New robust adaptive beamforming for imaging damages scattering coherent Lamb waves

The Lamb wave imaging approach based on adaptive beamforming method, notably the minimum variance distortionless response beamforming algorithm, is analyzed to explain its serious performance degradation or even complete invalidation, when the scattering signals generated by damages are coherent. It is demonstrated that in such case, the covariance matrix of the received scattering signals becomes rank-deficient, and when decomposed into the description form of the array manifold matrix left and conjugate right multiplied by a matrix P, P is a non-diagonal matrix with off-diagonal elements representing the coherences among scattering signals. These factors result in the failure of the conventional adaptive beamforming algorithm. To break the above limitations, a covariance matrix fitting method using a weighted least squares criterion is proposed by constructing P as a diagonal matrix. Based on the fitted covariance matrix, a robust adaptive beamforming Lamb wave imaging approach for coherent scattering signals is presented. Extensive numerical simulations and imaging experiments conducted on an aluminum plate corroborate the effectiveness of the proposed algorithm. The results affirm that the proposed method preserves the performance levels achieved by non-coherent scattering signals Lamb wave imaging approaches.