Hierarchical Clustering Analysis for Positioning Two Intrusion Events at Different Locations Using Dual Mach-Zehnder Interferometers

Hierarchical clustering analysis is applied to the positioning of two simultaneously-occurring intrusion events in the case of a dual Mach-Zehnder interferometer used for intrusion detection. To simulate the two intrusion events, the sensing fibers of the dual Mach-Zehnder interferometer are heavily knocked at two different positions simultaneously. Then the clockwise (CW) and counter-clockwise (CCW) signals are loaded into a personal computer through a data acquisition module, and analyzed by Fourier transform method for determination of the time delay between the two signals. Hierarchical clustering analysis is then employed twice for dividing the data points in a feature space into several clusters according to the conditions required. To locate the two intrusions, the first clustering analysis is performed on the data points formed by signals detected in a 10 ms time period, with the centroid of the largest cluster being the location of a single intrusion event. Then, 100 pairs of CW and CCW signals detected sequentially are analyzed to give 100 locations. These 100 locations and their CP values (each standing for a ratio of a given spectral amplitude to the summation of the spectral amplitudes over the frequency band of 2500 to 5000 Hz) constitute 100 data points in a feature space for the second hierarchical clustering analysis, which then determines the respective locations of the two intrusion events. In the test of a 1036 m long fiber perimeter, we demonstrated an accuracy to within 21.55 m.