A Novel Classification Framework for VLF/LF Lightning-Radiation Electric-Field Waveforms

Abstract

The classification of very-low-frequency and low-frequency (VLF/LF) lightning-radiation electric-field waveforms is of paramount importance for lightning-disaster prevention and mitigation. However, traditional waveform classification methods suffer from the complex characteristics of lightning waveforms, such as non-stationarity, strong noise interference, and feature coupling, limiting classification accuracy and generalization. To address this problem, a novel framework is proposed for VLF/LF lightning-radiated electric-field waveform classification. Firstly, an improved Kalman filter (IKF) is meticulously designed to eliminate possible high-frequency interferences (such as atmospheric noise, electromagnetic radiation from power systems, and electronic noise from measurement equipment) embedded within the waveforms based on the maximum entropy criterion. Subsequently, an attention-based multi-fusion convolutional neural network (AMCNN) is developed for waveform classification. In the AMCNN architecture, waveform information is comprehensively extracted and enhanced through an optimized feature fusion structure, which allows for a more thorough consideration of feature diversity, thereby significantly improving the classification accuracy. An actual dataset from Anhui province in China is used to validate the proposed classification framework. Experimental results demonstrate that our framework achieves a classification accuracy of 98.9% within a processing time of no more than 5.3 ms, proving its superior classification performance for lightning-radiation electric-field waveforms.

1. Introduction

Very-low-frequency (VLF) and low-frequency (LF) lightning electric-field-radiation signals are of high intensity and possess a wide propagation range, making them significant observation targets for lightning detection systems [1,2,3]. These systems detect the electric-field waveforms in the VLF/LF bands generated by various lightning activities [4]. By matching and localizing these waveforms as well as inverting the parameters, the key physical parameters of lightning activities, such as the amplitude of lightning current, the head–tail time, and the speed of pilot development, can be obtained [5]. Rapid and accurate categorization of lightning-radiation electric fields from different lightning activities can provide a solid foundation for lightning protection design. Additionally, it also offers valuable data support for an in-depth study of lightning processes [6,7].

The lightning can be categorized into two types, ground flashes and cloud flashes, depending on where the lightning occurs [8]. The Return Stroke (RS) process is characterized by high current amplitude. With the deeper understanding of lightning discharge waveforms, some special waveforms associated with physical processes such as Preliminary Breakdown (PB) and Narrow Bipolar Events (NBE), which occur in both cloud-to-ground (CG) and intra-cloud (IC) flashes, have been found to be easily misclassified as RS waveforms [9,10]. In addition, the distribution of typical values of the same waveform parameters for the same type of electric field radiation waveform varies considerably in different regions. It is difficult to propose generalized waveform criteria for different types of waveforms under the influence of regional conditions (including meteorological factors such as humidity, temperature, and atmospheric electric field and geographic features such as latitude and altitude), land and sea topography, and other complex factors. Therefore, effective waveform classification methods are important.

In recent years, machine learning-based methods [11,12] have been attempted for waveform classification, achieving better performance in terms of both classification accuracy and processing efficiency [13]. To fulfill the detailed classification needs, machine learning methods have been applied to classify lightning-radiation electric-field waveforms. Algorithms such as support vector machine and logistic regression have been used to classify lightning waveforms, and the classification accuracy can reach 98% [14]. Traditional machine learning methods conduct training based on artificial prior knowledge and empirical criteria for feature extraction [15]. While their training process is simple and efficient, they still face several challenges or problems. First of all, the waveform features extracted by feature engineering contain only part of the waveform information, and the waveform information lost during the extraction process leads to a decrease in impact accuracy. Second, model performance is closely related to feature selection. Introducing manual selection in the feature selection process may lead to biased models and reduce model generalization.

Neural network-based methods have performed well in the field of complex waveform classification, as well as fault diagnosis, due to their autonomous feature extraction capability [16,17,18]. In order to reduce the dependence on feature engineering and further improve the classification accuracy, scholars have tried to introduce neural network methods into the field of lightning waveform classification. Peng et al. apply a convolutional model and achieve 98% classification accuracy with 51,000 signal samples [17]. Wang et al. apply a one-dimensional convolutional neural network (CNN) to classify lightning waveforms and achieve 97.5% accuracy after training by 50,000 signal samples [19]. Gao et al. construct a five-layer residual module to form a one-dimensional residual neural network with an average accuracy of 98% after training on 110,000 signal samples [20].

