Method for generating a ring current contribution prediction model and method for calculating a dst index

Abstract

The embodiment of the present disclosure discloses a method for generating a ring current contribution prediction model and a method for calculating a Dst index, relates to the technical field of geomagnetism, and specifically provides an embodiment of the method for generating a ring current contribution prediction model, which comprises the following steps: a data preprocessing step; a feature construction step; and a model training step, which comprises the following steps: introducing a plurality of input features into a neural network based on deep learning to obtain an estimated value, using a mean square error as a loss function, calculating the error between the estimated value and the corresponding output target, and adjusting the neural network based on the error to obtain a ring current contribution prediction model, wherein the plurality of input features comprise one or more of the following: a By input feature, a Bz input feature, a solar wind dynamic pressure input feature, and an L input feature; and the neural network based on deep learning comprises one or more network layers, such as a fully connected layer. Thus, an accurate way of calculating a Dst index is provided.

Description

Technical Field

[0001] This disclosure relates to the field of geomagnetic technology, and in particular to a method for generating a prediction model of loop current contribution and a method for calculating the Dst exponent. Background Technology

[0002] Circulating currents are a type of electrical system in the Earth's magnetosphere, primarily generated by the movement of high-energy charged particles within the magnetosphere. Their intensity and distribution directly affect disturbances in the Earth's magnetic field, leading to geomagnetic storms. Strong geomagnetic storms can severely impact various technological systems on Earth, such as satellite communications, navigation systems, and power grids.

[0003] The Disturbance Storm Time Index (Dst index), also known as the storm time index, is one of the most widely used geomagnetic activity indices in space physics. It is an important parameter for monitoring geomagnetic storm activity and changes in the equatorial ring current. The Dst index describes geomagnetic storm processes by measuring changes in the horizontal component of the Earth's magnetic field and reflects changes in the westward-flowing equatorial ring current, making it an important indicator for monitoring and forecasting space weather.

[0004] Studying the Dst index is crucial for understanding the formation mechanisms of geomagnetic storms, predicting geomagnetic disturbances, and mitigating their impacts on human activities. Furthermore, the Dst index provides insights into the interaction between the solar wind and the magnetosphere, helping researchers understand how solar wind pressure, interplanetary magnetic field (IMF) direction, and other solar phenomena influence geomagnetic activity. Therefore, accurate and real-time calculation and prediction of the Dst index are of paramount importance. Summary of the Invention

[0005] This disclosure is provided to briefly introduce the concepts, which will be described in detail in the subsequent Detailed Description section. This disclosure is not intended to identify key or essential features of the claimed technical solution, nor is it intended to limit the scope of the claimed technical solution.

[0006] In a first aspect, embodiments of this disclosure provide a method for generating a ring current contribution prediction model. The method includes: a data preprocessing step, comprising: storing the By, Bz, solar wind dynamic pressure, and L values ​​of the OMNI satellite at each time point, corresponding to the training ring current contribution J at each time point; wherein By represents the y-component of the solar wind magnetic field in the GSM coordinate system; Bz represents the z-component of the solar wind magnetic field in the GSM coordinate system; and L represents the magnetic shell parameter; a feature construction step, comprising: obtaining By input features, Bz input features, and solar wind dynamic pressure input features based on the stored By, Bz, and solar wind dynamic pressure, and using L as an input feature; and processing the training ring current contribution J... The preprocessing steps are as follows: Preprocessing is performed to obtain the output target; model training steps include: inputting multiple input features into a deep learning-based neural network to obtain a predicted value; using mean squared error as the loss function to calculate the error between the predicted value and the corresponding output target; adjusting the neural network based on the error to obtain a ring current contribution prediction model; wherein the multiple input features include one or more of the following: By input features, Bz input features, solar wind dynamic pressure input features, and L input features; wherein the deep learning-based neural network includes fully connected layers, which are used to: learn global features of the data and, through layer-by-layer refinement, output results for a regression task; and obtain the predicted value based on the regression task and the results.

[0007] In some embodiments, the fully connected layer includes a first fully connected layer, a second fully connected layer, a third fully connected layer, and an output layer connected in sequence; wherein the first fully connected layer is a fully connected layer with 64 neurons; the second fully connected layer is a fully connected layer with 32 neurons for further processing of features; the third fully connected layer is a fully connected layer with 16 neurons for further reducing the feature dimension to prepare for output; and the output layer is used to generate a predicted value.

[0008] In some embodiments, the method further includes: dynamically adjusting the learning rate of each parameter in the neural network using an RMSprop optimizer.

[0009] In some embodiments, the loop current contribution in the data preprocessing step is the training loop current contribution J, which is obtained based on a calculation step; wherein, the calculation step includes: calculating the particle number density, the average particle drift velocity, and the magnetic latitude of the magnetic field line reflection point; integrating to calculate the loop current; and based on the loop... , , , The loop current component at each L is obtained, and the components are summed to obtain the loop current contribution I at each L. L The loop current at each L contributes I L J is the contribution of the training loop current.

[0010] In some embodiments, the calculation of particle number density, average particle drift velocity, and magnetic latitude of the magnetic field line reflection point includes: calculating particle number density based on formulas (1) and (2), calculating average particle drift velocity based on formula (3), and calculating magnetic latitude of the magnetic field line reflection point based on formula (4); wherein,

[0011] Formula (1)

[0012] This represents the number density at each energy level and at each pitch angle. This represents the differential electron flux, where δ is the pitch angle. Let E be the velocity of the electron at energy E. Considering relativistic effects:

[0013] Formula (2)

[0014] For the current energy level, The rest mass of the electron is 9.10938356 × 10⁻⁶. -31 kg, where c is the speed of light;

[0015] Formula (3)

[0016] L represents the magnetic shell parameter, which defines the equatorial radius of the magnetic field lines in the equatorial plane; δ is the pitch angle; W is the energy of each particle; and q is the particle charge. , The radius of the Earth is 6,371,000 m.

