Reflector antenna electrical performance rapid calculation method considering structure uncertainty effect

Abstract

The invention discloses a reflector antenna electrical performance rapid calculation method considering a structural uncertainty effect, and the method comprises the steps: respectively obtaining uncertainty intervals of a feed source position, a feed source direction and an antenna surface structure error according to the structural deformation of a reflector antenna; establishing a reflector antenna structure uncertainty electromechanical coupling model, and dividing an antenna aperture surface; determining the phase error and the axial error of the panel under the influence of the surface error of the aperture surface shape of the divided antenna, and obtaining a surface error average power directional diagram function; and calculating the upper and lower exact boundaries of the uncertainty interval and the phase error interval quantity to obtain an interval average power pattern function, the upper and lower exact boundaries of the antenna power pattern interval and the upper and lower exact boundaries of the antenna aperture phase and the amplitude error interval, and obtaining the reflector antenna electrical performance considering the structure uncertainty effect. According to the method, multi-source uncertainty factors of the antenna can be associated with the electrical performance, and the electrical performance of the reflector antenna under the condition of uncertainty of three errors can be quickly and effectively calculated.

Description

Technical Field

[0001] The present invention belongs to the field of radar antennas, and is particularly a method for quickly calculating the electrical performance of a reflector antenna taking into account the effect of structural uncertainty, and can quickly realize the calculation of the electrical performance of a reflector antenna under the influence of structural uncertainty. Background Art

[0002] There is a strong coupling relationship between the electrical performance of the antenna and its mechanical structure, and the antenna performance is very sensitive to the structural accuracy. However, the complex service environment in the project and factors such as structural machining and installation errors will bring certain uncertainties to the antenna, resulting in the final performance of the antenna failing to meet the expected design goals and results. Therefore, it is necessary to analyze and quantify the impact of these uncertain factors.

[0003] At the beginning of the 21st century, Song Zhenhua applied the interval analysis method to the reflector antenna for the first time, and used the interval factor method to analyze the stress and dynamic characteristics of the antenna structure; Zhu Zengqing and Chen Jianjun proposed a random-interval hybrid finite element analysis method for antenna structure, which used discrete interval variables to calculate the upper and lower bounds of the stress response of the antenna back frame structure; Xu Xiaofeng used the interval matrix perturbation method to solve the interval finite element equation of the reflector antenna structure, and used the interval truncation method to obtain the interval value of the antenna surface deformation, and finally analyzed the far-field radiation pattern of the reflector antenna under the influence of the error interval.

[0004] However, existing research on antenna uncertainty factors mainly focuses on the impact of analytical errors on antenna performance, and has not deeply explored the impact mechanism of uncertainty factors, nor has it established a suitable electromechanical thermal coupling model of uncertainty factors and realized the rapid calculation of the electrical performance of reflector antennas under the influence of structural uncertainty. This makes it impossible to design antennas based on the changes in electrical performance under the actual service environment of the antenna, and it is necessary to simulate the performance of multiple aspects of the antenna in multiple simulation software, resulting in cumbersome antenna design steps that consider the impact of structural uncertainty on electrical performance, large amount of calculation, and low efficiency, which is not conducive to the development of antenna design work. Summary of the invention

[0005] In order to solve the above-mentioned defects existing in the prior art, the purpose of the present invention is to take the reflector antenna as the research object. The influence of structural uncertainty factors on the feed source and the main reflector shape of the reflector antenna will first be reflected in the structural deformation, and then affect the electrical performance. The interval expansion of the coupling model is carried out, and the aperture amplitude and phase changes caused by the uncertainty factors are combined with the ideal radiation pattern function, so that the multi-source uncertainty factors of the reflector antenna are linked to the electrical performance, thereby realizing the calculation of the uncertainty factors to the final performance.

[0006] The present invention is achieved through the following technical solutions.

