Rapid optimization design method for antenna satellite system based on proxy model

Abstract

The invention relates to an antenna satellite system rapid optimization design method based on an agent model, and belongs to the technical field of satellite design optimization. The method specifically comprises the following steps: step 1, for a to-be-optimized antenna satellite system, carding subjects involved in the design of the to-be-optimized antenna satellite system and a coupling relationship among the subjects; step 2, based on the coupling relationship, respectively constructing an analysis model corresponding to each subject; 3, taking the minimum whole satellite mass of the antenna satellite as an optimization target, taking the key parameters of each subject as optimization variables, and constructing an optimization function and constraint conditions based on the analysis model of the components in the step 2; and 4, solving the optimization function in the step 3 to obtain the optimal value of the optimization variable.

Description

Technical Field

[0001] The present invention relates to a rapid optimization design method for an antenna satellite system based on a surrogate model, belonging to the technical field of satellite design optimization. Background Art

[0002] With the rapid development of high-speed data transmission and mobile communication, high-gain antenna payloads have received increasing attention. They can support high-bandwidth and long-distance communication transmissions and have good application prospects in fields such as satellite communication broadcasting, earth observation, precise navigation, and positioning. Different from traditional satellites, due to the large size of the antenna payload and the large proportion of payload weight, antenna satellites face problems such as difficulties in matching the payload design with the platform design and structural damage caused by the low fundamental frequency during the launch of the entire satellite in the overall design. It is necessary to carry out the design optimization of antenna satellites to reduce the overall mass of the satellite while meeting the engineering constraints of the fundamental frequency of the entire satellite by designing a reasonable antenna model, satellite platform configuration, and connection structure.

[0003] Traditional optimization methods (such as genetic algorithms, particle swarm algorithms, etc.) often need to directly call the analysis model thousands of times to explore the design space, and are not suitable for the antenna satellite design optimization problem involving high-time-consuming analysis models. Summary of the Invention

[0004] In view of this, the present invention provides a rapid optimization design method for an antenna satellite system based on a surrogate model, which can improve the optimization efficiency, shorten the design cycle, and quickly realize the optimization and modification of the antenna satellite design scheme.

[0005] The purpose of the present invention is achieved through the following technical solutions

[0006] A rapid optimization design method for an antenna satellite system based on a surrogate model, the specific process is as follows:

[0007] Step 1, for the antenna satellite system to be optimized, sort out the disciplines involved in its design and the coupling relationships between the disciplines;

[0008] Step 2, based on the coupling relationship, respectively construct the analysis models corresponding to each discipline;

[0009] Step 3, taking the minimum mass of the entire antenna satellite as the optimization goal and the key parameters of each discipline as the optimization variables, construct an optimization function and constraint conditions based on the analysis models constructed in Step 2;

[0010] Step 4, by solving the optimization function in Step 3, obtain the optimal values of the optimization variables.

[0011] Optionally, the disciplines in the present invention include geometric occlusion, power supply and distribution, attitude control, structure, position holding, orbit transfer, and mass discipline.

[0012] Optionally, in the geometric occlusion model calculation process of the present invention: determine the number of boundary intersection points N between the shadow and the solar panel BI , determine the distances d between the projection of the geometric center of the load and the four boundaries of the solar wing array i , the relationship between i = 1, 2, 3, 4 and the load radius R, and combine this relationship and the number of intersection points N BI to obtain the area S of the occluded solar panel shading .

[0013] Optionally, the geometric occlusion model of the present invention is:

[0014] Case ①: N BI = 0, when min(d i ) > R, S sunward = L S W S , S shading = 0, when max(d i ) < R, S sunward = 0, S shading = L S W S ;

[0015] Case ②: N BI = 2, when the number of d i < R is N d = 0,

[0016] When N d = 1,

[0017] When N d = 2,

[0018] When N d = 3,

[0019] Case ③: N BI = 4, which can be divided into three categories according to the number of N d ;

[0020] When N d = 0,

[0021] When N d = 1,

[0022] When N d = 2,

[0023] Case ④: N BI = 6, there is only Nd For the case where it equals 1, integral analysis and calculation are adopted;

[0024]

[0025] where A B , B B (x b , y b ), C B (x c , y c ), D B , E B and F B (x f , y f ) represent the intersection points of the load projection and the boundary of the solar wing;

[0026] Case ⑤: N BI = 8, and there is only one case where N d = 0. Integral analysis and calculation are adopted;

[0027]

[0028] where A B , B B (x b , y b ), C B (x c , y c ), D B , D B , E B , F B (x f , y f ) and G B (x g , y g ) represent the intersection points of the load projection and the boundary of the solar wing.

[0029] Optionally, the structural discipline modeling of the present invention is as follows: The satellite platform uses the service module load-bearing cylinder as the main load-bearing structure. The platform also includes a top plate, a bottom plate, a docking ring, four partition plates, a surrounding plate surface, and four storage tanks, and the antenna load part includes a load-bearing cylinder and a hinge; the connection part is composed of a conical composite connection ring.

[0030] Optionally, the design variables of the structural discipline of the present invention are: W b represents the core thickness of the bottom plate of the service module, W m the core thickness of the top plate of the service module, W p the core thickness of the load-bearing cylinder, W bc the core thickness of the load-bearing cylinder of the service module, W btComposite ply thickness of the service floor, W mt Composite ply thickness of the service module top plate, W pt Composite ply thickness of the load bearing cylinder, W bct Composite ply thickness of the service module load bearing cylinder.

[0031] Optionally, for the station - keeping discipline of the present invention: four electric thrusters are symmetrically arranged and installed on the surface of the satellite platform. The thruster ignition scheme is as follows: Thrusters 1–4–2–3 work sequentially within each thrust unloading cycle, and the working longitudes of thrusters 1 and 2, and thrusters 3 and 4 are the same, with a working phase difference of 180° between the former and the latter.

