA _in , the phase adjustment amount of the excitation current Then the adjusted excitation current becomes:

Using the adjusted excitation current I _inc to replace the excitation current I _in of the ideal linear array electrical performance in the deformed linear array antenna array factor f _ias (θ), the electrical performance of the deformed linear array antenna after compensation can be obtained as:

In the formula, Indicates the amplitude coefficient adjustment amount of the excitation current; Indicates the adjustment amount of the phase of the excitation current.

Step 6. Determine whether all linear array antennas have been compensated

Judging whether the excitation current amplitude and phase adjustments have been calculated for all linear array antennas, if it is satisfied, the excitation current amplitude and phase adjustment of the area array unit are obtained, if not, extract the next linear array antenna, and repeat the steps ( 3) Go to step (6).

Step 7, area array antenna electromechanical coupling calculation

The obtained M linear array antenna units, that is, the adjustments of the excitation current amplitude and phase of all the area array antenna units, are brought into the electromechanical coupling model of the area array antenna, which is:

Step 8, judge whether the deformed area array antenna meets the design requirements after compensation

Calculate the electrical performance of the deformed linear array antenna after compensation, and obtain the electrical performance parameters of the antenna, including antenna gain, sidelobe level and beam pointing. Judging whether the electrical performance of the deformed area array antenna after compensation meets the index requirements, if it meets the requirements, it indicates that the excitation current amplitude and phase adjustment with the best electrical performance of the compensated deformed area array antenna have been obtained, so that the area array antenna can achieve the best performance in the service environment. Otherwise, modify the structural parameters of the area array antenna, including enhancing the structural stiffness of the antenna, modifying the constraint position of the area array antenna, etc., and repeat steps (1) to (8) until the requirements are met.

Advantage of the present invention can further illustrate by simulation experiment:

1. Determine the parameters of the area array antenna

In this example, take the rectangular area array antenna as an example, as shown in Figure 2, the central operating frequency is f = 10Ghz (wavelength λ = 30mm), and the radiating elements are arranged in a rectangular grid with equal intervals on the xoy plane, M = 12, N =12, a total of 144 radiating elements form an active phased array antenna array; d _x =0.5λ=15mm, d _y =0.5λ=15mm. The spatial geometric relationship of the observation point P relative to the coordinate system xyz is shown in Figure 3. The specific parameters of the material properties of the area array antenna are shown in Table 1.

Table 1 Material properties of the area array antenna

2. Calculate the compensation excitation current

1. Finite element analysis to get the front deformation

1.1 According to the geometric model size of the area array antenna, the geometric structure model of the area array antenna is established in ANSYS, as shown in Figure 4. The element type of the cold plate, T/R component, and rib is solid element SOLID92, and the element type of the radiation element is surface element SHELL63. According to the set material properties and element types, the geometric model of the area array antenna is meshed to obtain the area array antenna The finite element model of the structure is shown in Fig. 5. Among them, there is no relative displacement between the cold plate and the rib, between the cold plate and the T/R assembly, between the T/R assembly and the radiation unit, and between the rib and the radiation unit.

1.2 According to the constraints of the finite element model of the area array antenna structure and the given random vibration acceleration power spectrum (as shown in Figure 6), the random vibration deformation of the area array antenna is calculated by ANSYS software, and the deformation cloud diagram of the area array antenna structure is obtained (as shown in Figure 6 7), respectively extract the positional offsets (Δx _n , Δy _n , Δz _n ) of the center of the radiation element in the three directions of x, y, and z in the finite element model of the area array antenna structure under the vibration load. Among them, n∈(0,N-1).

2. Calculate the electrical performance of the antenna with the electromechanical coupling model of the linear array antenna

Divide the area array antenna into 12 linear array antennas, extract the i-th (1≤i≤12) linear array antenna, use the electromechanical coupling model of the linear array antenna, and calculate the electrical performance of the i-th deformed linear array antenna as follows:

In the formula, d is the distance between the radiating elements, I _in is the excitation current of the nth radiating element in the ith linear array antenna, where A _in is the amplitude of the excitation current, is the excitation current phase, k is the wave constant, k=2π/λ, λ is the working wavelength of the area array antenna, θ is the pitch angle of the line array antenna, Δy _in and Δz _in are the i-th line array, the n-th radiation The position error along the y-direction and z-direction generated by the unit, Δy _i0 and Δz _i0 are the position errors of the 0th radiating unit, that is, the initial radiating unit in the y-direction and z-direction in the i-th line array, respectively.

