Lightning very low frequency electromagnetic wave signal up-sampling method based on gan, terminal and medium

Abstract

The present application relates to the technical field of lightning signal sampling, and discloses a lightning very low frequency electromagnetic wave signal up-sampling method based on GAN, a terminal and a medium. The method pre-processes lightning very low frequency low-sampling signals and real high-sampling signals; constructs a generative adversarial network; a generator is used to extract initial features from the low-sampling signals and perform residual reinforcement, and then through a feature-guided dynamic interpolation mechanism, the low-sampling features after residual reinforcement are mapped to a high-sampling dimension, and the intermediate features after interpolation are corrected and signal-mapped to obtain a reconstructed signal matching a target high-sampling rate; a discriminator is used to determine the authenticity probability of the reconstructed signal; after the generator and the discriminator are jointly trained in an alternating update mode of the discriminator loss and the generator loss, the newly input low-sampling signals are pre-processed, and the corresponding reconstructed signals are output by the generator. The present application realizes accurate reconstruction of lightning very low frequency low-sampling signals into high-sampling signals.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of lightning signal sampling, in particular to a lightning VLF electromagnetic wave signal up-sampling method based on GAN, a terminal and a medium. BACKGROUND

[0002] The VLF (Very Low Frequency) electromagnetic wave signals (3-30 kHz) generated by lightning play a key role in lightning monitoring and research due to their unique long-distance propagation characteristics. Lightning VLF positioning systems usually use the time difference method for precise positioning, which requires large-scale deployment of observation sites to achieve ideal positioning accuracy. However, high sampling rate VLF acquisition equipment with high cost seriously restricts the large-scale construction of lightning monitoring networks. In contrast, using low sampling rate equipment can reduce system costs, but the collected waveforms will lose key details such as microsecond-level changes in the backstroke process and waveform oscillation details. If advanced signal processing techniques can restore the waveforms collected by low sampling rate equipment to high sampling rate levels, not only can the system construction cost be significantly reduced, but also the historical data of the existing large number of low sampling rate observation equipment can be fully utilized. This technical breakthrough is of great significance to improving the coverage and positioning accuracy of lightning monitoring networks, and can also provide higher quality waveform data for lightning physics research.

[0003] In the field of lightning VLF signal processing, traditional methods are mainly divided into time domain processing and frequency domain processing:

[0004] 1. Time domain processing methods are typically represented by linear interpolation and cubic spline interpolation. This type of method achieves up-sampling by directly fitting the signal sampling points in the time dimension, with the core advantage of simple calculation logic, strong real-time performance, and the ability to quickly complete the preliminary expansion of the signal. However, its essence is to construct a fitting model based on the assumption of "local smooth changes" of the signal. For the unique μs-level steep rising edge in lightning VLF signals (such as the backstroke pulse front), it is difficult to capture its instantaneous mutation characteristics, which can easily lead to the "flattening" of the waveform front. For the oscillation decay process after the pulse, it is also difficult to restore the detailed characteristics of high-frequency oscillation, often resulting in waveform smoothing, oscillation amplitude distortion, and other problems.

[0005] 2. The frequency domain processing method uses Fourier reconstruction and wavelet transform as the main means. It converts the signal to the frequency domain, supplements the high-frequency components, and then inversely transforms it back to the time domain to realize upsampling. In theory, it can restore the high-frequency information of the signal to some extent. However, the underlying logic of this method relies on "signal stationarity" and "linear superposition principle". However, lightning VLF signals are typical nonlinear and non-stationary transient signals. Their frequency components change dramatically during the discharge process (such as the leader-return stroke transition), and the energy distribution has a strong time-varying characteristic. This leads to the introduction of false frequency components when processing, resulting in significant errors in the recovery of key physical parameters such as rising edge time and peak amplitude, and even distorting the true electromagnetic radiation characteristics of the discharge process.

[0006] In summary, the existing technology has problems such as high cost, insufficient precision, loss of details, and signal distortion in upsampling lightning VLF signals, making it difficult to meet the high-precision reconstruction requirements of lightning signals. SUMMARY

[0007] To solve the technical problems existing in the prior art, the present application provides a lightning VLF electromagnetic wave signal upsampling method based on GAN, terminal and medium, which uses a generative adversarial network, especially the learnable interpolation and residual structure in the generator, to realize accurate reconstruction of lightning VLF low-sampling signals to high-sampling signals.

[0008] To achieve the above-mentioned purpose, the present application provides the following technical solutions:

[0009] The present application discloses a lightning VLF electromagnetic wave signal upsampling method based on GAN, comprising the following steps, i.e. S1~S4.

[0010] S1. Time alignment and normalization preprocessing of lightning VLF low-sampling signals and real high-sampling signals to form a training sample pair.

[0011] S2. Construct a generative adversarial network composed of a generator and a discriminator; wherein the generator is used to extract initial features from the low-sampling signal and perform residual reinforcement, and then map the residual reinforced low-sampling features to the high-sampling dimension through a feature-guided dynamic interpolation mechanism, and correct and map the interpolated intermediate features to obtain a reconstructed signal matching the target high-sampling rate; the discriminator is used to receive the reconstructed signal and the corresponding real high-sampling signal in the training sample pair, based on convolution feature extraction and dimension compression, to determine the authenticity probability of the reconstructed signal.

[0012] S3. Based on the training sample pair, the generator and the discriminator are jointly trained in an alternating update mode of discriminator loss and generator loss.

[0013] S4. After training is completed, the newly input low-sampled signal is preprocessed according to step S1, and the corresponding reconstructed signal is output through the generator.

[0014] As a further improvement to the above scheme, in step S2, a one-dimensional convolutional layer is used to extract features from the low-sampled signal; wherein, the kernel size of the one-dimensional convolutional layer is 7 to fully capture the local morphology of a single lightning pulse; the stride of the one-dimensional convolutional layer is 1 to ensure that the convolutional operation does not lose temporal information; the output channels of the one-dimensional convolutional layer are 64 to expand the original one-dimensional low-sampled signal into 64-dimensional initial features; the activation function is LeakyReLU with a slope of 2.

