A method for on-orbit thermal design of mesh antenna based on genetic algorithm

Abstract

The present invention belongs to the technical field of satellite-borne antennas, and relates to an on-orbit thermal design method for a mesh antenna based on a genetic algorithm. The present invention completes the on-orbit thermal design of a mesh antenna through twelve steps, including morphological design of a cable net structure, compilation of cable unit material type selection, establishment of a finite element model of a cable net structure, calculation of node displacement under the influence of temperature, calculation of the shape error of a reflective surface, judgment of whether the current temperature meets the termination condition, updating the current temperature, calculation of the maximum shape error value within the temperature range, judgment of whether the evolutionary generation meets the termination criterion, evolution of population individuals, interpretation of individuals with the minimum maximum shape error, and production of a cable net structure of a mesh antenna. The present invention utilizes the complementary characteristics between different materials, reasonably selects the material type of the cable unit in the cable net structure, reduces the sensitivity of the node displacement of the reflective surface in the cable net structure to the temperature change, improves the thermal stability of the cable net structure, and improves the shape accuracy within the temperature range.

Description

Technical Field

[0001] The invention belongs to the technical field of satellite-borne antennas, and in particular relates to an on-orbit thermal design method of a mesh antenna based on a genetic algorithm. Background Art

[0002] For a precision structure like a satellite antenna, maintaining the stability of the shape is the most important thing after completing the high-precision design. Generally speaking, the shape of the antenna should not change significantly with the change of external temperature. However, as the satellite moves, the satellite antenna will periodically receive thermal radiation from objects such as the sun and the earth, and often experience a large range of high and low temperature changes, and produce thermal stress and thermal deformation in the structure. Excessive thermal deformation will directly affect the electrical performance of the antenna. Relevant data show that the maximum thermal deformation of a 10m reflector antenna can reach 12mm, the root mean square error of the reflector can reach 3.8mm, and the antenna gain will be reduced by 1.5dB.

[0003] Therefore, in order to ensure that the mesh reflector antenna has high thermal stability, it is necessary to conduct thermal analysis on it in a space environment and carry out thermal control based on this. Summary of the invention

[0004] The present invention provides an on-orbit thermal design method for a mesh antenna based on a genetic algorithm, aiming to provide a method capable of solving the problem of decreased shape accuracy of the mesh antenna in a space thermal environment.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is:

[0006] A method for on-orbit thermal design of a mesh antenna based on a genetic algorithm comprises the following steps:

[0007] Step 1: Design the cable net structure

[0008] The shape of the cable net structure is obtained by the shape-finding method, and the node coordinates of the cable net structure at the reference temperature T0, the connection relationship of the cable unit, and the tension and length of the cable unit are obtained; between any two adjacent nodes in the cable net structure is a cable unit;

[0009] Step 2: Compile the cable element material type selection

[0010] Different materials are selected as the raw materials of the cable element. The rules for selecting raw materials are as follows:

[0011] Two materials are used to make the cable net structure of the mesh antenna. The elastic modulus, cross-sectional area, and thermal expansion coefficient of the first material are E (1) , A (1) , α (1)The elastic modulus, cross-sectional area, and thermal expansion coefficient of the second material are E (2) , A (2) , α (2) ; When a material is randomly selected to make the cable unit, for any cable unit k, its material property is expressed as

[0012]

[0013] in,

[0014]

[0015] Assume that the operating temperature range of the satellite antenna is T∈[T min ,T max ], the interval is divided into t working conditions with a step size of ΔT, that is, [T1, T2, …, T t ]; In order to reduce the influence of ambient temperature on the surface accuracy of the mesh antenna, the cable unit material type is used as the design variable, the cable unit tension is used as the constraint condition, and the maximum value of the corresponding surface error under all temperature conditions is used as the optimization target. The material topology optimization model is established as follows

[0016]

[0017] Where m is the total number of cable elements, RMS(T) is the surface error at ambient temperature T, and F k is the tension of the kth cable unit;

[0018] When selecting the material type of the cable unit of the cable net structure, when the kth cable unit selects the first material, β k =1, when the kth cable unit selects the second material, β k =0, therefore, a 0,1 string generated by the binary character set {0,1} is used to represent the candidate solution of the material topology optimization model; then, a genetic algorithm is used to solve the material topology optimization model; when solving, a population is first established, and each individual in the population represents a cable unit material selection method of a cable net structure, and each gene in the individual represents the type of material selected by the cable unit. When the kth cable unit selects the first material, the value on the kth gene position is 1, and when the kth cable unit selects the second material, the value on the kth gene position is 0;

[0019] In the genetic algorithm, a binary parameter vector with a number of individuals NP and a dimension of m for each individual is used as a population, where each individual is represented by

[0020] h i,g (i=1,2,…,NP) (4)

[0021] Among them, i represents the serial number of the individual in the corresponding population, and g represents the genetic generation;

[0022] The individuals of the population need to be initially encoded to establish an optimized search starting point; assuming that all initialized individuals of the population conform to random uniform distribution, the initial value of the i-th individual can be obtained by the following formula:

[0023] h i,0 =randint(1,m)(i=1,2,…,NP) (5)

[0024] Among them, randint(1,m) means randomly selecting integers between {0,1} to form a row vector of length m;

[0025] Step 3: Establish the finite element model of the cable net structure;

[0026] Step 4: Calculate the node displacement under the influence of temperature;

[0027] Step 5: Calculate the shape error of the reflecting surface;

[0028] Step 6: Determine whether the current temperature meets the termination condition