3. Decompose the electrical performance of the i-th deformed linear array antenna

Decompose the array factor pattern of the i-th deformed linear array antenna:

in, Indicates the electrical performance change item caused by the structural deformation of the i-th linear array antenna; f _ia (θ) indicates the ideal electrical performance of the i-th linear array antenna. The comparison of the far-field pattern of the ideal and deformed rear array antennas is shown in Figure 8.

4. Use FFT to calculate the excitation current amplitude and phase compensation amount of deformed linear array antenna

Perform FFT transformation on the i-th linear array ideal electrical performance and electrical performance change items respectively, and calculate the excitation current compensation amount of the deformed linear array antenna. The specific steps are as follows:

4.1 Perform FFT transformation on the excitation current I _{in in} the ideal electrical performance of the ith linear array:

Among them, α _im is the Fourier series of the excitation current, and m represents the serial number of the current signal after fast Fourier transform.

In the ideal linear array antenna main beam direction Above, the Fourier transform relationship between the electrical performance of the antenna and the excitation current is established, and the FFT transformation is performed on the ideal electrical performance f _ia (u) of the i-th linear array antenna:

Among them, u=sinθ; Indicates the spatial phase generated by the radiating element of the linear array antenna under ideal conditions; Indicates the main beam direction of the linear array antenna.

4.2 For the electrical performance disturbance term f _iae (θ) of the linear array antenna, establish its Fourier series expression. Using FFT transformation, make β _im =FFT[kI _in (Δy _in -Δy _i0 )], γ _im =FFT[kI _in (Δz _in -Δz _i0 )], because discrete Fourier transform satisfies linear superposition, so f _iae The Fourier series form of (θ) can be expressed as:

At this time, the Fourier series form of the antenna array factor pattern f _ias (θ) with structural errors is:

4.3 Perform FFT inverse transformation on the Fourier series F _ias (u) of the array factor pattern of the deformed linear array antenna, and obtain the array factor pattern of the deformed linear array antenna as follows:

in, Indicates the excitation current that contains structural errors in the ith deformed linear array antenna. Usually, adjusting this current can compensate the influence of structural deformation on the electrical performance of the linear array.

4.4 Main beam pointing of line array antenna On, the adjustment amount of excitation current amplitude and phase is calculated. On the main beam pointing u _m , the excitation current I _ins including the structure error is:

The relationship between this current and the excitation current I _in of the linear array antenna in an ideal state is as follows:

in,

Indicates the amplitude disturbance coefficient caused by structural errors in the excitation current of the deformed area array antenna; Indicates the phase disturbance caused by the structural error in the excitation current of the deformed area array antenna.

4.5 The excitation current amplitude disturbance coefficient ΔA _n and phase disturbance caused by the structural deformation of the linear array antenna A correction is made to compensate for the effect of structural deformation on the electrical performance of the linear array antenna. Introduce the amplitude coefficient adjustment amount of the excitation current ΔA _inc = -ΔA _in , the phase adjustment amount of the excitation current Then the adjusted excitation current becomes:

Using the adjusted excitation current I _inc to replace the excitation current I _in in the deformed linear array antenna factor f _ias (θ), the electrical performance of the compensated deformed linear array antenna can be obtained as follows:

In the formula, Indicates the amplitude coefficient adjustment amount of the excitation current; Indicates the adjustment amount of the phase of the excitation current.

5. Determine whether all linear array antennas have been compensated

Determine whether the excitation current amplitude and phase adjustments have been calculated for all linear array antennas. If satisfied, obtain the excitation current amplitude and phase adjustment of the area array unit. If not, extract the next linear array antenna and repeat step 2 Go to step 4.

6. Electromechanical coupling of area array antenna to calculate antenna electrical performance

The obtained 12 linear array antenna units, that is, the adjustments of the excitation current amplitude and phase of all the area array antenna units, are brought into the electromechanical coupling model of the area array antenna, which is:

3. Simulation results and analysis

It can be seen from the above that the structural deformation of the area array antenna will cause the decrease of antenna gain, the increase of sidelobe level, and the deviation of beam pointing, which will lead to the deterioration of antenna performance. Bring the obtained compensated excitation current into the pattern function of the deformed area array antenna to obtain the pattern function of the area array antenna after compensation, and draw the pattern of the area array antenna in the ideal situation and the pattern of the area array antenna after compensation on the same In the coordinate system, as shown in Figure 9. It can be seen from Fig. 9 that the antenna pattern function after compensation is very close to the antenna pattern function under ideal conditions, and the compensation effect is better. Table 2 gives the electrical performance parameters of the array antenna under the ideal condition, vibration deformation condition and three different states after compensation, including gain, sidelobe level and beam pointing.

