Quantitative ultrasonic characterization of fractal-based pore distribution homogeneity with variable observation scales in heterogeneous medium

Abstract

The characterization of pore distribution homogeneity in heterogeneous medium is difficult due to the lack of quantitative description of homogeneity, and the degree of homogeneity is closely related to measurement method and observation scale. In this paper, a kind of quantitative ultrasonic characterization strategy based on fractal theory, which takes into account the principle of matching observation scale with acoustic beam size, is proposed. The ultrasonic signals containing information about heterogeneous seal coating are extracted through water-immersed ultrasonic pulse-echo reflection method to characterize pore distribution homogeneity. The fractal dimension D and multifractal spectral symmetry B are specifically used to parameterize pore distribution homogeneity of microscopic images within acoustic beam size. By establishing simulation models combined with experimental microscopic images, the effects of pore number and size distribution on ultrasonic attenuation coefficient α are analyzed. Furthermore, the relationships between attenuation coefficient and the above two fractal parameters are established to quantitatively characterize pore distribution homogeneity with porosity of 1 %∼6 % and scales ranging from several to tens of microns. Finally, correlation coefficient R and root mean square error RMSE of the attenuation coefficient varying with two fractal parameters at variable observation scales of 3 mm, 2 mm, 1 mm, and 0.5 mm are compared. It should be noticed that considering the principle of matching observation scale with the acoustic beam size is crucial for quantitative ultrasonic characterization of fractal-based pore distribution homogeneity in heterogeneous medium. And the observation scale should be equal to or larger than acoustic beam size, which is ≥ 2 mm, under the testing conditions in this research.