Elsevier

Optics Communications

Volume 475, 15 November 2020, 126215
Optics Communications

The detection of non-Gaussian vibration with improved sensing performance in Φ-OTDR

https://doi.org/10.1016/j.optcom.2020.126215Get rights and content

Highlights

  • We propose a 3rd-order cumulants algorithm to detect the non-Gaussian vibration.

  • We use the probability distribution of Rayleigh signal to extract the vibration.

  • We conclude that the system can detect non-Gaussian vibration with improved SNR.

Abstract

In structural health monitoring, vibrations often behave as non-Gaussian process, such as gear and engine failure. In this paper, a high-order cumulants algorithm-based phase-sensitive optical time-domain reflectometry is proposed to detect and analyze non-Gaussian vibration. When disturbances with non-Gaussian probability distribution are applied on the sensing fiber, the probability distribution of the Rayleigh backscattering deviates from the standard Gaussian distribution. The 3rd-order cumulant of the Rayleigh backscattering is calculated to extract the non-Gaussian signal from background white noises. Simulations and experiments are carried out. The experimental results indicate that the signal-to-noise ratio is improved by up to 14 dB with 1500 m long sensing fiber. Due to the cubic operation of the algorithm, the spatial resolution is further enhanced to 5 m with pulse width of 100 ns.

Introduction

Fiber distributed sensing based on Rayleigh scattering is a promising technique to detect the internal stress changes along the fiber. Phase-sensitive OTDR (φ-OTDR) attracts attentions due to the capability of high-sensitivity, distributed measurements and cost-effective [1]. The φ-OTD R is widely used in perimeter security, health monitoring of structures and pipe line protection, etc. [2], [3]. High reliability and precision of the location are vital in intelligent fault diagnoses. In health monitoring, vibration failures are often non-Gaussian and non-stable, such as gear failure or engine failure.

The continuous wavelet transforms (CWT) is adopted in the φ-OTDR system to simultaneously acquire the vibration information in both frequency-domain and time-domain [4]. The time–frequency information is determined by the CWT scalogram with wavelet ridge detection. The position information is acquired by the wavelet global spectrum, which is determined by the amplitude differences among the global wavelet spectrums of time sequences. A vibration separation method based on phase-measuring scheme is introduced [5]. A double-source vibration is experimentally identified and separated, which demonstrates the improvement of reliability in practical OTDR system. A two-dimensional edge detection method has been proposed to extract location information of intruder in φ-OTDR system [6]. The location SNR of 8.4 dB is achieved by two-dimensional edge detection with the Sobel operator. Later, a spectral subtraction method by reducing wide-band background noises is proposed to enhance the spectrum SNR of the vibration signal [7]. The characteristic vector is extracted from the original vibration signal by wavelet energy spectrum analysis to identify the vibration signal [8]. A classification macro-accuracy of 88.60% is obtained. A time-gated digital optical frequency domain reflectometry based on frequency-division-multiplexing is studied to realize a spectrum gain of 10 dB [9]. The distributed vibration sensing by sub-Nyquist additive random sampling was demonstrated recently [10], and the detection of broadband vibration signal is achieved.

The distributed detection and location of non-Gaussian vibrations, e.g., gear failure and engine failure, is studied in this paper. The higher-order cumulants (HOC) algorithm is used to analyze the vibration signal of the φ-OTDR system. The sampled Rayleigh backscattering has a random walk process induced optical intensity fluctuations, thermal noise and shot noise, which behaves as the Gaussian distribution. The vibration signal with non-Gaussian probability distribution is extracted from the background noises by the statistic of probability distribution. First, the tendency of amplitude changes is subtracted from the average of backscattering traces; second, the 3rd-order cumulant of backscattering traces are calculated to extract non-Gaussian features; finally, the vibration signal is located by value of 3rd-order cumulant. The proposed technique can detect and locate non-Gaussian vibrations with improved reliability and precision.

Section snippets

Theoretical analysis

Cumulants can reveal the statistic characteristic of time-domain signal. Given a sampled sequence Xn={x1,x2,,xn}, where X denotes a collection of stationary random variables with zero-mean. The function f (x1,,xn) is the joint probability density of the sequence. The Fourier transform of f (x1,,xn) can be expressed as Φ(ω1,,ωk)=E{expj(ω1x1++ωkxk)}=++f(x1,,xk)ej(ω1x1++ωkxk)dx1dxk,where ωi represent the angular frequency and E represents the mathematical expectation. The joint

Simulations

Detections and analysis of non-Gaussian vibration signal by HOC algorithm are simulated. Xn={x1,x2,,xn} and c3,Xn (n=1, 2, 3, 4, 5, 6) are sampled vibration signal and corresponding values of the 3rd-order cumulant, respectively. The probability density of sequence X1 follows the standard normal distribution with zero-mean and variance of one. The probability density of the signal is represented by a histogram with a finite length sequence [−3.46, 3.46], as shown in Fig. 1(a).

Non-Gaussian

Experimental results and discussions

The schematic diagram is illustrated in Fig. 3. A narrow line-width laser (NLL) with line-width less than 100 kHz outputs continuous laser. The average optical power is 10 mW. The light source is then modulated into optical pulses by an acoustic-optic modulator (AOM), which is driven by a waveform generator (WG). After amplified by an erbium-doped fiber amplifier (EDFA), the light pulses are injected into a 1500 m long sensing fiber (Corning SMF28e) through an optical circulator (OC). The

Conclusion

In conclusion, a higher-order cumulants based phase-sensitive OTDR to detect the non-Gaussian vibration is presented in this paper. The proposed technique can suppress Gaussian noises, e.g. the state of polarization noise and the thermal noise. The experimental results show that the demonstrated method can improve the location SNR by 10 dB. In addition, the spatial resolution is improved to 5 m with optical pulse width of 100 ns. The proposed system is promising in the detection and location

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work is funded by Scientific Research Project of Hunan Provincial Department of Education Grant NO. 19B003, Hunan Natural Science Foundation Grant NO. 2020JJ5601 and 2020JJ5565.

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