Adaptive and shape-stable configuration optimization method and system for spherical resistance-increasing deorbit device

Abstract

The invention discloses a self-adaption and shape stability configuration optimization method and system for a spherical resistance-increasing deorbit device, and relates to the field of deorbit device engineering design. The method comprises the following steps: acquiring information data of a spacecraft deorbit system; constructing a rarefied flow environment orbit dynamic model based on the information data; determining an estimated area-mass ratio according to the expected deorbit time and the orbit height based on the proxy model; the data set is a database which takes the deorbit time and the orbit height as input and takes the area-mass ratio as output by selecting different orbit heights and area-mass ratios as initial values for simulation based on a rarefied flow environment orbit dynamic model; correcting the estimated area-mass ratio by adopting a halving cycle correction method; and designing the configuration of the spherical resistance-increasing deorbit device according to the adaptive area-mass ratio by adopting a projection area calculation method and a multi-objective optimization method of an object in any shape, and determining the configuration of the spherical resistance-increasing deorbit device. According to the invention, the efficiency and reliability of the deorbit process can be improved.

Description

Technical Field

[0001] This application relates to the field of off-track device engineering design, and in particular to an adaptive and shape-stabilized configuration optimization method and system for a spherical drag-increasing off-track device. Background Technology

[0002] To reduce debris generation, equipping constellation satellites with active deorbiting devices is considered a necessary cleanup measure. In low Earth orbit, drag-increasing deorbiting devices are used to increase atmospheric drag by increasing the effective surface area of ​​the spacecraft, achieving rapid deorbiting. Considering the influence of multi-source disturbances and attitude-orbit coupling, the dynamic model of drag-increasing deorbiting devices is complex; moreover, the variety of deorbiting targets and the large orbital span make it difficult to quickly obtain a drag-increasing deorbiting device configuration that adapts to engineering constraints. In addition, the attitude and shape stability of the device affects deorbiting efficiency and reliability. Summary of the Invention

[0003] The purpose of this application is to provide an adaptive and shape-stabilized configuration optimization method and system for a spherical drag-increasing derailment device, which can increase the efficiency and reliability of the derailment process.

[0004] To achieve the above objectives, this application provides the following solution:

[0005] In a first aspect, this application provides an adaptive and shape-stabilized configuration optimization method for a spherical drag-increasing deorbiting device, applied to a spacecraft deorbiting system; the spacecraft deorbiting system includes a spacecraft and a drag-increasing deorbiting device; the method includes:

[0006] Acquire information data from the spacecraft deorbiting system; the information data includes position vectors and velocity vectors.

[0007] Based on the aforementioned information data, a rarefied flow environment orbital dynamics model is constructed. This rarefied flow environment orbital dynamics model is a mathematical model that considers the effects of atmospheric drag perturbation, solar radiation pressure perturbation, Earth shape perturbation, and lunar perturbation on the spacecraft's orbital motion in order to determine the rate of change of the orbital state vector.

[0008] The estimated surface-to-mass ratio is determined based on the expected de-orbit time and orbital altitude using a surrogate model. The surrogate model is obtained by training a backpropagation neural network on a dataset. The dataset is obtained by simulating the orbital dynamics model in the rarefied flow environment by selecting different orbital altitudes and surface-to-mass ratios as initial values, resulting in a database with de-orbit time and orbital altitude as inputs and surface-to-mass ratio as output.

[0009] The estimated surface-to-material ratio is corrected using a bisectional cyclic correction method to obtain the suitable surface-to-material ratio;

[0010] Using methods for calculating the projected area of ​​objects of arbitrary shapes and multi-objective optimization, the configuration of the spherical drag-enhancing deorbiting device is designed based on the adapted surface-to-mass ratio, and the configuration of the spherical drag-enhancing deorbiting device is determined. The configuration of the spherical drag-enhancing deorbiting device is used to meet the post-mission handling requirements of constellation satellites, increase the environmental forces and effective area of ​​the spacecraft, and achieve rapid deorbiting.

[0011] Secondly, this application provides an adaptive and shape-stabilized configuration optimization system for a spherical drag-increasing derailment device, comprising:

[0012] The information data acquisition module is used to acquire information data from the spacecraft deorbiting system; the information data includes position vectors and velocity vectors.

[0013] The model building module is used to construct a rarefied flow environment orbital dynamics model based on the information data; the rarefied flow environment orbital dynamics model is a mathematical model that considers the effects of atmospheric drag perturbation, solar radiation pressure perturbation, Earth shape perturbation and lunar perturbation on the spacecraft's orbital motion to determine the rate of change of the orbital state vector;

[0014] The estimated surface-to-mass ratio determination module is used to determine the estimated surface-to-mass ratio based on the expected de-orbit time and orbital height using a surrogate model. The surrogate model is obtained by training a backpropagation neural network on a dataset. The dataset is a database obtained by simulating the orbital dynamics model of the rarefied flow environment by selecting different orbital heights and surface-to-mass ratios as initial values, with de-orbit time and orbital height as inputs and surface-to-mass ratio as output.

[0015] The correction module is used to correct the estimated surface-to-material ratio using a bisectional cyclic correction method to obtain a suitable surface-to-material ratio.

[0016] The configuration optimization design module is used to design the configuration of the spherical drag-enhancing deorbiting device based on the adaptive surface-to-mass ratio using the projected area calculation method for objects of arbitrary shapes and the multi-objective optimization method. The configuration of the spherical drag-enhancing deorbiting device is used to meet the post-mission handling requirements of the constellation satellites, increase the environmental forces and effective area of ​​the spacecraft, and achieve rapid deorbiting.

