Pitfalls of data-driven peaks-over-threshold analysis: Perspectives from extreme ship motions

A popular peaks-over-threshold (PoT) method of Extreme Value Theory to quantify the probabilities of rare events is examined here on data generated from a nonlinear random oscillator model, describing a qualitative behavior of rolling of a ship in irregular seas. The restoring force in the oscillator model has a softening shape associated with the ship rolling application, and the response is also made bounded, so as to eliminate the possibility of "capsizing." As a result, the tail of the resulting probability density function of the response undergoes three regimes: the Gaussian core, the heavy tail and the short bounded tail. By considering several scenarios where data are available in one but not another regime, it is shown that the PoT method can produce unsatisfactory results. Some refined methods from Extreme Value Theory, for example, those based on mixture models, are also examined, but without much success. It is thus argued that a data-driven application of the PoT method may fail, if the physical aspects of the system under study are not taken into account.