A space target trajectory parallel mapping method based on physical information network

Abstract

The application provides a space target trajectory parallel mapping method based on a physical information network, and belongs to the field of time series data processing in deep learning. In view of the problems that there are a large amount of repetitive work and time-consuming and labor-consuming in the analysis modeling of the physical system of the space target movement and the cumulative error correction process, the application fits the kinematics equation of the space target in the parallel digital space through a parameterized neural network, introduces known physical equation information, restricts the process of the network in the hypothesis space to find the optimal hypothesis, converts the parallel space modeling mapping process into the solution of the parameter inversion problem in the target domain, so that the parallel digital space is quickly constructed. Meanwhile, with the increase of the input sample data, the cross-cycle space-time attention module designed by the method can capture the space target movement characteristics more and more strongly, and in the continuous iteration process, the dynamic correction of the error is realized.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of time series data processing in deep learning, and particularly relates to a space target trajectory parallel mapping method based on a physics-informed neural network. BACKGROUND

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

[0003] For a space target motion physical system, the general research steps are as follows: first, abstractly representing the problem domain, establishing a parallel mathematical space model, then mapping the measured data in the real physical space to the parallel space, and finally performing related processing and analysis. In this process, the modeling angle of the parallel digital space is different under different research objectives; different modeling angles of the parallel digital space require different data mapping strategies; in addition, when long time series data are involved, due to different modeling granularities and key parameter values, there is error accumulation between the parallel space model and the measured results, which needs to be periodically corrected. Usually, these works are manually completed by industry experts based on work experience and field knowledge, which consumes manpower and involves a lot of repetitive work.

[0004] Therefore, a space target trajectory parallel mapping method based on data driving is researched, a parametric neural network is used to fit the kinematics equation of the space target in the parallel digital space, and known physical equation information is introduced to constrain the network to find the optimal hypothesis in the hypothesis space, thereby converting the parallel space modeling and mapping process into a solution to the parameter inversion problem in the target domain, so as to realize the rapid construction of the parallel digital space. SUMMARY

[0005] The application faces the problem that the existing space target trajectory analysis digital model modeling process is repetitive and complicated, and needs to be periodically maintained, and proposes a space target trajectory parallel mapping method based on a physics-informed neural network.

[0006] To achieve the above purpose, the technical solution adopted by the application is as follows:

[0007] A space target trajectory parallel mapping method based on a physics-informed neural network comprises the following steps:

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

[0009] (2) A spatial target trajectory parallel mapping network is constructed, including a data fusion module, a feature extraction module, a cross-cycle spatio-temporal 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 spatio-temporal attention module is used to extract the intermediate layer feature values of the time points The output module is used to output two groups of parameters Ψ and Λ using 1*1 convolution layer operation. Ψ represents the predicted values of the spatial target's position, velocity, and acceleration at a set of future time points. Λ represents the related parameters of the spatio-temporal reference system.

[0010] (3) After the network is built, a loss function is designed to guide the optimization process of the network parameters on the sample set. The loss function is composed of three parts weighted sum, 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 certain time point to be consistent with the true value; loss b (Ψ,Λ) is the physics-driven loss, which is used to constrain the fitting degree of the network to the kinematics equation of the spatial target; loss c (Λ) is the boundary condition constraint, which is used to constrain the effective range of the network for the constant value of the spatio-temporal reference system; θ represents the neural network parameters; ω a , ω b , and ω c are the weights of each part, and ω a + ω b + ω c = 1.

[0013] (4) The training strategy is set, and the RMSProp optimizer is used to preliminarily train the spatial target trajectory parallel mapping network.

[0014] (5) After the preliminary training of the network is completed, the fluctuation of the output parameter Λ of the tracking monitoring network is tracked. When the fluctuation reaches a set threshold, the network is deployed into the parallel digital space, otherwise step (4) is returned to continue iterative training.

[0015] ​Further, the specific processing procedure of the cross-period spatio-temporal attention module in step (2) is as follows:

[0016] (201) assuming that the sequence of network input at a certain moment is {X t-n-1 ,...,X t}, then taking t as the time reference point, the middle layer feature value at the time point is extracted wherein the cross-period sampling interval is set as one fourth of the space target orbit period, that is, k=4; T represents the orbit period of the space target, and n is the time window width;

[0017] (202) the middle layer feature value is sequentially fused through splicing and convolution to generate a feature vector matching the channel number of ; wherein, represents the network middle layer feature corresponding to the current moment t;

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

[0019] (204) the feature weight is multiplied by the feature of the current moment to realize the expansion of the time span of the information flow.

