As the oil industry moves into deeper water in the search for additional supplies of oil and gas, new technology is emerging at a rapid peace for the development of new concepts for offshore platforms. The size of conventional fixed leg platforms is approaching the economic limit due to the very large amount of steel required and limitations imposed by fabrication and installation methods.

Several concepts have been proposed for enhancing the water depth capability of platforms, specifically Tension Leg Platforms (TLP), guyed and articulated tower platforms.

The TLPs are floating structures whose mooring system is constituted by vertical tethers. This cherecteristic makes the structure very rigid in the vertical direction and very flexible in the horizontal plane. Both these features result particularly attractive. The vertical rigidity helps to tie in wells for production, while, the horizontal compliance makes the platform insensitive to the primary effect of waves. However, it is well known that the second-order, slowly varying drift forces at low frequency, caused by the cross-modulation between different harmonic components of the waves, may result in the low frequency resonant oscillation of TLPs. On the other hand, since the harmonic content of the wind action in concentrated at low frequency, in this kind of structures it may produce significant dynamic effects.

The mechanics of such structures is deeply nonlinear because the large displacement and the nonlinear interaction between the structure and fluid motion. The dynamic response of nonlinear systems with random excitation is usually studied in the time domain by means of simulation tools. This approach, conceptually straightforward, has the drawback of being extremely time-consuming, in particular if used for the study of the extreme value of the response. As an alternative, in the last decade, some frequency-domain-based techniques were developed, mainly in the field of the offshore engineering (Donley & Spanos 1990, Tognarelli et al. 1997). These are based on the Volterra series expansion in which the actual nonlinear system is replaced by an assemblage of parallel systems with integer order i.e. linear, quadratic, cubic, etc. Such systems are defined by suitable multi-dimensional kernels (one-dimensional for the linear system, two-dimensional for the quadratic, etc).

Expressions for the kernels can be readily obtained if the nonlinearity has a polynomial form. If it is not the case, an approximation is introduced. At the present state of the art, a third-order polynomial is believed to be sufficient for representing a wide class of nonlinear systems. For the choice of the coefficients in the polynomial approximation, two specific techniques have been proposed: the Mean Square Error Minimization (MSEM) and the Moment Based Hermite Transformation (MBHT). With the MSEM technique, the coefficients are selected in such a way to minimize the mean square of the error. In the MBHT technique the nonlinearity is expanded in a series of Hermite polynomials and the coefficients are selected to match the first four cumulants of the actual nonlinear expression. The latter approach is particularly efficient thanks to the orthogonality of the Hermite polynomials. This has resulted in a more effective procedure for many applications in offshore engineering.

These techniques have been widely applied for single-degree-of-freedom systems, while, for multi-degree-of-freedom systems, only some examples related to particular applications have been presented (Li and Kareem 1993, Benfratello et al. 1998). This aspect is presently subject of study. Some preliminary results are presented in (Carassale & Kareem 2001).