[0007] In one aspect of the present invention, a method for quickly calculating the electrical performance of a reflector antenna taking into account the effect of structural uncertainty is provided, comprising the following steps:

[0008] According to the deformation of the reflector antenna structure, the uncertainty intervals of the feed position, feed pointing and antenna surface structure error are obtained respectively;

[0009] Based on the uncertainty interval of structural error, the electromechanical coupling model of reflector antenna structure uncertainty is established, and the impact of structural error on the electromechanical coupling model is analyzed;

[0010] The antenna aperture plane is divided based on the aperture field method;

[0011] Determine the phase error of the panel under the influence of the antenna aperture surface shape error after division, extract the axial error in the shape error, and obtain the antenna average power pattern function under the influence of the shape error;

[0012] The axial error is expanded into an uncertainty error, represented by interval quantity parameters, and the upper and lower bounds of the uncertainty interval are calculated;

[0013] Based on the surface axial error interval quantity, the phase error interval quantity and the interval average power pattern function are calculated;

[0014] According to the interval phase error and the interval average power pattern function, the upper and lower bounds of the interval average power pattern function under the influence of the uncertainty of the shape error are calculated;

[0015] Calculate the upper and lower bounds of the antenna aperture plane phase error interval caused by the feed position uncertainty error and the upper and lower bounds of the antenna aperture plane amplitude error interval caused by the feed pointing uncertainty error respectively;

[0016] According to the upper and lower bounds of the antenna power pattern interval and the upper and lower bounds of the aperture plane phase and amplitude error interval, the electrical performance of the reflector antenna considering the effect of structural uncertainty is obtained.

[0017] Preferably, the uncertainty intervals of the feed position, feed pointing and antenna surface structure errors include:

[0018] According to the optical path difference caused by the change in the feed position when the reflector antenna undergoes structural deformation, the aperture surface phase error caused by the optical path difference is obtained; and the uncertainty interval of the feed position is determined;

[0019] Based on the change of feed pointing before and after the error and its influence on the amplitude term of the reflector antenna, the uncertainty of feed pointing error feed pointing error interval is obtained;

[0020] According to the aperture surface optical path difference caused by the deformation of the reflector antenna array, which causes the aperture surface phase error, the uncertainty interval of the antenna surface structure error is determined.

[0021] Preferably, the average power pattern function of the antenna under the influence of the surface error is calculated, including:

[0022] Based on the aperture surface phase error caused by the deformation of the nth ring and the mth panel under the influence of the shape error, the main influencing factor of the aperture surface phase error, the axial error, is obtained;

[0023] According to the ideal reflector pattern function of the reflector antenna after the aperture surface is divided into rings and blocks, the reflector antenna function when the shape error exists is determined;

[0024] Get the antenna power pattern function under the influence of shape error;

[0025] The root mean square error in the power pattern function under the influence of the shape and surface error is substituted into the antenna power pattern function under the influence of the shape and surface error to obtain the average power pattern function under the influence of the shape and surface error.

[0026] Preferably, the interval phase error caused by the axial error interval of the n-th ring panel is calculated according to the root mean square of the axial error interval on the n-th ring panel;

[0027] Substitute the interval phase error into the average power pattern function to calculate the interval average power pattern function.

[0028] The present invention adopts the above technical solution, which has the following beneficial effects:

[0029] 1. The present invention aims at reflector antennas, performs coupling range expansion modeling based on their structural uncertainty factors, and proposes a fast calculation method for the electrical performance of reflector antennas taking into account the effect of structural uncertainty, thereby achieving a fast and accurate analysis of the impact of uncertainty factors on the electrical performance of reflector antennas, improving the efficiency of targeted regulation of antenna performance, and providing favorable conditions for stable observation of radio telescope antennas.

[0030] 2. The present invention is a method for quickly calculating electrical performance that takes into account the uncertainty of feed position, feed pointing and antenna shape, which is more in line with engineering practice, ensures the accuracy of electrical performance calculation results and improves the design efficiency of reflector antennas. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The drawings described herein are used to provide a further understanding of the present invention, constitute a part of the present application, and do not constitute an improper limitation of the present invention. In the drawings:

[0032] Figure 1 It is a flow chart of a method for quickly calculating the electrical performance of a reflector antenna taking into account the effect of structural uncertainty of the present invention;

[0033] Figure 2It is a schematic diagram of the error range of the reflector antenna feed position;

[0034] Figure 3 It is a schematic diagram of the pointing error range of the reflector antenna feed;

[0035] Figure 4 It is a schematic diagram of the error range of the main reflector of the reflector antenna;

[0036] Figure 5 It is a local magnified diagram of the error of the main reflector surface of the reflector antenna;

[0037] Figure 6 This is a schematic diagram of the aperture surface panel being divided into blocks. DETAILED DESCRIPTION

[0038] The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments. The exemplary embodiments and descriptions of the present invention are used to explain the present invention but are not intended to limit the present invention.

