A method for estimating low-thrust rendezvous burn using neural networks

Abstract

The present invention discloses a method for estimating low-thrust rendezvous fuel consumption using a neural network. The method first obtains a training data set with a one-to-one correspondence between initial and target orbits, rendezvous duration, and fuel consumption. Two neural networks are then constructed: one to establish a proxy model for the feasibility of the low-thrust rendezvous trajectory, and the other to establish a proxy model for calculating the low-thrust rendezvous fuel consumption. The neural networks are trained using sampled data. Finally, arbitrary initial and target orbits are input as input layer data and substituted into the first neural network to obtain output layer data, representing the feasibility of the low-thrust rendezvous. If the orbit transfer is feasible, the output data is then substituted into the second neural network to obtain the low-thrust rendezvous velocity increment. This method solves the problems of high computational complexity, poor convergence performance, and low approximation accuracy in existing low-thrust trajectory optimization methods.

Description

Technical Field

[0001] The present invention belongs to the technical field of aerospace navigation control, and in particular relates to a method for estimating low-thrust rendezvous fuel consumption by using a neural network. Background Art

[0002] Rendezvous trajectory optimization is one of the basic technologies for spacecraft orbit design. In low-Earth orbit, rendezvous must take into account the influence of perturbations. When the dynamic model is not a two-body model, traditional low-thrust trajectory optimization methods all have the phenomenon of increased computational complexity and reduced convergence performance. In some mission design scenarios, it may only be necessary to quickly evaluate whether the rendezvous is feasible and the required propellant, without directly obtaining an accurate rendezvous trajectory. To meet this demand, using a neural network to obtain a proxy model for rendezvous propellant or fuel consumption can significantly improve computational efficiency. However, a series of problems such as the structural design of the neural network and the preprocessing of input variables need to be solved. The present invention introduces a neural network to estimate the low-thrust rendezvous fuel consumption, uses the optimization results obtained by other methods as samples, and obtains an approximate relationship between the fuel consumption and the number of starting and target orbital elements and the transfer time through large-scale training and learning, which can achieve a higher approximation accuracy. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for estimating low-thrust rendezvous fuel consumption using a neural network, which solves the problems of high computational complexity, low convergence performance and low approximation accuracy in the low-thrust trajectory optimization method in the prior art.

[0004] The technical solution adopted by the present invention is a method for estimating low-thrust rendezvous fuel consumption using a neural network, which is specifically implemented according to the following steps:

[0005] Step 1: Obtain a training dataset with one-to-one correspondence between the initial and target orbits, rendezvous duration, and fuel consumption;

[0006] Step 2: Build two neural networks, one to establish a proxy model for the feasibility of the low-thrust rendezvous trajectory, and the other to establish a proxy model for the calculation of the low-thrust rendezvous fuel consumption;

[0007] Step 3: Use the sampled data to train the neural network and obtain the optimal weight of the network. The optimal weight is used as the training result of the neural network and is used as the actual root number input in the next step.

[0008] Step 4: Based on the input of any initial orbit and target orbit, first substitute them into the first neural network as the input layer data to obtain the output layer data, which is the feasibility of low-thrust rendezvous. If the orbit transfer is feasible, continue to substitute them into the second neural network to obtain the output data, which is the low-thrust rendezvous velocity increment.

[0009] The present invention is also characterized in that:

[0010] Step 1 is implemented as follows:

[0011] First, use random numbers to generate the initial and target orbits. Let x

[12] be a set of randomly generated numbers between -1 and 1. Then the six components of the initial orbit roots are expressed as

[0012]

[0013] where a0,e x0 ,e y0 ,i0,Ω0,u0 are the six numbers of the initial orbit, They represent the sampling median values ​​of the given semi-major axis, eccentricity vector x component, eccentricity vector y component, inclination, ascending node right ascension and latitude argument respectively. δa, δe, δi, δΩ, δu represent the maximum range of random variation of the given data. The six components of the target orbital elements are also expressed as

