Material parameter inversion using cross-entropy optimization based on Lamb Wave dispersion spectra

Abstract

For plate-like structures, non-destructive testing using ultrasonic Lamb waves has found many applications as oscillation modes and dispersion properties depend directly on the elastic material parameters. However, the dispersive nature of these modes complicates the analysis in the temporal–spatial domain. Instead, the frequency–wavenumber domain has proven advantageous because it allows the separation of simultaneously excited modes. Inversion of dispersion information to determine material properties is still a matter of research.

This paper proposes an algorithm based on the cross-entropy method which has been proven successful for many challenging optimization problems. This algorithm is used to determine the elastic properties (specific Lamé parameters) and the layer thickness of isotropic samples directly from the dispersion data of Lamb waves. This allows a full characterization of the elastic properties of the material in the case of known density. A cost function is developed that works directly on the raw dispersion data, requiring no thresholding or mode detection. The convergence of this method is shown to be wide with parameter search ranges of 300% or more.

The properties of the cost function were investigated by parameter study. The algorithm is evaluated through finite element simulations of Lamb wave propagation in three different isotropic materials. The findings indicate an average error of less than 1%. Measurement data for four samples (two steel plates; fused silica and lithium niobate wafers) show a strong correlation with literature values for the elastic parameters. The estimated thicknesses align with the measured values within the $5\mu m$ and are in agreement with literature values.