[0017] Formula (4)

[0018] α is the equatorial elevation angle. It is the magnetic latitude.

[0019] In some embodiments, the integral calculation of the loop current includes: integrating over the magnetic latitude to obtain the current density on the magnetic field line, and summing the contributions of the solid angle element and the energy bandwidth element and multiplying by the L*Re interval to obtain the loop current contribution at each time moment.

[0020] In some embodiments, based on the ring current contribution I L Calculate the magnetic field disturbance at point L. The contribution of the loop current includes: the magnetic field disturbance at each L calculated according to formula (5). ;

[0021] Formula (5)

[0022] Permeability of free space;

[0023] L represents the magnetic shell parameter, specifically the number of times the magnetic field lines in the Earth's magnetic field cross the Earth's radius at the magnetic equator.

[0024] R E This represents the Earth's radius.

[0025] Secondly, embodiments of this application provide a method for calculating the Dst exponent. Based on the ring current contribution prediction model generated in the first aspect, the ring current contribution is integrated along L and then substituted into Formula 5 to approximate the Dst exponent. OMNI solar wind data is used as input, and the Dst exponent value is output.

[0026] In some embodiments, the method further includes: using a scatter plot to characterize the relationship between solar wind data and the output Dst index value, wherein the display format of the Dst index value is related to the magnitude of the Dst index value.

[0027] Thirdly, embodiments of this application provide a method for calculating the ring current contribution at each L, the method comprising: calculating the particle number density, the average particle drift velocity, and the magnetic latitude of the magnetic field line reflection point; integrating to calculate the ring current; and calculating the ring current based on the ring... , , , The loop current component at each L is obtained, and the components are summed to obtain the loop current contribution I at each L. L . Attached Figure Description

[0028] The above and other features, advantages, and aspects of the embodiments of this disclosure will become more apparent from the accompanying drawings and the following detailed description. Throughout the drawings, the same or similar reference numerals denote the same or similar elements. It should be understood that the drawings are schematic, and the originals and elements are not necessarily drawn to scale.

[0029] Figure 1 This is a schematic diagram of an embodiment of the method for generating a prediction model of ring current contribution according to the present disclosure;

[0030] Figure 2 This is a schematic diagram of a scenario based on the method for generating a prediction model of ring current contribution according to this disclosure;

[0031] Figure 3 This is a schematic diagram of an embodiment of the method for calculating the Dst exponent according to the present disclosure;

[0032] Figure 4 This is a schematic diagram of an embodiment of the method for calculating the loop current contribution at each L according to the present disclosure;

[0033] Figure 5 This is an exemplary scenario diagram of an embodiment of the method for calculating the contribution of loop current according to this disclosure;

[0034] Figure 6 This is a schematic diagram of the basic structure of an electronic device according to an embodiment of the present disclosure. Detailed Implementation

[0035] Embodiments of this disclosure will now be described in more detail with reference to the accompanying drawings. While some embodiments of this disclosure are shown in the drawings, it should be understood that this disclosure can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of this disclosure. It should be understood that the accompanying drawings and embodiments of this disclosure are for illustrative purposes only and are not intended to limit the scope of protection of this disclosure.

[0036] It should be understood that the steps described in the method embodiments of this disclosure may be performed in different orders and / or in parallel. Furthermore, the method embodiments may include additional steps and / or omit the steps shown. The scope of this disclosure is not limited in this respect.

[0037] The term "comprising" and its variations as used herein are open-ended inclusions, meaning "including but not limited to". The term "based on" means "at least partially based on". The term "one embodiment" means "at least one embodiment"; the term "another embodiment" means "at least one additional embodiment"; the term "some embodiments" means "at least some embodiments". Definitions of other terms will be given in the description below.

[0038] It should be noted that the concepts of "first" and "second" mentioned in this disclosure are used only to distinguish different devices, modules or units, and are not used to limit the order of functions performed by these devices, modules or units or their interdependencies.

[0039] It should be noted that the terms "a" and "a plurality of" used in this disclosure are illustrative rather than restrictive, and those skilled in the art should understand that, unless otherwise expressly indicated in the context, they should be understood as "one or more".

[0040] The names of messages or information exchanged between multiple devices in the embodiments of this disclosure are for illustrative purposes only and are not intended to limit the scope of such messages or information.

[0041] Here, we first present some concepts that may be involved in this disclosure.

[0042] Electron mass: Used to calculate particle velocity and related dynamic properties.

[0043] Proton mass: used to calculate particle velocity and related dynamic properties.

[0044] Electron charge: The fundamental charge carried by an electron, used to calculate electromagnetic properties such as current density.

[0045] Proton charge: The fundamental charge carried by a proton, used to calculate electromagnetic properties such as current density.

[0046] Area conversion factor: used to convert electron flux from centimeter square units to meter square units to ensure unit consistency.

[0047] Energy conversion factor: used to convert energy from electron volts (keV) to international standard units (J).

[0048] Earth's surface magnetic field strength: used to simulate particle behavior in a magnetic field.

[0049] Earth's radius: a fundamental reference scale for calculating the effects of the Earth's magnetic field and orbital motion.

[0050] FEDU: Represents the measured electron flux. This data is crucial, used to calculate the electron number density at each energy and pitch angle in space, and thus to deduce the loop current. In some related technologies, a large number of invalid values ​​exist in the FEDU.

[0051] FPDU: Represents the measured Proton flux is a key data point, used to calculate the proton number density at each energy level and pitch angle in space, and thus to deduce the loop current.

[0052] FHeDU: Indicates the measured value. Proton flux is a key data point, used to calculate the proton number density at each energy level and pitch angle in space, and thus to deduce the loop current.

[0053] FODU: Indicates the measured Proton flux is a key data point, used to calculate the proton number density at each energy level and pitch angle in space, and thus to deduce the loop current.