[0029] The current temperature value T reaches the upper limit T of the temperature range max As the termination condition of the inner loop, if the termination condition is met, the loop ends, the range of shape and surface error within the temperature range is output, and the next step is performed by going to step eight; otherwise, the loop goes to step seven and continues to calculate the shape and surface error under the next temperature condition;

[0030] Step 7: Update the current temperature

[0031] Update the current ambient temperature and go to step 4 to continue the calculation. The temperature update formula is:

[0032] T=T+ΔT (6)

[0033] The initial value of the ambient temperature T is set to T = T min , ΔT is the temperature increment;

[0034] Step 8: Calculate the maximum surface error value within the temperature range

[0035] For all individuals in the population, follow the operations from step 3 to step 7 to calculate the range of shape surface error within the temperature range, and obtain the maximum shape surface error value corresponding to all individuals in the population as

[0036] RMS max =[RMS max,1 RMS max,2 … RMS max,NP ] (7)

[0037] Among them, RMS max,i Indicates that the maximum surface error value in the temperature range corresponding to the i-th individual is

[0038] RMS max,i =max{RMS(T1) RMS(T2) … RMS(T t )} (8)

[0039] Step 9: Determine whether the evolutionary generation satisfies the termination criteria

[0040] The termination criterion of the outer loop is that the current evolutionary generation reaches the maximum generation of the genetic algorithm; if the termination criterion is met, go to step 11 and output the individual with the smallest current maximum shape error; otherwise, go to step 10 to perform genetic operations on the population and calculate the next generation;

[0041] Step 10: Evolution of population individuals;

[0042] Step 11: Decipher the individual with the smallest maximum shape error

[0043] Interpret the individual with the smallest maximum shape error to determine the raw materials to be selected;

[0044] Step 12: Make the cable net structure of the mesh antenna

[0045] According to the interpretation result of step 11, a cable net structure of the mesh antenna is made.

[0046] The finite element model of the cable net structure is established in the step three by using finite element analysis software; the node coordinates, the connection relationship of the cable unit, and the tension and length of the cable unit obtained in step one are substituted into the finite element analysis software, and for the i-th individual, that is, the material type selection method of the i-th cable unit, the finite element model of the cable net structure is established; wherein the material type of the i-th cable unit is selected one by one according to the coding in step two.

[0047] The method for calculating the node displacement under the influence of temperature in step 4 is: in the finite element analysis software, a temperature load T is applied to the finite element model of the cable net structure, and the displacement ΔR of the reflecting surface node under the influence of temperature is calculated, that is,

[0048] ΔR=[Δx Δy Δz] T (9)

[0049] Wherein, Δx represents the displacement of the reflection surface node in the X direction, Δy represents the displacement of the reflection surface node in the Y direction, and Δz represents the displacement of the reflection surface node in the Z direction.

[0050] The specific method for calculating the reflection surface shape error in step 5 is as follows:

[0051] The node coordinates R(T) of the reflection surface under the influence of ambient temperature T are:

[0052] R(T)=R0+ΔR (10)

[0053] Where R0 represents the coordinate vector of the reflection surface node at the reference temperature T0, that is,

[0054] R0=[x0 y0 z0] T (11)

[0055] Wherein, x0 represents the displacement of the reflection surface node in the X direction at the reference temperature T0, y0 represents the displacement of the reflection surface node in the Y direction at the reference temperature T0, and z0 represents the displacement of the reflection surface node in the Z direction at the reference temperature T0;

[0056] For the mesh reflector antenna, the node root mean square deviation between the deformed reflector and the ideal parabola is used to describe the shape error of the reflector. Therefore, the shape error RMS(T) of the mesh antenna under the influence of ambient temperature T is:

[0057]

[0058] Where n is the total number of reflection surface nodes, F p is the focal length of the ideal parabola, x r represents the displacement of the rth reflection surface node in the X direction under the influence of the current temperature T, y r represents the displacement of the rth reflection surface node in the Y direction under the influence of the current temperature T, z r Indicates the displacement of the rth reflection surface node in the Z direction under the influence of the current temperature T.

[0059] The evolution of all population individuals in step 10 is completed through selection operation, crossover operation and mutation operation.

[0060] The specific method of the selection operation is as follows: the proportion of each individual's fitness is used to determine the possibility of its offspring retention; if the fitness of the i-th individual is fit i , then the probability of it being selected is P si Expressed as

[0061]

[0062] Among them, the maximum surface error within the temperature range is used to describe the individual fitness fit i , after normalization,

[0063]

[0064] Among them, max(RMS max ) and min(RMS max ) represent the RMS max Take maximum and minimum operations;

[0065] The design goal is the shape error value. The smaller the maximum value of the shape error in the temperature range, the better the individual fitness is, and the greater the chance of being selected; vice versa. Each round generates a uniform random number r in [0,1] s , if P si <r s , then keep the current individual, otherwise discard it;

[0066] To ensure that the total number of the population remains unchanged, the above selection operation is performed for multiple rounds.

[0067] The specific method of the crossover operation is as follows:

[0068] The selected odd individuals h 2i-1,g and even individuals h 2i,g For each pair of individuals, the crossover probability P c Exchange some genes between them; the specific steps are: first, take out a pair of individuals to be mated; then, for the pair of individuals to be mated, randomly select an integer in [1,m] as the crossover point; finally, generate a random number r in the interval [0,1] c , and then according to the crossover probability P c Implement crossover operation, if r c <P c , the paired individuals exchange part of their genes at the crossover position, thus forming a new pair of individuals.

