# Sensor Placement with Two-Dimensional Equal Arc Length Non-Uniform Sampling for Underwater Terrain Deformation Monitoring

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## Abstract

**:**

## 1. Introduction

#### 1.1. Monitoring Methods for Underwater Terrain Deformation

#### 1.2. Sensor Placement Schemes for Underwater Terrain Deformation

## 2. Two-Dimensional Non-Uniform Sampling Condition with Equal Arc Length

#### 2.1. Mathematical Model of Two-Dimensional Uniform Sampling

#### 2.2. Two-Dimensional Non-Uniform Sampling Condition with Equal Arc Length

## 3. Terrain Deformation Simulation Experiment

#### 3.1. Experiment Design

^{−5}) at frequencies of $u>0$ and $v>0$, and is close to zero when $u\ne 0$ and $v\ne 0$. The amplitude spectrum of the underwater terrain is $\left[-\xi ,\xi \right]\times \left[-\eta ,\eta \right]$ and rectangular; $\xi $ and $\eta $ are the maximum frequencies in the $u$ and $v$ directions.

#### 3.2. Experimental Results

## 4. A Water Tank Experiment

#### 4.1. Experiment Design

#### 4.2. Experimental Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**Two-dimensional amplitude spectrum of shape #1-1. Full graph (

**left**), partial enlargement graph (

**right**).

**Figure 6.**Two-dimensional amplitude spectrum of shape #1-2. Full graph (

**left**), partial enlargement graph (

**right**).

**Figure 7.**The two-dimensional amplitude spectrum of shape #1-3. Full graph (

**left**), partial enlargement graph (

**right**).

Shape #1-1 | Shape #1-2 | Shape #1-3 | |
---|---|---|---|

Highest frequency (u, v) (m^{−1}) | (0.94, 1.10) | (1.41, 1.10) | (0.94, 1.10) |

Shape #1-1 | Shape #1-2 | Shape #1-3 | |
---|---|---|---|

Mean absolute error (cm) | 1.12 | 0.97 | 1.09 |

MRE (%) | 6.47 | 6.87 | 5.09 |

RRMSE (%) | 6.01 | 5.53 | 4.43 |

Shape #2-1 | Shape #2-2 | Shape #2-3 | |
---|---|---|---|

Highest frequency (u, v) (m^{−1}) | (1.25, 2.5) | (2.5, 2.5) | (1.25, 2.5) |

Shape #2-1 | Shape #2-2 | Shape #2-3 | Shape #2-4 | Shape #2-5 | |
---|---|---|---|---|---|

MRE (%) | 3.29 | 5.62 | 3.36 | 5.71 | 3.48 |

RRMSE (%) | 3.52 | 5.89 | 3.45 | 6.73 | 3.02 |

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**MDPI and ACS Style**

Xu, C.; Hu, J.; Chen, J.; Ge, Y.; Liang, R.
Sensor Placement with Two-Dimensional Equal Arc Length Non-Uniform Sampling for Underwater Terrain Deformation Monitoring. *J. Mar. Sci. Eng.* **2021**, *9*, 954.
https://doi.org/10.3390/jmse9090954

**AMA Style**

Xu C, Hu J, Chen J, Ge Y, Liang R.
Sensor Placement with Two-Dimensional Equal Arc Length Non-Uniform Sampling for Underwater Terrain Deformation Monitoring. *Journal of Marine Science and Engineering*. 2021; 9(9):954.
https://doi.org/10.3390/jmse9090954

**Chicago/Turabian Style**

Xu, Chunying, Junwei Hu, Jiawang Chen, Yongqiang Ge, and Ruixin Liang.
2021. "Sensor Placement with Two-Dimensional Equal Arc Length Non-Uniform Sampling for Underwater Terrain Deformation Monitoring" *Journal of Marine Science and Engineering* 9, no. 9: 954.
https://doi.org/10.3390/jmse9090954