# Pipeline Leak Detection and Location Based on Model-Free Isolation of Abnormal Acoustic Signals

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Acoustic Sensor-Based Leak Detection System

## 3. Model-Free Isolation Principle of Abnormal Acoustic Signals

#### 3.1. Decomposition of an Acoustic Signal

#### 3.2. Principle of the Model-Free Isolation Method

**Lemma**

**1.**

**Lemma**

**2.**

**Lemma 1**and Equation (4).

**Theorem**

**1.**

**Proof**

**of**

**Theorem**

**1.**

**Theorem**

**2.**

**Proof**

**of**

**Theorem**

**2.**

**Theorem**

**3.**

**Proof**

**of**

**Theorem**

**3.**

**Theorem 2**, it is known that ${\sigma}_{k}$ is larger than ${\sigma}_{k+1}$. Hence, ${\Delta}_{k}=10\mathrm{log}({\sigma}_{k}^{2}/{\sigma}_{k+1}^{2})>0$. Combined with Equation (13),

**Theorem 3**is proved. □

**Lemma 2**and Equation (5), if the actual number of abnormal sub-signals is m, then:

#### 3.3. Isolation of Abnormal Sub-Signals

## 4. Leak Location

#### 4.1. Analysis of the Influence of Operation Sub-Signals on Leak Location

#### 4.2. Leak Location Based on Filtering Operation Sub-Signals

## 5. Experimental Results

#### 5.1. Field Test

#### 5.2. Comparison of Methods

- WPE. Wavelet basis function: Daubechies 1 wavelet (db 1); decomposition level: 5; window width: 100; sliding step length: 10.
- SVDD.Group number: 200; feature-frequency: 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7; Gaussian kernel function: ${\sigma}_{\mathrm{svdd}}$ = 0.28.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 7.**The signal to noise ration (SNR) sequence ${\mathbf{S}}_{k}$ of normal and abnormal acoustic signals varies with the number k of abnormal sub-signals. (

**a**) Normal acoustic signal: the actual number of abnormal sub-signals is m = 0. (

**b**) Abnormal acoustic signal: the actual number of abnormal sub-signals is m = 2.

Up/Down | ${\mathbf{y}}_{\mathbf{sub}}\left({\mathit{b}}_{1}\right){|}_{+}$ | ${\mathbf{y}}_{\mathbf{sub}}\left({\mathit{b}}_{2}\right){|}_{-}$ | ${\mathbf{y}}_{\mathbf{sub}}\left({\mathit{b}}_{3}\right){|}_{+}$ | ${\mathbf{y}}_{\mathbf{sub}}\left({\mathit{b}}_{4}\right){|}_{+}$ | ${\mathbf{y}}_{\mathbf{sub}}\left({\mathit{b}}_{5}\right){|}_{-}$ | ${\mathbf{y}}_{\mathbf{sub}}\left({\mathit{b}}_{6}\right){|}_{+}$ |
---|---|---|---|---|---|---|

${\mathbf{x}}_{\mathrm{sub}}\left({a}_{1}\right){|}_{+}$ | −3.16 s | -- | × | × | -- | × |

${\mathbf{x}}_{\mathrm{sub}}\left({a}_{2}\right){|}_{-}$ | -- | −3.16 s | -- | -- | × | -- |

${\mathbf{x}}_{\mathrm{sub}}\left({a}_{3}\right){|}_{-}$ | -- | 3.98 s | -- | -- | × | -- |

${\mathbf{x}}_{\mathrm{sub}}\left({a}_{4}\right){|}_{+}$ | × | -- | 11.73 s | −13.38 s | -- | × |

${\mathbf{x}}_{\mathrm{sub}}\left({a}_{5}\right){|}_{-}$ | -- | × | -- | -- | −13.36 s | -- |

${\mathbf{x}}_{\mathrm{sub}}\left({a}_{6}\right){|}_{+}$ | × | -- | × | −7.82 s | -- | −13.14 s |

${\mathbf{x}}_{\mathrm{sub}}\left({a}_{7}\right){|}_{+}$ | × | -- | × | 10.38 s | -- | 5.74 s |

Parameters | Value/Unit | |
---|---|---|

Naphtha | Crude oil | |

Total length | 15.511 km | 15.600 km |

Pipeline diameter | 150 mm | 250 mm |

Pipeline thickness | 6 mm | unknown |

Fluid density | 0.76 g· cm${}^{-3}$ | 0.86 g· cm${}^{-3}$ |

Acoustic velocity | 1055 m· s${}^{-1}$ | 1179 m· s${}^{-1}$ |

Upstream pressure | 2.18 MPa | 2.80 MPa |

Downstream pressure | 0.48 MPa | 0.67 MPa |

Leak point to upstream | 9.476 km | 6.000 km |

Leak aperture | <4 mm, 4 mm, <8 mm, 8 mm | 4 mm |

Pipeline material | metal | |

Sampling frequency | 50 Hz | |

Sampling precision | 12 bit A/D |

Pipeline | Sample | Location (km) | |
---|---|---|---|

Before | After | ||

Naphtha | 1 | 9.496 | 9.496 |

2 | 9.444 | 9.444 | |

3 | 9.496 | 9.496 | |

4 | 9.512 | 9.512 | |

5 | 9.507 | 9.507 | |

6 | 9.496 | 9.496 | |

7 | 9.444 | 9.444 | |

8 | 9.475 | 9.475 | |

9 | 9.438 | 9.438 | |

10 | 9.444 | 9.444 | |

11 | 9.475 | 9.475 | |

12 | 9.517 | 9.517 | |

13 | 9.465 | 9.465 | |

14 | 9.517 | 9.517 | |

15 | 9.507 | 9.507 | |

Crude oil | 1 | −0.116 | 5.981 |

2 | −0.152 | 5.957 | |

3 | −0.069 | 5.946 | |

4 | −0.042 | 5.934 | |

5 | 5.364 | 5.840 | |

6 | −0.140 | 5.946 |

**Table 4.**Comparison of offline test between the model-free-based (proposed), support vector domain description (SVDD)-based and WPE-based methods on the naphtha pipeline.

Pipeline | Method | Running Time (s) | Number of Alarms | Largest Location Error (m) | ||
---|---|---|---|---|---|---|

Leak | False | Missing | ||||

Naphtha | Model-free | $0.041$ | 15 | 0 | 0 | 41 |

SVDD | $0.083$ | 15 | 0 | 0 | 64 | |

WPE | $53.187$ | 13 | 4 | 2 | 64 | |

Crude oil | Model-free | $0.041$ | 6 | 0 | 0 | 160 |

SVDD | $0.083$ | 1 | 1 | 5 | 636 | |

WPE | $53.187$ | 1 | 3 | 5 | 636 |

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## Share and Cite

**MDPI and ACS Style**

Wang, F.; Lin, W.; Liu, Z.; Qiu, X. Pipeline Leak Detection and Location Based on Model-Free Isolation of Abnormal Acoustic Signals. *Energies* **2019**, *12*, 3172.
https://doi.org/10.3390/en12163172

**AMA Style**

Wang F, Lin W, Liu Z, Qiu X. Pipeline Leak Detection and Location Based on Model-Free Isolation of Abnormal Acoustic Signals. *Energies*. 2019; 12(16):3172.
https://doi.org/10.3390/en12163172

**Chicago/Turabian Style**

Wang, Fang, Weiguo Lin, Zheng Liu, and Xianbo Qiu. 2019. "Pipeline Leak Detection and Location Based on Model-Free Isolation of Abnormal Acoustic Signals" *Energies* 12, no. 16: 3172.
https://doi.org/10.3390/en12163172