[0069] The specific method of the mutation operation is as follows:

[0070] For each individual in the crossover population, the mutation probability P m Change the gene values ​​at some loci to other allele values; the specific steps are: in the population after crossover, for the i-th individual, generate a random number r in the interval [0,1] m , and then randomly select an integer in [1,m] as the position of the mutant gene. If r m <P m , if the gene value on the selected variant gene is 1, its value becomes 0; if the gene value on the selected variant gene is 0, its value becomes 1.

[0071] The method for interpreting the individual with the smallest maximum shape error in step 11 is as follows: when the value on the kth gene position on the individual with the smallest maximum shape error is 1, it means that the kth root rope unit selects the first material; when the value on the kth gene position is 0, it means that the kth root rope unit selects the second material.

[0072] Beneficial effects:

[0073] The present invention establishes a material topology optimization model for a cable net structure and provides a solution strategy based on a genetic algorithm. First, the cable net structure is morphologically designed according to the shape-finding method, and the tension and length of each cable unit are calculated; secondly, the cable unit material type is compiled using a binary character set to generate an initial population in the genetic algorithm, and each individual in the population represents a cable unit material type selection method in the cable net structure; then, a finite element model of the cable net structure is established in the finite element analysis software, and a temperature load is applied to calculate the surface error variation range of the cable net reflection surface under the influence of temperature; then, it is determined whether the evolutionary generation of the genetic algorithm has been reached. If the maximum generation has been reached, and the maximum surface error corresponding to an individual in the population is the smallest, then the individual is regarded as the optimal individual, otherwise the individuals in the population are genetically operated and the next generation is calculated; finally, the optimal individual is interpreted and converted into a material type selection method for the cable unit in the cable net structure. The present invention takes into account the complementary characteristics between different materials, reasonably selects the material type of the cable unit in the cable net structure, reduces the sensitivity of the free node displacement in the cable net structure to the temperature change, improves the thermal stability of the cable net structure, and greatly improves the surface accuracy in the entire temperature range.

[0074] The above description is only an overview of the technical solution of the present invention. In order to more clearly understand the technical means of the present invention and implement it according to the contents of the specification, the preferred embodiments of the present invention are described in detail below. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0076] Figure 1 It is a flow chart of the present invention;

[0077] Figure 2 It is a front view of the cable net structure of the mesh antenna of the present invention;

[0078] Figure 3 A top view of the cable net structure of the mesh antenna of the present invention;

[0079] Figure 4 It is the evolution curve diagram of the genetic algorithm of the present invention;

[0080] Figure 5 It is a schematic diagram of cable unit material distribution of the front cable net of the present invention;

[0081] Figure 6 It is a schematic diagram of cable unit material distribution of the rear cable net of the present invention;

[0082] Figure 7 It is a schematic diagram of cable unit material distribution of the vertical cable of the present invention;

[0083] Figure 8 It is a distribution diagram of the shape error of the mesh antenna of the present invention under the influence of temperature;

[0084] Fig. 9 Comparison diagram of surface errors calculated using different methods.

[0085] The above description is only an overview of the technical solution of the present invention. In order to more clearly understand the technical means of the present invention and implement it according to the contents of the specification, the following is a detailed description of the preferred embodiments of the present invention. DETAILED DESCRIPTION

[0086] The technical solution of the present invention will be clearly and completely described below in conjunction with the embodiments. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0087] Embodiment 1:

[0088] Reference Figure 1-Figure 3 The on-orbit thermal design method of a mesh antenna based on a genetic algorithm includes the following steps:

[0089] Step 1: Design the cable net structure

[0090] The shape of the cable net structure is obtained by the shape-finding method, and the node coordinates of the cable net structure at the reference temperature T0, the connection relationship of the cable unit, and the tension and length of the cable unit are obtained; between any two adjacent nodes in the cable net structure is a cable unit;

[0091] Step 2: Compile the cable element material type selection

[0092] Different materials are selected as the raw materials of the cable element. The rules for selecting raw materials are as follows:

[0093] Two materials are used to make the cable net structure of the mesh antenna. The elastic modulus, cross-sectional area, and thermal expansion coefficient of the first material are E (1) , A (1) , α (1) The elastic modulus, cross-sectional area, and thermal expansion coefficient of the second material are E (2) , A (2) , α (2) ; When a material is randomly selected to make the cable unit, for any cable unit k, its material property is expressed as

[0094]

[0095] in,

[0096]

[0097] Assume that the operating temperature range of the satellite antenna is T∈[T min ,T max ], the interval is divided into t working conditions with a step size of ΔT, that is, [T1, T2, …, T t ]; In order to reduce the influence of ambient temperature on the surface accuracy of the mesh antenna, the cable unit material type is used as the design variable, the cable unit tension is used as the constraint condition, and the maximum value of the corresponding surface error under all temperature conditions is used as the optimization target. The material topology optimization model is established as follows

[0098]

[0099] Where m is the total number of cable elements, RMS(T) is the surface error at ambient temperature T, and F k is the tension of the kth cable unit;

[0100] When selecting the material type of the cable unit of the cable net structure, when the kth cable unit selects the first material, β k =1, when the kth cable unit selects the second material, β k =0, therefore, a 0,1 string generated by the binary character set {0,1} is used to represent the candidate solution of the material topology optimization model; then, a genetic algorithm is used to solve the material topology optimization model; when solving, a population is first established, and each individual in the population represents a cable unit material selection method of a cable net structure, and each gene in the individual represents the type of material selected by the cable unit. When the kth cable unit selects the first material, the value on the kth gene position is 1, and when the kth cable unit selects the second material, the value on the kth gene position is 0;

