Research on the Detection Model of Kernel Anomalies in Ionospheric Space Electric Fields

Abstract

Research has found kernel anomaly regions in the power spectrum images of ionospheric electric fields in space, which are widely distributed. To effectively detect these kernel abnormal regions, this paper proposes a new kernel abnormal region detection method, KANs-Unet, based on KANs and U-net networks. The model embeds the KAN-Conv convolutional module based on KANs in the encoder section, introduces the feature pyramid attention module (FPA) at the junction of the encoder and decoder, and introduces the CBAM attention mechanism module in the decoder section. The experimental results show that the improved KANs-Unet model has a mIoU improvement of about 10% compared to the PSPNet algorithm and an improvement of about 7.8% compared to the PAN algorithm. It has better detection performance than the currently popular semantic segmentation algorithms. A higher evaluation index represents that the detected abnormal area is closer to the label value (i.e., the detected abnormal area is more complete), indicating better detection performance. To further investigate the characteristics of kernel anomaly areas and the differences in features during magnetic storms, the author studied the characteristics of kernel anomaly areas during two different intensities of magnetic storms: from November 2021 to October 2022 and from 1 May 2024 to 13 May 2024 (large magnetic storm), and from 11 October 2023 to 23 October 2023 (moderate magnetic storm). During a major geomagnetic storm, the overall distribution of kernel anomaly areas shows a parallel trend with a band-like distribution. The spatial distribution of magnetic latitudes is relatively scattered, especially in the southern hemisphere, where the magnetic latitudes are wider. Additionally, the number of orbits with kernel anomaly areas during ascending increases, especially during peak periods of major geomagnetic storms. The overall spatial distribution of moderate geomagnetic storms does not change significantly, but the global magnetic latitude distribution is relatively concentrated.

1. Introduction

The Chinese electromagnetic monitoring test satellite (Zhangheng-1) was successfully launched into its designated orbit on 2 February 2018 from the Jiuquan Satellite Launch Base, marking China’s first platform dedicated to space-based seismic stereo observations. This satellite carries an important scientific mission, which is to monitor and study electromagnetic phenomena in the space ionosphere, covering multiple aspects such as earthquake monitoring and prediction, in-depth exploration of the Earth’s space physical field, and scientific research on abnormal disturbances in the space ionosphere electromagnetic field [1]. In order to comprehensively monitor the electromagnetic environment, the “Zhangheng-1” is equipped with eight types of payloads, which work together to form a powerful electromagnetic environment monitoring system that can produce rich scientific data. Among them, the electric field detector is one of the core payloads of the satellite, which is used to accurately measure electric field changes in the ionosphere. The data obtained by the electric field detector provide detailed information about the changes in the electric field, which is crucial for further exploring the mechanism of anomalous disturbances in the ionospheric electric field in space. The observation frequency range of the electric field detector is very wide, covering the frequency range from 0 to 3 MHz, including four frequency bands: ultra-low-frequency (ULF 0–16 Hz), extremely low-frequency (ELF 6 Hz~2.2 kHz), very-low-frequency (VLF 1.8 kHz~20 kHz), and high-frequency (HF 18 kHz~3 MHz). This feature enables electric field detectors to capture more detailed electromagnetic field information, providing richer and more accurate data support for scientific research [2,3,4].

Due to the influence of various interference factors, various types of abnormal disturbance events will occur in the ionosphere. Different abnormal disturbance events will produce different electromagnetic signal values, and these abnormal disturbance events will cause different shaped features to be displayed on the image. Studying these anomalous disturbance events has significant scientific significance for human understanding of space electromagnetic fields, disturbance phenomena of anomalous events, and exploration of the characteristics of space electromagnetic signals [5,6,7]. Significant achievements have been made in the field of anomalous disturbances of spatial ionospheric electric fields caused by both earthquake and non-earthquake factors. Especially in the field of abnormal disturbances in ionospheric electric fields caused by earthquakes, researchers have conducted an in-depth analysis of the fluctuations and changes in ionospheric electric fields before and after earthquakes in order to achieve effective monitoring and prediction of earthquakes [8,9]. Specifically, in the ultra-low-frequency (ULF) band, researchers innovatively used a combination of empirical mode decomposition and sample entropy to conduct a detailed analysis of ionospheric anomalies before and after earthquakes [10]. Research has revealed that during the critical period of 15 to 10 days before an earthquake occurs, the height and signal-to-noise ratio of the ionosphere show a synchronous decrease trend and gradually return to normal after the earthquake [11,12]. In the extremely low-frequency (ELF) band, researchers have adopted both the C-value method and the signal-to-noise ratio method to conduct in-depth calculations and analyses of the earthquake-prone areas before and after the earthquake [13,14]. They not only summarized the regular patterns of C-value changes in the seismogenic zone before and after earthquakes but also delved into the unique characteristics of ionospheric electric field changes before and after earthquakes [15,16,17]. The study found a significant correlation between earthquakes with a magnitude of 6.0 or above and the anomalous electric field disturbances exhibited by the spatial ionosphere in the very-low-frequency band [18,19,20]. This discovery opens up new perspectives and potential practical avenues for earthquake prediction research. Scholars have analyzed the different requirements for earthquake precursor electric field data services observed by satellites and summarized the data processing methods used in different stages of ionospheric anomalies caused by earthquakes. They have also pointed out the adaptation conditions and environments of different methods and provided examples of several typical algorithms for analysis [21,22,23].

