# Partial Discharge Fault Diagnosis Based on Multi-Scale Dispersion Entropy and a Hypersphere Multiclass Support Vector Machine

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. PD Fault Diagnosis Based on VMD-MDE and HMSVM

#### 2.1. VMD Algorithm

_{k}, which has specific sparsity. This procedure gets the minimum bandwidth estimation of each modal [31]. The procedure of signal decomposition is to solve the variational problem. The variational model with constraint condition is as follows:

_{t}means the partial derivatives of t, and f is the original signal.

- (1)
- Initialize each modal component $\left\{{u}_{k}^{1}\right\}$, center frequency $\left\{{\omega}_{k}^{1}\right\}$ and operators $\left\{{\lambda}^{1}\right\}$. Set n = 0.
- (2)
- Update ${u}_{k}$ in non-negative frequency intervals:$${\widehat{u}}_{k}^{n+1}(\omega )\leftarrow \frac{\widehat{f}(\omega )-{\displaystyle \sum _{i<k}{\widehat{u}}_{i}^{n+1}(\omega )}-{\displaystyle \sum _{i>k}{\widehat{u}}_{i}^{n}(\omega )}+\frac{{\widehat{\lambda}}^{n}(\omega )}{2}}{1+2\alpha {(\omega -{\omega}_{k}^{n})}^{2}}$$
- (3)
- Update ${\omega}_{k}$.$${\omega}_{k}^{n+1}\leftarrow \frac{{\displaystyle {\int}_{0}^{\infty}\omega {\left|{\widehat{u}}_{k}^{n+1}(\omega )\right|}^{2}d\omega}}{{\displaystyle {\int}_{0}^{\infty}{\left|{\widehat{u}}_{k}^{n+1}(\omega )\right|}^{2}d\omega}}$$
- (4)
- Update λ in non-negative frequency intervals:$${\widehat{\lambda}}^{n+1}\leftarrow {\widehat{\lambda}}^{n}+\tau (\widehat{f}(\omega )-{\displaystyle \sum _{k}{\widehat{u}}_{i}^{n+1}(\omega ))}$$
- (5)
- For a given precision $\epsilon >0$, if $\frac{{\displaystyle \sum _{k}{\Vert {\widehat{u}}_{k}^{n+1}-{\widehat{u}}_{k}^{n}\Vert}_{2}^{2}}}{{\Vert {\widehat{u}}_{k}^{n}\Vert}_{2}^{2}}<\epsilon $, then stop iteration. Otherwise, return to (2).

#### 2.2. Theory of Multiscale Dispersion Entropy

#### 2.2.1. Dispersion Entropy

- (1)
- Map ${x}_{j}(j=1,2,\cdots ,N)$ into $y=\{{y}_{1},{y}_{2},\cdots ,{y}_{N}\}$ from 0 to 1 with the normal cumulative distribution function:$${y}_{j}=\frac{1}{\sigma \sqrt{2\pi}}{\displaystyle \underset{-\infty}{\overset{{x}_{j}}{\int}}{e}^{\frac{-{(t-\mu )}^{2}}{2{\sigma}^{2}}}}dt$$
- (2)
- Assign each y
_{j}to an integer from Label 1 to c using a linear algorithm. The mapped signal can be defined as follows:$${z}_{j}^{c}=round(c.{y}_{j}+0.5)$$ - (3)
- Define embedding vector ${z}_{i}^{m,c}$ with embedding dimension m and time delay d as:$${z}_{i}^{m,c}=\{{z}_{i}^{c},{z}_{i+d}^{c},\cdots ,{z}_{i+(m-1)d}^{c}\},\text{}i=1,2,\cdots ,N-(m-1)d$$Each time series ${z}_{i}^{m,c}$ is mapped to a dispersion pattern ${\pi}_{{v}_{0}{v}_{1}\cdots {v}_{m-1}}$, where:$${z}_{i}^{c}={v}_{0},{z}_{i+d}^{c}={v}_{1}.\cdots ,{z}_{i+(m-1)d}^{c}={v}_{m-1}$$
- (4)
- For each dispersion pattern, the relative frequency can be obtained as:$$p({\pi}_{{v}_{0}{v}_{1}\cdots {v}_{m-1}})=\frac{Number\left\{i|i\le N-(m-1)d,{z}_{i}^{m,c}\text{}has\text{}\mathrm{type}\text{}{\pi}_{{v}_{0}{v}_{1}\cdots {v}_{m-1}}\right\}}{N-(m-1)d}$$
- (5)
- Based on Shannon’s definition of entropy, dispersion entropy with embedding dimension m, time delay d, and the number of classes c can be defined as$$DE(x,m,c,d)=-{\displaystyle \sum _{\pi =1}^{{c}^{m}}p({\pi}_{{v}_{0}{v}_{1}\cdots {v}_{m-1}})\cdot \mathrm{ln}(p({\pi}_{{v}_{0}{v}_{1}\cdots {v}_{m-1}}))}$$