[0054] L: L-shell value, representing a magnetic shell parameter, specifically indicating how many times the magnetic field lines in the Earth's magnetic field cross the Earth's radius at the magnetic equator. The L-value is an important parameter for studying the Earth's magnetic field and loop currents, describing a specific location within the Earth's magnetic field.

[0055] MLT: MLT represents a position in the magnetic field: In the Earth's magnetosphere, MLT represents the "time" of a position relative to the Earth's magnetic axis, similar to local time on Earth. An MLT value of 0 corresponds to "magnetic noon," which is the area of ​​the magnetosphere directly illuminated by the sun; an MLT value of 12 corresponds to "magnetic midnight," which is the shaded side of the Earth's magnetosphere.

[0056] Epoch: Timestamp data, which usually indicates the specific point in time when the data was collected.

[0057] FEDU_Energy: This represents the energy of the electron flux measured at a specific energy level. The unit is usually keV.

[0058] FEDU_Alpha_Eq: This is the pitch angle in the magnetic equatorial plane, commonly used to study the trajectory of electrons in a magnetic field. The pitch angle is the angle between the direction of particle motion and the direction of the magnetic field. It is crucial for analyzing the particle distribution along magnetic field lines.

[0059] FEDU_Energy_DELTA_plus and FEDU_Energy_DELTA_minus: These data represent the uncertainty or error range of the energy level, and are usually used to define the upper and lower limits of the electron energy value to help determine the bandwidth.

[0060] One or more embodiments of this disclosure provide a method for calculating ring current. By utilizing the ring current contribution and a deep neural network architecture, a ring current contribution prediction model is established. Then, by integrating the ring current contribution with respect to L, the global average magnetic field disturbance is calculated using Formula 5, providing a scientific and accurate approximate representation for the Dst index. This establishes a Dst index calculation model, thereby realizing the calculation and prediction of the Dst index.

[0061] One or more embodiments of this disclosure propose a ring current calculation method based on radiation belt dynamics. A bilinear plus nearest-neighbor hybrid interpolation method is employed to fill in invalid values ​​in FEDU, FPDU, FHeDU, and FODU data, improving data integrity and stability. By calculating particle number density, average drift velocity, and magnetic latitude of magnetic field line reflection points in detail, the electron motion characteristics at different energy levels and pitch angles can be accurately described. In particular, the consideration of relativistic effects makes the ring current calculation closer to actual physical processes, effectively helping to solve the problem of insufficient precision in physical process simulation. Accurate calculation of number density and velocity at each energy level and pitch angle, combined with multi-scale integration methods, solves the problem of limited spatial and temporal resolution in ring current calculation. The method for calculating the global average magnetic field disturbance Bd provided in this embodiment provides a scientific and accurate approximate representation of the Dst exponent, solving the problem of the lack of an accurate description of the global average magnetic field disturbance.

[0062] One or more embodiments of this disclosure propose establishing a prediction model for ring current contribution based on deep learning. By standardizing the input features, it ensures that all features have the same dimensions during model training, thus addressing the problems of insufficient data preprocessing and standardization. Data is converted into PyTorch tensors, and an efficient DataLoader object is created to achieve fast data loading and processing. The RMSprop optimizer is used to dynamically adjust the learning rate, improving the model's convergence speed and training efficiency, thus solving the problems of low data loading and training efficiency. This invention not only evaluates model performance using metrics such as mean squared error (MSE), but also uses visualization methods such as scatter plots to show the relationship between the prediction results and actual observations, intuitively verifying the model's prediction effect and addressing the problems of insufficient evaluation and visualization methods.

[0063] Please refer to Figure 1 This illustrates a schematic diagram of an embodiment of a method for generating a ring current contribution prediction model according to the present disclosure. Figure 1 The method shown for generating a prediction model of loop current contribution includes:

[0064] Step 101, data preprocessing step, includes: storing the By, Bz, solar wind dynamic pressure, L value of the OMNI satellite and the training loop current contribution J for each L value.

[0065] Where By is the y-component of the solar wind magnetic field in the GSM coordinate system. Bz is the z-component of the solar wind magnetic field in the GSM coordinate system.

[0066] Step 102, the feature construction step, includes: obtaining By input features, Bz input features, and solar wind dynamic pressure input features based on the stored By, Bz, and solar wind dynamic pressure, and using L as the input feature; preprocessing the training loop current contribution J as the output target.

[0067] As an example, By, Bz, and solar wind dynamic pressure can be stored at a one-minute resolution based on data measured by the OMNI satellite, and then logarithmically or normally processed to obtain the input features; the training loop current contribution J at every third preset interval is preprocessed and used as the output target.

[0068] Step 103, the model training step, includes: importing multiple input features into a deep learning-based neural network to obtain a prediction value, using mean squared error as a loss function, calculating the error between the prediction value and the corresponding output target, and adjusting the neural network based on the error to obtain a prediction model for the ring current contribution.

[0069] The AE index, or polar magnetic substorm intensity index, is used to describe the intensity of polar geomagnetic substorms. It is calculated by measuring the temporal variation of the northward component of the magnetic field observed by stations uniformly distributed along the auroral belt, with units of nanotesla (nT). The AE index represents the total disturbance intensity, i.e., the distance between the upper and lower envelopes. The upper envelope gives the AU index, representing the maximum magnetic field disturbance caused by eastward current flow; the lower envelope gives the AL index, representing the maximum magnetic field disturbance caused by westward current flow flow.

[0070] The KP index is an index that measures global geomagnetic activity. It is calculated based on the K-index data from 13 geomagnetic stations in the Global Geomagnetic Network, with a value every 3 hours, ranging from 0 to 9, and divided into 28 levels. A higher KP index indicates a stronger geomagnetic disturbance. In practical applications, the KP index is often used to classify the level of geomagnetic activity; for example, KP=5 or 6 is considered a small to medium-sized geomagnetic storm, while KP=7, 8, or 9 is considered a large geomagnetic storm.

