Wave Front Shape-Based Approach to Acoustic Source Localization in a Homogeneous Anisotropic Plate

Abstract

An acoustic source localization approach based on the analysis of elastic wave front shapes is proposed for homogeneous anisotropic plates. The proposed approach is free from the unrealistic assumption of elastic waves propagating along linear paths in anisotropic solids, and enables one to estimate the source location without requiring to have knowledge of exact values of the elastic properties of the plate material. To implement the proposed methodology, sensors need to be installed on the plate surface in the form of clusters. The signals captured by the clusters are analyzed to estimate the angle of wave-incidence at each cluster's location. This angle is then related to the geometric feature of an idealized wave front shape to obtain a system of simultaneous nonlinear equations to be solved. Two situations regarding the orientation of the plate axes of symmetry are considered: (a) when this orientation is known and (b) when this orientation is unknown. The unknowns for the system of equations comprise the source coordinates and curve parameters (and for Situation (b), also the angle between the plate axes of symmetry and the axes of the plate coordinate system). The system is solved in the least squares sense by minimizing an objective function. Two idealized shapes, namely, an ellipse and a parametric curve, are proposed to model the wave fronts resulting from the propagation of the second wave groups. Thus, two localization techniques, namely, ellipse- and parametric curve-based techniques, are developed for both Situations (a) and (b) considering L-shaped clusters. The proposed approach is demonstrated with the help of numerical examples. Both techniques in both situations are observed to yield sufficiently accurate estimates for the source location. A new square-shaped cluster arrangement is proposed next to improve the accuracy of the estimation of the wave-incidence angle. A numerical illustration reveals that the wave front shape-based approach while used together with square-shaped clusters generally produces better localization results in terms of accuracy than while used together with L-shaped clusters.