[0039] Reference Figure 1 The present invention provides a method for quickly calculating the electrical performance of a reflector antenna taking into account the effect of structural uncertainty. The specific steps are as follows:

[0040] Step 1: According to the deformation of the reflector antenna structure, the uncertainty intervals of the three structural errors of feed position, feed pointing and antenna shape are obtained respectively.

[0041] 1.1. The aperture phase error of the reflector antenna is mainly caused by the optical path difference. When the reflector antenna is deformed, the feed position will change, causing the optical path difference. Assume that the feed position error is Then the optical path difference caused by the feed position error is

[0042]

[0043] The aperture plane phase error caused by this optical path difference is

[0044]

[0045] refer to Figure 1 , where is the distance from the feed source to the reflecting surface on the aperture plane; for The unit direction vector of is the distance from the feed source to the reflecting surface on the aperture plane; It is the displacement of antenna structure caused by various uncertain factors of antenna. are the structural design variables of the antenna, including the size, shape, type, etc. of the structure; T is the temperature field to which the antenna is subjected; γ is the wind load to which the antenna is subjected; ζ is other uncertain loads such as snow accumulation; and k is the wave constant.

[0046] Generally, when the feed source displacement is small, it is believed that the effect of the displacement on the amplitude of the aperture surface can be ignored, and it only affects the phase of the aperture surface.

[0047] Based on the influence of feed position error on antenna electrical performance, the uncertainty of feed position error is expressed as interval quantity: In the formula, is the supremum of the interval expression of the uncertainty of the feed position error, is the lower bound.

[0048] 1.2. Different from the effect of feed position error on aperture phase, feed pointing error mainly affects the amplitude term of the antenna pattern.

[0049] refer to Figure 3 , assuming that the pointing error of the feed source in the ξ direction is Ξ, and the pointing error in the φ′ direction is the interval quantity Φ, then from the geometric relationship, it can be seen that the actual pointing direction of the feed source is

[0050]

[0051]

[0052] refer to Figure 3 , where ξ and φ′ are the ideal pointing directions of the feed source, ξ′ and φ″ are the actual pointing directions of the feed source after the error occurs; Ξ is the pointing error of the feed source in the ξ direction; Φ is the pointing error of the feed source in the φ′ direction.

[0053] When the feed pointing range is small, the feed pointing error mainly affects the change of the feed primary radiation pattern, and mainly affects the amplitude term of the antenna radiation pattern.

[0054] Based on the change of feed source pointing before and after the error and its influence on the amplitude term of the reflector antenna, the feed source pointing error parameter expressed as an interval quantity is obtained as Ξ=[Ξ inf ,Ξ sup ]Φ=[Φ inf ,Φ sup ].

[0055] In the formula, inf is the supremum of the interval expression of the uncertainty of the pointing error of the feed in the ξ direction, Ξ sup is the lower bound; similarly, Φ inf is the supremum of the interval expression of the uncertainty of the pointing error of the feed in the φ′ direction, Φ sup is the lower bound.

[0056] 1.3. Similar to the feed position error, the deformation of the reflector antenna array mainly causes the aperture optical path difference and thus the aperture phase error. Let the deformation of the main reflector be expressed as It represents the deformation of the main reflective surface. Under the influence of the deformation of the main reflective surface, the optical path difference of the aperture surface caused is

[0057]

[0058] In the formula, S represents the optical path difference of the aperture surface; Indicates the deformation of the main reflective surface; reference Figure 4 , Figure 5 , ξ is the feed observation angle.

[0059] The aperture phase error caused by this optical path difference is

[0060]

[0061] In summary, based on the calculation of the aperture phase error, the deformation parameter of the reflector antenna array with uncertainty expressed in intervals is obtained: In the formula, is the supremum of the interval expression of the uncertainty of the reflector antenna array deformation, is the lower bound.

[0062] Step 2: Based on the uncertainty interval of the structural error, an electromechanical coupling model of the reflector antenna structure uncertainty is established to analyze the impact of the structural error on the electromechanical coupling model.

