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

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.