An intelligent prediction method for space target orbit combining with orbit dynamics constraints

Abstract

The application relates to the technical field of aerospace and artificial intelligence, and provides a space target orbit intelligent prediction method fusing an orbit dynamics constraint, which comprises the following steps: preprocessing original orbit data of a space target to generate a complete time series data set with continuity and uniform time intervals; constructing a physical information neural network model which represents input and output in the form of time series data, and performing differential calculation on an output sequence by using an automatic differentiation mechanism; designing and introducing a loss function with an adaptive weighting mechanism to dynamically balance loss terms of network modules and physical modules in a training process; training the physical information neural network model; setting a data subset sampling rate, constructing a multi-scale data scene, and evaluating performance of the physical information neural network model under different data scale conditions. The application can improve modeling capability for a long-time orbit evolution process and realize dynamic adjustment of weights of various loss terms.

Description

A method for intelligent prediction of space target orbits that integrates orbital dynamics constraints Technical Field

[0001] This invention relates to the fields of aerospace and artificial intelligence, and in particular to an intelligent prediction method for the orbit of a space target that integrates orbital dynamics constraints. Background Technology

[0002] As space debris environments become increasingly congested, the potential risks posed by the "Kessler effect" continue to rise, making the demand for efficient space situational awareness and space traffic management technologies increasingly urgent. As a core foundation supporting the realization of these technologies, trajectory prediction methods are crucial for ensuring the safety and sustainable development of space activities, and their accuracy and efficiency are of paramount importance.

[0003] Traditional orbit prediction methods primarily rely on analytical solutions or numerical integration methods of orbital dynamics. However, due to the existence of unmodeled dynamics and the high complexity of differential calculations, these methods struggle to achieve an effective trade-off between computational accuracy and efficiency. In recent years, artificial intelligence methods have been extensively studied in various fields and have demonstrated superior performance in orbit prediction tasks. However, because these methods are essentially "black box" models and heavily reliant on data-driven mechanisms, they face problems such as insufficient interpretability and susceptibility to violating physical laws in practical applications, thus limiting their widespread adoption and application in scenarios with high reliability requirements. Summary of the Invention

[0004] This invention addresses the shortcomings of existing data-driven artificial intelligence methods for orbit prediction in satisfying physical prior constraints. It proposes an intelligent prediction method for space target orbits that integrates orbital dynamic constraints. By introducing orbital dynamic constraints into the loss function of the time series prediction model, a physical information neural network for orbit prediction is constructed to improve the modeling ability of long-term orbit evolution processes and to achieve dynamic adjustment of the weights of various loss terms, thereby further improving the performance and stability of the model in long-term orbit prediction tasks.

[0005] This invention provides an intelligent prediction method for the orbit of a space target that integrates orbital dynamics constraints, comprising the following processes:

[0006] Step S1: Preprocess the raw orbital data of the space target to generate a complete time series dataset with continuity and uniform time intervals;

[0007] Step S2: Construct a physical information neural network model that represents the input and output in the form of time series data, and use an automatic differentiation mechanism to perform differentiation calculation on the output sequence;

[0008] Step S3: Design and introduce an adaptive weighting loss function to dynamically balance the loss terms of network modules and physical modules during training;

[0009] Step S4: Divide the complete time series into training, validation, and test sets, and train the physical information neural network model;

[0010] Step S5: Set the data subset sampling rate, construct multi-scale data scenarios, and evaluate the performance of the physical information neural network model under different data scale conditions.

[0011] Furthermore, step S1 includes the following steps S101 to S104:

[0012] Step S101: Extract and structure key time series data for orbit prediction from the original orbit data file; the time series data includes timestamps, position components, and velocity components;

[0013] Step S102: Convert the string-formatted timestamp into a numerical Julian calendar;

[0014] Step S103: Transform the extracted raw time series data from the ITRS coordinate system to the ECI coordinate system;

[0015] Step S104: Based on the timestamp, select the time-continuous subsequences as the final time series data.

