STOR Colloquium: Vadim Belenky (David Taylor Model Basin-NSWC/CD))

Challenges of Statistics of Large Roll Motions of a Ship in Waves

This presentation reviews some problems and solutions related to the statistics of large amplitude roll motions and capsizing of a ship in irregular (random) waves.

Roll motion of a ship in irregular waves is described by a system of integro‐differential equations and can be characterized by significant nonlinearity. The probabilistic properties of roll response are quite complex; its statistical characteristics cannot be estimated based on a single record of practical length (this is known as “practical non‐ergodicity”). This process is non‐Gaussian and there is a significant dependence between the process and its first derivative.

The reasonable estimation of the probability of large roll angles or capsizing represents a significant challenge. Advanced numerical simulations and/or model experiments are the only methods to obtain reliable information on roll motions. Large roll angles are too rare and the sample volume is too small to directly estimate the probability. Therefore, extrapolation is the only practical way to conduct the analysis.

One of the most promising methods of extrapolation is the split‐time method. The split‐time method is capable of estimating the probability of large roll angles, including capsize. The idea is to separate a difficult problem into two related problems that are individually more manageable to solve. The first problem is an upcrossing of a specified intermediate level (typically associated with a physical threshold). This level may be also too high to get sufficient sample volume for direct counting of upcrossings. A Peak‐over‐Threshold method is applied to estimate the upcrossing rate.

The second problem is in finding critical conditions at the instant of upcrossing that will lead to a given large roll angle or capsizing. This problem can be formulated as an estimation of a distribution of a dependent process at the instant of upcrossing. The derivation of a theoretical solution and a practical approximate method is considered in the presentation.

Refreshments will be served at 3:30pm in the 3rd floor lounge of Hanes Hall