A physical-guided neural network based method and system for inversion of vertical frequency hog graph

Abstract

The application discloses a physical guidance neural network-based inversion method of vertical frequency height graph, comprising the following steps: acquiring vertical frequency height graph observation data and inputting the vertical frequency height graph observation data into a trained vertical frequency height graph inversion model to output an electron density logarithmic profile; the training of the model comprises the following steps: acquiring vertical frequency height graph observation data and electron density profile label data and preprocessing, constructing an observation virtual height vector of a fixed frequency grid and an electron density logarithmic profile label of a fixed height grid; constructing a frequency prior distribution curve according to the vertical frequency height graph observation data; based on the observation virtual height vector and the electron density logarithmic profile label, a frequency attention module and a residual backbone network are adopted to acquire a frequency attention weight graph and an electron density logarithmic profile prediction result; inputting the electron density logarithmic profile prediction result into a physical decoding module to obtain a reconstructed virtual height trajectory; respectively calculating a profile supervision loss, an attention prior constraint loss and a physical consistency loss, and constructing a joint loss function to train the model.

Description

Technical Field

[0001] This invention relates to the fields of geophysics and ionospheric detection technology, specifically to a method and system for inverting vertical frequency-elevation maps based on a physical-guided neural network. Background Technology

[0002] The ionosphere, an atmospheric layer at an altitude of approximately 80–1000 km, is a crucial component of the near-Earth electromagnetic environment. The electron density distribution within the ionosphere directly influences the propagation path, propagation delay, refraction characteristics, and absorption characteristics of radio waves. Therefore, accurate modeling and inversion of the ionosphere are of great significance for applications such as shortwave communication, satellite positioning and navigation, radar detection, space target monitoring, and space weather forecasting.

[0003] Currently, the main techniques for obtaining ionospheric electron density profiles include vertical ionospheric sounding, empirical model inversion, and incoherent scattering radar detection. Vertical ionospheric sounding can acquire vertical frequency maps and virtual height information, offering advantages such as relatively low observation costs and suitability for widespread application. However, its traditional processing methods heavily rely on human experience and lack automated inversion capabilities for complex ionospheric structures. Empirical models can provide background ionospheric parameter distributions, but their ability to describe local anomalous disturbances and rapid dynamic changes is limited. Incoherent scattering radar can directly measure parameters such as electron density with high detection accuracy, but its high equipment investment and operation and maintenance costs make it difficult to meet the needs of wide-area, continuous, and routine applications.

[0004] In recent years, deep learning methods have been applied in ionospheric parameter inversion and have shown certain advantages in modeling complex nonlinear relationships. However, existing methods still have the following shortcomings: First, they do not make sufficient use of the ionospheric propagation mechanism and lack a physical constraint mechanism consistent with the observed virtual height information; second, they lack effective differentiation of the importance of different frequency positions in the vertical frequency-height map, making it difficult to fully highlight key frequency information; and third, the model design for the mapping relationship between fixed-frequency grid input and fixed-height grid output is not perfect. Summary of the Invention

[0005] To overcome the shortcomings of existing deep learning methods in ionospheric parameter inversion, such as the lack of physical constraints consistent with observed virtual height information, difficulty in fully highlighting key frequency information, and imperfect model design for the mapping relationship between fixed frequency grid input and fixed height grid output, this invention provides a vertical frequency-height map inversion method and system based on a physical guided neural network. It uses vertical frequency-height map observation data as the observation input and electron density logarithmic profile labels on a fixed height grid as the inversion output. A physical decoding module maps the predicted electron density logarithmic profile results to a reconstructed virtual height trajectory. Under the combined effect of profile supervision constraints, attention prior constraints, and physical consistency constraints, high-precision inversion of the ionospheric electron density profile is achieved.

[0006] According to one aspect of the present invention, a method for inverting a vertical frequency-height map based on a physical guided neural network is provided, comprising: acquiring vertical frequency-height map observation data to be inverted; inputting the vertical frequency-height map observation data to be inverted into a trained vertical frequency-height map inversion model, and outputting a corresponding logarithmic electron density profile; wherein, the training of the vertical frequency-height map inversion model includes: acquiring and preprocessing the vertical frequency-height map observation data and electron density profile label data to construct an observation virtual height vector on a fixed frequency grid and an electron density logarithmic profile label on a fixed height grid; training the constructed vertical frequency-height map inversion model based on the vertical frequency-height map observation data, the observation virtual height vector, and the electron density logarithmic profile label, including: constructing a support condition for the observation frequency based on the vertical frequency-height map observation data. The corresponding frequency prior distribution curve; based on the observed virtual height vector and the electronic density logarithmic profile label, the frequency attention module and residual backbone network are used to obtain the frequency attention weight map and the electronic density logarithmic profile prediction results on the fixed height grid; the electronic density logarithmic profile prediction results are input into the physical decoding module, and the reconstructed virtual height trajectory is obtained by sequentially performing electronic density recovery, plasma frequency calculation, propagation relationship construction and integration along the height direction; the profile supervision loss between the electronic density logarithmic profile prediction results and the electronic density logarithmic profile label, the attention prior constraint loss between the frequency attention weight map and the frequency prior distribution curve, and the physical consistency loss between the reconstructed virtual height trajectory and the observed virtual height vector are calculated respectively, and a joint loss function is constructed to train the vertical frequency height map inversion model.

[0007] Further, constructing a frequency prior distribution curve corresponding to the observed frequency support based on the vertical frequency elevation map observation data includes: constructing an effective frequency mask based on the frequency coverage range of the vertical frequency elevation map observation data; calculating the distance from each fixed frequency point to the corresponding nearest original observed frequency point, and constructing a sample effective mapping based on the distance; multiplying the sample effective mapping with the effective frequency mask, and averaging and normalizing along the sample dimension to obtain the frequency prior distribution curve.

