Theoretical Model for SPC

This manuscript proposes a theoretical model of memoryless polynomial nonlinearity for SPC-based ultrasonic NDE. The results show that only linear effects produce spectral peaks at low nonlinearity levels, and higher harmonics and mixed modes also contribute to the number of observable spectral peaks at higher nonlinearity levels. However, the total number of peaks does not increase with nonlinearity; it can even decrease when the spectrum transitions from a linearly dominated leakage spectrum to a nonlinearly dominated spectrum. The number of nonlinear spectral peaks depends only on the order of the nonlinearity, not its strength, which is what the SPC technique attempts to monitor by applying upper and lower thresholds for counting. The results also suggest that high-pass filtering of the received signal more effectively increases both the selectivity and sensitivity of ultrasonic NDE to changes in nonlinearity than previously proposed SPC-based evaluation techniques.