Table 2 Electrical performance parameters of ideal, deformed and compensated rear array antennas

It can be seen from the data in Table 2 that when the area array antenna is affected by random vibrations, the antenna gain decreases, the sidelobe level increases, and the beam pointing deviation is caused. The compensation method of the present invention is used to compensate the electrical performance of the antenna. After compensation, the antenna gain loss is reduced from 1.08dB to 0.058dB, which reduces the gain loss by an order of magnitude, and meets the project’s requirement that the gain loss is less than 0.5dB; the sidelobe level is reduced from -26.08dB to -29.45dB , the sidelobe level is significantly improved; the beam pointing deviation is changed from 0.1° to 0°, and the beam pointing is more accurate. From this example, it can be seen that the electrical performance compensation method of deformed area array antenna based on electromechanical coupling and Fourier transform has a good compensation effect on the electrical performance of the antenna, and the electrical performance of the antenna after compensation meets the index requirements, so this method can be applied To the actual service work of the electrical performance of the antenna.

Claims (8)

1. based on electromechanical coupling and Fourier transform deformable area array antenna electric performance compensation method, it is characterized in that, comprises following process: (1) According to the structural parameters of the area array antennas in M rows and N columns, that is, M line array antennas, determine the geometric model parameters and material properties of the area array antenna, and determine the operating parameters of the area array antenna; (2) Establish the structure finite element model of the area array antenna according to the geometric model parameters and material properties of the area array antenna; determine the constraints of the antenna finite element model according to the installation form of the area array antenna; apply the airborne random vibration power to the area array antenna finite element model spectrum, calculate the structural deformation of the area array antenna, and extract the position offset of the central node of the area array antenna radiating element in the x, y, and z directions; (3) Extract the position offset of the i-th line array antenna and the central node of its radiating unit among the M line array antennas, where 1≤i≤M; Electrical performance of a linear array antenna after deformation; (4) Decompose the electrical performance of the ith deformed linear array antenna into the electrical performance of the ideal linear array and the change item of the electrical performance of the linear array caused by structural deformation, where the electrical performance change item of the linear array is determined by the excitation current I _in and antenna space phase error caused by structural deformation; (5) Perform fast Fourier transform on the ideal linear array electrical performance and the linear array electrical performance change item respectively, and obtain the excitation current amplitude and phase adjustment amount for compensating the spatial phase error of the antenna; Specifically: (5a) Express the excitation current I _in of the ideal linear array electrical performance of the ith deformed linear array antenna as a Fourier series form; In the direction of the main beam of the ideal linear array antenna, the Fourier transform relationship between the electrical performance of the antenna and the excitation current I _in of the ideal linear array electrical performance is established, and the ideal linear array electrical performance f _ia of the i-th deformed linear array antenna (u) carry out fast Fourier transform, obtain Fourier series expression F _ia (u); (5b) For the electrical performance disturbance term f _iae (u) of the linear array antenna, establish its Fourier series expression F _iae (u); convert the influence of structural deformation on the direction u to the main beam of the linear array antenna The effect of pointing to u _m , the adjustment value of the excitation current is calculated on the main beam of the line array