[0032] Optionally, the station - keeping discipline of the present invention models 4 electric thrusters as:

[0033]

[0034] In the formula, M ep is the fuel mass consumed by the electric thruster for on - orbit station - keeping, Δv e is the velocity increment of the electric thruster; m1 is the initial in - orbit mass of the satellite; I e sp is the specific impulse of the electric propellant; η p is the thruster efficiency; F e p is the thrust magnitude of the electric thruster; Δt is the working duration of the thruster, g represents the acceleration due to gravity, ΔV represents the velocity increment required due to the influence of perturbations, and Δv e ≥|ΔV|.

[0035] Optionally, the present invention takes the minimum total mass of the antenna - satellite as the optimization objective, with the key parameters of each discipline as the optimization variables, and constructs an optimization function and constraint conditions based on the analysis model of the components in step two; specifically:

[0036] find X = [L s ,W s ,C s ,H W ,W b ,W m ,W p ,W bc ,W bt ,W mt ,W pt ,W bct ,d N ,d T

[0037] min f(X) = M total

[0038] ​

[0039] Among them, L s and W s are the length and width of the solar panel, C s is the nominal capacity of the battery, H W is the angular momentum, W b , W m , W p , W bc , W bt , W mt , W pt , W bct are the design variables of the structural discipline, d N , d T represents the coordinates of the electric thruster.

[0040] M total = M solar + M battery + M control + M ep + M cp + M structure + M other

[0041] Among them, M solar is the mass of the solar array, M battery is the mass of a single set of batteries, M control is the mass of the momentum wheel, M ep is the mass of the fuel consumed by the electric thruster for on-orbit position keeping, M cp represents the fuel consumption of the variable-orbit transfer chemical propellant, M structure is the thickness of the satellite platform, M other is the set mass of other systems;

[0042] Among them, P BOL is the initial power of the solar array at the beginning of its life, P EOL is the power of the solar array at the end of its life, DOD is the depth of discharge of the battery, C A is the C momentum wheel unloading margin, f x , f y and f z represent the bending modes of the three axes, i max represents the maximum deviation of the orbital inclination when the satellite is working in orbit, λ max represents the maximum deviation of the mean longitude when working in orbit, and X represents the total mass of the satellite.

[0043] Optionally, in step four of the present invention, a comprehensive feasible probability algorithm based on Pareto fitness is used to optimize the antenna satellite optimization problem.

[0044] Beneficial effects

[0045] First, the present invention discloses a rapid optimization design method for an antenna satellite system based on a surrogate model, and constructs an overall design scheme of the antenna satellite according to the mission requirements of the antenna satellite. First, the design structure matrix is used to construct the data coupling relationship between the key disciplines related to the antenna satellite design (geometric occlusion, power supply and distribution, attitude control, structure, position keeping, orbit transfer, and mass), and parametric models of each discipline are constructed, which can efficiently and conveniently obtain the performance index parameters of each subsystem that meet the performance consistency requirements of each discipline of the antenna satellite, improve the design efficiency of the antenna satellite, and solve the problems of difficult matching between payload design and platform design and satellite damage caused by low fundamental frequency during the overall design of the antenna satellite.

[0046] Second, the present invention discloses a rapid optimization design method for an antenna satellite system based on a surrogate model. By approximating high-time-consuming analysis models such as the finite element analysis and long-time numerical integration of the antenna satellite through the surrogate model, the rapid prediction of the performance indicators of each subsystem of the antenna satellite is realized, which can reduce the number of calls to the high-time-consuming models of the antenna satellite, improve the optimization efficiency of the overall design scheme of the antenna satellite, shorten the design cycle of the antenna satellite, and improve the satellite design efficiency.

[0047] Third, the present invention discloses a rapid optimization design method for an antenna satellite system based on a surrogate model. By exploring the global optimality of the antenna satellite scheme design through the Pareto fitness comprehensive probability algorithm and adopting the feasible probability sampling and adding point criterion based on Pareto fitness to improve the convergence speed of local search, the overall mass of the antenna satellite is reduced under the condition of meeting the engineering constraints of each subsystem, which can effectively reduce the cost required for the launch of the antenna satellite. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required to be used in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0049] Figure 1 is a reference image of the antenna satellite model disclosed by the present invention;

[0050] Figure 2 is the design structure matrix of the antenna satellite design disclosed by the present invention;

[0051] Figure 3 is a schematic diagram of the geometric occlusion analysis of the antenna satellite disclosed by the present invention;

[0052] Figure 4 is a schematic diagram of four occlusion situations of the solar panel of the present invention;

[0053] Figure 5 It is the schematic diagram 2 of the situation where the solar panel of the present invention is blocked;

[0054] Figure 6 It is the schematic diagram 3 of the situation where the solar panel of the present invention is blocked;

[0055] Figure 7 It is the schematic diagram 4 of the situation where the solar panel of the present invention is blocked;

[0056] Figure 8 It is the schematic diagram 5 of the situation where the solar panel of the present invention is blocked;

[0057] Figure 9 It is the redundant assembly scheme of three positive and one inclined four momentum wheels disclosed by the present invention;

[0058] Figure 10 It is the design of the antenna satellite structure disclosed by the present invention, (a) schematic diagram of the antenna satellite structure configuration, (b) three-dimensional modeling diagram of the antenna satellite;

[0059] Figure 11 It is the layout scheme of four electric thrusters disclosed by the present invention;

[0060] Figure 12 It is the entire orbital maneuver process disclosed by the present invention;

[0061] Figure 13 It is the schematic diagram of a single orbital maneuver disclosed by the present invention;

[0062] Figure 14 It is the flow chart of the Pareto fitness comprehensive feasible probability optimization algorithm disclosed by the present invention.

