Near-earth satellite orbit prediction method based on LSTM and CW-PINN network

Abstract

The invention relates to a near-earth satellite orbit prediction method based on an LSTM and a CW-PINN network, and belongs to the field of satellite orbit prediction. And designing and training a near-earth satellite orbit prediction model based on the LSTM and the CW-PINN network on the basis of real-time observation data of the near-earth satellite to obtain network parameters of the optimal near-earth satellite orbit prediction model based on the LSTM and the CW-PINN network so as to realize near-earth satellite orbit prediction. According to the method, the LSTM is used for realizing the utilization of satellite orbit state sequence information, so that the CW equation is combined with the PINN network to realize the physical constraint fusion, low data dependence and high prediction efficiency of near-earth satellite orbit prediction, and finally, the near-earth satellite orbit prediction in the near-earth orbit is realized in a fast, low-calculation-cost and high-efficiency manner.

Description

Technical Field

[0001] The present invention belongs to the field of near-Earth satellite orbit prediction, and in particular relates to a satellite orbit prediction method based on LSTM and CW-PINN networks. Background Art

[0002] In the past decade, with the continuous advancement of aerospace technology, near-Earth orbit prediction technology has become a hot research field. Especially in the field of aerospace safety and space traffic management, accurate prediction and control of satellite orbits are particularly important. For example, complex scenarios such as satellite formation flying[1-4], avoiding space debris[5-7], and pursuit-escape games[8-12] all require orbit observation and prediction.

[0003] It is worth pointing out that most existing satellite orbit prediction methods rely on traditional physical models and numerical integration techniques. The prediction results of these traditional methods may not be accurate enough to adapt to the rapidly changing space environment and the real-time requirements of satellite operations, thus affecting the planning and execution of satellite missions.

[0004] The difficulty in designing a near-Earth satellite orbit prediction method based on LSTM and CW-PINN networks is:

[0005] First, the orbit observation errors of near-Earth satellites are easy to accumulate, resulting in a monotonically increasing observation error.

[0006] Second: the trajectory evolution of the satellite is affected by unknown parameters. For example, as the satellite pulse control proceeds, the mass and moment of inertia of the satellite will change, resulting in uncertainty in these parameters.

[0007] Third: Using complex neural networks and supervised learning algorithms to train prediction networks requires a large computational cost, so it is necessary to design new prediction methods to achieve accurate predictions with low computational costs.

[0008] References:

[0009] [1]Cheng W, Li J, Gao F, et al.Dynamic Modeling and Control of SatelliteFormation Configuration Maintenance Under the Influence of Space Environment[C] / / 20246th International Conference onElectronic Engineering andInformatics(EEI).IEEE,2024:1816-1821.

[0010] [2]Qian Y,Li J,Zhang H.Formation control of satellites in low Earthorbit by using moving masses[J].Aerospace Science andTechnology,2023,132:108073.

[0011] [3]Ito T.Formation-flying interferometry in geocentric orbits[J].Astronomy&Astrophysics,2024,682:A38.

[0012] [4]Zeng Q,Zhu X,Wang J.Fuel-optimal satellite formationreconfiguration method with best passive safetyparameters[J].Advances inSpaceResearch,2024,74(2):987-1000.

[0013] [5]Ryu K,Bouvier J B,Lalani S,et al.Risk-Sensitive Orbital DebrisCollisionAvoidance using DistributionallyRobustChance Constraints[J].arXivpreprint arXiv:2412.17358,2024.

[0014] [6]Elahian S,Kazemi H.Surveying space debris management methods:Revealing essential requirements for effective solutions[J].Journal of SpaceSafety Engineering,2024.

[0015] [7]Yang Z,Wang H,Liu Y,et al.Satellite trajectory planning for spacedebris collision avoidance[C] / / International Conference on AutonomousUnmanned Systems.Singapore:Springer Nature Singapore,2022:2789-2798.