[0101] In the genetic algorithm, a binary parameter vector with a number of individuals NP and a dimension of m for each individual is used as a population, where each individual is represented by

[0102] h i,g (i=1,2,…,NP) (4)

[0103] Among them, i represents the serial number of the individual in the corresponding population, and g represents the genetic generation;

[0104] The individuals of the population need to be initially encoded to establish an optimized search starting point; assuming that all initialized individuals of the population conform to random uniform distribution, the initial value of the i-th individual can be obtained by the following formula:

[0105] h i,0 =randint(1,m)(i=1,2,…,NP) (5)

[0106] Among them, randint(1,m) means randomly selecting integers between {0,1} to form a row vector of length m;

[0107] Step 3: Establish the finite element model of the cable net structure;

[0108] Step 4: Calculate the node displacement under the influence of temperature;

[0109] Step 5: Calculate the shape error of the reflecting surface;

[0110] Step 6: Determine whether the current temperature meets the termination condition

[0111] The current temperature value T reaches the upper limit T of the temperature range max As the termination condition of the inner loop, if the termination condition is met, the loop ends, the range of shape and surface error within the temperature range is output, and the next step is performed by going to step eight; otherwise, the loop goes to step seven and continues to calculate the shape and surface error under the next temperature condition;

[0112] Step 7: Update the current temperature

[0113] Update the current ambient temperature and go to step 4 to continue the calculation. The temperature update formula is:

[0114] T=T+ΔT (6)

[0115] The initial value of the ambient temperature T is set to T = T min , ΔT is the temperature increment;

[0116] Step 8: Calculate the maximum surface error value within the temperature range

[0117] For all individuals in the population, follow the operations from step 3 to step 7 to calculate the range of shape surface error within the temperature range, and obtain the maximum shape surface error value corresponding to all individuals in the population as

[0118] RMSmax =[RMS max,1 RMS max,2 … RMS max,NP ] (7)

[0119] Among them, RMS max,i Indicates that the maximum surface error value in the temperature range corresponding to the i-th individual is

[0120] RMS max,i =max{RMS(T1) RMS(T2) … RMS(T t )} (8)

[0121] Step 9: Determine whether the evolutionary generation satisfies the termination criteria

[0122] The termination criterion of the outer loop is that the current evolutionary generation reaches the maximum generation of the genetic algorithm; if the termination criterion is met, go to step 11 and output the individual with the smallest current maximum shape error; otherwise, go to step 10 to perform genetic operations on the population and calculate the next generation;

[0123] Step 10: Evolution of population individuals;

[0124] Step 11: Decipher the individual with the smallest maximum shape error

[0125] Interpret the individual with the smallest maximum shape error to determine the raw materials to be selected;

[0126] Step 12: Make the cable net structure of the mesh antenna

[0127] According to the interpretation result of step 11, a cable net structure of the mesh antenna is made.

[0128] In specific applications, the present invention establishes a material topology optimization model for a cable net structure and provides a solution strategy based on a genetic algorithm. First, the cable net structure is designed in shape according to the shape-finding method, and the tension and length of each cable unit are calculated; secondly, the cable unit material type is compiled using a binary character set to generate an initial population in the genetic algorithm, and each individual in the population represents a cable unit material type selection method in the cable net structure; then, a finite element model of the cable net structure is established in the finite element analysis software, and a temperature load is applied to calculate the surface error variation range of the cable net reflection surface under the influence of temperature; then, it is determined whether the evolutionary generation of the genetic algorithm has been reached. If the maximum generation has been reached, and the maximum surface error corresponding to an individual in the population is the smallest, then the individual is regarded as the optimal individual, otherwise the individuals in the population are genetically operated and the next generation is calculated; finally, the optimal individual is interpreted and converted into a material type selection method for the cable unit in the cable net structure. The present invention takes into account the complementary characteristics between different materials, and by reasonably selecting the material type of the cable unit in the cable net structure, the surface accuracy in the entire temperature range is greatly improved. The present invention takes into account the complementary characteristics between different materials, reasonably selects the material type of the cable unit in the cable net structure, reduces the sensitivity of the free node displacement in the cable net structure to the temperature change, improves the thermal stability of the cable net structure, and greatly improves the surface accuracy in the entire temperature range.

[0129] The cable net structure is designed by the existing form-finding method, which is convenient and concise.

[0130] Embodiment 2:

[0131] Reference Figure 2 and Figure 3 A genetic algorithm-based on-orbit thermal design method for mesh antennas is shown.

[0132] Define any two adjacent nodes as a cable unit, and the cable net structure that makes up the mesh antenna can be divided into several cable units. According to certain rules, different materials are selected as the raw materials of the cable units, and then they are made according to the length and tension requirements. The material selection rules are as follows:

[0133] The present invention uses two materials to make the cable net structure of the mesh antenna. The elastic modulus, cross-sectional area and thermal expansion coefficient of the first material are E (1) , A (1) , α (1) The elastic modulus, cross-sectional area, and thermal expansion coefficient of the second material are E (2) , A (2) , α (2) When a material is randomly selected to make a cable unit, the material properties of any cable unit k can be expressed as

[0134]

[0135] in,

[0136]

[0137] Assume that the operating temperature range of the satellite antenna is T∈[T min ,T max ], the interval is divided into t working conditions with a step size of ΔT, that is, [T1, T2, …, T t ]; In order to reduce the influence of ambient temperature on the surface accuracy of the mesh antenna, the cable unit material type is used as the design variable, the cable unit tension is used as the constraint condition, and the maximum value of the corresponding surface error under all temperature conditions is used as the optimization target. The material topology optimization model is established as follows

[0138]

[0139] Where m is the total number of cable elements, RMS(T) is the surface error at ambient temperature T, and F k is the tension of the kth cable unit, F k >0 is to ensure that the cable element does not relax during the design process.