[0063] The uncertainty of the feed position will affect the phase term of the ideal pattern, the uncertainty of the feed pointing will affect the amplitude term of the ideal pattern, and the uncertainty of the main reflector shape will affect the phase term of the ideal pattern. Based on the superposition of the spatial phase of electromagnetic waves, the coupling model of the multi-source uncertainty factors of the electromechanical and thermal reflector antenna can be obtained as follows:

[0064]

[0065] In the formula, It is the feed pattern under feed pointing uncertainty caused by multi-source uncertainty factors of the reflector antenna, which mainly affects the aperture amplitude term; and They are the aperture phase influence items caused by the uncertainty of the feed position and the uncertainty of the main reflector shape; r0 is the distance from the feed to the reflector on the aperture plane; reference Figure 2 , ρ′ is the distance from the point on the aperture plane where the electromagnetic wave radiated by the feed source returns to the feed source after being reflected by the reflecting surface; θ represents the angle between the far-field observation direction and the z-axis; φ represents the angle between the far-field observation direction and the z-axis; j is an imaginary unit.

[0066] Step 3: divide the antenna aperture plane based on the aperture field method.

[0067] refer to Figure 6 , divide the antenna aperture into N rings, each ring is divided into M n By projecting the division scheme onto the reflection surface, the influence of the surface uncertainty of each small panel on the aperture surface phase term can be calculated.

[0068] Step 4, determine the phase error of the nth ring panel under the influence of the antenna aperture surface shape error after division, extract the axial error, the main influencing factor in the shape error, and further calculate the antenna average power pattern function under the influence of the shape error.

[0069] 4.1. Under the influence of the shape error, the aperture phase error δ caused by the deformation of the nth ring and the mth panel n,m for:

[0070] δ n,m =2kε n,m cos 2 ξ n,m

[0071]

[0072] refer to Figure 4 , where ξ n,m represents the observation angle of the feed source of the nth ring and the mth panel; ε n,m It represents the axial error caused by the deformation of the mth panel of the nth ring; F is the distance from the center of the aperture surface to the symmetry center of the reflection surface.

[0073] Based on the aperture surface phase error expression, the axial error, the main influencing factor of the aperture surface phase error, can be extracted.

[0074] 4.2. After the aperture plane is divided into rings and blocks, the ideal reflector pattern function of the reflector antenna can be expressed as

[0075]

[0076] Where N is the maximum number of rings; M n Indicates the maximum number of blocks; E n,m It represents the far-field pattern of the nth ring and the mth aperture.

[0077]

[0078] In the formula, φ′ m,n represents the angle between the mth block, the nth ring and the x-axis; r n Represents the radius of the nth ring.

[0079] Then the ideal power pattern function of the antenna can be expressed as

[0080]

[0081] In the formula, E * E represents the conjugate expression of the aperture face to the far-field pattern; n,i Indicates the far-field pattern of the nth ring and the ith aperture; M m Indicates the maximum number of blocks in the mth ring; It represents the conjugate expression of the far-field pattern of the mth ring and the lth block aperture; m, n represent the number of rings, i, l represent the number of blocks.

[0082] When there is a shape error, the reflector antenna pattern function becomes

[0083]

[0084] In the formula, δ n,m It represents the aperture surface phase error caused by the axial error brought about by the deformation of the nth ring and the mth panel.

[0085] Then the antenna power pattern function under the influence of the shape error becomes

[0086]

[0087] In the formula, δ n,i represents the aperture phase error caused by the deformation of the nth ring and the ith panel; δ m,l represents the aperture phase error caused by the deformation of the mth ring and the lth panel; exp j[δ n,i -δ m,l ] represents the influence coefficient of aperture plane phase error on the radiation pattern function.

[0088] 4.3. Assume that the phase errors on each small panel are independent of each other, and satisfy the mean of 0 and the variance of σ n,m When the Gaussian distribution is , the influence coefficient of the aperture phase error on the power pattern function under the influence of the shape error exp j[δ n,i -δ m,l The mean of ] can be expressed as

[0089]

[0090] In the formula, σ n and σ m They represent the phase root mean square error on the nth loop and the mth loop respectively, which can be calculated by the following formula

[0091]

[0092]

[0093] In the formula, ε n,i represents the axial error on the ith panel of the nth ring; ξ n is the feed observation angle of the nth ring panel; ε n(rms) represents the root mean square average of the axial error on the nth ring panel; ε m,l represents the aperture phase error caused by the deformation of the mth ring and the lth panel; ξ m is the feed observation angle of the mth ring panel; ε m(rms) It represents the RMS average value of the axial error on the mth ring panel.

