Statistics of Mooring-Line Tension in Random Waves
Authors: Shaw P-K. 
Published: October 2008

ABSTRACT
Dynamics and fatigue analysis have been used quite frequently to evaluate mooring systems for permanent applications. In a conventional frequency domain approach, the distribution of tension amplitudes is obtained from the spectral density function of tension variation assuming, that the amplitudes are governed by the Rayleigh distribution. The expected fatigue damage may then be calculated from the tension amplitude distribution and the effective number of cycles. This procedure may be applied only in low sea states.
A modified discrete wave approach for deriving the Probability distribution of tension amplitudes is presented here. The expected fatigue damage is obtained from the higher moments of the tension amplitude. This procedure was used to model the behavior of an example mooring system. It is shown to better describe the tension amplitude distribution in higher sea states and provides an upper bound to the expected fatigue damage.

INTRODUCTION
A mooring line is one of the most critical structural components of a moored floating drilling or production system. For long term mooring applications, it, is necessary to evaluate the fatigue life of the mooring line in random seas. In general, frequency and time domain methods both are used to estimate fatigue damage incurred by mooring lines. The frequency domain method is restricted to linear system behavior and the cumbersome time domain method is impractical for most applications. A hybrid time-frequency domain fatigue analysis method has been proposed to include the nonlinear response of deepwater platforms, Reference [1]. This method utilizes a pseudo transfer function for given sea states and is also adopted for mooring applications, [2]. The fatigue damage estimate is still based on the spectral density of the response.
In this paper, a procedure similar to the recently published 'discrete wave approach, Reference [3], 'is proposed to derive the statistical properties of mooring line tension response. From these statistical properties, the fatigue damage can be calculated directly using a linear damage-accumulation law. The approach is shown to better describe the mooring line tension response under random wave excitations which is highly nonlinear, see [4], [5], and [6]. In such cases, the conventional frequency domain approach combined with the assumption that the response is a closely narrow banded random process can be non-conservative in estimating the, fatigue damage.
The present approach is based on a statistical description of wave height and period for statistically stationary sea conditions. Sea surface elevation and the tension variation in the mooring line are both considered to be stationary random processes. The probability distribution function and the higher moments of the tension amplitude are derived from a direct transformation of the joint probability density function of the wave periods and amplitudes. The proposed approach was used to simulate the mooring line tension statistics obtained in a model test and to compare with the conventional frequency domain method.