A Novel Approach for Three-Dimensional Acoustic Source Localization in Orthotropic Medium

Abstract

This work investigates the three-dimensional localization of acoustic emission sources in a cartesian orthotropic medium using a geometric approach. The proposed method minimizes a constrained nonlinear objective function formulated from arrival times, computed via the 3D Christoffel equation for wave propagation in orthotropic solids. Acoustic test points (ATPs) and emission times were randomly generated to evaluate the robustness of the localization procedure. Localization was performed under two scenarios: first, assuming known material parameters; and second, jointly estimating both the source coordinates and the material parameters. This increased the number of unknowns from four (source position and emission time) to ten, with the six additional variables corresponding to the 3D Hankinson parameters characterizing wave velocity anisotropy. The study examined the effects of both number of sensors (ranging from 4 to 14) and spatial configuration (eight distinct arrangements) on localization accuracy. Two global optimization algorithms (DIRECT and differential evolution) were employed to minimize the objective function. Results have revealed that localization performance is influenced more by sensor placement than by sensors quantity. The differential evolution algorithm exhibited greater robustness with and less sensitivity to sensor positioning. The findings confirmed the effectiveness of the proposed methodology for accurate acoustic source localization and concurrent estimation of material parameters in orthotropic media.