Feature optimisation for the sparse reconstruction of Lamb waves multimodal and dispersive characteristics

Ultrasonic Lamb waves serve as a powerful investigative tool in the domains of structural health monitoring and non-destructive testing. The accurate extraction of dispersion curves is critical for illustrating wave propagation mechanisms in structures and providing the foundational basis for damage localisation. This paper proposed a novel feature optimisation method for plate-like structures, aimed at extracting high-frequency dispersion information with a minimal number of measurement points and enhancing sparse reconstruction performance. The feature optimisation method was developed based on the sparse optimisation model of l2−l1−2. To enhance the high-frequency dispersion characteristics, multiple-scaling methods are integrated into the sparse optimisation model. Comparative analysis of scaling methods reveals that the sparse optimisation model with the standard scalar performs exceptionally, which is defined as the improved l2−l1−2 method for sparse Lamb waves reconstruction. The proposed method requires only a minimal number of measurement points for sparse reconstruction of dispersion curves, enabling effective reconstruction of high-frequency dispersion characteristics. Numerical simulations on a steel plate and experiments on composite laminates were conducted to validate the efficacy of the proposed method. The reconstruction performance of improved l2−l1−2 method is up to 142.52% higher than the l2−l1−2 method.