In the study of anomalous disturbances in the spatial ionospheric electric field caused by non-seismic factors, many researchers tend to explore anomalous disturbances in the ionosphere from the perspective of image analysis [24]. The anomalies caused by non-seismic factors in the space ionosphere will exhibit different shapes in the image. Based on the characteristics of these different shapes, the corresponding electromagnetic disturbance events can be predicted, which is of great significance. For example, lightning whistle waves exhibit a typical L-dispersion pattern in the image, while artificially transmitted very-low-frequency radio waves and interference generated by satellite platforms themselves appear as clear horizontal straight lines in the image [25,26,27]. In addition, the characteristics of plasma laminated sound in the image are manifested as intermittent periodic short diagonal patterns, etc. Previous research has mainly focused on using computer vision technology and edge detection technology to achieve an accurate detection of anomalous disturbances in horizontal electromagnetic waves [28,29,30]. Meanwhile, pattern recognition, target detection, and intelligent speech recognition technologies have been widely applied in detecting anomalous disturbances in the L-dispersion morphology of lightning whistle waves, and significant research results have been achieved [31,32]. However, compared with the development of research on abnormal disturbances of ionospheric electric fields before and after earthquakes, the research progress in the field of abnormal disturbances of ionospheric electric fields caused by non-seismic factors is relatively slow.

In the development process of semantic segmentation, well-known algorithms include FCN [33], U-net [34], DeepLabV3 [35], PSPNet [36], LinkNet [37], FPN [38], DeepLabV3+ [39], Unet++ [40], PAN [41], Manet [42], and so on. Traditional semantic segmentation algorithms have certain shortcomings in detecting kernel anomaly regions, such as low segmentation accuracy, insufficient feature fusion, and high computational complexity. To detect and analyze these kernel abnormal areas, the author used edge detection technology for detection, but did not obtain ideal detection results; reusing traditional semantic segmentation techniques for its detection also yields unsatisfactory results. In response to these shortcomings, the author improved the traditional semantic segmentation algorithm using the KAN algorithm and proposed a new semantic segmentation model, the Kolmogorov–Arnold U-shaped network(KANs-Unet).

The improved model embeds the KAN-Conv convolution module based on KANs in the encoder section, implements learnable activation functions at the network edge, reduces model parameters, improves network generalization ability, enhances model performance, and shortens the training period for achieving optimal results. The feature pyramid attention module (FPA) is introduced at the junction of the encoder and decoder to enhance the model’s ability to capture features of different scales. The CBAM attention mechanism module has been introduced in the decoder section, effectively enhancing the network’s ability to selectively focus on the most important features or regions in the input data while ignoring irrelevant parts, effectively improving the detection of kernel abnormal regions. At the same time, it significantly improved the mIou of the model, achieving effective detection of kernel abnormal regions. The structure of the rest of this article is as follows. The second section introduces data sources and data preprocessing. The third section introduces the kernel anomaly detection model. The fourth section is the analysis and comparative experiment of the performance of the kernel anomaly detection model. The fifth section discusses further analyses of the kernel anomaly regions. The sixth section presents the conclusion.

2. Data Sources and Preprocessing

To better meet the needs of practical work and meet the research on detecting anomalous ionospheric disturbance areas in space using China Seismo-Electromagnetic Satellite transmission electric field detector power spectrum images, the author used power spectrum images as the research object. In the study of power spectrum images in the very-low-frequency band, the author discovered some anomalous regions of spatial ionospheric electric fields. The shape of this region is similar to that of a cell nucleus, with a higher energy value at the center and gradually diverging towards the periphery, forming a kernel abnormal area [27], as shown in Figure 1. The kernel anomaly area is the elliptical area on the right side.

To detect kernel anomaly areas using semantic segmentation technology, the author created 1115 power spectrum images in the very-low-frequency frequency band of electric field detectors. The data required for the experiment were all from the China Earthquake Electromagnetic Satellite. To meet the needs of experimental images, the HDF5 file collected by the satellite is first processed, and the logarithm of the power spectral density data in the very-low-frequency band is taken to reduce the dynamic range of the data and solve the problem of data spanning multiple orders of magnitude. Then, the power spectral density data are rotated counterclockwise by 90 degrees in the two-dimensional direction, laying the foundation for a more intuitive power spectral plot. Finally, the processed power spectral density data are used to draw a power spectral image. Through observation, it was found that in the X, Y, and Z components of the satellite power spectrum image, the kernel anomaly area in the Z component is more pronounced compared to the X and Y components. Therefore, the power spectrum image of the Z component was selected as the research object. For the production of pixel-level labels for kernel anomaly areas, the author used the LabelImg labeling tool to label the power spectrum image. Then, when processing the labeled power spectrum image, the pixel mapping classification of the kernel anomaly area is 1, and the pixel mapping classification of the remaining areas is 0. The processed power spectrum image and label image are shown in Figure 2. The label values in the black area of the label map are mapped to 0, and the label values in the white area are mapped to 1.