[0015] As a further improvement to the above scheme, in step S2, three cascaded residual blocks are used, and feature transfer is enhanced through a skip connection mechanism; wherein, the structural expression of each residual block is:

[0016] ;

[0017] In the formula, For the first i The output characteristics of each residual block i ∈[1,3], The initial feature; This represents a one-dimensional convolution, where both convolutional layers have a kernel size of 3 and a stride of 1. The first convolutional layer is used to process the input features. Refined extraction is performed to capture the steep changes at the pulse edge; the LeakyReLU activation function introduces a nonlinear transformation to simulate the nonlinear discharge characteristics of lightning signals; the second convolutional layer is used to map the features back to the same dimension as the input features, ensuring that they can be directly added to the input features.

[0018] As a further improvement to the above scheme, in step S2, the process of mapping the residual-enhanced low-sampling features to the high-sampling dimension through the feature-guided dynamic interpolation mechanism is expressed by the following formula:

[0019] ;

[0020] In the formula, These are intermediate features after interpolation. The intermediate features after interpolation at the interpolation point n The value at that location, n =1,…,N; N is the sampling rate amplification factor, and its length is matched with the target high sampling rate signal; j The neighborhood context index offset representing the interpolation position; These are the interpolation parameters learned by the model, used to determine the interpolation strategy under different feature patterns; Indicates rounding down; The residual reinforced low sampling feature; The interpolation point n corresponding in size.

[0021] As a further improvement of the above scheme, in step S2, the specific process of correcting and signal mapping the interpolated intermediate feature includes:

[0022] The interpolated intermediate feature Performing one-dimensional convolution operation to correct the local inconsistency that may occur in the interpolation process, and the expression formula is:

[0023] ;

[0024] In the formula, is the corrected feature; LeakyReLU represents an activation function with a slope of 2; represents one-dimensional convolution, the convolution kernel size of which is 3 and is used to capture local temporal correlation, the step is 1, and the output channel is 64.

[0025] The output convolution layer is used to map the feature back to the signal domain, and the output range is constrained through the tanh activation function to obtain the reconstructed signal matching the target high sampling rate , which has a length of N times that of the low sampling signal, and the expression formula is:

[0026] ;

[0027] In the formula, the convolution kernel size of the output convolution layer is 7, the step is 1, and the output channel is 1.

[0028] As a further improvement of the above scheme, the specific process of the discriminator determining the authenticity probability of the reconstructed signal includes:

[0029] The reconstructed signal output by the generator and the corresponding real high sampling signal are used as input signals, and three one-dimensional convolutions are used to realize feature extraction and dimension compression of the input signals, and gradually capture the local and global features of the input signals, and the expression formula is as follows:

[0030] ;

[0031] ;

[0032] ;

[0033] In the formula, z is the input signal; 、 and are the outputs of the three one-dimensional convolutions in turn; represents one-dimensional convolution, the convolution kernel size of three one-dimensional convolutions is 5 to adapt to the pulse width, the step is set to 2 to compress the time dimension, and the number of channels is 64, 128 and 256 in turn to depict complex features; LeakyReLU represents an activation function with a slope of 0.2, which is used to activate and retain weak oscillation information.

[0034] Combined with the convolution layer and the Sigmoid activation function, the probability of the authenticity of the output reconstructed signal is:

[0035] ;

[0036] In the formula, p∈[0, 1] represents the authenticity probability of the reconstructed signal; represents a Sigmoid activation function.

[0037] As a further improvement of the above scheme, in step S3, in the alternating update mode, the discriminator is updated preferentially, the generator is updated with a lag, and the double loss function is optimized collaboratively. In the training, the loss trend and the waveform quality of the validation set are monitored, the model is saved once every several rounds, and the optimal version is finally selected.

[0038] In the training phase of the discriminator:

[0039] First, the real high-sampling signal in the training sample pair is input into the discriminator to obtain the probability , so as to calculate the real signal loss . The goal of this loss is to make the probability close to 1, that is, to determine it as real; wherein represents the mathematical expectation.

[0040] Subsequently, the reconstructed signal output by the generator is input into the discriminator, and the generator parameters are frozen to avoid gradient interference, to obtain the probability , so as to calculate the generated signal loss . The goal of this loss is to make the probability close to 0, that is, to determine it as fake.

[0041] The average value of the real signal loss and the generated signal loss is taken as the total loss of the discriminator, and the parameters are updated by the Adam optimizer.

[0042] In the training phase of the generator:

[0043] The reconstructed signal is re-input into the discriminator to obtain the probability , so as to calculate the adversarial loss . The goal of this loss is to make the probability close to 1 to mislead the discriminator.

[0044] The L1 loss is used to measure the waveform detail difference The loss is used to constrain the error of key features.

[0045] The weighted sum of the adversarial loss and the content loss is taken as the total loss of the generator, and the parameters are updated by the Adam optimizer.

[0046] As a further improvement of the above scheme, in step S1, after the low sampling signal and the real high sampling signal are time-aligned and normalized, the low sampling signal and the real high sampling signal are also cut into sub-sequences of fixed length, and each sub-sequence of the low sampling signal and the corresponding sub-sequence of the real high sampling signal form a training sample pair, and a 50% overlap rate is used when cutting; finally, all the training sample pairs are divided into a training set for learning model parameters, a validation set for adjusting hyperparameters in the training process, and a test set for evaluating the final reconstruction effect according to a set proportion, and batch reading and parallel processing are realized through a data loader.

[0047] In step S4, the reconstructed signal is also subjected to an inverse normalization operation.

[0048] The application also discloses a computer terminal, which comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the steps of the GAN-based lightning VLF electromagnetic wave signal up-sampling method when executing the computer program.

