A method for estimating rendezvous pulses using neural network

Abstract

The present invention discloses a method for estimating a rendezvous pulse using a neural network. First, a training data set with one-to-one correspondence between the initial and target orbits, the rendezvous duration and the velocity increment is obtained. Then, a neural network structure is designed, including the number of layers of the neural network, the number of nodes in each layer, and the data type of the input layer. The neural network is trained using sampled data to obtain the optimal weight of the network. Finally, the rendezvous pulse size is calculated using the trained neural network. The present invention is able to quickly calculate the optimal velocity increment size of a pulse rendezvous considering perturbations, given the rendezvous moment and the transfer flight duration, and given the number of roots of the initial and target orbits.

Description

Technical Field

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

[0002] The solution to the multi-pulse orbit rendezvous optimization problem considering perturbations generally uses an evolutionary algorithm to perform a global search for pulse size and time, which has a large amount of calculation and is very inefficient. When designing and analyzing rendezvous missions or optimizing multi-satellite rendezvous sequences, accurate pulse transfer trajectories may not be required, and the total rendezvous velocity increment only needs to be obtained quickly. At this time, it is necessary to design an efficient estimation method to replace the complex dynamic process solution. The traditional estimation algorithm establishes an analytical or semi-analytical set of constraint equations based on the difference between the starting and target orbital elements of the rendezvous, and superimposes the velocity increments corresponding to each component of the orbital element, which cannot take into account both accuracy and efficiency. The present invention introduces a neural network to estimate the pulse rendezvous velocity increment, uses the precise optimization results of the evolutionary algorithm as samples, and obtains the approximate relationship between the rendezvous velocity increment and the starting and target orbital elements through training and learning, which can achieve a higher estimation accuracy. Summary of the invention

[0003] The purpose of the present invention is to provide a method for estimating rendezvous pulses using a neural network, which can quickly calculate the optimal velocity increment size of a pulse rendezvous taking perturbations into account given the rendezvous moment and transfer flight duration, and given the number of starting and target orbital elements.

[0004] The technical solution adopted by the present invention is a method for estimating intersection pulses using a neural network, which is specifically implemented according to the following steps:

[0005] Step 1: Obtain a training data set with one-to-one correspondence between the initial and target orbits, the rendezvous duration, and the velocity increment;

[0006] Step 2: Design the neural network structure, including the number of neural network layers, the number of nodes in each layer, and the data type of the input layer;

[0007] Step 3: Use the sampled data to train the neural network and obtain the optimal weight of the network.

[0008] Step 4: Calculate the intersection pulse size using the trained neural network.

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

[0010] Step 1 is implemented according to the following steps:

[0011] Step 1.1, first use random numbers to generate the initial and target orbits. Assume x[0] to x

[11] is a set of randomly generated numbers between -1 and 1. Then the six components of the initial orbit roots, i.e. the first kind of singular point-free roots, are expressed as:

[0012]

[0013] Among them, a0,e x0 ,e y0 ,i0,Ω0,u0 represent the six elements of the target orbital elements; represents the given semi-major axis sampling mean, Respectively represent the sampling means of the two components of the eccentricity vector, represents the sampling mean of the inclination, represents the sampling mean of the right ascension of the ascending node, represents the sampling mean of the latitude argument; δa, δe, δi, δΩ, δu represent the random variation range of the semi-major axis, eccentricity, inclination, right ascension of the ascending node and the latitude argument respectively;

[0014] Step 1.2, the six components of the target orbital elements, i.e., the first kind of singular point-free elements, are expressed as:

[0015]

[0016] The definitions of δa, δe, δi, δΩ, and δu are the same as those in formula (1).