[0140] The specific design method is as follows:

[0141] Step 1: Use form-finding method to design the shape of the cable net structure

[0142] Since the cable net surface that makes up the mesh antenna needs to form a specific shape (such as a parabola), the cable net structure needs to be morphologically designed. At the reference temperature T0, the node coordinates of the cable net structure, the connection relationship of the cable unit, and the tension and length of the cable unit are calculated.

[0143] Step 2: Compile the cable element material type selection

[0144] From the above analysis, when we need to select the material type for the cable unit of the cable net structure, we can use the 0,1 string generated by the binary character set {0,1} to represent the candidate solution of the material topology optimization model. Therefore, the binary character set is used here to compile the optimization variables. Furthermore, the genetic algorithm is used to solve the material topology optimization model, that is, each individual in the population represents a material selection method for the cable unit of the cable net structure, and each gene in the individual represents the material type selected by the cable unit. When the kth cable unit selects the first material, the value on the kth gene position is 1, and when the kth cable unit selects the second material, the value on the kth gene position is 0.

[0145] In the genetic algorithm, a binary parameter vector with a number of individuals NP and a dimension of m for each individual is used as a population, where each individual is represented by

[0146] h i,g (i=1,2,…,NP) (4)

[0147] Among them, i represents the serial number of the individual in the corresponding population, and g represents the genetic generation.

[0148] The individuals of the population need to be initially encoded to establish an optimized search starting point. Assuming that all initialized individuals of the population conform to random uniform distribution, the initial value of the i-th individual can be obtained by the following formula:

[0149] h i,0 =randint(1,m)(i=1,2,…,NP) (5)

[0150] Among them, randint(1,m) means randomly selecting integers between {0,1} to form a row vector of length m.

[0151] Step 3: Establish the finite element model of the cable net structure

[0152] Substitute the result of the morphological design in step 1 into the finite element analysis software, and establish the finite element model of the cable net structure for the material type selection method of the i-th individual, that is, the i-th cable unit. Among them, the material type of the i-th cable unit is based on the h in step 2. i,g Select the codes in one by one.

[0153] Step 4: Calculate the nodal displacements at temperature

[0154] In the finite element analysis software, a temperature load T is applied to the finite element model of the cable net structure, and the displacement of the reflection surface node under the influence of temperature is calculated, that is,

[0155] ΔR=[Δx Δy Δz] T (9)

[0156] Wherein, Δx represents the displacement of the reflection surface node in the X direction, Δy represents the displacement of the reflection surface node in the Y direction, and Δz represents the displacement of the reflection surface node in the Z direction.

[0157] Step 5: Calculate the shape error of the reflective surface

[0158] The node coordinates R(T) of the reflection surface under the influence of ambient temperature T are:

[0159] R(T)=R0+ΔR (10)

[0160] Where R0 represents the coordinate vector of the reflection surface node at the reference temperature T0, that is,

[0161] R0=[x0 y0 z0] T (11)

[0162] Wherein, x0 represents the displacement of the reflection surface node in the X direction at the reference temperature T0, y0 represents the displacement of the reflection surface node in the Y direction at the reference temperature T0, and z0 represents the displacement of the reflection surface node in the Z direction at the reference temperature T0.

[0163] For the mesh reflector antenna, the node root mean square deviation between the deformed reflector and the ideal parabola is used to describe the shape error of the reflector. Therefore, the shape error RMS(T) of the mesh antenna under the influence of ambient temperature T is:

[0164]

[0165] Where n is the total number of reflection surface nodes, F p is the focal length of the ideal parabola, x r represents the displacement of the rth reflection surface node in the X direction under the influence of the current temperature T, y r represents the displacement of the rth reflection surface node in the Y direction under the influence of the current temperature T, z r Indicates the displacement of the rth reflection surface node in the Z direction under the influence of the current temperature T.

[0166] Step 6: Determine whether the termination condition is met

[0167] The current temperature value T reaches the upper limit T of the temperature range max As the termination condition of the inner loop, the purpose is to calculate the shape error of the reflective surface in the entire temperature range. If the termination condition is met, the loop ends, the shape error variation range in the temperature range is output, and the next step is to go to step 8; otherwise, go to step 7 and continue to calculate the shape error under the next temperature condition.

[0168] Step 7: Update the current temperature

[0169] In order to calculate the surface error under the next temperature condition, it is necessary to update the current ambient temperature and go to step 4 to continue the calculation. The temperature update formula is:

[0170] T=T+ΔT (6)

[0171] The initial value of the ambient temperature T is set to T = T min , ΔT is the temperature increment;

[0172] Step 8: Calculate the maximum error value within the temperature range

[0173] All individuals in the population can calculate the range of shape surface error within the temperature range by following the operations in steps 3 to 7. Therefore, the maximum shape surface error value corresponding to all individuals in the population is

[0174] RMS max =[RMS max,1 RMS max,2 … RMS max,NP ] (7)

[0175] Among them, RMS max,i Indicates that the maximum surface error value in the temperature range corresponding to the i-th individual is

[0176] RMS max,i =max{RMS(T1) RMS(T2) … RMS(T t )} (8)

[0177] Calculate the maximum error value within the temperature range to prepare for the selection operation of the evolutionary population individuals in step ten.

