Space target trajectory parallel mapping method based on physical information network

Abstract

The invention provides a space target trajectory parallel mapping method based on a physical information network, and belongs to the field of time sequence data processing in deep learning. Aiming at the problems that a large amount of repetitive work exists and time and labor are consumed in the process of space target motion physical system analysis modeling and accumulative error correction, the method comprises the steps of fitting a kinematics equation of a space target in a parallel digital space through a parameterized neural network, and introducing known physical equation information; and the constraint network searches an optimal hypothesis process in a hypothesis space, and a parallel space modeling mapping process is converted into solution of a parameter inversion problem in a target domain, so that rapid construction of a parallel digital space is realized. Meanwhile, along with the increase of input sample data, the ability of the cross-cycle space-time attention module designed by the method for capturing the motion characteristics of the space target is stronger and stronger, and dynamic correction of errors is realized in a continuous iteration process.

Description

Technical Field

[0001] The present invention belongs to the field of time series data processing in deep learning, and specifically relates to a space target trajectory parallel mapping method based on a physical information network. Background Art

[0002] With the development of artificial intelligence technology, physics-informed neural network (PINN) has gained wide attention in the industry in the direction of physical field analysis and prediction. Through deep network structure, it can learn high-dimensional, nonlinear, and multimodal feature representations, and can effectively complete tasks such as rapid prediction of physical systems under different design parameters and accurate reconstruction of physical fields based on partial observation results.

[0003] For the physical system of space target motion, the general research steps are to first abstractly represent the problem domain, establish a parallel mathematical space model, then map the measured data in the real physical space to the parallel space, and finally perform relevant processing and analysis. In this process, the modeling angles of parallel digital space are different for different research objectives; different modeling angles of parallel digital space require corresponding different data mapping strategies; in addition, when long time series data are involved, due to the differences in modeling granularity and key parameter values, there is an accumulation of errors between the parallel space model and the measured results, which requires periodic correction. Usually, these tasks are mostly completed manually by industry experts based on their work experience and domain knowledge, which is labor-intensive and involves a lot of repetitive work.

[0004] Therefore, a data-driven parallel mapping method of space target trajectories is studied. The kinematic equations of space targets in the parallel digital space are fitted by parameterized neural networks. The known physical equation information is introduced to constrain the network's search for the optimal hypothesis in the hypothesis space. The parallel space modeling and mapping process is converted into the solution of the parameter inversion problem in the target domain, thereby realizing the rapid construction of the parallel digital space. Summary of the invention

[0005] Aiming at the problem that the existing digital modeling process of space target trajectory analysis is repetitive and cumbersome and requires periodic maintenance, the present invention proposes a space target trajectory parallel mapping method based on physical information network.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] A space target trajectory parallel mapping method based on a physical information network comprises the following steps:

[0008] (1) The input spatial target position sequence data is parsed based on the SGP4 algorithm, and then the sliding time window strategy is used to truncate the parsed spatial target position sequence data to construct a sample set;

[0009] (2) Construct a parallel mapping network of space target trajectories, which includes a data fusion module, a feature extraction module, a cross-cycle spatiotemporal attention module, and an output module; the data fusion module is used to fuse the spatial target position sequence data through merging and convolution operations to expand the feature vector dimension; the feature extraction module is used to extract the time series features of the fused data through three LSTM units in series; the cross-cycle spatiotemporal attention module is used to extract the time points through a sampling strategy across 1 / k orbital cycles. The intermediate layer eigenvalues The output module is used to use 1*1 convolutional layer operations to output two sets of parameters, Ψ and Λ. Ψ represents the predicted values ​​of the position, velocity and acceleration of the spatial target at a set time point in the future; Λ represents the relevant parameters of the space-time reference system;

[0010] (3) After the network is built, a loss function is designed to guide the optimization process of network parameters on the sample set. The loss function consists of a weighted sum of three parts, and the calculation method is as follows:

[0011]

[0012] In the formula, loss a (Ψ) is the data-driven loss, which is used to constrain the predicted value of the neural network at a specific time point to be consistent with the true value; loss b (Ψ, Λ) is the physical driving loss, which is used to constrain the network's fit to the kinematic equations of the space target; loss c (Λ) is the boundary condition constraint, which is used to constrain the effective range of the network for the space-time reference system constant; θ represents the neural network parameter; ω a ,ω b and ω c is the weight of each part, and ω a +ω b +ω c =1;

[0013] (4) Setting the training strategy and using the RMSProp optimizer to perform preliminary training on the spatial target trajectory parallel mapping network;

[0014] (5) After completing the initial network training, track and monitor the fluctuation of the network output parameter Λ. When the fluctuation reaches the set threshold, deploy the network into the parallel digital space. Otherwise, return to step (4) to continue iterative training.