[0017] According to the specific embodiments provided in this application, the following technical effects are disclosed:

[0018] This application provides an adaptive and shape-stable configuration optimization method and system for a spherical drag-increasing deorbiting device. The method involves acquiring information data about the spacecraft deorbiting system; constructing a rarefied flow environment orbital dynamics model based on this data; determining the estimated surface-to-mass ratio (SMR) based on a surrogate model according to the desired deorbiting time and orbital altitude; obtaining a database with deorbiting time and orbital altitude as input and SMR as output based on simulations using the rarefied flow environment orbital dynamics model; correcting the estimated SMR using a bipartite cyclic correction method; and designing the spherical drag-increasing deorbiting device configuration based on an adaptive SMR using a method for calculating the projected area of ​​an arbitrary-shaped object and a multi-objective optimization method. This application constructs a surrogate model of the drag-increasing deorbiting system dynamics model in a rarefied flow atmosphere based on a neural network, enabling intelligent and rapid calculation of the adaptive SMR of the drag-increasing deorbiting device to adapt to engineering constraints. Then, through a multi-objective optimization algorithm, a shape-stable configuration that meets the SMR requirements and maximizes drag is obtained, improving the efficiency of the deorbiting process. This increases the efficiency and reliability of the deorbiting process. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 A flowchart of an adaptive and shape-stabilized configuration optimization method for a spherical drag-increasing derailment device;

[0021] Figure 2 This is a schematic diagram illustrating the relationship between deorbit time and orbital altitude.

[0022] Figure 3 This is a schematic diagram illustrating the relationship between off-orbit time and surface-to-mass ratio.

[0023] Figure 4 This is a schematic diagram showing the initial derailment year in the relationship between derailment time and initial derailment date.

[0024] Figure 5 This is a schematic diagram illustrating the 11-year cycle of solar activity parameters corresponding to the relationship between deorbit time and initial deorbit date.

[0025] Figure 6 This is a schematic diagram of the proxy model topology.

[0026] Figure 7 This is a schematic diagram illustrating how the mean squared error changes with the number of training rounds;

[0027] Figure 8 For error histogram;

[0028] Figure 9 This is a schematic diagram of the test results;

[0029] Figure 10 This diagram illustrates the relationship between the required surface-to-mass ratio and the expected deorbit time and orbital altitude.

[0030] Figure 11 This is a flowchart based on the bisection cycle correction;

[0031] Figure 12 Schematic diagram of a spherical drag-increasing derailment device;

[0032] Figure 13 Flowchart for calculating the projected area of ​​an object of arbitrary shape;

[0033] Figure 14 This is a schematic diagram illustrating the error in the windward area.

[0034] Figure 15 Flowchart illustrating the design concept of an adaptive and shape-stabilized configuration optimization method for a spherical drag-increasing derailment device;

[0035] Figure 16 The structural diagram of the adaptive and shape-stabilized configuration optimization system for the spherical drag-increasing derailment device. Detailed Implementation

[0036] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0037] This application addresses a spherical drag-enhancing derailment device. It constructs a surrogate model of the drag-enhancing derailment system in a rarefied atmospheric environment based on a neural network, enabling intelligent and rapid calculation of the adaptive surface-to-mass ratio of the drag-enhancing derailment device to adapt to engineering constraints. Then, through a multi-objective optimization algorithm, a shape-stable configuration that meets the surface-to-mass ratio requirements and maximizes drag is obtained, improving the efficiency of the derailment process.

[0038] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0039] In one exemplary embodiment, an adaptive and shape-stabilized configuration optimization method for a spherical drag-increasing deorbiting device is provided, applied to a spacecraft deorbiting system; the spacecraft deorbiting system includes a spacecraft and a drag-increasing deorbiting device. Figure 1As shown, the adaptive and shape-stabilized configuration optimization method for the spherical drag-increasing derailment device includes:

[0040] Step 100: Acquire information data from the spacecraft deorbiting system. This information data includes the position vector and velocity vector.

[0041] Step 200: Construct an orbital dynamics model for a rarefied flow environment based on information data. The orbital dynamics model for a rarefied flow environment is a mathematical model that considers the effects of atmospheric drag perturbations, solar radiation pressure perturbations, Earth shape perturbations, and lunar perturbations on the spacecraft's orbital motion to determine the rate of change of the orbital state vector.

[0042] The mathematical expression corresponding to the orbital dynamics model in a rarefied flow environment is:

[0043]

[0044] Where m is the mass of the spacecraft deorbiting system; r is the position vector of the spacecraft deorbiting system; v is the velocity vector of the spacecraft deorbiting system; F A , represents atmospheric drag; F S Solar radiation pressure; F U To account for the Earth's central gravitational force due to perturbations in the Earth's shape; F T To account for the gravitational pull of the Sun and Moon due to perturbations in the Earth's shape; The velocity vector of the spacecraft's deorbiting system; This represents the acceleration vector of the spacecraft's deorbiting system.

[0045] Step 300: Determine the estimated surface-to-mass ratio based on the expected deorbit time and orbital altitude using the surrogate model. The surrogate model is obtained by training a backpropagation neural network on a dataset; the dataset is a database obtained by simulating a rarefied flow environment orbital dynamics model by selecting different orbital altitudes and surface-to-mass ratios as initial values, with deorbit time and orbital altitude as inputs and surface-to-mass ratio as output.

[0046] The methods for determining the proxy model specifically include:

[0047] Construct a dataset and normalize it to obtain a processed dataset; divide the processed dataset into training, validation, and test sets according to a set ratio; construct a backpropagation neural network.

[0048] The training set is input into the backpropagation neural network, and the gradient descent method is used to train the backpropagation neural network based on both forward and backward propagation processes to obtain the trained backpropagation neural network.

[0049] The backpropagation neural network trained with the validation set input values ​​is validated to obtain the validated backpropagation neural network; the test set is input into the validated backpropagation neural network, and the mean squared error is used as the evaluation metric to test it to obtain the tested backpropagation neural network; the tested backpropagation neural network is determined as the surrogate model.

