# Anchor Fault Identification Method for High-Voltage DC Submarine Cable Based on VMD-Volterra-SVM

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. VMD-Volterra-SVM Algorithm

#### 2.1. VMD Principle

#### 2.2. Principle of the Volterra Model

#### 2.3. SVM Principle

#### 2.4. VMD-Volterra-SVM Algorithm Flow

## 3. Simulation Analysis

#### 3.1. Finite Element Model Building

^{3}, projection of the anchor bottom against the water surface to A = 0.048 m

^{2}, seawater density to ρ

_{w}= 1030 kg/m

^{3}, seawater resistance coefficient to C

_{D}= 1.1, medium gravity acceleration to g = 9.8 m/s

^{2}, velocity of the anchor striking the cable to v, ignore the influence of sea tide on the anchor, and use the motion equation of a ship anchor in the process of falling, which is as follows:

^{2}is applied to the entire model, and a downward velocity $v$ is applied to the anchor separately. In this paper, $v$ is taken as 7 m/s. To prevent the anchor from sliding during the anchor smashing process, the movement of the anchor in the x and z directions is constrained so that the anchor can only move in the y direction. Since the anchor damage failure only occurs locally in the submarine cable, the length is much smaller than the total length of the submarine cable, so the two sections of the submarine cable can be completely fixed with the bottom end on the soil.

#### 3.2. Finite Element Simulation Results

## 4. VMD-Volterra-SVM Algorithm Validation

#### 4.1. VMD Decomposition and Feature Extraction

^{−7}, the decomposed modal components are obtained, and the waveforms of each modal component are shown in Figure 5. The horizontal axis represents time, measured in seconds, while the vertical axis represents the magnitude of the acceleration. From Figure 5, it can be seen that the VMD decomposition results are more reasonable and can effectively suppress the modal mixing phenomenon.

#### 4.2. Fault Identification Results and Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**Vibration acceleration curve of the submarine cable. (

**a**) Vibration acceleration curve at the moment of anchor smashing; (

**b**) vibration acceleration curve at the moment of scouring.

**Figure 5.**The VMD decomposition waveform of a submarine cable vibration signal. (

**a**) Scouring vibration signal decomposition; (

**b**) anchor smash vibration signal decomposition.

Submarine Cable Status | Sample | IMF1 | IMF2 | IMF3 | IMF4 | IMF5 | H |
---|---|---|---|---|---|---|---|

Scrubbing | Sample 1 | 2.5037 | 1.1586 | 0.6795 | 0.3894 | 0.1958 | 1.5193 |

Sample 2 | 2.5023 | 1.1659 | 0.6775 | 0.3954 | 0.1965 | 1.5237 | |

Sample 3 | 2.5113 | 1.1548 | 0.6804 | 0.3904 | 0.2005 | 1.5272 | |

Anchor smash | Sample 1 | 2.3902 | 1.0962 | 0.5535 | 0.2973 | 0.1159 | 1.2056 |

Sample 2 | 2.4037 | 1.0804 | 0.5221 | 0.2932 | 0.1522 | 1.2061 | |

Sample 3 | 2.3954 | 1.0965 | 0.5361 | 0.2896 | 0.1561 | 1.2105 |

Hyperparameter | Size | Hyperparameter | Size |
---|---|---|---|

Quadratic penalty factor α | 2000 | Convergence parameter ε | 10^{−7} |

Lagrange multiplier step τ | 0 | Penalty parameter | 3.568 |

Number of IMF decomposition K | 5 | Non-negative relaxation factor ζ_{i} | 2.248 |

Confusion Matrix | True Value | |||
---|---|---|---|---|

Scrubbing | Anchor Smash | |||

Predicted Value | VMD | Scrubbing | 20 | 0 |

Anchor smash | 0 | 20 | ||

EMD | Scrubbing | 17 | 2 | |

Anchor smash | 3 | 18 | ||

EEMD | Scrubbing | 19 | 1 | |

Anchor smash | 1 | 19 |

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**MDPI and ACS Style**

Zhu, W.; Fan, C.; Xu, C.; Dong, H.; Guo, J.; Liang, A.; Zhao, L.
Anchor Fault Identification Method for High-Voltage DC Submarine Cable Based on VMD-Volterra-SVM. *Energies* **2023**, *16*, 3053.
https://doi.org/10.3390/en16073053

**AMA Style**

Zhu W, Fan C, Xu C, Dong H, Guo J, Liang A, Zhao L.
Anchor Fault Identification Method for High-Voltage DC Submarine Cable Based on VMD-Volterra-SVM. *Energies*. 2023; 16(7):3053.
https://doi.org/10.3390/en16073053

**Chicago/Turabian Style**

Zhu, Wenwei, Chenyang Fan, Chenghao Xu, Hantuo Dong, Jingen Guo, Aiwu Liang, and Long Zhao.
2023. "Anchor Fault Identification Method for High-Voltage DC Submarine Cable Based on VMD-Volterra-SVM" *Energies* 16, no. 7: 3053.
https://doi.org/10.3390/en16073053