antenna. At this time, the Fourier series F _ia (u) of the ideal electrical performance of the line array antenna and the Fourier of the electrical performance disturbance item Leaf series F _iae (u) are superimposed to obtain the Fourier series form F _ias (u) of the antenna array factor pattern f _ias (u) with structural errors; (5c) Carry out inverse fast Fourier transform to the Fourier series F _ias (u) of the deformed linear array antenna array factor pattern, obtain the array factor pattern of the deformed linear array antenna, and the excitation current I in the pattern _ins is the excitation current of the deformed linear array antenna that contains structural errors. Adjusting this current can compensate the influence of structural deformation on the electrical performance of the linear array; (5d) Calculate the adjustment value of the amplitude and phase of the excitation current, and obtain the amplitude disturbance caused by the structural error in the excitation current of the deformed linear array antenna according to the relationship between the excitation current I _ins including the structural error and the excitation current I _in of the ideal linear array electrical performance Coefficient ΔA _in and phase perturbation due to structural errors (5e) The excitation current amplitude disturbance coefficient ΔA _in and phase disturbance caused by the structural deformation of the linear array antenna Make corrections to compensate for the influence of structural deformation on the electrical performance of the linear array antenna; introduce the amplitude coefficient adjustment amount of the excitation current ΔA _inc = -ΔA _in , the phase adjustment amount of the excitation current Then the adjusted excitation current I _inc is obtained; Using the adjusted excitation current I _inc to replace the excitation current I _in of the ideal linear array electrical performance in the deformed linear array antenna array factor f _ias (θ), the electrical performance of the deformed linear array antenna after compensation can be obtained; (6) Judging whether the adjustments of excitation current amplitude and phase have been calculated for all M linear array antennas, if yes, the adjustments of excitation current amplitude and phase of M linear array antennas are obtained, otherwise extract the next line array Antenna, and repeat step (3) to step (6); (7) Bring the obtained M linear array antennas, that is, the adjustments of the excitation current amplitude and phase of all the area array antennas, into the electromechanical coupling model of the area array antenna, and calculate the electrical performance of the deformed area array antenna; (8) Determine whether the electrical performance of the deformed area array antenna after compensation meets the index requirements. If it meets the requirements, it indicates that the excitation current amplitude and phase adjustment with the best electrical performance of the compensated deformed area array antenna have been obtained, so that the area array antenna can be used in the service environment. The optimal performance is achieved; otherwise, modify the structural parameters of the area array antenna, and repeat steps (1) to (7) until the requirements are met. 2. the deformed area array antenna electrical performance compensation method based on electromechanical coupling and Fourier transform according to claim 1, characterized in that, in step (1), the geometric model parameters of the area array antenna include area array The position distribution, number, size, and unit spacing of antenna radiation elements, the size parameters of T/R components, cold plates, and stiffeners; the material properties of the area array antenna, including density ρ, elastic modulus E, and Poisson’s ratio μ ; The electromagnetic working parameters of the area array antenna include the center operating frequency f of the area array antenna, the amplitude and phase of the excitation current. 