Abstract
Majority of pipeline infrastructure are old and susceptible to possible catastrophic failures due to fatigue. Timely maintenance is the key to keep pipeline in serviceable and safe condition. This paper proposed a Bayesian inference methodology based on the observed crack growth measurements and cycle data that predicts the probability density of failure after initially estimating the equivalent initial flaw size (EIFS). The model was first developed based on one-dimensional crack growth problem in plate with edge crack. Then the model was expanded to two-dimensional crack growth problem in pipe wall. Stress intensity factors (SIF) at the crack tip in pipe model were calculated using finite element (FE) analysis for different crack lengths and depths. Polynomial function and Gaussian process were used to develop surrogate models of SIF. The analysis demonstrated that the proposed Bayesian inference method with hyperparameters generated accurate inferred results for probability density function (PDF) of both EIFS and the number of cycles to failure.
Highlights
Fatigue cracking is an inherently stochastic problem affected by various sources of variability and uncertainty
In this equation where we have introduced a prior probability for equivalent initial flaw size (EIFS), p(θ| α), which is conditioned on α
In this paper a Bayesian inference methodology was implemented to accurately estimate the time when the structure has the most probability of failure based on observed crack growth measurements and cycle data which was generated synthetically
Summary
Fatigue cracking is an inherently stochastic problem affected by various sources of variability and uncertainty. After selecting the appropriate step size for both standard deviation range and mean range a θ distribution can be generated (bounds of θ (EIFS) was chosen from zero to close to maximum possible crack depth or plate thickness, b) . For each synthetic data point generated using the algorithm that was introduced earlier, the number of cycles to the failure point corresponding to the sampled EIFS and failure crack depth is estimated.
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