Higher-Order Spectral Analysis of TLP Tendon-Tension Data
Authors: Powers E.J. , Yi E.J. , Beynet P. , Bhat S. 
Published: October 2008

Abstract
In this paper we consider model basin measurements of random wave excitation of a TLP and the associated tendon tension. The tendon tension power spectrum exhibits a peak at the wave excitation frequency and a smaller, but still significant, peak at the higher vertical plane natural (springing) frequencies. Decomposition of the tendon power spectrum using an orthogonal third-order Volterra-like model indicates that third-order (i.e. cubic) effects are primarily responsible for the peak at the springing frequency.

INTRODUCTION
Tension leg platforms [1] are compliant-type structures with positive buoyancy and are tethered to the ocean floor through tendons under tension. An attractive feature of TLPs lies in the fact that their cost is relatively(compared to fixed structures, for example) insensitive to water depth. The natural periods of motion in the horizontal plane are typically well above characteristic wave periods, while those in the vertical plane are below. Although the horizontal natural period is greater than the characteristic wave period, it is well known that second-order effects enable energy to be extracted from the waves and then down-converted (through quadratic frequency mixing processes [2]) to reappear in low-frequency drift motion [3]. One reason such motion is of interest is because it may result in minimum deck clearance. Vertical plane natural periods typically lie well below the characteristic wave period but, If these natural frequencies are excited (through nonlinear mechanisms, for example), the resulting springing motion [4] takes on significance because of its impact on tendon fatigue. There have been many studies dealing with various aspects of TLP tendons (see, for example, [5]). In this paper we consider an experimental study of the tendon tension of a TLP subjected to random wave excitation. A unique feature of the work reported on herein involves the use of a recently developed third-order orthogonal frequency domain Volterra-like model to model the tendon-tension response to wave excitation. From the point of view of this study, the principal advantage utilizing this state-of-the-art modeling technique lies in the fact that it permits the tendon-tension response power spectrum to be decomposed into its constituent linear, quadratic and cubic components as a function of frequency. Thus, this approach allows one to quantify the relative degree of linearity and nonlinearity (quadratic and cubic) at each frequency in the tendon-tension response. In Secs. 2 and 3 we provide a brief overview of the key ideas underlying frequency-domain Volterra models and the third-order orthogonal Volterra-like model. Respectively, the TLP tendon-tension data utilized in this paper were generated by a model test carried out at the Offshore Technology Research Center Model Basin located at Texas A & M University. Descriptions of the experiment and the data collected are presented in See. 4. Also in Sec. 4 the third-order orthogonal Volterra model is utilized to decompose the tendon response into its constituent linear, quadratic, and cubic components as a function of frequency. We find that cubic effects dominate at the springing frequencies. We conclude the paper in Sec. 5 with brief discussion.