[0063] Figure 15 It is the schematic diagram of the iteration curve of the present invention. Detailed implementation manners

[0064] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0065] To solve the problems faced by antenna satellites in the overall design, such as the difficulty in matching the payload design with the satellite platform design and the low fundamental frequency leading to satellite damage during the whole-satellite launch into orbit, the technical problems mainly solved by a rapid optimization design method for antenna satellite systems based on surrogate models disclosed in the present invention are described as follows: Analyze the mission requirements of antenna satellites, construct reasonable antenna satellite structure models, geometric occlusion models, power models, attitude control models, position-keeping models, orbit transfer models, and mass analysis models, etc. for optimization. Considering that there are high-time-consuming analysis models such as finite element analysis and long-time numerical integration in the optimization process of antenna satellites, the surrogate model approximation optimization method is combined to replace the antenna satellite for disciplinary model analysis and optimization. On the premise of meeting the various engineering constraints of the antenna satellite, while further increasing the overall fundamental frequency of the satellite, the launch mass is reduced.

[0066] An embodiment of the present application provides a rapid optimization design method for antenna satellite systems based on surrogate models, including the following steps:

[0067] Step 1: For the antenna satellite system to be optimized, sort out the disciplines involved in its design and the coupling relationships between the disciplines;

[0068] Sort out the key disciplines involved in the antenna satellite design, and use the structural design matrix to sort out the parameter relationships between the disciplines. For example, Figure 1 analyze the antenna satellite model in and the normal working condition of the satellite. Since the area of the antenna payload is large after deployment, it will affect the power supply of the solar panels. Therefore, it is necessary to analyze the occlusion relationship between the payload and the solar panels after the antenna satellite payload is deployed, and consider the influence of the solar panel area on the power supply and distribution of the antenna satellite. In addition, when considering the normal operation of the antenna satellite, due to the large surface mass, the influence of the solar space environment disturbance torque is aggravated. Therefore, it is necessary to carry out research on the attitude control and on-orbit position-keeping of the antenna satellite to quantitatively analyze the influence of the space environment on the attitude and orbit of the satellite; considering the integrity of the antenna satellite launch mission, it is necessary to carry out an orbit transfer analysis model to realize the mission of the satellite maneuvering from the transfer orbit to the geostationary orbit after "separation of the satellite and the rocket". And the mass distribution is the top priority of the satellite design. Therefore, it is necessary to carry out the mass estimation and distribution summary analysis of each subsystem. Finally, the structural design is the core of the antenna satellite design. It needs to take into account both the payload design and the platform design, which is the key to improving the comprehensive performance of the antenna satellite.

[0069] After the above task analysis, the antenna satellite design involves disciplines such as geometric occlusion, power supply and distribution, attitude control, structure, position-keeping, orbit transfer, and mass. Use the design structure matrix to sort out its coupling relationship, as Figure 2 shown.

[0070] Step 2: Based on the coupling relationship, construct the analysis models corresponding to each discipline respectively;

[0071] Step 201: Geometric occlusion model construction. Based on Figure 1 the antenna-satellite model, draw the basic configuration to analyze the occlusion of the satellite solar panel by the antenna payload, as Figure 3 shown.

[0072] Construct a satellite body coordinate system at the centroid of the satellite body. Take the centroid of the satellite platform as the origin, the direction parallel to the long side of the solar panel as the Y B axis, the direction parallel to the surface of the satellite platform and perpendicular to Y B as the X B axis, the direction along the forward direction of the satellite is positive, and the normal direction of the satellite platform surface is the Z B axis, with the direction pointing to the payload being positive. Consider the design parameters of the satellite platform: the length of the satellite body is l1, the width is w1; the length of the solar panel is L s , the width is W s ; the radius of the payload is R, the height from the surface of the satellite body is h; the angle between the solar panel and the Y B OX B plane is β; consider the sunlight as a parallel vector and use the unit vector e = [l, m, n] T to represent, where l, m, and n are the components in the satellite body coordinate system, M (the three-dimensional space coordinates are [a, b, c] T ), P (the three-dimensional space coordinates are [x, y, z] T ) represent any point on the payload and the solar panel respectively. When the formula (1) is satisfied, it can be explained that the solar panel is occluded by the payload. According to the number of intersection points N BI of the shadow and the boundary of the solar panel, it is divided into five categories for discussion, as Figure 4 shown. Then, further classify and analyze according to the relationship between the projection of the geometric center of the payload and the distances d i (i = 1, 2, 3, 4) of the four boundaries of the solar wing array and the radius R of the payload, so as to obtain the occluded area S shading of the solar panel.

[0073]

[0074] Case ①: N BI = 0, which can be divided into min(d i ) > R, that is, the solar wing is not occluded by the payload at all, S sunward = L S W S , S shading = 0; or max(d i ) < R, that is, the solar wing is completely occluded by the payload, S sunward = 0, S shading = L S W S。Case ②: N BI = 2. According to d i < the number N of R d it can be divided into four categories, as Figure 5 shown;

[0075]

[0076] Among them, B i (x i , y i ), i = 1, 2, 3, 4 represent the four boundary points of the single-sided solar wing; C p (x p c , y p c ) are respectively the projection points of the load geometric center on the surface of the solar wing; A B and B B represent the intersection points of the load projection and the boundary of the solar wing. Case ③: N BI = 4. According to the number of N d it can be divided into three categories, as Figure 6 shown. Taking N d = 2 as an example for analysis and integral calculation;

[0077] When N d = 0,

[0078] When N d = 1,

[0079] When N d = 2,

[0080] (3) Among them, A B , B B (x b , y b ), C B (x c , y c ) and D B represent the intersection points of the load projection and the boundary of the solar wing.

[0081] Case ④: N BI = 6. There is only one category of situation where N d = 1, as Figure 7 shown. Integral analysis and calculation are adopted;

[0082]

[0083] Among them, A B , B B (x b , yb ), C B (x c , y c ), D B , E B and F B (x f , y f ) represent the intersection points of the load projection and the boundary of the solar panel wing.

