Identification of correlated damage parameters under noise and bias using Bayesian inference

This article presents statistical model parameter identification using Bayesian inference when parameters are correlated and observed data have noise and bias. The method is explained using the Paris model that describes crack growth in a plate under mode I loading. It is assumed that the observed data are obtained through structural health monitoring systems, which may have random noise and deterministic bias. It was found that a strong correlation exists (a) between two parameters of the Paris model, and (b) between initially measured crack size and bias. As the level of noise increases, the Bayesian inference was not able to identify the correlated parameters. However, the remaining useful life was predicted accurately because the identification errors in correlated parameters were compensated by each other. It was also found that the Bayesian identification process converges slowly when the level of noise is high.