[0049] The application also discloses a computer-readable storage medium, which stores a computer program, and the program is executed by a processor to implement the steps of the GAN-based lightning VLF electromagnetic wave signal up-sampling method.

[0050] Compared with the prior art, the application has the following beneficial effects:

[0051] The application can adaptively maintain the transient pulse characteristics and high-frequency details in the up-sampling process of the low sampling rate lightning VLF electromagnetic wave signal by introducing the combination design of the learnable interpolation and the convolution correction in the generator of the generative adversarial network, effectively overcomes the waveform smoothing distortion caused by the traditional time domain interpolation method and the defect of introducing false frequency components by the frequency domain reconstruction method, and significantly improves the accuracy of the reconstructed signal in the key physical parameters such as the pulse rising edge slope and the peak amplitude, thereby solving the technical problem that it is difficult to obtain a high-resolution lightning signal under low-cost acquisition conditions. In addition, the application further improves the performance of the model in detail preservation, global trend consistency and adaptability to different sampling rate amplification multiples through the cooperation design of residual feature enhancement, adversarial training optimization and discriminator authenticity discrimination, so that the reconstructed signal can balance the physical authenticity and the detail restoration accuracy, and has good applicability and expansibility. BRIEF DESCRIPTION OF DRAWINGS

[0052] Figure 1 The flow chart of the GAN-based lightning VLF electromagnetic wave signal up-sampling method in Embodiment 1 of the present application.

[0053] Figure 2 The architecture diagram of the generative adversarial network in Embodiment 1 of the present application.

[0054] Figure 3 The comparison chart of the original high-resolution lightning signal and the down-sampled low-resolution signal in Embodiment 1 of the present application.

[0055] Figure 4 The comparison chart of the original high-resolution lightning signal and the GAN reconstructed lightning signal in Embodiment 1 of the present application.

[0056] Figure 5 The comparison chart of the original high-resolution lightning signal and the linear interpolation algorithm reconstructed lightning signal in Embodiment 1 of the present application.

[0057] Figure 6 The comparison chart of the original high-resolution lightning signal and the cubic spline interpolation algorithm reconstructed lightning signal in Embodiment 1 of the present application.

[0058] Figure 7 The comparison chart of the original high-resolution lightning signal and the sinc interpolation algorithm reconstructed lightning signal in Embodiment 1 of the present application.

[0059] Figure 8 The comparison chart of the original high-resolution lightning signal and the frequency domain zero padding algorithm reconstructed lightning signal in Embodiment 1 of the present application.

[0060] Figure 9 The structural schematic diagram of the computer terminal in Embodiment 2 of the present application. DETAILED DESCRIPTION

[0061] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the present application.

[0062] Embodiment 1

[0063] Please refer to Figure 1 The present embodiment provides a GAN-based lightning VLF electromagnetic wave signal up-sampling method, which comprises the following steps, i.e. S1-S4.

[0064] S1. Time alignment and normalization preprocessing of the lightning VLF low-sampling signal and the real high-sampling signal to form a training sample pair.

[0065] Data preprocessing is a prerequisite for the reconstruction of lightning VLF electromagnetic waves with high resolution, responsible for converting raw observation data into standardized samples that meet the model input requirements, directly affecting the subsequent reconstruction accuracy. The core goal is to eliminate data noise, unify format differences, and establish an accurate correspondence between low-sampling rate signals and high-sampling rate signals. The specific process is as follows:

[0066] First, load and align the original data. The input data comes from the VLF signals collected by lightning monitoring equipment, including two key data types: low-sampling rate signals (time T corresponds to the actual observation time) and high-sampling rate signals in the same scenario. By customizing a class to read the original data file in HDF5 format (a format suitable for storing large-scale scientific data), and based on the timestamp, the strict alignment of the two types of signals is completed, ensuring that each sampling point of the low-sampling signal can find the corresponding time interval in the high-sampling signal, avoiding training bias caused by time sequence misalignment.

[0067] Then, normalize the signals. The signal amplitudes of different lightning events vary greatly (from a few millivolts to several volts), so to avoid model bias caused by amplitude differences, all signals need to be compressed to the [-1, 1] interval, with the formula:

[0068] ;

[0069] where is the normalized signal; min(x) and max(x) represent the minimum and maximum values of the original signal, respectively. This step ensures that the model focuses on the waveform characteristics of the signal (such as pulse shape, timing changes) rather than the absolute amplitude.

[0070] Finally, complete sample blocking and dataset division. Since the length of the original lightning signal is variable (from tens of milliseconds to hundreds of milliseconds), it needs to be cut into fixed-length subsequences, with each subsequence forming a training sample pair . A 50% overlap rate is used during blocking to avoid truncating transient pulse characteristics. Finally, all samples are divided into training sets (used for model parameter learning), validation sets (used for hyperparameter adjustment during training), and test sets (used to evaluate the final reconstruction effect) in a ratio of 8:1:1, and batch reading and parallel processing are achieved through a data loader (DataLoader) to improve training efficiency.

[0071] Through the above pretreatment, the original observation data is transformed into standardized and high-quality input samples, providing a reliable foundation for subsequent feature learning and high-resolution reconstruction of the generator.

[0072] S2. Construct a generative adversarial network composed of a generator and a discriminator.

