On the selection of distance functions and signal processing techniques for guided wave-based damage identification through a likelihood-free Bayesian framework

Guided wave (GW)-based structural health monitoring (SHM) has been widely used for damage detection in mechanical, civil and aerospace structures. Bayesian method has been integrated with GW-based approaches to enhance the reliability of defect identification and quantify associated uncertainties. Recently, Approximate Bayesian computation (ABC) has attracted increasing attention as a more general and straightforward alternative in Bayesian damage detection frameworks. ABC performs Bayesian inference through a defined distance function to directly assess the similarity between simulated and measured GW signals, eliminating the need to assume an explicit likelihood function to represent the unknown uncertainty distributions inherent in the data generation process. While extensive studies have been conducted to refine ABC sampling algorithms to improve computational efficacy and effectiveness, the effects of different distance functions and signal processing techniques of GW on the performance of ABC have not been reported. This study proposes an advanced ABC framework for damage identification using GW signals. An advanced ABC algorithm based on nested sampling (ABC-NS) is employed to enhance sampling efficiency. The Spectral finite element (SFE) method for numerical GW simulation is utilised to reduce the computational demand in Bayesian inference. A comprehensive performance assessment of the proposed ABC framework is conducted using experimentally measured GW signals from beam-like structures. The focus is directed to the effects of different combinations of signal processing techniques and distance functions on the damage identification results, convergence efficiency, and the degrees of quantified uncertainties. Based on the results, the damage identification accuracy along with the ability of uncertainty quantification are illustrated using the proposed ABC framework. Recommendations are also provided for the selection of the distance functions and signal processing techniques. Finally, the findings of this research offer insights into further development and improvement of likelihood-free Bayesian framework for the applications in GW based SHM.