# Numerical Methods for Stochastic Dynamics of Offshore Systems

### Motivation

Floating offshore systems are generally subject to irregular sea waves, which can be described by sea spectra such as the JONSWAP or the Pierson-Moskowitz spectrum. Due to the stochastic forcing, the responses of the considered systems are stochastic processes as well. Within the framework of stochastic dynamics we are dealing with stochastic equations of motion excited by colored noise. In offshore engineering, the frequency domain approach is usually the method of choice for obtaining solutions when the considered systems are assumed to be linear. However, the analyses of transients and nonlinear systems require time domain methods.

The direct Monte Carlo method is the simplest method for treating stochastic ordinary differential equations in time domain and is widely applied throughout the ocean engineering community. It is well known that the accuracy of the solution obtained with the direct Monte Carlo method scales inversely to the square root of the number of samples, i. e. in general the Monte Carlo method is computationally expensive if a high accuracy is desired.

### Method

We develop numerical methods for computing stochastic responses of offshore systems. An example is the touchdown of a jack-up vessel during offshore wind park installation, for which we developed a method to compute impact forces, link. We have a strong interest in applying the recently developed generalized Polynomial Chaos (gPC) approach to offshore problems. The gPC is a method for solving stochastic differential equations. Numerical examples show a substantial speed-up compared to the direct Monte Carlo method. Although many parts of the scientific computing community have taken great interest in the gPC framework in the recent years, there are not many applications to problems in offshore engineering so far. Our work tries to fill this gap. At GAMM 2015 we reported the application of gPC to a heaving cylinder in random waves, link.

## Contact

Dipl.-Ing. Eugen Solowjow, M.-TecM

Prof. Dr.-Ing. habil. Prof. E.h. Edwin Kreuzer