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

[0021]

[0022] wherein τ is the weight of each parameter, λ∈Λ, λ * is the standard value of the corresponding parameter, and a and σ * are constants used to control the discrete degree of the value.

[0023] Further, the output Λ of the space target trajectory parallel mapping network adopts the strategy that multiple output nodes are used to represent the same Λ parameter, and multiple output nodes are set to represent the high h-bit, middle h-bit and low h-bit significant digits of the parameter in sequence, and h is a constant.

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

[0025] 1. The space target trajectory parallel mapping method based on a physical information network provided by the present application uses a parameterized neural network to fit the kinematics equation of the space target in the parallel digital space, so that the original observation data can be quickly mapped to different abstract modeling fields and the model error can be dynamically corrected. ​

[0026] 2. The space target trajectory parallel mapping method based on a physical information network provided by the application realizes logical isolation of data production environment and application scenarios while ensuring data precision and readability, and effectively guarantees data security in the process of guiding data outward for use. BRIEF DESCRIPTION OF DRAWINGS

[0027] Figure 1 FIG. 1 is a schematic diagram of the principle of the space target trajectory parallel mapping method based on a physical information network.

[0028] Figure 2 FIG. 2 is a schematic diagram of the network structure of the space target trajectory parallel mapping method based on a physical information network. DETAILED DESCRIPTION

[0029] The application will be further described in detail below in combination with the drawings and specific embodiments.

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

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

[0032] Step (1) comprises the following steps:

[0033] (101) The space target position sequence data is decoded, parsed by the SGP4 algorithm, and other steps, and the identification parameters, check parameters and other data fields are removed, and 16 effective parameters including TLE duration, average motion first-order time derivative, average motion second-order time derivative, orbital inclination, ascending node right ascension, eccentricity, perigee argument, perihelion angle, average angular velocity, orbital semi-major axis, orbital semi-minor axis, eccentricity, longitude, latitude, height, and speed are retained.

[0034] (102) When truncating the data, a sliding time window strategy is used, and {x i+0 , x i+1 ,..., x i+n} is taken as input and {x i+n+1 , x i+n+2 ,..., x i+n+m} is taken as label to construct a sample set. Wherein, n is the time window width, and m is the network prediction time step. ​

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

[0036] (2) A spatial target trajectory parallel mapping network is constructed, and the structure is as shown in Figure 2 The network as a whole comprises a data fusion module, a feature extraction module, a cross-period spatio-temporal attention module, and an output module; the data fusion module is used for fusing the spatial target position sequence data by merging and convolution operation to expand the feature vector dimension; the feature extraction module is used for extracting the time sequence features of the fused data by three LSTM units in series; the cross-period spatio-temporal attention module is used for extracting the intermediate layer feature values at the time point by using a sampling strategy across 1 / k orbital periods; The output module is used for outputting two groups of parameters Ψ and Λ by using a 1*1 convolution layer operation, Ψ represents the prediction values of the position, velocity and acceleration of the spatial target at a set of future time points; and Λ represents the related parameters of the spatio-temporal reference system;

[0037] Without considering active orbit transfer and collision factors, the motion of the spatial on-orbit target has a strict period constraint, but due to the proportion of the actual measurement data time interval to the orbital period and the gradient disappearance limit, such a related dependence relationship is difficult to be captured by the conventional LSTM unit. Therefore, the method proposes a cross-period spatio-temporal attention module composed of a leap layer linking structure.

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

[0039] (201) Assuming that the network obtains the input {X t-n-1 ,...,X t} at time t, the time sequence of the input is sequentially spliced (i.e., Concatenation in the figure) and Conv1D convolution processing is performed to obtain the data fusion result X t ';

[0040] (202) The X′ t is input into a series network module composed of three layers of LSTM units for time sequence feature extraction to obtain a feature sequence , wherein each LSTM unit will inherit the long-term memory and the short-term memory of the network at the previous time, and the short-term memory of the current LSTM unit is passed to the next LSTM unit;

[0041] (203) From the time point t as the time reference point, the intermediate layer feature value sequence at the time point is extracted i.e. and transverse fusion through concatenation (i.e. Concatenation in the figure) and convolution (i.e. Conv in the figure), to generate a feature vector matching the number of channels. In the cross-period spatio-temporal attention module, in order to alleviate the overfitting phenomenon and considering the symmetry of the spatial orbit, the cross-period sampling interval is set to one-fourth of the period of the spatial target orbit, i.e. k = 4;

[0042] (204) The feature vector obtained in step (203) is normalized by a softmax layer to generate the feature weight of each channel, and multiplied by to realize the superposition of the cross-period spatio-temporal attention features.

