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BY 4.0 license Open Access Published by De Gruyter Open Access February 10, 2023

An outlier detection method with CNN for BeiDou MEO moderate-energy electron data

  • Tian Chao EMAIL logo , Cui Ruifei , Zhang Riwei , Xu Peikang , Chen Libo , Shang Jie , Quan Lin , Wan Yujun , Hu Sihui , Yue Fulu and Su Xing
From the journal Open Astronomy

Abstract

BeiDou Medium Earth Orbit moderate-energy electron detection data play an important role in space environment effect analysis including satellite anomaly diagnosis, satellite risk estimation, etc. However, the data contain outliers which cause obstacle for the subsequent usage significantly. To solve this problem, we propose an outlier detection method based on convolutional neural networks (CNNs) which can learn a rule from labeled historical data and detect outliers from the detection data. With this method, we can identify outliers and do some follow-up operations to improve the data quality. In comparison with general methods, this CNN method provides a more reliable and rapid way to build dataset for the follow-up work.

1 Introduction

Satellites are usually placed and operated in terrestrial space. Satellites especially Medium Earth Orbit (MEO) and GEO satellites immerse in or pass through the outer radiation and suffer the dramatic and frequent change in the electronic environment. To study charging and discharging effects caused by the energetic and electronic environment, research such as geomagnetic storms, magnetospheric substorms, and high-energy electron disturbance mechanisms has been done (Roberts 1969, West et al. 1973, Morioka et al. 2001, Horne et al. 2003, Summers and Thorne 2003, Baker et al. 2005, Li et al. 2005, 2009, 2016, 2017, 2018, Li and Wang 2018, Gannon et al. 2007, Yu et al. 2015). But with the development of astronautics, more satellites have been launched and more anomalies were caused by high-energy electron which is also called “killer electrons.” Recent research shows that more than half of the MEO satellite anomalies are suspected to be caused by the “killer electrons” in the outer radiation belt (Yu et al. 2016). In this circumstance, the satellite long-term management and control task puts forward higher requirements to detect terrestrial space energetic electronic environment. With the development of high-precision energy spectrum and pitch angle measurement, different electronic environment detectors have been carried on satellites such as NOAA-POES, GPS, and RBSP to fulfil energetic electronic environment monitoring and scientific research need (Evans and Greer 2004, Tuszewski et al. 2004, Blake et al. 2013, Yang et al. 2015). Meanwhile, some BeiDou MEO satellites also carry similar detectors to do research such as space environment monitoring and early warning, satellite anomalies analysis, and space environment risk assessment. However, in practical application, we can find many outliers hidden in the detection data which might be caused by instrument failures, data transmission error, or ground data processing error. These outliers not only affect the rationality of electronic environment monitoring, but also limit the accuracy of space environment events for early warning, satellite anomalies analysis, and risk estimation. Furthermore, these negative impacts will reduce the effectiveness of satellite protection, evaluation, and long-term management and operation. Therefore, the outlier detection method for BeiDou electron detection data is an urgent problem to be solved.

Generally, numerical outlier method (Buzzi-Ferraris and Manenti 2012, Zimek et al. 2012, Pang et al. 2018), Z-score method (Seo 2006, Cousineau and Chartier 2010, Kannan et al. 2015, Aggarwal et al. 2019), DBSCAN method (Çelik, et al. 2011, Thang and Kim 2011, Jin et al. 2019, Ghallab et al. 2020), and Isolation Forest method (Ding and Fei 2013, Cheng et al. 2019, Heigl et al. 2021) can be used for outlier detection. Among these methods, the numeric outlier and the Z-score method are only suitable to analyze the one-dimensional or low-dimensional data, the DBSCAN method and the Isolated Forest method can deal with multi-dimensional data but might lead to feature loss between different dimensions. Unfortunately, BeiDou MEO moderate-energy electron data are multi-dimensional data (highest dimension is 72) which are saved according to time series (Cui et al. 2021). These data imply strong physical meaning and show obvious time correlation. As a result, we cannot use outlier detection methods above to detect the outliers among the BeiDou MEO moderate-energy electron data. To solve this problem, we attempt to use machine learning technology and hope to find a new method to detect outliers among the BeiDou electron detection data. During the experiment, we find that Convolutional neural network (CNN) is outstanding in terms of detection accuracy and time cost. This work proposes this CNN-based outlier detection method and shows the performance which indicates CNN method is a more reliable and rapid way to detect outliers among BeiDou MEO moderate-energy electron data (Walach and Wolf 2016, Bydder et al. 2019).