[0014]

[0015] Among them, a f ,e xf ,e yf ,i f ,Ω f ,u f is the initial orbital six numbers;

[0016] At the same time, use a random number k between 0 and 1 t Represents the rendezvous time Δt, and uses a random number from 0 to 1 to represent the ratio of the current thrust to mass of the spacecraft, that is, the small thrust acceleration acc:

[0017]

[0018] where acc max Indicates the maximum value of the spacecraft's small thrust acceleration, Δt min is the minimum rendezvous time, Δt max is the maximum rendezvous duration. Δt represents the rendezvous duration, k acc Indicates the ratio of the thrust acceleration of the sampled data to the maximum thrust acceleration;

[0019] An integer with the value of 0 or 1 is used to record the feasibility of low-thrust rendezvous for each set of sampling data, where 0 indicates unfeasible and 1 indicates feasible.

[0020] Finally, we obtain a data set consisting of the small thrust feasibility and rendezvous fuel consumption corresponding to the given x

[12] .

[0021] Step 2 is implemented as follows:

[0022] Both neural networks use four-layer neural networks, including an input layer, two hidden layers and an output layer, which are connected by activation functions. The two neural networks are different only in the output layer. The output of the first neural network is 0 or 1, and the output of the second neural network is a real number. The input layer data is x

[12] and k in step 1. t Perform preprocessing and convert the input layer data into a 10-dimensional array, including the following data:

[0023]

[0024] The physical meaning of each row in formula (4) represents the starting orbit semi-major axis, the difference between the starting and target semi-major axes, the difference between the starting and target eccentricities, the starting inclination, the difference between the starting and target inclinations, the right ascension difference of the ascending node at the time of intersection, and the difference in the latitude argument at the time of intersection. is the right ascension drift rate of the ascending node of the initial orbit:

[0025]

[0026] Where J2 is the Earth’s non-spherical gravitational perturbation constant, R e is the Earth's equatorial radius, is the average angular velocity of the orbit, μ is the gravitational constant of the Earth, is the perigee argument drift rate of the initial orbit:

[0027]

[0028] The output layer is defined as follows: 0 or 1 indicates whether the orbital rendezvous is feasible, and a real number represents the speed increment required for rendezvous, i.e., the fuel consumption. It is a one-dimensional real number. Both hidden layers are set to 64 dimensions. The activation function of all nodes uses the RELU function. The second neural network output layer used to calculate the fuel consumption does not use an activation function and directly outputs floating-point numbers. The output layer of the neural network that approximates the feasibility of small thrust uses a sigmoid activation function.

[0029] Step 3 is implemented as follows:

[0030] The two neural networks are trained using the keras and tensorflow frameworks respectively, and the parameter settings are as follows:

[0031] For the low-thrust feasibility calculation, in the Keras framework, the optimizer for training is set to 'adams', the loss function is set to 'bce', the accuracy evaluation method is set to 'accuracy', and other parameters use the default values. The training data uses the dataset obtained in step 1.

[0032] For the fuel consumption calculation, the optimizer was set to 'rmsprop', the loss function was set to 'mse', the accuracy evaluation method was set to 'mape', and other parameters were left at their default values. Only the data in the training data that was achievable at low thrust rendezvous was used. After training, a neural network structure was obtained that could quickly calculate low thrust achievability and fuel consumption.

[0033] During prediction, it is only necessary to back-calculate the 10-dimensional input value of the neural network according to equations (1) to (4) based on the actual given number of starting and target orbit elements and the rendezvous duration. First, substitute the 10-dimensional input value into the neural network for low-thrust feasibility calculation. If the output value is greater than 0.5, it means that the rendezvous is feasible. Then, substitute the 10-dimensional input value into the neural network for fuel consumption calculation to obtain the approximate fuel consumption. If the output value of the neural network for low-thrust feasibility calculation is less than 0.5, it means that the given input conditions cannot achieve low-thrust rendezvous.