[0084] Case ⑤: N BI = 8, there is only one type of case where N d = 0, as shown in Figure 8 , and integral analysis and calculation are adopted;

[0085]

[0086] Among them, A B , B B (x b , y b ), C B (x c , y c ), D B , D B , E B , F B (x f , y f ) and G B (x g , y g ) represent the intersection points of the load projection and the boundary of the solar panel wing.

[0087] The above is the occlusion analysis of one-sided solar panels. For the occlusion analysis of the other side, only the solar light vector e = [l, m, n] T needs to be corrected to e = [l, -m, n] T .

[0088] The unoccluded solar panel area S is obtained through Equation (6) sunward .

[0089] S sunward = 2L S W S - S shading (6)

[0090] Step 202: Modeling of the power supply and distribution model. Based on the geometric occlusion analysis model, obtain the occluded solar panel area S shading and the unoccluded solar panel area S sunward, obtain the power supply of the solar panels according to the empirical formula, and consider the interference of the space environment resulting in the decline of the output power of the solar array, and obtain the output power at the end of the life of the solar array to ensure that the power supply and distribution discipline can effectively meet the power supply requirements during the on-orbit operation of the satellite as shown in Equation (7).

[0091]

[0092] Among them, S0 is the solar constant, X is the correction factor for the oblique incidence of sunlight on the solar array, X s is the seasonal change factor of sunlight, X e is the gain factor of the output power of the solar array due to the reflection of the earth, X0 is other correction factors; ε is the light transmission coefficient when the payload is blocked, η s is the photoelectric conversion efficiency of a single solar cell, F c is the combined loss factor of the solar array; β p is the power temperature coefficient of the solar array (unit: % / °C), ΔT is the difference between the orbital operating temperature of the solar cell and the standard temperature (°C), χ is the angle between the sunlight and the normal direction of the solar array; L t year is the on-orbit operating life of the satellite, d y is the annual average power decline of the solar wing during on-orbit operation. P BOL is the power at the initial stage of the life of the solar array, P EOL is the power at the end of the life of the solar array.

[0093] The mass of the solar array is obtained by multiplying the area of the solar wing by the material density, as shown in (8), where ρ solar (unit: kg / m 2 ) is the average density of the solar wing.

[0094] M solar = ρ solar ×(S sunward + S shading ) (8)

[0095] Among them, M solar is the mass of the solar array.

[0096] The depth of discharge DOD of the battery is defined as the ratio of the discharge capacity C of the battery to its nominal capacity C s . The power demand of the whole satellite during the shadow period is P e . Considering that the general battery pack uses the north-south battery pack power supply method, the discharge power P bat of a single battery pack is P e / 2. The calculation formula for the depth of discharge of the battery is as follows:

[0097]

[0098] Among them, T e is the time of the geostationary orbit shadow period, and V bat is the average discharge voltage of the battery pack.

[0099] On this basis, the calculation formula for the mass of a single battery pack is obtained.

[0100] M battery = C s ·V bat / γ b (10)

[0101] Among them, γ b is the specific energy of the battery.

[0102] Step 203: In the attitude control discipline, construct the models of the gravity gradient torque and the solar radiation pressure torque acting on the antenna satellite during on-orbit operation. During the overall design phase, it is necessary to ensure that the momentum wheel unloading torque is greater than or equal to the accumulated solar radiation pressure torque within the unloading period. The constructed gravity gradient torque model is shown in Equation (11), where I xx , I yy , I zz , I xy , I xz , and I yz respectively represent the principal axis moment of inertia and the product of inertia in the working state of the antenna satellite; r x , r y , and r z respectively represent the vector components from the earth's center to the satellite's center of mass.

[0103]

[0104] The constructed solar radiation pressure torque is shown in Equation (13):

[0105]

[0106] Among them, l p is the vector from the satellite's center of mass to the center of pressure, α is the solar absorption coefficient of the satellite component surface, c rd is the solar diffuse reflection coefficient of the satellite component surface, c rs is the solar specular reflection coefficient of the satellite component surface, p is the average pressure of solar radiation pressure, d A is the area of the satellite irradiated by incident light / projected, τ A and n A are the unit vectors in the solar direction and the normal vector of the satellite surface, θ is the incident angle of sunlight, and H(·) is the Heaviside function, and the specific representation is shown in Equation (14).

[0107]

[0108] During the unloading period, the angular momentum to be unloaded by the antenna satellite momentum wheel is as shown in Equation (15), which can be obtained by integrating the solar radiation pressure moment and the gravity gradient moment. Among them, η is the design redundancy of the momentum wheel unloading. The attitude control discipline adopts a redundant assembly scheme of four momentum wheels with three positive and one oblique, as Figure 9 shown. Therefore, during one unloading period, the momentum wheel unloading margin is as shown in Equation (16), and the momentum wheel mass is determined by Equation (17).

[0109]

[0110] C A C = Hw - max(Hwx, Hwy, Hwz) (16)

[0111] M control = 4×(5.8 + 17(H w - 6) / 90) + 90.4 (17)

[0112] Among them, M control is the momentum wheel mass.

[0113] Step 204: In the structural discipline, use the Patran three-dimensional finite element modeling and analysis software to construct the model of the antenna satellite in the stowed state as Figure 10 shown. The satellite platform uses a cylindrical barrel with a diameter of 1000 mm as the main load-bearing structure. The platform also includes a top plate, a bottom plate, a docking ring, four partition plates, the surrounding plate surfaces, and four storage tanks. In addition, the antenna load part consists of a cylindrical barrel with a diameter of 1000 mm and 10 hinges with a simplified diameter of 40 mm; the connection part is composed of a conical composite connection ring. This finite element model contains a total of 8562 elements and 10908 nodes, and its design parameters and constraint conditions are sorted out in Table 1.