[0008] Further, based on the observed virtual height vector and the electronic density logarithmic profile label, a frequency attention module and a residual backbone network are used to obtain the frequency attention weight map and the electronic density logarithmic profile prediction results on the fixed-height grid. This includes: normalizing the virtual height vector and the electronic density logarithmic profile label on the fixed-frequency grid to obtain normalized data; assembling the normalized data into a network input tensor and inputting it into the frequency attention module to generate a frequency attention weight map through frequency-dimensional convolution and nonlinear transformation; multiplying the frequency attention weight map element-wise with the input virtual height vector to obtain weighted input features; and inputting the weighted input features into the residual backbone network to extract deep features and output the electronic density logarithmic profile prediction results on the fixed-height grid.

[0009] Further, the predicted result of the logarithmic electron density profile is input into the physical decoding module, and the reconstructed virtual height trajectory is obtained by sequentially performing electron density recovery, plasma frequency calculation, propagation relationship construction, and integration along the height direction. This includes: performing inverse normalization processing on the predicted result of the logarithmic electron density profile to recover the true physical magnitude of the predicted result; obtaining the plasma frequency distribution based on the recovered predicted result of the logarithmic electron density profile; constructing the propagation relationship based on the plasma frequency distribution using a simplified propagation expression to obtain the plasma refractive index; introducing a gating unit and a smoothing unit to perform continuous processing on the propagation conditions in the plasma refractive index, and integrating the continuous plasma refractive index along the height direction to obtain the reconstructed virtual height trajectory.

[0010] Furthermore, by constructing the propagation relationship using a simplified propagation expression, the plasma refractive index is obtained, and the corresponding formula is:

[0011] ,

[0012] ,

[0013] in, The trajectory is artificially inflated based on simplified propagation expressions. The refractive index of the plasma, The height of the bottom of the ionosphere. The height of the point where the radio wave is reflected. For radio wave frequency, For plasma frequency distribution, The predicted results are the logarithmic profile of the recovered electron density. The amount of electron charge. Represents the free space dielectric constant. Indicates electron mass.

[0014] Furthermore, a gating unit and a smoothing unit are introduced to perform continuous processing on the propagation conditions in the plasma refractive index, and the continuous plasma refractive index is integrated along the height direction to obtain the reconstructed virtual height trajectory. The corresponding formula is:

[0015] ,

[0016] ,

[0017] ,

[0018] in, To reconstruct the virtual height trajectory based on simplified propagation representation, gating units, and smoothing units, For gated unit functions, For smoothing unit functions, This is the maximum height for the points. For the gate slope parameter, For the Sigmoid function, This is the smoothing constant.

[0019] Furthermore, the joint loss function is expressed as follows:

[0020] ,

[0021] ,

[0022] ,

[0023] ,

[0024] in, For joint losses, For profile monitoring loss, For attention prior constraint loss, For physical consistency loss, Weights are assigned to the loss based on attention prior constraints. Weights for physical consistency loss. Indicates a grid point at a fixed height. The predicted logarithmic value of the electron density at that location. Indicates the corresponding reference label, Indicates the number of grid points at a fixed height. This represents the attention weights output by the frequency attention module. Represents the frequency prior distribution curve. For fixed frequency grid length, For grid index variables, The total number of effective frequency points, The reconstructed virtual height trajectory vector output by the physical decoding module. To observe the virtual height vector, This is the smoothing constant.

[0025] Furthermore, the frequency attention module includes a first convolutional layer, a second convolutional layer, a third convolutional layer, a first activation layer, a second activation layer, and a third activation layer. The first and second convolutional layers are 7×1 convolutional layers, the third convolutional layer is a 1×1 convolutional layer, the first and second activation layers are both ReLU activation layers, and the third activation layer is a Sigmoid activation layer.

[0026] Furthermore, the residual backbone network includes an input feature extraction module, a first residual module, a first pooling layer, a second residual module, a third residual module, a fourth residual module, a global average pooling layer, a first fully connected layer, a fourth activation layer, a Dropout layer, and a second fully connected layer. The input feature extraction module includes a fourth convolutional layer, a batch normalization layer, and a fifth activation layer. The fourth convolutional layer is a 7×1 convolutional layer, and both the fourth and fifth activation layers are ReLU activation layers. The input feature extraction module has 32 output channels. The first residual module performs a mapping from 32 to 64 channels, the second residual module performs a mapping from 64 to 128 channels, the third residual module performs a mapping from 128 to 256 channels, and the fourth residual module performs a mapping from 256 to 512 channels. The first fully connected layer has an output dimension of 512, and the second fully connected layer has an output dimension of a fixed-height grid length.