[0094] 4.4. The influence coefficient of aperture plane phase error on the pattern function exp j[δ n,i -δ m,l ] is substituted into the antenna power pattern function under the influence of the surface error obtained in step 4.2, then the average power pattern function under the influence of the surface error is

[0095]

[0096]

[0097] In the formula, E n,n-1 It indicates the far-field pattern of the n-th ring and the n-1-th aperture; represents the conjugate expression of the far-field pattern of the m-th ring and the m-1th aperture; r n Represents the distance from the nth ring to the center.

[0098] Step 5: Expand the axial error into uncertainty error, express it with interval quantity parameters, and calculate the upper and lower bounds of the uncertainty interval.

[0099] When the axial error of the reflective surface is expressed as an interval quantity, let the axial error interval on the nth ring and the mth panel be

[0100] Then the RMS of the axial error interval on the nth ring panel is

[0101]

[0102] In the formula, is the interval expression for the uncertainty of the root mean square of the axial error on the nth ring panel; They represent the upper and lower bounds of the uncertainty interval of the axial error of the nth ring and the i-th panel respectively; They are respectively the upper and lower bounds of the interval expression of the uncertainty of the root mean square of the axial error on the nth ring panel.

[0103] Taking the ideal surface as the reference, assuming that the axial error of the convex part of the surface is positive and the axial error of the concave part is negative. In particular, according to the calculation criteria of the interval number, the upper and lower bounds of the interval expression of the axial error uncertainty are calculated as There are three possible results:

[0104] when Sometimes, there is

[0105]

[0106] Right now

[0107]

[0108] when Sometimes, there is

[0109]

[0110] Right now

[0111]

[0112] when Sometimes, there is

[0113]

[0114] Right now

[0115]

[0116] In the formula, They are the upper and lower bounds of the uncertainty interval of the axial error caused by the deformation of the nth ring and the i-th panel, respectively; They are respectively the upper and lower bounds of the interval expression of the axial error uncertainty of the ith block of the nth ring.

[0117] In summary, the upper and lower bounds of the interval expression of the axial error uncertainty in different situations can be obtained.

[0118] Step 6, based on the surface axial error interval, calculate the phase error interval; and combine the average power pattern function in step 4 to obtain the interval average power pattern function.

[0119] 6.1. Using the axial error interval RMS obtained in step 5, calculate the interval phase error caused by the axial error interval of the n-ring panel:

[0120]

[0121] In the formula, They represent the upper and lower bounds of the interval phase error caused by the axial error interval of the n-ring panel respectively; ξ is the feed observation angle of the panel; are the upper and lower bounds of the interval expression of the uncertainty of the root mean square of the axial error on the nth ring panel; λ is the antenna wavelength.

[0122] 6.2. Substitute the interval phase error into the average power pattern function in step 4, and calculate the interval average power pattern function as

[0123]

[0124] In the formula, represents the average power pattern function under the influence of surface error; P inf , P sup are the upper and lower bounds of the interval average power pattern respectively; It represents the sum of squares of phase errors caused by the axial error interval of the n-ring and m-ring panels.

[0125] And order

[0126]

[0127] Then the interval average power pattern function is simplified to:

[0128]

[0129] In the formula, express The simplified form of express The simplified form of .

[0130] Step 7, combining the interval phase error and the interval average power pattern function, calculate the upper and lower bounds of the interval average power pattern under the influence of the uncertainty of the surface error. When the interval power pattern is inf and the supremum P sup for

[0131]

[0132] when When the interval power pattern is inf and the supremum P sup for

[0133]

[0134] In the formula, It represents the conjugate expression of the far-field pattern of the m-th ring and the m-1-th aperture face; N represents the maximum number of rings; The conjugate expression for the far-field pattern of the n-th ring and the n-1-th aperture face; express The simplified form of express The simplified form of .

[0135] Step 8, calculate the upper and lower bounds of the antenna aperture phase error interval caused by the feed position uncertainty error.

[0136] The upper and lower bounds of the aperture phase error interval caused by the feed position uncertainty error obtained in step 1 are extended and calculated, that is, When , the upper and lower bounds of the aperture phase error are

[0137]

[0138] In the formula, represents the aperture plane phase error interval; They represent the upper and lower bounds of the uncertainty interval of the aperture plane phase error respectively; They represent the upper and lower bounds of the uncertainty interval of the feed position error respectively.