For data preprocessing, the author used the Albumentations [43] data augmentation library to enhance the power spectrum images. To avoid overfitting and sample imbalance during the training process of the kernel anomaly detection model, the author enhanced the power spectrum images of the training set from various aspects in the data preprocessing stage, such as adding random noise that follows Gaussian distribution, scale translation and rotation, image translation, scaling, and rotation. Horizontal flipping is the process of flipping the power spectrum image along the vertical axis, with a flipping probability of 50% for each image. Scale translation and rotation is the process of increasing sample diversity in power spectral images through transformations such as translation, scaling, and rotation. Random noise that follows a Gaussian distribution is added to change the appearance of an image. Random numbers that follow a Gaussian distribution are generated based on a specified mean and standard deviation and applied to each pixel value of the image as the intensity of the noise. To prevent information loss caused by the excessive changes in image features, the probability of Gaussian noise data enhancement for each image is set to 20%. In addition, some other data augmentation methods were used (as shown in

Table 1. Data enhancement methods.

Enhanced Mode	Enhanced Probability	Enhancement Effect
Resize	1	Resizes the image
HorizontalFlip	0.4	Flips the image horizontally
ShiftScaleRotate	0.4	Scale translation and rotation of images
GaussNoise	0.2	Adding Gaussian noise interference to images
CLAHE	0.5	Performs histogram equalization on images
RandomBrightnessContrast	0.8	Randomly applies brightness contrast to images
RandomGamma	0.8	Performs random gamma afFine transformation on images
Sharpen	0.8	Sharpens the image
Blur	0.8	Randomly blurs the image
MotionBlur	0.8	Applies motion blur to images
HueSaturationValue	0.8	Randomly changes the hue and saturation values of an image

) for verification purposes. The first column of the table is the data augmentation method, the second column is the data augmentation probability, and the third column is the explanation of the data augmentation method.

3. Detection Method for Kernel Anomaly Areas

To address the shortcomings of traditional semantic segmentation algorithms and better achieve the task of detecting kernel abnormal regions, the author improved the U-net network based on its characteristics and developed the KANs-Unet model, which is more suitable for detecting kernel abnormal regions.

3.1. MobileNetV3

The kernel anomaly detection model adopts the encoding and decoding architecture design of the U-net network. The author selected the MobileNetV3 [44] network as the encoder part (i.e., downsampling module) of the model and optimized the downsampling module accordingly. MobileNetV3 network is a lightweight convolutional neural network proposed by the Google team in 2019, which aims to improve computational efficiency and performance while maintaining low computational complexity and compact model size. The core design concept of this network is reflected in two aspects: firstly, it adopts deep separable convolution technology, and secondly, it incorporates a lightweight SE attention mechanism with an inverted residual structure.

The first aspect is that depthwise separable convolution consists of two core components: depthwise convolution and pointwise convolution. Compared to traditional convolution operations, where convolution kernels act on multiple channels simultaneously, deep convolution adopts a more refined processing approach, which assigns an independent convolution kernel to each input channel for separate convolution operations. The subsequent point-by-point convolution uses a 1 × 1 convolution kernel to perform convolution operations between channels. Based on deep convolution, the information of each channel is further linearly combined. This design significantly reduces the computational complexity and parameter count, thereby improving overall computational efficiency. On the other hand, the inverted residual structure, embedded with a lightweight SE attention mechanism, is ingeniously constructed by three key steps. Firstly, by using a 1 × 1 expansion convolution, the number of channels in the input feature map is upscaled to a higher dimension, aiming to enhance the model’s expressive power. Next, using a depthwise separable convolution with a size of 3 × 3, convolution operations are performed separately for each channel. At the same time, a lightweight SE attention mechanism learns the weight allocation between feature channels, dynamically adjusts the channel features of the feature map, and achieves effective feature filtering and enhancement. Finally, a dimension reduction operation is performed through a 1 × 1 point-by-point convolution to compress the number of channels in the feature map output by deep convolution back to the original quantity, thereby integrating information and reducing the dimensionality of the feature map. In addition, the structure cleverly introduces skip connections, which directly superimpose the input feature map onto the output of point-by-point convolution to generate the final output. This design not only enriches feature representation but also helps alleviate the problem of gradient vanishing, making the network training process more stable and reliable.

3.2. U-Net Network

The U-net network was designed by Olaf Ronneberger et al. in 2015, and was initially designed for medical image segmentation tasks, such as precise segmentation of cells, tissue organs, and lesion areas, and has demonstrated excellent performance in experiments. The author introduced the network to the task of detecting kernel anomaly regions in spatial ionospheric power spectrum images. Due to the complex and irregular boundaries of the kernel anomaly region in the power spectrum image, coupled with the low contrast between the target and background, it is difficult to distinguish them clearly. In addition, the high-resolution characteristics of power spectrum images further increase the processing difficulty and place extremely high demands on computing resources. Given these circumstances, segmentation algorithms must be able to accurately capture these fine details, and efficient and precise algorithms and models are particularly important. Therefore, the U-net network model has become a suitable choice for detecting kernel anomaly regions due to its excellent segmentation ability.

The network structure of the U-net model presents a symmetrical “U”-shaped encoding and decoding architecture, which ingeniously integrates the three following major components: the encoder, skip connection, and decoder. Firstly, the encoder section (also known as the downsampling module) is typically constructed based on a classification network, with its core function being to extract multi-scale features from the input image and condense and extract semantic information from the image during this process. Subsequently, the skip connection serves as a bridge in this structure, capturing and transmitting more accurate positioning information to the decoder section. The specific implementation method is to finely concatenate the feature maps of the encoder at the same level as those of the decoder at the previous level in the channel dimension and then adjust the number of channels through convolution operation to ensure seamless fusion of information. Finally, the decoder part (i.e., the upsampling module) takes on the responsibility of gradually restoring the feature maps’ output by the encoder during the downsampling stage to the original image size. By fusing feature maps from different downsampling levels, it ultimately outputs accurate segmentation prediction maps, achieving precise restoration of image details and accurate depiction of segmentation targets.