[0027] According to one aspect of the present invention, a vertical frequency-height map inversion system based on a physical guided neural network is provided, comprising: a vertical frequency-height map observation data acquisition module for acquiring vertical frequency-height map observation data to be inverted; and an electron density logarithmic profile acquisition module for inputting the vertical frequency-height map observation data to be inverted into a trained vertical frequency-height map inversion model and outputting a corresponding electron density logarithmic profile; wherein, the training of the vertical frequency-height map inversion model includes: acquiring and preprocessing the vertical frequency-height map observation data and electron density profile label data to construct an observation virtual height vector on a fixed frequency grid and an electron density logarithmic profile label on a fixed height grid; and training the constructed vertical frequency-height map inversion model based on the vertical frequency-height map observation data, the observation virtual height vector, and the electron density logarithmic profile label, including: training the vertical frequency-height map inversion model according to ... and training the vertical frequency-height map inversion model according to the vertical frequency-height map observation data, the observation virtual height vector, and the electron density logarithmic profile label, including: training the vertical frequency-height map inversion model according to the vertical frequency-height map observation data, the observation virtual height vector, and the electron density logarithmic profile label, and training the vertical frequency-height map inversion model according to the vertical frequency-height map observation data, the observation virtual height vector, and the electron density logarithmic profile label, and The observation data is used to construct a frequency prior distribution curve corresponding to the observed frequency support. Based on the observed virtual height vector and the electron density logarithmic profile label, a frequency attention module and a residual backbone network are used to obtain the frequency attention weight map and the electron density logarithmic profile prediction results on a fixed height grid. The electron density logarithmic profile prediction results are input into the physical decoding module, and the reconstructed virtual height trajectory is obtained by sequentially performing electron density recovery, plasma frequency calculation, propagation relationship construction, and integration along the height direction. The profile supervision loss between the electron density logarithmic profile prediction results and the electron density logarithmic profile label, the attention prior constraint loss between the frequency attention weight map and the frequency prior distribution curve, and the physical consistency loss between the reconstructed virtual height trajectory and the observed virtual height vector are calculated respectively. A joint loss function is constructed to train the vertical frequency height map inversion model.

[0028] The above technical solution includes the following steps: First, acquire vertical frequency-height map observation data and its corresponding electron density profile label data to construct trace-profile paired samples; then, preprocess the vertical frequency-height map observation data and profile label data to construct the observed virtual height vector on a fixed frequency grid and the electron density logarithmic profile label on a fixed height grid; next, construct an effective frequency point mask and frequency prior distribution curve based on the vertical frequency-height map observation data, and input the normalized virtual height vector and electron density logarithmic profile label into the frequency attention module and the residual backbone network to obtain the electron density logarithmic profile prediction result; subsequently, input the electron density logarithmic profile prediction result into the physical decoding module, and obtain the reconstructed virtual height trajectory through electron density recovery, plasma frequency calculation, propagation relationship construction, and integration along the height direction; further, construct a joint loss function composed of profile supervision loss, attention prior constraint loss, and physical consistency loss to train the network; finally, input the vertical frequency-height map to be inverted into the trained model, output the corresponding electron density logarithmic profile, and extract ionospheric feature parameters. This method can improve the physical consistency and inversion accuracy of the vertical frequency height map inversion results, enhance the ability to extract information in key frequency regions, and achieve accurate inversion of ionospheric electron density profiles and their characteristic parameters.

[0029] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0030] (1) In the feature extraction stage, the present invention introduces prior information of the ionosphere and combines it with a prior-guided frequency attention module to enhance the key frequency region, which can improve the feature extraction capability and inversion accuracy under complex ionospheric conditions.

[0031] (2) The present invention employs a convolutional neural residual backbone network and a physical decoding module to work together to reverse the reconstruction of the observed virtual height trajectory while outputting the electron density profile, thereby establishing a mapping relationship between the observation space and the physical profile space, and enhancing the physical consistency and interpretability of the model.

[0032] (3) By jointly constructing profile supervision loss, attention prior constraint loss and reconstructed virtual height trajectory loss, the present invention enables the inversion results to simultaneously meet the requirements of data fitting accuracy and physical consistency, which is beneficial to improving the stability, convergence and generalization ability of the model. Attached Figure Description

[0033] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0034] Figure 1 This is a schematic diagram of the overall structure of a vertical frequency-elevation map inversion method based on a physical guided neural network provided in an embodiment of the present invention.

[0035] Figure 2 A frequency attention module diagram provided for an embodiment of the present invention.

[0036] Figure 3 This is a residual backbone network structure diagram provided in an embodiment of the present invention.

[0037] Figure 4 This is a residual module diagram provided for an embodiment of the present invention.

[0038] Figure 5 This is a diagram of the physical decoding module provided in an embodiment of the present invention.

[0039] Figure 6 This is a schematic diagram illustrating the data construction, training, and inversion process provided in an embodiment of the present invention.

[0040] Figure 7 This is a comparison diagram of the inversion profile and the label profile provided in one embodiment of the present invention.

[0041] Figure 8 This is a scatter plot comparing ionospheric parameters provided in one embodiment of the present invention. Detailed Implementation

[0042] It should be noted that:

[0043] The terms “comprising” and “having”, and any variations thereof, in the specification, claims, and accompanying drawings of this invention are intended to cover a non-exclusive inclusion, such as a process, method, system, product, or apparatus that includes a series of steps or units, not necessarily limited to those explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0044] The block diagrams shown in the accompanying drawings are merely functional entities and do not necessarily correspond to physically independent entities. That is, these functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices. The flowcharts shown in the accompanying drawings are merely illustrative and do not necessarily include all content and operations / steps, nor do they necessarily have to be performed in the described order. For example, some operations / steps can be decomposed, while others can be combined or partially combined; therefore, the actual execution order may change depending on the specific circumstances.

[0045] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. In addition, the technical features of the various embodiments or individual embodiments provided by the present invention can be arbitrarily combined to form new technical solutions. Such combinations are not bound by the order of steps and / or structural composition patterns, but must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0046] like Figure 1 As shown, this invention provides a vertical frequency-height map inversion method based on a physically guided neural network. This method uses vertical frequency-height map observation data as input and electron density logarithmic profile labels on a fixed-height grid as inversion output. A physical decoding module maps the predicted electron density logarithmic profile results to a reconstructed virtual height trajectory. Under the combined effects of profile supervision constraints, frequency prior constraints, and physical consistency constraints, high-precision inversion of the ionospheric electron density profile is achieved. The specific steps are as follows:

[0047] Step S1: Obtain the vertical frequency-elevation map observation data to be inverted.