[0050] A backpropagation neural network consists of an input layer, hidden layers, and an output layer.

[0051] During the positive propagation process:

[0052] The input layer is used to acquire the training set and transmit it to the hidden layer. The hidden layer uses a nonlinear transformation method to process the training set to obtain the hidden layer output. The expression for the hidden layer output is:

[0053]

[0054] The output layer is used to determine the output result of the output layer based on the output result of the hidden layer; the expression corresponding to the output result of the output layer is:

[0055]

[0056] Where g is the activation function of the hidden layer; x is the input node, y is the hidden node, and w is the activation function of the hidden layer. (1) The weights from the input layer to the hidden layer. z is the input layer bias; z is the output node, w (2) The weights from the hidden layer to the output layer. This is for the hidden layer bias.

[0057] During the backpropagation process, gradient descent is used to optimize the weight parameters with the goal of minimizing the loss function; the expression for the loss function is:

[0058]

[0059] Where Loss is the loss function; z- is the predicted output; ) represents the actual output.

[0060] Step 400: The estimated dough-to-material ratio is corrected using a bisectional correction method to obtain the suitable dough-to-material ratio.

[0061] The method of refining the estimated surface-to-quality ratio using a bisectional cyclic correction method to obtain the suitable surface-to-quality ratio includes:

[0062] The estimated surface-to-mass ratio was initially corrected for solar activity level to obtain the solar activity index and the corrected surface-to-mass ratio.

[0063] The solar activity index and the corrected surface-to-mass ratio were corrected by a bisectional differential method to obtain the suitable surface-to-mass ratio.

[0064] The expression for the solar activity index is:

[0065]

[0066] The expression corresponding to the corrected surface-to-weight ratio is:

[0067]

[0068] Where β = is the solar activity index; y is the divisor; = F107(y) is the average solar activity index for the corresponding year in a solar cycle; AMR0 is the corrected surface-to-mass ratio; AMR R To estimate the surface-to-texture ratio.

[0069] In one embodiment, a bisectional cyclic correction method is used to perform bisectional differential correction on the solar activity index and the corrected surface-to-mass ratio to obtain the suitable surface-to-mass ratio, specifically including:

[0070] Using the corrected surface-to-quality ratio as a boundary, the surface-to-quality ratio is multiplied or divided by 2 by the magnitude of the derailment time and the expected derailment time until a surface-to-quality ratio that differs from the corrected surface-to-quality ratio is found as another boundary of the array.

[0071] The bounded array is sorted in ascending order. Based on the given target value, the search is performed within the set search range from the middle position of the bounded array according to the set search rules based on the solar activity index to determine the suitable surface-to-mass ratio.

[0072] Specifically, setting search rules includes:

[0073] If the search value is exactly equal to the middle element value, the index of the middle element value is returned; if the search value is smaller than the middle element value, the first half of the entire search range is used as the new search range; if the search value is larger than the middle element value, the second half of the entire search range is used as the new search range.

[0074] Step 500: Using methods for calculating the projected area of ​​objects of arbitrary shapes and multi-objective optimization, the configuration of the spherical drag-enhancing deorbiting device is designed based on the suitable surface-to-mass ratio, and the configuration of the spherical drag-enhancing deorbiting device is determined. The spherical drag-enhancing deorbiting device configuration is used to meet the post-mission handling requirements of the constellation satellites, increase the environmental forces and effective area of ​​the spacecraft, and achieve rapid deorbiting.

[0075] As an optional implementation method, an arbitrary-shaped object projection area calculation method and a multi-objective optimization method are used to design the configuration of the spherical drag-increasing derailment device based on the suitable surface-to-mass ratio. The specific configuration of the spherical drag-increasing derailment device includes:

[0076] The projected area of ​​the spherical drag-increasing derailment device is determined by projecting it in different directions using a method for calculating the projected area of ​​objects of arbitrary shapes.

[0077] The objective function is determined by taking shape stability and cost as optimization objectives.

[0078] The optimization problem is determined based on the projected area and the adapted surface-to-weight ratio.

[0079] A genetic algorithm is used to solve the optimization problem in multiple objectives based on the objective function, and the solution results are obtained. Based on the solution results, the configuration of the spherical drag-increasing derailment device is designed and the configuration of the spherical drag-increasing derailment device is determined.

[0080] The expression for the objective function is:

[0081]

[0082] The mathematical expression for the optimization problem is:

[0083]

[0084] Where f1 is the first objective function; n is the number of petal moduli; Δ is the windward area error; f2 is the second objective function; R is the radius; m b The mass of the deorbiting device's membrane sphere is given by ρ; P is the weighting coefficient; m is the mass of the spacecraft's deorbiting system; AMR E To adapt to the dough-to-texture ratio; S min N represents the minimum projected area; N+ represents a positive integer.

[0085] In practical applications, different engineering missions require different spacecraft masses, orbital altitudes, deorbit start dates, and deorbit time requirements. Therefore, it is necessary to quickly estimate the surface-to-mass ratio of the required drag-enhancing deorbiting device, guided by mission objectives and time constraints, to facilitate subsequent configuration design and optimization.

[0086] The deorbiting system is subject to complex and variable disturbances, and the deorbiting time is long, which leads to long calculation times for orbital dynamics propagation. To achieve efficient mission-oriented size prediction, a surrogate model for the orbital propagation of the deorbiting system is established, constructing a mapping from orbital altitude and expected deorbiting time to the surface-to-mass ratio (SMR), enabling rapid acquisition of the initial SMR. Finally, a bisection method is used to correct it, and combined with the mission target mass, a more accurate required SMR can be obtained.

[0087] 1. Construct a trajectory dynamics model for a rarefied flow environment.