#### 2.2.2. Multiscale Dispersion Entropy

#### 2.3. Theory of HMSVM

#### 2.3.1. HMSVM

_{m}(m = 1, 2, …, M) is given. Assume that each X

_{m}contains m-dimension sample x

_{mi}, i = 1, 2…l

_{m}, which represents i-th element in m-class.

_{m},R

_{m}) for each sample X

_{m}, where a

_{m}is the center of sphere, R

_{m}is the radius of suprasphere. The objective function of m-th suprasphere can be defined as follows:

_{m}is the penalty factor, representing the trade-off between R

_{m}and target samples. ξ

_{m}

_{,i}is the slack variable of HMSVM allowing remote samples staying outside the sphere.

_{m}using the formula below:

_{m}= D(x

_{i}), where x

_{i}represents the support vector. Therefore, the category assigned to the unknown sample d can be determined according to the comparison between R

_{m}and D(d).

#### 2.3.2. Kernel Function Selection

#### 2.4. PD Fault Diagnosis Based on VMD-MDE and HMSVM

## 3. Experiments and Analysis

#### 3.1. Experimental Setup

#### 3.2. Signal Extraction

## 4. Results and Analysis

#### 4.1. VMD Decomposition

#### 4.2. IMF Selection

#### 4.3. Feature Extraction

_{s}is the number of effective IMFs calculated as described in Section 4.2.

#### 4.4. PCA-Based Dimension Reduction

_{1}, the covariance matrix is constructed to obtain the principal components. The eigenvalue and eigenvector of the covariance matrix are solved for linear transformation of original vectors. To achieve the goal of dimension reduction, those factors whose eigenvalues are greater than 1 are selected as principal components. The eigenvalue and corresponding contribution rates of the covariance matrix are shown in Table 6.

_{2}, K

_{3}and K

_{4}can be obtained, shown in Table 7.