[0017] a f ,e xf ,e yf ,i f ,Ω f ,u f Six elements representing the target orbital elements;

[0018] At the same time, use a random number k between 0 and 1 t Express the rendezvous time Δt:

[0019] Δt=Δt min +k t Δt max (3)

[0020] According to equations (1), (2) and (3), a track rendezvous optimization problem is defined, and the velocity increment Δυ is obtained by optimization. After multiple sampling and optimization calculations, the data set for the neural network in step 2 is obtained.

[0021] Step 2 is implemented as follows:

[0022] A four-layer neural network is used, including an input layer, two hidden layers and an output layer. The input data is x[0] to

[11] and k t The output is the intersection pulse size. Both hidden layers are set to 60 dimensions, and the activation function of all nodes uses the RELU function. The weight of each layer in the neural network is an unknown quantity, which needs to be trained and solved through a large amount of sampled data.

[0023] Here, the input is preprocessed to reduce the effective data dimension to 9, including the following data:

[0024]

[0025] in, is the right ascension drift rate of the ascending node of the initial orbit:

[0026]

[0027] 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:

[0028]

[0029] Step 3 is implemented as follows:

[0030] The neural network in step 3 is trained using the keras and tensorflow frameworks. The parameter settings are as follows: optimizer = 'rmsprop', loss function = 'mse', evaluation function = 'mape', and other parameters use the default values;

[0031] After training, the neural network weights for quickly estimating the intersection velocity increment can be obtained.

[0032] Step 4 is implemented according to the following steps:

[0033] After a training, the neural network can quickly calculate the rendezvous pulse size according to any given initial orbital elements, target orbital elements and rendezvous time Δt.

[0034] Specifically: First, according to equations (1), (2) and (3), reversely calculate x[0] to x

[11] and k t The value of , and then according to formula (4) to obtain the value of the 9-dimensional input vector, and then substitute it into the neural network, the result of the forward operation output of the neural network is the approximate estimated intersection pulse size.

[0035] The beneficial effect of the present invention is a method for estimating rendezvous pulses using a neural network. The advantage is that after completing sampling and training at one time and obtaining the optimal neural network weights, by inputting any spacecraft starting orbit, target rendezvous orbit and rendezvous duration within a given range, the rendezvous velocity increment can be quickly estimated with high estimation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 This is a schematic diagram of the neural network structure in step 2 of the present invention;

[0037] Figure 2 This is the prediction error graph after training in step 3 of the present invention. DETAILED DESCRIPTION

[0038] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0039] The present invention provides a method for estimating intersection pulses using a neural network, combined with Figure 1 , Figure 2 , follow the steps below:

[0040] Step 1: Obtain a training data set with one-to-one correspondence between the initial and target orbits, the rendezvous duration, and the velocity increment;

[0041] Step 1 is implemented according to the following steps:

[0042] Step 1.1, first use random numbers to generate the initial and target orbits. Assume x[0] to x

[11] is a set of randomly generated numbers between -1 and 1. Then the six components of the initial orbit roots, i.e. the first kind of singular point-free roots, are expressed as:

[0043]

[0044] Among them, a0,e x0 ,e y0 ,i0,Ω0,u0 represent the six elements of the target orbital elements; represents the given semi-major axis sampling mean, Respectively represent the sampling means of the two components of the eccentricity vector, represents the sampling mean of the inclination, represents the sampling mean of the right ascension of the ascending node, represents the sampling mean of the latitude argument; δa, δe, δi, δΩ, δu represent the random variation range of the semi-major axis, eccentricity, inclination, right ascension of the ascending node and the latitude argument respectively;

[0045] Step 1.2, the six components of the target orbital elements, i.e., the first kind of singular point-free elements, are expressed as:

[0046]

[0047] The definitions of δa, δe, δi, δΩ, and δu are the same as those in formula (1).

[0048] a f ,e xf ,e yf ,i f ,Ω f ,u f Six elements representing the target orbital elements;

[0049] At the same time, use a random number k between 0 and 1 t Express the rendezvous time Δt:

[0050] Δt=Δt min +k t Δt max (3)

[0051] According to equations (1), (2) and (3), a track rendezvous optimization problem is defined, and the velocity increment Δυ is obtained by optimization. After multiple sampling and optimization calculations, the data set for the neural network in step 2 is obtained.