In contrast to traditional machine learning approaches, neural network-based models offer key advantages for lightning waveform classification. First, traditional machine learning methods lack architecture to parse the sequential logic of raw dynamic waveforms and rely on manual feature engineering, making direct processing of raw waveforms infeasible. Second, unlike traditional methods dependent on manual predefined features, neural networks optimize feature patterns via backpropagation using labeled data. Moreover, neural networks capture hierarchical features in an end-to-end manner, better modeling complex non-linear relationships in variable lightning waveforms and thus enhancing accuracy and generalization. However, to comprehensively extract the inherent characteristics of signal samples, neural network models often encompass millions of parameters. Consequently, they necessitate substantial arithmetic resources during both the training and deployment stages, thereby restricting their applicability in arithmetic-constrained environments, such as edge computing devices.

To improve feature extraction specificity and mitigate the issue of irrelevant feature interference in traditional CNNs, attention-based mechanisms have been widely integrated into neural network architectures in recent years [21]. Among these, the Convolutional Block Attention Module (CBAM) has become a representative approach [22], where the channel attention and the spatial attention are given. This design has been proven effective in improving the accuracy of image classification, time-series analysis, and other tasks without significantly increasing computational complexity. Additionally, there are some other edge-computing-oriented waveform classifiers, such as lightweight transformers and MobileNet variants [23]. However, lightweight transformers tend to the dilute local critical features of lightning waveforms due to global attention and have higher latency, while MobileNet variants lack dedicated attention modules to distinguish similar patterns.

To further enhance the accuracy and speed of classifying lightning-radiation electric-field waveforms for embedded devices with limited computational resources, this paper introduces a lightweight classifier specifically designed for VLF/LF lightning waveform classification, and the main contributions are listed as follows:

• To extract effective VLF/LF lightning waveform information, an improved Kalman filter (IKF) is proposed to eliminate high-frequency interferences. In IKF, the Kalman gain can be adjusted dynamically based on the maximum entropy criterion, contributing to an optimal cutoff frequency.
• To enhance feature representativeness and recognition capabilities, an attention-based multi-fusion convolutional neural network (AMCNN) is proposed to identify different VLF/LF lightning waveforms. Moreover, an optimized feature fusion structure based on attention module is developed to improve classification accuracy and speed.
• Integrated with the IKF and AMCNN, a novel detection framework called IKF-AMCNN is further presented for VLF/LF lightning waveform classification. Extensive experiments are carried out and the comparative result validates the effectiveness of the IKF-AMCNN.

Notably, the IKF-AMCNN framework, while focusing on classification, preserves key waveform features linked to lightning physical properties through IKF’s noise-suppression and AMCNN’s adaptive feature extraction. Specifically, it captures typical time scales by retaining temporal characteristics, enabling differentiation between short-duration processes and longer ones. For VLF/LF energy characteristics, the framework preserves undistorted waveform shape, allowing inference of radiation energy, which differs between processes like return strokes and intracloud flashes. This extends the framework’s utility to support insights into these physical aspects.

The remainder of this article is organized as follows: the waveform dataset and IKF are presented in Section 2. In Section 3, the AMCNN is proposed. Then, the IKF-AMCNN framework is introduced in Section 4. In Section 5, multiple experiments are carried out. Finally, Section 6 summarizes this article.

2. Improved Kalman Filter

2.1. Lightning Waveform Dataset

The dataset used in this article comes from 13 detection sites in the Hefei region of China during 2023. Lightning waveforms are captured by VLF/LF band lightning radiation electric field measurement devices. Each measurement device consists of an electric field detection antenna as well as a data acquisition unit. The antenna is a flat capacitive antenna with an operating bandwidth of 2 kHz–3.4 MHz. The data acquisition unit is integrated into the FPGA and ARM boards. The sampling rate of the acquisition unit is 10 MHz, the ADC is 16-bit, the sampling time is 200 ms, and the pre-trigger time is 100 ms. The data acquisition unit also integrates a high-precision GPS module to ensure timing synchronization with a timing error of less than 50 ns.