3.3. Improved U-Net Network

In order to more effectively complete the detection task of kernel anomaly areas, the author innovatively improved the classic U-net network and designed a new KANs-U-net network architecture. This architecture integrates the KAN-Conv module into the backbone classification network MobileNetV3 for optimizing the encoder part. This module not only maintains the high accuracy of the model but also significantly reduces the number of parameters, thereby improving the optimization efficiency and generalization ability of the model by introducing a learning activation function based on the spline function. In the connection between the encoder and decoder, a feature pyramid attention module (FPA) is introduced. This module can enhance the feature information extraction of the target area at different scales and more comprehensively express the details and key information in the image. Meanwhile, by using convolution kernels of different sizes for convolution operations, the receptive field of the model is further expanded, which is particularly advantageous for the accurate classification of smaller target areas. In the decoder section, a CBAM attention mechanism module is embedded. This module can enhance the weight of the target area of the fusion result after upsampling so as to further improve the detection accuracy of the model for the target area.

3.3.1. KAN-Conv Module

The convolution kernels of conventional convolution modules are composed of fixed-weight matrices, which are learned during the training process of the model. This limits the ability of the model to learn from kernel abnormal regions through convolution operations, resulting in the model being unable to flexibly handle complex data. The KAN-Conv module solves this problem. The KAN-Conv module applies Kolmogorov–Arnold networks (KANs) [45] to the convolutional layers. Unlike traditional multilayer perceptrons (MLPs), KANs utilize Kolmogorov–Arnold’s theorem to integrate spline functions instead of traditional linear weight matrices, implementing learnable activation functions at the network edge, reducing model parameters, and improving the network’s generalization ability. The convolutional kernel of the KAN-Conv module consists of learnable nonlinear functions that are dynamically adjusted during training, thereby reducing the number of required parameters. In addition, it can also adapt more flexibly to complex patterns and nonlinear relationships in data, enabling the model to better capture complex features in images. The comparison between KAN and traditional MLP is shown in Figure 3. Taking the semantic segmentation task of kernel abnormal regions as an example, one of the core challenges of this task is to accurately identify and outline the edges of abnormal regions in the image. Traditional convolution methods, although performing well in handling some basic edge features, often struggle to capture complex and varied abnormal region edges and can only capture relatively rough edge contours. In contrast, the KAN-Conv module, with its unique piecewise linear function design, can more finely approximate these complex and variable edge features. This feature enables KAN-Conv to significantly improve the accuracy of edge recognition when dealing with kernel anomaly regions, thereby optimizing the performance of the entire semantic segmentation task.

3.3.2. FPA Attention Module

Due to the irregular edges of kernel anomaly regions, which have important features at multiple scales, it is necessary to extract the edge features from feature maps at multiple scales. Through hierarchical feature map processing, the model can effectively integrate features from fine-grained to coarse-grained scales. At the same time, the attention mechanism added by this module can adaptively select important features on feature maps of different scales. To overcome these difficulties, the author added a feature pyramid attention module (FPA) at the junction of the encoder and decoder to enhance the model’s ability to capture features at different scales. The purpose of this module is to extract precise pixel-level attention from the high-level feature map generated by the last layer of the encoder (downsampling module) and effectively increase the receptive field to extract semantic information from the details of the kernel abnormal regions in the high-level feature map, providing detailed information for the decoder (the upsampling part).

The structural diagram of FPA is shown in Figure 4. The structure of the FPA is also similar to a “U-shaped” structure. In the decoder section, convolution kernels with sizes of 7 × 7, 5 × 5, and 3 × 3 are used to perform convolution operations, extracting detailed semantic information from high-level feature maps while increasing the receptive field. Gradually integrate the detailed semantic information extracted by the decoder using convolution kernels of different sizes in the encoder section to more accurately combine semantic information of different scales in the context. Then, use a 1 × 1 convolution kernel to process the high-level feature map and multiply it with the semantic information extracted from the pyramid structure. At the same time, adding the channel-based feature map obtained through direct global pooling to the output feature map further enhances the performance of the feature pyramid attention module (FPA). For example, when using semantic segmentation techniques to analyze high-resolution satellite images in detail, the FPA (feature pyramid attention) module helps the model capture both macro background features in the image space and sensitively identify local features of subtle abnormal areas. Through its built-in global pooling technology and attention mechanism, the FPA module enables the model to dynamically adjust its “line of sight” and focus more on the most critical abnormal region features in the current task. This process greatly enhances the model’s ability to fuse and understand features at different scales, enabling more accurate and efficient image segmentation in complex and variable power spectrum images.