[0114] Table 1 Design variables and constraint conditions of the structural discipline

[0115]

[0116] Step 205: In the position-keeping discipline, to ensure that the on-orbit working position accuracy of the antenna satellite meets the requirements, four electric thrusters are symmetrically arranged and installed on the surface of the satellite platform, as Figure 11 shown. To eliminate the interference torque in the space environment, the thruster ignition scheme is as follows: Thrusters 1–4–2–3 work sequentially in each thrust unloading period, and the working longitudes of thrusters 1 and 2, and thrusters 3 and 4 are the same, and the former and the latter have a working phase difference of 180°. The representations of the electric thrusters in the satellite body coordinate system are (-d T , d N , h c ), (d T , d N , hc ), (-d T , -d N , h c ) and (d T , -d N , h c ), so the thrust coefficients of the four-point thruster vectors are expressed as shown in Equation (18).

[0117]

[0118] The dynamic linear characterization of the electric thruster position-keeping maneuver can be described as shown in Equation (19). Among them, the orbital drift rate D is the angular rate of the GEO satellite relative to the standard geostationary orbit, λ represents the mean longitude of the working position of the electric thruster, e x and e y respectively represent the orbital eccentricity vector components, i x and i y respectively represent the orbital inclination vector components, ΔV R 、ΔV T 、ΔV N are the orbital radial, tangential, and normal velocity increments respectively, V s is the geostationary orbit velocity, and l represents the mean longitude of the working position of the electric thruster engine.

[0119]

[0120] Combining Equation (18) and Equation (19), the small-thrust geostationary orbit position-keeping control strategy is as shown in (20), where ΔV = [ΔV1 ΔV2 ΔV3 ΔV4] T respectively represent the velocity increments of the four electric thrusters, and K is the control matrix. According to the right ascension of the ascending node of the thruster startup and the installation layout parameters, the control matrix K can be obtained. In addition, according to the perturbation equation, the orbital element change vector Y in each small control period can be calculated. Therefore, the thruster velocity increment in each small control period is as shown in (21). According to the Tsiolkovsky formula, the propellant consumption and the velocity increment are as shown in Equation (22). Among them, m1 is the initial in-orbit mass of the satellite; I e sp is the specific impulse of the electric propellant; η p is the thruster efficiency; F e p is the thrust magnitude of the electric thruster; Δt is the working duration of the thruster.

[0121]

[0122] ΔV = K -1 Y (21)

[0123]

[0124] Wherein, M ep is the fuel mass consumed by the electric thruster for on-orbit position keeping, and Δv e is the velocity increment of the electric thruster.

[0125] Step 206: For the orbit transfer discipline, considering the characteristics of the large satellite mass and the more mature and stable chemical propulsion technology, the problem of the transfer of the chemical propulsion orbit transfer strategy from the GTO orbit to the GEO orbit is carried out. The ground station monitoring and observation constraints during the engine ignition operation are not considered temporarily, and only the engine continuous operation propulsion time constraint is considered. The orbit transfer process is divided into N ∈ [3, 8] stages. Considering the maximum single-thrust propulsion duration constraint of the engine, one or more parking orbits in the orbit transfer process are selected in sequence. Since the pulse required to change the inclination at the apogee is the smallest, and the GTO intersects and is inscribed with the GEO at the apogee, the satellite can effectively complete the orbit transfer by applying an apogee pulse. In this study, since the propulsion working duration constraint of the chemical propulsion will limit the pulse size, the ideal single apogee pulse needs to be divided into multiple apogee pulses. Therefore, several intermediate parking orbits need to be selected, and its orbit transfer process is as Figure 12 shown, where the single orbit maneuver is as Figure 13 shown.

[0126] Calculate the maximum pulse capability that can be provided currently as shown in Equation (23), and the fuel consumption of the entire orbit transfer and the satellite mass after orbit transfer are as shown in Equation (24). Among them, m0 represents the satellite mass before the orbit transfer; M cp represents the fuel consumption of the chemical propellant for the orbit transfer.

[0127] ΔV max = gI c sp [lnm0 - ln(m0 - F c t max / gI c sp )] (23)

[0128] M cp = m0[1 - exp(-||Δv c || / gI c sp )] (24)

[0129] Wherein, ΔV max is the maximum velocity increment that the chemical engine can provide for the satellite when the initial launch mass is m0 under the action of the maximum working duration t max ; I c sp is the specific impulse of the chemical propellant; Δv c is the velocity increment generated by the chemical thruster; M cpThe fuel mass required for a chemical thruster to transfer a satellite from a GTO large elliptical orbit to a GEO orbit.

[0130] Step 207: In the mass analysis discipline, the total mass of the satellite system consists of seven parts: the mass of the solar panels, the mass of the battery, the mass of the momentum wheel, the dry mass of the structure, the mass of the chemical propellant, the mass of the electric propulsion working fluid, and other masses. Among them, the mass of the solar panels and the battery are directly obtained from the power supply and distribution discipline model; the mass of the momentum wheel is directly obtained from the attitude control discipline model; the dry weight of the structure is obtained by finite element analysis of the structure discipline; the mass of the chemical propellant is obtained according to the orbit discipline. Considering the stability of the engine operation, the mass of the chemical propulsion fuel is increased by 10% as the final orbital transfer propellant carrying amount; for the other given masses, the mass composition of the final antenna satellite is shown in Equation (21).

[0131] M total = M solar + M battery + M control + M ep + M cp + M structure + M other (25)

[0132] Among them, M solar is the mass of the solar array, M battery is the mass of a single set of batteries, M control is the mass of the momentum wheel, M ep is the fuel mass consumed by the electric thruster for on-orbit position keeping, M cp represents the fuel consumption of the chemical propulsion for orbit transfer, M structure is the thickness of the satellite platform, M other is the set mass of other systems; in this embodiment, M other = 300 kg can be taken.

[0133] Step three: Construct an antenna satellite optimization problem model, with the minimum overall mass of the antenna satellite as the objective, the key parameters of each key discipline as optimization variables, and satisfying the constraints such as the initial and final on-orbit working power of the antenna satellite, the depth of discharge of the storage battery, the fundamental frequency of the whole satellite, and the on-orbit working position keeping accuracy.

