A Robust Hyperboloid Method for Velocity-Free MS/AE Source Localization with Heavy-Tailed Proximity Metric

Traditional localization techniques often depend significantly on pre-defined wave velocities and the quality of arrival time picking. However, in actual engineering applications, there is a prevalent issue of abnormal errors in arrival time selection. To this end, this paper proposes a robust hyperboloid method for velocity-free microseismic/acoustic emission (MS/AE) localization with a heavy-tailed proximity metric. First, a velocity-free hyperbolic equation using the time difference of arrivals is constructed and a proximity metric is established for evaluating the distance between the guess point and the hyperboloid. Second, the proximity metric is weighted using a heavy-tailed distribution to reduce the impact of outliers further. Third, a coordinate transformation matrix is derived to align the proximity metrics of individual sensors from their local coordinate systems into a total proximity metric within the global coordinate system. Finally, a particle swarm optimization algorithm is employed to minimize the total proximity metric for the robust location result. The results of the lead-breaking experiments show that the method has better positioning accuracy (less than 7.3 mm). In addition, simulation tests show that with the increase in the number and scale of outliers, the positioning error of the proposed method is always stable. In contrast, the average positioning errors of the existing method increase significantly. Furthermore, the applicability study of the proposed method is conducted by using mine blast monitoring data, and the results show that the average localization error of the proposed method is only 8.09 m, with an accuracy improvement of over 58% compared to the existing five methods.