[0071] The SYM_H index, also known as the geomagnetic storm loop current index, is obtained by averaging the hourly changes in geomagnetic horizontal intensity from four geomagnetic stations selected at evenly spaced longitudes near the Earth's equator. Its unit is nanotesla (nT), and its value can range from tens of nanotesla to thousands of negative nanotesla, with a gradually decreasing value indicating a gradually increasing magnitude of magnetic disturbance. The SYM_H index reflects the changes in the loop current in the Earth's magnetosphere caused by the energy input from the solar wind and is an important parameter describing the intensity of geomagnetic storms.

[0072] MLT: MLT represents a position in the magnetic field: In the Earth's magnetosphere, MLT represents the "time" of a position relative to the Earth's magnetic axis, similar to local time on Earth. An MLT value of 0 corresponds to "magnetic noon," which is the area of ​​the magnetosphere directly illuminated by the sun; an MLT value of 12 corresponds to "magnetic midnight," which is the shaded side of the Earth's magnetosphere.

[0073] The loop current contribution, which serves as the output target, can be the historical loop current contribution or can be calculated or measured using various other methods.

[0074] In some embodiments, the deep learning-based neural network includes one or more of the following network layers: a fully connected layer, used to learn global features of the data and, through layer-by-layer refinement, outputs a result for a regression task, and obtains the estimated value based on the regression task and the result; and a regularization layer, set in the fully connected layer, used to randomly shut down some neurons during training.

[0075] In some embodiments, the method further includes: dynamically adjusting the learning rate of each parameter in the neural network using an RMSprop optimizer.

[0076] In some scenarios, deep learning-based prediction models for ring current contributions are mainly divided into four stages (e.g.) Figure 2 (as shown)

[0077] Phase 1: Data Preprocessing

[0078] Data preprocessing may include geomagnetic activity index matching, data reading and merging, and time series feature reading. The By, Bz, solar wind dynamic pressure, L value, and loop current contribution for each time point are matched using Epoch-based time indexing and saved to a single CSV file. This CSV file is read, ensuring the file path is correct, and the data is stored in a DataFrame within the `data` object.

[0079] Phase 2: Feature Construction and Standardization

[0080] Based on data measured by the OMNI satellite, By, Bz, and solar wind dynamic pressure are stored as input features at a resolution of one minute; solar wind dynamic pressure and L are used as input features, and the ring current contribution is used as output feature J, and the output feature J is predicted.

[0081] Select multiple input features (including By, Bz, solar wind dynamic pressure, and L value) and output feature J, and perform logarithmic or standardized processing on them to ensure that the features have the same dimensions during model training.

[0082] Phase 3: Model Training Phase

[0083] The model training phase can include data segmentation, model building, and actual model training.

[0084] 1. Data Splitting: The dataset is proportionally split into a training set (70%), a validation set (15%), and a test set (15%) for subsequent model training, validation, and testing. Input features and output targets are converted into PyTorch tensors, and DataLoader objects are created for efficient data loading during training.

[0085] 2. Model Construction: This model is a complex deep neural network architecture designed for regression tasks. It leverages the advantages of Multilayer Perceptrons (MLPs) to enhance feature extraction capabilities and improves generalization ability through regularization techniques. The detailed structure and advantages of the model are as follows:

[0086] (1) Fully Connected Layers

[0087] The model includes three hidden layers (fc1, fc2, fc3) and one output layer (fc4), with 64, 32, and 16 neurons respectively, using different activation functions:

[0088] fc1: LeakyReLU activation function, suitable for mini-batch data, alleviates gradient vanishing.

[0089] fc2: ELU activation function, which helps improve the model's performance in the negative region.

[0090] fc3: Tanh, mainly used for compression range, keeping the value in (−1,1)(-1, 1)(−1,1).

[0091] fc4: The last fully connected layer directly outputs the predicted value.

[0092] The introduction of these fully connected layers allows the model to learn the global features of the data and, through layer-by-layer refinement, ultimately output results suitable for regression tasks.

[0093] (2) Dropout Regularization

[0094] The model introduces a Dropout regularization layer in the fully connected layer:

[0095] Dropout: Randomly "turns off" some neurons during training (i.e., doesn't update their weights), which helps reduce overfitting. In this way, the model doesn't become overly reliant on the outputs of certain neurons, thus improving its robustness.

[0096] 3. Specific Model Training: The model is trained on the training set, using mean squared error (MSE) as the primary loss function to evaluate the error between the predicted and true values. To effectively handle unstable gradient problems and improve model performance across different data types, the RMSprop optimizer is used for parameter updates. RMSprop maintains an adaptive learning rate for each parameter, enabling more stable convergence during training and effectively addressing gradient explosion or vanishing issues in deep neural networks. Through this optimization strategy, the model exhibits stronger robustness and faster convergence speed on complex time-series data.

[0097] Phase 4: Model Evaluation and Testing

[0098] The model performance was evaluated on the validation and test sets to calculate the average loss and determine the model's generalization ability. A scatter plot was used to visualize the relationship between the predicted ring current contribution and the L value. Colors represent the magnitude of the predicted values, thus visually demonstrating the model's predictive effectiveness.

[0099] In some embodiments, the loop current contribution in the data preprocessing step is a training J, which is obtained based on a calculation step; wherein, the calculation step includes: calculating the particle number density, the average particle drift velocity, and the magnetic latitude of the magnetic field line reflection point; integrating to calculate the loop current; and converting the loop current contribution I at each L... L J is used for training.