[0178] Step 9: Determine whether the evolutionary generation satisfies the termination criteria

[0179] The termination criterion of the outer loop is that the current evolutionary generation reaches the maximum generation of the genetic algorithm; if the termination criterion is met, go to step 11 and output the individual with the smallest current maximum shape error; otherwise, go to step 10 to perform genetic operations on the population and calculate the next generation;

[0180] Through multiple generations of evolution, the optimal individual is finally obtained, that is, the individual with the smallest current maximum shape error. This step serves as the condition for the genetic algorithm to stop running.

[0181] Step 10: Evolving Population Individuals

[0182] In order to obtain the next generation of population individuals, the individuals in the current population are selected, crossed, and mutated. The specific process is as follows:

[0183] ①Select operation

[0184] The proportion of each individual's fitness is used to determine the possibility of its offspring retention. If the fitness of the i-th individual is fit i , then the probability of it being selected is expressed as

[0185]

[0186] Among them, the maximum surface error within the temperature range is used to describe the individual fitness fit i , after normalization,

[0187]

[0188] Among them, max(RMS max ) and min(RMS max ) represent the RMS max Take maximum and minimum operations.

[0189] The design goal is the shape error value. The smaller the maximum value of the shape error in the temperature range, the better the individual fitness is, and the greater the chance of being selected; vice versa. Each round generates a uniform random number r in [0,1] s , if P si <r s , then keep the current individual, otherwise discard it. Finally, in order to ensure that the total number of the population remains unchanged, multiple rounds of selection are required.

[0190] ②Cross operation

[0191] The selected odd individuals h 2i-1,g and even individuals h 2i,g For each pair of individuals, with the crossover probability P c Exchange some genes between them; the specific steps are: first, take out a pair of individuals to be mated; then, for the pair of individuals to be mated, randomly select an integer in [1,m] as the crossover point; finally, generate a random number r in the interval [0,1] c , and then according to the crossover probability P c Implement crossover operation, if r c <P c , the paired individuals exchange part of their genes at the crossover position, thus forming a new pair of individuals.

[0192] ③ Mutation operation

[0193] For each individual in the crossover population, the mutation probability P m Change the gene values ​​at some loci to other allele values; the specific steps are: in the population after crossover, for the i-th individual, generate a random number r in the interval [0,1] m , and then randomly select an integer in [1,m] as the position of the mutant gene. If r m <P m , if the gene value on the selected variant gene is 1, its value becomes 0; if the gene value on the selected variant gene is 0, its value becomes 1.

[0194] Step 11: Interpret the optimal individual

[0195] When the population has completed all generations of evolution, there is an individual in the population whose maximum shape error is the smallest. This individual is considered the best individual. Since the output individual is a string of 0,1, it needs to be interpreted. The interpretation process is: when the value of the k-th gene position on the best individual is 1, it means that the k-th root cable unit selects the first material; when the value of the k-th gene position is 0, it means that the k-th root cable unit selects the second material.

[0196] Step 12: Make the cable net structure of the mesh antenna

[0197] According to the interpretation result of step 11, a cable net structure of the mesh antenna is made.

[0198] The present invention reduces the sensitivity of the displacement of the reflection surface nodes in the cable net structure to the temperature change by reasonably selecting the material type of the cable unit in the cable net structure, improves the thermal stability of the cable net structure, and achieves a reduction in the shape and surface error in the entire temperature range.

[0199] In this embodiment, step three of establishing the finite element model of the cable net structure is performed using finite element analysis software ANSYS, where ANSYS is the name of the software.

[0200] Embodiment three:

[0201] The effect of the present invention is verified through simulation experiments.

[0202] From experimental research and simulation analysis, it can be seen that the temperature variation range of the satellite antenna is about -200℃~100℃, that is, the ambient temperature T∈[-200,100]℃. Accordingly, the reference temperature T0 can generally be taken as 20℃.

[0203] The present invention is applied to a 10m diameter mesh antenna for simulation analysis. It is assumed that the elastic modulus, cross-sectional area, and thermal expansion coefficient of the first material are 20 GPa and 0.785 mm 2 , -2×10 -6 / ℃, the elastic modulus, cross-sectional area and thermal expansion coefficient of the second material are 80GPa and 0.785mm 2 , 2×10 -6 / ℃. In the genetic algorithm, the population size is set to 50, the crossover rate and mutation rate are 0.85 and 0.05 respectively, and the maximum evolutionary generation is 100. The evolution curve is as follows Figure 4 As shown in the figure, the cable unit material type distribution of the front cable net is as follows: Figure 5 As shown in the figure, the cable unit material type distribution of the rear cable net is as follows: Figure 6 As shown in the figure, the material type distribution of the cable unit of the vertical network is as follows Figure 7As shown; the solid line indicates that the cable unit adopts the first material, and the dotted line indicates that the cable unit adopts the second material.

[0204] like Figure 8 As shown, under -200℃ working condition, the shape surface error is reduced from 2.93mm (using the first material) and 3.05mm (using the second material) to 1.59mm (using both materials at the same time); under 100℃ working condition, the shape surface error is reduced from 1.03mm (using the first material) and 1.15mm (using the second material) to 0.61mm (using both materials at the same time); the maximum value of the shape surface error in the whole temperature range is reduced by 45.73% (using the first material) and 47.87% (using the second material). Therefore, compared with the traditional cable net manufacturing that only selects one material, the present invention improves the shape surface accuracy in the whole temperature range to a great extent by reasonably selecting the material type of the cable unit.