#### 4.5. PD Pattern Recognition

_{1}= 2, c

_{2}= 2, the maximum number of iterations N = 200. The penalty parameter C is between 1/n and 1, while the searching range of the kernel parameter σ is between 1 and 100. The optimum fitness reaches the maximum value of 96.98% after 19 iterations, when σ = 12.26 and C = 0.35. Similarly, HMSVM parameters with different feature extraction methods are obtained as follows.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Firuzi, K.; Vakilian, M.; Darabad, V.P.; Phung, B.T.; Blackburn, T.R. A novel method for differentiating and clustering multiple partial discharge sources using S transform and bag of words feature. IEEE Trans. Dielectr. Electr. Insul.
**2018**, 24, 3694–3702. [Google Scholar] [CrossRef] - Zhou, Z.L.; Zhou, Y.X.; Huang, X.; Zhang, Y.X. Feature Extraction and Comprehension of Partial Discharge Characteristics in Transformer Oil from Rated AC Frequency to Very Low Frequency. Energies
**2018**, 11, 1702. [Google Scholar] [CrossRef] - Hammarstrom, T.J.A. Partial discharge characteristics within motor insulation exposed to multi-level PWM waveforms. IEEE Trans. Dielectr. Electr. Insul.
**2018**, 25, 559–567. [Google Scholar] [CrossRef] - Mota, H.D.O.; Vasconcelos, F.H.; Castro, C.L.D. A comparison of cycle spinning versus stationary wavelet transform for the extraction of features of partial discharge signals. IEEE Trans. Dielectr. Electr. Insul.
**2016**, 23, 1106–1118. [Google Scholar] [CrossRef] - Castillo, J.; Mocquet, A.; Saracco, G. Wavelet transform: A tool for the interpretation of upper mantle converted phases at high frequency. Geophys. Res. Lett.
**2018**, 28, 4327–4330. [Google Scholar] [CrossRef] - Li, Y.B.; Xu, M.Q.; Liang, X.H.; Huang, W.H. Application of Bandwidth EMD and Adaptive Multiscale Morphology Analysis for Incipient Fault Diagnosis of Rolling Bearings. IEEE Trans. Ind. Electron.
**2017**, 64, 6506–6517. [Google Scholar] [CrossRef] - Bustos, A.; Rubio, H.; Castejon, C.; Garcia-prada, J.C. EMD-Based Methodology for the Identification of a High-Speed Train Running in a Gear Operating State. Sensors
**2018**, 18, 793. [Google Scholar] [CrossRef] - Xiao, B.; Fang, L.J.; Li, J.F.; Qi, X.S.; Bai, Y.R. An EMD Method for Ascertaining Maximal Value of Cellular Load in Spatial Load Forecasting. J. Northeast Electr. Power Univ.
**2018**, 38, 8–14. [Google Scholar] - Dragomiretskiy, K.; Zosso, D. Variational Mode Decomposition. IEEE Trans. Signal Process.
**2014**, 62, 531–544. [Google Scholar] [CrossRef] - Yao, J.C.; Xiang, Y.; Qian, S.; Wang, S. Noise source identification of diesel engine based on variational mode decomposition and robust independent component analysis. Appl. Acoust.
**2017**, 116, 184–194. [Google Scholar] [CrossRef] - Zhang, L.; Veitch, D. Learning Entropy. Lect. Notes Comput. Sci.
**2017**, 6640, 15–27. [Google Scholar] - Shannon, C.E. A mathematical theory of communications. Bell Syst. Tech. J.
**1948**, 27, 379–423. [Google Scholar] [CrossRef] - Pincus, S. Approximate entropy (ApEn) as a complexity measure. Chaos
**1995**, 5, 110–117. [Google Scholar] [CrossRef] [PubMed] - Wu, H.T.; Yang, C.C.; Lin, G.M.; Haryadi, B. Multiscale Cross-Approximate Entropy Analysis of Bilateral Fingertips Photoplethysmographic Pulse Amplitudes among Middle-to-Old Aged Individuals with or without Type 2 Diabetes. Entropy
**2017**, 19, 145. [Google Scholar] [CrossRef] - Richman, J.S.; Moorman, J.R. Physiological time-series analysis using approximate entropy and sample entropy. Am. J. Physiol. Heart Circ. Physiol.
**2000**, 278, H2039. [Google Scholar] [CrossRef] [PubMed] - George, M.; Md, A.; Roberto, S. Low Computational Cost for Sample Entropy. Entropy
**2018**, 20, 61. [Google Scholar] [CrossRef] - Bandt, C.; Pompe, B. Permutation entropy: A natural complexity measure for time series. Phys. Rev. Lett.
