A Probabilistic Approach to Small Fatigue Crack Initiation and Sizing Using Acoustic Emission

Abstract

Abstract:One of the major concerns in structural health management (SHM) is the early detection of a growing crack. Using this, future damage due to crack propagation can be mitigated or eliminated by implementing proper repair and maintenance. Acoustic Emission (AE) is a non-destructive testing (NDT) method with potential applications for locating and monitoring fatigue cracks. The research presented in this paper focuses on SHM using AE. A novel AE signal analysis approach was proposed in order to detect crack initiation and assess small crack lengths. Experimental investigation indicated that initiation of a crack could be identified through the statistical analysis of the resulting features of the AE signals. A probabilistic AE-based model for small fatigue crack sizing was developed and the uncertainties of the model were estimated. In addition, a probabilistic model validation approach was implemented to confirm accurate estimation of the results. The outcome of this research can be used to evaluate the integrity of structures under fatigue loading. The proposed approach can also be applied as an approach to manage health and assess prognosis of structures.

A recursive Bayesian approach to small fatigue crack propagation and detection modeling

“…Since crack length a is largely unknown, it is considered the unobserved value in this model. The AE variables cumulative count C and cumulative amplitude A are known, 4 so these constitute the observed values in the model. The mathematical form for this probabilistic CP model is expressed by the posterior PDF…”

“…where a l t h is the smallest crack length that can be detected and a h t h is the largest crack length that can be missed using the NDT technique described in Georgiou. 7 These crack lengths are then fit to a signal response POD function and the number of fatigue cycles, N , 7 is related to the AE intensity defined by Keshtgar 4 as I ( N ) = ( C ( N ) A ( N ) ) / ( A 0 ) , where C ( N ) is the AE signal cumulative count, A ( N ) is the AE amplitude, and I ( N ) is the AE intensity…”

“…In equation (19), σ a represents the standard deviation associated with the error between log forms of the AE intensity I ^ and the true AE intensity I 4,7 written as…”

“…The initial results of using AE for crack initiation and propagation used three AE features as input, but the error in estimating the crack growth averaged at 46%. 4 Using the same data, the GPR propagation model with nine CSFs in form of loading and material properties as input resulted in a much lower error that averaged about 29%. 10 The GPR propagation model has an advantage over most CP models since it has a stricter adherence to the non-linear characteristics of the source data depending on the kernel functions used to train the GPR model.…”

“…Flagship empirical models such as by Paris and Erdogan, 1 Forman et al, 2 and Walker 3 relate crack propagation (CP) to various loading and material properties. These models have made way for propagation models based on non-destructive testing (NDT) indicators such as acoustic emission (AE) 4 and dissipated thermal energy. 5 Similarly, crack detection, or probability of detection (POD) of small cracks, was originally modeled by binomial 6 cumulative density functions (CDFs).…”