RI 8692 Acoustic Emission Source Location - A Mathematical Analysis

Newton's method of solving a nonlinear equation is employed to develop a least-squares acoustic emission source location method in which the spatial residuals of the location equations are minimized. These residuals, related to the distances from the least-squares source location perpendicular to the surfaces described by the location equations, permit location error to be estimated to first order along the spatial axes. The solutions obtained by this method are the best spatial solutions to the location equations in the least-squares sense. Also presented is a procedure by which the geometrical control of a transducer array can be evaluated using the rate of change of source location with fractional velocity change.