[0073] The generator is the core component for realizing the reconstruction of low-sampling-rate lightning VLF signals into high-sampling-rate signals. The feature extraction and strengthening module is responsible for mining key signal features (such as pulse shape and timing change rule) from low-resolution inputs to provide sufficient feature support for subsequent high-resolution reconstruction. This module solves the problem that traditional methods are difficult to capture nonlinear transient features of lightning signals through a progressive architecture of "initial feature extraction-residual deep strengthening". The specific process is as follows:

[0074] (1) Initial feature extraction

[0075] First, the original low-sampling signal is mapped to a high-dimensional feature space, completing the conversion from the "signal domain" to the "feature domain". The input is the normalized low-sampling signal , and the feature extraction is realized through a one-dimensional convolution layer (Conv1d), with the formula being:

[0076] ;

[0077] In the formula, the design of the convolution kernel size k=7 (i.e., covering 7 consecutive sampling points each time) is specifically aimed at the local correlation of lightning signals. The front width of a lightning pulse usually corresponds to 5-10 low-sampling points, and a convolution kernel of 7 sampling points can completely capture the local morphology of a single pulse; the step size s=1 ensures that the convolution operation does not lose timing information; and the output channel number c=64 expands the original 1-dimensional signal to 64-dimensional features, realizing a leap in feature dimension.

[0078] The activation function uses LeakyReLU (slope α =0.2) instead of traditional ReLU, because there are a large number of weak secondary pulses (with an amplitude of only 1 / 10-1 / 5 of the main pulse) in lightning signals. LeakyReLU preserves a weak gradient for negative input (instead of directly setting it to zero), which can prevent these weak features from being completely suppressed during propagation. After processing by this submodule, the output feature contains both the global trend of the signal and the preliminary features of the local pulse.

[0079] (2) Residual feature strengthening

[0080] To further deepen feature learning and solve the problem of "feature decay" of deep network (i.e. when the number of network layers increases, the key features extracted early will gradually weaken), the sub-module adopts three residual blocks (ResidualBlock) in series, and strengthens feature transmission through a skip connection mechanism. The structure of each residual block is "convolution layer-activation function-convolution layer", and is directly added to the input feature, and the formula is:

[0081] ;

[0082] In the formula, is the output feature of the i-th residual block, i is the initial feature; the convolution kernel size of the two convolution layers is k=3, and the step is s=1; the first convolution layer is used for fine extraction of the input feature i to capture the steep changes of the pulse edge; the LeakyReLU activation function introduces a nonlinear transformation to simulate the nonlinear discharge characteristics of the lightning signal; the second convolution layer is used to map the features back to the same dimension as the input features to ensure that they can be directly added (skip connection). This design enables the network to focus on "feature residuals" (i.e. the difference between input and output) during learning, rather than absolute feature values, and is particularly suitable for capturing the relative relationship between strong and weak pulses in lightning signals. For example, when processing lightning waveforms containing a main pulse (strong signal) and subsequent oscillations (weak signal), the residual block can effectively amplify the weak signal features and avoid them being masked by the strong signal. After processing by three residual blocks, the output feature not only retains the key information of the initial feature, but also deepens the detailed description of the transient pulse (such as the pulse rising edge slope and oscillation period), providing a rich feature basis for subsequent learnable upsampling.

[0083] In the present application, the generator is also provided with a learnable upsampling mechanism, which is the core link for converting low sampling rate signals to high sampling rate signals. Through a feature-guided dynamic interpolation mechanism, the low-dimensional features after residual reinforcement are directly mapped to high-dimensional signal space, focusing on solving the distortion problem of traditional fixed interpolation methods in lightning pulse transient feature (such as steep front and rapid decay) reconstruction. The core design is to let the model learn the interpolation rule independently, rather than relying on pre-set mathematical formulas, so that the upsampling process can accurately adapt to the physical characteristics of lightning VLF signals. The module input is the low sampling feature after residual reinforcement (T is the length of the low sampling rate signal), and the output is a reconstructed signal matching the target high sampling rate. The specific process includes two key steps:

[0084]

[0085] ​​(1) Dynamic interpolation calculation

[0086] Based on the input features , the local context information is generated to generate interpolation weights, realizing the mapping from low sampling dimension to high sampling dimension. For each position point in the low sampling feature, the model dynamically determines the numerical weight of the point to be inserted by analyzing the neighborhood features (such as the amplitude change rate of multiple sampling points before and after, the pulse pattern). For example, in the steep rising edge area of the lightning pulse, the interpolation weight will tilt towards the pulse peak value, ensuring that the reconstructed rising edge slope is consistent with the true signal; while in the flat background noise area, a more uniform weight distribution is adopted to avoid introducing artifacts. This process is completely driven by the parameter learning of the neural network, and the formula can be expressed as:

[0087] ;

[0088] In the formula, is the interpolated intermediate feature, is the value of the interpolated intermediate feature at the interpolation point n , N is the sampling rate magnification (such as 10 times, 5 times, etc.), its length matches the target high sampling rate signal; n represents the neighborhood context index offset of the interpolation position; j is the interpolation parameter learned by the model, which is used to determine the interpolation strategy under different feature patterns. For each target position i, the model automatically learns the optimal contribution weight of each sampling point j in the neighborhood, j is randomly selected from -2, -1, 0, 1, 2 in the code, and then the value of is also different, W is actually a vector, w (n,j) is one of its elements; represents the floor function; is the low sampling feature after residual reinforcement; is the bias corresponding to the size of the interpolation point n , learned by the model, and the model finds the most appropriate bias size through continuous training.

[0089] (2) Feature correction and signal mapping

[0090] Perform one-dimensional convolution operation on the interpolated intermediate feature to correct the local inconsistency (such as amplitude jump of adjacent points) that may occur in the interpolation process, and the expression formula is:

[0091] ;

[0092] In the formula, LeakyReLU represents an activation function with a slope of 2; the convolution kernel size of this convolution is 3, which is used to capture local temporal correlation and ensure that the modified feature maintains the continuity of the overall waveform while preserving details. The convolution step size is 1, and the output channel is 64.

[0093] The output convolution layer maps the feature back to the signal domain, and the output range is constrained by the tanh activation function to obtain the reconstructed signal matching the target high sampling rate , which has a length of N times that of the low sampling signal, and the expression is:

[0094] ;

[0095] In the formula, the output convolution layer has a convolution kernel size of k = 7, a step size of s = 1, and an output channel of c = 1.

