A methodology for estimating guided wave scattering patterns from sparse transducer array measurements

Ultrasonic guided waves are one of the primary methods being investigated for structural health monitoring of plate-like components. A common practice is to collect measurements from a sparse transducer array using the pitch-catch method, which enables interrogation of defects from multiple directions. Thus, knowledge of how guided waves scatter from defects is very useful for detection, localization, and characterization of damage. One way to describe scattering patterns is with a matrix indexed by incident angle and scattered angle, and sparse array measurements essentially sample this matrix. A methodology is proposed in this paper to estimate the complete scattering matrix from these limited array measurements. First, recorded array signals are compensated for geometric spreading loss, wave packet spreading loss, and transducer differences. Initial scattering values are then extracted from the scattered wave packets after baseline subtraction and are augmented using transducer reciprocity and any a priori knowledge of defect geometric symmetry. Finally, radial basis function interpolation is performed on these values to obtain the complete scattering matrix. Scattering matrices are generated from experimental data by cutting notches of different lengths originating from a through-hole in an aluminum plate specimen that is instrumented with a sparse transducer array. The methodology is validated by laser vibrometry measurements performed on a nominally identical specimen for one notch length.