2 Data characteristics

Before the introduction of the CNN outlier detection model, spatial-temporal features of BeiDou moderate-energy electron detection data are introduced as follows.

2.1 Characteristics of the detection data

Normally, electron detection data reflect the physical changes in electronic environment in time and space. The characteristic of the BeiDou MEO moderate-energy electron data includes spatial, temporal, and physical characteristics. Because the detection data are stored as a time series, the temporal characteristic is reflected in the chronological order.

The spatial characteristic of the data is determined by the Imaging energetic electron spectrometer (IES-II) structure and probe angle of the detector. The schematic diagram of IES-II is shown in Figure 1.

Figure 1 
                  Structure schematic diagram of IES-II detector. (a) Structure of probe and (b) structure diagram of the IES-II detector.
Figure 1

Structure schematic diagram of IES-II detector. (a) Structure of probe and (b) structure diagram of the IES-II detector.

As seen in Figure 1, each probe covers 20° of view and the detection data are numbered from D1 to D9 and saved in the form of data frames by the detector management host on-board the satellite (Ye et al. 2021). Therefore, BeiDou moderate-energy electron detection data reflect the electronic environment within 180° field of view around the installation position of the detector. Obviously, the interchange over different energy channels will destroy the spatial characteristics of the detection data.

Meanwhile, according to the theory of radiation belt electronic environment, electrons in terrestrial space have the law of day and night alternating and show a Gaussian-like distribution with bimodal structure (Roberts 1969, West et al. 1973, Morioka et al. 2001, Horne et al. 2003, Summers and Thorne 2003, Baker et al. 2005), and this distribution reflects the physical characteristic. Therefore, the electron detection data need to continuously cover a certain energy range in the energy spectrum. Table 1 shows the energy spectrum range for BeiDou moderate-energy electron data.

Table 1

Energy spectrum range of BeiDou MEO moderate-energy electron data

Energy channel Energy spectrum range (keV)
1 50–68
2 68–93
3 93–130
4 130–170
5 170–240
6 240–320
7 320–440
8 440–600

From Table 1, it can be seen that the detection data cover the electronic environment within the energy range from 50 to 600 keV continuously, and the interchange over different energy channels will destroy the physical characteristic of the detection data. The detection data from July 3, 2020 to July 4, 2020 are shown in Figure 2.

Figure 2 
                  BeiDou moderate-energy electron data from July 3 to July 4, 2020.
Figure 2

BeiDou moderate-energy electron data from July 3 to July 4, 2020.

2.2 Characteristics of outliers

When exceptions such as detector failures, data transmission error, and ground data processing error occur, the characteristic of the detection data will change obviously. Normally, we regard detection data with significant changes in characteristics as outliers. The outliers are shown in Figure 3.

Figure 3 
                  The outliers of BeiDou moderate-energy electron data from July 1 to July 7, 2019.
Figure 3

The outliers of BeiDou moderate-energy electron data from July 1 to July 7, 2019.

It can be seen from Figure 3 that the detection data in each direction are chaotic when an abnormal situation occurs. It specifically represents that (І) The detection data occurs significantly abnormal at the same time and (ІІ) The distribution law of the outliers is very different from the normal detection data. Figure 4 shows the outliers in direction 3. It can be seen that the value is saturated in some energy levels and the law and characteristic of each energy level is quite different from the normal state.

Figure 4 
                  Outliers in direction 3.
Figure 4

Outliers in direction 3.

We compare the characteristic of detection data in different conditions including peace time and storm time of electronic environment, and the outliers in Figure 5. It can be seen that the energy spectrum of the detection data is relatively high in the storm time. That is, the peak of each energy channel shifts to the higher energy level, but the proportional relationship between each direction is basically maintained unchanged compared with the peace time. But for outliers, whether it is in peace or storm time, the proportional relationship is disturbed between the detection data of each direction and each energy level within a single direction.

Figure 5 
                  The data characteristics of detection data and outliers. (a) Characteristics in peace time; (b) characteristics in storm time; and (c) characteristics of outliers.
Figure 5

The data characteristics of detection data and outliers. (a) Characteristics in peace time; (b) characteristics in storm time; and (c) characteristics of outliers.

Based on the above analysis, BeiDou MEO moderate-energy electron data have certain characteristics in space, time, and physics, while the outliers have very different characteristics. To accomplish outlier detection, care must be taken to avoid corrupting the above characteristics of the detection data.

