Two-dimensional matrix pencil method for improved local wavenumber estimation in adhesively bonded plates

Local wavenumber analysis based on full ultrasonic guided wavefield is a powerful tool to image anomalies in plate-like structures, but the wavenumber resolution is limited due to spatial windowing and spectral leakage in Fourier transform-based methods. Benefitting from the far-field propagation model of guided waves, the two-dimensional matrix pencil method is applied to estimate the local wavenumber, which reduces the influence of interference modes and measurement noise, circumvents zero padding and spectral leakage, and characterizes the size of bonding accurately. This method involves local enhanced matrix construction, singular value decomposition, poles extracting and pairing and local wavenumber calculation. Its performance in noisy conditions was analyzed using straight- and circular-crested guided wave propagation models. The estimated wavenumber is accurate for straight-crested waves, but slightly smaller for circular-crested waves. The estimation error for circular-crested waves will be reduced when the point source moves away from the subarray, since the wavefront is locally straight in the far-field over the subarray area. In addition, the effectiveness was verified by the numerical simulation conducted on an aluminum plate with a square and H-shaped bonding, as well as the experiments conducted on a stiffened composite plate. It outperforms the Fourier transform-based method when the size of the subarray aperture and spatial window is less than 1.5 times the wavelength of the dominant mode.