[0016] Furthermore, step S2 includes the following steps S201 to S203:

[0017] Step S201: Determine the input and output layers of the physical information neural network;

[0018] In step S2, the input layer of the physical information neural network receives the original orbital data time series containing the position and velocity characteristics of the space target. and the corresponding predicted timestamp sequence The output layer generates time series of predicted orbit data containing future orbital position and velocity features. ;

[0019] Step S202: Constructing a data sequence for predicting orbits A physical information neural network model;

[0020] The aforementioned method for predicting orbital data sequences The physical information neural network model is constructed as follows:

[0021] ;

[0022] In the formula, This represents the network part of a neural network that represents physical information. Represents the physical residual. and These represent the loss values ​​for the network component and the physical component, respectively. This represents the true value of the corresponding predicted sequence. and Indicates the weight of each loss;

[0023] Step S203: Perform differential calculation on the output sequence using an automatic differential mechanism;

[0024] The automatic differentiation mechanism is implemented by automatically executing the orbital data sequence predicted by the network part during the training process of the physical information neural network model. Relative to its corresponding timestamp sequence The differential operation is performed to obtain the orbital dynamics constraint sequence of the physical information neural network used for orbital time series prediction. .

[0025] Furthermore, the adaptive weighting mechanism in step S3 is as follows: the loss of the network part is based on the Gaussian distribution assumption, and the loss of the position and velocity components of the physical part is based on the multivariate Gaussian distribution assumption. By constructing a negative log-likelihood function, the adaptive weighting mechanism of each loss component is realized.

[0026] The loss function introduced in step S3, which employs an adaptive weighting mechanism, is as follows:

[0027]

[0028] This loss function is a general loss function used for the physical information neural network model in step S2.

[0029] Furthermore, the ratio of the dataset to be divided in step S4 is 70% for the training set, 15% for the validation set, and 15% for the test set.

[0030] Furthermore, the training method for the physical information neural network model described in step S4 is as follows:

[0031] The model network takes standardized historical sequence data and predicted time series data from the training set as input and outputs the corresponding predicted sequence results.

[0032] The obtained prediction results are de-standardized and then used to solve the orbital dynamics constraints. The corresponding loss values ​​and performance evaluation indicators are calculated on the validation set.

[0033] After training the physical information neural network model, its performance was evaluated and tested on the test set.

[0034] Furthermore, the method for setting the data subset sampling rate in step S5 is as follows: during the data loading stage before model training, the sampling rate of the data subset is set. This is to control the size of the data used for training, thereby simulating the model's performance under different data sizes.

[0035] This invention provides an intelligent prediction method for space target orbits that integrates orbital dynamic constraints. Based on a long-term series prediction model using a physical neural network, it enhances the data-driven model's ability to characterize orbital dynamics by adding soft constraints, thereby improving the model's prediction accuracy and generalization performance. An adaptive weighting mechanism for loss is designed based on a multivariate Gaussian distribution, automatically adjusting the weight parameters of various loss terms during model training. This dynamic adjustment effectively avoids empirical biases and parameter adjustments introduced by manual weight setting, further improving the stability of the training process and model performance, thus enhancing the model's performance and stability in long-term orbit prediction tasks.

[0036] This invention enables high-precision time-series prediction of the orbital state vector of space targets, covering key components of position and velocity. The prediction results are in the form of a continuous time series of orbital states, rather than the single-moment orbital positions in traditional methods. This allows for an effective characterization of the long-term evolution of space target orbits, more comprehensively reflecting their dynamic evolution characteristics. This method boasts advantages such as lightweight design, accuracy, and efficiency, and has promising application prospects in the aerospace field. By integrating prior physical knowledge of orbital dynamics with data-driven methods, and employing a physical neural network approach, physical law constraints are added to the loss function to improve the physical consistency of the model's prediction results. For the position and velocity components in the physical part, a multivariate Gaussian distribution is introduced to construct an adaptive weighting mechanism to enhance the model's stability during training. Furthermore, this invention uses a data subset sampling rate to simulate experimental environments with different data scales, allowing for system testing of the model's performance under varying data sizes.

[0037] This invention helps to improve the adaptability and practicality of artificial intelligence models in orbit prediction tasks in the aerospace field, and has important theoretical value and engineering application significance. Attached Figure Description

[0038] Figure 1 is a flowchart illustrating the implementation of the intelligent prediction method for space target orbits that integrates orbital dynamic constraints provided by the present invention.