3. the deformed area array antenna electric performance compensation method based on electromechanical coupling and Fourier transform according to claim 1, is characterized in that, in step (3), adopts linear array antenna electromechanical coupling model, the ith of calculation The electrical performance f _ias (θ) of the deformable linear array antenna is realized by the following formula: <mrow><msub><mi>f</mi><mrow><mi>i</mi><mi>a</mi><mi>s</mi></mrow></msub><mrow><mo>(</mo><mi>&amp;theta;</mi><mo>)</mo></mrow><mo>=</mo><munderover><mo>&amp;Sigma;</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover><msub><mi>I</mi><mrow><mi>i</mi><mi>n</mi></mrow></msub><mi>exp</mi><mo>{</mo><mi>j</mi><mi>k</mi><mo>&amp;lsqb;</mo><mi>n</mi><mi>d</mi><mi></mi><mi>s</mi><mi>i</mi><mi>n</mi><mi>&amp;theta;</mi><mo>+</mo><mrow><mo>(</mo><msub><mi>&amp;Delta;y</mi><mrow><mi>i</mi><mi>n</mi></mrow></msub><mo>-</mo><msub><mi>&amp;Delta;y</mi><mrow><mi>i</mi><mn>0</mn></mrow></msub><mo>)</mo></mrow><mi>s</mi><mi>i</mi><mi>n</mi><mi>&amp;theta;</mi><mo>+</mo><mrow><mo>(</mo><msub><mi>&amp;Delta;z</mi><mrow><mi>i</mi><mi>n</mi></mrow></msub><mo>-</mo><msub><mi>&amp;Delta;z</mi><mrow><mi>i</mi><mn>0</mn></mrow></msub><mo>)</mo></mrow><mi>c</mi><mi>o</mi><mi>s</mi><mi>&amp;theta;</mi><mo>&amp;rsqb;</mo><mo>}</mo></mrow> In the formula, d is the distance between the radiating elements; I _in is the excitation current of the ideal linear array electrical performance of the nth radiating element in the ith linear array antenna, where A _in is the amplitude of the excitation current, is the excitation current phase; j is the imaginary number unit; k is the wave constant, k= _2π /λ, _λ is the working wavelength of the area array antenna; θ is the pitch angle of the line array antenna; , the position error along the y-direction and z-direction generated by the nth radiation unit; Δy _i0 and Δz _i0 are the position errors of the 0th radiation unit, that is, the initial radiation unit in the y-direction and z-direction, respectively, in the i-th line array . 4. the deformed area array antenna electrical performance compensation method based on electromechanical coupling and Fourier transform according to claim 1, is characterized in that, in step (4), the i deformed linear array antenna electrical performance is decomposed into ideal Line array electrical properties and changes in line array electrical properties caused by structural deformation, specifically: When the structural deformation of the radiating element of the linear array antenna is not greater than 0.06λ/πcos(λ/2d), the array factor pattern of the deformed linear array antenna is decomposed: <mfenced open=""close=""><mtable><mtr><mtd><mrow><msub><mi>f</mi><mrow><mi>i</mi><mi>a</mi><mi>s</mi></mrow></msub><mrow><mo>(</mo><mi>&amp;theta;</mi><mo>)</mo></mrow><mo>=</mo><munderover><mo>&amp;Sigma;</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover><msub><mi>I</mi><mrow><mi>i</mi><mi>n</mi></mrow></msub><mi>exp</mi><mo>{</mo><mi>j</mi><mi>k</mi><mo>&amp;lsqb;</mo><mi>n</mi><mi>d</mi><mi></mi><mi>s</mi><mi>i</mi><mi>n</mi><mi>&amp;theta;</mi><mo>+</mo><mrow><mo>(</mo><msub><mi>&amp;Delta;y</mi><mrow><mi>i</mi><mi>n</mi></mrow></msub><mo>-</mo><msub><mi>&amp;Delta;y</mi><mrow><mi>i</mi><mn>0</mn></mrow></msub><mo>)</mo></mrow><mi>s</mi><mi>i</mi><mi>n</mi><mi>&amp;theta;</mi><mo>+</mo><mrow><mo>(</mo><msub><mi>&amp;Delta;z</mi><mrow><mi>i</mi><mi>n</mi></mrow></msub><mo>-</mo><msub><mi>&amp;Delta;z</mi><mrow><mi>i</mi><mn>0</mn></mrow></msub><mo>)</mo></mrow><mi>c</mi><mi>o</mi><mi>s</mi><mi>&amp;theta;</mi><mo>&amp;rsqb;</mo><mo>}</mo></mrow></mtd></mtr><mtr><mtd><mrow><mo>&amp;ap;</mo><munderover><mo>&amp;Sigma;</mo><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>N</mi><mo>-</mo><mn>1</mn></mrow></munderover><msub><mi>I</mi><mrow><mi>i</mi><mi>n</mi></mrow></msub><mi>exp</mi><mrow><mo>(</mo><mi>j</mi><mi>k</mi><mi>n</mi><mi>d</mi><mi>sin</mi><mi>&amp;theta;</mi><mo>)</mo></mrow><mo>{</mo><mn>1</mn><mo>+</mo><mi>j</mi><mi>k</mi><mo>&amp;lsqb;</mo><mrow><mo>(</mo><msub><mi>&amp;Delta;y</mi><mrow><mi>i</mi><mi>n</mi></mrow></msub><mo>-</mo><msub><mi>&amp;Delta;y</mi><mrow><mi>i</mi><mn>0</mn></mrow></msub><mo>)</mo></mrow><mi>s</mi><mi>i</mi><mi>n</mi><mi>&amp;theta;</mi><mo>+</mo><mrow><mo>(</mo><msub><mi>&amp;Delta;z</mi><mrow><mi>i</mi><mi>n</mi></mrow></msub><mo>-</mo><msub><mi>&amp;Delta;z</mi><mrow><mi>i</mi><mn>0</mn></mrow></msub><mo>)</mo></mrow><mi>c</mi><mi>o</mi><mi>s</mi><mi>&amp;theta;</mi><mo>&amp;rsqb;</mo><mo>}</mo></mrow></mtd></mtr><mtr><mtd><mrow><mo>=</mo><msub><mi>f</mi><mrow><mi>i</mi><mi>a</mi></mrow></msub><mrow><mo>(</mo><mi>&amp;theta;</mi><mo>)</mo></mrow><mo>+</mo><msub><mi>f</mi><mrow><mi>i</mi><mi>a</mi><mi>e</mi></mrow></msub><mrow><mo>(</mo><mi>&amp;theta;</mi><mo>)</mo></mrow></mrow></mtd></mtr></mtable></mfenced> in, Indicates