Dual Mach–Zehnder Interferometers With Hierarchical Clustering Analysis Method Applied for Positioning the Intrusion

Abstract

The method of hierarchical clustering is for the first time employed to locate the intrusion-induced disturbance on the sensing fibers of a dual Mach–Zehnder interferometer (DMZI). Such an intrusion-induced disturbance is located by finding the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${x}$ </tex-math></inline-formula> coordinate of the centroid of the largest cluster on the Euclidean plane through hierarchical clustering with an appropriate linkage criterion employed for determining the distance between two observations. We compare average linkage and complete linkage criteria in the clustering analysis to see which one provides better locating accuracy. In the clustering analysis, the number of clusters is set to be 3–8 in finding the location of disturbance. To reduce the locating error, we also use differential signals here in the clustering analysis. Twelve intrusion events are simulated by knocking the sensing fibers to induce disturbances at a given location. The location of disturbance is determined through the clustering analysis for each intrusion event. The mean of the absolute values of locating errors [mean absolute error (MAE)] for the 12 intrusion events is then estimated. The experimental results in this study demonstrate a maximum MAE of 11.55 m in locating an intrusion with average linkage criterion employed for five-cluster analysis. Also, the MAE could be 3.55 m smaller by using the differential signals for clustering analysis, compared with the case when directly detected signals are used for clustering analysis. The results also confirm that the average linkage criterion provides only a small amount of improvement in MAE over complete linkage criterion.