[0043] (205) Finally, the calculation result of step (204) is input into the output module to obtain the final output through 1*1 convolution (i.e. Conv1x1 in the figure).

[0044] In addition, the output result of the output module of the method includes two parts Ω = {Ψ, Λ}. Wherein, Ψ represents the predicted values of the position, velocity and acceleration of the spatial target at m future time points, Ψ = {r t+1 ,r t+2 ,...,r t+m}, wherein Λ represents the related parameters of the space-time reference system, wherein G is the gravitational constant, M e is the total mass of the earth, M s is the mass of the spatial target, C D is the atmospheric drag coefficient, C DP is the atmospheric drag coefficient of the maximum cross section of the spatial target, A P is the maximum cross section of the spatial target, a e is the average radius of the earth at the equator, ρ is the atmospheric density, λ and are the longitude and latitude of the earth center respectively, and N is the polynomial order in the non-spherical gravitational perturbation of the earth. Since the effective number of digits of parameters such as G, M e , C D , C DP , A P is relatively long, the method adopts the strategy of segmenting the representation of multiple output nodes, and sets multiple output nodes to represent a part of the parameters in order. In the implementation of the method, the network predicts the future state of the spatial target for 5 time steps, i.e. m = 5.

[0045] It is worth mentioning that in practical applications, the network output corresponding to different mapping target spaces and the number of network layers are different. Therefore, in order to explain the model capability of the proposed method in detail, the network structure and training strategy are explained in the following with the perturbed elliptical geometric orbit model as the mapping target. The perturbed elliptical geometric orbit model selected by the present method only considers the influence of two-body gravity, the perturbation of the non-spherical part of the earth, the perturbation of the sun and moon gravity, and the perturbation of the atmospheric drag of the earth, and other perturbations are not considered.

[0046] (3) After the network is built, the processed sample data is accessed to guide the optimization process of the network through the loss function. The network loss function designed by the present method is composed of three parts weighted summation, 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 certain time point to be consistent with the true value; loss b (Ψ,Λ) is the physics-driven loss, which is used to constrain the fitting degree of the network to the kinematic equation 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 constant value of the space-time reference system; θ represents the neural network parameters; ω a , ω b , ω c are the weights of each part, and ω a + ω b + ω c = 1.

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

[0050]

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

[0052] The physics-driven loss loss b (Ψ,Λ) in step (3) is the deviation between the output orbit parameters of the network and the position state vector, which is used to evaluate the fitting degree of the neural network to the kinematic equation of the space target. The calculation method is as follows:

[0053]

[0054] where, In ideal case, φ(r) is equal to .

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

[0056]

[0057]

[0058]

[0059] where, r, and respectively represent the position, velocity and acceleration vector of the space target at time t, G is the universal gravitation constant, M e is the total mass of the earth, is the earth gravitation acceleration, is the vector sum of the perturbation acceleration, is the earth non-spherical gravitation perturbation, is the sun and moon gravitation perturbation, is the atmospheric resistance perturbation.

[0060] wherein the calculation formula of the earth non-spherical gravitation perturbation is as follows:

[0061]

[0062] wherein λ and are the geocentric longitude and latitude respectively; a e is the average radius of the earth equator; is the normalized associated Legendre polynomial; and are the earth gravitation potential coefficients; p and q are the order and degree of the polynomial, Q is the highest order of q; M s is the mass of the space target.

[0063] wherein the calculation formula of the perturbation acceleration of the space target caused by the moon and sun gravitation is as follows:

[0064]

[0065] wherein Δ j =r-r j ; r j is the position vector of the moon (sun); r is the position vector of the space target (sun); S and L respectively refer to the sun and moon.

[0066] where the perturbation acceleration caused by atmospheric drag is The calculation formula is:

[0067]

[0068] where C D is the atmospheric drag coefficient; p is the atmospheric density; V R is the space target operating speed; A / M is the ratio of the reference area and mass of the space target; C DP is the atmospheric drag coefficient of the maximum cross section of the space target; A P / M is the ratio of the maximum cross section and mass of the space target; and a is the angle between the normal direction of the maximum cross section of the space target and the direction of the speed of the space target relative to the atmosphere.

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

[0070]

[0071] where τ is the weight of each parameter, λ∈Λ, λ * is the standard value corresponding to the parameter value, a and σ * are constants used to control the discrete degree 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, and the like, which will not be described one by one.

