A Bayesian Model for the Probability Distribution of Fatigue Damage in Tubular Joints

Abstract

A Bayesian framework is used for updating the probability distributions of the parameters of a fracture mechanics model and of crack size in tubular joints using information from inspection reports of fixed offshore structures. An error model, defined as the logarithmic difference between measured crack size during inspection and crack size predicted by the fracture mechanics model, is assumed to have a normal distribution with known mean and uncertain variance. The distribution of the error variance is modeled by a conjugate distribution for samples of normal variables with known mean and uncertain variance. Based on these assumptions, an analytical model is obtained using a Bayesian approach for the updated distributions of the parameters of the fracture mechanics model and of crack size based. The capabilities of the model are illustrated by means of examples using the Paris-Erdogan formulation for crack growth. The examples illustrate the effects of inspection times, measured crack size, and the distribution of stress ranges on the updated density functions of crack size, time varying reliability and expected cost of failure.