[0016] [8]Tang X,Ye D,Huang L,et al.Pursuit-evasion game switchingstrategies for spacecraft with incomplete-information[J].Aerospace Scienceand Technology,2021,119:107112.

[0017] [9]Qian H,Chen Z,Wang X,et al.A Swarm-Independent Behaviors-basedOrbit Maneuvering Approach for Target-attacker-defender Games ofSatellites[J].Information Sciences,2024:121790.

[0018]

[10] Zhou J,Cheng J,Wang S,et al.Input-delay satellite optimaltracking control based on differential games[C] / / 2019Chinese ControlConference(CCC).IEEE,2019:1941-1945.

[0019]

[11] Fu S,Gong S,Shi P.Analytical Pursuit-Evasion Game Strategy inArbitrary Keplerian Reference Orbits[J].arXiv preprint arXiv:2411.15912,2024.

[0020]

[12] Zhang ZX, Zhang K, Xie XP, et al. Fixed-time Zero-sum Pursuit-evasion Game Control of Multi-satellite via Adaptive Dynamic Programming[J]. IEEE Transactions on Aerospace and Electronic Systems, 2024. Summary of the invention

[0021] The purpose of the present invention is to solve the problems existing in the background technology and provide a near-Earth satellite orbit prediction method based on LSTM and CW-PINN network. LSTM is used to realize the utilization of satellite orbit state sequence information, so that the CW equation is combined with the PINN network to realize the physical constraint fusion, low data dependence, and prediction efficiency of near-Earth satellite orbit prediction, thereby ultimately realizing fast, low computational cost, and high-efficiency near-Earth satellite orbit prediction in near-Earth orbit.

[0022] To achieve the above-mentioned purpose, the technical solution of the present invention is: a near-Earth satellite orbit prediction method based on LSTM and CW-PINN network, based on real-time observation data of near-Earth satellites, a near-Earth satellite orbit prediction model based on LSTM and CW-PINN network is designed and trained to realize near-Earth satellite orbit prediction.

[0023] In one embodiment of the present invention, the method comprises the following steps:

[0024] Step 1: Observe the near-Earth satellite in real time, sample the real-time position and velocity information of the near-Earth satellite at fixed time intervals and store the results to generate data at each moment;

[0025] Step 2: Based on LSTM, a prediction network is designed for the near-Earth satellite. The network input is the data of k consecutive time steps in the data generated in step 1, and the output is the data of the k+1th time step as well as unknown parameters and the near-Earth satellite control input signal.

[0026] Step 3: Based on the discretized CW equation, a CW-PINN network is constructed to construct the state iteration estimation data of the near-Earth satellite, that is, the data of the k+1th step is calculated according to the data of the kth time step, the unknown parameters and the near-Earth satellite control input signal;

[0027] Step 4, calculate the loss function, including the weighted sum of two parts of errors, one is the quadratic error between the k+1 step data output by the near-Earth satellite design prediction network and the k+1 step data sampled, and the other is the quadratic error between the k+1 step data calculated by the CW equation and the k+1 step data sampled;

[0028] Step 5: Use automatic differentiation technology to back propagate and calculate gradient information, and update the near-Earth satellite design prediction network and CW-PINN network parameters;

[0029] Step 6: Repeat steps 2-5 until the iteration stop condition is met.

[0030] In one embodiment of the present invention, in step 1, based on the observation of the operation status of the near-Earth satellite, the data of the kth time step is set to X based on the fixed time τ sampling. k =(x k ,y k ,z k ,v x,k ,v y,k ,v z,k ), where x k ,y k ,z k ,v x,k ,v y,k ,v z,k They respectively represent the position and velocity of a low-Earth orbit satellite in the x, y, and z directions based on a reference point.

[0031] In one embodiment of the present invention, in step 2, the input is the data of the first k time steps, namely X1, X2, ..., X k , the output is X * k+1 ,θ * k+1 ,u * k+1 , that is, the data of the k+1th step as well as the unknown parameters and satellite control input signals.