[0073] (4) The RMSProp optimizer is used to train the neural network model. Other training strategies such as learning rate and normalization used in the method are all adopted by conventional methods.

[0074] where step (4) is specifically:

[0075] In view of the problem that the effective number of digits of part of the space-time reference system parameters output by the network is too large and the value is sensitive, the method uses a variable weighting strategy for output nodes representing different numerical intervals of the same parameter, and gradually adjusts the weights of nodes in different numerical intervals with the training process. The loss weight of the high-bit node is set to be larger in the early stage, and is gradually attenuated to be consistent with the low-bit node.​

[0076] (5) The method adopts a model error correction strategy based on data driving to automatically maintain the parallel digital model. After the preliminary training of the model is completed and the parallel digital space is deployed, the source data is continuously used to iteratively train the neural network model, and the fluctuation of the output network output parameter Λ is tracked and monitored. When the parameter Λ changes and fluctuates to a certain threshold, the model parameter Λ is deployed into the parallel digital space, thereby realizing the periodic correction of the error.

[0077] Finally, it should be noted that the above-described embodiments are only specific implementations of the present application, which are used to illustrate the technical solutions of the present application, but not to limit them. The protection scope of the present application is not limited to this. Although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can modify or easily think of changes to the technical solutions recorded in the foregoing embodiments, or make equivalent replacements to some technical features, within the technical range disclosed by the present application. These modifications, changes or replacements do not make the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application, and should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method for parallel mapping of spatial target trajectories based on physical information networks, characterized in that, It includes the following steps: (1) 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; (2) Construct a parallel mapping network for spatial target trajectories, which includes a data fusion module, a feature extraction module, a cross-period spatiotemporal attention module, and an output module. The data fusion module is used to fuse spatial target position sequence data through merging and convolution operations to expand the dimension of feature vectors. The feature extraction module is used to extract temporal features from the fused data through three LSTM units connected in series. The cross-period spatiotemporal attention module is used to extract time points using a sampling strategy spanning 1 / k orbital periods. intermediate layer eigenvalues The output module is used to perform 1*1 convolutional layer operations and 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 spatiotemporal reference frame. (3) After the network is built, design a loss function to guide the optimization process of the 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) represents the data-driven loss, used to constrain the neural network's predictions to match the actual values ​​at a specific time point; loss b (Ψ,Λ) represents the physics-driven loss, used to constrain the network's fit to the kinematic equations of the spatial target; loss c (Λ) represents the boundary condition constraint, used to constrain the effective range of the network's values ​​for the spatiotemporal reference frame constants; θ represents the neural network parameters; ω a ω b and ω c Let ω be the weight of each part, and ω be the weight of each part. a +ω b +ω c =1; (4) Set the training strategy and use the RMSProp optimizer to perform preliminary training on the spatial target trajectory parallel mapping network; (5) After completing the initial training of the network, track and monitor the fluctuation of the network output parameter Λ. When the fluctuation reaches the set threshold, deploy the network in the parallel digital space; otherwise, return to step (4) to continue iterative training. The specific processing procedure of the cross-cycle spatiotemporal attention module in step (2) is as follows: (201) Suppose that the sequence of network input at a certain moment is {X} t-n-1 ,...,X t }, then taking t as the time reference point, the extracted time point is intermediate layer eigenvalues Wherein, the cross-period sampling interval is set to one-quarter of the orbital period of the space target, i.e., k = 4; T represents the orbital period of the space target, and n is the width of the time window; (202) Eigenvalues ​​of the intermediate layer Laterally fused by sequentially splicing and convolution, a result is generated that is similar to... The number of channels matches the feature vector; where, This represents the intermediate layer features of the network at the current time t; (203) The feature vector generated in step (202) is normalized through a softmax layer to generate... Feature weights for each channel; (204) Combine the feature weights with the features at the current time. By performing weighted multiplication, the time span of the information flow can be extended.

2. The method for parallel mapping of spatial target trajectories based on physical information networks according to claim 1, characterized in that, Boundary condition constraint loss in step (3) c (Λ) means: In the formula, τ represents the weight of each parameter, λ∈Λ, λ * For the standard values ​​of the corresponding parameters, a and σ * It is a constant used to control the degree of dispersion of its values.

3. The method for parallel mapping of spatial target trajectories based on physical information networks according to claim 1, characterized in that, The output Λ of the parallel mapping network for spatial target trajectories adopts a strategy of segmenting the same Λ parameter into 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, with h being a constant.

Images