[0048] Step S2: Input the vertical frequency-elevation map observation data to be inverted into the trained vertical frequency-elevation map inversion model, and output the corresponding logarithmic electron density profile; wherein, the training of the vertical frequency-elevation map inversion model includes:

[0049] Step S21: Obtain vertical frequency height map observation data and its corresponding electron density profile label data, and construct trace-profile paired samples.

[0050] In step S21, the vertical frequency-elevation map observation data is represented as raw frequency-virtual height pairs. Electron density profile label data is represented as raw height-electron density pairs. .

[0051] In this embodiment, ionospheric data for the entire year of 2015 was generated based on the IRI model. The geographical location was selected as 100 degrees east longitude and 40 degrees north latitude, and the time range was from January 2015 to December 2015, with a time sampling step of 1 hour. Corresponding electron density profile label data was generated according to the above geographical location and time conditions, and the corresponding vertical frequency-elevation map observation data was further constructed to form a one-to-one paired input-output sample, namely, trace-profile paired sample.

[0052] Step S22: Preprocess the trace-profile paired samples to construct the observation virtual height vector on the fixed frequency grid and the electronic density logarithmic profile label on the fixed height grid.

[0053] In step S22, the original trace data (i.e., vertical frequency-height map observation data constructed based on the IRI model) and electron density profile label data are preprocessed. This preprocessing includes non-finite value filtering, sorting, deduplication, outlier removal, and interpolation. Then, a fixed-frequency grid is constructed. and fixed height grid The original trace data is sorted by frequency, deduplicated, and interpolated to a fixed-frequency grid. The observed virtual height vector on the fixed frequency grid is obtained above. The original profile data (i.e., electron density profile label data) is sorted by height, deduplicated, and interpolated to a fixed-height grid. The electron density profile on a grid of fixed height is obtained. Then take the logarithm to obtain the logarithmic profile of the electron density. .

[0054] In this embodiment, , ,in, A fixed frequency grid, in MHz. This is a fixed-height grid, with units in km. Understandably, both fixed-frequency and fixed-height grids can be set according to actual needs and are not limited here.

[0055] Step S23: Construct an effective frequency mask based on the vertical frequency elevation map observation data, and construct a frequency prior distribution curve corresponding to the observed frequency support situation.

[0056] In step S23, the effective frequency mask refers to a binary label vector used to characterize whether each frequency point in the fixed frequency grid has observational data support. When observational frequency data exists near a fixed frequency point, the corresponding position is set to 1; otherwise, it is set to 0. Observational frequency support refers to the coverage and distribution characteristics of the observational frequency data within the entire fixed frequency grid. The frequency prior distribution curve refers to the frequency weight distribution curve obtained statistically based on the observational support level of each fixed frequency point in the training samples. The specific steps are as follows:

[0057] First, construct an effective frequency mask based on the frequency coverage range of the vertical frequency elevation map observation data. If a fixed frequency point is located between the minimum and maximum frequencies of the vertical frequency elevation map observation data, the effective frequency mask corresponding to that frequency point is set to 1; otherwise, the effective frequency mask corresponding to that frequency point is set to 0.

[0058] Secondly, for each fixed frequency point, calculate its distance to the nearest original observation frequency point (i.e., the frequency points of the vertical elevation map observation data, which consist of several observation frequency points), and construct an effective sample mapping based on the distance:

[0059] (1)

[0060] (2)

[0061] in, Indicates a fixed frequency point. Indicates a fixed frequency point The nearest original observation frequency point, Indicates the first A sample at a fixed frequency point Reaching the most recent original observation frequency point distance, Indicates the first The original observation frequency set of each sample Indicates a valid mapping of samples. Represents an exponential function. The distance attenuation parameter is preferably set to 0.2MHz.

[0062] Finally, the effective sample mapping is multiplied by the effective frequency mask, zeroed out outside the coverage area, and the weight values ​​of all samples in the training set at the same fixed frequency point are averaged and normalized to obtain the frequency prior distribution curve. Frequency prior distribution curve This is used to constrain the distribution of the frequency attention weight map so that it is consistent with the statistical regularity supported by observations.

[0063] Step S24: Based on the observed virtual height vector and the electronic density logarithmic profile label, the frequency attention module and residual backbone network are used to obtain the frequency attention weight map and the electronic density logarithmic profile prediction results on the fixed height grid. The specific steps are as follows:

[0064] Step S241: Normalize the dummy height vector on the fixed frequency grid and the logarithmic profile label of the electron density on the fixed height grid to obtain normalized data; assemble the normalized data into a network input tensor and input it into the frequency attention module to generate a frequency attention weight map through frequency dimension convolution and nonlinear transformation; multiply the frequency attention weight map element-wise with the input dummy height vector to obtain weighted input features.

[0065] First, the trace-profile paired samples are randomly divided into a training set, a validation set, and a test set, with a preferred ratio of 70%:15%:15%. Then, the fixed-frequency grid virtual height vectors in the training set, validation set, and test set are analyzed respectively. And the corresponding logarithmic electron density profile label The input data is normalized, and then assembled into a network input tensor. The preferred size is... ,in, For fixed frequency grid length, The number of samples in a batch is preferably 64.

[0066] Subsequently, the network input tensor input frequency attention module (such as...) Figure 2 As shown, the frequency attention module adopts a single-channel input structure and includes a first convolutional layer, a second convolutional layer, a third convolutional layer, a first activation layer, a second activation layer, and a third activation layer. The first and second convolutional layers are 7×1 convolutional layers, and the third convolutional layer is a 1×1 convolutional layer. The first and second activation layers are ReLU activation layers, and the third activation layer is a Sigmoid activation layer. The first convolutional layer has 16 output channels, the second convolutional layer has 8 output channels, and the third convolutional layer has 1 output channel. After Sigmoid activation, a frequency attention weight map distributed along a fixed frequency grid is generated. .