[0032] In one embodiment of the present invention, in step 3, a discretized CW equation is constructed. Where X ** k+1 is the predicted state at time step k+1, and the characteristic matrix of the CW equation is and k (τ,θ k ), is the state transition matrix, Ψ k is the control input matrix, θ k is the unknown parameter vector of the system, which affects the state transfer matrix in the CW equation and the control input matrix Ψk ,u k represents the control force applied to the satellite at time k, expressed by Ψ k The matrix acts on the state of the system.

[0033] In one embodiment of the present invention, in step 4, the loss function L=L1+L2 is calculated, where L1=||X * k+1 -X k+1 || 2 , L2=||X ** k+1 -X k+1 || 2 .

[0034] In one embodiment of the present invention, in step 5, the automatic differentiation technology is used to back propagate and calculate the gradient information, wherein the gradient information of the near-Earth satellite design prediction network is calculated by referring to the pytorch library, and the gradient information of the CW-PINN network is obtained by reverse calculation based on the discretized CW equation.

[0035] In one embodiment of the present invention, in step 6, steps 2-5 are iterated repeatedly until an iteration stop condition is met, including the number of iterations reaching a set upper limit value and the prediction error reaching a set lower limit value.

[0036] The present invention also provides an electronic device, comprising a memory, a processor, and computer program instructions stored in the memory and capable of being executed by the processor. When the processor executes the computer program instructions, the method steps described above can be implemented.

[0037] The present invention also provides a computer-readable storage medium, on which computer program instructions that can be executed by a processor are stored. When the processor executes the computer program instructions, the method steps described above can be implemented.

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] 1. Through the coupling of LSTM network and CW equation, the orbit prediction network of near-Earth satellite can process time series information without causing error accumulation and monotonically increasing;

[0040] 2. Based on the actual operation of low-Earth orbit satellites, circular orbit assumptions and linearization processing are made, and the CW equation is introduced to describe the law of orbit change. The PINN network based on the CW equation is used to predict the orbit of low-Earth satellites, which has theoretical reliability and explainability;

[0041] 3. The uncertain parameters and control inputs are output as prediction signals, which makes the LSTM and CW-PINN networks more robust and suitable for orbit prediction during the orbit change process of controlled near-Earth satellites. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 The figure is a flow chart of the method of the present invention.

[0043] Figure 2 The present invention is a method flow chart of an example. DETAILED DESCRIPTION

[0044] The technical solution of the present invention is described in detail below in conjunction with the accompanying drawings.

[0045] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0046] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0047] The present invention provides a near-Earth satellite orbit prediction method based on LSTM and CW-PINN network. Based on the real-time observation data of near-Earth satellites, a near-Earth satellite orbit prediction model based on LSTM and CW-PINN network is designed and trained to realize near-Earth satellite orbit prediction.

[0048] The following is the specific implementation process of the present invention.

[0049] like Figure 1 , 2 As shown, this embodiment provides a near-Earth satellite orbit prediction method based on LSTM and CW-PINN network, comprising the following steps:

[0050] Step 1: Observe the near-Earth satellite in real time, sample the real-time position and velocity information of the near-Earth satellite at fixed time intervals and store the results to generate data at each moment;

[0051] Step 2: Based on LSTM, a prediction network is designed for near-Earth satellites; the network input is the data of k consecutive time steps in the data generated in step 1, and the output is the data of the k+1th time step, as well as unknown parameters and satellite control input signals;

[0052] Step 3: Based on the discretized CW equation, a CW-PINN network is constructed to construct the satellite's state iteration estimation data, that is, the data of the k+1th step is calculated based on the data of the kth time step, the unknown parameters and the satellite control input signal;

[0053] Step 4: Calculate the loss function, which includes the weighted sum of two errors: one is the quadratic error between the k+1 step data output by the LSTM network and the k+1 step data sampled; the other is the quadratic error between the k+1 step data calculated by the CW equation and the k+1 step data sampled;

[0054] Step 5: Use automatic differentiation technology to back propagate and calculate gradient information, and update the LSTM network parameters;

[0055] Step 6: Repeat steps 2-5 until the iteration stop condition is met.