3.3.3. CBAM Attention Module

In order to significantly enhance the performance of the model in extracting kernel anomaly regions and optimize the accuracy of image segmentation, the author integrated the CBAM [46] attention mechanism module in the decoder (i.e., the upsampling module). The power spectrum image contains delicate signal fluctuations in the frequency domain, where spatial variations can map the temporal and frequency characteristics of the signal, and different channels correspond to different frequency bands of the signal. Given the uniqueness of power spectrum images, the spatial layout and channel relationships for capturing features are particularly important. In addition, power spectrum images are often affected by noise or background clutter, and spatial attention mechanisms can effectively filter out these interference factors in such scenarios. The CBAM attention module utilizes both channel attention and spatial attention mechanisms to achieve precise extraction of kernel abnormal regions. Specifically, the channel attention mechanism can enhance the network’s attention to key features, thereby improving the expression ability of features. The spatial attention mechanism guides the network to focus on nuc kernel lear anomaly regions, significantly enhancing the recognition efficiency of features. By integrating these two attention mechanisms, the CBAM module demonstrates a more flexible feature extraction capability, which can not only effectively extract feature information of kernel abnormal regions but also effectively suppress irrelevant features, thereby further improving the overall performance of the model.

The CBAM attention mechanism module is a serial structure that connects the channel attention module with the spatial attention module, as shown in Figure 5. Firstly, through the channel attention module, the spatial size of the feature map is compressed by global average pooling and global maximum pooling, resulting in two global feature description vectors. These two vectors are then fused using a shared multilayer perceptron network for feature fusion. Finally, the channel attention weights are obtained through Sigmoid activation. Multiply the input feature map by the channel attention weight to obtain a channel attention-weighted feature map. Then, the weighted feature maps are passed through the spatial attention module and subjected to average pooling and max pooling in the channel dimension to obtain two feature maps. These two feature maps are concatenated by channel and then convolved to obtain spatial attention weights using the Sigmoid activation function. Multiply the channel attention-weighted feature map by the spatial attention weight to obtain the final attention-weighted feature map.

Taking the semantic segmentation task of kernel abnormal regions as an example, the goal is to accurately distinguish and label kernel abnormal regions in the image. The channel attention module of CBAM can identify which image channels carry more critical information. For example, it will identify certain specific channels (such as channels that capture changes in energy values in abnormal areas) that are crucial for identifying kernel anomalies, and these channels will be given higher weights. At the same time, the spatial attention module of CBAM conducts a search on the spatial layout of the image, searching for clues that are crucial for identifying anomalous regions. It will lock the key features, such as the shape and contour of the abnormal area, and the features of these key areas will be further enhanced, making them more eye-catching in the classification process, thereby greatly improving the accuracy of classification. By using the CBAM attention mechanism, accurately capture kernel anomaly regions in complex and variable power spectrum images.

3.4. KANs-Unet Network

The author used the U-net network with the encoding and decoding structure as the basic model and improved it to adapt to the detection of kernel anomaly areas. A new KANs-Unet model was designed, and the overall framework structure is shown in Figure 6. To overcome the complexity of capturing data with a large number of parameters and the difficulty in learning complex nonlinear relationships in conventional convolution, this model uses the MobileNetV3 classification network as the encoder (downsampling module) and introduces the KAN-Conv module on top of it, achieving more effective processing of complex data structures and with similar accuracy to traditional convolution with fewer parameters. At the same time, to extract the detailed semantic information in the high-level feature map more accurately, a feature pyramid attention module (FPA) is introduced at the junction of the encoder and decoder. This module processes the high-level feature map output by the last layer of the encoder (downsampling module) and extracts detailed semantic information at multiple scales. Finally, to better integrate the detailed semantic information in the high-level feature map, a CBAM attention module was embedded in the decoder (downsampling module) to enhance the feature expression of the kernel anomaly region.

3.5. Joint Loss Function

In the training process of the KANs-Unet model, the author quantitatively evaluated the performance of the model, better measured the difference between the true value and the predicted value, guided the model to learn the features of the kernel anomaly region, and further improved the generalization ability of the model. The author designed a joint loss function for the task of detecting kernel anomaly regions. The joint loss function is composed of the DiceLoss loss function and CrossEntropyLoss loss function, and the specific formulas are shown in (1) to (4).

Among them, Formula (1) calculates the Dice coefficient, which is a part of the 2DiceLoss loss function. Formula (3) calculates the CrossEntropyLoss loss function, while Formula 4 calculates the joint loss function, which is a combination of the first three formulas.

$$Dice={\displaystyle \frac{2|X\cap Y|}{\left|X\right|+\left|Y\right|}}$$

(1)

$$DiceLoss=1-Dice$$

(2)

$$H(p,q)CrossEntropyLoss=-{\sum }_{i=1}^{n}p\left(x_i\right)logq\left(x_i\right)=-\sum \left(p\right(x\left)logq\right(x\left)\right)$$

(3)

$$Loss=CrossEntropyLoss-log\left(DiceLoss\right)$$

(4)

Among them, A represents the intersection of the true value and the predicted value, $\left|X\right|$ and $\left|Y\right|$ represent the predicted label and the number of elements in the true label, $p\left(x_i\right)$ and $q\left(x_i\right)$ represent the probability distribution vectors of the true label and the model prediction, ∑ represents the sum of all categories, and $log$ represents the natural logarithm.

4. Algorithm Performance Analysis

In order to verify the performance of the constructed KANs-Unet model in detecting kernel anomaly areas, the author designed a comparative experiment. In the experiment, the author adopted the kernel anomaly region dataset constructed in Section 2 and comprehensively compared the newly designed KANs-Unet model with various semantic segmentation models. These comparative models cover classic network architectures such as U-net, Unet++, DeepLabV3, DeepLabV3+, LinkNet, PSPNet, FPN, PAN, and MAnet. In addition, the author also included traditional unsupervised edge detection methods as comparative objects, aiming to further highlight the necessity and superiority of using supervised deep learning semantic segmentation methods in handling such tasks through this series of comparative analyses. This series of comparative experiments not only validates the excellent performance of the KANs-Unet model but also provides new perspectives and inspirations for research in the field of kernel anomaly detection.

