SBFEM and Bayesian inference for efficient multiple flaw detection in structures

Abstract

Bayesian inference is a powerful technique for damage/flaw detection in critical structures. This paper explores the application of Bayesian inference to identify the flaws (voids/inclusions) and its parameters, assuming no information about the flaws is known a priori. Multiple flaws are represented by a parameter vector that contains the locations and the geometric information. In the inverse problem framework, the Scaled Boundary Finite Element Method (SBFEM) with quadtree decomposition is used to solve the forward problem. The flaw parameters are statistically quantified using the Bayesian inference. The likelihood function and prior information update the joint distribution of the number of flaws and their corresponding flaw parameters. The sampling to estimate the posterior distribution of the flaw parameters is based on the trans-dimensional Reversible Jump Markov Chain Monte Carlo (RJMCMC). Also, the impact of additive Gaussian noise on the observed data is investigated. Numerical examples include identifying multiple voids of different shapes such as circle and ellipse and identifying voids and inclusions, using the proposed approach with input sensor data at different noise levels.