# Recognition of a Phase-Sensitivity OTDR Sensing System Based on Morphologic Feature Extraction

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Φ-OTDR Signal Characteristics

_{0}and the optical phase is therefore modulated by the vibration, with variation Φ.

_{1}and E

_{2}are the Rayleigh scattering field intensities before and after the intrusion event, respectively.

_{0}is the initial phase of the Φ-OTDR system. The value of ϕ in Equation (4) not only changes in the time domain but also in the spatial domain. The attenuation of ϕ in the spatial domain can be expressed as:

_{0}is the position of the intrusion event and d is the range of the intrusion force. $\Delta \mathrm{\delta}$ is the phase variation in the time domain. The schematic diagram is shown in Figure 3.

**Figure 6.**(

**a**) Calculated signal of vehicle passing; (

**b**) Experimentally measured signal of vehicle passing.

## 3. Feature Extraction Based on Morphology

#### 3.1. Preprocessing

**Figure 7.**(

**a**) Grey level histogram of vehicle passing; (

**b**) Grey level histogram of digging. (

**c**) Grey level histogram of walking.

**Figure 8.**(

**a**) Image of walking after threshold segmentation; (

**b**) Image of digging after threshold segmentation; (

**c**) Image of vehicle passing after threshold segmentation.

**Figure 9.**(

**a**) Image of walking showing events which are labeled in different colors; (

**b**) Image of digging showing events which are labeled in different colors; (

**c**) Image of vehicle passing showing events which are labeled in different colors.

#### 3.2. Feature Extraction

_{i}

_{max}and the minimum distance D

_{i}

_{min}can be easily obtained. The shape feature is calculated using Equation (12):

Feature | Definition |
---|---|

Amp | Amplitude of time-space domain signal |

Cen | Minimum interval between regions |

Shape | Roundness of the region |

Con | Pixel number of the convex hull |

Area | Pixel number of the region |

Ecc | Eccentricity of ellipse which has the same second moment as the event region |

Maj | Length of the long axis of the ellipse which has the same second moment as the event region |

Min | Length of the short axis of the ellipse which has the same second moment as the event region |

Equ | Diameter of a circle which has the same total area as the event region |

Eul | Remaining number of objects, excluding holes in the image region |

Event Type | Con | Cen | Area | Amp | Ecc |
---|---|---|---|---|---|

Walking | 279 | 271.373 | 245 | 10.2871 | 0.7574 |

Digging | 224 | 1000 | 205 | 12.6634 | 0.8751 |

Vehicle passing | 2413 | 118.0326 | 1461 | 8.5084 | 0.9118 |

Shape | Maj | Min | Equ | Eul | |

Walking | 8.1041 | 24.4843 | 12.9812 | 17.3192 | 1 |

Digging | 14.6010 | 25.9145 | 10.6407 | 16.1559 | 1 |

Vehicle passing | 46.7452 | 84.0348 | 40.5031 | 43.1287 | −1 |

#### 3.3. Feature Selection

_{ω}is the scatter matrix in the class and S

_{m}is the hybrid scatter matrix calculated using Equation (14):

_{b}is the scatter matrix between classes.

${x}_{ik}$ | Feature | Value of ${i}_{k}$ |
---|---|---|

${x}_{i2}$ | Shape | 159.8173 |

${x}_{i3}$ | Area | 71.8518 |

${x}_{i4}$ | Amp | 71.8435 |

${x}_{i5}$ | Maj | 11.8 |

${x}_{i6}$ | Min | 11.7677 |

${x}_{i7}$ | Equ | 11.7333 |

${x}_{i8}$ | Eul | 7.7 |

${x}_{i9}$ | Con | 7.6 |

${x}_{i10}$ | Ecc | 3.6 |

## 4. Experiments

Sample Model | Walking | Digging | Vehicle Passing |
---|---|---|---|

Sample size | 20 | 20 | 20 |

Walking | 20 | 1 | 0 |

Digging | 0 | 19 | 0 |

Vehicle passing | 0 | 0 | 20 |

Accuracy (%) | 100 | 95 | 100 |

Method | Average Precision (%) | Recognition Time (s) |
---|---|---|

WFE-RVM | 80 | 10.526 |

RDFE-RVM | 85.4 | 2.169 |

MFE-RVM | 97.8 | 0.7028 |

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Sun, Q.; Feng, H.; Yan, X.; Zeng, Z.
Recognition of a Phase-Sensitivity OTDR Sensing System Based on Morphologic Feature Extraction. *Sensors* **2015**, *15*, 15179-15197.
https://doi.org/10.3390/s150715179

**AMA Style**

Sun Q, Feng H, Yan X, Zeng Z.
Recognition of a Phase-Sensitivity OTDR Sensing System Based on Morphologic Feature Extraction. *Sensors*. 2015; 15(7):15179-15197.
https://doi.org/10.3390/s150715179

**Chicago/Turabian Style**

Sun, Qian, Hao Feng, Xueying Yan, and Zhoumo Zeng.
2015. "Recognition of a Phase-Sensitivity OTDR Sensing System Based on Morphologic Feature Extraction" *Sensors* 15, no. 7: 15179-15197.
https://doi.org/10.3390/s150715179