Prediction of the shape of inline wave force and free surface elevation using First Order Reliability Method (FORM)

In design of substructures for offshore wind turbines, the extreme wave loads which are of interest in Ultimate Limit States are often estimated by choosing extreme events from linear random sea states and replacing them by either stream function wave theory or the NewWave theory of a certain design wave height.

As these wave theories super from limitations such as symmetry around the crest, other methods to estimate the wave loads are needed. In the present paper, the First Order Reliability Method, FORM, is used systematically to estimate the most likely extreme wave shapes. Two parameters of maximum crest height and maximum inline force are used to define the extreme events.

FORM is applied to first and second-order irregular waves in both 2D and 3D. The application is validated against the NewWave model and also the NewForce model, which is introduced as the force equivalent of NewWave theory, that is, the most likely time history of inline force around a force peak of given value.

The results of FORM and NewForce are linearly identical and show only minor deviations at second order. The FORM results are then compared to wave averaged measurements of the same criteria for crest height and peak force value. Relatively good agreement between the FORM results of free surface elevation including the second order effects, and the wave averaged measurements is observed.

However, the inline force time series reproduced using the numerical method are not as consistent with the measurements as the free surface elevation time series. The discrepancies between the FORM results and the measurements is found to be a result of more nonlinearity in the selected events than second order and negligence of the drag forces above still water level in the present analysis.

This paper is one step toward more precise prediction of extreme wave shape and loads. Ultimately such waves can be used in the design process of offshore structures. The approach can be generalized to fully nonlinear models.