[0067] Finally, the frequency attention weight map The weighted input features are obtained by multiplying them element-wise with the input virtual height vector:

[0068] (3)

[0069] in, Indicates weighted input features, This represents the input virtual height vector, which is the virtual height vector on a fixed frequency grid.

[0070] Step S242: Input the weighted input features into the residual backbone network, extract deep features, and output the prediction results of the logarithmic profile of electron density on the grid with fixed height.

[0071] Among them, residual backbone network (such as Figure 3 The diagram (shown) includes an input feature extraction module (i.e., the stem layer), a first residual module, a first pooling layer, a second residual module, a second pooling layer, a third residual module, a fourth residual module, a global average pooling layer, a first fully connected layer, a fourth activation layer, a Dropout layer, and a second fully connected layer. The stem layer includes a fourth convolutional layer, a first batch of normalization layers, and a fifth activation layer. The fourth convolutional layer is a 7×1 convolutional layer, and both the fourth and fifth activation layers are ReLU activation layers. The number of output channels of the stem layer is preferably set to 32.

[0072] Four residual modules (such as) Figure 4 All (as shown) employ a stable residual structure, with each residual module containing two residual blocks. The first residual module performs the mapping from 32 to 64 channels, the second residual module performs the mapping from 64 to 128 channels, the third residual module performs the mapping from 128 to 256 channels, and the fourth residual module performs the mapping from 256 to 512 channels. The first two residual modules are followed by a 2×1 max-pooling layer to expand the receptive field, while the latter two residual modules do not have a pooling layer to retain more high-level features.

[0073] After deep feature extraction via the residual backbone network, the layers sequentially pass through a global average pooling layer, a first fully connected layer with an output dimension of 512, a ReLU activation layer, a Dropout layer, and a layer with a fixed-height grid length in the output dimension. The second fully connected layer ultimately outputs the predicted logarithmic profile of electron density on a grid with a fixed height. The dropout probability is preferably 0.2.

[0074] Step S25: Input the predicted result of the logarithmic profile of the electron density into the physical decoding module, and obtain the reconstructed virtual height trajectory by sequentially performing electron density recovery, plasma frequency calculation, propagation relationship construction, and integration along the height direction.

[0075] In step S25, the physical decoding module first performs denormalization on the normalized prediction result output in step S24 (i.e., the prediction result of the logarithmic profile of electron density on a fixed-height grid) to restore the true physical magnitude of the logarithmic profile of electron density. Then, the restored logarithmic profile prediction result is converted from logarithmic electron density values ​​to electron density values, and further converted to plasma frequency distribution. Based on the plasma frequency distribution, a simplified propagation expression is used to construct the propagation relationship, obtaining the plasma refractive index. Finally, a gating unit and a smoothing unit are introduced to perform continuous processing on the propagation conditions in the plasma refractive index, and the continuous plasma refractive index is integrated along the height direction to obtain the reconstructed virtual height trajectory (e.g., ...). Figure 6 (As shown).

[0076] Among them, the physical decoding module (such as Figure 5 (As shown) includes a fifth convolutional layer, a second batch normalization layer, a sixth activation layer, a sixth convolutional layer, a third batch normalization layer, a third fully connected layer, a seventh activation layer, and both the fifth and sixth convolutional layers are 3x3. The first convolutional layer, the sixth activation layer and the seventh activation layer are both ReLU activation layers.

[0077] Furthermore, the physical decoding module is constructed based on the theory of radio wave propagation in the ionosphere. Among these, the plasma refractive index is characterized... The Appleton-Hartree formula is expressed as follows:

[0078] (4)

[0079] in, Here, j is the plasma refractive index, and j is the imaginary unit. The angle between the wave vector and the Earth's magnetic field. For the Appleton parameter, the expression is as follows:

[0080] (5)

[0081] (6)

[0082] (7)

[0083] in, The collision frequency between free electrons and ions. The plasma angular frequency, It is the angular frequency of the radio wave. It is the gyrofrequency. It is the unit vector representing the direction of the Earth's magnetic field.

[0084] The physics decoding module establishes a mapping relationship from the electron density profile to the virtual height trajectory using a simplified propagation expression, while neglecting the effects of collisions and the geomagnetic field, that is, letting =0 and =0. The simplified AH formula expression is:

[0085] (8)

[0086] in, The refractive index of the plasma, For plasma frequency distribution, It represents the radio wave frequency.

[0087] The formula for calculating plasma frequency is:

[0088] (9)

[0089] in, For plasma frequency distribution, The restored electron density profile, in meters. -3 , The value of electron charge is... C, Denotes the free space permittivity, its value is F / m, Represents the electron mass, its value is kg.

[0090] The corresponding expression for the virtual high integral is:

[0091] (10)

[0092] in, The trajectory is artificially inflated based on simplified propagation expressions. The height of the bottom of the ionosphere. The height of the point where the radio wave is reflected. It represents the radio wave frequency.

[0093] Building upon the simplified propagation relationship described above, gating units and smoothing units are further introduced to process the propagation conditions continuously, enabling the aforementioned propagation mapping to participate in end-to-end training of the neural network. The gating unit function is defined as follows:

[0094] (11)

[0095] in, For gated unit functions, For the gate slope parameter, The Sigmoid function has the following expression:

[0096] (12)

[0097] Define the smoothing unit function as follows:

[0098] (13)

[0099] in, For smoothing unit functions, To prevent the smoothing constant from having a denominator of 0, it is preferable to take 1e. -4 The Softplus function expression is:

[0100] (14)

[0101] Therefore, the expression for the virtual high integral can be represented as:

[0102] (15)

[0103] in, To reconstruct the virtual height trajectory based on simplified propagation representation, gating units, and smoothing units, For gated unit functions, For smoothing unit functions, The height of the bottom of the ionosphere is preferably 90 km. The upper limit of the integration altitude is preferably set at 500km.

