Real-time sinusoidal parameter estimation for damage growth monitoring during ultrasonic very high cycle fatigue tests

Ultrasonic fatigue tests (UFT) are used to study the fatigue life behavior of metallic components undergoing a very high number of cycles (typically ≥ 107 − 109 cycles) under relatively low mechanical loads. By soliciting fatigue specimens at 20 kHz, ultrasonic fatigue machines are indispensable for monitoring damage growth and fatigue failures in a reasonable amount of time. As fatigue damage accumulates in the specimen, the specimen’s free-end exhibits a nonlinear dynamic response. The resulting quasi-stationary, harmonic signals have sinusoidal parameters (frequency and amplitude) which are slowly time-varying with respect to the excita-tion frequency. The discrete Fourier transform (DFT) is typically used to extract these evolving sinusoidal parameters from a window of finite data of the vibration signal. Alternative spectral estimation methods, specifically line spectra estimators (LSEs), exploit a priori information of the signal via their modeling basis and overcome limitations seen by the DFT. Many LSEs are known to have state-of-the-art results when benchmarked on purely stationary signals with unit amplitudes. However, their performances are unknown in the context of slowly time-varying signals typical of UFT, leading to a widespread use of the DFT. Thus, this paper benchmarks classical and modern LSEs against specific synthetic signals which arise in UFTs. Adequate algorithms are then recommended and made publicly available to process experimental data coming from ultrasonic fatigue tests depending on performance metrics and experimental restraints