# A Modular Method for GPR Hyperbolic Feature Detection and Quantitative Parameter Inversion of Underground Pipelines

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Works

## 3. Basic Principle of GPR

## 4. Detection of GPR Hyperbolic Features Based on YOLOv7

#### 4.1. Data Preparation

#### 4.2. Comparison of Results

## 5. Parameter Inversion of Pipeline Based on Key Point Annotation

#### 5.1. Physical Model of GPR Detection

#### 5.2. Coordinate Transformation of Key Points

#### 5.3. Two-Stage Curve Fitting and Inversion of the Parameters

#### 5.4. Introduction of the Graphical User Interface

#### 5.5. Performance Analysis with Synthetic Data

- Homogeneous medium model

- •
- Non-homogeneous medium model

#### 5.6. Performance Analysis with Measured Data

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A. .in File of Six Synthetic Data

## References

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Models | Labels | Before Correction | After Correction | Relative Error |
---|---|---|---|---|

a | Upper edge | 0.3691 | ||

Middle point | 0.3803 | |||

Lower edge | 0.3908 | |||

b | Upper edge | 0.3691 | 0.3 | 0% |

Middle point | 0.3819 | 0.3016 | 0.50% | |

Lower edge | 0.39 | 0.2992 | 0.30% | |

c | Upper edge | 0.5704 | 0.5013 | 2.60% |

Middle point | 0.5803 | 0.5 | 0% | |

Lower edge | 0.5892 | 0.4984 | 0.30% |

Models | Labels | Before Correction | After Correction | Relative Error |
---|---|---|---|---|

a | Upper edge | 0.0599 | ||

Middle point | 0.0458 | |||

Lower edge | 0.0215 | |||

b | Upper edge | 0.0057 | 0.0458 | 8.40% |

Middle point | −0.0031 | 0.0511 | 2.20% | |

Lower edge | −0.0269 | 0.0516 | 3.20% | |

c | Upper edge | 0.0682 | 0.1083 | 8.30% |

Middle point | 0.0502 | 0.1044 | 4.40% | |

Lower edge | 0.0248 | 0.1033 | 3.30% |

Models | Before Correction | After Correction | Relative Error |
---|---|---|---|

a | 0.4389 | / | |

b | 0.4389 | 0.3 | 0% |

c | 0.6869 | 0.548 | 9.60% |

Models | Before Correction | After Correction | Relative Error |
---|---|---|---|

a | −0.0939 | / | |

b | −0.1354 | 0.0585 | 17% |

c | −0.0799 | 0.1140 | 14% |

GPR System | Antenna Frequency | Measuring Line Length | Channel Spacing | Number of A-Scan | Sampling Time Interval | Sampling Points | |
---|---|---|---|---|---|---|---|

Data1 | GSSI | 200 MHz | 25.8 m | 0.02 m | 1291 | 0.2153 ns | 512 |

Data2 | GSSI | 400 MHz | 21.27 m | 0.03333 m | 639 | 0.1761 ns | 510 |

Data3 | MALA | 250 MHz | 22.32 m | 0.03033 m | 737 | 0.2821 ns | 415 |

No. 1 Hyperbola | No. 2 Hyperbola | No. 3 Hyperbola | No. 4 Hyperbola | |||||||
---|---|---|---|---|---|---|---|---|---|---|

Before | After | Before | After | Relative Error | Before | After | Relative Error | Before | After | |

Data1 | 2.11 | / | 2.54 | 1.33 | 11.30% | 3.28 | 2.07 | 1.40% | 3.54 | 2.34 |

Data2 | 1.64 | 2.08 | 1.34 | 10.70% | 2.87 | 2.13 | 1.40% | 3.11 | 2.37 | |

Data3 | 1.95 | 2.43 | 1.38 | 8.00% | 3.16 | 2.11 | 0.50% | 3.41 | 2.36 |

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**MDPI and ACS Style**

Zhu, C.; Ye, H.
A Modular Method for GPR Hyperbolic Feature Detection and Quantitative Parameter Inversion of Underground Pipelines. *Remote Sens.* **2023**, *15*, 2114.
https://doi.org/10.3390/rs15082114

**AMA Style**

Zhu C, Ye H.
A Modular Method for GPR Hyperbolic Feature Detection and Quantitative Parameter Inversion of Underground Pipelines. *Remote Sensing*. 2023; 15(8):2114.
https://doi.org/10.3390/rs15082114

**Chicago/Turabian Style**

Zhu, Chengke, and Hongxia Ye.
2023. "A Modular Method for GPR Hyperbolic Feature Detection and Quantitative Parameter Inversion of Underground Pipelines" *Remote Sensing* 15, no. 8: 2114.
https://doi.org/10.3390/rs15082114