[0088] For low-Earth orbit spacecraft equipped with drag-enhancing deorbiting devices, atmospheric drag perturbations, solar radiation pressure perturbations, Earth shape perturbations, and lunar perturbations are important factors affecting the spacecraft's orbital motion. The rate of change of the orbital state vector can be defined as:

[0089]

[0090] In the thin atmosphere of low Earth orbit, the characteristic dimensions of a spacecraft are close to the mean free path of the atmosphere. Therefore, a continuous medium model cannot be directly used to describe the gas flow field. Instead, a free molecular flow model is used to calculate the atmospheric drag on the system. This model describes the motion of the spacecraft in the atmospheric flow field as the collisions between gas molecules and the spacecraft surface. By applying a surface integral to the normal pressure per unit surface area on the system surface, the expression for atmospheric drag can be obtained as follows:

[0091]

[0092] θ is the angle between the incoming gas flow and the normal to a unit surface element of the system. σ is the tangential angle between the incoming gas and a unit surface element of the system. n T is the momentum adaptation coefficient. u T is the system surface temperature. ∞ m represents the incident molecular density and temperature. ∞ Let ρ be the mass of a gas molecule, ρ be the atmospheric density, and Q be the molecular velocity ratio.

[0093] The solar radiation pressure perturbation force acting on the system is expressed as:

[0094]

[0095] p SR The solar pressure is given by 1 astronomical unit (AU), η is the reflection coefficient, and K is the solar pressure. S The solar visibility coefficient at the system's location is related to the Earth's shadow model used, u s is the unit vector in the direction of the sun in the inertial frame. r is the position vector of the spacecraft; when the variable is not bold, r is the magnitude of the vector.

[0096] The central gravitational force considering the non-spherical perturbation of the Earth is expressed as follows:

[0097]

[0098] R e denoted as the Earth's average equatorial radius, J2 as the harmonic coefficient, and μ as the Earth's gravitational constant.

[0099] The Sun and Moon exert gravitational force on the system, and this perturbation force is:

[0100]

[0101] μ sun μ moon The gravitational constants of the Sun and the Moon, respectively; r sun r moon These are the position vectors of the Sun and the Moon, respectively.

[0102] Substituting formulas (2), (4), (5), and (6) into formula (1) yields the system's orbital dynamics model (orbital dynamics model in a rarefied flow environment).

[0103] 2. Based on the dynamic model obtained above, simulations were conducted using different orbital altitudes and areal-to-mass ratios as initial values. A database was obtained with off-orbit time and orbital altitude as inputs and areal-to-mass ratio as output. Furthermore, based on the Back Propagation neural network method, a proxy model for off-orbit time, orbital altitude, and areal-to-mass ratio was constructed to quickly obtain the estimated areal-to-mass ratio (AMR). R .

[0104] A backpropagation neural network is used to establish the surrogate model.

[0105] Step 1: Build the database.

[0106] Based on the established system orbital dynamics model, the system's deorbit time is mainly determined by orbital altitude, surface-to-mass ratio, and initial deorbit date, with specific effects as follows: Figure 2 and Figure 3 As shown in the figure, the initial deorbit date affects solar activity parameters and geomagnetic activity parameters, which in turn affect atmospheric density, significantly impacting the deorbit process. However, it is difficult to give a definite range for the initial deorbit date. Therefore, when constructing the database, only the influence of orbital altitude and surface-to-mass ratio on deorbit time is considered. In the simulation process, solar activity parameters F107, F107A, and geomagnetic activity parameter Ap are considered constants. Here, F107 is the solar radio flux at a wavelength of 10.7 cm, F107A is the 81-day average F107, and Ap is the exponent of the global daily geomagnetic disturbance intensity. Since the influence of solar activity on atmospheric density exhibits an 11-year cycle, the average values ​​of solar activity parameters and geomagnetic activity parameters over the past 33 years are used as the initial values ​​for the simulation. After obtaining the fitted area results from the surrogate model, corrections are made to account for the initial deorbit date. Figure 4 and Figure 5 This is a schematic diagram illustrating the relationship between derailment time and initial derailment date.

[0107] To improve fitting accuracy, the orbital height and surface area ratio (AMR) are sampled using a logarithmic function. Specifically, a sparser mesh is used when the orbital height is low, and a denser mesh is used when the orbital height is high; similarly, a denser mesh is used when the AMR is low, and a sparser mesh is used when the semi-major axis (AMR) is high. The orbital height H ranges from [200, 700] km, and the AMR ranges from [0.01, 2] kg / m². 2 .

[0108] Step 2: Data preprocessing.

[0109] Step one yields a set of corresponding orbital height, surface-to-mass ratio, and departure time, where orbital height and departure time are the inputs to the neural network, and surface-to-mass ratio is the output of the neural network.

[0110] The input data needs to be processed. First, considering practical engineering applications, extreme cases with off-orbit times of less than one day and greater than 25 years are excluded. Second, normalization is performed. By adjusting the data distribution and scaling it to a uniform range, scale differences are eliminated, which not only helps accelerate model training but also improves model convergence and stability. The min-max normalization method can scale data to the range [0, 1], suitable for data with known and stable numerical ranges.

[0111]

[0112] Step 3: Divide the data obtained in Step 2 into training set, validation set and test set. 70% is used for training; 15% is used to verify whether the network is generalizing and to stop training before overfitting; 15% is used to independently test the network's generalization and to train and fine-tune the model through parameters.

[0113] The Back Propagation neural network consists of three spatial layers: the input layer, the hidden layer, and the output layer.

[0114] The core idea is to use gradient descent to perform calculations, and with the help of this advanced technique, the mean square error between the network's expected transmission value and the actual output value can be minimized.

[0115] The entire process involves two steps: forward propagation of the signal and backward propagation of the error. The specific surrogate model topology is as follows: Figure 6 As shown.