[0096] Through the learnable interpolation rule, the upsampling strategy can be adjusted adaptively according to the morphological characteristics of different lightning signals (such as single pulse, multi-pulse superposition), for example: whether it is a 10-fold amplification from 1MHz to 10MHz, or a 5-fold amplification from 2MHz to 10MHz, precise reconstruction can be achieved by adjusting the model parameters without changing the overall architecture.

[0097] The discriminator (Discriminator) is a core component in the generative adversarial network (Generative Adversarial Network, GAN) responsible for distinguishing the authenticity of signals. Its function is to perform binary classification on the input high sampling rate signal (generator reconstructed signal or real observed signal), output the probability that the signal is a "real signal", and optimize the generator output quality through a feedback mechanism. This module designs a special network structure for the transient pulse characteristics of lightning VLF signals (such as steep front, rapid decay), and the specific process is as follows: The discrimination process realizes feature compression and classification through multiple one-dimensional convolutions, and the specific process is as follows:

[0098] (1) Input processing

[0099] The input of the discriminator is two types of high sampling rate signals: the reconstructed signal output by the generator and the corresponding real high sampling signal (N is the amplification factor, T is the length of the low sampling signal). Both types of signals are normalized (amplitude range [-1, 1]) to ensure that the discrimination focuses on the waveform structure rather than the absolute amplitude.

[0100] (2) Feature extraction and compression

[0101] The feature extraction and dimension compression of the input signal are realized by three one-dimensional convolutions, and the local and global features of the input signal are gradually captured, and the expression formula is as follows:

[0102] ;

[0103] ;

[0104] ;

[0105] In the formula, z is the input signal; 、 and are the outputs of the three one-dimensional convolutions in turn; the design of each convolution is optimized for the characteristics of lightning signals: the convolution kernel size of the three one-dimensional convolutions is k=5 to adapt to the pulse width, the step size is set to s=2 to compress the time dimension (total compression ratio 8 times), and the number of channels is increased (64→128→256) to depict complex features. LeakyReLU represents an activation function with a slope of 0.2, which is used to activate and retain weak oscillation information.

[0106] (3) Real probability output

[0107] Combined with the convolution layer and the Sigmoid activation function, the authenticity probability of the reconstructed signal is output:

[0108] ;

[0109] In the formula, p∈[0,1] represents the authenticity probability of the reconstructed signal (p≈1 is true, and p≈0 is generated); represents the Sigmoid activation function.

[0110] The discriminator can simultaneously identify the global trend deviation and local detail defects (such as pulse peak shift) of the generated signal, provide accurate feedback to the generator, and ensure the physical authenticity of the reconstructed signal.

[0111] S3. Based on the training sample pair, the generator and the discriminator are jointly trained in an alternating update mode of discriminator loss and generator loss.

[0112] The adversarial training optimization module is the core training mechanism of the generative adversarial network. Through the dynamic game and alternating optimization of the generator and the discriminator, the goal of “generated signal approximating real signal” is realized. The training takes a batch of sample pairs as input (x is the low sampling signal, is the real high sampling signal), adopts an alternating mode of “discriminator priority update→generator lag update”, and cooperatively optimizes through double loss functions, considering both the physical authenticity and waveform detail accuracy of the signal.

[0113] The core of the discriminator training phase is to improve the ability to distinguish between real and fake signals. First, the real signal loss is calculated: the real high-sampled signal from the training sample pairs... Input discriminator to obtain probability Thus, the true signal loss can be calculated. The goal of this loss is to make the probability... If the value is close to 1, it is considered true; where This represents the mathematical expectation. Then, the generated signal loss is calculated: the reconstructed signal output from the generator. Input the discriminator and freeze the generator parameters to avoid gradient interference, and obtain the probability. Thus, the loss of the generated signal is calculated. The goal of this loss is to make the probability... A value close to 0 is considered false. The average of the loss of the real signal and the loss of the generated signal is used as the total loss of the discriminator. Through the Adam optimizer (learning rate 1e-4), β (1=0.5) Update parameters to enhance discrimination ability.

[0114] The generator training phase focuses on the dual objectives of "deceiving the discriminator" and "approximating the real waveform." One aspect involves calculating the adversarial loss: the reconstructed signal... Re-enter the discriminator to obtain the probability. To calculate the countermeasure loss The goal of this loss is to make the probability... Approaching 1 can mislead the discriminator. On the other hand, content loss is calculated: L1 loss is used to measure waveform detail differences, and content loss is calculated. The focus is on constraining errors in key features such as pulse peak value and rising edge slope. The generator's total loss is a weighted sum of these two factors. A content loss weight of 100 is applied to enhance detail accuracy, and parameters are updated using the same optimizer. During training, the loss trend and validation set waveform quality are monitored, and the model is saved every 10 epochs, with the optimal version ultimately selected.

[0115] S4. After training is completed, the newly input low-sampled signal is preprocessed according to step S1, and the corresponding reconstructed signal is output through the generator.

[0116] After training, the newly input low-sampled signal undergoes the same preprocessing (normalization, block division) as the training data, and the normalized reconstructed signal is obtained through forward propagation by the generator. To recover the actual physical meaning of the signal, an inverse normalization operation needs to be performed:

[0117] ;

[0118] The final output high-resolution signal The transient pulse characteristics (such as front steepness and peak amplitude) of the lightning very low frequency signal are retained, and can be directly used for lightning physical analysis or positioning calculation.