[0034] The beneficial effect of the present invention is a method for estimating low-thrust rendezvous fuel consumption using a neural network. The advantage is that after completing sampling and training at one time and obtaining the optimal neural network weights, any spacecraft starting orbit, target rendezvous orbit and rendezvous duration can be input within a given range. It is possible to quickly calculate whether the input conditions can achieve orbital rendezvous, as well as the approximate fuel consumption, and the estimation accuracy is very high. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 This is a schematic diagram of the neural network structure in step 2 of the present invention;

[0036] Figure 2 This is a flow chart of the neural network predicting low thrust fuel consumption in step 3 of the present invention. DETAILED DESCRIPTION

[0037] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0038] The present invention uses a method for estimating low-thrust rendezvous fuel consumption using a neural network. First, the orbit semi-major axis, eccentricity, inclination, right ascension of the ascending node, argument of perigee and mean anomaly, and rendezvous transfer time are sampled within a certain range to obtain a large number of input data sets. Then, public methods in other literature are used to optimize and calculate accurate low-thrust rendezvous trajectories and fuel consumption results to obtain a training data set. Then, a neural network structure with two hidden layers is designed, and the input and output parameters are normalized. Finally, the training data and a mature deep learning framework are used for training to obtain an optimal neural network proxy model.

[0039] The method for estimating low-thrust rendezvous fuel consumption using a neural network in the present invention is specifically implemented according to the following steps:

[0040] Step 1: Obtain a training dataset with one-to-one correspondence between the initial and target orbits, rendezvous duration, and fuel consumption;

[0041] Step 1 is implemented as follows:

[0042] First, use random numbers to generate the initial and target orbits. Let x

[12] be a randomly generated sequence of numbers between -1 and 1 (12 refers to the 12th dimension, which is x[0] to x

[11] below). Then the six components of the initial orbital roots (the first kind of non-singular point roots) are expressed as

[0043]

[0044] where a0,e x0 ,e y0 ,i0,Ω0,u0 are the six numbers of the initial orbit, denote the sampling median values ​​of the given semi-major axis, eccentricity vector x component, eccentricity vector y component, inclination, ascending node right ascension, and latitude argument, respectively. δa, δe, δi, δΩ, and δu denote the maximum range of random variation of the given data. Similarly, the six components of the target orbital elements (first kind of non-singular point elements) are also expressed as

[0045]

[0046] Among them, a f ,e xf ,e yf ,i f ,Ω f ,u f is the initial orbital six numbers;

[0047] At the same time, use a random number k between 0 and 1 t Represents the rendezvous time Δt, and uses a random number from 0 to 1 to represent the ratio of the current thrust to mass of the spacecraft, that is, the small thrust acceleration acc:

[0048]

[0049] where acc max Indicates the maximum value of the spacecraft's small thrust acceleration, Δt min is the minimum rendezvous time, Δt max is the maximum rendezvous duration. Δt represents the rendezvous duration, k acc Indicates the ratio of the thrust acceleration of the sampled data to the maximum thrust acceleration;

[0050] According to equations (1), (2), and (3), a low-thrust orbit rendezvous optimization problem can be defined, and the fuel consumption Δm can be obtained by using existing methods in other fields. After multiple sampling and optimization calculations, a data set for the neural network is obtained. During the low-thrust rendezvous optimization, if the acceleration generated by the spacecraft's own thrust is too small, the two orbits will be too far apart, making rendezvous impossible. In the present invention, the low-thrust rendezvous feasibility of each set of sampled data is recorded as an integer with a value of 0 or 1, where 0 indicates unfeasible and 1 indicates feasible.

[0051] Finally, we obtain a data set consisting of the small thrust feasibility (0 or 1) and the rendezvous fuel consumption corresponding to the given x

[12] .

