Flaw detection in plates using Bayesian inference

This paper presents a statistical framework for identifying circular flaws in structures using natural frequency data and Bayesian inference, explicitly addressing uncertainties arising from modeling errors and measurement noise. In this approach, the circular flaw is characterized by parameters such as the center coordinates and radius. The natural frequencies of the structure, measured under known boundary conditions, serve as the input data for the identification process. The smoothed finite element method (SFEM) forward model predicts the natural frequency shifts due to the presence of flaws and is integrated into the analysis. By combining observed frequency data with prior knowledge, Bayes’ theorem is employed to refine the probability distributions of the flaw parameters. The Markov chain Monte Carlo (MCMC) algorithm is utilized to sample from the posterior distributions of the parameters, ensuring robust uncertainty quantification. A numerical case study validates the proposed method, highlighting its accuracy and effectiveness in detecting and characterizing circular flaws.