In the liquefied natural gas (LNG) shipping industry, the phenomenon of
sloshing can lead to the occurrence of very high pressures in the tanks of the
vessel. The issue of modelling or estimating the probability of the
simultaneous occurrence of such extremal pressures is now crucial from the risk
assessment point of view. In this paper, heavy-tail modelling, widely used as a
conservative approach to risk assessment and corresponding to a worst-case risk
analysis, is applied to the study of sloshing. Multivariate heavy-tailed
distributions are considered, with Sloshing pressures investigated by means of
small-scale replica tanks instrumented with d >1 sensors. When attempting to
fit such nonparametric statistical models, one naturally faces computational
issues inherent in the phenomenon of dimensionality. The primary purpose of
this article is to overcome this barrier by introducing a novel methodology.
For d-dimensional heavy-tailed distributions, the structure of extremal
dependence is entirely characterised by the angular measure, a positive measure
on the intersection of a sphere with the positive orthant in Rd. As d
increases, the mutual extremal dependence between variables becomes difficult
to assess. Based on a spectral clustering approach, we show here how a low
dimensional approximation to the angular measure may be found. The
nonparametric method proposed for model sloshing has been successfully applied
to pressure data. The parsimonious representation thus obtained proves to be
very convenient for the simulation of multivariate heavy-tailed distributions,
allowing for the implementation of Monte-Carlo simulation schemes in estimating
the probability of failure. Besides confirming its performance on artificial
data, the methodology has been implemented on a real data set specifically
collected for risk assessment of sloshing in the LNG shipping industry