[0052] Step 2: Build two neural networks, one to establish a proxy model for the feasibility of the low-thrust rendezvous trajectory, and the other to establish a proxy model for the calculation of the low-thrust rendezvous fuel consumption;

[0053] Combine Figure 1 , step 2 is implemented according to the following steps:

[0054] Both neural networks use four-layer neural networks, including an input layer (9-dimensional input layer), two hidden layers (both 64-dimensional hidden layers) and an output layer. The structure is shown in the attached figure. Figure 1 Among them, the left column is the input layer, the right column is the output layer, and the middle column is the hidden layer. They are connected by activation functions. The two neural networks are different only in the output layer. The output of the first neural network is 0 or 1, and the output of the second neural network is a real number. The input layer data is x

[12] and k in step 1. t Perform preprocessing and convert the input layer data into a 10-dimensional array, including the following data:

[0055]

[0056] The physical meaning of each row in formula (4) represents the starting orbit semi-major axis, the difference between the starting and target semi-major axes, the difference between the starting and target eccentricities (two-dimensional vector), the starting inclination, the difference between the starting and target inclinations, the right ascension difference of the ascending node at the time of rendezvous (taking into account the perturbation drift), and the difference in the latitude argument at the time of rendezvous (taking into account the perturbation drift). is the right ascension drift rate of the ascending node of the initial orbit:

[0057]

[0058] Where J2 is the Earth’s non-spherical gravitational perturbation constant, R e is the Earth's equatorial radius, is the average angular velocity of the orbit, μ is the gravitational constant of the Earth, is the perigee argument drift rate of the initial orbit:

[0059]

[0060] The output layer is defined as follows: 0 or 1 indicates whether orbital rendezvous is feasible (first neural network), and a real number represents the velocity increment required for rendezvous, i.e., the fuel consumption (second neural network). It is a one-dimensional real number. Both hidden layers are set to 64 dimensions, and the activation function of all nodes uses the RELU function. It should be noted that the output layer of the second neural network used to calculate the fuel consumption does not use an activation function and directly outputs floating-point numbers; the output layer of the neural network that approximates the feasibility of small thrust uses the sigmoid activation function.

[0061] Step 3: Use the sampled data to train the neural network and obtain the optimal weight of the network. The optimal weight is used as the training result of the neural network and is used as the actual root number input in the next step.

[0062] Combine Figure 2 , step 3 is implemented as follows:

[0063] The two neural networks are trained using the keras and tensorflow frameworks respectively, and the parameter settings are as follows:

[0064] For the low-thrust feasibility calculation, in the Keras framework, the optimizer for training is set to 'adams', the loss function is set to 'bce', the accuracy evaluation method is set to 'accuracy', and other parameters use the default values. The training data uses the dataset obtained in step 1.

[0065] For the fuel consumption calculation, the optimizer was set to 'rmsprop', the loss function to 'mse', and the accuracy evaluation method to 'mape'. All other parameters were left at their default values. Only the portion of the training data that was achievable at low thrust rendezvous was used. The detailed process for coding the neural network definition and training can be found in various public literature and will not be repeated here. After training, a neural network structure was obtained that could rapidly calculate low thrust achievability and fuel consumption.

[0066] During prediction, it is only necessary to back-calculate the 10-dimensional input value of the neural network according to equations (1) to (4) based on the actual given number of starting and target orbit elements and the rendezvous duration. First, substitute the 10-dimensional input value into the neural network for low-thrust feasibility calculation. If the output value is greater than 0.5, it means that the rendezvous is feasible. Then, substitute the 10-dimensional input value into the neural network for fuel consumption calculation to obtain the approximate fuel consumption. If the output value of the neural network for low-thrust feasibility calculation is less than 0.5, it means that the given input conditions cannot achieve low-thrust rendezvous.

[0067] Step 4. When the neural network is actually applied, any initial orbit and target orbit can be input as input layer data, and first substituted into the first neural network to obtain the output layer data, which is the feasibility of low-thrust rendezvous. If the orbit transfer is feasible, continue to substitute into the second neural network to obtain the output data, which is the low-thrust rendezvous velocity increment.

