# An Efficient Compression Method for Lightning Electromagnetic Pulse Signal Based on Convolutional Neural Network and Autoencoder

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}area in southern Texas. In the recognition and classification task of lightning data, Morales et al. [9] compared Multi-resolution analysis (MRA) with Artificial Neural Network (ANN), K-Nearest Neighbors (KNN) and Support Vector Machine (SVM)—which are machine learning methods—to analyze transmission line lightning events and achieve good classification results. Zhu et al. [10] used the SVM algorithm to classify representative cloud-to-ground and intracloud lightning, and its accuracy could reach 97%. In locating lightning events, Karami et al. [11] proposed using a machine learning method to locate the lightning strike point based on the lightning-induced voltage value measured by sensors on the transmission line. Recently, Wang et al. [12] also combined the lightning positioning method with artificial intelligence, and used the deep-learning encoding feature matching method to improve the speed, accuracy and anti-interference ability of the original positioning algorithm.

## 2. Model and Methods

#### 2.1. Data Sets Collected by Sensor Networks

#### 2.2. Autoencoder

#### 2.3. Structure of Compression and Reconstruction Model LCSAE

#### 2.4. Model Hyperparameter

#### 2.4.1. Activation Function

#### 2.4.2. Training Loss Function and Optimizer

## 3. Results and Evaluation

#### 3.1. Evaluation Index

#### 3.2. Experimental Results

#### 3.3. Test and Analysis

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Bao, R.; Zhang, Y.; Ma, B.J.; Zhang, Z.; He, Z. An Artificial Neural Network for Lightning Prediction Based on Atmospheric Electric Field Observations. Remote Sens.
**2022**, 14, 4131. [Google Scholar] [CrossRef] - LeCun, Y.; Bengio, Y.; Hinton, G. Deep learning. Nature
**2015**, 521, 436–444. [Google Scholar] [CrossRef] [PubMed] - Luo, L.; Yang, Z.; Yang, P.; Zhang, Y.; Wang, L.; Lin, H.; Wang, J. An attention-based BiLSTM-CRF approach to document-level chemical named entity recognition. Bioinformatics
**2018**, 34, 1381–1388. [Google Scholar] [CrossRef] [PubMed] [Green Version] - He, K.; Zhang, X.; Ren, S.; Sun, J. Deep residual learning for image recognition. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Las Vegas, NV, USA, 27–30 June 2016; pp. 770–778. [Google Scholar]
- Gao, J.; Yang, T. Face detection algorithm based on improved TinyYOLOv3 and attention mechanism. Comput. Commun.
**2022**, 181, 329–337. [Google Scholar] [CrossRef] - Tauqeer, M.; Rubab, S.; Khan, M.A.; Naqvi, R.A.; Javed, K.; Alqahtani, A.; Alsubai, S.; Binbusayyis, A. Driver’s emotion and behavior classification system based on Internet of Things and deep learning for Advanced Driver Assistance System (ADAS). Comput. Commun.
**2022**, 194, 258–267. [Google Scholar] [CrossRef] - Mostajabi, A.; Finney, D.L.; Rubinstein, M.; Rachidi, F. Nowcasting lightning occurrence from commonly available meteorological parameters using machine learning techniques. Npj Clim. Atmos. Sci.
**2019**, 2, 41. [Google Scholar] [CrossRef] [Green Version] - Kamangir, H.; Collins, W.; Tissot, P.; King, S.A. A deep-learning model to predict thunderstorms within 400 km2 South Texas domains. Meteorol. Appl.
**2020**, 27, e1905. [Google Scholar] [CrossRef] [Green Version] - Morales, J.; Orduña, E.; Rehtanz, C. Classification of lightning stroke on transmission line using multi-resolution analysis and machine learning. Int. J. Electr. Power Energy Syst.
**2014**, 58, 19–31. [Google Scholar] [CrossRef] - Zhu, Y.; Bitzer, P.; Rakov, V.; Ding, Z. A machine-learning approach to classify cloud-to-ground and intracloud lightning. Geophys. Res. Lett.
**2021**, 48, e2020GL091148. [Google Scholar] [CrossRef] - Karami, H.; Mostajabi, A.; Azadifar, M.; Rubinstein, M.; Zhuang, C.; Rachidi, F. Machine learning-based lightning localization algorithm using lightning-induced voltages on transmission lines. IEEE Trans. Electromagn. Compat.
**2020**, 62, 2512–2519. [Google Scholar] [CrossRef] - Wang, J.; Zhang, Y.; Tan, Y.; Chen, Z.; Zheng, D.; Zhang, Y.; Fan, Y. Fast and Fine Location of Total Lightning from Low Frequency Signals Based on Deep-Learning Encoding Features. Remote Sens.
**2021**, 13, 2212. [Google Scholar] [CrossRef] - Adekitan, A.; Rock, M. Application of machine learning to lightning strike probability estimation. In Proceedings of the 2020 International Conference on Electrical Engineering and Informatics (ICELTICs), Aceh, Indonesia, 27–28 October 2020; IEEE: Piscataway, NJ, USA, 2020; pp. 1–9. [Google Scholar]
- Coughlan, R.; Di Giuseppe, F.; Vitolo, C.; Barnard, C.; Lopez, P.; Drusch, M. Using machine learning to predict fire-ignition occurrences from lightning forecasts. Meteorol. Appl.