4.1. Experimental Environment

The experimental environment for the KANs-Unet kernel anomaly detection model is a server environment under the Linux operating system. The hardware environment configuration for the training process comprised an NVIDIA Tesla V100 with 64 GB of RAM and a GeForce RTX3090 with 24 GB of graphics card. The software environment was the Ubuntu 18.04 operating system, and Pytorch version 1.9.1 was used to build and train the deep neural network model framework.

4.2. Evaluating Indicator

To verify the effectiveness of the KANs-Unet model and objectively compare its performance differences with other different models during the training process of the same task, the authors used evaluation metrics based on the confusion matrix, namely the mean intersection over union (mIoU) and mean pixel accuracy (mPA). The confusion matrix is shown in

Table 2. Confusion matrix.

	Predicted as Positive	Predicted as Negative
Actual positive class	True Positive	False Negative
Actual negative class	False Positive	True Negative

.

The average intersection-to-union ratio measures the degree of overlap between the predicted results of the model and the actual annotated pixels. The method used calculates the IoU of each category and then averages it. The calculation method of IoU is used to calculate the true class (TP), false-positive class (FP), and false-negative class (FN) of each category and then calculate TP/(TP+FP+FN) to obtain it. The average pixel accuracy is a measure of the pixel classification accuracy of a model in each category. The method is used to calculate the PA of each category and then average it. The calculation method of the PA is similar to that of the IoU, obtained by calculating (TP+TN)/(TP+FP+FN+TN). The calculation formulas for the mIoU and mPA are shown in (5) and (6):

$$mIoU={\displaystyle \frac{1}{k+1}}\sum _{I=0}^k{\displaystyle \frac{p_{ii}}{{\sum }_{J=0}^k{p}_{ij}+{\sum }_{j=0}^k{p}_{ji}-p_{ii}}}$$

(5)

$$mPA={\displaystyle \frac{{\sum }_{i=0}^k{p}_{ii}}{{\sum }_{i=0}^k{\sum }_{j=0}^k{p}_{ij}}}$$

(6)

where k and (k + 1), respectively, represent the number of target categories and the total number of categories after adding background categories, and i and j, respectively, represent the actual pixel values and the pixel values predicted by the model. $p_{ij}$ represents predicting i as the value of j, $p_{ji}$ represents predicting j as the value of i, and $p_{ii}$ represents predicting i as the correctly predicted value of i; that is, the pixel value is equal to the true value.

4.3. Parameter Settings

To optimize the detection results of the kernel anomaly regions, maximize the performance of the model, and ensure that the KANs-Unet model can achieve the best performance on both training and testing data, it is necessary to set the parameters of the model. After multiple experimental verifications and analyses, the parameter settings of the KANs-Unet model are listed in

Table 3. Parameter settings.

Parameter	Parameter Values
classes	2
Epoch	600
batch_Size	16/16
optimizer	Adam
learning_Rate	0.001

. The entire training dataset for the kernel anomaly region was fully processed using the KANs-Unet model, with a forward and backward propagation process set to 600 epochs. This is because extensive experiments have shown that the model can obtain the optimal evaluation metrics before 600 epochs. The number of images placed in the model at once is set to 16 for both the training and testing sets. This is because when the batch size is 16, it can maximize the utilization of the GPU and adapt to model training. The optimizer used for model training adopts an update rule of gradient-based first-order moment estimation and second-order moment estimation to dynamically adjust the learning rate using Adam (adaptive moment estimation). This is because the optimizer can better automatically and dynamically adjust the learning rate. The initial learning_rate is set to 0.001 because a learning rate of 0.001 can provide relatively stable performance and achieve good results.

4.4. Comparative Experiment

Before using supervised deep learning semantic segmentation techniques for detecting kernel abnormal regions, the author used traditional visual edge detection techniques to detect kernel abnormal regions. Edge detection can identify regions in images with significant brightness changes, which typically represent the boundaries or other important features of objects. However, edge detection is susceptible to noise, leading to inaccurate results. Common edge detection algorithms include the Sobel operator, Prewitt operator, Canny edge detection, and Laplacian operator. After an experimental comparison and analysis, the author chose Canny edge detection for detecting kernel anomaly areas. The result of Canny edge detection is shown in subgraph (b) of Figure 7. It is observed that the contour of the kernel anomaly area cannot be detected, and the effect is not good. Therefore, it is necessary to use supervised deep learning semantic segmentation techniques for the detection task of kernel abnormal regions.

To demonstrate the superiority of the KANs-Unet model in detecting kernel anomaly regions and compare and evaluate the performance differences between different algorithms, the author used the kernel anomaly region dataset created in Section 2 above to conduct experiments on the KANs-Unet model and nine other classic semantic segmentation algorithms. The evaluation metrics mIoU and mPA for each algorithm are shown in

Table 4. Comparison results of image segmentation algorithms.

Model	mIoU	mPA
KANs-Unet	0.785743	0.998973
U-net	0.741681	0.998994
DeepLabv3	0.718519	0.998905
PSPNet	0.685374	0.998711
LinkNet	0.716289	0.998867
FPN	0.708899	0.998785
DeepLabv3+	0.720010	0.998965
Unet++	0.700127	0.998845
PAN	0.707727	0.998922

. Among them, the first column of data is the model used in the comparative experiment, the second column is the evaluation index mIoU of the model, and the third column is the evaluation index mPA of the model.

