Vibration Detection in Distributed Acoustic Sensor with Threshold-based Technique: a statistical view and analysis

Detecting vibrations with high probability and low false alarm probability is crucial for prompting distributed acoustic sensors (DASs) to real applications. It is known that detection performance mainly depends on signal-to-noise ratio (SNR) and many efforts have been made to improve it. However, the relationship between SNR and detection performance has not been quantitatively analyzed so far. Threshold-based vibration detection is a simple and commonly used technique, but how to set the decision threshold in DAS is still an open question. In this work, for the first time, we propose a model to quantify the relationship between SNR and detection performance and provide a method for setting the decision threshold. Firstly, we build a model to differentiate vibrations from the background noise based on their short-time average energy. This model reveals that setting decision threshold requires perfect knowledge of noise power, which is a difficult task in DAS since noise power varies frequently with time and position. To solve this problem, secondly, we propose a noise-irrelevant threshold setting method based on autocorrelation-energy. Finally, experimental validation is performed on a DAS system along 47.4km sensing fiber with 5m spatial resolution. Results of autocorrelation-energy-based method show 100% and 98.1% detection probability for two vibrations with <formula><tex>$1.1210^{-7}$</tex></formula> false alarm probability in a one-hour measurement period.