[0100] In some embodiments, the calculation of particle number density, average particle drift velocity, and magnetic latitude of the magnetic field line reflection point includes:

[0101] The particle number density is calculated based on formulas (1) and (2); where,

[0102] Formula (1)

[0103] This represents the number density at each energy level and at each pitch angle. This represents the differential electron flux, where δ is the pitch angle. Let E be the velocity of the electron at energy E. Considering relativistic effects:

[0104] Formula (2)

[0105] For the current energy level, The rest mass of the electron is 9.10938356 × 10⁻⁶. -31 kg, where c is the speed of light;

[0106] The average drift velocity of the particles is calculated based on formula (3);

[0107] Formula (3)

[0108] L represents the magnetic shell parameter, which defines the equatorial radius of the magnetic field lines in the equatorial plane; δ is the pitch angle; W is the energy of each particle; and q is the particle charge. , The radius of the Earth is 6,371,000 m.

[0109] Calculate the magnetic latitude of the magnetic field line reflection point based on formula (4);

[0110] Formula (4)

[0111] α is the equatorial elevation angle. It is the magnetic latitude.

[0112] In some embodiments, the integral calculation of the loop current includes: integrating over the magnetic latitude to obtain the current density on the magnetic field line, integrating over the magnetic latitude to obtain the current density on the magnetic field line, and summing the contributions of the solid angle element and the energy bandwidth element and multiplying by the L*Re interval to obtain the loop current contribution at each time moment.

[0113] In some embodiments, based on the ring current contribution I L Calculate magnetic field disturbance B d This includes: calculating the magnetic field disturbance B at each L according to formula (5). d Ring current contribution value;

[0114] Formula (5)

[0115] Permeability of free space;

[0116] L represents the magnetic shell parameter, specifically the number of times the magnetic field lines in the Earth's magnetic field cross the Earth's radius at the magnetic equator.

[0117] R E This represents the Earth's radius.

[0118] In some scenarios, the computation process may include three stages.

[0119] Phase 1: Data preparation; Phase 2: Calculation of particle number density, average particle drift velocity, and magnetic latitude of the magnetic field line reflection point; Phase 3: Integral calculation of the ring current contribution. Details are as follows.

[0120] Phase 1: Data Preparation

[0121] Data constants: (1) Electronics, , , Mass: Used to calculate particle velocity and related dynamic properties. (2) Electron, , , Charge: (3) Area conversion factor: used to convert electron flux from centimeter square units to meter square units to ensure unit consistency. (4) Energy conversion factor: used to convert energy from electron volts (keV) to international standard units (J). (5) Magnetic field strength of the Earth's surface: used to simulate particle behavior in a magnetic field. (6) Earth's radius: used as the basic reference scale for calculating the influence of the geomagnetic field and orbital motion.

[0122] The actual measurement data is as follows:

[0123] FEDU: Represents the measured electron flux. This data is crucial, used to calculate the electron number density at each energy and pitch angle in space, and thus to deduce the loop current. FEDU contains a large number of invalid values. Here, we consider using an interpolation strategy that can be called "nearest neighbor plus local mean hybrid interpolation." This strategy can preserve the local characteristics of the data while filling in invalid values, achieving a smooth transition and enhancing the integrity and stability of the data.

[0124] L: L-shell value, representing a magnetic shell parameter, specifically indicating how many times the magnetic field lines in the Earth's magnetic field cross the Earth's radius at the magnetic equator. The L-value is an important parameter for studying the Earth's magnetic field and loop currents, describing a specific location within the Earth's magnetic field.

[0125] MLT: MLT represents a position in the magnetic field: In the Earth's magnetosphere, MLT represents the "time" of a position relative to the Earth's magnetic axis, similar to local time on Earth. An MLT value of 0 corresponds to "magnetic noon," which is the area of ​​the magnetosphere directly illuminated by the sun; an MLT value of 12 corresponds to "magnetic midnight," which is the shaded side of the Earth's magnetosphere.

[0126] Epoch: Timestamp data, which usually indicates the specific point in time when the data was collected.

[0127] FEDU_Energy: This represents the energy of the electron flux measured at a specific energy level. The unit is usually keV.

[0128] FEDU_Alpha_Eq: This is the pitch angle in the magnetic equatorial plane, commonly used to study the trajectory of electrons in a magnetic field. The pitch angle is the angle between the direction of particle motion and the direction of the magnetic field. It is crucial for analyzing the particle distribution along magnetic field lines.

[0129] FEDU_Energy_DELTA_plus and FEDU_Energy_DELTA_minus: These data represent the uncertainty or error range of the energy level, and are typically used to define the upper and lower limits of electron energy values. They are used to help determine the bandwidth.

[0130] The second stage involves calculating the particle number density, average particle drift velocity, and magnetic latitude of the magnetic field line reflection point.

[0131] (1) Particle number density:

[0132] Formula (1)

[0133] This represents the number density at each energy level and at each pitch angle. Represents differential electron flux. Let E be the velocity of the electron at energy E. Considering relativistic effects:

[0134] Formula (2)

[0135] E represents the current energy level. The rest mass of the electron. c is the speed of light.

[0136] (2) Average drift speed:

[0137] Formula (3)

[0138] L represents the magnetic shell parameter (or the Michael Belt parameter), which defines the equatorial radius of the magnetic field lines in the equatorial plane. Let W be the pitch angle, W be the energy of each particle, and q be the particle charge. , The radius of the Earth is 6,371,000 m.

[0139] (3) Magnetic latitude of the magnetic field line reflection point

[0140] Calculate the magnetic latitude of the mirror point

[0141] Formula (4)

[0142] The elevation angle at the equator. It is the magnetic latitude.

[0143] Phase 3: Integral Calculation of Loop Current Contribution

[0144] The current density on the magnetic field line is obtained by integrating over the magnetic latitude. The contribution of the solid angle element and the energy bandwidth element is summed and multiplied by the L*Re interval to obtain the loop current contribution at each time step.

[0145] Then based on contribution I L Calculate the magnetic field disturbance B at each L. d， Take I L The overall loop current contribution is obtained by integrating the disturbance along the L direction. The average magnetic field disturbance trend is consistent with the Dst exponent, which is obtained by using formula (5).