[0104] Step S26: Calculate the profile supervision loss between the predicted results of the logarithmic profile of electron density and the label of the logarithmic profile of electron density, the attention prior constraint loss between the frequency attention weight map and the frequency prior distribution curve, and the physical consistency loss between the reconstructed illusory height trajectory and the observed illusory height vector, and construct a joint loss function to train the network.

[0105] In step S26, the profile supervision loss between the predicted profile (i.e., the predicted result of the logarithmic electron density profile in step S25) and the reference profile (i.e., the logarithmic electron density profile label on the fixed-height grid in step S22) is calculated. Attention prior constraint loss between the frequency attention weight map and the frequency prior distribution curve And the physical consistency loss between the reconstructed virtual height trajectory and the observed virtual height vector. A joint loss function was constructed to train the vertical frequency and height map inversion model.

[0106] The profile supervision loss function is expressed as follows:

[0107] (16)

[0108] in, For profile monitoring loss, Indicates a grid point at a fixed height. The predicted logarithmic profile of the electron density at the location is predicted to be... This indicates the corresponding reference label (i.e., the label of the logarithmic electron density profile on a fixed-height grid). ), This indicates the number of grid points at a fixed height.

[0109] The expression for the attention prior constraint loss function is:

[0110] (17)

[0111] in, For attention prior constraint loss, This represents the frequency attention weight map output by the frequency attention module. Represents the frequency prior distribution curve. For fixed frequency grid length, For grid index variables.

[0112] The physical consistency loss function is expressed as follows:

[0113] (18)

[0114] in, For physical consistency loss, The total number of effective frequency points, The reconstructed virtual height trajectory vector output by the physical decoding module (and the reconstructed virtual height trajectory in formula (15)) Equivalent, (This is to distinguish the observed virtual height vector) For the observation of the virtual height vector (i.e., the observation of the virtual height vector on a fixed frequency grid) ), To prevent constants with a denominator of 0.

[0115] The joint loss function is expressed as follows:

[0116] (19)

[0117] in, For joint losses, For profile monitoring loss, For attention prior constraint loss, For physical consistency loss, To determine the optimal weights for the loss based on attention prior constraints, the following selection is made: , To compensate for the physical consistency loss weights, a warm-up and ramp-up strategy is adopted, where the weights are set to 0 for the first few training rounds and then gradually increased to the maximum value over a preset number of rounds. .

[0118] In this embodiment, the vertical frequency-height map inversion model is trained using a mini-batch iterative method, with a batch size of 64 and an initial learning rate of [value missing]. The training rounds were set to 150, and the optimizer used the Adam optimization algorithm.

[0119] Finally, the vertical frequency-height map observation data to be inverted is preprocessed in the same way as in the training phase and then input into the trained model. The corresponding logarithmic electron density profile is output, and ionospheric characteristic parameters are further extracted. Based on the predicted electron density profile, the peak height of the F2 layer of the ionosphere can be extracted. and critical frequency Key parameters, etc. Among them, This represents the height position at which the electron density profile reaches its peak, in kilometers. This is the critical frequency of the F2 ionosphere. The peak electron density is calculated using the plasma frequency formula, and the corresponding calculation expression is:

[0120] (20)

[0121] in, This represents the peak electron density of the F2 layer of the ionosphere, in meters. -3 , The value of electron charge is... C, Denotes the free space permittivity, its value is F / m, Represents the electron mass, its value is kg.

[0122] The inversion method of this invention utilizes the strong feature extraction and large-scale sample learning capabilities of deep learning. By introducing a frequency attention module, a residual backbone network, and a physical decoding module, and under the combined effects of profile supervision constraints, frequency prior constraints, and physical consistency constraints, it achieves fine inversion of the electron density profile and extraction of ionospheric feature parameters from vertical frequency height maps. Its effectiveness can be seen from... Figure 7 and Figure 8 The comparison results show that... Figure 7 This is a comparison diagram of the inverted electron density profile and the reference tag profile in an embodiment of the present invention. One curve represents the inverted profile obtained by the method described in the present invention, and the other curve represents the reference tag profile. Figure 7It can be seen that the method described in this invention can reconstruct the overall shape and peak position of the electron density profile well, reflecting the distribution characteristics of the ionospheric electron density along the height direction. Figure 8 Ionospheric characteristic parameters in embodiments of the present invention , A scatter plot comparing the data points, where the horizontal axis represents the reference value and the vertical axis represents the predicted value obtained by the method described in this invention. Figure 8 As can be seen, the scattered points are generally distributed near the diagonal, indicating that the method described in this invention can accurately invert key parameters of the ionosphere, and has good accuracy and reliability.

