Sloshing of liquefied natural gas (LNG) in large transport tankers is an important issue that limits the operational envelope of ships and leads to conservative designs. However, many uncertainties are affecting the accuracy of sloshing predictions; for example, the filling level, the motion of the ship, and the physical properties of the fluid. We are using state-of-the-art Uncertainty Quantification (UQ) methods to assess the effect of such uncertainties on the loads that the cargo containment system (CCS) has to withstand.

In current UQ techniques, smoothness of the quantity of interest (in this caseloads on the CCS) is assumed to arrive at efficient methods – for example, generalized polynomial chaos, or stochastic collocation. In our case, the response can in principle depend in a non-smooth manner on the parameters. An example of a sloshing simulation is shown in the figure below.

With a slight change in initial condition, the response can look significantly different. We therefore propose a novel approach for non-intrusive uncertainty propagation. The method is an adaptive sampling algorithm based on minimum spanning trees combined with a domain decomposition method based on support vector machines. The minimum spanning tree determines new sample locations based on both the probability density of the input parameters and the gradient in the quantity of interest. The support vector machine efficiently decomposes the random space in multiple elements, avoiding the appearance of Gibbs phenomena near discontinuities. On each element, local approximations are constructed by means of least orthogonal interpolation, in order to produce stable interpolation on the unstructured sample set. The resulting minimum spanning tree multi-element method does not require initial knowledge of the behaviour of the quantity of interest and automatically detects whether discontinuities are present. In the figure below, we show the adaptive sampling procedure (left) and the quantity of interest (maximum loading, right), which automatically clusters near high gradients.

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