[0139] By calculating the interval number, we can get

[0140]

[0141]

[0142] In the formula, and yes The direction cosines of yes The unit direction vector, k = 2π / λ is the wave constant, and λ is the wavelength of the electromagnetic wave.

[0143] Step 9, calculate the upper and lower bounds of the antenna aperture plane amplitude error range caused by the feed source pointing uncertainty error.

[0144] Expand the calculation step 1 to find the upper and lower bounds of the aperture amplitude error interval caused by the feed pointing uncertainty error, that is,

[0145]

[0146] In the formula, E0′ represents the aperture amplitude error interval; Indicates the upper bound of the aperture amplitude error interval; the lower bound of the aperture amplitude error interval; reference Figure 3 , ξ and φ′ are the ideal pointing directions of the feed source; inf is the supremum of the pointing error interval of the feed in the ξ direction; sup is the infimum of the pointing error interval of the feed source in the ξ direction; Φ is the pointing error of the feed source in the φ′ direction.

[0147] Step 10, combining the upper and lower bounds of the antenna power pattern interval with the upper and lower bounds of the aperture plane phase and amplitude error interval to obtain the electrical performance of the reflector antenna taking into account the effect of structural uncertainty.

[0148] 10.1. Based on the analysis of step 2, the uncertainty of feed position brings about two aperture phase errors, and the uncertainty of feed pointing brings about two aperture amplitude errors. Then the contribution of the nth ring aperture to the far-field pattern will become

[0149]

[0150] Right now

[0151]

[0152] Where η(ρ′,φ′) is the distribution coefficient related to ρ′ and φ′, which can be obtained based on the simulation statistical data of the antenna feed.

[0153] 10.2. The upper and lower bounds of the antenna power pattern under the influence of the uncertainty of the surface error calculated in step 7 are combined; substituting the upper and lower bounds of the aperture surface phase error interval calculated in step 8 and the upper and lower bounds of the aperture surface amplitude error interval obtained in step 9, the fast calculation formula for the electrical performance of the reflector antenna considering the effect of structural uncertainty can be obtained:

[0154] when hour

[0155]

[0156] when hour

[0157]

[0158] In the formula, It represents the supremum of the interval of the far-field pattern of the n-th ring and the n-1-th aperture face; It represents the infimum of the interval of the far-field pattern of the n-th ring and the n-1-th aperture face; It represents the interval supremum of the conjugate expression of the m-th ring and the m-1-th aperture face to the far-field pattern; It represents the infimum of the conjugate expression of the m-th ring and the m-1-th aperture face to the far-field pattern; It represents the interval supremum of the conjugate expression of the nth ring and the n-1th aperture face to the far-field pattern; It represents the infimum of the conjugate expression interval of the far-field pattern of the n-th ring and the n-1-th aperture face.

[0159] The obtained fast calculation formula for the electrical performance of the reflector antenna considering the effect of structural uncertainty can link the multi-source uncertainty factors of the reflector antenna with the electrical performance, and quickly and effectively calculate the electrical performance of the reflector antenna considering the uncertainty of the three key errors of array element position, array element pointing and surface error. Based on this fast calculation formula, the antenna is further analyzed for efficient performance.

[0160] The present invention is not limited to the above-mentioned embodiments. On the basis of the technical solution disclosed in the present invention, technicians in this field can make some substitutions and deformations to some technical features therein according to the disclosed technical content without creative labor, and these substitutions and deformations are all within the protection scope of the present invention.

Claims

1. A method for quickly calculating the electrical performance of a reflector antenna taking into account the effect of structural uncertainty, characterized in that: The following steps are involved: According to the deformation of the reflector antenna structure, the uncertainty intervals of the feed position, feed pointing and antenna surface structure error are obtained respectively; Based on the uncertainty interval of structural error, the electromechanical coupling model of reflector antenna structure uncertainty is established, and the impact of structural error on the electromechanical coupling model is analyzed; The antenna aperture plane is divided based on the aperture field method; Determine the phase error of the panel under the influence of the antenna aperture surface shape error after division, extract the axial error in the shape error, and obtain the antenna average power pattern function under the influence of the shape error; The axial error is expanded into an uncertainty error, represented by interval quantity parameters, and the upper and lower bounds of the uncertainty interval are calculated; Based on the surface axial error interval quantity, the phase error interval quantity and the interval average power pattern function are calculated; According to the interval phase error and the interval average power pattern function, the upper and lower bounds of the interval average power pattern function under the influence of the uncertainty of the shape error are calculated; Calculate the upper and lower bounds of the antenna aperture plane phase error interval caused by the feed position uncertainty error and the upper and lower bounds of the antenna aperture plane amplitude error interval caused by the feed pointing uncertainty error respectively; According to the upper and lower bounds of the antenna power pattern interval and the upper and lower bounds of the aperture plane phase and amplitude error interval, the electrical performance of the reflector antenna considering the effect of structural uncertainty is obtained.