Notably, despite the detectors operating primarily in the VLF/LF band, high-frequency (HF) components may still be embedded in the captured waveforms, originating from three main sources, including internal electronic noise from the measurement system, external electromagnetic interference, and transient high-frequency emissions associated with lightning discharges. Some examples of waveforms in categories RS, PB, NBE, and IC are shown in Figure 1.

The waveforms in Figure 1 correspond to physically distinct lightning processes, with measurable characteristics consistent with global observations [24] and regional features of the Hefei area. Their differences in duration, peak electric field, and VLF/LF energy directly reflect underlying discharge mechanisms: RS involves ground–cloud charge transfer, driving intense, short-duration radiation; IC arises from in-cloud charge separation, producing weaker, longer pulses; PB marks the initial breakdown of air insulation; and NBE is associated with rapid, localized charge acceleration. These distinctions are critical for practical applications: RS classification informs structural lightning protection design, while NBE detection aids in mitigating radio frequency interference. Thus, accurate classification of these waveforms enables targeted assessment of lightning-related risks.

As shown in Figure 1a–d, the waveform signals contain obvious high-frequency interference. Such interference can severely distort the original characteristics of the signals, affecting the accuracy of the subsequent classification process. To ensure the validity and reliability of the waveform signals, it is essential to perform high-frequency filtering processing to eliminate or suppress these unwanted high-frequency components.

2.2. Principle of KF

Based on the above description, the IKF is proposed to eliminate high-frequency interferences in waveform signals. Considering the enormous number of data sampling points, directly applying the IKF to the original signal would lead to excessive computational complexity and may even affect the real-time performance of waveform classification. Motivated by [18], a downsampling process is performed on the waveform signal at a ratio of one out of ten, resulting in each waveform containing only 1000 points. In this way, it can retain core lightning waveform features while reducing data volume, fully meeting the real-time processing needs of edge lightning monitoring devices. Notably, adjacent ratios are also feasible for other regions. Then, it is set to the waveform input $x\left(n\right)$.

Considering the high-frequency interference, the observation equation of the waveform input $x\left(n\right)$ can be expressed as

$$x\left(n\right)=s\left(n\right)+v\left(n\right)$$

(1)

where $s\left(n\right)$ is the actual waveform signal and $v\left(n\right)$ denotes the high-frequency interference, which is also called the observation noise.

In the Kalman filter (KF), the state equation of $s\left(n\right)$ is defined as

$$s\left(n\right)=a·s(n-1)+w\left(n\right)$$

(2)

where a is the autoregressive coefficient, which represents the slow time-varying nature of the waveform signal and is close to 1, and $w\left(n\right)$ is the process noise.

The prediction step can be described as

$$\hat{s}\left(n\right|n-1)=a·\hat{s}(n-1|n-1)$$

(3)

$$P\left(n\right|n-1)=a^2·P(n-1|n-1)+Q$$

(4)

where $\hat{s}$ represents the the estimated value or predicted value of the state variable s, P represents the error covariance, and Q represents the process noise covariance, which quantifies the uncertainty or randomness.

After the prediction step, the update step can be expressed

$$K\left(n\right)={\displaystyle \frac{P\left(n\right|n-1)}{P\left(n\right|n-1)+R}}$$

(5)

$$\hat{s}\left(n\right|n)=\hat{s}\left(n\right|n-1)+K\left(n\right)·[x\left(n\right)-\hat{s}\left(n\right|n-1)]$$

(6)

$$P\left(n\right|n)=(1-K\left(n\right))·P(n|n-1)$$

(7)

where $K\left(n\right)$ is the Kalman gain and R represents the observation noise covariance, which characterizes the uncertainty or noise in the measurement process.

For the waveform input $x\left(n\right)$, the KF infers the underlying actual waveform signal $s\left(n\right)$ by iterative prediction and update. However, it strictly assumes linear system dynamics and Gaussian-distributed process and measurement noise, which rarely hold in real-world applications with non-linearities or non-Gaussian disturbances. To address this, the IKF is developed for effective high-frequency interference elimination.