[0039] Figure 2 is a schematic diagram of the training strategy of the physical information neural network of the present invention;

[0040] Figure 3 shows the performance index changes of the model of the present invention under different data scales. Detailed Implementation

[0041] To make the technical problems solved by this invention, the technical solutions adopted, and the technical effects achieved clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings, not all of them.

[0042] As shown in Figure 1, an embodiment of the present invention provides a method for intelligent prediction of the orbit of a space target that incorporates orbital dynamic constraints, comprising the following processes:

[0043] Step S1: Preprocess the raw orbital data of the space target to generate a complete time series dataset with continuity and uniform time intervals.

[0044] High-precision raw track data was selected.

[0045] Step S1 includes the following steps S101 to S104:

[0046] Step S101: Extract and structure key time series data for orbit prediction from the original orbit data file; the time series data includes timestamps, position components, and velocity components.

[0047] The raw orbit data files were precise orbit products from the Sentinel-3B satellite observed by DORIS, provided in .sp3 format and obtained from the CDDIS website system. Timestamps, position components, and velocity components were extracted from all files and saved into a single spreadsheet file.

[0048] Step S102: Convert the string-formatted timestamp into a numerical Julian calendar.

[0049] During the training of deep learning models, the models cannot directly process timestamps in string format. Python tools are used to convert the timestamps to Julian calendar format to standardize the time features and meet the input requirements for model training.

[0050] Step S103: Transform the extracted raw time series data from the ITRS (International Terrestrial Reference System) coordinate system to the ECI (Earth-Centered Inertial) coordinate system.

[0051] To ensure the physical consistency of the data used in orbit prediction, the conversion between different coordinate systems needs to be considered. Since orbit dynamics models are usually built in the ECI coordinate system, while the original observation data comes from ground observations and their position information is usually represented in the ITRS coordinate system, a coordinate system conversion step needs to be introduced in the data preprocessing stage to convert the data in the ITRS coordinate system to the ECI coordinate system, thereby ensuring the consistency and physical rationality of the model input.

[0052] Step S104: Based on the timestamp, select the time-continuous subsequences as the final time series data.

[0053] Due to factors such as failures in the actual observation system and interruptions in signal transmission, there are certain degrees of missing data in the original data. To ensure the continuity of the time series data and to preserve as much of the inherent structure and information of the actual observation data as possible, a traversal method was used to analyze the original data, extract data segments with good continuity, and select the longest continuous segment as the data basis for subsequent experiments.

[0054] Step S2: Construct a physical information neural network model that represents the input and output in the form of time series data, and use an automatic differentiation mechanism to perform differentiation calculation on the output sequence;

[0055] Step S2 includes the following steps S201 to S203:

[0056] Step S201: Determine the input and output layers of the physical information neural network.

[0057] In step S2, the input layer of the physical information neural network receives the original orbital data time series containing the position and velocity characteristics of the space target. and the corresponding predicted timestamp sequence The output layer generates time series of predicted orbit data containing future orbital position and velocity features. .

[0058] The physical information neural network model uses serialized inputs and outputs to ensure its ability to perform long-term time-series predictions of orbital states. In this embodiment, the input sequence length is... The length of the output sequence is The input sequence covers a complete orbital period to provide sufficient information on orbital evolution; the output sequence is used to evaluate the model's performance in long-term prediction tasks.

[0059] Step S202: Constructing a data sequence for predicting orbits The physical information neural network model.

[0060] The aforementioned method for predicting orbital data sequences The physical information neural network model is constructed as follows:

[0061]

[0062]

[0063] In the formula, This represents the network part of a neural network that represents physical information. Represents the physical residual. and These represent the loss values ​​for the network component and the physical component, respectively. This represents the true value of the corresponding predicted sequence. and This indicates the weight of each loss.

[0064] To ensure the physical information neural network (PIN) possesses long-term orbit prediction capabilities, both input and output are serialized in the PIN architecture design, encompassing both orbital position and velocity components. Considering the Sentinel-3B satellite selected for this implementation scheme, a typical low-Earth orbit (LEO) space target, atmospheric drag and J2 perturbations are incorporated into the physical modeling to improve the accuracy and rationality of physical constraints. Furthermore, weighting factors are introduced into the loss function design to adjust the influence ratio between the physical module and the network module during training, thereby enhancing the model's training stability and predictive performance.