[0134] Its mathematical model is shown in Equation (26), which includes a total of 7 disciplines, 14 design variables, and 9 constraint conditions.

[0135]

[0136] Among them, L s and W s are the length and width of the solar sail, and C s is the nominal capacity of the battery.

[0137] Step 4: Optimize the antenna-satellite optimization problem using the comprehensive feasible probability algorithm based on Pareto fitness. The constraint functions and objective functions in the optimization problem are determined in Step 2.

[0138] Taking the minimum mass of the whole satellite as the optimization objective, by optimizing the key discipline parameters involved in the antenna-satellite design, under the conditions of meeting the constraints such as the initial and final in-orbit working power of the antenna-satellite, the discharge depth of the storage battery, the first-order in-space mode of the whole satellite, and the in-orbit working position holding accuracy, an antenna-satellite design scheme is optimized. The specific implementation steps are as follows, and its optimization process is as Figure 14 shown.

[0139] Step 401: According to Step 3, determine the design variables, objective function, constraint conditions, and algorithm initial parameters (including the initial sampling number, the number of new samples, the constraint violation degree, the maximum number of calls) of the optimization problem, and set the iteration number k to 0.

[0140] Step 402: Use the Latin hypercube technique to obtain / update sample points in the design space.

[0141] Step 403: Based on Steps 2 and 3, obtain the true response values of the objective function and each constraint, and construct a KS constraint aggregation equation using the approximate models of each constraint, and save the sample points and response values to the sample database.

[0142] Step 404: Based on the information in the current sample database, construct the Kriging models of the objective function and constraint functions respectively, as shown in Equation (27)

[0143]

[0144] where, and are the Kriging models of the objective function and the i-th constraint function respectively; and are the predicted mean and predicted variance of the Kriging model of the objective function respectively; and are the predicted mean and predicted variance of the Kriging model of the i-th constraint function respectively.

[0145] Step 405: Use the Kriging models of the objective function and constraint functions to replace the original true models for optimization, and solve the optimization problem in Equation (28) through the Genetic Algorithm (GA), where x LB and x UB are the lower and upper bounds of the design variables respectively. Take the optimized design scheme as the current pseudo-optimal solution, and calculate The true model response value and add it to the sample database.

[0146]

[0147] Step 406: Determine whether the optimization meets the convergence condition. If the current number of model calls NFE is greater than NFE max , then the optimization process terminates and outputs the current feasible optimal design scheme; otherwise, the optimization process enters Step 7.

[0148] Step 407: The filling sampling process based on the comprehensive probability of Pareto fitness is as follows:

[0149] Step 7-1: Construct the Kriging prediction models of the constraint function and the objective function based on the existing samples in the database as shown in Equation (28), and construct the prediction equation of the KS equation as shown in Equation (29).

[0150]

[0151] In the formula, and are the predicted mean and predicted variance of the Kriging model of the KS equation respectively, and ρ represents the shape coefficient.

[0152] Step 7-2: Construct the expected improvement function (EI) of the objective function and the feasible probability function (PoF) of

[0153]

[0154] as shown in Equation (30). min where Ф(·) and φ(·) are the Gaussian probability distribution function and the Gaussian probability density function respectively; f min is the minimum value of the objective function of the current sample point set.

[0155] Step 7-3: In order to consider both the EI and PoF functions simultaneously, use the non-dominated sorting genetic algorithm II (NSGA-II) to solve the following multi-objective optimization problem.

[0156]

[0157] After optimization, use the PF function to sort the Pareto front as shown in Equation (32)

[0158]

[0159] In the formula, X i and Xj are the i-th and j-th Pareto solutions. Therefore, n with higher PF values are selected. v Candidates The larger the PF value of a design is, the closer it is to the optimal solution of the current design theory.

[0160] Step 7-4: Use the influence function (IF) to calculate pseudo-frontier candidate sample points and the current pseudo optimal solution The higher the IF value, the closer it is to the pseudo-optimal solution.

[0161]

[0162] Step 7-5: The expected constraint improvement fitness formula is shown in formula (34). Select the candidate design with the highest fitness value as the filling sample point. Return to step 3 and increase the number of iterations k by 1.

[0163] CFPPF(x)=f PF (x) · IF(x) (34)

[0164] Embodiment 1:

[0165] Step 1: Sort out the key disciplines involved in antenna satellite design, and use the structural design matrix to sort out the parameter relationships between disciplines. Figure 1 The overall design of antenna satellite involves geometric shielding, power supply and distribution, attitude control, structure, position keeping, orbit transfer and quality disciplines, and the Gauss-Seidel fixed-point iteration method is used to solve the antenna satellite design structure matrix to obtain a consistent satellite design solution that meets the requirements of various disciplines.

[0166] Step 2: According to the key disciplines sorted out, the analysis models of each key discipline are constructed respectively, and the design parameters and constraints of each discipline are sorted out as shown in Tables 2 and 3. Among them, the relevant fixed parameters involved in the power supply and distribution discipline, position keeping and structure discipline refer to the literature (Shi R, Liu L, Long T, et al. Surrogate assisted multidisciplinary design optimization for an all-electric GEO satellite [J]. Acta Astronautica, 2017, 138: 301-17), and the relevant fixed parameters of the attitude control discipline and orbit transfer discipline refer to the literature (Zhou Zhicheng, Qu Guangji. Communication Satellite Overall Design and Dynamic Analysis [M]. China Science and Technology Press, 2013.)