the electrical performance change item caused by the structural deformation of the i-th linear array antenna; f _ia (θ) indicates the ideal electrical performance of the i-th linear array antenna; In order to perform subsequent fast Fourier transform on the ideal electrical properties and electrical properties change items of the linear array, u is used to represent sinθ, then f _ia (θ) and f _iae (θ) are expressed as: <mrow><msub><mi>f</mi><mrow><mi>i</mi><mi>a</mi></mrow></msub><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>=</mo><munderover><mo>&amp;Sigma;</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover><msub><mi>I</mi><mrow><mi>i</mi><mi>n</mi></mrow></msub><mi>exp</mi><mrow><mo>(</mo><mi>j</mi><mi>k</mi><mi>n</mi><mi>d</mi><mi>u</mi><mo>)</mo></mrow></mrow> <mrow><msub><mi>f</mi><mrow><mi>i</mi><mi>a</mi><mi>e</mi></mrow></msub><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>=</mo><mi>j</mi><mi>k</mi><munderover><mo>&amp;Sigma;</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover><msub><mi>I</mi><mrow><mi>i</mi><mi>n</mi></mrow></msub><mo>&amp;lsqb;</mo><mrow><mo>(</mo><msub><mi>&amp;Delta;y</mi><mrow><mi>i</mi><mi>n</mi></mrow></msub><mo>-</mo><msub><mi>&amp;Delta;y</mi><mrow><mi>i</mi><mn>0</mn></mrow></msub><mo>)</mo></mrow><mi>u</mi><mo>+</mo><mrow><mo>(</mo><msub><mi>&amp;Delta;z</mi><mrow><mi>i</mi><mi>n</mi></mrow></msub><mo>-</mo><msub><mi>&amp;Delta;z</mi><mrow><mi>i</mi><mn>0</mn></mrow></msub><mo>)</mo></mrow><msqrt><mrow><mn>1</mn><mo>-</mo><msup><mi>u</mi><mn>2</mn></msup></mrow></msqrt><mo>&amp;rsqb;</mo><mi>exp</mi><mrow><mo>(</mo><mi>j</mi><mi>k</mi><mi>n</mi><mi>d</mi><mi>u</mi><mo>)</mo></mrow><mo>.</mo></mrow> 5. the deformed area array antenna electrical performance compensation method based on electromechanical coupling and Fourier transform according to claim 1, is characterized in that, in step (5), the ideal line array of the ith deformed line array antenna is respectively Fast Fourier transform is performed on the electrical performance and the line array electrical performance change items, specifically: (5a) Express the excitation current I _in of the ideal linear array electrical performance of the i-th deformed linear array antenna in the form of Fourier series: <mrow><msub><mi>&amp;alpha;</mi><mrow><mi>i</mi><mi>m</mi></mrow></msub><mo>=</mo><mfrac><mn>1</mn><mi>N</mi></mfrac><munderover><mo>&amp;Sigma;</mo><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>N</mi><mo>-</mo><mn>1</mn></mrow></munderover><msub><mi>I</mi><mrow><mi>i</mi><mi>n</mi></mrow></msub><mo>.</mo><msup><mi>e</mi><mrow><mi>j</mi><mfrac><mrow><mn>2</mn><mi>&amp;pi;</mi></mrow><mi>N</mi></mfrac><mi>n</mi><mi>m</mi></mrow></msup><mo>,</mo><mn>0</mn><mo>&amp;le;</mo><mi>m</mi><mo>&amp;le;</mo><mi>N</mi><mo>-</mo><mn>1</mn></mrow> Among them, _αim is the Fourier series of the excitation current, and m represents the serial number of the current signal in the Fourier series; In the ideal linear array antenna main beam direction Above, establish the Fourier transform relationship between the electrical performance of the antenna and the excitation current I _in of the ideal linear array electrical performance, and perform fast Fourier transform on the ideal linear array electrical performance f _ia (u) of the ith deformed linear array antenna transform: <mrow><mtable><mtr><mtd><mrow><msub><mi>F</mi><mrow><mi>i</mi><mi>a</mi></mrow></msub><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mn>1</mn><mi>N</mi></mfrac><munderover><mo>&amp;Sigma;</mo><mrow><mi>m</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>N</mi><mo>-</mo><mn>1</mn></mrow></munderover><msub><mi>&amp;alpha;</mi><mrow><mi>i</mi><mi>m</mi></mrow></msub><mo>.