Bayesian reasoning aimed at a prediction of failure patterns of fire induced pressure vessel explosions

Abstract

The problem of assessing damage due to explosions of cylindrical pressure vessels is considered. The attention is focussed on a prediction of the arrangement of cracks in the vessel wall prior to its explosion. This arrangement of cracks is called the failure pattern. It is seen as essential information for forecasting ejection and projection of fragments generated by an explosion. Thermally induced explosions known as boiling liquid expanding vapour explosions are studied. The problem of prediction of failure patterns is formulated as a problem of estimating probabilities of these patterns. The scarcity of data on occurrences of failure patterns in the past explosion accidents was an incentive to estimate the failure pattern probabilities by means of Bayesian statistics. The main finding of the study is that the failure pattern probabilities can be handled within the Dirichlet-multinomial model and the epistemic uncertainty in these probabilities expressed by Dirichlet prior and posterior distributions. The Bayesian estimation of failure pattern probabilities is viewed as a way allowing to introduce the prediction of vessel fragmentation into the formal probabilistic risk analysis. The so-called minimally informative Dirichlet prior distribution is suggested for the probability estimation as a prior suitable to Bayesian updating with scarce data. It is stated that currently the probabilistic prediction of failure patterns on the basis of past accident data is the only practicable way to assess the potential type of vessel fragmentation. A conventional (deterministic) mechanical and/or metallurgical analysis does not provide reliable models for failure pattern prediction in case of explosions under study.