The author presented a visual comparison chart of the prediction results between the KANs-Unet model and other semantic segmentation models in the comparative experiment, as shown in Figure 8. From these visual comparison graphs, it is evident that the KANs-Unet algorithm proposed by the author performs outstandingly in predicting results. There are some shortcomings in the detection of other comparative experimental models, especially in the left half of subgraphs d and e in Figure 8. The kernel anomaly area on the left side of the image was not fully detected, and only the part with the highest energy value was identified, which did not cover the entire kernel anomaly area. This may be because the model failed to fully consider its global features when segmenting kernel anomaly regions, resulting in missing feature maps and affecting detection performance. The significant predictive performance of the KANs-Unet algorithm, in most cases, still strongly demonstrates its efficiency and accuracy in detecting kernel anomaly regions.

5. Algorithm Application

In order to further study the distribution of central frequency points in the kernel anomaly area, the distribution of ascending and descending orbits of the orbit, and the changes during magnetic storms (including large and toxic storms), the author analyzed the data of major geomagnetic storms from November 2021 to October 2022, 11 May 2024 (specifically 1 May 2024 to 13 May 2024), and moderate geomagnetic storms from 21 October 2023 (specifically 11 October 2023 to 23 October 2023). Among them, the annual data were distributed in 453 kernel anomaly areas on 402 tracks. During a major geomagnetic storm, there were 162 kernel anomaly regions distributed on 114 orbits. During a moderate geomagnetic storm, there were 90 kernel anomaly areas distributed on 79 orbits.

5.1. Center Frequency Distribution

To explore the frequency range of the distribution of the center frequency points in the kernel anomaly area (considering the highest energy value of the center of the kernel anomaly area as the center frequency point), the author analyzed the frequency points where the center of the kernel anomaly area is located throughout the year. It was found that the center frequency points of the vast majority of kernel anomaly areas are distributed between 3 KHz and 12.4 KHz, with only one case of center frequency points located at higher frequencies during winter. The overall trend of the central frequency point of the kernel anomaly area throughout the year shows a wave-like fluctuation along the 6.2 KHz range. The distribution of central frequency points in the kernel anomaly area throughout the year is shown in Figure 9. The horizontal axis represents the number of kernel anomaly areas, and the vertical axis represents the frequency. The four colors blue, red, yellow, and green in the legend represent the four seasons of spring, summer, autumn, and winter, respectively.

5.2. Distribution of Ascending and Descending Tracks of the Track

The working mode of a satellite is to rotate around the Earth. The orbit from the south latitude to the north latitude is called the ascending orbit, and the orbit from the north latitude to the south latitude is called the descending orbit. To analyze the distribution of ascending and descending orbits in areas with kernel anomalies and whether the distribution of ascending and descending orbits is related to seasonal factors, the author analyzed the trajectories of kernel anomaly areas from November 2021 to October 2022, dividing them into four seasons. It was found that in the distribution of ascending and descending orbits in spring, summer, and autumn, the ascending orbits were all redundant or equal to the descending orbits. Only in winter was there a significant difference in the trajectories of kernel anomaly areas, with significantly more descending orbits than ascending orbits. The number of orbits with kernel anomaly areas in spring, summer, and autumn is significantly higher than that in winter. The distribution of ascending and descending trajectories in the kernel anomaly area is shown in Figure 10. The horizontal axis represents the four seasons of spring, summer, autumn, and winter, the vertical axis represents the number of kernel anomaly areas, and the legend represents ascending and descending orbits, with yellow indicating the ascending orbits and green indicating the descending orbits.

5.3. Changes During Geomagnetic Storms

In addition to analyzing the distribution of central frequency points and the distribution of ascending and descending orbits in the kernel anomaly area, this article also analyzed the distribution and changes in the kernel anomaly area during large geomagnetic storms. From November 2021 to October 2022, the geographic spatial distribution of the kernel anomaly area is mostly between 40° and 70° north latitude, and the spatial distribution of magnetic latitude is mostly between 58° and 80° south and north magnetic latitude. The overall distribution trend shows a wave shape with the rise and fall of magnetic latitude, and there is a band-like distribution with parallel trends between north and south magnetic latitude. The spatial magnetic latitude distribution is shown in Figure 11. The horizontal axis represents longitude, the vertical axis represents latitude, and the red, blue, green, and orange represent the kernel anomaly areas in the four seasons of spring, summer, autumn, and winter.

The author selected the large geomagnetic storm on 11 May 2024 as an example to analyze the data of the 13 days before the occurrence of the storm (specifically from 1 May 2024 to 13 May 2024). It was found that the overall spatial distribution of the kernel anomaly area did not change much between the south and north latitudes of 40°~70°, but its magnetic latitude distribution was relatively scattered. The magnetic latitude distribution in the northern hemisphere was between 60° and 80°, and there were more kernel anomaly areas in the southern hemisphere at higher magnetic latitudes, ranging from 54° to 86°. The spatial distribution of magnetic latitude during a major geomagnetic storm is shown in Figure 12. The green origin represents the kernel anomaly area during a major geomagnetic storm.