3 Analysis of methods and data processing

3.1 Analysis of CNN

In the field of deep learning, scientists invented and designed a CNN with the characteristics of weight reduction, local connection, and weight sharing in order to overcome the shortcoming of traditional neural networks, such as too many weights required, too much calculation, and large training sample set demand. Generally, CNN includes input layer, convolutional layer, pooling layer, full connected layer, and output layer. Through the abovementioned approach, CNN method reduces the number of parameters that the neural network needs to train through receptive field and weight sharing. A typical CNN structure (LeNet-5) is shown in Figure 6.

Figure 6 
                  Typical CNN structure used in LeNet-5.
Figure 6

Typical CNN structure used in LeNet-5.

At present, CNN is often used to extract the features of things with a specific model, and then classify, identify, predict, or make decisions based on the features. Based on the conclusion of data characteristic analysis in Section 2, we know that there are significant differences between outliers and detection data which are implied by the distribution characteristics of orbital electrons in the direction and energy spectrum. After analysis, we think CNN method has the ability to extract and identify features from outliers and normal detection data. And an outlier detection method based on CNN will be suitable for outlier detection of BeiDou MEO moderate-energy electron data.

3.2 Data processing

Primarily, the method for outlier detection of MEO orbital electron data needs to solve the problem of conversion between detection data and quasi-grayscale image data. The monitoring data are an unsigned single-precision floating-point number (unsigned float, ranges from 0 to 6.8 × 1038), while the pixel data in the grayscale image is a gray scale value (the value ranges from 0 to 255). If we directly normalize the detection data to the grayscale value, it will lead to the loss of precision. This will result in the fuzziness of grayscale image data features and hence, is not conducive for the outlier detection based on image features. To solve this problem, we proposed a solution as follows:

  1. Remove the useless information in the detection data, such as the repeated or direction incomplete data;

  2. Convert the structural data into matrix data (acts like a quasi-grayscale image).

With this transformation, only eight energy spectrum detection gears in nine directions in each detection period are retained. After preliminary treatment, we can obtain the quasi-grayscale image data corresponding to the pixel value and the electron data one-to-one. The specific form is shown in Figure 7. On this foundation, the data solidification processing is shown in Figure 8.

Figure 7 
                  The converted quasi-grayscale data.
Figure 7

The converted quasi-grayscale data.

Figure 8 
                  Data processing flow chart.
Figure 8

Data processing flow chart.

4 Outlier detection model design and implementation

This section introduces the design process of the outlier detection model. It includes the design of the outlier detection model based on CNN and the model training and testing process.

4.1 Implementation of the outlier detection model

Based on the data characteristics analysis, we can draw conclusions as follows:

  1. The feature image data should be a matrix with 9 rows and 8 columns (represented as 72 pixels in the quasi-grayscale image data);

  2. There are obvious spatial distribution characteristics over different directions of the detection data. These characteristics are reflected in the transition of brightness information in each column of pixels in Figure 6, and the characteristic area contains at least two pixels;

  3. The different energy levels of the detection data in the same direction have obvious energy distribution characteristics. These characteristics are reflected in the transition of brightness information in each row of pixels in Figure 7, and the characteristic area contains at least two pixels;

  4. There are obvious differences between the peace time and the storm time which are reflected in the change in the high-frequency component area of the image in Figure 5a and b, and the characteristic area contains at least 2 × 2 pixels;

  5. For the outliers, the image characteristics are obviously different. These characteristics are reflected in the change in the high-frequency features of the image in Figure 5c.

On the basis of conclusions above, the design ideas of the CNN model are determined as follows:

  1. The input of the CNN model is a matrix with 9 rows and 8 columns.

  2. The model contains two convolutional layers for extracting image features. In convolutional layer 1, the size of the kernels is 3 × 3, the number of convolution kernels is 6, and the stride is 1. In convolutional layer 2, the size of convolution kernels is 3 × 3, the number of convolution kernels is 16, and the step size is 1.

  3. The pooling layer is used to reduce the complexity of the model and avoid over-fitting. This step is done by global pooling.

  4. The fully connected layer is used to integrate the extracted image features, and the ReLU function is selected as the excitation function of this layer.

  5. The output layer is used to output the model detection results, where the normal label is 1, while the abnormal label is 0.

Based on the above CNN model design, the structure of the CNN outlier detection model is shown in Figure 9.