[0123] Based on the same technical concept as the foregoing embodiments, the present invention also provides a vertical frequency-height map inversion system based on a physical guided neural network, comprising: a vertical frequency-height map observation data acquisition module, used to acquire vertical frequency-height map observation data to be inverted; an electron density logarithmic profile acquisition module, used to input the vertical frequency-height map observation data to be inverted into a trained vertical frequency-height map inversion model, and output the corresponding electron density logarithmic profile; wherein, the training of the vertical frequency-height map inversion model includes: acquiring and preprocessing the vertical frequency-height map observation data and electron density profile label data to construct an observation virtual height vector on a fixed frequency grid and an electron density logarithmic profile label on a fixed height grid; training the constructed vertical frequency-height map inversion model based on the vertical frequency-height map observation data, the observation virtual height vector, and the electron density logarithmic profile label, including: according to the vertical frequency-height map observation data, the observation virtual height vector, and the electron density logarithmic profile label, the training includes: according to the vertical frequency-height map observation data, the observation virtual height vector, and the electron density logarithmic profile label, the training includes: according to the vertical frequency-height map observation data, the training module ... The frequency prior distribution curve corresponding to the observed frequency support is constructed from the frequency measurement height map observation data. Based on the observed virtual height vector and the electron density logarithmic profile label, the frequency attention module and residual backbone network are used to obtain the frequency attention weight map and the electron density logarithmic profile prediction results on the fixed height grid. The electron density logarithmic profile prediction results are input into the physical decoding module, and the reconstructed virtual height trajectory is obtained by sequentially performing electron density recovery, plasma frequency calculation, propagation relationship construction, and integration along the height direction. The profile supervision loss between the electron density logarithmic profile prediction results and the electron density logarithmic profile label, the attention prior constraint loss between the frequency attention weight map and the frequency prior distribution curve, and the physical consistency loss between the reconstructed virtual height trajectory and the observed virtual height vector are calculated respectively, and a joint loss function is constructed to train the vertical frequency measurement height map inversion model.

[0124] In summary, this invention belongs to the field of geophysics and ionospheric detection technology, specifically relating to a vertical frequency-height map inversion method based on a physics-guided neural network. The method includes the following steps: First, acquiring vertical frequency-height map observation data and its corresponding electron density profile label data to construct trace-profile paired samples; then, preprocessing the original trace data and profile label data to construct a virtual height vector input on a fixed frequency grid and an electron density logarithmic profile label on a fixed height grid; next, constructing an effective frequency mask and frequency prior distribution curve based on the original trace data, and inputting the normalized virtual height vector into a frequency attention module and a residual backbone network to obtain the electron density logarithmic profile prediction result; subsequently, inputting the predicted profile into a physics decoding module, obtaining the reconstructed virtual height trajectory through electron density recovery, plasma frequency calculation, propagation relationship construction, and integration along the height direction; further, constructing a joint loss function composed of profile supervision loss, attention prior constraint loss, and physical consistency loss to train the network; finally, inputting the vertical frequency-height map to be inverted into the trained model, outputting the corresponding electron density logarithmic profile, and extracting ionospheric feature parameters. This method can improve the physical consistency and inversion accuracy of the vertical frequency height map inversion results, enhance the ability to extract information in key frequency regions, and achieve accurate inversion of ionospheric electron density profiles and their characteristic parameters.

[0125] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the technical solutions of the embodiments of the present invention.

Claims

1. A method for inverting vertical frequency-elevation maps based on a physically guided neural network, characterized in that, include: Obtain the vertical frequency-elevation map observation data to be inverted; The vertical frequency-elevation map observation data to be inverted is input into the trained vertical frequency-elevation map inversion model, which outputs the corresponding logarithmic electron density profile; wherein, the training of the vertical frequency-elevation map inversion model includes: Acquire vertical frequency-height map observation data and electron density profile label data and preprocess them to construct observation virtual height vectors on fixed frequency grids and electron density logarithmic profile labels on fixed height grids; Based on the vertical frequency-height map observation data, the observed virtual height vector, and the logarithmic profile label of the electron density, the constructed vertical frequency-height map inversion model is trained, including: Based on the vertical frequency elevation map observation data, construct a frequency prior distribution curve corresponding to the observed frequency support situation; Based on the observed virtual height vector and the electronic density log profile label, the frequency attention module and the residual backbone network are used to obtain the frequency attention weight map and the electronic density log profile prediction results on the fixed height grid. The predicted results of the logarithmic profile of electron density are input into the physical decoding module, and the reconstructed virtual height trajectory is obtained by sequentially performing electron density recovery, plasma frequency calculation, propagation relationship construction, and integration along the height direction. The profile supervision loss between the predicted results of the logarithmic profile of electron density and the label of the logarithmic profile of electron density, the attention prior constraint loss between the frequency attention weight map and the frequency prior distribution curve, and the physical consistency loss between the reconstructed dummy height trajectory and the observed dummy height vector are calculated respectively. A joint loss function is then constructed to train the vertical frequency height map inversion model.

2. The vertical frequency-elevation map inversion method based on a physically guided neural network as described in claim 1, characterized in that, Based on the vertical frequency elevation map observation data, a priori frequency distribution curve corresponding to the observed frequency support is constructed, including: Construct an effective frequency mask based on the frequency coverage range of the vertical frequency elevation map observation data; Calculate the distance from each fixed frequency point to the corresponding nearest original observation frequency point, and construct an effective sample mapping based on the distance; The effective mapping of the sample is multiplied by the effective frequency mask, and the average is calculated and normalized along the sample dimension to obtain the frequency prior distribution curve.

3. The vertical frequency-elevation map inversion method based on a physically guided neural network as described in claim 1, characterized in that, Based on the observed virtual height vector and the electronic density logarithmic profile label, a frequency attention module and a residual backbone network are used to obtain the frequency attention weight map and the electronic density logarithmic profile prediction results on a fixed-height grid, including: The virtual height vector on the fixed frequency grid and the logarithmic profile label of the electron density on the fixed height grid are normalized to obtain normalized data; The normalized data is assembled into a network input tensor and then input into the frequency attention module to generate a frequency attention weight map through frequency-dimensional convolution and nonlinear transformation. The frequency attention weight map is multiplied element-wise with the input dummy height vector to obtain the weighted input features; The weighted input features are input into the residual backbone network to extract deep features and output the prediction results of the logarithmic profile of electron density on a grid with a fixed height.

