Time domain extraction method of ultrasonic nonlinear coefficient

Abstract

During the extraction of the fundamental and second harmonic components, factors such as noise, spectral leakage, and the picket fence effect can reduce the accuracy of the ultrasonic nonlinearity coefficient β calculated using the Fast Fourier Transform (FFT) method. To address this issue, two time-domain extraction methods, Supplementary Zero Least Squares (SZ-LS) and Reduction of Noise Preprocessing Prony (RN-Prony) are proposed. The SZ-LS method employs supplementary zero on the truncated signal, ensuring that the number of data points satisfies an integer multiple relationship between the frequency resolution and the fundamental frequency, thereby reducing the impact of picket fence effect on the accuracy of the least squares calculation. The RN-Prony method utilizes The Fast Empirical Wavelet Transform (FEWT) to reduce noise in the signal, followed by Prony's method to calculate the amplitudes of the fundamental and second harmonic components. Simulation studies demonstrate that SZ-LS offers higher accuracy than FFT, but its results still fail to accurately obtain β within the error limits when the number of signal cycles is large. RN-Prony effectively reduces the influence of noise, improving the SNR of the processed signal by average of 54 % compared to the original signal, and achieves higher accuracy than the other two methods. The SZ-LS, RN-Prony and FFT methods are then applied to a set of martensitic stainless steel fatigue specimens and 6061-T6 aluminum alloy tensile specimens where the changes in the ultrasonic nonlinearity coefficient β with the degree of failure are determined. The β parameters processed with the RN-Prony method produce trends that make better physical sense than those processed with the SZ-LS method and FFT.