Figure 9 
                  Structure diagram of CNN outlier detection model.
Figure 9

Structure diagram of CNN outlier detection model.

4.2 Model training and testing

Considering the dynamic characteristics of terrestrial space electronic environment, the training set and test set of the outlier detection model should cover the below three situations:

  1. The dataset should contain outliers of BeiDou moderate-energy electron data;

  2. The normal detection data of BeiDou moderate-energy electron data include electronic environment peace time and storm time;

  3. The outliers should be continuous in time with normal detection data.

To satisfy the above situations, we choose a dataset which contains 578 days’ detection data from December 1, 2018 to June 20, 2020. During this period, terrestrial space electronic environment peace time and storm time each lasted for 493 days and 85 days, respectively, and outliers lasted for 123 days. Among the outliers, the terrestrial space electronic environment peace time and storm time each lasted for 75 days and 48 days, respectively. The basic properties of the dataset are shown in Figure 10.

Figure 10 
                  Basic properties of the dataset. (a) BeiDou moderate-energy electron data in total. (b) Outliers of BeiDou moderate-energy electron data. (c) Normal BeiDou moderate-energy electron data.
Figure 10

Basic properties of the dataset. (a) BeiDou moderate-energy electron data in total. (b) Outliers of BeiDou moderate-energy electron data. (c) Normal BeiDou moderate-energy electron data.

After data processing, we get 139,644 frame quasi-grayscale image data in the dataset. To avoid repetitive training caused by repetitive training sets, K-fold method which is shown in Figure 11 was used to divide the data into different test sets. In this way, the dataset is randomly divided into five data folds. In order to achieve cross validation, in the process of model training and testing, one data fold is selected as the test set and the remaining four data folds are used as the training set. Through this way, the construction of five training and test sets for cross-validation is completed.

Figure 11 
                  K-fold methods.
Figure 11

K-fold methods.

Meanwhile, methods such as Ada Boost, Bagging Tree, Decision Tree, Linear Regression, and SVM were selected as comparison for the CNN method during the cross validation. The performance of different methods in validation tests were evaluated by counting the number of true positive (TP), false positive (FP), true negative (TN), and false negative (FN) and the above four indicators constitute the confusion matrix shown in Figure 12. In the confusion matrix, true positives and true negatives indicate that the result of outlier detection is correct. Conversely, false positives and false negatives indicate that the outlier detection is wrong.

Figure 12 
                  Schematic diagram of confusion matrix.
Figure 12

Schematic diagram of confusion matrix.

The result of cross validation shows that Ada Boost method gives 4,178 false negatives and 1 false positive, Bagging Tree method gives 2 false negatives and 11 false positives, Decision Tree method gives 2 false negatives and 10 false positives, Linear Regression method gives 2 false negatives and 1,557 false positives, SVM method gives 1,585 false negatives and 1 false positive, and CNN method gives 3 false negatives and 1 false positive. The results show that the outlier detection method based on CNN has obvious accuracy advantages compared with other methods in the outlier detection of BeiDou MEO moderate-energy electron data. The cross-validation result of each method is shown in Table 2.

Table 2

Cross validation results of each method

Cross-validation method Ada Boost Bagging Tree Decision Tree Linear Regression SVM CNN
Validation 1 False positive 0 0 0 0 0 0
False negative 0 0 0 0 0 0
Validation 2 False positive 1 11 10 1 1 1
False negative 0 0 0 0 0 0
Validation 3 False positive 0 0 0 1,556 0 0
False negative 4,178 2 2 2 1,585 3
Validation 4 False positive 0 0 0 0 0 0
False negative 0 0 0 0 0 0
Validation 5 False positive 0 0 0 0 0 0
False negative 0 0 0 0 0 0
Errors in total 4,179 13 12 1,559 1,586 4

Through the confusion matrix, we can calculate indexes such as accuracy, precision, recall, and F1_Score as the model evaluation parameters by using formulas in formula (1) to formula (4).

(1) Accuracy = TP + TN TP + FP + FN + TN ,

(2) Precision = TP TP + FP ,

(3) Recall = TP TP + FN ,

(4) F 1_Score = 2 × Precision × Recall Precision + Recall .

As a result, we get the model evaluation results in Table 3.