2.3. Proposed IKF

In IKF, it dynamically adjusts noise covariances using residual entropy estimates, enabling robust handling of non-Gaussian noise while maintaining the recursive efficiency of the Kalman framework. The maximum entropy criterion ensures the filter retains optimal uncertainty quantification under partial information, enhancing stability for complex waveform signals.

Built upon the KF, the maximum entropy distribution of noise can be described as

$$p\left(v\right)\propto exp\left(-{\displaystyle \frac{{(v-\mu )}^2}{2{\sigma }^2}}+{\lambda }_1(v-\mu )+{\lambda }_2(v^2-{\sigma }^2-{\mu }^2)\right)$$

(8)

where $\mu$ and ${\sigma }^2$ represent the noise mean and variance, respectively, and ${\lambda }_1$ and ${\lambda }_2$ are Lagrange multipliers. The noise specifically refers to the observation noise $v\left(n\right)$ in the waveform input, as well as the process noise $w\left(n\right)$ in the state equation.

After defining the residual $e\left(n\right)=x\left(n\right)-\hat{s}\left(n\right|n-1)$, its entropy can be expressed as

$$H\left(e\right)=-\sum _{i}p\left(e_i\right)lnp\left(e_i\right)$$

(9)

When the residual $e\left(n\right)$ strictly follows a Gaussian distribution, its entropy value equals $H_0$, which can be described as

$$H_0={\displaystyle \frac{1}{2}}ln\left(2\pi e{\sigma }^2\right)$$

(10)

In this research, the kernel density estimation is used to approximate the residual entropy $H\left(e\right)$. When the actual residual entropy $H\left(e\right)$ exceeds $H_0$, it indicates that the residual distribution deviates from Gaussian characteristics. To address this, a dynamic adjustment strategy is presented in IKF, which can be described as

$$R\left(n\right)=R(n-1)+\beta ·(H\left(e\right)-H_0)$$

(11)

where $\beta$ is an adaptive step parameter that controls the adjustment rate. In this research, it is set to 0.05, which is selected to balance the IKF’s responsiveness to non-Gaussian noise and the stability of the covariance update process.

In this case, the $R\left(n\right)$ is increased to reduce the weight of observations by adjusting the $\beta$. By comparing $H\left(e\right)$ with $H_0$, the IKF can automatically detect the presence of non-Gaussian noise and respond dynamically, thereby enhancing its robustness.

By incorporating an entropy regularization term, the state estimation can be transformed as

$$\hat{s}\left(n\right|n)=arg\underset{s}{min}\left\{{[x\left(n\right)-s]}^2/R\left(n\right)+{[s-a\hat{s}(n-1|n-1)]}^2/Q+\alpha H\left(p\left(s\right)\right)\right\}$$

(12)

where $\alpha$ represents the regularization coefficient. In this research, it is set to 0.1, which is selected to appropriately weight the entropy regularization term to refine state estimation without over-constraining the solution space.

After differentiating with respect to s, the modified Kalman gain in IKF can be obtained, described as

$$K_m\left(n\right)={\displaystyle \frac{P\left(n\right|n-1)+\alpha ·\partial H(p\left(s\right))/\partial s}{P\left(n\right|n-1)+R(n)}}$$

(13)

From (13), the maximum entropy improvement achieves an adaptive cutoff frequency by dynamically adjusting $K_m\left(n\right)$. Under conditions of strong high-frequency interference, indicated by high residual entropy, $K_m\left(n\right)$ is increased to enhance low-pass characteristics. Conversely, when the waveform signal is stable, $K_m\left(n\right)$ is decreased to preserve waveform details.

The update process of the IKF can be further achieved based on the modified Kalman gain. Moreover, a smoothing process is applied to the IKF, refining filtered states via the combination of forward and backward estimates. In this way, residual high-frequency fluctuations in the filtered results can be further reduced. The filtering result for four typical types of waveforms in Figure 1 using the IKF is listed in Figure 2.

From Figure 2, the filtered waveform signals exhibit high continuity with negligible residual high-frequency noise, while key features are well preserved. Then, the z-score method is employed to normalize the waveform signal, thereby optimizing the convergence efficiency for waveform classification. After extracting effective VLF/LF lightning waveform information, an attention-based multi-fusion convolutional neural network is proposed for waveform classification.