[0167] Table 2 Design Variables for Multidisciplinary Simulation

[0168]

[0169] Table 3 Output Parameters for Multidisciplinary Simulation

[0170]

[0171] Step 3: Construct an antenna-satellite optimization problem model. With the minimum mass of the entire antenna-satellite as the objective, the key parameters of each key discipline are used as optimization variables, and it satisfies the constraints such as the on-orbit working power at the beginning and end of the antenna-satellite, the depth of discharge of the energy storage battery, the first-order space mode of the entire satellite, and the on-orbit working position holding accuracy. Its mathematical model is shown in Equation (40), which includes a total of 7 disciplines, 14 design variables, and 9 constraint conditions.

[0172]

[0173] Step 4: Use the comprehensive feasible probability algorithm based on Pareto fitness to optimize the antenna-satellite optimization problem. The constraint functions and objective functions in the optimization problem are determined in Step 2. With the minimum mass of the entire satellite as the optimization objective, by optimizing the key discipline parameters involved in the antenna-satellite design, under the conditions of satisfying the constraints such as the on-orbit working power at the beginning and end of the antenna-satellite, the depth of discharge of the energy storage battery, the first-order space mode of the entire satellite, and the on-orbit working position holding accuracy, an antenna-satellite design scheme is optimized. The specific implementation steps are as follows, and its optimization process is as Figure 9 shown.

[0174] Step 1: According to Step 3, determine the design variables, objective function, constraint conditions, and algorithm initial parameters (including the initial sampling number, the number of newly added samples, the constraint violation degree, and the maximum number of calls) of the optimization problem, and set the iteration number k to 0.

[0175] Step 2: Use the Latin hypercube technique to obtain / update sample points in the design space.

[0176] Step 3: Based on Steps 2 and 3, obtain the true response values of the objective function and each constraint, and use the approximate models of each constraint to construct a KS constraint aggregation equation, and save the sample points and response values to the sample database.

[0177] Step 4: Based on the information in the current sample database, construct Kriging models of the objective function and constraint functions respectively, as shown in Equation (41)

[0178]

[0179] where, and The Kriging models of the objective function and the \(i\)-th constraint function respectively; and The predicted mean and predicted variance of the Kriging model of the objective function respectively; and The predicted mean and predicted variance of the Kriging model of the \(i\)-th constraint function respectively.

[0180] Step 5: Use the Kriging models of the objective function and the constraint functions to replace the original true models for optimization, and solve the optimization problem in Equation (42) through the Genetic Algorithm (GA), where \(x\) LB and \(x\) UB are the lower and upper bounds of the design variables respectively. Take the optimized design scheme as the current pseudo-optimal solution, calculate the response value of the true model and add it to the sample database.

[0181]

[0182] Step 6: Judge whether the optimization meets the convergence condition. If the current number of model calls \(NFE\) is greater than \(NFE\) max , the optimization process terminates, and the current feasible optimal design scheme is output; otherwise, the optimization process enters Step 7.

[0183] Step 7: The filling sampling process based on the comprehensive probability of Pareto fitness is as follows:

[0184] Step 7-1: Based on the samples existing in the database, construct the KRG prediction models of the constraint function and the objective function as shown in Equation (41), and construct the prediction equation of the KS equation as shown in Equation (43).

[0185]

[0186] In the formula, and are the predicted mean and predicted variance of the Kriging model of the KS equation respectively, and \(\rho\) represents the shape coefficient.

[0187] Step 7-2: Construct the expected improvement function (EI) of the objective function and the probability of feasibility function (PoF) of

[0188]

[0189] where Ф(·) and φ(·) are the Gaussian probability distribution function and the Gaussian probability density function respectively; f min is the minimum value of the objective function for the current sample point set.

[0190] Step 7-3: To consider both the EI and PoF functions simultaneously, the non-dominated sorting genetic algorithm II (NSGA-II) is used to solve the following multi-objective optimization problem.

[0191]

[0192] After optimization, the PF function is used to sort the Pareto front, as shown in Equation (46)

[0193]

[0194] where X i and X j are the i-th and j-th Pareto solutions. Therefore, n v candidate designs with higher PF values are selected. The larger the PF value, the closer it is to the current theoretically optimal solution.

[0195] Step 7-4: The relevance function (Influence Function, IF) is used to calculate the relevance between the pseudo-front candidate sample points and the current pseudo-optimal solution , as shown in Equation (47). A higher IF value indicates that it is closer to the pseudo-optimal solution

[0196]

[0197] Step 7-5: The expected constraint improved fitness formula is shown in Equation (48). The candidate design with the highest fitness value is selected as the filling sample point. Return to Step 3, and the iteration number k is incremented by 1.

[0198] CFPPF(x) = f PF (x)·IF(x) (48)

[0199] The results before and after optimization are compared in Tables 4 and 5. The objective function and the maximum constraint degree iteration curves of the antenna satellite optimization in the implementation case of the present invention are as Figure 15 shown.

[0200] Table 4 Comparison of design variables before and after optimization of the overall antenna satellite design scheme

[0201]

[0202]

[0203] Table 5 Objective function and constraint conditions before and after the optimization of the overall design scheme of the antenna satellite

[0204]

[0205] The above optimization design results show that the present invention can obtain a set of solutions that meet the requirements of the operating power of the antenna satellite, attitude control and position keeping requirements, and the first-order modal requirements of the project during satellite launch at a relatively low computational cost. Moreover, the total weight of the antenna satellite is reduced by 223.27 kg (8.63%), achieving the expected invention purpose and verifying the rationality, effectiveness and engineering practicability of the present invention.

[0206] The above specific description further details the purpose, technical solution and beneficial effects of the invention. It should be understood that the above is only a specific embodiment of the present invention and is not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

[0207] In summary, the above is only a preferred embodiment of the present invention and is not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A rapid optimization design method for an antenna satellite system based on a surrogate model, characterized in that The specific process is as follows: Step 1: For the antenna satellite system to be optimized, sort out the disciplines involved in its design and the coupling relationships between disciplines; Step 2: Based on the coupling relationships, construct analysis models corresponding to each discipline respectively; Step 3: Taking the minimum overall satellite mass of the antenna satellite as the optimization objective and the key parameters of each discipline as optimization variables, construct an optimization function and constraint conditions based on the analysis models constructed in Step 2; Step 4: By solving the optimization function in Step 3, obtain the optimal values of the optimization variables.

