High-resolution Lamb waves dispersion curves estimation and elastic property inversion

Ultrasonic Lamb waves have been widely used for non-destructive evaluation and testing. However, the inversion from the measured guided signals to the material properties is still a challenging task in terms of multimodal dispersive signal processing and parameter estimation. This paper presents a robust strategy including the high-resolution extraction of the multimodal dispersion curves and model-based elastic property estimation. First, the estimation of signal parameters via rotation invariant technique (ESPRIT) is employed to extract the dispersion curves of the Lamb waves in the plates. Then, the particle swarm optimization (PSO) algorithm is used to retrieve the optimal model parameters by maximizing the objective function built from the dispersion equations. The elastic properties (i.e., two independent constants for the isotropic plate and four constants for the transversely isotropic plate) can thus be determined. Results of the steel, aluminum and composite plates demonstrate that the estimates are in agreement with the references. The root mean squared errors (RMSEs) between the estimated and theoretical dispersion curves calculated by the inversed model parameters for simulation, steel, aluminum and composite experiments are 0.027 rad/mm, 0.032 rad/mm, 0.033 rad/mm and 0.102 rad/mm respectively. The estimated error of thickness is less than 1%. The proposed model-based inversion strategy offers several advantages: (1) the high-resolution estimation of dispersion curves allows the objective function built for the parameter inversion without a peak-finding process. (2) The ESPRIT based dispersion curves extraction strategy offers a sharp objective function in the parameter space. (3) The inverse problem for ultrasonic waveguide characterization is solved using the PSO optimizer which can be implemented with ease and few parameters need to be tuned.