[0065] Step S203: Perform differential calculation on the output sequence using an automatic differential mechanism.

[0066] The implementation of the automatic differentiation mechanism for the orbital data sequence in step S2 is as follows: during the training of the physical information neural network model, the orbital data sequence predicted by the network part is automatically executed. Relative to its corresponding timestamp sequence The differential operation is performed to obtain the orbital dynamics constraint sequence of the physical information neural network used for orbital time series prediction. .

[0067] To ensure that the differentiation process truly participates in the model training process, an automatic differentiation method is used instead of the traditional numerical differencing method. The sequential representation of automatic differentiation not only improves the accuracy and stability of gradient calculation but also effectively guarantees that the model output follows the physical laws of orbital evolution. The automatic differentiation mechanism used in this embodiment is implemented based on the autograd module integrated into the PyTorch framework.

[0068] Step S3: Design and introduce an adaptive weighting loss function to dynamically balance the loss terms of network modules and physical modules during training;

[0069] The adaptive weighting mechanism in step S3 is as follows: the loss of the network part is based on the Gaussian distribution assumption, and the loss of the position and velocity components of the physical part is based on the multivariate Gaussian distribution assumption. By constructing a negative log-likelihood function, the adaptive weighting mechanism of each loss component is realized.

[0070] An adaptive weighting mechanism based on the negative log-likelihood function is introduced, which can adaptively allocate the relative weights of each loss component according to the training data without manual adjustment, thereby improving the robustness and generalization ability of the model and making each loss term more interpretable in the overall optimization. To address the scale difference between the position and velocity components in the physics part, a multivariate Gaussian distribution assumption is further introduced, which not only preserves the correlation between the physical components but also helps to improve the overall modeling accuracy.

[0071] The loss function introduced in step S3, which employs an adaptive weighting mechanism, is as follows:

[0072]

[0073] This loss function is a general loss function used for the physical information neural network model in step S2.

[0074] Step S4: Divide the complete time series into training, validation, and test sets, and train the physical information neural network model;

[0075] Optionally, the proportion of the dataset to be divided in step S4 is 70% for the training set, 15% for the validation set, and 15% for the test set.

[0076] The training set is used to learn and optimize model parameters, the validation set is used to monitor model performance and perform hyperparameter tuning during training, and the test set is used to evaluate the model's generalization ability and final performance after training is completed.

[0077] As shown in Figure 2, the training method for the physical information neural network model in step S4 is as follows: the model network takes the standardized historical sequence data and the predicted time series from the training set as input, and outputs the corresponding predicted sequence results. The obtained prediction results are de-standardized and used to solve the orbital dynamics constraints, and the corresponding loss value and performance evaluation index are calculated on the validation set. After completing the training of the physical information neural network model, the performance of the physical information neural network model is finally evaluated and tested on the test set.

[0078] During model training, standardization helps improve the stability of the training process and accelerates model convergence. In solving orbital dynamics constraints, destandardization is necessary to ensure the accuracy of physical calculations. Furthermore, using destandardized data to calculate relevant performance metrics during model evaluation provides a more intuitive reflection of the model's predictive ability and performance on a real-world physical scale.

[0079] Step S5: Set the data subset sampling rate, construct multi-scale data scenarios, and evaluate the performance of the physical information neural network model under different data scale conditions.

[0080] The method for setting the data subset sampling rate in step S5 is as follows: during the data loading stage before model training, the sampling rate of the data subset is set. This is to control the size of the data used for training, thereby simulating the model's performance under different data sizes.

[0081] A subset sampling rate was introduced to simulate experimental scenarios with different data scales, testing the model's performance on small datasets. Mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE) were used as performance metrics to evaluate the model's performance. MAE reflects the average deviation of the model's prediction results, RMSE measures the overall prediction accuracy, and MAPE measures the relative magnitude of the prediction error as a percentage. Table 1 shows the model's performance metrics at normal scales under different sampling rate settings. The results indicate that the proposed physical information neural network model for orbit prediction exhibits excellent prediction performance on complete datasets and maintains good results on small datasets. This demonstrates that the model, guided by physical constraints, can effectively capture the inherent patterns of orbit data, thereby achieving high-precision prediction of orbit sequences. Figure 3 visualizes the changing trends.