[0205] At the same time, the results calculated by the method proposed in the present invention are compared with those calculated by the method proposed in the literature to verify the effectiveness of the method proposed in the present invention. Fig. 9 As shown, compared with the method proposed in the literature, the method proposed in the present invention achieves a decrease in the shape error under all working conditions within the temperature range, and the decrease is greater (under the condition of -200°C, the shape error calculated by the method proposed in the literature is reduced from 2.93mm to 2.01mm, a reduction of 31.40%). (Reference: Rui Nie, Baiyan He, Shaoze Yan, Xiaofei Ma, Optimization design method for the cable network of mesh reflector antennas considering space thermal effects, Aerospace Science and Technology, 2019, 94: 105380.)

[0206] In the absence of conflicts, technicians in this field can combine the relevant technical features in the above examples according to actual conditions to achieve corresponding technical effects. The specific combinations are not described here one by one.

[0207] It should be noted that all directional indications in the embodiments of the present invention (such as up, down, left, right, front, back, inside, outside...) are only used to explain the relative position relationship, movement status, etc. between the components under a certain specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication will also change accordingly.

[0208] The above are only preferred embodiments of the present invention. The present invention will not be limited to the embodiments shown herein, but should conform to the widest scope consistent with the principles and novel features disclosed herein. Any simple modification, equivalent changes and modifications made to the above embodiments according to the technical essence of the present invention still fall within the scope of the technical solution of the present invention.

Claims

1. A method for on-orbit thermal design of mesh antenna based on genetic algorithm, characterized in that: The following steps are included: Step 1: Design the cable net structure The shape of the cable net structure is obtained by the shape-finding method, and the node coordinates of the cable net structure at the reference temperature T0, the connection relationship of the cable unit, and the tension and length of the cable unit are obtained; between any two adjacent nodes in the cable net structure is a cable unit; Step 2: Compile the cable element material type selection Different materials are selected as the raw materials of the cable element. The rules for selecting raw materials are as follows: Two materials are used to make the cable net structure of the mesh antenna. The elastic modulus, cross-sectional area, and thermal expansion coefficient of the first material are E (1) , A (1) , α (1) The elastic modulus, cross-sectional area, and thermal expansion coefficient of the second material are E (2) , A (2) , α (2) ; When a material is randomly selected to make the cable unit, for any cable unit k, its material property is expressed as in, Assume that the operating temperature range of the satellite antenna is T∈[T min ,T max ], the interval is divided into t working conditions with a step size of ΔT, that is, [T1, T2, …, T t ]; In order to reduce the influence of ambient temperature on the surface accuracy of the mesh antenna, the cable unit material type is used as the design variable, the cable unit tension is used as the constraint condition, and the maximum value of the corresponding surface error under all temperature conditions is used as the optimization target. The material topology optimization model is established as follows Where m is the total number of cable elements, RMS(T) is the surface error at ambient temperature T, and F k is the tension of the kth cable unit; When selecting the material type of the cable unit of the cable net structure, when the kth cable unit selects the first material, β k =1, when the kth cable unit selects the second material, β k =0, therefore, a 0,1 string generated by the binary character set {0,1} is used to represent the candidate solution of the material topology optimization model; then, a genetic algorithm is used to solve the material topology optimization model; when solving, a population is first established, and each individual in the population represents a cable unit material selection method of a cable net structure, and each gene in the individual represents the type of material selected by the cable unit. When the kth cable unit selects the first material, the value on the kth gene position is 1, and when the kth cable unit selects the second material, the value on the kth gene position is 0; In the genetic algorithm, a binary parameter vector with a number of individuals NP and a dimension of m for each individual is used as a population, where each individual is represented by h i,g (i=1,2,…,NP) (4) Among them, i represents the serial number of the individual in the corresponding population, and g represents the genetic generation; The individuals of the population need to be initially encoded to establish an optimized search starting point; assuming that all initialized individuals of the population conform to random uniform distribution, the initial value of the i-th individual can be obtained by the following formula: h i,0 =randint(1,m)(i=1,2,…,NP) (5) Among them, randint(1,m) means randomly selecting integers between {0,1} to form a row vector of length m; Step 3: Establish the finite element model of the cable net structure; Step 4: Calculate the node displacement under the influence of temperature; Step 5: Calculate the shape error of the reflecting surface; Step 6: Determine whether the current temperature meets the termination condition The current temperature value T reaches the upper limit T of the temperature range max As the termination condition of the inner loop, if the termination condition is met, the loop ends, the range of shape and surface error within the temperature range is output, and the next step is performed in step eight; otherwise, step seven is entered to continue calculating the shape and surface error under the next temperature condition; Step 7: Update the current temperature Update the current ambient temperature and go to step 4 to continue the calculation. The temperature update formula is: T=T+ΔT (6) The initial value of the ambient temperature T is set to T = T min , ΔT is the temperature increment; Step 8: Calculate the maximum surface error value within the temperature range For all individuals in the population, follow the operations from step 3 to step 7 to calculate the range of shape surface error within the temperature range, and obtain the maximum shape surface error value corresponding to all individuals in the population as RMS max =[RMS max,1 RMS max,2 …RMS max,NP ] (7) Among them, RMS max,i Indicates that the maximum surface error value in the temperature range corresponding to the i-th individual is RMS max,i =max{RMS(T1) RMS(T2)…RMS(T t )} (8) Step 9: Determine whether the evolutionary generation satisfies the termination criteria The termination criterion of the outer loop is that the current evolutionary generation reaches the maximum generation of the genetic algorithm; if the termination criterion is met, go to step 11 and output the individual with the smallest current maximum shape error; otherwise, go to step 10 to perform genetic operations on the population and calculate the next generation; Step 10: Evolution of population individuals; Step 11: Decipher the individual with the smallest maximum shape error Interpret the individual with the smallest maximum shape error to determine the raw materials to be selected; Step 12: Make the cable net structure of the mesh antenna According to the interpretation result of step 11, a cable net structure of the mesh antenna is made.