[0015] Furthermore, the specific processing process of the cross-period spatiotemporal attention module in step (2) is as follows:

[0016] (201) Suppose the sequence of network input at a certain moment is {X t-n-1 ,...,X t}, then take t as the time reference point and extract the time point as The intermediate layer eigenvalues Among them, the cross-cycle sampling interval is set to one quarter of the orbital period of the space target, that is, k = 4; T represents the orbital period of the space target, and n is the time window width;

[0017] (202) For the intermediate layer eigenvalue Through concatenation and convolution, horizontal fusion is performed in sequence to generate The number of channels matches the feature vector; among them, Represents the network middle layer features corresponding to the current time t;

[0018] (203) The feature vector generated in step (202) is normalized through a softmax layer to generate Feature weights of each channel;

[0019] (204) The feature weight is combined with the feature at the current moment Perform weighted multiplication to expand the time span of information flow.

[0020] Furthermore, the boundary condition constraint loss in step (3) c (Λ) is:

[0021]

[0022] In the formula, τ is the weight of each parameter, λ∈Λ,λ * is the standard value of the corresponding parameter, a and σ * A constant used to control the discreteness of the value.

[0023] Furthermore, the output Λ of the parallel mapping network of the space target trajectory adopts the strategy of segmentally representing the same Λ parameter with multiple output nodes, and multiple output nodes are set to represent the high h bits, middle h bits and low h bits of the parameter in sequence, and h is a constant.

[0024] Compared with the prior art, the present invention has the following beneficial effects:

[0025] 1. The present invention proposes a method for parallel mapping of space target trajectories based on a physical information network. It uses a parameterized neural network to fit the kinematic equations of space targets in a parallel digital space, which can realize the rapid mapping of original observation data to different abstract modeling fields and the dynamic correction of model errors.

[0026] 2. The present invention proposes a method for parallel mapping of space target trajectories based on a physical information network. In the process of externalizing the data for use, the dynamic model obtained based on the data-driven mode replaces the original high-precision observation data. While ensuring data accuracy and readability, it realizes the logical isolation of the data production environment and the application scenario, effectively ensuring data security. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 The schematic diagram is a principle diagram of a method for parallel mapping of space target trajectories based on a physical information network according to the present invention.

[0028] Figure 2 This is a schematic diagram of a network structure of parallel mapping of space target trajectories based on a physical information network according to the present invention. DETAILED DESCRIPTION

[0029] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0030] like Figure 1 As shown, a space target trajectory parallel mapping method based on a physical information network includes the following steps:

[0031] (1) The spatial target position sequence data input by the method is in standard TLE format. First, the input spatial target position sequence data is parsed based on the SGP4 algorithm, and then the parsed spatial target position sequence data is truncated using a sliding time window strategy to construct a sample set.

[0032] Wherein step (1) comprises the following steps:

[0033] (101) The space target position sequence data is decoded and analyzed by the SGP4 algorithm, and the identification parameters, check parameters and other data fields are removed, retaining 16 valid parameters including TLE duration, first-order time derivative of average motion, second-order time derivative of average motion, orbit inclination, right ascension of ascending node, eccentricity, perigee angle, mean anomaly, mean angular velocity, orbit semi-major axis, orbit semi-minor axis, eccentricity, longitude, latitude, altitude and velocity.

[0034] (102) When truncating the data, a sliding time window strategy is adopted, and {x i+0 , x i+1 , ..., x i+n} as input, with {x i+n+1 , x i+n+2 , ..., x i+n+m} as labels to construct sample sets. Where n is the time window width and m is the network prediction time step.

[0035] In the embodiment of the method, the network input is data of 10 time steps, and the output is the future prediction value of 5 time steps, that is, n=10, m=5.