3. Attention-Based Multi-Fusion Convolutional Neural Network

Lightning waveforms, in the same way as voltage or current waveforms, are essentially one-dimensional time series [25,26]. To accurately classify lightning waveforms, this article proposes a lightweight one-dimensional AMCNN model.

3.1. Principle of CNN

Convolutional Neural Networks (CNNs), as paradigmatic deep learning frameworks, have established themselves as preeminent tools for automated feature extraction. Notably, one-dimensional CNN effectively leverages this capability for processing sequential data such as waveform signals. Unlike their two-dimensional counterparts designed for grid-structured data, one-dimensional CNN employs convolution kernels that traverse the temporal dimension, making them particularly well-suited for sequential signal processing. Therefore, the one-dimensional CNN is utilized as the basic structure for waveform classification. Within this study, the term CNN denotes exclusively the one-dimensional convolutional neural network architecture.

The standard CNN architecture comprises an input layer, convolutional layers, pooling layers, fully connected layers, and an output layer. In this study, the input layer receives the waveform signals. Subsequent convolutional layers extract discriminative features from these waveform signals. Pooling layers then reduce the dimensionality of the feature maps, enhancing computational efficiency. Typically, the network incorporates multiple stacked convolutional and pooling layers for accurate classification. The fully connected layers integrate these high-level features non-linearly, mapping them to the output layer. Crucially, these layers primarily leverage the extracted, complex feature representations for classification rather than performing further feature extraction. Finally, the output layer produces the CNN’s waveform classification result.

Referring to [21,27], traditional CNNs, with fixed convolutional kernels and sequential feature extraction, struggle to adapt to the unique characteristics of complex signals such as lightning waveforms: (1) Lightning waveforms exhibit strong non-stationarity and time–frequency coupling, which fixed-kernel CNNs fail to capture dynamically. (2) Similar waveform types have subtle discriminative features that shallow CNNs often overlook, while deepening the network leads to overfitting to noise or regional variations. (3) Standard CNNs lack mechanisms to focus on critical segments, resulting in redundant feature extraction from irrelevant regions. These factors collectively degrade classification performance for complex lightning datasets. To reconcile the competing demands of high identification accuracy and low-latency detection, the AMCNN model is developed.

3.2. Proposed AMCNN

The AMCNN enhances waveform feature extraction via an optimized feature fusion structure that contains two key mechanisms: multi-scale feature capture and attention-based feature refinement. On the one hand, it employs convolutional kernels of diverse sizes, replacing single-size kernels, to extract features across varying receptive fields, capturing both broad global patterns and fine-grained local details within the waveform signal. This generates a richer and multi-scale feature representation. On the other hand, an integrated attention module strategically weights these features, amplifying salient characteristics pertinent to waveform signals while suppressing irrelevant information. This targeted refinement further enhances the feature map for waveform classification.

Given the waveform signal input S, the convolution operation is defined as

$$C_v^z=f\left(W_v^z\ast S+b_v^z\right)$$

(14)

where ∗ is the convolution operator, $W_v^z$ and $b_v^z$ represent the weights and biases in the v-th convolutional layer with the size z, respectively, and f represents the activation function. In our work, the size z is set to $1\times 3$ and $1\times 7$, respectively, aiming to extract more waveform details and reducing loss. Additionally, batch normalization (BN) is added to accelerate convergence and improve generalization by normalizing convolutional outputs. Instead of the standard Rectified Linear Unit (ReLU), the Parametric Rectified Linear Unit (PReLU) is deployed as the activation function, which can provide adaptive negative slopes to prevent dying neurons and improve information propagation, defined as

$$PReLU\left(s_j\right)=\left\{\begin{array}{cc}{s}_j,\hfill & \mathrm{if}{s}_j>0\hfill \\ {\alpha }_j{s}_j,\hfill & \mathrm{if}{s}_j\le 0\hfill \end{array}\right.$$

(15)

where ${\alpha }_j$ is a learnable control parameter in the jth channel.

To further enhance the model’s ability to focus on meaningful waveform features, motivated by CBAM, a channel attention module is deployed after the convolutional layer, which is shown in Figure 3.