[0052] Step 2: Design the neural network structure, including the number of neural network layers, the number of nodes in each layer, and the data type of the input layer;

[0053] Step 2 is implemented as follows:

[0054] A four-layer neural network is used, including an input layer, two hidden layers and an output layer. The structure is shown in the attached Figure 1 The input data is x[0] to

[11] and k t The output is the intersection pulse size (i.e., the total velocity increment, a one-dimensional real number). Both hidden layers are set to 60 dimensions, and the activation function of all nodes uses the RELU function. The weight of each layer in the neural network is an unknown quantity, which needs to be trained and solved through a large amount of sampled data.

[0055] Here, the input is preprocessed to reduce the effective data dimension to 9, including the following data:

[0056]

[0057] in, is the right ascension drift rate of the ascending node of the initial orbit:

[0058]

[0059] 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:

[0060]

[0061] Step 3: Use the sampled data to train the neural network and obtain the optimal weight of the network.

[0062] Step 3 is implemented as follows:

[0063] The neural network in step 3 is trained using the keras and tensorflow frameworks. The parameter settings are as follows: optimizer = 'rmsprop', loss function = 'mse', evaluation function = 'mape', and other parameters use the default values;

[0064] The detailed process of coding to realize the definition and training of the neural network can be found in various public documents, and the present invention will not repeat them. After training, the neural network weights for quickly estimating the intersection velocity increment can be obtained.

[0065] Step 4: Calculate the intersection pulse size using the trained neural network.

[0066] Step 4 is implemented according to the following steps:

[0067] After a training, the neural network can quickly calculate the rendezvous pulse size according to any given initial orbital elements, target orbital elements and rendezvous time Δt.

[0068] Specifically: First, according to equations (1), (2) and (3), reversely calculate x[0] to x

[11] and k t The value of , and then according to formula (4) to obtain the value of the 9-dimensional input vector, and then substitute it into the neural network, the result of the forward operation output of the neural network is the approximate estimated intersection pulse size (i.e., velocity increment).

[0069] Example

[0070] like Figure 2 The figure shows a specific embodiment of a method for estimating a rendezvous pulse using a neural network according to the present invention, which is used to estimate a rendezvous pulse between sun-synchronous orbits at an altitude of about 700 km. The steps and results are as follows:

[0071] Step 1: Obtain a training dataset with one-to-one correspondence between the initial and target orbits, rendezvous duration, and velocity increment.

[0072] 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 value range is -180° to 180°), and the rendezvous time ranges from 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 Take 1 and 29 days.

[0073] On this basis, 10,000 different sets of x

[12] and k are randomly selected. t , generate 10,000 sets of starting and target orbit elements and rendezvous transfer durations, and apply the existing evolutionary algorithm optimization method to calculate the precise rendezvous velocity increment.

[0074] Step 2: Design the neural network structure, including the number of network layers, the number of nodes in each layer, and the data type of the input layer. According to the format of formula (4), calculate the 9-dimensional input value of 10,000 sets of sample data.

[0075] Step 3: Use the sampled data to train the neural network and obtain the optimal weight of the network. The keras and tensorflow frameworks are used to train the neural network, and the number of training generations is set to 800. The first 8200 groups of data are used as the training set, and the last 1800 groups of data are used as the validation set. The final mape (average relative error) is only 1.7%. In most cases, the prediction relative error is less than 4%, indicating that a high-precision neural network estimator has been obtained. The speed increment prediction error of each group of data in the validation set is shown in the attached Figure 2 .