[0036] (2) Construct a parallel mapping network of space target trajectories, with the following structure: Figure 2 The network as a whole includes a data fusion module, a feature extraction module, a cross-cycle spatiotemporal attention module and an output module; the data fusion module is used to fuse the spatial target position sequence data through merging and convolution operations to expand the feature vector dimension; the feature extraction module is used to extract the time series features of the fused data through three LSTM units in series; the cross-cycle spatiotemporal attention module is used to extract the time points through a sampling strategy across 1 / k orbital cycles. The intermediate layer eigenvalues The output module is used to use 1*1 convolutional layer operations to output two sets of parameters, Ψ and Λ. Ψ represents the predicted values ​​of the position, velocity and acceleration of the spatial target at a set time point in the future; Λ represents the relevant parameters of the space-time reference system;

[0037] Without considering active orbit change and collision factors, the motion of space on-orbit targets has strict periodic constraints, but due to the ratio of the measured data time interval to the orbit period and the limitation of gradient vanishing, this kind of related dependency is difficult to be captured by conventional LSTM units. To this end, this method proposes a cross-period spatiotemporal attention module composed of a jump-layer link structure.

[0038] The parallel mapping network processing process of space target trajectory is as follows Figure 2 As shown, the specific steps are as follows:

[0039] (201) Assume that the network obtains the input {X t-n-1 ,...,X t}, the input time series are concatenated (i.e., Concatenation in the figure) and Conv1D convolution processed in turn to obtain the data fusion result X t ';

[0040] (202) X′ t Input into the series network module composed of three layers of LSTM units to extract time series features and obtain feature sequences Among them, each LSTM unit will inherit the long-term memory of the network at the previous moment Short-term memory And the short-term memory of the current LSTM unit Pass to the next LSTM unit;

[0041] (203) From t as the time reference point, extract the time point The intermediate layer eigenvalue sequence of Right now And through splicing (i.e. Concatenation in the figure) and convolution (i.e. Conv in the figure) horizontal fusion is generated The number of channels matches the feature vector. In the cross-cycle spatiotemporal attention module, in order to alleviate the overfitting phenomenon and take into account the symmetry of the spatial orbit, the cross-cycle sampling interval is set to one quarter of the orbit period of the spatial target, that is, k = 4;

[0042] (204) The feature vector obtained in step (203) is normalized through the softmax layer to generate The feature weights of each channel are combined with Perform weighted multiplication (i.e., prod in the figure) to achieve the superposition of cross-period spatiotemporal attention features;

[0043] (205) Finally, the calculation result of step (204) is input into the output module, and a 1*1 convolution (i.e., Conv1×1 in the figure) is performed to obtain the final output.

[0044] In addition, the output result of the output module designed by this method includes two parts Ω = {Ψ, Λ}. Among them, Ψ represents the predicted value of the position, velocity and acceleration of the space target at the next m time points, and Ψ = {r t+1 ,r t+2 ,...,r t+m},in Λ represents the relevant parameters of the space-time reference system, Where G is the gravitational constant, M e is the total mass of the Earth, M s is the space target mass, C D is the atmospheric drag coefficient, C DP is the atmospheric drag coefficient of the maximum cross section of the space target, A P is the maximum cross section of the space target, a e is the average radius of the Earth's equator, ρ is the atmospheric density, λ and are the geocentric longitude and latitude respectively, and N is the polynomial order in the non-spherical gravitational perturbation of the Earth. e ,C D ,C DP ,A P The number of effective digits of parameters such as φ and φ is relatively long. This method adopts a strategy of segmented representation using multiple output nodes, and sets multiple output nodes to represent a part of the parameter segment by segment in sequence. When this method is implemented, the network predicts the future state of the space target for 5 time steps, that is, m=5.

[0045] It is worth noting that in practical applications, different mapping target spaces correspond to different network outputs and network layers. Therefore, in order to explain the model capabilities proposed by this method in detail, the network structure and training strategy are explained in the following with the perturbation force elliptical geometric orbit model as the mapping target. The perturbation force elliptical geometric orbit model selected by this method only considers the influence of two-body gravity, the perturbation influence of the non-spherical part of the earth, the perturbation influence of the sun and the moon, and the perturbation influence of the earth's atmospheric resistance. Other perturbation influences are not considered.