[0146] Formula (5)

[0147] is the vacuum permeability.

[0148] B d This reflects the magnetic field disturbance caused by the contribution of the loop current at a certain L.

[0149] Phase 4: Obtaining the result using the same method based on , , I at each L obtained L The obtained electrons, , , The four results are summed to obtain the total loop current contribution at each L, which is used for training J.

[0150] In one embodiment of this disclosure, such as Figure 3 As shown, a method for calculating the Dst exponent is provided, which may include steps 301, 302 and 303.

[0151] Step 301: Obtain the ring current contribution values ​​at different times, different L values, and different solar winds based on the ring current contribution prediction model.

[0152] Step 302: Based on the time resolution, multiply the ring current contribution value by the interval of L*Re to obtain the ring current contribution value at different L locations.

[0153] Step 303, based on the ring current contribution value I L Obtain the average magnetic field perturbation And approximate the average magnetic field disturbance as the Dst exponent.

[0154] In some embodiments, the average magnetic field disturbance is obtained according to formula (5), which is approximately the Dst exponent.

[0155] In some embodiments, the method further includes: using a scatter plot to characterize the relationship between the date and the predicted Dst index value, wherein the display format of the Dst index value is related to the magnitude of the Dst index value.

[0156] For details on the implementation and technical effects of this embodiment, please refer to the descriptions in other parts of this application, which will not be repeated here.

[0157] Please refer to Figure 4 This illustrates a schematic diagram of an embodiment of a method for calculating the loop current contribution at each L according to the present disclosure. Figure 4 The method shown for calculating the contribution of loop current includes:

[0158] Step 401: Calculate the particle number density, average particle drift velocity, and magnetic latitude of the magnetic field line reflection point.

[0159] Step 402: Integrate and calculate the loop current.

[0160] Step 403 will be based on electronics, , , The summation of the ring current contributions at each L point yields the combined ring current contribution of protons and electrons at each L point.

[0161] In some embodiments, the loop current contribution I at each L L J can be used for training.

[0162] In some application scenarios, the Dst approximation calculation method based on radiation belt dynamics is mainly divided into three stages (such as...). Figure 5 (as shown)

[0163] Phase 1: Data Preparation

[0164] Data constants: (1) Electron mass: used to calculate particle velocity and related dynamic properties. (2) Electron charge: the fundamental charge carried by an electron, used to calculate electromagnetic properties such as current density. (3) Area conversion factor: used to convert electron flux from centimeter square units to meter square units to ensure unit consistency. (4) Energy conversion factor: used to convert energy from electron volts (keV) to international standard units (J). (5) Earth's surface magnetic field strength: used to simulate particle behavior in a magnetic field. (6) Earth's radius: used as a basic reference scale for calculating the influence of the geomagnetic field and orbital motion.

[0165] The actual measurement data is as follows:

[0166] FEDU: Represents the measured electron flux. This data is crucial, used to calculate the electron number density at each energy and pitch angle in space, and thus to deduce the loop current. FEDU contains a large number of invalid values. Here, we consider using an interpolation strategy that can be called "nearest neighbor plus local mean hybrid interpolation." This strategy can preserve the local characteristics of the data while filling in invalid values, achieving a smooth transition and enhancing the integrity and stability of the data.

[0167] L: L-shell value, representing a magnetic shell parameter, specifically indicating how many times the magnetic field lines in the Earth's magnetic field cross the Earth's radius at the magnetic equator. The L-value is an important parameter for studying the Earth's magnetic field and loop currents, describing a specific location within the Earth's magnetic field.

[0168] MLT: MLT represents a position in the magnetic field: In the Earth's magnetosphere, MLT represents the "time" of a position relative to the Earth's magnetic axis, similar to local time on Earth. An MLT value of 0 corresponds to "magnetic noon," which is the area of ​​the magnetosphere directly illuminated by the sun; an MLT value of 12 corresponds to "magnetic midnight," which is the shaded side of the Earth's magnetosphere.

[0169] Epoch: Timestamp data, which usually indicates the specific point in time when the data was collected.

[0170] FEDU_Energy: This represents the energy of the electron flux measured at a specific energy level. The unit is usually keV.

[0171] FEDU_Alpha_Eq: This is the pitch angle in the magnetic equatorial plane, commonly used to study the trajectory of electrons in a magnetic field. The pitch angle is the angle between the direction of particle motion and the direction of the magnetic field. It is crucial for analyzing the particle distribution along magnetic field lines.

[0172] FEDU_Energy_DELTA_plus and FEDU_Energy_DELTA_minus: These data represent the uncertainty or error range of the energy level, and are typically used to define the upper and lower limits of electron energy values. They are used to help determine the bandwidth.

[0173] The second stage involves calculating the particle number density, average particle drift velocity, and magnetic latitude of the magnetic field line reflection point.

[0174] (1) Particle number density:

[0175] Formula (1)

[0176] This represents the number density at each energy level and at each pitch angle. Represents differential electron flux. Let E be the velocity of the electron at energy E. Considering relativistic effects:

[0177] Formula (2)

[0178] E represents the current energy level. The rest mass of the electron. c is the speed of light.

[0179] (2) Average drift speed:

[0180] Formula (3)

[0181] L represents the magnetic shell parameter (or the Michael Belt parameter), which defines the equatorial radius of the magnetic field lines in the equatorial plane. Let W be the pitch angle, W be the energy of each particle, and q be the particle charge. , The radius of the Earth is 6,371,000 m.

[0182] (3) Magnetic latitude of the magnetic field line reflection point

[0183] Calculate the magnetic latitude of the mirror point

[0184] Formula (4)

[0185] The elevation angle at the equator. It is the magnetic latitude.