**2021**, 28, e1973. [Google Scholar] [CrossRef] - Booysens, A.; Viriri, S. Detection of lightning pattern changes using machine learning algorithms. In Proceedings of the International Conference on Communications, Signal Processing and Computers, Guilin, China, 5–8 August 2014; pp. 78–84. [Google Scholar]
- Zhang, H.; Dong, Z.; Wang, Z.; Guo, L.; Wang, Z. CSNet: A deep learning approach for ECG compressed sensing. Biomed. Signal Process. Control
**2021**, 70, 103065. [Google Scholar] [CrossRef] - Hua, J.; Rao, J.; Peng, Y.; Liu, J.; Tang, J. Deep Compressive Sensing on ECG Signals with Modified Inception Block and LSTM. Entropy
**2022**, 24, 1024. [Google Scholar] [CrossRef] - Zabalza, J.; Ren, J.; Zheng, J.; Zhao, H.; Qing, C.; Yang, Z.; Du, P.; Marshall, S. Novel segmented stacked autoencoder for effective dimensionality reduction and feature extraction in hyperspectral imaging. Neurocomputing
**2016**, 185, 1–10. [Google Scholar] [CrossRef] [Green Version] - Šaliga, J.; Andráš, I.; Dolinský, P.; Michaeli, L.; Kováč, O.; Kromka, J. ECG compressed sensing method with high compression ratio and dynamic model reconstruction. Measurement
**2021**, 183, 109803. [Google Scholar] [CrossRef] - Wang, J.; Huang, Q.; Ma, Q.; Chang, S.; He, J.; Wang, H.; Zhou, X.; Xiao, F.; Gao, C. Classification of VLF/LF lightning signals using sensors and deep learning methods. Sensors
**2020**, 20, 1030. [Google Scholar] [CrossRef] [Green Version] - Hinton, G.E.; Salakhutdinov, R.R. Reducing the dimensionality of data with neural networks. Science
**2006**, 313, 504–507. [Google Scholar] [CrossRef] [Green Version] - Rumelhart, D.E.; Hinton, G.E.; Williams, R.J. Learning representations by back-propagating errors. Nature
**1986**, 323, 533–536. [Google Scholar] [CrossRef] - Bourlard, H.; Kamp, Y. Auto-association by multilayer perceptrons and singular value decomposition. Biol. Cybern.
**1988**, 59, 291–294. [Google Scholar] [CrossRef] - Rifai, S.; Vincent, P.; Muller, X.; Glorot, X.; Bengio, Y. Contractive auto-encoders: Explicit invariance during feature extraction. In Proceedings of the ICML, Bellevue, WA, USA, 28 June–2 July 2011. [Google Scholar]
- Vincent, P.; Larochelle, H.; Lajoie, I.; Bengio, Y.; Manzagol, P.-A.; Bottou, L. Stacked denoising autoencoders: Learning useful representations in a deep network with a local denoising criterion. J. Mach. Learn. Res.
**2010**, 11, 3371–3408. [Google Scholar] - Ng, A. Sparse autoencoder. CS294A Lect. Notes
**2011**, 72, 1–19. [Google Scholar] - Kingma, D.P.; Welling, M. Auto-encoding variational bayes. arXiv
**2013**, arXiv:1312.6114. [Google Scholar] - An, J.; Cho, S. Variational autoencoder based anomaly detection using reconstruction probability. Spec. Lect. IE
**2015**, 2, 1–18. [Google Scholar] - Cho, K.; Van Merriënboer, B.; Gulcehre, C.; Bahdanau, D.; Bougares, F.; Schwenk, H.; Bengio, Y. Learning phrase representations using RNN encoder-decoder for statistical machine translation. arXiv
**2014**, arXiv:1406.1078. [Google Scholar] - Badrinarayanan, V.; Kendall, A.; Cipolla, R. Segnet: A deep convolutional encoder-decoder architecture for image segmentation. IEEE Trans. Pattern Anal. Mach. Intell.
**2017**, 39, 2481–2495. [Google Scholar] [CrossRef] - Vaswani, A.; Shazeer, N.; Parmar, N.; Uszkoreit, J.; Jones, L.; Gomez, A.N.; Kaiser, Ł.; Polosukhin, I. Attention is all you need. In Proceedings of the Advances in Neural Information Processing Systems 30: Annual Conference on Neural Information Processing Systems 2017, Long Beach, CA, USA, 4–9 December 2017; Volume 30. [Google Scholar]
- LeCun, Y.; Bottou, L.; Bengio, Y.; Haffner, P. Gradient-based learning applied to document recognition. Proc. IEEE
**1998**, 86, 2278–2324. [Google Scholar] [CrossRef] [Green Version] - Wan, X.; Jin, Z.; Wu, H.; Liu, J.; Zhu, B.; Xie, H. Heartbeat classification algorithm based on one-dimensional convolution neural network. J. Mech. Med. Biol.
**2020**, 20, 2050046. [Google Scholar] [CrossRef] - Yildirim, O.; San Tan, R.; Acharya, U.R. An efficient compression of ECG signals using deep convolutional autoencoders. Cogn. Syst. Res.
**2018**, 52, 198–211. [Google Scholar] [CrossRef] - Nair, V.; Hinton, G.E. Rectified linear units improve restricted boltzmann machines. In Proceedings of the ICML, Haifa, Israel, 21–24 June 2010. [Google Scholar]