2. The rapid optimization design method of the antenna satellite system based on the surrogate model according to claim 1, characterized in that The disciplines include geometric occlusion, power supply and distribution, attitude control, structure, position keeping, orbit transfer, and mass discipline.

3. The method for rapid optimization design of an antenna satellite system based on an agent model according to claim 2, characterized in that, The calculation process of the geometric occlusion model: Determine the number of boundary intersection points N between the shadow and the solar panel BI , determine the distance d between the projection of the geometric center of the payload and the four boundaries of the solar wing array i , the relationship between i = 1, 2, 3, 4 and the payload radius R, and combine this relationship and the number of intersection points N BI to obtain the area S of the occluded solar panel shading .

4. The rapid optimization design method of the antenna satellite system based on the surrogate model according to claim 3, wherein, The geometric occlusion model is: Case ①: N BI = 0, when min(d i ) > R, S sunward = L S W S , S shading = 0, when max(d i ) < R, S sunward = 0, S shading = L S W S ; Case ②: N BI = 2, when d i < number of R N d = 0, When N d = 1, When N d = 2, When N d = 3, Case ③: N BI = 4. It can be divided into three categories according to the number of N d ; When N d = 0, When N d = 1, When N d = 2, Case ④: N BI = 6, only N d = 1 of a certain case, using integral analysis and calculation; Among them, A B , B B (x b , y b ), C B (x c , y c ), D B , E B and F B (x f , y f ) represent the intersection points of the load projection and the boundaries of the solar wing; Case ⑤: N BI = 8, there is only one type of case where N d = 0, and integral analysis and calculation are adopted; Among them, A B , B B (x b , y b ), C B (x c , y c ), D B , D B , E B , F B (x f , y f ), and G B (x g , y g ) represent the intersection points of the load projection and the boundaries of the solar wings.

5. The rapid optimization design method of the antenna satellite system based on the surrogate model according to claim 1, wherein The structure discipline is modeled as: The satellite platform consists of a service module load-bearing cylinder as the main load-bearing structure, and the platform also includes a top plate, a bottom plate, a docking ring, four partitions, a surrounding plate surface, and four storage tanks, and the antenna load part consists of a load-bearing cylinder and a hinge; The connection part is composed of a conical composite connection ring.

6. The rapid optimization design method of the antenna satellite system based on the surrogate model according to claim 5, characterized in that The design variables of the structural discipline are: W b Indicates the core thickness of the service module bottom plate, W m The core thickness of the service module top plate, W p The core thickness of the load bearing cylinder, W bc The core thickness of the service module bearing cylinder, W bt The composite ply thickness of the service bottom plate, W mt The composite ply thickness of the service module top plate, W pt The composite ply thickness of the load bearing cylinder, W bct The composite ply thickness of the service module bearing cylinder.

7. The rapid optimization design method of the antenna satellite system based on the surrogate model according to claim 1, characterized in that The position keeping discipline: Four electric thrusters are symmetrically arranged on the surface of the satellite platform, and the thruster ignition scheme is: Thrusters 1–4–2–3 work sequentially within each thrust unloading cycle, and the working longitudes of thrusters 1 and 2, and thrusters 3 and 4 are the same, and the former and the latter have a working phase difference of 180°.

8. The method for rapid optimization design of an antenna satellite system based on an agent model according to claim 7, wherein The position keeping discipline is modeled with 4 electric thrusters as: Where M ep is the fuel mass consumed by the electric thruster for on-orbit position keeping, Δv e is the velocity increment of the electric thruster; m1 is the initial in-orbit mass of the satellite; I e sp is the specific impulse of the electric propellant; η p is the efficiency of the thruster; F e p is the thrust magnitude of the electric thruster; Δt is the working duration of the thruster, g represents the acceleration due to gravity, ΔV represents the velocity increment required due to the influence of perturbations, and Δv e ≥|ΔV|.

9. The method for rapid optimization design of an antenna satellite system based on an agent model according to claim 1, characterized in that, It is clear that taking the minimum overall satellite mass of the antenna satellite as the optimization objective and the key parameters of each discipline as optimization variables, construct an optimization function and constraint conditions based on the analysis models constructed in Step 2; Specifically: find X=[L s ,W s ,C s ,H W ,W b ,W m ,W p ,W bc ,W bt ,W mt ,W pt ,W bct ,d N ,d T ​ min f(X) = M total Among them, L s and W s are the length and width of the solar panel, C s is the nominal capacity of the storage battery, H W angular momentum, W b ,W m ,W p ,W bc ,W bt ,W mt ,W pt ,W bct is a design variable for the structural discipline, d N ,d T represents the coordinates of the electric thruster; M total = M solar + M battery + M control + M ep + M cp + M structure + M other Among them, M solar is the mass of the solar array, M battery is the mass of a single set of batteries, M control is the mass of the momentum wheel, M ep is the mass of the fuel consumed by the electric thruster for on-orbit position keeping, M cp represents the fuel consumption of the chemical propellant for orbit transfer, M structure is the thickness of the satellite platform, M other is the mass of other systems set; Among them, P BOL is the power of the solar array at the initial stage of its life, P EOL is the power of the solar array at the end of its life, DOD is the depth of discharge of the battery, C A is the momentum wheel unloading margin of C, f x , f y and f z represent the bending modes of the three axes, i max represents the maximum deviation of the orbital inclination when the satellite is operating in orbit, λ max represents the maximum deviation of the mean longitude when operating in orbit, and X represents the total mass of the satellite.

10. The method for rapid optimization design of an antenna satellite system based on an agent model according to claim 1, wherein In Step 4, the comprehensive feasible probability algorithm based on Pareto fitness is used to optimize the antenna satellite optimization problem.

Images