2. The method for on-orbit thermal design of a mesh antenna based on a genetic algorithm as claimed in claim 1, characterized in that: The step three of establishing the finite element model of the cable net structure is carried out through finite element analysis software; the node coordinates, the connection relationship of the cable unit, and the tension and length of the cable unit obtained in step one are substituted into the finite element analysis software, and for the i-th individual, that is, the material type selection method of the i-th cable unit, the finite element model of the cable net structure is established; wherein the material type of the i-th cable unit is selected one by one according to the coding in step two.

3. The on-orbit thermal design method of a mesh antenna based on a genetic algorithm as claimed in claim 1, characterized in that: The method for calculating the node displacement under the influence of temperature in step 4 is: in the finite element analysis software, a temperature load T is applied to the finite element model of the cable net structure, and the displacement ΔR of the reflecting surface node under the influence of temperature is calculated, that is, ΔR=[Δx Δy Δz] T (9) Wherein, Δx represents the displacement of the reflection surface node in the X direction, Δy represents the displacement of the reflection surface node in the Y direction, and Δz represents the displacement of the reflection surface node in the Z direction.

4. The method for on-orbit thermal design of mesh antenna based on genetic algorithm as claimed in claim 1, characterized in that: The specific method for calculating the reflection surface shape error in step 5 is as follows: The node coordinates R(T) of the reflection surface under the influence of ambient temperature T are: R(T)=R0+ΔR (10) Where R0 represents the coordinate vector of the reflection surface node at the reference temperature T0, that is, R0=[x0 y0 z0] T (11) Wherein, x0 represents the displacement of the reflection surface node in the X direction at the reference temperature T0, y0 represents the displacement of the reflection surface node in the Y direction at the reference temperature T0, and z0 represents the displacement of the reflection surface node in the Z direction at the reference temperature T0; For the mesh reflector antenna, the node root mean square deviation between the deformed reflector and the ideal parabola is used to describe the shape error of the reflector. Therefore, the shape error RMS(T) of the mesh antenna under the influence of ambient temperature T is: Where n is the total number of reflection surface nodes, F p is the focal length of the ideal parabola, x r represents the displacement of the rth reflection surface node in the X direction under the influence of the current temperature T, y r represents the displacement of the rth reflection surface node in the Y direction under the influence of the current temperature T, z r Indicates the displacement of the rth reflection surface node in the Z direction under the influence of the current temperature T.

5. The method for on-orbit thermal design of mesh antenna based on genetic algorithm as claimed in claim 1, characterized in that: The evolution of all population individuals in step 10 is completed through selection operation, crossover operation and mutation operation.

6. The method for on-orbit thermal design of mesh antenna based on genetic algorithm as claimed in claim 5, characterized in that: The specific method of the selection operation is as follows: the proportion of each individual's fitness is used to determine the possibility of its offspring retention; if the fitness of the i-th individual is fit i , then the probability of it being selected is P si Expressed as Among them, the maximum surface error within the temperature range is used to describe the individual fitness fit i , after normalization, Among them, max(RMS max ) and min(RMS max ) represent the RMS max Take maximum and minimum operations; The design goal is the shape error value. The smaller the maximum value of the shape error in the temperature range, the better the individual fitness is, and the greater the chance of being selected; vice versa. Each round generates a uniform random number r in [0,1] s , if P si <r s , then keep the current individual, otherwise discard it; To ensure that the total number of the population remains unchanged, the above selection operation is performed for multiple rounds.

7. The method for on-orbit thermal design of mesh antenna based on genetic algorithm as claimed in claim 5, characterized in that: The specific method of the crossover operation is as follows: The selected odd individuals h 2i-1,g and even individuals h 2i,g For each pair of individuals, the crossover probability P c Exchange some genes between them; the specific steps are: first, take out a pair of individuals to be mated; then, for the pair of individuals to be mated, randomly select an integer in [1,m] as the crossover point; finally, generate a random number r in the interval [0,1] c , and then according to the crossover probability P c Implement crossover operation, if r c <P c , the paired individuals exchange part of their genes at the crossover position, thus forming a new pair of individuals.

8. The method for on-orbit thermal design of mesh antenna based on genetic algorithm as claimed in claim 5, characterized in that: The specific method of the mutation operation is as follows: For each individual in the crossover population, the mutation probability P m Change the gene values ​​at some loci to other allele values; the specific steps are: in the population after crossover, for the i-th individual, generate a random number r in the interval [0,1] m , and then randomly select an integer in [1,m] as the position of the mutant gene. If r m <P m , if the gene value on the selected variant gene is 1, its value becomes 0; if the gene value on the selected variant gene is 0, its value becomes 1.

9. The method for on-orbit thermal design of mesh antenna based on genetic algorithm as claimed in claim 1, characterized in that: The method for interpreting the individual with the smallest maximum shape error in step 11 is as follows: when the value on the kth gene position on the individual with the smallest maximum shape error is 1, it means that the kth root rope unit selects the first material; when the value on the kth gene position is 0, it means that the kth root rope unit selects the second material.

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