[0068] like Figure 2 The figure shows a specific embodiment of the present invention's method for estimating low-thrust rendezvous fuel consumption using a neural network, which is used to approximate low-thrust rendezvous between sun-synchronous orbits at an altitude of approximately 700 km. The steps and results are as follows:

[0069] Step 1: Obtain a training dataset with a one-to-one correspondence between the initial and target orbits, rendezvous duration, and velocity increments.

[0070] The orbit altitude selected for sampling is 700km±200km, the inclination is 98°±2°, the two components of eccentricity are less than 0.014, the right ascension and latitude of the ascending node are not restricted (the values ​​are -180° to 180°), and the rendezvous duration is 1 to 30 days. They are taken as 6378km, 0, 0, 98°, 0, 0 respectively. δa, δe, δi, δΩ, δu are taken as 200km, 0.014, 0.014, 2°, 180°, 180° respectively. Δt min and Δt max The sampling range of the spacecraft's low-thrust acceleration is 5e-4 m / s. 2 to 1.4e-3m / s 2 .

[0071] On this basis, 30,000 different sets of x

[12] and k are randomly selected. t , generate 30,000 sets of starting and target orbit elements and rendezvous transfer duration, and apply other existing mature algorithms to calculate the precise low-thrust feasibility and rendezvous fuel consumption when rendezvous can be achieved.

[0072] Step 2: Design two neural networks, one to establish a proxy model for the feasibility of the low-thrust rendezvous trajectory, and the other to establish a proxy model for the calculation of the low-thrust rendezvous fuel consumption.

[0073] Step 3: Use the sampled data to train the neural network and obtain the optimal network weights. The neural network was trained using the Keras and TensorFlow frameworks, with a training iteration count of 800. The first 24,000 data sets served as the training set, and the last 6,000 data sets served as the validation set. The final low-thrust feasibility calculation accuracy was 97%, and the MAPPE (mean relative error) for fuel consumption was only 2.2%. In most cases, the prediction relative error was less than 3%, demonstrating a highly accurate neural network proxy model.

[0074] A practical example demonstrates that the method of the present invention is only time-consuming in the first step, requiring 30,000 calls to other optimization algorithms, which takes approximately one day. After obtaining the optimal neural network, each prediction only requires six vector-matrix dot multiplication operations (for both neural networks, matrix orders are 9*64, 64*64, and 64*1). Furthermore, dot multiplication operations can be parallelized to further shorten the runtime, requiring less than 2e-6 seconds on a typical desktop computer. This demonstrates that this method can solve the problem of rapidly calculating the feasibility and fuel consumption of low-thrust rendezvous.

Claims

1. A method for estimating low-thrust rendezvous fuel consumption using a neural network, characterized in that: Please follow the steps below to implement it: Step 1: Obtain a training dataset with one-to-one correspondence between the initial and target orbits, rendezvous duration, and fuel consumption; Step 2: Build two neural networks, one for establishing a proxy model for the feasibility of the low-thrust rendezvous trajectory, and the other for establishing a proxy model for calculating the low-thrust rendezvous fuel consumption. Step 2 is specifically implemented as follows: Both neural networks use four-layer neural networks, each consisting of an input layer, two hidden layers, and an output layer, connected by an activation function. The two neural networks differ only in the output layer. The output of the first neural network is 0 or 1, and the output of the second neural network is a real number. The output layer is defined as follows: 0 or 1 indicates whether the orbit rendezvous is feasible, and the real number represents the speed increment required for rendezvous, that is, the fuel consumption, which is a one-dimensional real number. Both hidden layers are set to 64 dimensions. The activation function of all nodes uses the RELU function. The output layer of the second neural network used to calculate the fuel consumption does not use an activation function and directly outputs floating-point numbers; the output layer of the neural network that approximates the feasibility of small thrust uses a sigmoid activation function. Step 3: Use the sampled data to train the neural network and obtain the optimal weight of the network. The optimal weight is used as the training result of the neural network and is used as the actual root number input in the next step. Step 4: Based on the input of any initial orbit and target orbit, first substitute them into the first neural network as the input layer data to obtain the output layer data, which is the feasibility of low-thrust rendezvous. If the orbit transfer is feasible, continue to substitute them into the second neural network to obtain the output data, which is the low-thrust rendezvous velocity increment.