From Figure 3, the the max-pooling layer and average-pooling layer are utilized in the channel attention module, which can extract the differential feature information and comprehensive feature information, respectively. Subsequently, a shared multi-layer perceptron (MLP) is utilized to complete the channel attention mapping. Finally, an element-wise addition operation is employed to integrate the outputs. The entire generation process of channel attention can be expressed as

$$A_c\left(C_v^z\right)=\sigma (MLP(Maxpool\left(C_v^z\right))+MLP(Avgpool\left(C_v^z\right)\left)\right)$$

(16)

where Maxpool and Avgpool denote max-pooling and average-pooling, respectively, and $\sigma$ denotes the Sigmoid function.

After the attention module, the feature output can be described as

$${\mathrm{Q}}_v^z=C_v^z\otimes A_c\left(C_v^z\right)$$

(17)

where ⊗ represents element-wise multiplication.

Then, a feature fusion layer is designed after the downsampling process is finished by the max-pooling layer, which can effectively integrate the broad global patterns and fine-grained local details provided by convolutional kernels of diverse sizes. This can be described as

$$F_v=Maxpool\left({\mathrm{Q}}_v^{1\times 3}\right)+Maxpool\left({\mathrm{Q}}_v^{1\times 7}\right)$$

(18)

In contrast to a single convolutional layer with a fixed kernel size, the fusion layer combines outputs from convolutions with kernel sizes of $1\times 3$ and $1\times 7$. This enables the capture of both fine-grained local features and relatively global contextual information, thereby providing more comprehensive waveform feature representation. Such a design contributes to enhancing AMCNN’s discriminative capability and further improving the overall recognition performance.

4. Waveform Classification Framework Based on IKF and AMCNN

Built upon IKF and AMCNN, a classification framework called IKF-AMCNN is further proposed for VLF/LF lightning-radiated electric-field waveform classification. Its framework is depicted in Figure 4, which contains two main parts, namely feature extraction and waveform classification. The key model parameters of the AMCNN are given in

Table 1. Key model parameters of AMCNN.

Layer Type	Branch	Kernel Size	Output Channels	Stride	Activation
Input Feature	/	/	64	/	/
Conv 1 × 3	Branch 1	1 × 3	64	1	PReLU
Channel Attention	Branch 1	/	64	/	Sigmoid
Max-Pooling	Branch 1	1 × 2	32	2	/
Conv 1 × 7	Branch 2	1 × 7	64	1	PReLU
Channel Attention	Branch 2	/	64	/	Sigmoid
Max-Pooling	Branch 2	1 × 2	32	2	/
Fusion 1	/	/	64	/	/
Conv 1 × 3 Second Block	Branch 1	1 × 3	64	1	PReLU
Channel Attention	Branch 1	/	64	/	Sigmoid
Max-Pooling	Branch 1	1 × 2	32	2	/
Conv 1 × 7 Second Block	Branch 2	1 × 7	64	1	PReLU
Channel Attention	Branch 2	/	64	/	Sigmoid
Max-Pooling	Branch 2	1 × 2	32	2	/
Fusion 2	/	/	64	/	/

. The specific description of the classification framework is listed as follows.

• Feature extraction using IKF: Eliminate high-frequency interferences by using the IKF method, where the Kalman gain can be adjusted dynamically based on the maximum entropy criterion, enhancing the robustness of feature extraction. Next, effective waveform features are obtained and then inputted into the classifier after normalization processing.
• Waveform classification using AMCNN: Establish an AMCNN classification model where the convolution $1\times 3$ and convolution $1\times 7$ are used to extract the fine-grained local details and broad global patterns by integrating the channel attention module, respectively. Then, different distinct information is combined at the fusion layer, enhancing the effectiveness of the waveform information. Following two fusion layers, the AMCNN employs five fully connected layers to produce the final waveform classification output.

In our work, the Adaptive Moment Estimation (Adam) is deployed for diverse parameter optimization. Thereby, the proposed waveform classification IKF-AMCNN framework is further validating by multiple comparative experiments.