[0116] During forward propagation, the input signal is primarily applied to the output node via the hidden layer using a nonlinear transformation, resulting in a strong output signal. The hidden layer output is as follows:

[0117]

[0118] Convert to matrix form:

[0119]

[0120] Where g is the activation function of the hidden layer, using the sigmoid function; x is the input node, y is the hidden node, and w is the input node. (1) The weights from the input layer to the hidden layer. This is the input layer bias.

[0121] Similarly, the output layer outputs:

[0122]

[0123] Where z is the output node, w (2) The weights from the hidden layer to the output layer. This is for the hidden layer bias.

[0124] During backpropagation, the gradient descent principle is used to find the optimal threshold and weights. For the parameter w, optimization is performed according to the chain rule to minimize the loss function.

[0125]

[0126] z is the actual output, z is the predicted output, and η is the transmission speed.

[0127] The mean squared error (MSE) is a commonly used metric for evaluating the accuracy of surrogate models. The closer the MSE is to 0, the higher the accuracy of the model.

[0128]

[0129] Z represents the actual output, z represents the predicted output, and N represents the actual output. k It represents the total number of samples.

[0130] Based on neural networks, the latent functional relationships are learned through training on data. The mean squared error changes with the number of training rounds as follows: Figure 7 The minimum value is 2.1464 × 10⁻⁶ in round 9402. -6 The training session ended at this point.

[0131] Error histogram as follows Figure 8 As shown, the blue bars represent training data, the green bars represent validation data, and the red bars represent test data. Above 95% of the data has a quality ratio error of less than 0.0013m. 2 Within / kg.

[0132] To test the surrogate model results, 20 sets of orbital altitudes and expected deorbit times were randomly selected within the main research scope of this application (the area within the red box in the figure), and the estimated surface-to-mass ratio was obtained through the surrogate model. This surface-to-mass ratio and orbital altitude were then substituted into the orbital dynamics model to obtain the simulated deorbit time. The percentage errors of the expected deorbit time and the simulated deorbit time are shown below. Figure 9 As shown, the Percentage Error is within 1%, with an average error of 0.35%, verifying the accuracy of the neural network.

[0133] Based on this proxy model, the relationship between the required surface-to-mass ratio and the desired deorbit time and orbital altitude can be quickly obtained, such as... Figure 10 As shown.

[0134] 3. Based on the estimated surface-to-mass ratio (AMR) obtained from the proxy model R The estimated dimensions of the drag-increasing sphere, AMR, are obtained through a bivariate cyclic correction method. E .

[0135] Based on the obtained surrogate model, the initial surface-to-mass ratio (SMR) that meets the constraints of the target orbital altitude and expected deorbit time under the condition of mean solar activity can be obtained. Considering the influence of the initial deorbit date, the estimated SMR is differentially corrected based on a bipartite cycle to achieve the prediction of the drag-increasing sphere's fit size.

[0136] The estimated surface-to-mass ratio (AMR) obtained from the surrogate model R First, the solar activity level of the initial deorbit year is considered for preliminary correction. Then, the resulting surface-to-mass ratio (AMR0) is used as input for binary differential correction to obtain a more accurate fitted surface-to-mass ratio (AMR). E .

[0137] Step 1: Analyze the estimated surface-to-mass ratio (AMR) obtained from the surrogate model. R To make preliminary corrections to the solar activity level, we can obtain the solar activity index and AMR0.

[0138] The solar activity index β is introduced, representing the level of solar activity as a dimensionless scalar value, as shown in Table 1. The formulas for calculating the solar activity index and AMR0 are as follows.

[0139] y = mod(year, 11) + 1 (15)

[0140]

[0141] In the formula, mod(x, y) is the remainder, x is the dividend, and y is the divisor.

[0142] Table 1 Solar Activity Index

[0143]

[0144] Step 2: Perform a binary differential correction on the solar activity index and AMR0 obtained in Step 1 to obtain a more accurate fit surface-to-mass ratio (AMR). E .

[0145] When an array or collection contains a large number of elements, the conventional way to track the position or existence of a specific element is to loop through each element until the desired element is found. This search method is very inefficient. In such cases, a binary search approach is needed to improve search efficiency. Assuming the bounded array is sorted in ascending order, for a given target value, the search starts from the middle of the array: 1. If the search value is exactly equal to the middle element, return the index of the middle element; 2. If the search value is smaller than the middle value, use the first half of the entire search range as the new search range; 3. If the search value is larger than the middle value, use the second half of the entire search range as the new search range.

[0146] The process based on bisectional cyclic correction is as follows: Figure 11 As shown. Figure 11 The yellow section calculates array boundaries, with AMR0 as one boundary. It multiplies or divides the surface-to-mass ratio by 2 based on the difference between the deorbit time and the expected deorbit time, continuing until a different surface-to-mass ratio is found, which becomes the other boundary of the array. The red section performs a bisection loop, i.e., a bisection search. The blue section outputs the adaptive surface-to-mass ratio. AMR0 is the predicted surface-to-mass ratio after solar activity correction. E The fitted surface-to-mass ratio is the result of binary differential correction, R is the fitted size of the drag-enhancing sphere (i.e., the radius of the sphere), T is the deorbit time, TT is the desired deorbit time, and ΔT is the deorbit time error. The dynamic model used is the established system orbit model, and the initial deorbit date also needs to be input.

[0147] Table 2 provides an example of calculating the fit surface-to-mass ratio (using an AMD Ryzen 7 5800X8 CPU @ 3800MHz). It can be seen that when the percentage error of the off-orbit time is less than 2%, this method can obtain the fit surface-to-mass ratio in a relatively short time. Then, considering the mass of the off-orbit target and the mass of the drag-increasing sphere itself, the size of the fit drag-increasing sphere can be obtained.

[0148] Table 2. Surface-to-mass ratio based on bisectional cycle correction.

