Imprecise probabilistic subset simulation for rigorous bounding of the failure probability
Über dieses Buch
One of the most challenging tasks in reliability engineering, namely the estimation of small failure probabilities can be efficiently performed through subset simulation (SuS). Given a performance function and a critical level, which defines failure, SuS uses Markov chain Monte Carlo sampling, to gradually explore the input domain of the performance function with a nested sequence of larger domains, until samples over the critical threshold and into the failure domain are generated. P-SuS, proposed by (Hristov and DiazDelaO, 2023), generalises the original subset simulation algorithm by adapting it to work with probabilistic numerical models (PNM). P-SuS was shown to be able to discover and populate the failure domain, only based on partially converged simulations. However, the probabilistic description of its estimator for the failure probability is not calibrated, in that it does not cover the failure probability for the deterministic model, estimated by SuS or does so only at very small numerical uncertainties and with inappropriately large bounds. This problem is strongly influenced by the assumptions of independence of the intermediate failure events and the independence of the probabilities of the levels. The result of these assumptions has a knock-on simplification effect on how the final estimator is computed. The work described in this paper relaxes these assumptions by reformulating parts of the P-SuS algorithm through the use of dependence bounds analysis to compute uncertain number convolutions without assuming a particular dependence. We show that the resulting probability-box estimator more appropriately accounts for the uncertainty present in the output of the PNM.