[0046] (3) After the network is built, the processed sample data is connected and the network optimization process is guided by the loss function. The network loss function designed by this method consists of a weighted sum of three parts, and the calculation method is as follows:

[0047]

[0048] In the formula, loss a (Ψ) is the data-driven loss, which is used to constrain the predicted value of the neural network at a specific time point to be consistent with the true value; loss b (Ψ, Λ) is the physical driving loss, which is used to constrain the network's fit to the kinematic equations of the space target; loss c (Λ) is the boundary condition constraint, which is used to constrain the effective range of the network for the space-time reference system constant; θ represents the neural network parameter; ω a ,ω b ,ω c is the weight of each part, and ω a +ω b +ω c =1.

[0049] The data-driven loss in step (3) a (Ψ), is the root mean square error between the position vector predicted by the network and the original position vector, calculated as follows:

[0050]

[0051] In the formula, r pre,i Represents the position state vector of the network prediction output, r true,t+i The position state vector of the original input space target trajectory data calculated by the SGP4 algorithm.

[0052] The physical drive loss in step (3) b (Ψ,Λ) is the deviation between the orbital parameters output by the network and the position state vector, which is used to evaluate the degree of fit of the neural network to the kinematic equations of the space target. The calculation method is as follows:

[0053]

[0054] In the formula, In an ideal situation, φ(r) is equal.

[0055] This method aims to fit the kinematic equation of the space target in the parallel simulation space through a parameterized neural network. The kinematic equation of the space target is as follows:

[0056]

[0057]

[0058]

[0059] In the formula, r, and They represent the position, velocity and acceleration vector of the space target at time t, G is the gravitational constant, M e is the total mass of the Earth, is the Earth's gravitational acceleration, is the vector sum of the perturbation acceleration, is the non-spherical gravitational perturbation of the Earth, The gravitational perturbation of the sun and the moon, is the atmospheric drag perturbation.

[0060] Among them, the non-spherical gravitational perturbation of the earth The calculation formula is:

[0061]

[0062] In the formula, λ and are geocentric longitude and latitude respectively; a e is the mean radius of the Earth at the equator; is the normalized adjoint Legendre polynomial; and is the gravitational potential coefficient of the earth; p and q are the order and degree of the polynomial, Q is the highest order of q; M s The quality of the space target.

[0063] Among them, the space target is subject to the perturbation acceleration caused by the gravity of the moon and the sun. The calculation formula is:

[0064]

[0065] In the formula, Δ j =rr j ; r j is the moon (sun) position vector; r is the space target (sun) position vector; S and L refer to the sun and the moon respectively.

[0066] Among them, the perturbation acceleration caused by atmospheric drag The calculation formula is:

[0067]

[0068] In the formula, C D is the atmospheric drag coefficient; ρ is the atmospheric density; V R is the running speed of the space target; A / M is the ratio of the reference area to the mass of the space target; C DP A is the atmospheric drag coefficient of the maximum cross section of the space target; P / M is the ratio of the maximum cross-section to the mass of the space object; It is the angle between the normal direction of the maximum cross section of the space target and the direction of the space target's velocity relative to the atmosphere.

[0069] Boundary condition constraint loss in step (3) c (Λ), by calculating the deviation between the network output space-time reference system parameter Λ and the standard value, the neural network's modeling ability for parallel digital space is strengthened. The calculation formula is:

[0070]

[0071] In the formula, τ is the weight of each parameter, λ∈Λ,λ * is the standard value of the corresponding parameter, a and σ * A constant used to control the discreteness of the value.

[0072] The space-time reference system parameter Λ usually has a reference value, such as the gravitational constant G = (6.67428 ± 0.00067) × 10 -11 m 3 / (kg s 2 ), the total mass of the Earth M e =5.9722×10 24 kg, etc., will not be listed here one by one.

[0073] (4) This method uses the RMSProp optimizer to train the neural network model. Other training strategies used in this method, such as learning rate and normalization, all adopt conventional methods.

[0074] The specific step (4) is as follows:

[0075] In order to solve the problem that some spatiotemporal reference system parameters in the network output have too many effective digits and are sensitive to value, this method adopts a variable weighting strategy for the output nodes representing different digital intervals of the same parameter, and gradually adjusts the weights of nodes in different digital intervals as the training progresses. In the early stage, the loss weight of high-order nodes is set to be larger, and then gradually decays to be consistent with low-order nodes.