[0149]

[0150] 3. Based on the estimated size AMR of the drag-enhancing ball obtained in step 2 above. EThe optimal configuration of the drag-increasing derailment device is designed using methods for calculating the projected area of ​​objects of arbitrary shapes and multi-objective optimization.

[0151] For spherical devices, attitude stability has little impact on the windward area. The windward area error and mass can be reduced by optimizing the radius R and the number of petal moduli n (hereinafter referred to as petal number) while satisfying the adaptive surface-to-mass ratio constraint, so that it has omnidirectional drag-increasing characteristics and economy.

[0152] Model of spherical drag-increasing off-track device as follows Figure 12 As shown.

[0153] The radius R and the number of lobes n affect shape stability and quality, where shape stability is represented by the projected area error, defined as follows:

[0154]

[0155] Among them, S max and S min These are the maximum and minimum projected areas, respectively. The average projected area.

[0156] The maximum projected area is the area of ​​a circle with radius R, and the minimum projected area is the side length. The area of ​​a regular n-gon is calculated as follows:

[0157] S max =πR 2 (19)

[0158]

[0159] To calculate the average projected area The projected area in each direction needs to be calculated.

[0160] Considering that the drag-increasing derailment system is an irregular object containing curved and concave surfaces, a method for calculating the projected area of ​​an arbitrary-shaped object based on the finite element method is proposed. The flowchart is as follows: Figure 13 As shown.

[0161] (1) Establish a solid coordinate system and a projection plane coordinate system, and calculate the coordinate transformation matrix.

[0162] Assume the normal vector of the projection plane is n v,b =[n v,b_x n v,b_y n v,b_z ] T The projection plane passes through point P_p = [-2a -2b -2c] T Then the equation of the projection plane is:

[0163] n v,b_x×(x+2a)+n v,b_y ×(y+2b)n v,b_z ×(z+2c)=0 (21)

[0164] The coordinates of the projection of any point i on the plane are:

[0165] i_p=i+[n v,b ·(P_p-i)]n v,b (twenty one)

[0166] To obtain the coordinate transformation matrix between a 3D coordinate system and a 2D coordinate system, we need to find the coordinates of three non-collinear points whose connecting lines are not perpendicular in both coordinate systems. Taking points O, A, and B as an example, their coordinates in the 2D coordinate system are as follows:

[0167]

[0168] The coordinate transformation matrix between the two coordinate systems is:

[0169] P = [O p A p B p [O_p A_p B_p] -1 (twenty four)

[0170] Wherein, the subscript "p" represents the coordinates of the projected point in the planar coordinate system, and the subscript "_p" represents the coordinates of the projected point in the spatial coordinate system.

[0171] (2) Divide the object surface into a grid and project each point of the object grid onto the projection plane.

[0172] (3) Divide the projection plane into a grid and determine whether the object's projection point is within the grid. If it is, set the matrix element corresponding to this grid to 1; otherwise, set it to 0. Add all the elements of the matrix to get the projected area of ​​the system.

[0173] This method allows us to obtain the projected area of ​​the spherical drag-increasing off-track device in different directions.

[0174] The fitting formula is shown below. The coefficient of determination R0 2 =0.9999, indicating a very good fit. As n approaches infinity, It converges to the area of ​​a circle, which is consistent with the physical principle.

[0175]

[0176] Substituting into the formula for calculating the windward area error (Formula 18), as n increases, the windward area error decreases, and the shape stability improves. A schematic diagram corresponding to the windward area error is shown below. Figure 14.

[0177]

[0178] However, increasing the number of lobes leads to an increase in mass, and this factor must be considered when optimizing the number of lobes. In SolidWorks software, spherical device models with different numbers of lobes and radii are created. The surface area is obtained using the software and fitted, then multiplied by the areal density σ. m This refers to the mass of the spherical membrane. Let σ be the areal density of the heat sealant required to bond the spherical segments. g Each bonding width is d g The mass of the heat sealant is shown in the following formula. The smaller the mass of the heat sealant, the lower the cost.

[0179]

[0180] For the two optimization objectives of shape stability and cost, the objective function is as follows:

[0181]

[0182] For multi-objective optimization, assuming the weight coefficient of f2 is P, its physical meaning is the proportion of the sunlight-facing area considered in the objective function, ranging from [0,1]. Then the entire optimization problem is equivalent to the following:

[0183]

[0184] The objective is to minimize the projected area error and the mass of the spherical device; the constraints are that the minimum projected area is greater than the total mass multiplied by the adaptive surface-to-mass ratio, the radius is greater than 0, and the number of lobes is a positive integer greater than or equal to 4.

[0185] Genetic algorithms are designed based on the evolutionary laws of organisms in nature. They are computational models that simulate the biological evolutionary process of natural selection and genetic mechanisms in Darwin's theory of evolution, and are a method for searching for optimal solutions by simulating the natural evolutionary process. Through optimization using genetic algorithms, the optimal configuration of the spherical drag-increasing derailment device is obtained, balancing shape stability and mass while ensuring a minimum windward area that meets the adaptive surface-to-mass ratio.

[0186] Assuming the system mass is 50 kg, the adaptive surface-to-mass ratio and the corresponding optimization results are shown in Table 3.

[0187] Table 3. Optimization Results of the Spherical Drag-Increasing Derailment Device Configuration

[0188] Case <![CDATA[AMR E / m 2 ·kg -1 ]]> <![CDATA[S E / m 2 ]]> R / m n A 0.0047 0.235 0.2756 10 B 0.050 2.5 0.9163 8 C 1.558 77.9 5.1152 8 D 0.740 37 3.5842 7

[0189] To meet the post-mission handling requirements of constellation satellites and protect environmental safety and sustainable development, spacecraft can be equipped with drag-increasing deorbiting devices that amplify environmental forces, thereby increasing the spacecraft's effective surface area and enabling rapid deorbiting. For example... Figure 15 As shown, this application takes the deorbiting at the end of a spacecraft's lifespan as a background, fully considering the effects of environmental perturbations such as atmospheric drag, and establishes a system dynamics model that includes a drag-enhancing deorbiting device. A surrogate model is constructed using a neural network to perform efficient and intelligent adaptive surface-to-mass ratio calculations for the drag-enhancing deorbiting device. For a spherical drag-enhancing deorbiting device, a method for calculating the projected area of ​​an arbitrary-shaped object is proposed. Configuration optimization is performed with shape stability and mass as objectives, increasing the efficiency and reliability of the deorbiting process and laying the foundation for the engineering design and on-orbit application of drag-enhancing deorbiting devices.

