Analyzing nonlinear behavior of ultrasound wave in phase-space domain

This paper presents phase-space analysis of nonlinear ultrasound in concrete materials subjected to different compression loads. Nonlinearities due to defects and material properties can alter frequency content of transmitted and received ultrasound waveforms. As a result, nonlinear ultrasound waveforms are traditionally analyzed in frequency domain. However, using frequency domain to analyze ultrasound behavior has several shortcomings. Different sources of nonlinearities can make the same change in the frequency domain. This can make the identification of the source of ultrasound nonlinearities impossible. In addition, it is hard to observe and explain complex nonlinearities such as chaotic behavior of ultrasound waveforms in the frequency domain. Analyzing nonlinear ultrasound behavior in phase-space domain allows for a better understanding of ultrasound behavior. Fractal analysis of phase space portrait is used to quantitatively evaluate topography of phase space portrait of ultrasound waveforms. Fractal analysis is a quantitative feature to describe geometry evolution and it can enhance quantitative analysis of phase space portrait. The phase-space along with fractal analysis is proven to be a powerful tool in analyzing ultrasound nonlinearities and determining chaotic behavior.