Risk assessment in sloshing: How to deal with multidimensional datasets

In the liquefied natural gas (LNG) shipping industry, the phenomenon of sloshing can lead to the occurrence of high pressures on the tanks walls 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 since the probability of failure of the system depends of the area of the sloshing impact. 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 ℝ^d. 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.