# A New Method of Using Sensor Arrays for Gas Leakage Location Based on Correlation of the Time-Space Domain of Continuous Ultrasound

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Location Method

_{1},y

_{1}), (x

_{2},y

_{2}) are known, thus to obtain the source position (x,y), θ

_{1}and θ

_{2}are necessary:

_{1}and θ

_{2}using a continuous signal by the traditional method, so this needs to be further explored. According to the previous location method [20], the k-domain distribution of a sensor array can be acquired by using high precision space sampling, and then the directional information of the leakage source can be obtained. However, this method is limited by the spatial resolution requirements, thus the array requires a high number of sensors to achieve a higher orientation accuracy.

## 3. Algorithm Theory

_{i}is the distance between leakage hole and the i-th sensor.

_{i}is usually more than 50 times longer than λ and the sound waveform can be considered as plane wave [28].

_{r,k}(t) which represents the noise at the location of the reference sensor can be expressed as a function of the frequency in the k mode (Equation (2)). In this research, the first sensor is defined as the reference sensor. ${A}_{k}(f)$ is a random amplitude and frequency’s spectrum of the leak noise at the location of the reference sensor in the k mode. f represents the single frequency that varies within the range f

_{0}–f

_{n}:

_{i}can be rewritten as:

_{i}combines the distance- and frequency-dependent attenuation effect of geometric diffraction, material absorption, and radiation loss (into the air):

_{i,k}(t) can be delayed in the opposite direction of the acoustic wave propagation.

_{i,k}(t, Δθ) to get the output of L-type array under the specific angle Δθ, thus, P

_{Σ,k}(t, Δθ) can be rewritten as:

_{i}, assuming α = α

_{i}, and Equation (8) can be simplified as follows:

_{Σ,k}(t, Δθ) is the maximum in the k mode assuming that the estimated direction is the same as the actual leakage source.

_{Σ,A0}(t, Δθ) is a function of $\mathrm{\Delta}\theta $ and t. Selecting the time window as (t

_{a},t

_{b}) and integrating the Equation (16), the energy output of sensor array (E) can be obtained under the specific angle $\mathrm{\Delta}\theta $:

^{®}: the angle corresponding to the maximum power peak gives the estimated position of the acoustic source.

## 4. Experimental Setup

#### 4.1. Assembly of the Apparatus

^{®}software. Vacuum grease ensures coupling between the sensors array and the plate. A pre-amplifier (gain set to 40 dB) is installed between the sensor array and the data acquisition system, to boost the signal and reduce the effects of noise and interference. A vacuum pump with a vacuum nozzle provided the loading, and thus the leakage pressure. The leakage hole is connected with the vacuum pump through the vacuum suction nozzle as shown in Figure 5. By starting the vacuum pump air is drawn off from the vacuum nozzle and a leakage source is simulated. The ultrasonic signal generated by the leakage can be detected and acquired. The ultrasonic signal attenuation is very low when it propagates in metal media, thus both resonance and scattering can occur [20]. Moreover, the environmental noise affects the low frequency signal. Thus, in order to avoid these interferences the 100–300 kHz frequency band is selected. Figure 6 shows the experimental apparatus.

Material | Modulus of Elasticity E (KN/mm^{2}) | Poisson’s Ratio σ | Density ρ (g·cm^{−3}) |
---|---|---|---|

302 Stainless steel | 210 | 0.305 | 7.93 |

Magnesium aluminum alloy | 40 | 0.275 | <1.8 |

_{1}) and 3115 m/s (c

_{s}) respectively. For the magnesium aluminum alloy plate, c

_{l}is 5991 m/s, and c

_{s}is 3266 m/s. By substituting these values into the dispersion equation [29], using the MATLAB

^{®}software, the c(f) of the two materials can be calculated. The c(f) curves are shown in Figure 7.

**Figure 7.**Dispersion curve of the experimental plates (A0: flexural mode, S0: extensional mode; Solid line: 302 steel, Dotted line: magnesium aluminum alloy).