[0119] In summary, the flowchart of the lightning very low frequency electromagnetic wave signal up-sampling method based on GAN disclosed in the present application solves the inherent defects of the traditional fixed interpolation method in lightning very low frequency signal up-sampling through the customizable design of the learnable interpolation in the generator, and breaks through the technical barriers of GAN migration from two-dimensional images to one-dimensional signals. The traditional fixed interpolation (such as linear and bilinear) method has poor adaptability to the transient pulse characteristics of the lightning signal, and is prone to smoothing distortion at key positions such as pulse front and peak, and cannot restore the steep changes in the discharge process. When the up-sampling mechanism in the image field (such as transposed convolution) is directly migrated to one-dimensional signals, non-physical artifacts may occur in the reconstructed waveform due to the neglect of the time sequence correlation. The learnable interpolation mechanism of the generator in the present application solves this problem through the combination strategy of "dynamic interpolation + convolution correction". The interpolation weight is dynamically adjusted based on the local characteristics of the input low-sampling signal, rather than a fixed mathematical formula, and then the interpolation result is modified for time sequence consistency through a one-dimensional convolution layer, so that the up-sampling process can not only enlarge the signal resolution, but also accurately retain the transient characteristics of the lightning pulse. This design is specially adapted to the physical characteristics of the lightning signal "strong transient and fast change", and overcomes the limitations of fixed interpolation and general up-sampling methods.

[0120] Meanwhile, the combination of learnable interpolation and residual structure further solves the problem of detail loss in low-sampling rate signal up-sampling, and strengthens the ability of GAN to capture subtle features of the lightning signal. The traditional method often leads to loss of high-frequency details due to insufficient information in the up-sampling process. The generator is designed with three levels of residual blocks and two levels of learnable up-sampling, which constructs a progressive learning path of "feature enhancement-resolution improvement". The residual block avoids feature attenuation in deep networks through jump connection, ensuring that weak discharge features in the low-sampling signal are not submerged. The learnable interpolation adaptively fills in high-frequency details based on the previously extracted features at each resolution improvement, rather than simply copying the adjacent values. This architecture enables the model to accurately capture nanosecond-level pulse changes in the lightning signal. Under the constraint of the loss function, the final high-sampling rate reconstructed signal not only matches the overall waveform, but also has key physical parameters such as pulse width and rising edge slope highly consistent with the real signal, solving the technical pain points of traditional methods "shape preservation difficult, detail preservation even more difficult".

[0121] This embodiment takes the generation of a 10Mhz sampling rate waveform from a 1Mhz sampling rate waveform as an example.

[0122] Step 1: Data preparation and parameter initialization

[0123] Please refer to Figure 3 , Figure 3 The original high-resolution lightning signal (blue) is compared with the down-sampled low-resolution signal (red). It can be seen that the low-resolution signal loses a lot of high-frequency details, the waveform edges become smooth, and the pulse peak amplitude is also reduced. This embodiment stores the paired low-resolution (1 MHz) and high-resolution (10 MHz) signal data in HDF5 format. The data is divided into training set, validation set and test set in the ratio of 8:1:1. During training, dynamic batch processing technology is used, each batch contains 8 randomly selected 3000 point signal segments, and a time offset of ±5 sampling points is applied for enhancement to improve the robustness of the model to signal phase changes.

[0124] Second step, generator and discriminator design

[0125] The generator adopts an encoding-decoding structure. First, a 9-point convolution layer (padding=4) is used to extract low-level features of the signal, and a PReLU activation function is used to enhance the non-linear expression ability. Then, three residual blocks (each containing two 3-point convolution and batch normalization) are used for deep feature extraction, and the jump connection effectively alleviates the gradient disappearance problem. The core innovation lies in two levels of learnable upsampling: the first level uses 5 times linear interpolation combined with 3-point convolution (channel number 64) for feature adjustment, and the second level further refines it through 2 times interpolation and convolution of the same structure. Finally, a 9-point convolution is used to output the high-resolution waveform. This phased upsampling strategy (5x2=10 times) can better preserve the waveform detail features compared to direct 10 times upsampling.

[0126] The discriminator is composed of 4 layers of convolutional networks, each layer uses 3-point convolution with a step of 2 to realize down-sampling, and is combined with LeakyReLU (negative slope 0.2) and batch normalization (except the first layer). The first two layers mainly extract time domain envelope features, and the special receptive field (theoretically covering about 40 original sampling points) of the third layer (256 channels) can significantly capture the high-frequency details of the signal. Finally, adaptive average pooling is used to unify the input of different lengths into a 512-dimensional feature vector, and the Sigmoid output discriminates the probability. Experiments show that this structure has a sensitivity of 0.83 to local distortion in the waveform, which is 27% higher than traditional schemes.

[0127] Third step, adversarial training and result analysis

[0128] Figures 4 to 8 The reconstructed results (red dashed line) are compared with the real high sampling rate signal (blue solid line). Figure 4 Lightning signal reconstructed using GAN model; Figure 5 Lightning signal reconstructed using linear interpolation algorithm; Figure 6 Lightning signal reconstructed using cubic spline interpolation algorithm;Figure 7 The lightning signal is reconstructed by using a sine interpolation algorithm; Figure 8 The lightning signal reconstructed by using a frequency domain zero padding algorithm; it can be seen that, compared with traditional algorithms such as linear interpolation, cubic spline interpolation, sine interpolation and frequency domain zero padding, the signal reconstruction method based on GAN proposed in the application has significant advantages in waveform fidelity and detail restoration capability, and can more effectively reconstruct high-resolution lightning signals with high-frequency details and closer to the original physical process.

[0129] Embodiment 2

[0130] The embodiment provides a computer terminal, including a memory, a processor and a computer program stored in the memory and executable on the processor, when the processor executes the computer program, the steps of the up-sampling method of the lightning very low frequency electromagnetic wave signal based on GAN are realized.

[0131] As shown in Figure 9 , the computer terminal provided in the embodiment includes at least one processor 101 and a memory 102 connected with the at least one processor 101, and the specific connection medium between the processor 101 and the memory 102 is not limited in the embodiment, Figure 9 and the connection between the processor 101 and the memory 102 through the bus 100 is taken as an example. The bus 100 is represented by a thick line in Figure 9 , and the connection mode between other components is only schematically described and is not limited. The bus 100 can be divided into an address bus, a data bus, a control bus and the like, and for the convenience of representation, Figure 9 only one thick line is represented in the embodiment, but it does not mean that there is only one bus or one type of bus. Alternatively, the processor 101 can also be called a controller, and the name is not limited.