[0056] The specific steps for the above operation are as follows:

[0057] In step 1 above, an observation system is set up to observe the state of the near-Earth satellite in real time, a fixed time interval τ is determined for sampling, and the obtained data is sorted according to the timestamp. For each time point t, a state data point X containing the speed and position is generated. t =(x t ,y t ,z t ,v x,t ,v y,t ,v z,t ), where x t ,y t ,z t is the coordinate of the satellite in three-dimensional space, v x,t ,v y,t ,v z,t is the component of the satellite in the x, y, and z directions. For example, the data of the kth time step is set to X k =(x k ,y k ,z k ,v x,k ,v y,k ,v z,k ).

[0058] In step 2 above, considering that the LSTM network consists of multiple LSTM units, the network structure can be expressed as LSTMX1,X2,…,X K) =h k , where h k is the hidden state after k time steps. The input data consists of k consecutive time steps: X i =(xi ,y i ,z i ,v x,i ,v y,i ,v z,i ), where i = 1, 2, ..., k. Design the connection layer to connect the hidden state h of the LSTM network after k time steps k Mapped to the predicted output, the k+1th step data can be expressed as X * k+1 ,θ * k+1 ,u * k+1 , where X * k+1 ,θ * k+1 ,u * k+1 They are the position velocity, unknown parameters and control input signal of the k+1th step respectively.

[0059] In step 3 above, the discretized CW equation is constructed Where X ** k+1 is the predicted state at time step k+1, X k is the actual state at the kth time step, is the state transition matrix, Ψ k is the control input matrix.

[0060] In the above step 4, the LSTM network output error L1=||X can be defined by steps 2 and 3 * k+1 -X k+1 || 2 , L1 is the state vector X output by the LSTM network at the k+1 step * k+1 The state vector X obtained by actual sampling k+1 The quadratic error between them. L1 expansion gives:

[0061]

[0062] Where X * (k+1),i and X (k+1),i Represents X * k+1 and X k+1 Next, define the discretized CW equation output error L2 = ||X ** k+1 -X k+1 || 2, L2 is the state vector X output by the discretized CW equation at the k+1 step ** k+1 The state vector X obtained by actual sampling k+1 The quadratic error between them. Finally, the overall loss function L is obtained by weighting the two errors obtained above. In order to give appropriate weights to the two errors, regularization parameters α and β are introduced to satisfy α+β=1. The overall loss function is obtained:

[0063] L=αL1+βL2=α||X * k+1 -X k+1 || 2 +β||X ** k+1 -X k+1 || 2

[0064] In step 5 above, the automatic differentiation technique is used to update the parameters of the LSTM network through the back-propagation algorithm using the PyTorch library. Assume that the output hidden state h of the loss function L1 for the last time step k has been obtained. k Gradient First, calculate the loss for the cell state c t The gradient of , for any time step t∈[0,k] is:

[0065]

[0066] in, represents the loss function for the hidden state h at time step t k The gradient of t represents the activation value of the output gate at time step t. t+1 represents the activation value of the forget gate at time step t+1, which determines how much cell state information from the previous time step should be retained to the current time step.

[0067] Secondly, calculate the gradient of loss for each gate,

[0068] Forget Gate:

[0069]

[0070] in, Represents the loss function for the forget gate f at time step t t and cell state c t The gradient of f′ t Represents the derivative of the forget gate activation function.

[0071] Input Gate:

[0072]

[0073] in, represents the gradient of the loss function with respect to the input gate at time step t, Represents the value of the candidate cell state at time step t. i′ t Represents the derivative of the input gate activation function.

[0074] Candidate cell states:

[0075]

[0076] in, Represents the gradient of the loss function with respect to the candidate cell state at time step t.

[0077] Output Gate:

[0078]

[0079] in, represents the gradient of the loss function with respect to the output gate at time step t, o′ t Represents the derivative of the output gate activation function. This allows parameter updates.