5. Experimental Analysis

In this section, four types of waveforms, namely RS, PB, NBE, and IC (hereafter labeled 1, 2, 3, and 4, respectively, with sample quantities of 1990 for RS-1, 1925 for PB-2, 1935 for NBE-3, and 1885 for IC-4), are used to validate the proposed IKF-AMCNN framework. The dataset consisting of these four waveform types is randomly divided into three parts: a training set, a validation set, and a test set, with a ratio of 6:2:2. Notably, for the RS-1 category, a polarity-proportional division strategy is adopted to maintain the original positive RS and negative RS ratio (approximately 1:3) across all subsets. This is a common ratio for model performance verification that can ensure sufficient training samples to avoid underfitting, while the 20% validation set stabilizes hyperparameter tuning and the 20% test set reliably evaluates generalization. To further eliminate the impact of accidental bias in a single dataset partition on model generalization evaluation and fully verify the stability of the IKF-AMCNN framework, five-fold cross-validation is implemented based on the above data division principle.

Specifically, the automated classification of the four waveform categories is achieved through the collaborative operation of the IKF and AMCNN. Namely, the filtered waveforms provided by the IKF are directly fed into the AMCNN without the need for key feature extraction. This design allows AMCNN to autonomously learn intrinsic patterns from the entire filtered waveforms, preserving more comprehensive temporal and amplitude information that might be lost during manual feature selection.

5.1. Training and Verification

To validate the effectiveness of the proposed framework, the IKF-AMCNN model is evaluated using the Deep Learning Toolbox in Matlab 2024a. The implemented model is tested on an Nvidia GeForce RTX 3070 GPU installed in a computer with 32 GB of RAM and a 2.9 GHz processor. Under the above configuration conditions, the trends of the training accuracy, training loss, validation accuracy, and validation loss are shown in Figure 5, respectively.

From Figure 5, it can be seen that the classification accuracy of the proposed IKF-AMCNN framework increases as the number of epochs becomes larger, eventually reaching 98.9%, as shown in Figure 6 and

Table 2. Classification performance across the four waveform categories.

Type	Accuracy (%)	Average (%)
RS	100	98.9
PB	100
NBE	97.2
IC	98.4

. It is worth noting that the model training time for this classifier does not exceed 1 min when the epoch reaches 30. The average time of the classifier for a single classification does not exceed 5.3 ms, indicating the proposed IKF-AMCNN framework achieves an excellent balance between classification accuracy and computational efficiency.

5.2. Classification Performance Under Different Training Set Proportions

To evaluate the generalization ability of the proposed IKF-AMCNN, the classification performance of IKF-AMCNN is evaluated under different training proportions. Specifically, the training set proportions are set at 5%, 10%, 20%, 40%, 70%, and 80%, respectively. The classification accuracy of the proposed IKF-AMCNN framework under different training set proportions is presented in Figure 7.

As evidenced in Figure 7, the classification accuracy of the proposed method demonstrates a consistent upward trend with increasing test set proportions. The overall recognition accuracy climbs from 95.97% to 99.48%. Notably, even when trained with merely 5% of the dataset, the method maintains a robust overall accuracy of 95.97%. This performance confirms that our approach effectively captures discriminative features across diverse waveforms with minimal training samples, demonstrating strong generalization capability and significant potential for practical applications.

5.3. Verification for IKF-AMCNN

To verify the proposed IKF-AMCNN framework, multiple comparative experiments are designed and carried out. In these experiments, three other combinations are selected as the comparison, including CNN, KF-CNN, IKF-CNN, and KF-AMCNN, which can effectively highlight the improvement effect of the innovative points in the IKF-AMCNN. The classification results of the four models on the four types of waveforms are shown in

Table 3. Verification result for IKF-AMCNN.

Method	Accuracy
	RS	PB	NBE	IC
CNN	93.6% ± 0.8%	93.0% ± 0.6%	91.7% ± 0.8%	93.5% ± 0.8%
KF-CNN	94.2% ± 0.6%	93.5% ± 0.5%	92.5% ± 0.8%	93.9% ± 0.7%
IKF-CNN	95.4% ± 0.4%	95.1% ± 0.6%	94.3% ± 0.5%	94.7% ± 0.4%
KF-AMCNN	98.5% ± 0.3%	97.1% ± 0.4%	96.1% ± 0.5%	96.3% ± 0.3%
IKF-AMCNN	100% ± 0.0%	100% ± 0.0%	97.2% ± 0.2%	98.4% ± 0.3%

.