[0132] In the embodiment, the memory 102 stores instructions executable by the at least one processor 101, and the at least one processor 101 can execute the foregoing method by executing the instructions stored in the memory 102.

[0133] The processor 101 is the control center of the device, can connect all parts of the control equipment through various interfaces and lines, and can perform various functions and process data of the device by running or executing the instructions stored in the memory 102 and calling the data stored in the memory 102, so as to perform overall monitoring on the device.

[0134] In a possible design, the processor 101 can include one or more processing units, and the processor 101 can integrate an application processor and a modem processor, where the application processor mainly processes operating systems, user interfaces, and application programs, and the modem processor mainly processes wireless communication. It can be understood that the foregoing modem processor can also not be integrated into the processor 101. In some embodiments, the processor 101 and the memory 102 can be implemented on the same chip, and in some embodiments, they can also be implemented on separate chips respectively.

[0135] The processor 101 can be a general-purpose processor, for example, a central processing unit (CPU), a digital signal processor, an application-specific integrated circuit, a field programmable gate array, or other programmable logic device, a discrete gate or transistor logic device, a discrete hardware component, and can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the GAN-based lightning VLF electromagnetic wave signal up-sampling method disclosed in Embodiment 1 can be directly embodied by a hardware processor for execution, or a combination of hardware and software modules in the processor 101 for execution.

[0136] The memory 102, as a non-volatile computer-readable storage medium, can be used to store non-volatile software programs, non-volatile computer-executable programs, and modules. The memory 102 can include at least one type of storage medium, for example, can include a flash memory, a hard disk, a multimedia card, a card-type memory, a random access memory (RAM), a static random access memory (SRAM), a programmable read-only memory (PROM), a read-only memory (ROM), an electrically erasable programmable read-only memory (EEPROM), a magnetic memory, a magnetic disk, an optical disk, and the like. The memory 102 is any other medium capable of carrying or storing desired program codes in the form of instructions or data structures and capable of being accessed by a computer, but is not limited thereto. The memory 102 in the present embodiment can also be a circuit or any other device capable of implementing a storage function, for storing program instructions and / or data.

[0137] Through design and programming of the processor 101, the code corresponding to the GAN-based lightning VLF electromagnetic wave signal up-sampling method introduced in the foregoing embodiments can be fixed into the chip, so that the chip can executeFigure 1 The steps of the GAN-based lightning VLF electromagnetic wave signal up-sampling method shown. How to design and program the processor 101 is known to those skilled in the art, and will not be repeated here.

[0138] Embodiment 3

[0139] The embodiment provides a computer readable storage medium, which stores a computer program, and the program is executed by a processor to realize the steps of the GAN-based lightning VLF electromagnetic wave signal up-sampling method.

[0140] The computer readable storage medium can include a flash memory, a hard disk, a multimedia card, a card-type memory (e.g., an SD or DX memory, etc.), a random access memory (RAM), a static random access memory (SRAM), a read-only memory (ROM), an electrically erasable programmable read-only memory (EEPROM), a programmable read-only memory (PROM), a magnetic memory, a magnetic disk, an optical disk, etc. In some embodiments, the storage medium can be an internal storage unit of a computer device, such as a hard disk or a memory of the computer device. In other embodiments, the storage medium can also be an external storage device of the computer device, such as a plug-in hard disk, a smart memory card, a secure digital card, a flash memory card, etc. equipped on the computer device. Of course, the storage medium can also include both the internal storage unit and the external storage device of the computer device. In the embodiment, the memory is usually used to store an operating system and various application software installed on the computer device, etc. In addition, the memory can also be used to temporarily store various data that have been output or will be output.

[0141] The above description is only the preferred embodiment of the present application, but the protection scope of the present application is not limited to this. Any skilled person in the art can make equivalent replacements or changes to the technical solution and the inventive concept of the present application within the technical range disclosed by the present application, which should be covered by the protection scope of the present application.

Claims

1. A method for up-sampling a lightning very low frequency electromagnetic wave signal based on GAN, characterized in that, The method comprises the following steps: S1. Time alignment and normalization preprocessing of the lightning very low frequency low sampling signal and the real high sampling signal to form a training sample pair; S2. Constructing a generative adversarial network composed of a generator and a discriminator; wherein the generator is used to extract initial features from the low sampling signal and perform residual reinforcement, and then map the residual reinforced low sampling features to the high sampling dimension through a feature guided dynamic interpolation mechanism, and correct and map the interpolated intermediate features to obtain a reconstructed signal matching the target high sampling rate; the discriminator is used to receive the reconstructed signal and the corresponding real high sampling signal in the training sample pair, and determine the authenticity probability of the reconstructed signal based on convolution feature extraction and dimension compression; S3. Based on the training sample pair, the generator and the discriminator are jointly trained in an alternating update mode of discriminator loss and generator loss; S4. After training, the new input low sampling signal is preprocessed according to step S1, and the corresponding reconstructed signal is output through the generator.

2. The GAN-based up-sampling method of lightning VLF electromagnetic wave signals according to claim 1, characterized in that, In step S2, a one-dimensional convolution layer is used to extract features from the low sampling signal; wherein the convolution kernel size of the one-dimensional convolution layer is 7 to completely capture the local morphology of a single lightning pulse; the step length of the one-dimensional convolution layer is 1 to ensure that the convolution operation part does not lose timing information; the output channel of the one-dimensional convolution layer is 64 to expand the original one-dimensional low sampling signal to 64-dimensional initial features; and the activation function adopts LeakyReLU with a slope of 2.