[0186] Phase 3: Integral Calculation of Loop Current

[0187] The current density along the magnetic field lines is obtained by integrating over the magnetic latitude. The contribution of the solid angle element and the energy bandwidth element is summed and multiplied by the L*Re interval to obtain the loop current contribution at each time step. Then, based on the loop current contribution I... L Calculate the average magnetic field disturbance B d :

[0188] Formula (5)

[0189] is the vacuum permeability.

[0190] B d It reflects the average magnetic field disturbance caused by the loop current and can be used as an approximate representation of the Dst exponent.

[0191] Using the same method, we obtained electron-based... , , The obtained ring current contribution at each L will yield the obtained electrons, , , The summation of the obtained ring current contributions yields the ring current contribution at each L. In one embodiment of this disclosure, such as... Figure 3 As shown, a method for calculating the Dst exponent is provided, which may include step 301, namely, taking time, L and solar wind data as input and outputting the ring current contribution at L based on the ring current contribution prediction model generated by any embodiment of the present disclosure.

[0192] The following is for reference. Figure 6 The diagram illustrates a structural schematic of an electronic device suitable for implementing embodiments of the present disclosure. The terminal devices in the embodiments of the present disclosure may include, but are not limited to, mobile terminals such as mobile phones, laptops, digital broadcast receivers, PDAs (personal digital assistants), PADs (tablet computers), PMPs (portable multimedia players), in-vehicle terminals (e.g., in-vehicle navigation terminals), and fixed terminals such as digital TVs and desktop computers. Figure 6 The electronic device shown is merely an example and should not be construed as limiting the functionality and scope of the embodiments disclosed herein.

[0193] like Figure 6As shown, the electronic device may include a processing unit (e.g., a central processing unit, a graphics processing unit, etc.) 601, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 602 or a program loaded from a storage device 608 into a random access memory (RAM) 603. The RAM 603 also stores various programs and data required for the operation of the electronic device 600. The processing unit 601, ROM 602, and RAM 603 are interconnected via a bus 604. An input / output (I / O) interface 605 is also connected to the bus 604.

[0194] Typically, the following devices can be connected to I / O interface 605: input devices 606 including, for example, touchscreens, touchpads, keyboards, mice, cameras, microphones, accelerometers, gyroscopes, etc.; output devices 607 including, for example, liquid crystal displays (LCDs), speakers, vibrators, etc.; storage devices 608 including, for example, magnetic tapes, hard disks, etc.; and communication devices 609. Communication device 609 allows electronic devices to communicate wirelessly or wiredly with other devices to exchange data. Although Figure 6 Electronic devices with various devices are shown, but it should be understood that it is not required to implement or have all of the devices shown. More or fewer devices may be implemented or have instead.

[0195] In particular, according to embodiments of this disclosure, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of this disclosure include a computer program product comprising a computer program carried on a non-transitory computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via a communication device 609, or installed from a storage device 608, or installed from a ROM 602. When the computer program is executed by the processing device 601, it performs the functions defined in the methods of embodiments of this disclosure.

[0196] It should be noted that the computer-readable medium described in this disclosure can be a computer-readable signal medium or a computer-readable storage medium, or any combination thereof. A computer-readable storage medium can be, for example,—but not limited to—an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of a computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this disclosure, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. In this disclosure, a computer-readable signal medium can include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A computer-readable signal medium can be any computer-readable medium other than a computer-readable storage medium, which can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the computer-readable medium can be transmitted using any suitable medium, including but not limited to: wires, optical fibers, RF (radio frequency), etc., or any suitable combination thereof.

[0197] In some implementations, clients and servers can communicate using any currently known or future-developed network protocol such as HTTP (Hypertext Transfer Protocol), and can interconnect with digital data communication (e.g., communication networks) of any form or medium. Examples of communication networks include local area networks (“LANs”), wide area networks (“WANs”), the Internet (e.g., the Internet of Things), and peer-to-peer networks (e.g., ad hoc peer-to-peer networks), as well as any currently known or future-developed networks.

[0198] The aforementioned computer-readable medium may be included in the aforementioned electronic device; or it may exist independently and not assembled into the electronic device.

[0199] The aforementioned computer-readable medium carries one or more programs, which, when executed by the electronic device, cause the electronic device to: a data preprocessing step, including: storing By, Bz, and solar wind dynamic pressure at a one-minute resolution based on data measured by the OMNI satellite, using By, Bz, solar wind dynamic pressure, and L as input features; preprocessing the training loop current contribution J at every third preset time interval as the output target; and a model training step, including: importing multiple input features into a deep learning-based neural network to obtain a predicted value, using the mean squared error as the loss function, and calculating the predicted value. The error between the estimated value and the corresponding output target is used to obtain a ring current contribution prediction model based on the error-adjusted neural network. The multiple input features include one or more of the following: By input features, Bz input features, solar wind dynamic pressure input features, and L input features. The deep learning-based neural network includes one or more of the following network layers: a fully connected layer, used to learn global features of the data and, through layer-by-layer refinement, outputs results for a regression task, and the estimated value is obtained based on the regression task and the results; and a regularization layer, set within the fully connected layer, used to randomly disable some neurons during training.

[0200] The aforementioned computer-readable medium carries one or more programs, which, when executed by the electronic device, cause the electronic device to: based on the Dst exponent calculation model generated in any embodiment of the present disclosure, take time and L value as input, and output the Dst exponent value.

[0201] The aforementioned computer-readable medium carries one or more programs that, when executed by the electronic device, cause the electronic device to: calculate the particle number density, the average particle drift velocity, and the magnetic latitude of the magnetic field line reflection point; and integrate the calculation of the ring current contribution I at each L. L .

[0202] Computer program code for performing the operations of this disclosure can be written in one or more programming languages ​​or a combination thereof, including but not limited to object-oriented programming languages ​​such as Java, Smalltalk, and C++, as well as conventional procedural programming languages ​​such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0203] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this disclosure. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0204] The functions described above in this document can be performed at least in part by one or more hardware logic components. For example, exemplary types of hardware logic components that can be used, without limitation, include: field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), application-specific standard products (ASSPs), system-on-a-chip (SoCs), complex programmable logic devices (CPLDs), and so on.

