Fatigue crack growth prediction in nuclear piping using Markov chain Monte Carlo simulation

Abstract

In this paper, we present and demonstrate a methodology to improve probabilistic fatigue crack growth (FCG) predictions by using the concept of Bayesian updating using Markov chain Monte Carlo simulations. The methodology is demonstrated on a cracked pipe undergoing fatigue loading. Initial estimates of the FCG rate are made using the Paris law. The prior probability distributions of the Paris law parameters are taken from the tests on specimen made of the same material as that of pipe. Measured data on crack depth over number of loading cycles are used to update the prior distribution using the Markov chain Monte Carlo. The confidence interval on the predicted FCG rate is also estimated. In actual piping placed in a plant, the measured data can be considered equivalent to the data received from in‐service inspection. It is shown that the proposed methodology improves the fatigue life prediction. The number of observations used for updating is found to leave a significant effect on the accuracy of the updated prediction.

Reliability-Based Inspection Planning of the Ship Structure Exposed to Fatigue Damages

“…The Bayesian theory can be rewritten based on probability distribution functions (PDFs). Hence, in this regard, R and S represent the model parameter and measured parameter, respectively [9]:…”

“…To update the parameter x, it starts from an initial value x1 in a chain and the value xi+1 is produced in a way that is independent of x1, ..., xi-1, xi. This process is as the following [9]:…”

“…According to this method, multiple chains should be created with different starting points. Variances within each chain are compared with the variances between chains [9]. The large difference between these two values indicates a lack of convergence.…”

The analysis of initial probability distribution in Markov Chain model for lifetime estimation

“…These random factors explained the influencing of the uncertainty factors to the fatigue crack growth process, and it contributes to the scattering of the crack size. There is significant number of research works that have focused on fatigue crack growth models: these include models presented in [11][12][13][14][15]. Many of these models rely on the experiment.…”

MCMC‐Based Fatigue Crack Growth Prediction on 2024‐T6 Aluminum Alloy

“…The in-service inspection data can be used as experimental observation, which conjuncts the prior distribution of the model parameters to reduce the uncertainty in the prediction of fatigue crack growth curve for one component [7]. The posterior distribution can be used to make updated estimates of model parameter for the crack growth behavior.…”