2. The method for rapid calculation of electrical performance of reflector antenna considering structural uncertainty according to claim 1 is characterized in that: The uncertainty range of feed position, feed pointing and antenna surface structure error includes: According to the optical path difference caused by the change in the feed position when the reflector antenna undergoes structural deformation, the aperture surface phase error caused by the optical path difference is obtained; and the uncertainty interval of the feed position is determined; Based on the change of feed pointing before and after the error and its influence on the amplitude term of the reflector antenna, the uncertainty of feed pointing error feed pointing error interval is obtained; According to the aperture surface optical path difference caused by the deformation of the reflector antenna array, which causes the aperture surface phase error, the uncertainty interval of the antenna surface structure error is determined.

3. The method for rapid calculation of electrical performance of reflector antenna considering structural uncertainty according to claim 1 is characterized in that: The uncertain electromechanical coupling model of the reflector antenna structure is: In the formula, It is the feed pattern under the uncertainty of feed pointing caused by the multi-source uncertainty factors of the reflector antenna. and They are the aperture phase influence terms caused by the uncertainty of the feed position and the uncertainty of the main reflecting surface shape; k is the wave constant; j is the imaginary unit; r0 is the distance from the feed to the reflecting surface on the aperture surface; ρ′ is the distance from the point on the aperture surface where the electromagnetic wave radiated by the feed returns to the feed after being reflected by the reflecting surface; θ represents the angle between the far-field observation direction and the z-axis; φ represents the angle between the far-field observation direction and the z-axis.

4. The method for rapid calculation of electrical performance of reflector antenna considering structural uncertainty according to claim 1 is characterized in that: The average power pattern function of the antenna under the influence of the surface error is calculated, including: Based on the aperture surface phase error caused by the deformation of the nth ring and the mth panel under the influence of the shape error, the main influencing factor of the aperture surface phase error, the axial error, is obtained; According to the ideal reflector pattern function of the reflector antenna after the aperture surface is divided into rings and blocks, the reflector antenna function when there is a surface error is determined to be In the formula, E n，m Indicates the far-field pattern of the nth ring and the mth aperture; N indicates the maximum number of rings; M n Indicates the maximum number of blocks in the nth ring; j is an imaginary unit; δ n，m It represents the aperture surface phase error caused by the deformation of the nth ring and the mth panel; The antenna power pattern function under the influence of surface error is obtained: In the formula, E ＊ E represents the conjugate expression of the aperture face to the far-field pattern; n，i Indicates the far-field pattern of the nth ring and the ith aperture; M m Indicates the maximum number of blocks in the mth ring; The conjugate expression of the far-field pattern of the mth ring and the lth aperture face; δ n，i represents the aperture phase error caused by the deformation of the nth ring and the ith panel; δ m，l It represents the aperture surface phase error caused by the deformation of the mth ring and the lth panel; Substitute the root mean square error in the power pattern function under the influence of the shape and surface error into the antenna power pattern function under the influence of the shape and surface error to obtain the average power pattern function under the influence of the shape and surface error: In the formula, E n，n-1 It represents the far-field pattern function of the n-th ring and the n-1-th aperture face; The conjugate expression for the far-field pattern of the n-th ring and the n-1-th aperture face; It represents the conjugate expression of the far-field pattern of the m-th ring and the m-1-th aperture plane; Q(ρ′) is the amplitude distribution on the aperture plane; represents the phase root mean square error between the nth ring and the mth ring; φ′ represents the angle between the actual far-field observation direction and the z-axis; r n represents the distance from the nth ring to the center; k is the wave constant; ρ′ is the distance from the point on the aperture plane where the electromagnetic wave radiated by the feed source is reflected by the reflecting surface to the feed source; θ represents the angle between the far-field observation direction and the z-axis; φ represents the angle between the far-field observation direction and the z-axis.