[0190] In one exemplary embodiment, such as Figure 16 As shown, an adaptive and shape-stabilized configuration optimization system for a spherical drag-increasing derailment device is provided, comprising:

[0191] The information data acquisition module is used to acquire information data from the spacecraft deorbiting system; the information data includes position vectors and velocity vectors.

[0192] The model building module is used to construct orbital dynamics models for rarefied flow environments based on information data. The orbital dynamics model for rarefied flow environments is a mathematical model that considers the effects of atmospheric drag perturbation, solar radiation pressure perturbation, Earth shape perturbation, and lunar perturbation on the orbital motion of spacecraft in order to determine the rate of change of the orbital state vector.

[0193] The module for determining the estimated surface-to-mass ratio is used to determine the estimated surface-to-mass ratio based on the expected de-orbit time and orbital altitude using a surrogate model. The surrogate model is obtained by training a backpropagation neural network on a dataset. The dataset is a database obtained by simulating a rarefied flow environment orbital dynamics model by selecting different orbital altitudes and surface-to-mass ratios as initial values, with de-orbit time and orbital altitude as inputs and surface-to-mass ratio as output.

[0194] The correction module is used to correct the estimated surface-to-material ratio using a bisectional correction method to obtain the appropriate surface-to-material ratio.

[0195] The configuration optimization design module is used to design the configuration of the spherical drag-enhancing deorbiting device based on the adaptive surface-to-mass ratio using the projected area calculation method for objects of arbitrary shapes and multi-objective optimization methods. The configuration of the spherical drag-enhancing deorbiting device is used to meet the post-mission handling requirements of constellation satellites, increase the environmental forces and effective area of ​​the spacecraft, and achieve rapid deorbiting.

[0196] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0197] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for adaptive and shape-stabilized configuration optimization of a spherical drag-increasing derailment device, characterized in that, Applied to spacecraft deorbiting systems; the spacecraft deorbiting system includes a spacecraft and a drag-increasing deorbiting device; the method includes: Acquire information data from the spacecraft deorbiting system; the information data includes position vectors and velocity vectors. Based on the aforementioned information data, a rarefied flow environment orbital dynamics model is constructed. This rarefied flow environment orbital dynamics model is a mathematical model that considers the effects of atmospheric drag perturbation, solar radiation pressure perturbation, Earth shape perturbation, and lunar perturbation on the spacecraft's orbital motion in order to determine the rate of change of the orbital state vector. The estimated surface-to-mass ratio is determined based on the expected de-orbit time and orbital altitude using a surrogate model. The surrogate model is obtained by training a backpropagation neural network on a dataset. The dataset is obtained by simulating the orbital dynamics model in the rarefied flow environment by selecting different orbital altitudes and surface-to-mass ratios as initial values, resulting in a database with de-orbit time and orbital altitude as inputs and surface-to-mass ratio as output. The estimated surface-to-material ratio is corrected using a bisectional cyclic correction method to obtain the suitable surface-to-material ratio; Using methods for calculating the projected area of ​​objects of arbitrary shapes and multi-objective optimization, the configuration of the spherical drag-enhancing deorbiting device is designed based on the adapted surface-to-mass ratio, and the configuration of the spherical drag-enhancing deorbiting device is determined. The configuration of the spherical drag-enhancing deorbiting device is used to meet the post-mission handling requirements of constellation satellites, increase the environmental forces and effective area of ​​the spacecraft, and achieve rapid deorbiting.

2. The adaptive and shape-stabilized configuration optimization method for the spherical drag-increasing derailment device according to claim 1, characterized in that, The mathematical expression corresponding to the orbital dynamics model of the rarefied flow environment is: Where m is the mass of the spacecraft deorbiting system; r is the position vector of the spacecraft deorbiting system; v is the velocity vector of the spacecraft deorbiting system; F A , represents atmospheric drag; F S Solar radiation pressure; F U To account for the Earth's central gravitational force due to perturbations in the Earth's shape; F T To account for the gravitational pull of the Sun and Moon due to perturbations in the Earth's shape; The velocity vector of the spacecraft's deorbiting system; This represents the acceleration vector of the spacecraft's deorbiting system.

3. The adaptive and shape-stabilized configuration optimization method for the spherical drag-increasing derailment device according to claim 1, characterized in that, The method for determining the proxy model specifically includes: Construct a dataset and normalize it to obtain a processed dataset; The processed dataset is divided into training set, validation set and test set according to a set ratio; Construct a backpropagation neural network; The training set is input into the backpropagation neural network, and the backpropagation neural network is trained using the gradient descent method based on both forward and backward propagation processes to obtain the trained backpropagation neural network. The backpropagation neural network trained with the input values ​​of the validation set is used for validation to obtain the validated backpropagation neural network. The test set is input into the validated backpropagation neural network, and the mean squared error is used as the evaluation index to test it, thus obtaining the tested backpropagation neural network. The backpropagation neural network after testing was determined as the surrogate model.