As can be seen from Table 3, both IKF-CNN and KF-AMCNN achieve different degrees of improvement compared with KF-CNN and CNN, which fully verifies the effectiveness of the proposed IKF and AMCNN methods. Taking the RS as an example, the accuracies of CNN and KF-CNN are 93.6% and 94.2%, respectively, while those of IKF-CNN and KF-AMCNN are 95.4% and 98.5%, respectively. More importantly, the proposed IKF-AMCNN achieves the highest accuracy of 100%, which demonstrates that the innovative design of IKF-AMCNN can better adapt to the characteristics of the lightning waveforms and thus obtain more reliable classification results. Moreover, a lower standard deviation for IKF-AMCNN proves its statistical robustness.

5.4. Comparison with Other Methods

To verify the advantages of the proposed IKF-AMCNN model in lightning-radiation electric-field waveform recognition, some other classification methods, including support vector machine (SVM) [13], random forest (RF) [28], and one-dimensional residual network (1D ResNet) [20], are used for comparison. In the SVM model, the 20,000 data points in the samples are reduced to 2000 points through downsampling, which serve as feature vectors. A Radial Basis Function (RBF) is adopted as the kernel function. The RF model combines the 2000 downsampled points with three manually extracted waveform parameters, namely, the rise time, fall time, and zero-crossing time, to form a feature vector of length 2000. The number of decision trees is set to 100, and the maximum tree depth is set to unlimited. In the 1D ResNet, a five-layer residual module is constructed for waveform feature extraction. The accuracy of SVM, RF, 1D ResNet, and the proposed IKF-AMCNN in classifying different types of waveforms on the same dataset is shown in

Table 4. Classification accuracy under different classification methods.

Method	Accuracy
	RS	PB	NBE	IC
SVM	90.2% ± 0.9%	89.6% ± 1.1%	91.2% ± 1.2%	87.5% ± 1.4%
RF	88.2% ± 1.3%	85.7% ± 1.5%	89.7% ± 1.1%	86.5% ± 1.5%
1D ResNet	97.0% ± 0.5%	96.1% ± 0.6%	94.6% ± 0.8%	95.8% ± 0.5%
IKF-AMCNN	100% ± 0.0%	100% ± 0.0%	97.2% ± 0.2%	98.4% ± 0.3%

.

As shown in the Table 4, the proposed IKF-AMCNN obtains the highest classification accuracy. SVM and RF perform worse than 1D ResNet and IKF-AMCNN, which indicates that the manual setting of feature vector composition introduces bias, limiting the classification performance of the models. Additionally, the proposed IKF-AMCNN also has the lowest standard deviation. The results demonstrate that the IKF-AMCNN framework not only has efficient training and inference capabilities but also can provide the best statistical robustness, thus outperforming traditional machine learning models and other deep learning models, further confirming the superiority of the IKF-AMCNN framework in waveform classification.

6. Conclusions

In this article, a novel framework, IKF-AMCNN, was proposed for identifying VLF/LF lightning-radiated electric-field waveforms. Firstly, an improved Kalman filter based on the maximum entropy criterion was designed to remove high-frequency interferences and strong noises from the original waveforms, preserving the main essential characteristics of the lightning waveform. Then, an attention-based multi-fusion convolutional neural network was developed for classifying the cleaned and filtered waveforms. A series of experiments were carried out to validate the IKF-AMCNN framework. The results demonstrated that the proposed IKF-AMCNN classifier could rapidly and accurately identify four types of lightning waveform with a classification accuracy of 98.9%. Specifically, on the experimental platform built in this work, the model training time for the proposed classifier did not exceed 1 min, with a single classification taking no longer than 5.3 ms, indicating promising performance for waveform classification tasks.

However, the dataset used in this work is collected from Anhui province, which may introduce geographic bias, potentially limiting the direct generalization of the model to other regions. Additionally, relying on a single-region dataset raises the risk of subtle overfitting, as the model may implicitly learn region-specific features that are not universal to lightning phenomena. Future work will focus on addressing these limitations by expanding the waveform dataset to include multi-region samples, optimizing the lightweight design of the network structure, and integrating the framework with lightning warning systems to further enhance its practicality and scalability.