Probabilistic Model Updating for Sizing of Hole-Edge Crack Using Fiber Bragg Grating Sensors and the High-Order Extended Finite Element Method

Abstract

This paper presents a novel framework for probabilistic crack size quantification using fiber Bragg grating (FBG) sensors. The key idea is to use a high-order extended finite element method (XFEM) together with a transfer (T)-matrix method to analyze the reflection intensity spectra of FBG sensors, for various crack sizes. Compared with the standard FEM, the XFEM offers two superior capabilities: (i) a more accurate representation of fields in the vicinity of the crack tip singularity and (ii) alleviation of the need for costly re-meshing as the crack size changes. Apart from the classical four-term asymptotic enrichment functions in XFEM, we also propose to incorporate higher-order functions, aiming to further improve the accuracy of strain fields upon which the reflection intensity spectra are based. The wavelength of the reflection intensity spectra is extracted as a damage sensitive quantity, and a baseline model with five parameters is established to quantify its correlation with the crack size. In order to test the feasibility of the predictive model, we design FBG sensor-based experiments to detect fatigue crack growth in structures. Furthermore, a Bayesian method is proposed to update the parameters of the baseline model using only a few available experimental data points (wavelength versus crack size) measured by one of the FBG sensors and an optical microscope, respectively. Given the remaining data points of wavelengths, even measured by FBG sensors at different positions, the updated model is shown to give crack size predictions that match well with the experimental observations.

Multiple crack detection in 3D using a stable XFEM and global optimization

“…Availability of monitoring data drives the inverse problem formulation, which aims to minimize the difference between the model prediction and the structural response data acquired via monitoring. This may often be solved by means of optimization methods based on least squares or based on Bayesian analysis [ 12 , 13 ].…”

A Fatigue Crack Size Evaluation Method Based on Lamb Wave Simulation and Limited Experimental Data

“…Structural health monitoring (SHM) is an integrated approach combining data acquisition and interpretation. It provides a means for damage status assessment and remaining useful life prediction [ 1 , 2 , 3 , 4 ]. In recent years, guided ultrasonic waves have gained widespread applications in the field of SHM as a method of non-destructive evaluations (NDE) due to its ability of traveling large distances in structures with little energy loss [ 5 , 6 , 7 , 8 , 9 ].…”

Material‐dependent crack‐tip enrichment functions in XFEM for modeling interfacial cracks in bimaterials

“…While retaining the original advantages of the standard FEM, the XFEM provides 2 superior capabilities that reproduce better the singular stress state at the crack tip and alleviate the need for conforming meshes and adaptive remeshing for arbitrary crack propagation. Several studies have demonstrated the efficiency of XFEM when applied to fracture mechanics problems and state‐of‐the‐art reviews of the XFEM can be found in Belytschko and Sukumar et al…”

“…28,29 While retaining the original advantages of the standard FEM, the XFEM provides 2 superior capabilities that reproduce better the singular stress state at the crack tip and alleviate the need for conforming meshes and adaptive remeshing for arbitrary crack propagation. Several studies [30][31][32][33][34][35][36][37][38] have demonstrated the efficiency of XFEM when applied to fracture mechanics problems and state-of-the-art reviews of the XFEM can be found in Belytschko 39 and Sukumar et al 40 While the original XFEM was designed for crack analysis in homogeneous isotropic materials, significant efforts have been made in the past to extend its application to bimaterial interface cracks. The following review of XFEM methods for bimaterials is by no means exhaustive but provides some important milestones.…”