Table 3

Evaluation parameters of outlier detection model

Parameters Value
Accuracy 0.99997
Precision 1
Recall 0.99986
F1_Score 0.99989

While evaluating the accuracy, we also make a statistical analysis of the timeliness of each detection method. Table 4 shows the scale of training/test set used in the cross validation and the time consumed by each method to detect outliers in the test set. The result shows that although the CNN method is not optimal in terms of timeliness, but the time consumption of the method to complete the detection of nearly 28,000 data is only about 0.194 s which is acceptable for outlier detection.

Table 4

Scale of training/test set and the time consumed by each method

Data size and method of cross validation Validation 1 Validation 2 Validation 3 Validation 4 Validation 5 Avg
Training set size 111,715 111,715 111,715 111,715 111,716 --
Test set size 27,929 27,929 27,929 27,929 27,928 --
Ada Boost time 0.138 s 0.027 s 0.023 s 0.058 s 0.036 s 0.056 s
Bagging Tree time 0.194 s 0.197 s 0.201 s 0.195 s 0.204 s 0.198 s
Decision Tree time 0.006 s 0.006 s 0.006 s 0.008 s 0.006 s 0.006 s
Linear Regression time 0.005 s 0.004 s 0.004 s 0.003 s 0.004 s 0.004 s
SVM time 0.583 s 0.564 s 0.454 s 0.511 s 0.487 s 0.520 s
CNN time 0.264 s 0.181 s 0.172 s 0.170 s 0.184 s 0.194 s

5 Conclusion

Compared with other outlier detection methods, this study has the following advantages.

5.1 Simplify the outlier detection process

The outlier detection using traditional terrestrial space analysis method needs professionals with physics background to make physical and statistical analysis. Outlier detection in this way will be more complex and consumes more time. But for the outlier detection method based on CNN we can see two advantages. On the one hand, the data processing method in this work can be used automatically to reduce human intervention. On the other hand, this CNN method converts the physical and spatial characteristic of data to image features, this approach ensures that no data characteristics are lost in outlier detection. This method enables the machine to complete the complex work that can be completed by the professionals before and simplifies the outlier detection process.

5.2 Improve the accuracy of outlier detection

In this work, we can see that the CNN method has obvious advantages in the accuracy of outlier detection for BeiDou moderate-energy electron data. But for manual detection method, although the entire outlier detection process is supported by standardized steps and a relatively complete theoretical system, there still exists influence from human subjective state at some key points. These influences will directly affect the accuracy of outlier detection. However, the outlier detection method based on CNN will maintain its accuracy stably.

5.3 Optimize the timeliness of data annotation

The outlier detection model based on CNN can complete the outlier detection of a large number of data in a very short time. At the same time, CNN method is based on image features, we can use TensorFlow to complete the construction of the CNN model. In this way we can make full use of the GPU computing advantages of TensorFlow which can increase the calculation rate several times or even dozens of times in massive data calculation, especially in matrix data calculation. In this way the timeliness of outlier detection will be optimized greatly.

5.4 Strong model generalization ability

The outlier detection based on CNN can adjust each step according to the data characteristic. For example, the current input data are 9 × 8 elements, the data preprocessing can reshape the data into 9 × 8 matrix data after data filtering, and the CNN model uses this as a standard for data labeling. Assuming that the input data are 7 × 7 elements, the data preprocessing can reshape the data into 7 × 7 matrix data after data filtering and the CNN model can be adapted to the data mode and perform outlier detection by adjusting the input parameters. The generalization ability of this model can be greatly enhanced by adjusting the form of the input parameters of the CNN model.

Acknowledgement

The authors would like to thank the team in Peking University (led by Prof. Hong Zou) for the development of the payload used in this work. The authors also would like to thank the team in State Key Laboratory of Astronautic dynamics (led by Dr. Jiang Yu) for the data processing technical guidance in this work.

  1. Funding information: National Natural Science Foundation of China (Key Program No. U21B2050).

  2. Author contributions: Tian Chao put forward the research idea, contributed to the algorithms and programs design, and proposed the validation method. Cui Ruifei contributed to the design of methodology and CNN model. Zhang Riwei contributed significantly for the analysis and manuscript preparation. Xu Peikang, Chen Libo, and Shang Jie contributed a lot to scrub data and maintain research data. Quan Lin and Wan Yujun contributed to specifical visualization of the study. Hu Sihui, Yue Fulu, and Su Xing contributed to the management and coordination responsibility for the research activity.

  3. Conflict of interest: We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

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Received: 2022-07-17
Revised: 2022-09-11
Accepted: 2022-10-03
Published Online: 2023-02-10

© 2023 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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