**2002**, 88, 174102. [Google Scholar] [CrossRef] - Zhou, S.H.; Qian, S.L.; Chang, W.B.; Xiao, Y.Y. A Novel Bearing Multi-Fault Diagnosis Approach Based on Weighted Permutation Entropy and an Improved SVM Ensemble Classifier. Sensors
**2018**, 18, 1934. [Google Scholar] [CrossRef] - Azami, H.; Rostaghi, M.; Fernandez, A.; Escudero, J. Dispersion entropy for the analysis of resting-state MEG regularity in Alzheimer’s disease. In Proceedings of the International Conference of the IEEE Engineering in Medicine and Biology Society, Orlando, FL, USA, 16–20 August 2016; p. 6417. [Google Scholar]
- Baldini, G.; Giuliani, R.; Steri, G.; Neisse, R. Physical layer authentication of Internet of Things wireless devices through permutation and dispersion entropy. In Proceedings of the Global Internet of Things Summit, Geneva, Switzerland, 6–9 June 2017; pp. 1–6. [Google Scholar]
- Azami, H.; Rostaghi, M.; Abasolo, D.; Escudero, J. Refined Composite Multiscale Dispersion Entropy and its Application to Biomedical Signals. IEEE Trans. Bio-Med. Eng.
**2017**, 99, 1. [Google Scholar] [CrossRef] - Goldberger, A.L.; Bruce, A.; Peng, C.K.; Costa, M. Multiscale entropy analysis of biological signals. Phys. Rev. E Stat. Nonlinear Soft Matter Phys.
**2005**, 71, 1–9. [Google Scholar] - Azami, H.; Escudero, J. Coarse-Graining Approaches in Univariate Multiscale Sample and Dispersion Entropy. Entropy
**2018**, 20, 138. [Google Scholar] [CrossRef] - Vapnik, V. Statistical Learning Theory; Wiley: New York, NY, USA, 1998. [Google Scholar]
- Velazquez-Pupo, R.; Sierra-Romero, A.; Torres-Roman, D.; Romero-Delgado, M. Vehicle detection with occlusion handling, tracking, and OC-SVM classification: A high performance vision-based system. Sensors
**2018**, 18, 374. [Google Scholar] [CrossRef] [PubMed] - Scholkopf, B.; Smola, A. Kernel Methods and Support Vector Machines; Academic Press Library in Signal Processing: Amsterdam, The Netherlands, 2003; pp. 857–881. [Google Scholar]
- Ai, Q.; Wang, A.; Wang, Y.; Sun, H.J. Improvements on twin-hypersphere support vector machine using local density information. In Progress in Artificial Intelligence; Springer: Berlin, Germany, 2018; pp. 1–9. [Google Scholar]
- Xu, T.; He, D.K. Theory of hypersphere multiclass SVM. Control Theory Appl.
**2009**, 26, 1293–1297. [Google Scholar] - Guo, Y.; Xiao, H. Multiclass multiple kernel learning using hypersphere for pattern recognition. Appl. Intell.
**2017**, 48, 1–9. [Google Scholar] [CrossRef] - Kennedy, J.; Eberhart, R. Particle Swarm Optimization. In Proceedings of the IEEE International Conference on Neural Networks, Perth, Western Australia, 27 November–1 December 1995; pp. 1942–1948. [Google Scholar]
- Wang, Z.; Jia, L.; Qin, Y. Adaptive Diagnosis for Rotating Machineries Using Information Geometrical Kernel-ELM Based on VMD-SVD. Entropy
**2018**, 20, 73. [Google Scholar] [CrossRef] - Rostaghi, M.; Azami, H. Dispersion Entropy: A Measure for Time-Series Analysis. IEEE Signal Process. Lett.
**2016**, 23, 610–614. [Google Scholar] [CrossRef] - Chen, S.; Mclaughlin, S.; Mulgrew, B. Complex-valued radial basic function network, Part I: Network architecture and learning algorithms. Signal Process.
**1994**, 35, 19–31. [Google Scholar] [CrossRef] - Pearson, K. On Lines and Planes of Closest Fit to Systems of Points in Space. Philos. Mag.
**1901**, 2, 559–572. [Google Scholar] [CrossRef] - Peng, Z.K.; Tse, P.W.; Chu, F.L. A comparison study of improved Hilbert-Huang transform and wavelet transform: Application to fault diagnosis for rolling bearing. Mech. Syst. Signal Process.
**2005**, 19, 974–988. [Google Scholar] [CrossRef] - Mostafizur, R.M.; Anowarul, F.S. Mental Task Classification Scheme Utilizing Correlation Coefficient Extracted from Interchannel Intrinsic Mode Function. BioMed Res. Int.
**2017**, 1–11. [Google Scholar] [CrossRef] - Shang, H.K.; Kwok, L.; Li, F. Partial Discharge Feature Extraction Based on Ensemble Empirical Mode Decomposition and Sample Entropy. Entropy
**2017**, 19, 439. [Google Scholar] [CrossRef] - Folkes, S.R.; Lahav, O.; Maddox, S.J. An artificial neural network approach to the classification of galaxy spectra. Mon. Notices R. Astron. Soc.
**2018**, 283, 651–665. [Google Scholar] [CrossRef]

