Small Crack Fatigue Growth and Detection Modeling with Uncertainty and Acoustic Emission Application

In the study of fatigue crack growth and detection modeling, modern prognosis and health management (PHM) typically utilizes damage precursors and signal processing in order to determine structural health. However, modern PHM assessments are also subject to various uncertainties due to the probability of detection (POD) of damage precursors and sensory readings, and due to various measurement errors that have been overlooked. A powerful non-destructive testing (NDT) method to collect data and information for fatigue damage assessment, including crack length measurement is the use of the acoustic emission (AE) signals detected during crack initiation and growth. Specifically, correlating features of the AE signals such as their waveform ring-count and amplitude with crack growth rate forms the basis for fatigue damage assessment. An extension of the traditional applications of AE in fatigue analysis has been performed by using AE features to estimate the crack length recognizing the Gaussian correlation between the actual crack length and a set of predefined crack shaping factors (CSFs). Beside the traditional physics-based empirical models, the Gaussian process regression (GPR) approach is used to model the true crack path and crack length as a function of the proposed CSFs. Considering the POD of the micro-cracks and the AE signals along with associated measurement errors, the properties of the distribution representing the true crack is obtained. Experimental fatigue crack and the corresponding AE signals are then used to make a Bayesian estimation of the parameters of the combined GPR, POD, and measurement error models. The results and examples support the usefulness of the proposed approach.