Mode Used | 302 Steel | Magnesium Aluminum Alloy | ||
---|---|---|---|---|

Mean Error (°) | Variance | Mean Error (°) | Variance | |

A0 mode | 0.29 | 1.9039 | 0.1925 | 1.252178 |

S0 mode | 6.04 | 388.8854 | 11.7425 | 700.4788 |

A0&S0 mode | 0.28 | 3.1546 | 0.54 | 3.206737 |

#### 4.2. Sizing of the Array

Item | Value |
---|---|

Peak Sensitivity, Ref V/(m/s) | 62 dB |

Peak Sensitivity, Ref V/μbar | −72 dB |

Operating Frequency Range | 125–750 kHz |

Resonant Frequency, Ref V/(m/s) | 140 kHz |

Resonant Frequency, Ref V/μbar | 300 kHz |

Directionality | ± 1.5 dB |

Diameter | 8 mm |

## 5. Results and Discussion

Actual Leakage Angle (°) | Proposed Method without the Sound Velocity’s Changing (c = 2000 m/s) | Proposed Method | |||
---|---|---|---|---|---|

Mean Error (°) | Variance | Mean Error (°) | Variance | ||

No.1 array | 78.7 | 5.7 | 208.01 | 0 | 3.38 |

No.2 array | 56.3 | 19.3 | 179.25 | 0.4 | 2.96 |

No.3 array | 60 | −13.1 | 152.77 | −0.1 | 3.19 |

The Coordinate of Leakage Point(mm) | The Coordinate of Estimate Leakage Point (mm) | Error d (mm) | |
---|---|---|---|

No.1 and No.2 array | (0,0) | (1.89,−9.67) | 9.85 |

No.1 and No.3 array | (0,0) | (−1.64,8.00) | 8.17 |

No.2 and No.3 array | (0,0) | (−5.51,1.22) | 5.64 |

Comprehensive result | (0,0) | (−5.26,−0.45) | 5.28 |

^{2}plate. Under these conditions, the proposed algorithm gives an error of 5.28 mm. Meanwhile, the location error is 9.85 mm when the worse-case from a geometric perspective (the distance between the two sensor arrays and the leak hole are both longer than in [20] as mentioned) is considered. According to the results, the leakage location accuracy can be further improved by integrating multiple acquisitions of different arrays positions to estimate the location area (the shadowed area of Figure 13).

## 6. Conclusions

- (1)
- Experimental tests show that the leakage-generated acoustic emission signal is influenced by some factors such as media characteristics, leakage hole size, and sensor response. Moreover, the distortion which is introduced by the sensors cannot be neglected in order to achieve higher location accuracy.
- (2)
- The leakage ultrasonic signal is a noise-like continuous broadband signal. According to the experimental results, the signal collected by an AE sensor is mainly in A0 mode (plate is less than 6 mm thick, and signal frequency within the range 100–300 kHz). Meanwhile, the S0 mode has an extremely small influence on the locating result, thus S0 can be neglected.
- (3)
- This research presents a high-accuracy leakage source location method using fewer sensors to compose the sensor array. Moreover, the study solves the gas continuous leakage real-time localization problem based on the correlation of the signal in the time-space domain, which is generated from the leakage hole. Experimental results show that when the size of plate is 1000 × 1000 × 2.5 mm and the diameter of the leakage hole is larger than 0.8 mm, the mean location error is 5.83 mm, and the maximum location error is generally less than 10 mm. These results are typical of many others we have obtained. Therefore, this method provides a new approach to successfully solve the problem of real-time detection of gas leakages and location in large pressure vessels.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Bian, X.; Zhang, Y.; Li, Y.; Gong, X.; Jin, S. A New Method of Using Sensor Arrays for Gas Leakage Location Based on Correlation of the Time-Space Domain of Continuous Ultrasound. *Sensors* **2015**, *15*, 8266-8283.
https://doi.org/10.3390/s150408266

**AMA Style**

Bian X, Zhang Y, Li Y, Gong X, Jin S. A New Method of Using Sensor Arrays for Gas Leakage Location Based on Correlation of the Time-Space Domain of Continuous Ultrasound. *Sensors*. 2015; 15(4):8266-8283.
https://doi.org/10.3390/s150408266

**Chicago/Turabian Style**

Bian, Xu, Yu Zhang, Yibo Li, Xiaoyue Gong, and Shijiu Jin. 2015. "A New Method of Using Sensor Arrays for Gas Leakage Location Based on Correlation of the Time-Space Domain of Continuous Ultrasound" *Sensors* 15, no. 4: 8266-8283.
https://doi.org/10.3390/s150408266