**Figure 5.**The connection diagram of PD experiment. 1—AC power source; 2—step up transformer; 3—resistance; 4—capacitor; 5—high voltage bushing; 6—small bushing; 7—PD model; 8—UHF sensor; 9—current sensor; 10—console.

**Figure 7.**Results of EMD decomposition. (

**a**) IMF of decomposition; (

**b**) Frequency spectrum of decomposition.

**Figure 8.**Results of VMD decomposition. (

**a**) IMF of decomposition; (

**b**) Frequency spectrum of decomposition.

PD Types | Initial Voltage/kV | Breakdown Voltage/kV | Testing Voltage/kV | Sample Number |
---|---|---|---|---|

FD | 2 | 7 | 3/4 | 50/50 |

ND | 8.8 | 12 | 9/10 | 50/50 |

BD | 3.5 | 10 | 5/6 | 50/50 |

CD | 4.5 | 10 | 6/7 | 50/50 |

Number of IMFs | Central Frequency/MHz | ||||||
---|---|---|---|---|---|---|---|

2 | 0.0079 | 7.3682 | |||||

3 | 0.0073 | 6.9573 | 12.3268 | ||||

4 | 0.0059 | 6. 8232 | 11.9803 | 13.2581 | |||

5 | 0.0055 | 6. 8041 | 12.0256 | 13.1263 | 13.3572 | ||

6 | 0.0059 | 6. 7855 | 11.7785 | 13.5579 | 13.2602 | 13.9348 | |

7 | 0.0053 | 6. 8034 | 12.1379 | 13.7877 | 13.9021 | 13.9975 | 14.2814 |

u1 | u2 | u3 | u4 | u5 | u6 | u7 | u8 | u9 | |
---|---|---|---|---|---|---|---|---|---|

VMD | 0.6809 | 0.5129 | 0.3583 | 0.0083 | - | - | - | - | - |

EMD | 0.7362 | 0.6035 | 0.4231 | 0.3026 | 0.2092 | 0.1123 | 0.0365 | 0.0086 | 0.0025 |

PD Type | K | α | τ | K_{s} |
---|---|---|---|---|

FD | 4 | 2000 | 0.1 | 3 |

ND | 5 | 2000 | 0.1 | 3 |

BD | 4 | 2000 | 0.1 | 4 |

CD | 4 | 2000 | 0.1 | 4 |

IMF | Vectors |
---|---|

K_{1} | O_{1}, O_{2}, O_{3}, O_{4}, O_{5}, O_{6}, O_{7}, O_{8}, O_{9}, O_{10}, O_{11}, O_{12} |

K_{2} | P_{1}, P_{2}, P_{3}, P_{4}, P_{5}, P_{6}, P_{7}, P_{8}, P_{9}, P_{10}, P_{11}, P_{12} |

K_{3} | Q_{1}, Q_{2}, Q_{3}, Q_{4}, Q_{5}, Q_{6}, Q_{7}, Q_{8}, Q_{9}, Q_{10}, Q_{11}, Q_{12} |

K_{4} | R_{1}, R_{2}, R_{3}, R_{4}, R_{5}, R_{6}, R_{7}, R_{8}, R_{9}, R_{10}, R_{11}, R_{12} |

Vectors | Eigenvalue | Contribution Rate/% | Accumulated Contribution Rate/% |
---|---|---|---|