[0076] Through example demonstration, it is only time-consuming to adopt the method of the present invention in the first step, and it is necessary to call the optimization algorithm 10000 times. After obtaining the optimal neural network, each prediction only needs to perform 3 vector and matrix point multiplication operations (matrix order is 9*60, 60*60 and 60*1). And the point multiplication operation can be parallelized to further shorten the running time, and the actual operation only needs less than 1e-6 seconds on an ordinary desktop computer. And the single evolutionary algorithm consumes more than 1 second, proving that the method solves the problem of fast estimation of pulse intersection speed increment, and can be better applied to the global optimization of multiple target intersection order and time, and greatly improves the computational efficiency of the evaluation objective function.

Claims

1. A method for estimating intersection pulses using a neural network, characterized in that: Follow the steps below to implement it: Step 1: Obtain a training data set with one-to-one correspondence between the initial and target orbits, the rendezvous duration, and the velocity increment; The step 1 is specifically implemented according to the following steps: Step 1.1, first use random numbers to generate the initial and target orbits. Assume x[0] to x[11] is a set of randomly generated numbers between -1 and 1. Then the six components of the initial orbit roots, i.e. the first kind of singular point-free roots, are expressed as: Among them, a0,e x0 ,e y0 ,i0,Ω0,u0 represent the six elements of the target orbital elements; represents the given semi-major axis sampling mean, Respectively represent the sampling means of the two components of the eccentricity vector, represents the sampling mean of the inclination, represents the sampling mean of the right ascension of the ascending node, represents the sampling mean of the latitude argument; δa, δe, δi, δΩ, δu represent the random variation range of the semi-major axis, eccentricity, inclination, right ascension of the ascending node and the latitude argument respectively; Step 1.2, the six components of the target orbital elements, i.e., the first kind of singular point-free elements, are expressed as: where δa, δe, δi, δΩ, and δu are defined in the same way as in formula (1). f ,e xf ,e yf ,i f ,Ω f ,u f Six elements representing the target orbital elements; At the same time, use a random number k between 0 and 1 t Express the rendezvous time Δt: Δt=Δt min +k t Δt max (3) According to equations (1), (2) and (3), a track rendezvous optimization problem is defined, and the velocity increment Δv is obtained by optimization. After multiple sampling and optimization calculations, the data set for the neural network in step 2 is obtained. Step 2: Design the neural network structure, including the number of neural network layers, the number of nodes in each layer, and the data type of the input layer; The step 2 is specifically implemented according to the following steps: A four-layer neural network is used, including an input layer, two hidden layers and an output layer. The input data is x[0] to [11] and k t , the output is the intersection pulse size, both hidden layers are set to 60 dimensions, the activation function of all nodes uses the RELU function, the weight of each layer in the neural network is an unknown quantity, which needs to be trained and solved through a large amount of sampling data; Here, the input is preprocessed to reduce the effective data dimension to 9, including the following data: in, is the right ascension drift rate of the ascending node of the initial orbit: 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: Step 3: Use the sampled data to train the neural network and obtain the optimal weight of the network; Step 4: Calculate the intersection pulse size using the trained neural network.

2. A method for estimating intersection pulses using a neural network according to claim 1, characterized in that: The step 3 is specifically implemented according to the following steps: The neural network in step 3 is trained using the keras and tensorflow frameworks. The parameter settings are as follows: optimizer = 'rmsprop', loss function = 'mse', evaluation function = 'mape', and other parameters use the default values; After training, the neural network weights for quickly estimating the intersection velocity increment can be obtained.

3. The method for estimating intersection pulses using a neural network according to claim 2, characterized in that: The step 4 is specifically implemented according to the following steps: After a training, the neural network can quickly calculate the rendezvous pulse size according to any given initial orbital elements, target orbital elements and rendezvous time Δt. Specifically: First, according to equations (1), (2) and (3), reversely calculate x[0] to x[11] and k t The value of , and then according to formula (4) to obtain the value of the 9-dimensional input vector, and then substitute it into the neural network, the result of the forward operation output of the neural network is the approximate estimated intersection pulse size.

Images