In addition, the author also selected 13 days of data from a moderate geomagnetic storm on 21 October 2023 (specifically from 11 October 2023 to 23 October 2023) for comparative analysis and research. The analysis found that the overall geographical distribution of the kernel anomaly areas has not changed much, but the global magnetic latitude distribution is relatively concentrated, with a significantly larger number in the northern hemisphere distributed between magnetic latitudes 68° and 82° and a smaller number in the southern hemisphere distributed between magnetic latitudes 56° and 76°. At the same time, the data of kernel anomaly areas in the ascending orbit are significantly higher than those in the descending orbit. The highest energy value in the kernel anomaly area of moderate geomagnetic storms is lower than that of large geomagnetic storms. The spatial distribution of magnetic latitude during moderate geomagnetic storms is shown in Figure 13. The red dots represent the kernel anomaly areas during moderate geomagnetic storms.

After comparing and analyzing the abnormal data during the geomagnetic storm period with the whole year, it was found that there were significant changes in the distribution of the orbit ascending and descending of the kernel anomaly area during the large geomagnetic storm period, but the overall change was not significant during the moderate geomagnetic storm period. During a major geomagnetic storm, the number of data showing kernel anomaly areas in the ascending orbits is significantly higher than that in the descending orbits. Analysis suggests that this may be the cause of the major geomagnetic storm. Due to the fact that ascending orbit is a daytime flight around the Earth from the south latitude to the north latitude, intense solar activity during the day leads to a higher number of kernel anomaly areas. At the same time, it was found that the highest energy value in the kernel anomaly area during a geomagnetic storm was higher than that during a non-large geomagnetic storm, and it displayed a darker color on the image. In addition, during the period of the geomagnetic storm, 11 May and 12 May are the peak periods of the geomagnetic storm. In the power spectrum image, it can be clearly observed that there are more kernel anomaly areas with higher energy values than those during the geomagnetic storm. Moderate geomagnetic storms did not show any significant anomalies. At the same time, we also discovered the phenomenon of dual events in the kernel anomaly region during the large geomagnetic storm, which means that two very similar kernel anomaly regions were simultaneously discovered on the same orbit, as shown in Figure 14.

The significant characteristics of kernel abnormal areas are mainly manifested as higher energy values and darker colors in the central area, while as the energy values gradually decrease towards the edges, the colors correspondingly become lighter and the edge morphology presents irregularity. Although existing models have been improved, accurate detection of the edges of anomalous regions remains a major challenge. In addition, the model has inherent limitations in extracting fine structure and boundary feature information, especially in the downsampling process, where the loss of some detailed information leads to unsatisfactory segmentation results in boundary areas and small-sized abnormal areas. Another issue that cannot be ignored is the presence of a significant amount of noise and interference in the image. When these factors reach a certain level of intensity, they can significantly affect the segmentation results, leading to misclassification or missed segmentation. In view of this, future research directions will focus on the following points:

(1) Optimization and refinement of algorithms: Continue to innovate and optimize algorithms to achieve higher accuracy in detecting the edges of kernel anomaly regions, thereby improving the evaluation indicators of detection performance.

(2) Expanding the detection range to other types of ionospheric signal anomalies in space: Based on the existing ability to detect kernel anomaly areas, explore and develop detection technologies for other types of ionospheric signal anomaly areas in space.

(3) Global distribution and influencing factors analysis of kernel anomaly areas: Based on the current research results on global spatial distribution, this study explores in depth the distribution patterns of kernel anomaly areas in recent years, as well as the potential impact of various factors on the global distribution patterns of kernel anomaly areas.

6. Conclusions

The author discovered kernel anomaly regions in spatial ionospheric electric field data. To better detect and analyze these regions, this paper improved the U-net algorithm and proposed a new KANs-Unet model. This model utilizes a new neural network architecture called KANs, which is an alternative to the current multilayer perceptron MLPs. It is integrated into a convolutional neural network and then applied to the algorithm designed in this study. Further analysis was conducted on the center frequency distribution, the ascending and descending orbit distributions of the kernel anomaly area, and the distribution changes in the kernel anomaly area during the major geomagnetic storms from November 2021 to October 2022 and from 1 May 2024 to 13 May 2024. The conclusions are as follows:

(1) Compared with existing classical semantic segmentation algorithms, the KANs-Unet algorithm has better performance and effectiveness and can effectively detect kernel abnormal regions.

(2) Analysis found that the central frequency distribution of the kernel anomaly area fluctuates up and down along 6.2 KHz, and the vast majority of them are distributed between 3 KHz and 12.4 KHz. Except in winter, there are more ascending orbits than descending orbits in the distribution of anomalous ascending and descending orbits.

(3) There are differences in the distribution of kernel anomaly areas between geomagnetic storms and non-magnetic storms. During a major geomagnetic storm, the overall spatial distribution is relatively consistent, but the spatial magnetic latitude distribution is relatively scattered, especially in the southern hemisphere, where the distribution range of magnetic latitude increases. Due to the influence of solar activity, there are significantly more orbits with kernel anomalies during the daytime, especially during the peak periods of the 11 May and 12 May geomagnetic storms. During moderate geomagnetic storms, the difference is small, but the number of abnormal areas in the northern hemisphere is significantly higher than that in the southern hemisphere. In addition, the phenomenon of dual events in kernel anomalous regions was discovered during large geomagnetic storms.

(4) The KANs-Unet algorithm can effectively detect kernel anomaly regions, which has reference significance for detecting other types of spatial electromagnetic field disturbances and lays the foundation for subsequent research on kernel anomaly regions.