O_{1} | 3.732 | 66.738 | 66.738 |

O_{2} | 2.169 | 25.843 | 92.581 |

O_{3} | 0.852 | 3.560 | 96.141 |

O_{4} | 0.603 | 1.435 | 97.576 |

O_{5} | 0.304 | 1.064 | 98.64 |

O_{6} | 0.124 | 0.626 | 99.266 |

O_{7} | 0.102 | 0.441 | 99.707 |

O_{8} | 0.075 | 0.152 | 99.859 |

O_{9} | 0.052 | 0.086 | 99.945 |

O_{10} | 0.036 | 0.027 | 99.972 |

O_{11} | 0.029 | 0.024 | 99.996 |

O_{12} | 0.003 | 0.004 | 100.00 |

IMF | KMO | Contribution Rate/% | Principle Component |
---|---|---|---|

K_{1} | 0.852 | 92.581 | O_{1}, O_{2} |

K_{2} | 0.767 | 88.379 | P_{1}, P_{2} |

K_{3} | 0.734 | 80.232 | Q_{1}, Q_{2}, Q_{3} |

K_{4} | 0.752 | 83.368 | R_{1}, R_{2} |

PD Type | Parameters | ||||
---|---|---|---|---|---|

K_{1} | K_{2} | K_{3} | K_{4} | K_{5} | |

FD | O_{1}, O_{2} | P_{1}, P_{2} | Q_{1}, Q_{2}, Q_{3} | R_{1}, R_{2} | - |

ND | O_{1}, O_{2} | P_{1}, P_{2} | Q_{1}, Q_{2} | R_{1}, R_{2} | S_{1}, S_{2} |

BD | O_{1}, O_{2}, O_{3} | P_{1}, P_{2} | Q_{1}, Q_{2} | R_{1}, R_{2} | - |

CD | O_{1}, O_{2} | P_{1}, P_{2}, P_{3} | Q_{1}, Q_{2} | R_{1}, R_{2} | - |

EMD Decomposition | VMD Decomposition | |||||
---|---|---|---|---|---|---|

Level | Scale | Principle Components Number | Level | Scale | Principle Components Number | |

MSE | 4 | 14 | 10 | 3 | 12 | 8 |

MPE | 3 | 10 | 8 | 3 | 10 | 8 |

MDE | 3 | 12 | 9 | 4 | 12 | 9 |

EMD-MSE | EMD-MPE | EMD-MDE | VMD-MSE | VMD-MPE | VMD-MDE | |
---|---|---|---|---|---|---|

C | 0.43 | 0.31 | 0.27 | 0.46 | 0.33 | 0.35 |

σ | 10.38 | 11.86 | 10.19 | 12.05 | 9.37 | 12.26 |

Classifier | Type | EMD-MSE | EMD-MPE | EMD-MDE | VMD-MSE | VMD-MPE | VMD-MDE |
---|---|---|---|---|---|---|---|

SVM | C | 0.25 | 0.28 | 0.45 | 0.44 | 0.38 | 0.46 |

σ | 8.39 | 10.57 | 8.32 | 9.18 | 8.25 | 10.22 | |

ANN | Input | 10 | 8 | 9 | 8 | 8 | 9 |

Output | 4 | 4 | 4 | 4 | 4 | 4 | |

Hidden layer | 16 | 12 | 14 | 12 | 10 | 12 |

Feature Types | ANN | SVM | HMSVM | |||
---|---|---|---|---|---|---|

Recognition Accuracy/% | Running Time/s | Recognition Accuracy/% | Running Time/s | Recognition Accuracy/% | Running Time/s | |

EMD- MSE | 86.00 | 6.88 × 10^{−4} | 88.50 | 6.92 × 10^{−4} | 86.50 | 6.75 × 10^{−4} |

EMD- MPE | 86.50 | 3.45 × 10^{−3} | 84.00 | 3.21 × 10^{−3} | 86.00 | 3.51 × 10^{−3} |

EMD- MDE | 88.00 | 5.39 × 10^{−4} | 90.50 | 5.36 × 10^{−4} | 91.50 | 1.68 × 10^{−3} |

VMD- MSE | 95.00 | 8.16 × 10^{−4} | 96.50 | 7.29 × 10^{−4} | 97.50 | 7.80 × 10^{−4} |

VMD- MPE | 98.00 | 7.45 × 10^{−4} | 97.50 | 7.12 × 10^{−4} | 99.00 | 7.42 × 10^{−4} |

VMD- MDE | 98.00 | 5.36 × 10^{−4} | 99.00 | 5.32 × 10^{−4} | 100.00 | 5.27 × 10^{−4} |

© 2019 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Shang, H.; Li, F.; Wu, Y.
Partial Discharge Fault Diagnosis Based on Multi-Scale Dispersion Entropy and a Hypersphere Multiclass Support Vector Machine. *Entropy* **2019**, *21*, 81.
https://doi.org/10.3390/e21010081

**AMA Style**

Shang H, Li F, Wu Y.
Partial Discharge Fault Diagnosis Based on Multi-Scale Dispersion Entropy and a Hypersphere Multiclass Support Vector Machine. *Entropy*. 2019; 21(1):81.
https://doi.org/10.3390/e21010081

**Chicago/Turabian Style**

Shang, Haikun, Feng Li, and Yingjie Wu.
2019. "Partial Discharge Fault Diagnosis Based on Multi-Scale Dispersion Entropy and a Hypersphere Multiclass Support Vector Machine" *Entropy* 21, no. 1: 81.
https://doi.org/10.3390/e21010081