4. The adaptive and shape-stabilized configuration optimization method for the spherical drag-increasing derailment device according to claim 3, characterized in that, The backpropagation neural network includes: an input layer, hidden layers, and an output layer; During the positive propagation process: The input layer is used to acquire the training set and transmit the training set to the hidden layer; The hidden layer employs a nonlinear transformation method to process the training set to obtain the hidden layer output; the expression for the hidden layer output is: The output layer is used to determine the output result based on the output result of the hidden layer; the expression corresponding to the output result of the output layer is: Where g is the activation function of the hidden layer; x is the input node, y is the hidden node, and w is the activation function of the hidden layer. (1) The weights from the input layer to the hidden layer. z is the input layer bias; z is the output node, w (2) The weights from the hidden layer to the output layer. This is for the hidden layer bias. During the backpropagation process, gradient descent is used to optimize the weight parameters with the goal of minimizing the loss function; the expression for the loss function is: Where Loss is the loss function; z- is the predicted output; ) represents the actual output.

5. The adaptive and shape-stabilized configuration optimization method for the spherical drag-increasing derailment device according to claim 1, characterized in that, The estimated surface-to-weight ratio is corrected using a bisectional cyclic correction method to obtain a suitable surface-to-weight ratio, specifically including: The estimated surface-to-mass ratio is initially corrected for solar activity level to obtain the solar activity index and the corrected surface-to-mass ratio. The solar activity index and the corrected surface-to-mass ratio are corrected by a bisectional differential correction method to obtain the suitable surface-to-mass ratio.

6. The adaptive and shape-stabilized configuration optimization method for the spherical drag-increasing derailment device according to claim 5, characterized in that, The expression corresponding to the solar activity index is: The expression corresponding to the corrected surface-to-mass ratio is: Where β = is the solar activity index; y is the divisor; = F107(y) is the average solar activity index for the corresponding year in a solar cycle; AMR0 is the corrected surface-to-mass ratio; AMR R To estimate the surface-to-texture ratio.

7. The adaptive and shape-stabilized configuration optimization method for the spherical drag-increasing derailment device according to claim 5, characterized in that, The solar activity index and the corrected surface-to-mass ratio are corrected by a bisectional differential method to obtain the suitable surface-to-mass ratio, specifically including: Using the corrected surface-to-mass ratio as a boundary, the surface-to-mass ratio is multiplied or divided by 2 by judging the magnitude of the derailment time and the expected derailment time until a surface-to-mass ratio that is different from the corrected surface-to-mass ratio is found as another boundary of the array. The bounded array is sorted in ascending order. Based on the given target value, the search is performed within the search range from the set middle position of the bounded array according to the set search rules based on the solar activity index, in order to determine the suitable surface-to-mass ratio. Specifically, setting search rules includes: If the search result is exactly equal to the middle element value, then return the index of the middle element value; If the value being searched is smaller than the value of the middle element, then the first half of the entire search range is used as the new search range. If the value being searched is greater than the value of the middle element, then the latter half of the entire search range will be used as the new search range.

8. The adaptive and shape-stabilized configuration optimization method for the spherical drag-increasing derailment device according to claim 1, characterized in that, Using methods for calculating the projected area of ​​objects of arbitrary shapes and multi-objective optimization, the configuration of the spherical drag-increasing derailment device is designed based on the adapted surface-to-mass ratio. The specific configuration of the spherical drag-increasing derailment device includes: The projected area of ​​the spherical drag-increasing and track-departing device is determined by projecting it in different directions using a method for calculating the projected area of ​​objects of arbitrary shapes. The objective function is determined by taking shape stability and cost as optimization objectives; The optimization problem is determined based on the projected area and the adapted surface-to-weight ratio. A genetic algorithm is used to perform multi-objective optimization on the optimization problem based on the objective function, and the solution result is obtained. Based on the solution results, the configuration of the spherical drag-increasing derailment device is designed and determined.

9. The adaptive and shape-stabilized configuration optimization method for the spherical drag-increasing derailment device according to claim 8, characterized in that, The expression for the objective function is: The mathematical expression corresponding to the optimization problem is: min[(1-P)f1+Pf2] Where f1 is the first objective function; n is the number of petal moduli; Δ is the windward area error; f2 is the second objective function; R is the radius; m b The mass of the deorbiting device's membrane sphere is given by ρ; P is the weighting coefficient; m is the mass of the spacecraft's deorbiting system; AMR E To adapt to the dough-to-texture ratio; S min N represents the minimum projected area; N+ represents a positive integer.

10. An adaptive and shape-stabilized configuration optimization system for a spherical drag-increasing derailment device, characterized in that, include: The information data acquisition module is used to acquire information data from the spacecraft deorbiting system; the information data includes position vectors and velocity vectors. The model building module is used to construct a rarefied flow environment orbital dynamics model based on the information data; the rarefied flow environment orbital dynamics model is a mathematical model that considers the effects of atmospheric drag perturbation, solar radiation pressure perturbation, Earth shape perturbation and lunar perturbation on the spacecraft's orbital motion to determine the rate of change of the orbital state vector; The estimated surface-to-mass ratio determination module is used to determine the estimated surface-to-mass ratio based on the expected de-orbit time and orbital height using a surrogate model. The surrogate model is obtained by training a backpropagation neural network on a dataset. The dataset is a database obtained by simulating the orbital dynamics model of the rarefied flow environment by selecting different orbital heights and surface-to-mass ratios as initial values, with de-orbit time and orbital height as inputs and surface-to-mass ratio as output. The correction module is used to correct the estimated surface-to-material ratio using a bisectional cyclic correction method to obtain a suitable surface-to-material ratio. The configuration optimization design module is used to design the configuration of the spherical drag-enhancing deorbiting device based on the adaptive surface-to-mass ratio using the projected area calculation method for objects of arbitrary shapes and the multi-objective optimization method. The configuration of the spherical drag-enhancing deorbiting device is used to meet the post-mission handling requirements of the constellation satellites, increase the environmental forces and effective area of ​​the spacecraft, and achieve rapid deorbiting.

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