**Figure 4.**Examples of various lightning electromagnetic pulse waveforms. (

**a**) negative cloud-to-ground flash (−CG); (

**b**) positive cloud-to-ground flash (+CG); (

**c**) negative narrow bipolar event (−NBE); (

**d**) positive narrow bipolar event (+NBE); (

**e**) cloud ground flash with ionosphere reflected signals (CG-IR); (

**f**) far-field skywave (SW).

**Figure 7.**The changing of experimental loss value MSE with training epochs under different CR for a −CG lightning signal collected by the sensor array.

**Figure 8.**The changing trend of experimental loss value MSE with validation epochs under different CR for −CG lightning signal collected by sensor array.

**Figure 14.**Statistics of the peak offset of the original LEMP waveform and the reconstructed waveform.

Module | No. | Layer | Filter | Kernel Size | Stride | Activation Function | Output Shape |
---|---|---|---|---|---|---|---|

Encoder | 1 | Input | - | - | - | - | 1000 × 1 |

2 | Conv1D | 8 | 64 | 2 | Tanh | 469 × 8 | |

3 | Conv1D | 16 | 64 | 1 | Tanh | 406 × 16 | |

4 | MaxPooling1D | - | - | - | - | 203 × 16 | |

5 | Conv1D | 32 | 64 | 1 | Tanh | 140 × 32 | |

6 | Conv1D | 64 | 64 | 2 | Tanh | 39 × 64 | |

7 | Conv1D | 16 | 32 | 1 | Tanh | 8 × 16 | |

Compression ratio adjustment module | 8 | Flatten | - | - | - | - | 128 × 1 |

9 | Dense | - | - | - | Tanh | x × 1 | |

10 | Dense | - | - | - | Tanh | 128 × 1 | |

11 | Reshape | - | - | - | - | 8 × 16 | |

Decoder | 12 | Conv1D | 16 | 32 | 1 | Tanh | 39 × 16 |

13 | Conv1D | 64 | 64 | 2 | Tanh | 140 × 64 | |

14 | Conv1D | 32 | 64 | 1 | Tanh | 203 × 32 | |

15 | UpSampling1D | - | - | - | - | 406 × 32 | |

16 | Conv1D | 16 | 64 | 1 | Tanh | 469 × 16 | |

17 | Conv1D | 8 | 64 | 2 | Tanh | 1000 × 8 | |

18 | Output | 1 | 1 | - | Linear | 1000 × 1 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Guo, J.; Wang, J.; Xiao, F.; Zhou, X.; Liu, Y.; Ma, Q.
An Efficient Compression Method for Lightning Electromagnetic Pulse Signal Based on Convolutional Neural Network and Autoencoder. *Sensors* **2023**, *23*, 3908.
https://doi.org/10.3390/s23083908

**AMA Style**

Guo J, Wang J, Xiao F, Zhou X, Liu Y, Ma Q.
An Efficient Compression Method for Lightning Electromagnetic Pulse Signal Based on Convolutional Neural Network and Autoencoder. *Sensors*. 2023; 23(8):3908.
https://doi.org/10.3390/s23083908

**Chicago/Turabian Style**

Guo, Jinhua, Jiaquan Wang, Fang Xiao, Xiao Zhou, Yongsheng Liu, and Qiming Ma.
2023. "An Efficient Compression Method for Lightning Electromagnetic Pulse Signal Based on Convolutional Neural Network and Autoencoder" *Sensors* 23, no. 8: 3908.
https://doi.org/10.3390/s23083908