[0076] (5) This method uses a data-driven model error correction strategy to automatically maintain the parallel digital model. After completing the initial model training and deploying it in the parallel digital space, the neural network model is iteratively trained using the source data, and the fluctuation of the output network output parameter Λ is tracked and monitored. When the fluctuation of the parameter Λ reaches a certain threshold, the model parameter Λ is deployed in the parallel digital space, thereby achieving periodic correction of the error.

[0077] Finally, it should be noted that the above-described embodiments are only specific implementations of the present invention, which are used to illustrate the technical solutions of the present invention, rather than to limit them. The protection scope of the present invention is not limited thereto. Although the present invention is described in detail with reference to the above-described embodiments, ordinary technicians in the field should understand that any technician familiar with the technical field can still modify the technical solutions recorded in the above-described embodiments within the technical scope disclosed by the present invention, or can easily think of changes, or make equivalent replacements for some of the technical features therein; and these modifications, changes or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A space target trajectory parallel mapping method based on physical information network, characterized in that: The following steps are included: (1) The input spatial target position sequence data is parsed based on the SGP4 algorithm, and then the sliding time window strategy is used to truncate the parsed spatial target position sequence data to construct a sample set; (2) Construct a spatial target trajectory parallel mapping network, which includes a data fusion module, a feature extraction module, a cross-cycle spatiotemporal attention module, and an output module; the data fusion module is used to fuse the spatial target position sequence data through merging and convolution operations to expand the feature vector dimension; the feature extraction module is used to extract the time series features of the fused data through three LSTM units in series; The cross-cycle spatiotemporal attention module is used to extract the time points as The intermediate layer eigenvalues The output module is used to use 1*1 convolutional layer operations to output two sets of parameters, Ψ and Λ. Ψ represents the predicted values ​​of the position, velocity and acceleration of the spatial target at a set time point in the future; Λ represents the relevant parameters of the space-time reference system; (3) After the network is built, a loss function is designed to guide the optimization process of network parameters on the sample set. The loss function consists of a weighted sum of three parts, and the calculation method is as follows: In the formula, loss a (Ψ) is the data-driven loss, which is used to constrain the predicted value of the neural network at a specific time point to be consistent with the true value; loss b (Ψ, Λ) is the physical driving loss, which is used to constrain the network's fit to the kinematic equations of the space target; loss c (Λ) is the boundary condition constraint, which is used to constrain the effective range of the network for the space-time reference system constant; θ represents the neural network parameter; ω a ,ω b and ω c is the weight of each part, and ω a +ω b +ω c =1; (4) Setting the training strategy and using the RMSProp optimizer to perform preliminary training on the spatial target trajectory parallel mapping network; (5) After completing the initial network training, track and monitor the fluctuation of the network output parameter Λ. When the fluctuation reaches the set threshold, deploy the network into the parallel digital space. Otherwise, return to step (4) to continue iterative training.

2. According to claim 1, a method for parallel mapping of space target trajectories based on a physical information network is characterized in that: The specific processing process of the cross-period spatiotemporal attention module in step (2) is as follows: (201) Suppose the sequence of network input at a certain moment is {X t-n-1 ,...,X t }, then take t as the time reference point and extract the time point as The intermediate layer eigenvalues Among them, the cross-cycle sampling interval is set to one quarter of the orbital period of the space target, that is, k = 4; T represents the orbital period of the space target, and n is the time window width; (202) For the intermediate layer eigenvalue Through concatenation and convolution, horizontal fusion is performed in sequence to generate The number of channels matches the feature vector; among them, Represents the network middle layer features corresponding to the current time t; (203) The feature vector generated in step (202) is normalized through a softmax layer to generate Feature weights of each channel; (204) The feature weight is combined with the feature at the current moment Perform weighted multiplication to expand the time span of information flow.

3. The method for parallel mapping of space target trajectories based on a physical information network according to claim 1, characterized in that: Boundary condition constraint loss in step (3) c (Λ) is: In the formula, τ is the weight of each parameter, λ∈Λ,λ * is the standard value of the corresponding parameter, a and σ * A constant used to control the discreteness of the value.

4. The method for parallel mapping of space target trajectories based on a physical information network according to claim 1, characterized in that: The output Λ of the parallel mapping network of the space target trajectory adopts the strategy of segmentally representing the same Λ parameter with multiple output nodes. Multiple output nodes are set to represent the high h bits, middle h bits and low h bits of the parameter in sequence and segment by segment, respectively, and h is a constant.

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