5. The method for rapid calculation of electrical performance of reflector antenna considering structural uncertainty according to claim 1 is characterized in that: The uncertainty interval upper and lower bounds are expressed and calculated using interval quantity parameters. The axial error interval root mean square on the nth ring panel is: In the formula, is the interval expression for the uncertainty of the root mean square of the axial error on the nth ring panel; They represent the upper and lower bounds of the uncertainty interval of the axial error of the nth ring and the i-th panel respectively; are the upper and lower bounds of the interval expression of the uncertainty of the root mean square of the axial error on the nth ring panel; M n Indicates the maximum number of blocks in the nth ring; i indicates the i-th panel.

6. The method for rapid calculation of electrical performance of reflector antenna considering structural uncertainty according to claim 5 is characterized in that: According to the calculation criteria of interval number, the upper and lower bounds of the interval expression of axial error uncertainty are calculated The results include: when Sometimes, there are Right now when Sometimes, there are Right now when Sometimes, there are Right now In the formula, are the upper and lower bounds of the uncertainty interval of the axial error caused by the deformation of the nth ring and the ith panel respectively; E n，i Represents the far-field radiation pattern of the nth ring and the i-th aperture.

7. The method for rapid calculation of electrical performance of reflector antenna considering structural uncertainty according to claim 1 is characterized in that: Based on the surface axial error interval, the phase error interval and the interval average power pattern are calculated, including: According to the axial error interval RMS on the nth ring panel The interval phase error caused by the axial error interval of the n-ring panel is calculated as follows: In the formula, They represent the upper and lower bounds of the interval phase error caused by the axial error interval of the n-ring panel respectively; ξ is the feed observation angle of the panel; are the upper and lower bounds of the interval expression of the uncertainty of the root mean square of the axial error on the nth ring panel, respectively; λ is the antenna wavelength; Substituting the interval phase error into the average power pattern function, the interval average power pattern function is calculated as: Where P inf , P sup are the upper and lower bounds of the interval average power pattern respectively; represents the square sum of the phase errors caused by the axial error interval of the n-ring and m-ring panels; E n，n-1 It indicates the far-field pattern of the n-th ring and the n-1-th aperture; The conjugate expression for the far-field pattern of the n-th ring and the n-1-th aperture face; It represents the conjugate expression of the far-field pattern of the m-1-th aperture face of the m-th ring; N represents the maximum number of rings.

8. The method for rapid calculation of electrical performance of reflector antennas considering structural uncertainty according to claim 7 is characterized in that: The upper and lower bounds of the interval average power pattern under the influence of the uncertainty of the shape error include: when When the interval power pattern is inf and the supremum P sup for when When the interval power pattern is inf and the supremum P sup for In the formula, express The simplified form of express The simplified form of .

9. The method for rapid calculation of electrical performance of reflector antenna considering structural uncertainty according to claim 1, characterized in that: The upper and lower bounds of the antenna aperture phase error interval caused by the uncertainty error of the feed position are calculated as: Where, Φ represents the aperture phase error interval; They represent the upper and lower bounds of the uncertainty interval of the aperture plane phase error respectively; They represent the upper and lower bounds of the uncertainty interval of the feed position error respectively; k is the wave constant; yes The unit direction vector of is the distance from the feed source to the reflecting surface on the aperture plane; The upper and lower bounds of the antenna aperture amplitude error range caused by the uncertainty error of the feed pointing are calculated as follows: In the formula, E′0 represents the aperture amplitude error interval; They represent the upper and lower bounds of the aperture amplitude error interval respectively; ξ and φ′ are the ideal pointing directions of the feed source; Ξ inf ,Ξ sup are the upper and lower bounds of the pointing error interval of the feed in the ξ direction; φ is the pointing error of the feed in the φ′ direction.

10. The method for rapid calculation of electrical performance of reflector antenna considering structural uncertainty according to claim 8, characterized in that: The electrical performance of the reflector antenna considering the structural uncertainty is: when hour when hour In the formula, They represent the upper and lower bounds of the interval of the far-field pattern of the n-th ring and the n-1-th aperture face respectively; They represent the upper and lower bounds of the conjugate expression interval representing the far-field directivity pattern of the m-th ring and the m-1-th aperture face respectively; They respectively represent the upper and lower bounds of the conjugate expression interval of the far-field radiation pattern of the n-th ring and the n-1-th aperture face.

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