[0082] Table 1. Model prediction performance test results under different data scales (inverse standardization)

[0083]

[0084] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications to the technical solutions described in the foregoing embodiments, or equivalent substitutions for some or all of the technical features, do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for intelligent prediction of the orbit of a space target integrating orbital dynamics constraints, characterized in that, The process includes the following steps: Step S1: Preprocess the raw orbital data of the space target to generate a complete time series dataset with continuity and uniform time intervals; Step S2: Construct a physical information neural network model that represents the input and output in the form of time series data, and use an automatic differentiation mechanism to perform differentiation calculation on the output sequence; Step S3: Design and introduce an adaptive weighting mechanism loss function to dynamically balance the loss terms of the network module and the physical module during training; Step S4: Divide the complete time series into training set, validation set, and test set, and train the physical information neural network model; Step S5: Set the data subset sampling rate, construct multi-scale data scenarios, and evaluate the performance of the physical information neural network model under different data scale conditions.

2. The intelligent prediction method for space target orbits incorporating orbital dynamic constraints according to claim 1, characterized in that, Step S1 includes the following steps S101 to S104: Step S101: Extract and structure key time series data for orbit prediction from the original orbit data file; the time series data includes timestamps, position components, and velocity components; Step S102: Convert the string-format timestamp into a numerical Julian calendar; Step S103: Convert the extracted raw time series data from the ITRS coordinate system to the ECI coordinate system; Step S104: Based on the timestamp, select the time-continuous subsequences as the final time series data.

3. The intelligent prediction method for space target orbits incorporating orbital dynamic constraints according to claim 1, characterized in that, Step S2 includes the following steps S201 to S203: Step S201: Determine the input layer and output layer of the physical information neural network; in step S2, the input layer of the physical information neural network receives the time series of raw orbital data containing the position and velocity characteristics of the space target. and the corresponding predicted timestamp sequence The output layer generates time series of predicted orbit data containing future orbital position and velocity features. Step S202: Construct time series data for predicting orbits. The physical information neural network model; the one used to predict orbital data time series The physical information neural network model is constructed as follows: ； In the formula, This represents the network part of a neural network that represents physical information. Represents the physical residual. and These represent the loss values ​​for the network component and the physical component, respectively. This represents the true value of the corresponding predicted sequence. and The weights of each loss are represented; Step S203: Differentiate the output sequence using an automatic differentiation mechanism; The automatic differentiation mechanism is implemented as follows: During the training of the physical information neural network model, the orbital data time series predicted by the network part are automatically executed. Relative to its corresponding timestamp sequence The differential operation is performed to obtain the orbital dynamics constraint sequence of the physical information neural network used for orbital time series prediction. 。 4. The intelligent prediction method for space target orbits incorporating orbital dynamic constraints according to claim 3, characterized in that, The adaptive weighting mechanism in step S3 is manifested as follows: the loss of the network component is based on the Gaussian distribution assumption, and the loss of the position and velocity components of the physical component is based on the multivariate Gaussian distribution assumption. An adaptive weighting mechanism for each loss component is achieved by constructing a negative log-likelihood function. The loss function introduced in step S3 using the adaptive weighting mechanism is: This loss function is a general loss function used for the physical information neural network model in step S2.

5. The intelligent prediction method for space target orbits incorporating orbital dynamic constraints according to claim 4, characterized in that, In step S4, the ratio of training set, validation set and test set in the complete time series is 70% for training set, 15% for validation set and 15% for test set.

6. The intelligent prediction method for space target orbits incorporating orbital dynamic constraints according to claim 4, characterized in that, The training method of the physical information neural network model in step S4 is as follows: the model network part takes the standardized historical sequence data and the predicted time series in the training set as input, and outputs the corresponding predicted sequence results; the obtained prediction results are de-standardized and used to participate in the solution of orbital dynamic constraints, and the corresponding loss value and performance evaluation index are calculated on the validation set; after the physical information neural network model training is completed, the performance of the physical information neural network model is finally evaluated and tested on the test set.

7. The intelligent prediction method for space target orbits incorporating orbital dynamic constraints according to claim 6, characterized in that, The method for setting the data subset sampling rate in step S5 is as follows: during the data loading stage before model training, the sampling rate of the data subset is set. This is to control the size of the data used for training, thereby simulating the model's performance under different data sizes.

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