# Dynamics and Extreme Value Problems for Moored Floating Platforms

[Doktorsavhandling]

This research deals with the dynamic response analyses and extreme value problems of moored floating platforms. It can be divided into three major subjects: first, the analysis of single cables and cable induced mooring damping; second, the dynamic analysis of the moored platforms, with special emphasis on the damping mechanisms and generation of the low-frequency excitation force time series; and third, the extreme wave-frequency responses and the combination of the low-frequency and wave-frequency extreme responses.

The catenary equation or shooting method can be used to obtain an initial estimation of the mooring cable configuration in calm water, after which non-linear static analysis is performed to find the final equilibrium position considering cable weight, current force and seabed friction. Around this equilibrium configuration, either a non-linear time-domain step-by-step integration or a linearized frequency domain analysis can be carried out to determine the response of the cable to various excitations. For the frequency-domain analysis, direct integration and statistic linearization methods are implemented. Example calculations show that the linearized frequency-domain solution and non-linear time-domain solution compare well with each other as well as with model tests and results obtained by others. We improve the quality and extend the applications of Huse's original quasi-static approach of estimating mooring-cable induced damping. By doing so, we could use the quasi-static approach to obtain an estimation of the mooring-cable induced damping that is comparable to the more time-consuming and complex time-domain or frequency-domain approaches.

The dynamic response of moored floating platforms to wave-frequency and low-frequency wave excitations is described. Formulae for low-frequency excitations are presented in both the time-domain and the frequency-domain. Four damping mechanisms for moored platforms are reviewed, with emphasis on mooring-cable induced damping, wave-drift damping and viscous damping, which are important for low-frequency response. The commonly used methods of generating wave-frequency and low-frequency excitation time series are discussed, and a one-dimensional convolution approach is proposed. In this approach, a random signal is passed through a filter, the filter coefficients are determined from the low-frequency excitation spectrum and the random signal follows the theoretical probability density function of low-frequency excitations.

The usual way of estimating the extreme mooring cable tensions is to run many time-domain simulations, which is rather time-consuming. Here however, only one or a few simulations plus the extreme value theory are needed to predict the extreme mooring cable tension. The order statistic theory, the generalised extreme value theory and the peaks-over-threshold methods are applied. A new approach is proposed to estimate the correlation coefficient between the low-frequency and wave-frequency extreme responses. This coefficient can then be used when we estimate the total combined platform motion or mooring cable tension.

**Nyckelord: **mooring cable, floating platform, low-frequency, wave-frequency, convolution, extreme value, time-domain, frequency-domain, quasi-static

Denna post skapades 2006-09-19. Senast ändrad 2013-09-25.

CPL Pubid: 1244