3. The GAN-based up-sampling method of lightning VLF electromagnetic wave signals according to claim 2, characterized in that, In step S2, three residual blocks are connected in series and the feature transmission is strengthened through a jump connection mechanism; wherein the structure expression of each residual block is: In the formula, is the output feature of the i-th residual block, i is the output feature of the i-th residual block, i ∈[1,3], is the initial feature; represents one-dimensional convolution, and the convolution kernel size of the two layers of convolution is 3, and the step is 1; the first layer of convolution is used for fine extraction of the input feature , and the steep change of the pulse edge is captured; the LeakyReLU activation function introduces a nonlinear transformation, simulating the nonlinear discharge characteristics of the lightning signal; the second layer of convolution is used for mapping the feature back to the same dimension as the input feature, ensuring that it can be directly added with the input feature.

4. The GAN-based up-sampling method of lightning VLF electromagnetic wave signals according to claim 1, characterized in that, In step S2, the process of mapping the residual reinforced low sampling features to the high sampling dimension through the feature guided dynamic interpolation mechanism is expressed by the formula: In the formula, is an interpolated intermediate feature, is a value of the interpolated intermediate feature at an interpolation point n , n = 1, …, N; N is a sampling rate magnification multiple, and its length matches a target high sampling rate signal; j represents a neighborhood context index offset of an interpolation position; is an interpolation parameter learned by a model, used to determine an interpolation strategy under different feature modes; represents a floor function; is a low sampling feature after the residual is reinforced; is a bias corresponding to the size of the interpolation point n .

5. The GAN-based up-sampling method of lightning VLF electromagnetic wave signals according to claim 4, characterized in that, In step S2, the specific process of correcting and mapping the interpolated intermediate features includes: intermediate features after interpolation performing a one-dimensional convolution operation to correct for local inconsistencies that can occur during the interpolation process, expressed by the formula: In the formula, is the modified feature; LeakyReLU represents an activation function with a slope of 2; represents a one-dimensional convolution, the convolution kernel size of which is 3 and which is used to capture local temporal correlation, the step is 1, and the output channel is 64; The feature map is mapped back to the signal domain through an output convolutional layer, and the output range is constrained through a tanh activation function to obtain a reconstructed signal matching the target high sampling rate , which is N times the length of the low sampling signal, and the expression formula is: In the formula, the output convolutional layer The convolution kernel size is 7, the stride is 1, and the output channel is 1.

6. The GAN-based up-sampling of thunder and VLF electromagnetic wave signals method of claim 1, wherein, The specific process of the discriminator determining the authenticity probability of the reconstructed signal includes: The reconstructed signal output by the generator and the corresponding real high sampling signal are taken as input signals, and three one-dimensional convolutions are used to extract features and compress dimensions of the input signals, gradually capturing local and global features of the input signals, and the expression formula is as follows: where z is an input signal; 、 and are the outputs of the three one-dimensional convolutions, respectively; denotes one-dimensional convolution, the kernel size of the three one-dimensional convolutions is 5 to adapt to the pulse width, the step size is set to 2 to compress the time dimension, and the number of channels is 64, 128 and 256, respectively, to depict complex features; LeakyReLU denotes an activation function with a slope of 0.2, used to activate and retain weak oscillation information; Combined with the convolution layer and the Sigmoid activation function, the authenticity probability of the reconstructed signal is output: In the formula, p ∈ [0, 1] represents the authenticity probability of the reconstructed signal; denotes a Sigmoid activation function.

7. The GAN-based up-sampling method of lightning VLF electromagnetic wave signals according to claim 1, characterized in that, In step S3, in the alternating update mode, the discriminator is updated first, the generator is updated later, and the double loss function is used for collaborative optimization; the loss trend and waveform quality of the validation set are monitored during training, the model is saved once every several rounds, and the optimal version is finally selected; In the training stage of the discriminator: First, the real high-sampling signal in the training sample pair is input into the discriminator to obtain a probability , so as to calculate a real signal loss ; the target of the loss is to make the probability close to 1, that is, to determine as real; wherein denotes a mathematical expectation; The reconstructed signal output by the generator is then input to the discriminator The generator parameters are frozen to avoid gradient interference The probability is calculated The loss is calculated The loss aims to make the probability close to 0, i.e. The average value of the real signal loss and the generated signal loss is taken as the total loss of the discriminator, and the parameters are updated by the Adam optimizer; In the training stage of the generator: reconstruct the signal re-input the discriminator to get a probability , thus computing an adversarial loss , whose goal is to make the probability close to 1 to mislead the discriminator; An L1 loss is used to measure the difference in waveform details, and a content loss is calculated The loss is used to constrain the error of key features; The weighted sum of the adversarial loss and the content loss is taken as the total loss of the generator, and the parameters are updated by the Adam optimizer.

8. The GAN-based up-sampling of thunder and VLF electromagnetic wave signals method according to claim 1, characterized in that, In step S1, after time alignment and normalization preprocessing of the low sampling signal and the real high sampling signal, the low sampling signal and the real high sampling signal are also cut into sub-sequences of fixed length, each sub-sequence of the low sampling signal and the corresponding sub-sequence of the real high sampling signal constitute a training sample pair, and a 50% overlap rate is used when cutting; finally, all training sample pairs are divided into a training set for model parameter learning, a validation set for adjusting hyperparameters in the training process, and a test set for evaluating the final reconstruction effect according to a set proportion, and batch reading and parallel processing are realized through a data loader; In step S4, the reconstructed signal is also subjected to an inverse normalization operation.

9. A computer terminal comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, The processor executes the computer program to implement the steps of the GAN-based lightning very low frequency electromagnetic wave signal up-sampling method according to any one of claims 1 to 8.

10. A computer-readable storage medium having stored thereon a computer program, characterized in that, The program is executed by the processor to implement the steps of the GAN-based lightning very low frequency electromagnetic wave signal up-sampling method according to any one of claims 1 to 8.

Images