[0080]

[0081] in, They represent the gradient of the loss function with respect to the weight matrix and bias, respectively. The subscript * represents a gate or state (such as input gate, forget gate, output gate or cell state). t Represents the input data at the current time step t.

[0082] For calculation The state transition matrix and Ψ k Control the gradient of the input matrix, applying the chain rule:

[0083]

[0084] From the above, we can get that for any time step k, the total gradient can be expressed as:

[0085]

[0086] Among them, L2 represents the discretized CW equation output error, T represents the maximum time index in the entire time series, n represents the ergodic variable in the summation range, and represents all subsequent time steps from k+1 to T-1.

[0087] In step 6 above, repeat steps 2-5 above and set a maximum number of iterations T maxWhen the number of iterations reaches this upper limit, the model stops training. During this training period, the model also stops training if the following two conditions are met:

[0088] 1. When the prediction error L reaches or is lower than the preset threshold ∈, stop training.

[0089] L≤∈

[0090] 2. When the error change rate in five consecutive iterations is less than the set threshold δ, stop training.

[0091] |L (i) -L (i-1) |<δ

[0092] Among them, L (i) represents the prediction error at the i-th iteration, L (i-1) Represents the prediction error at the i-1th iteration.

[0093] Assume that the maximum number of iterations is T max =100, prediction error threshold ∈ =0.01, error change rate threshold δ =0.001, then the training result is one of the following three cases:

[0094] 1. Reach the maximum number of iterations:

[0095] If the other stopping conditions are still not met at the 100th iteration, the training will stop after the 100th iteration.

[0096] 2. The prediction error reaches the threshold

[0097] If at the 80th iteration, the prediction error L has dropped to 0.01 or lower, the training will stop after the 80th iteration.

[0098] 3. The error change rate is less than the threshold.

[0099] If the error rate of change is less than 0.001 from the 70th to the 74th iteration, training stops after the 74th iteration.

[0100] At this point, all steps are completed. The present invention studies how to design a near-Earth satellite orbit prediction method based on LSTM and CW-PINN networks, which can achieve near-Earth satellite orbit prediction with low computational cost. For the near-Earth satellite orbit prediction problem, the mainstream of existing algorithms is based on physical models and numerical integration methods, that is, the satellite orbit is predicted based on known initial conditions and physical laws. This method is improved on the basis of existing theories. By combining deep learning with physical information neural networks, the orbit prediction algorithm has a strong generalization ability, including generalization from the orbit prediction of a single satellite to the orbit prediction of multiple satellites, and from simple orbital dynamics to complex controlled orbital dynamics. This feature can play an important role in many practical application scenarios, such as orbit prediction problems based on space debris monitoring, satellite formation flying, satellite collision warning, etc.

[0101] The present invention also provides an electronic device, comprising a memory, a processor, and computer program instructions stored in the memory and capable of being executed by the processor. When the processor executes the computer program instructions, the method steps described above can be implemented.

[0102] The present invention also provides a computer-readable storage medium, on which computer program instructions that can be executed by a processor are stored. When the processor executes the computer program instructions, the method steps described above can be implemented.

[0103] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0104] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0105] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0106] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0107] The above is only a preferred embodiment of the present invention, and does not limit the present invention in other forms. Any technician familiar with the profession may use the above disclosed technical content to change or modify it into an equivalent embodiment with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiment according to the technical essence of the present invention without departing from the technical solution of the present invention still belongs to the protection scope of the technical solution of the present invention.

Claims

1. A near-Earth satellite orbit prediction method based on LSTM and CW-PINN network, characterized in that: Based on the real-time observation data of low-Earth satellites, a low-Earth satellite orbit prediction model based on LSTM and CW-PINN network is designed and trained to realize low-Earth satellite orbit prediction.

