In this paper a bayesian framework is used for updating the probability distributions of the parameters of a fatigue model and of crack size in tubular joints using information from inspection reports of fixed offshore structures. For crack detection, the uncertainties are taken into account by means of probability-of-detection (POD) curves. According to the bayesian procedure, if during an inspection no crack is detected, the updated (posterior) distributions depend on the prior ones at time of such inspection and on the POD. On the other hand, if during an inspection a crack is detected and measured, the corresponding predicted crack depth at that time is estimated given values of parameters of a selected fatigue model and of the initial crack depth. Then, a sample value of the model and sizing error associated with the inspection performed, defined as the logarithmic difference between the measured and the predicted crack size, is calculated. Such error is considered to be a normally distributed random variable with known mean and uncertain variance. The distribution of the error variance is taken as a conjugate one for samples of normally distributed variables with known mean and uncertain variance. Based on these assumptions, an analytical expression is obtained for the updated (posterior) distributions of the parameters of the fatigue model and of crack size. It is shown that the updated distributions depend on POD and on the prior and updated parameters of the error variance distribution. Finally, the bayesian method proposed here is illustrated taking as a fatigue model the Paris-Erdogan relation, which estimates crack growth based on linear elastic fracture mechanics. Joint failure is considered to occur when the crack depth reaches the thickness of the element where the crack propagates. The evolution of reliability with time is assessed.
- Ocean, Offshore, and Arctic Engineering Division
Analytical Models for the Probability Distributions of Fatigue Parameters and Crack Size of Offshore Structures Based on Bayesian Updating
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Heredia-Zavoni, E, & Montes-Iturrizaga, R. "Analytical Models for the Probability Distributions of Fatigue Parameters and Crack Size of Offshore Structures Based on Bayesian Updating." Proceedings of the ASME 2002 21st International Conference on Offshore Mechanics and Arctic Engineering. 21st International Conference on Offshore Mechanics and Arctic Engineering, Volume 2. Oslo, Norway. June 23–28, 2002. pp. 121-127. ASME. https://doi.org/10.1115/OMAE2002-28111
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