</mo><mi>U</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><msup><mi>e</mi><mrow><mo>-</mo><mi>j</mi><mi>k</mi><mi>n</mi><mi>d</mi><mfrac><mrow><mi>m</mi><mi>&amp;lambda;</mi></mrow><mrow><mi>N</mi><mi>d</mi></mrow></mfrac></mrow></msup></mrow></mtd></mtr><mtr><mtd><mrow><mo>=</mo><mfrac><mn>1</mn><mi>N</mi></mfrac><munderover><mo>&amp;Sigma;</mo><mrow><mi>m</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>N</mi><mo>-</mo><mn>1</mn></mrow></munderover><msub><mi>&amp;alpha;</mi><mrow><mi>i</mi><mi>m</mi></mrow></msub><mo>.</mo><mi>U</mi><mrow><mo>(</mo><mi>u</mi><mo>-</mo><msub><mi>u</mi><mi>m</mi></msub><mo>)</mo></mrow></mrow></mtd></mtr></mtable><mo>,</mo><mn>0</mn><mo>&amp;le;</mo><mi>m</mi><mo>&amp;le;</mo><mi>N</mi><mo>-</mo><mn>1</mn></mrow> in, Indicates the spatial phase generated by the radiating element of the linear array antenna under ideal conditions; Indicates the main beam direction of the linear array antenna; (5b) For the electrical performance disturbance term f _iae (u) of the linear array antenna, establish its Fourier series expression; adopt fast Fourier transform, make β _im =FFT[kI _in (Δy _in -Δy _i0 ) ], γ _im ＝FFT[kI _in (Δz _in -Δz _i0 )], because discrete Fourier transform satisfies linear superposition, so the Fourier series form of f _iae (u) is expressed as: <mrow><msub><mi>F</mi><mrow><mi>i</mi><mi>a</mi><mi>e</mi></mrow></msub><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mi>j</mi><mi>N</mi></mfrac><munderover><mo>&amp;Sigma;</mo><mrow><mi>m</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>N</mi><mo>-</mo><mn>1</mn></mrow></munderover><mo>(</mo><mrow><mi>u</mi><mo>&amp;CenterDot;</mo><msub><mi>&amp;beta;</mi><mrow><mi>i</mi><mi>m</mi></mrow></msub><mo>+</mo><msqrt><mrow><mn>1</mn><mo>-</mo><msup><mi>u</mi><mn>2</mn></msup></mrow></msqrt><mo>&amp;CenterDot;</mo><msub><mi>&amp;gamma;</mi><mrow><mi>i</mi><mi>m</mi></mrow></msub></mrow><mo>)</mo><mo>&amp;CenterDot;</mo><mi>U</mi><mrow><mo>(</mo><mi>u</mi><mo>-</mo><msub><mi>u</mi><mi>m</mi></msub><mo>)</mo></mrow></mrow> The influence of the structural deformation on the direction u is converted into the influence on the main beam of the linear array antenna to u _m , then the adjustment of the excitation current is calculated on the main beam of the linear array antenna, and the above formula F _iae (u) becomes: <mrow><msub><mi>F</mi><mrow><mi>i</mi><mi>a</mi><mi>e</mi></mrow></msub><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mi>j</mi><mi>N</mi></mfrac><munderover><mo>&amp;Sigma;</mo><mrow><mi>m</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>N</mi><mo>-</mo><mn>1</mn></mrow></munderover><mo>(</mo><mrow><msub><mi>u</mi><mi>m</mi></msub><mo>&amp;CenterDot;</mo><msub><mi>&amp;beta;</mi><mrow><mi>i</mi><mi>m</mi></mrow></msub><mo>+</mo><msqrt><mrow><mn>1</mn><mo>-</mo><msup><msub><mi>u</mi><mi>m</mi></msub><mn>2</mn></msup></mrow></msqrt><mo>&amp;CenterDot;</mo><msub><mi>&amp;gamma;</mi><mrow><mi>i</mi><mi>m</mi></mrow></msub></mrow><mo>)</mo><mo>&amp;CenterDot;</mo><mi>U</mi><mrow><mo>(</mo><mi>u</mi><mo>-</mo><msub><mi>u</mi><mi>m</mi></msub><mo>)</mo></mrow></mrow> At this time, the Fourier series form of the antenna array factor pattern f _ias (u) with structural errors is: <mrow><msub><mi>F</mi><mrow><mi>i</mi><mi>a</mi><mi>s</mi></mrow></msub><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>=</mo><msub><mi>F</mi><mrow><mi>i</mi><mi>a</mi></mrow></msub><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>+</mo><msub><mi>F</mi><mrow><mi>i</mi><mi>a</mi><mi>e</mi></mrow></msub><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mn>1</mn><mi>N</mi></mfrac><munderover><mo>&amp;Sigma;</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>N</mi><mo>-</mo><mn>1</mn></mrow></munderover><mo>&amp;lsqb;</mo><msub><mi>&amp;alpha;</mi><mrow><mi>i</mi><mi>m</mi></mrow></msub><mo>+</mo><mi>j</mi><mrow><mo>(</mo><msub><mi>u</mi><mi>m</mi></msub><mo>&amp;CenterDot;</mo><msub><mi>&amp;beta;</mi><mrow><mi>i</mi><mi>m</mi></mrow></msub><mo>+</mo><msqrt><mrow><mn>1</mn><mo>-</mo><msup><msub><mi>u</mi><mi>m</mi></msub><mn>2</mn></msup></mrow></msqrt><mo>&amp;CenterDot;</mo><msub><mi>&amp;gamma;</mi><mrow><mi>i</mi><mi>m</mi></mrow></msub><mo>)</mo></mrow><mo>&amp;rsqb;</mo><mo>&amp;CenterDot;</mo><mi>U</mi><mrow><mo>(</mo><mi>u</mi><mo>-</mo><msub><mi>u</mi><mi>m</mi></msub><mo>)</mo></mrow><mo>;</mo></mrow> 3 (5c) Fast Fourier