4. The vertical frequency-elevation map inversion method based on a physically guided neural network as described in claim 1, characterized in that, include: The predicted result of the logarithmic profile of the electron density is input into the physical decoding module. Through sequential electron density recovery, plasma frequency calculation, propagation relationship construction, and integration along the height direction, the reconstructed virtual height trajectory is obtained, including: The predicted results of the logarithmic profile of electron density are denormalized to restore the true physical order of the predicted results of the logarithmic profile of electron density. Based on the predicted results of the recovered logarithmic electron density profile, the plasma frequency distribution is obtained; Based on the plasma frequency distribution, the propagation relationship is constructed using a simplified propagation expression to obtain the plasma refractive index; A gating unit and a smoothing unit are introduced to process the propagation conditions in the plasma refractive index continuously, and the plasma refractive index after continuous processing is integrated along the height direction to obtain the reconstructed virtual height trajectory.

5. The vertical frequency-elevation map inversion method based on a physically guided neural network as described in claim 4, characterized in that, By constructing the propagation relationship using a simplified propagation expression, the plasma refractive index is obtained, and the corresponding formula is: ， ， in, The trajectory is artificially inflated based on simplified propagation expressions. The refractive index of the plasma, The height of the bottom of the ionosphere. The height of the point where the radio wave is reflected. For radio wave frequency, For plasma frequency distribution, The predicted results are the logarithmic profile of the recovered electron density. The amount of electron charge. Represents the free space dielectric constant. Indicates electron mass.

6. The vertical frequency-elevation map inversion method based on a physically guided neural network as described in claim 5, characterized in that, A gating unit and a smoothing unit are introduced to perform continuous processing on the propagation conditions in the plasma refractive index. The continuous plasma refractive index is then integrated along the height direction to obtain the reconstructed virtual height trajectory. The corresponding formula is: ， ， ， in, To reconstruct the virtual height trajectory based on simplified propagation representation, gating units, and smoothing units, For gated unit functions, For smoothing unit functions, This is the maximum height for the points. For the gate slope parameter, For the Sigmoid function, This is the smoothing constant.

7. The vertical frequency-elevation map inversion method based on a physically guided neural network as described in claim 1, characterized in that, The joint loss function is expressed as follows: ， ， ， ， in, For joint losses, For profile monitoring loss, For attention prior constraint loss, For physical consistency loss, Weights are assigned to the loss based on attention prior constraints. Weights for physical consistency loss. Indicates a grid point at a fixed height. The predicted logarithmic value of the electron density at that location. Indicates the corresponding reference label, Indicates the number of grid points at a fixed height. This represents the attention weights output by the frequency attention module. Represents the frequency prior distribution curve. For fixed frequency grid length, For grid index variables, The total number of effective frequency points, The reconstructed virtual height trajectory vector output by the physical decoding module. To observe the virtual height vector, This is the smoothing constant.

8. The vertical frequency-elevation map inversion method based on a physically guided neural network as described in claim 1, characterized in that, The frequency attention module includes a first convolutional layer, a second convolutional layer, a third convolutional layer, a first activation layer, a second activation layer, and a third activation layer. The first and second convolutional layers are 7×1 convolutional layers, the third convolutional layer is a 1×1 convolutional layer, the first and second activation layers are both ReLU activation layers, and the third activation layer is a Sigmoid activation layer.

9. The vertical frequency-elevation map inversion method based on a physically guided neural network as described in claim 1, characterized in that, The residual backbone network comprises an input feature extraction module, a first residual module, a first pooling layer, a second residual module, a third residual module, a fourth residual module, a global average pooling layer, a first fully connected layer, a fourth activation layer, a Dropout layer, and a second fully connected layer. The input feature extraction module includes a fourth convolutional layer, a batch normalization layer, and a fifth activation layer. The fourth convolutional layer is a 7×1 convolutional layer, and both the fourth and fifth activation layers are ReLU activation layers. The input feature extraction module has 32 output channels. The first residual module maps from 32 to 64 channels, the second residual module maps from 64 to 128 channels, the third residual module maps from 128 to 256 channels, and the fourth residual module maps from 256 to 512 channels. The first fully connected layer has an output dimension of 512, and the second fully connected layer has an output dimension of a fixed-height grid length.

10. A vertical frequency-elevation map inversion system based on a physically guided neural network, characterized in that, include: The vertical frequency and height map observation data acquisition module is used to acquire the vertical frequency and height map observation data to be inverted; The electron density logarithmic profile acquisition module is used to input the vertical frequency-height map observation data to be inverted into the trained vertical frequency-height map inversion model and output the corresponding electron density logarithmic profile. The training of the vertical frequency-height map inversion model includes: acquiring and preprocessing the vertical frequency-height map observation data and electron density profile label data to construct observation virtual height vectors on a fixed frequency grid and electron density logarithmic profile labels on a fixed height grid; training the constructed vertical frequency-height map inversion model based on the vertical frequency-height map observation data, observation virtual height vectors, and electron density logarithmic profile labels, including: constructing a frequency prior distribution curve corresponding to the observation frequency support based on the vertical frequency-height map observation data; and training the model based on the observation virtual height vectors. The frequency attention module and residual backbone network are used to obtain the frequency attention weight map and the predicted electron density log profile on a fixed height grid, along with the electron density log profile label. The predicted electron density log profile is then input into the physical decoding module, which sequentially performs electron density recovery, plasma frequency calculation, propagation relation construction, and integration along the height direction to obtain the reconstructed virtual height trajectory. The profile supervision loss between the predicted electron density log profile and the electron density log profile label, the attention prior constraint loss between the frequency attention weight map and the frequency prior distribution curve, and the physical consistency loss between the reconstructed virtual height trajectory and the observed virtual height vector are calculated respectively. A joint loss function is then constructed to train the vertical frequency height map inversion model.

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