Separation of amplitude and frequency modulations in Vibro-Acoustic Modulation Nondestructive Testing Method

The Vibro-Acoustic Modulation (VAM) method utilizes nonlinear interaction of a high frequency ultrasonic wave (carrier signal) with frequency ω and a low frequency modulating vibration with frequency Ω << ω, in the presence of various flaws such as fatigue and stress-corrosion cracks, disbonds, etc. Most of the reported VAM studies correlate flaw presence and growth with the increase in the Modulation Index (MI) defined in the spectral domain as the ratio of the side-band spectral components at frequencies ω±Ω to the amplitude of the carrier. This approach, however, does not differentiate between amplitude, AM, or frequency, FM, modulations contributing to the MI. It has been assumed that the prevailing modulation is AM due to contact-type nonlinear mechanisms. However, there could be other mechanisms leading to phase/frequency modulation. The present study aims to develop an algorithm of AM/FM separation specifically for the VAM method. It is shown that the commonly used Hilbert Transform (HT) separation may not work for a typical VAM scenario. The developed In-phase/Quadrature Homodyne Separation algorithm addresses HT shortcomings. The algorithm has been tested both numerically and experimentally (for fatigue crack evolution) showing FM dominance at initial micro-crack growth stages and transition to AM dominance during macro-crack formation.The Vibro-Acoustic Modulation (VAM) method utilizes nonlinear interaction of a high frequency ultrasonic wave (carrier signal) with frequency ω and a low frequency modulating vibration with frequency Ω << ω, in the presence of various flaws such as fatigue and stress-corrosion cracks, disbonds, etc. Most of the reported VAM studies correlate flaw presence and growth with the increase in the Modulation Index (MI) defined in the spectral domain as the ratio of the side-band spectral components at frequencies ω±Ω to the amplitude of the carrier. This approach, however, does not differentiate between amplitude, AM, or frequency, FM, modulations contributing to the MI. It has been assumed that the prevailing modulation is AM due to contact-type nonlinear mechanisms. However, there could be other mechanisms leading to phase/frequency modulation. The present study aims to develop an algorithm of AM/FM separation specifically for the VAM method. It is shown that the commonly used Hilbert Transform (HT) separation...