[0205] In the context of this disclosure, a machine-readable medium can be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, apparatus, or device. A machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. A machine-readable medium can be, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0206] The above description is merely a preferred embodiment of this disclosure and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of this disclosure is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the above-described concept. For example, technical solutions formed by substituting the above features with (but not limited to) technical features disclosed in this disclosure that have similar functions.

[0207] Furthermore, while the operations are described in a specific order, this should not be construed as requiring these operations to be performed in the specific order shown or in a sequential order. In certain environments, multitasking and parallel processing may be advantageous. Similarly, while several specific implementation details are included in the above discussion, these should not be construed as limiting the scope of this disclosure. Certain features described in the context of individual embodiments may also be implemented in combination in a single embodiment. Conversely, various features described in the context of a single embodiment may also be implemented individually or in any suitable sub-combination in multiple embodiments.

[0208] Although the subject matter has been described using language specific to structural features and / or methodological logic, it should be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or actions described above. Rather, the specific features and actions described above are merely illustrative examples of implementing the claims.

Claims

1. A method for generating a prediction model of ring current contribution, characterized in that, The method includes: The data preprocessing steps include: storing the By, Bz, solar wind dynamic pressure, and L values ​​of the OMNI satellite at each time step, along with the training loop current contribution J at each time step; where By represents the y-component of the solar wind magnetic field in the GSM coordinate system; Bz represents the z-component of the solar wind magnetic field in the GSM coordinate system; and L represents the magnetic shell parameters. The feature construction steps include: obtaining By input features, Bz input features, and solar wind dynamic pressure input features based on the stored By, Bz, and solar wind dynamic pressure, and using L as an input feature; preprocessing the training loop current contribution J as the output target; The model training steps include: importing multiple input features into a deep learning-based neural network to obtain a predicted value; using mean squared error as a loss function to calculate the error between the predicted value and the corresponding output target; and adjusting the neural network based on the error to obtain a ring current contribution prediction model. Among these, the multiple input features include one or more of the following: By input features, Bz input features, solar wind dynamic pressure input features, and L input features. The deep learning-based neural network includes a fully connected layer, which is used to: learn global features of the data, and refine them layer by layer to output results for a regression task, and obtain the estimated value based on the regression task and the results.

2. The method according to claim 1, characterized in that, The neural network comprises three hidden layers and one output layer. The three hidden layers are fc1, fc2, and fc3, respectively. fc1 has 64 neurons, fc2 has 32 neurons, and fc3 has 16 neurons. fc1, fc2, and fc3 use different activation functions as follows: fc1 uses the LeakyReLU activation function to mitigate gradient vanishing for mini-batch data; fc2 uses the ELU activation function to improve the model's performance in the negative region; fc3 uses Tanh for compression range, keeping the value in (-1, 1); The output layer fc4, as the last fully connected layer, directly outputs the predicted value.

3. The method according to claim 1, characterized in that, The method further includes: The learning rate of each parameter in the neural network is dynamically adjusted using the RMSprop optimizer.

4. The method according to claim 1, characterized in that, The loop current contribution in the data preprocessing step is the training loop current contribution J, which is obtained based on the calculation step; wherein, the calculation step includes: Calculate the particle number density, average particle drift velocity, and magnetic latitude of the magnetic field line reflection point; Integral calculation of loop current; According to the ring , , , The loop current component at each L is obtained, and the components are summed to obtain the loop current contribution I at each L. L The loop current at each L contributes I L J is the contribution of the training loop current.

5. The method according to claim 4, characterized in that, The calculation of particle number density, average particle drift velocity, and magnetic latitude of the magnetic field line reflection point includes: The particle number density is calculated based on formulas (1) and (2), the average particle drift velocity is calculated based on formula (3), and the magnetic dimension of the magnetic field line reflection point is calculated based on formula (4); where, Official (1) This represents the number density at each energy level and at each pitch angle. This represents the differential electron flux, where δ is the pitch angle. Let E be the velocity of the electron at energy E. Considering relativistic effects: Official (2) For the current energy level, The rest mass of the electron is 9.10938356 × 10⁻⁶. -31 kg, where c is the speed of light; Official (3) L represents the magnetic shell parameter, which defines the equatorial radius of the magnetic field lines in the equatorial plane; δ is the pitch angle; W is the energy of each particle; and q is the particle charge. , The radius of the Earth is 6,371,000 m. Official (4) α is the equatorial elevation angle. It is the magnetic latitude.

6. The method according to claim 5, characterized in that, The integral calculation of the loop current includes: The current density on the magnetic field line is obtained by integrating over the magnetic latitude. The contribution of the solid angle element and the energy bandwidth element is summed and multiplied by the L*Re interval to obtain the loop current contribution at each time step.

7. A method for calculating the Dst exponent, characterized in that, The method includes: Based on the ring current contribution prediction model generated according to any one of claims 1-6, taking By, Bz, solar wind dynamic pressure, and L value as inputs, the output is the ring current contribution I at the L value. L ; Based on the contribution of the ring current I L Obtain the average magnetic field perturbation And approximate the average magnetic field disturbance as the Dst exponent.

8. The method according to claim 7, characterized in that, The contribution I based on the ring current L Obtain the average magnetic field perturbation ,include: According to formula (5) and the ring current contribution I L Calculate the magnetic field disturbance caused by the loop current at point L. ; Official (5) Permeability of free space; L represents the magnetic shell parameter, specifically the number of times the magnetic field lines in the Earth's magnetic field cross the Earth's radius at the magnetic equator. R E This represents the Earth's radius.

9. The method according to claim 8, characterized in that, The method further includes: A scatter plot is used to represent the relationship between time and the Dst exponent value, wherein the display format of the Dst exponent value is related to the magnitude of the Dst exponent value.

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