2. The method for estimating low-thrust rendezvous burn using a neural network according to claim 1, characterized in that: The step 1 is specifically implemented according to the following steps: First, use random numbers to generate the initial and target orbits. Let x[12] be a set of randomly generated numbers between -1 and 1. Then the six components of the initial orbit roots are expressed as in is the initial orbital six numbers, Represent the sampled median values ​​of the given semi-major axis, eccentricity vector x component, eccentricity vector y component, inclination, ascending node right ascension and latitude argument, respectively. Indicates the maximum range of random variation of given data, and the six components of the target orbital elements are also expressed as in, is the six element number of the target orbit; At the same time, use a random number from 0 to 1 Indicates the rendezvous duration , use a random number from 0 to 1 to represent the ratio of the current thrust to mass of the spacecraft, that is, the small thrust acceleration : in Indicates the maximum value of the spacecraft's small thrust acceleration, is the minimum rendezvous time, is the maximum rendezvous duration, Indicates the duration of the rendezvous. Indicates the ratio of the thrust acceleration of the sampled data to the maximum thrust acceleration; The low-thrust rendezvous feasibility of each set of sampled data is recorded using an integer with a value of 0 or 1, where 0 indicates unfeasible and 1 indicates feasible. Finally, a data set consisting of the low-thrust feasibility and rendezvous fuel consumption corresponding to a given x[12] is obtained.

3. The method for estimating low-thrust rendezvous burn using a neural network according to claim 2, characterized in that: The input layer data in step 2 is x[12] and Perform preprocessing and convert the input layer data into a 10-dimensional array, including the following data: The physical meaning of each row in formula (4) represents the starting orbit semi-major axis, the difference between the starting and target semi-major axes, the difference between the starting and target eccentricities, the starting inclination, the difference between the starting and target inclinations, the right ascension difference of the ascending node at the time of intersection, and the difference in the latitude argument at the time of intersection. is the right ascension drift rate of the ascending node of the initial orbit: in is the Earth's non-spherical gravitational perturbation constant, is the Earth's equatorial radius, is the average angular velocity of the orbit, is the Earth's gravitational constant, is the perigee argument drift rate of the initial orbit: 。 4. The method for estimating low-thrust rendezvous burn using a neural network according to claim 3, characterized in that: The step 3 is specifically implemented according to the following steps: The two neural networks are trained using the keras and tensorflow frameworks respectively, and the parameter settings are as follows: For the low-thrust feasibility calculation, in the Keras framework, the optimizer for training is set to 'adams', the loss function is set to 'bce', the accuracy evaluation method is set to 'accuracy', and other parameters use the default values. The training data uses the dataset obtained in step 1. For the fuel consumption calculation, the optimizer was set to 'rmsprop', the loss function to 'mse', the accuracy evaluation method to 'mape', and other parameters to their default values. Only the data from the training data that showed low-thrust rendezvous feasibility was used. After training, a neural network structure was obtained that could quickly calculate low-thrust feasibility and fuel consumption. When making predictions, it is only necessary to back-calculate the 10-dimensional input value of the neural network according to equations (1) to (4) based on the actual given number of starting and target orbital elements and the rendezvous duration. First, substitute the value into the neural network for low-thrust feasibility calculation. If the output value is greater than 0.5, it means that the rendezvous is feasible. Then substitute the value into the neural network for fuel consumption calculation to obtain the approximate fuel consumption. If the output value of the neural network for low-thrust feasibility calculation is less than 0.5, it means that the given input conditions cannot achieve low-thrust rendezvous.

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