inverse transform is performed on the Fourier series F _ias (u) of the array factor pattern of the deformed linear array antenna, and the array factor pattern of the deformed linear array antenna is obtained as follows: <mrow><msub><mi>f</mi><mrow><mi>i</mi><mi>a</mi><mi>s</mi></mrow></msub><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>=</mo><munderover><mo>&amp;Sigma;</mo><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>N</mi><mo>-</mo><mn>1</mn></mrow></munderover><msub><mi>I</mi><mrow><mi>i</mi><mi>n</mi><mi>s</mi></mrow></msub><mi>exp</mi><mrow><mo>(</mo><mi>j</mi><mi>k</mi><mi>n</mi><mi>d</mi><mi>u</mi><mo>)</mo></mrow></mrow> in, Indicates the excitation current containing structural errors in the i-th deformed linear array antenna, and adjusting this current can compensate the influence of structural deformation on the electrical performance of the linear array; (5d) Calculate the adjustment amount of excitation current amplitude and phase, the excitation current I _ins including structural error is: <mrow><msub><mi>I</mi><mrow><mi>i</mi><mi>n</mi><mi>s</mi></mrow></msub><mo>=</mo><msup><mi>FFT</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>&amp;lsqb;</mo><msub><mi>&amp;alpha;</mi><mi>m</mi></msub><mo>+</mo><mi>j</mi><mrow><mo>(</mo><msub><mi>u</mi><mi>m</mi></msub><mo>&amp;CenterDot;</mo><msub><mi>&amp;beta;</mi><mi>m</mi></msub><mo>+</mo><msqrt><mrow><mn>1</mn><mo>-</mo><msup><msub><mi>u</mi><mi>m</mi></msub><mn>2</mn></msup></mrow></msqrt><mo>&amp;CenterDot;</mo><msub><mi>&amp;gamma;</mi><mi>m</mi></msub><mo>)</mo></mrow><mo>&amp;rsqb;</mo></mrow> The relationship between this current and the excitation current I _in of the ideal linear array electrical performance is as follows: in, Represents the amplitude disturbance coefficient caused by structural errors in the excitation current of the deformed linear array antenna, and Re represents the real part of the imaginary number; Indicates the phase disturbance caused by structural errors in the excitation current of the deformed linear array antenna, and Im represents the imaginary part of the imaginary number; (5e) The excitation current amplitude disturbance coefficient ΔA _in and phase disturbance caused by the structural deformation of the linear array antenna Make corrections to compensate for the influence of structural deformation on the electrical performance of the linear array antenna; introduce the amplitude coefficient adjustment amount of the excitation current ΔA _inc = -ΔA _in , the phase adjustment amount of the excitation current Then the adjusted excitation current becomes: Using the adjusted excitation current I _inc to replace the excitation current I _in of the ideal linear array electrical performance in the deformed linear array antenna array factor f _ias (θ), the electrical performance of the deformed linear array antenna after compensation can be obtained as: In the formula, Indicates the amplitude system adjustment of the excitation current; Indicates the adjustment amount of the phase of the excitation current. 6. the deformed area array antenna electrical performance compensation method based on electromechanical coupling and Fourier transform according to claim 1, is characterized in that, in step (7), the M line array antennas obtained, i.e. all the area The adjustment amount of excitation current amplitude and phase of the array antenna is brought into the electromechanical coupling model of the area array antenna, which is: 7. the deformable area array antenna electrical performance compensation method based on electromechanical coupling and Fourier transform according to claim 1, is characterized in that, in step (7), calculates the deformed linear array antenna electrical performance after compensation, obtains comprising Antenna gain, sidelobe level and beam pointing antenna electrical performance parameters. 8. The deformed area array antenna electrical performance compensation method based on electromechanical coupling and Fourier transform according to claim 1, characterized in that, in step (8), modifying the structural parameters of the area array antenna includes enhancing the area array antenna Structural stiffness, modified area array antenna constraint location.