Framework for Small Fatigue Crack Propagation and Detection Joint Modeling Using Gaussian Process Regression

Abstract

Engineers have witnessed much advancement in the study of fatigue crack detection and propagation (CPD) modeling. More recently the use of certain damage precursors such as acoustic emission (AE) signals to assess the integrity of structures has been proposed for application to prognosis and health management of structures. However, due to uncertainties associated with small crack detection of damage precursors as well as crack size measurement errors of the detection technology used, applications of prognosis and health management assessments have been limited. This dissertation defines a new methodology for the assessment of CPD parameters and the minimization of uncertainties including detection and sizing errors associated with a series of known CPD models that use AE as the precursor to fatigue cracking. The first step of the procedure is defining the separate crack propagation and crack detection models that are to be used for the testing of a joint-CPD model. The two propagation models for this study are based on a Gaussian process regression model that correlates crack shaping factors (CSFs) to the propagation of the crack. One of these propagation models includes a particle filtering technique that includes several AE data. The testing of this joint-CPD model is facilitated by the Bayesian inference of the CPD likelihood where the posterior models are extracted and tested for correctness. The CSFs, the CPD data, and the AE signal data used for testing of this methodology come from a series of fatigue tests done on dog-bone Al 7075-T6 specimens. The data is first corrected for measurement error that is present based on the initial crack measurements. Then the data is used to generate the prior CPD models that is needed for the Bayesian inference procedure. With the resulting posterior CPD models, a correlation procedure that estimates the CPD model parameters of validation specimens based on the relationship that exists between the CSFs and the CPD model parameters is performed as well as a model error correction procedure. The result of this correlation provides reasonable estimates for the remaining useful life of a given validation specimen.