Fractal analysis of nonlinear ultrasonic waves in phase-space domain as a quantitative method for damage assessment of concrete structures

Abstract

The present paper applies fractal dimension as a mathematical tool to extract a quantitative geometric feature from nonlinear ultrasonic waves in phase-space domain. The feature is then used for damage assessment of concrete material under different service loads after experiencing extreme compressive loads. For this purpose, concrete samples are loaded in two different scenarios: the first loading part is set to initiate micro cracks and generate macro cracks, while the second loading procedure is set to simulate service loads and change the cracks' boundary conditions. Due to nonlinear ultrasonic waves’ sensitivity to cracks in early stages, nonlinear ultrasound test is performed. In contrast to traditional approaches which analyze nonlinear ultrasound waves in frequency domain, in this paper, nonlinear ultrasonic waves in phase-space domain are studied. Phase-space domain is a powerful mathematical tool that allows researchers to analyze data quantitatively and qualitatively using different signal processing techniques like fractal dimension. For the first time, fractal analysis of nonlinear ultrasound waves in phase-space domain is performed to measure the nonlinearity of the waves due to interactions with loaded-induced cracks in concrete materials. In general, fractal analysis makes it possible to assign dimension for sets that do not have integer dimension. To calculate fractal dimension, the box-counting method, as a pragmatic method, is used. A two-dimensional (2D) and three-dimensional (3D) box-counting method for calculating the fractal dimension of nonlinear ultrasonic waves in phase-space domain are utilized. It is shown that fractal dimension is a powerful signal processing tool for analyzing nonlinear ultrasonic signals in phase-space domain and extracting quantitative damage-sensitive features in presence of service load. In contrast, results of frequency domain analysis show a lack of noticeable trend, especially for large service loads. This observation indicates that features extracted in frequency domain may not be reliably used as damage-sensitive features for evaluating the level of cracking in concrete material under service load.