Waveform inversion for wavenumber extraction and waveguide characterization using ultrasonic Lamb waves

Abstract

Wavenumber dispersion of ultrasonic Lamb waves associating with the thickness and material property of plates plays an important role in waveguide characterization and non-destructive testing. Classical waveguide characterization with wavenumber estimation methods is performed based on a large amount of Lamb wave signals or sensitive to wave mode overlapping and noise. A genetic algorithms-based waveform inversion method is developed for wavenumber extraction of one Lamb wave signal and characterization of plate in this work. The individual chromosome is encoded in real number by the thickness and material properties of the structure. The elastic formula of Lamb waves is solved by the bisection method to further derive the wavenumber curves; then the wave mode signals are generated based on the propagation function, and are linearly combined to form the individual signal. The signal with the minimum residual ratio to the analysis signal is iteratively searched by the genetic algorithm. Finally, the plate properties and wavenumber of Lamb waves are identified with the chromosome of searched individual. Numerical and experimental studies prove the developed waveform inversion method can realize accurate wavenumber extraction of a Lamb wave signal, even though its time–frequency representation has low sparsity, and characterization of plate. The residual ratio between the inversion wavenumber and theory curves is around 1%; and the estimation deviation of material properties of plate is around 6%.