2. According to claim 1, a near-Earth satellite orbit prediction method based on LSTM and CW-PINN network is characterized in that: The method comprises the following steps: Step 1: Observe the near-Earth satellite in real time, sample the real-time position and velocity information of the near-Earth satellite at fixed time intervals and store the results to generate data at each moment; Step 2: Based on LSTM, a prediction network is designed for the near-Earth satellite. The network input is the data of k consecutive time steps in the data generated in step 1, and the output is the data of the k+1th time step as well as unknown parameters and the near-Earth satellite control input signal. Step 3: Based on the discretized CW equation, a CW-PINN network is constructed to construct the state iteration estimation data of the near-Earth satellite, that is, the data of the k+1th step is calculated according to the data of the kth time step, the unknown parameters and the near-Earth satellite control input signal; Step 4, calculate the loss function, including the weighted sum of two parts of errors, one is the quadratic error between the k+1 step data output by the near-Earth satellite design prediction network and the k+1 step data sampled, and the other is the quadratic error between the k+1 step data calculated by the CW equation and the k+1 step data sampled; Step 5: Use automatic differentiation technology to back propagate and calculate gradient information, and update the near-Earth satellite design prediction network and CW-PINN network parameters; Step 6: Repeat steps 2-5 until the iteration stop condition is met.

3. The method for predicting near-Earth satellite orbits based on LSTM and CW-PINN network according to claim 2, characterized in that: In step 1, according to the observation of the operation status of the near-Earth satellite, based on the fixed time τ sampling, the data of the kth time step is set to X k =(x k ,y k ,z k ,v x,k ,v y,k ,v z,k ), where x k ,y k ,z k ,v x,k ,v y,k ,v z,k They respectively represent the position and velocity of a low-Earth orbit satellite in the x, y, and z directions based on a reference point.

4. The method for predicting near-Earth satellite orbits based on LSTM and CW-PINN network according to claim 3, characterized in that: In step 2, the input is the data of the first k time steps, namely X1, X2, …, X k , the output is X * k+1 ,θ * k+1 ,u * k+1 , that is, the data of the k+1th step as well as the unknown parameters and satellite control input signals.

5. The method for predicting near-Earth satellite orbits based on LSTM and CW-PINN network according to claim 4, characterized in that: In step 3, the discretized CW equation is constructed Where X ** k+1 is the predicted state at time step k+1, and the characteristic matrix of the CW equation is and k (τ,θ k ), is the state transition matrix, Ψ k is the control input matrix, θ k is the unknown parameter vector of the system, which affects the state transfer matrix in the CW equation and the control input matrix Ψ k ,u k represents the control force applied to the satellite at time k, expressed by Ψ k The matrix acts on the state of the system.

6. The method for predicting near-Earth satellite orbits based on LSTM and CW-PINN network according to claim 5, characterized in that: In step 4, the loss function L = L1 + L2 is calculated, where L1 = || X * k+1 -X k+1 || 2 , L2=||X ** k+1 -X k+1 || 2 .

7. The method for predicting near-Earth satellite orbits based on LSTM and CW-PINN network according to claim 2, characterized in that: In step 5, the automatic differentiation technique is used to back propagate and calculate the gradient information, where the gradient information of the near-Earth satellite design prediction network is calculated by referring to the pytorch library, and the gradient information of the CW-PINN network is obtained by reverse calculation based on the discretized CW equation.

8. The method for predicting near-Earth satellite orbits based on LSTM and CW-PINN network according to claim 2, characterized in that: In step 6, steps 2-5 are iterated repeatedly until the iteration stop condition is met, including the number of iterations reaching the set upper limit value and the prediction error reaching the set lower limit value.

9. An electronic device, characterized in that: The method comprises a memory, a processor and computer program instructions stored in the memory and executable by the processor. When the processor executes the computer program instructions, the method steps as claimed in any one of claims 1 to 8 can be implemented.

10. A computer-readable storage medium storing computer program instructions that can be executed by a processor, wherein when the processor executes the computer program instructions, the method steps according to any one of claims 1 to 8 can be implemented.

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