Extreme and Fatigue Profiles for Kuroshio Current Using Inverse Reliability and Proper Orthogonal Decomposition Techniques
Authors: Kyo Masanori , Yamazaki Yasuyuki , Agarwal Puneet , Mcneill Scot , Aoike Kan , Miyazaki Eigo , Saruhashi Tomokazu , Sawada Ikuo 
Published: May 2013

Abstract
Kuroshio is a major global current that flows near the east coasts of Taiwan and Japan. Kuroshio is a relatively strong current with typical speeds of 3 to 5 knots at the water surface. It is important to properly understand extreme current profiles of these currents for any drilling activity since the response of deepwater risers is known to be sensitive to the shape of the current profile. This paper presents the derivation of profiles for extreme and fatigue analyses for Kuroshio currents at a site in Nankai Trough, Japan; water depth is almost 2000 m. About 6000 currents profiles measured over six months in 2010 by JAMSTEC are used. The inverse first-order reliability method (inverse FORM) and proper orthogonal decomposition (POD) technique are employed. While such methodology is well established, its use for this site posed several challenges. Firstly, the first seven modes, and not just the first two modes which is typical, needed to be included for accuracy. Second, to preserve the directionality in extreme currents, the inverse FORM problem for the two orthogonal components of the current velocity was simultaneously solved, so that extreme profiles for the two planar directions are obtained. A single extreme N-year profile is often sought in analysis, which is also derived from the set of N-year profiles that result from inverse FORM by selecting the profile which maximizes an assumed response function. The discussion on extreme profiles is intentionally kept brief in this paper and the main focus of this paper on the scatter diagram of current profiles for the fatigue analysis of risers. A scatter diagram of POD coordinates and associated profiles is developed by binning the data for first three POD coordinates, since it was found that the measured current speed magnitude process at this site can be accurately expressed using first three POD modes and not just the first two modes which is typically the for most sites. Additionally, improved accuracy of fatigue profiles was achieved by binning the dynamic part of the current speed magnitude process and using the mean profile from the sample. This procedure results in a different profile for each bin, and an occurrence probability associated with each such profile. This scatter diagram consisting of 591 bins is then used for estimating the cumulative fatigue life of a drilling riser for the four month duration when currents were measured. The cumulative fatigue life of the same riser is also estimated by using all (about 6000) profiles from the measured data. It is shown that the fatigue lives at all location on the riser from the two methods are almost exactly same, which establishes the accuracy of the scatter diagram derived using the POD modes. In summary, this paper presents extreme and fatigue current profiles for a region on which little literature exists, and introduces an improved methodology to derive such profiles from measured data.

Introduction
Japan Agency for Marine Earth Science and Technology (JAMSTEC) performs scientific drilling off the coast of Japan using the drillship Chikyu. One of the research activities of Chikyu is the Nankai Trough Seismogenic Zone Experiment (NanTroSEIZE) whose objective is to drill, sample, and instrument the earthquake-causing or the seismogenic portion of Earth's crust (Inoue et. al., 2010). Nankai Trough (NT) is a subduction zone located south of Japan's island of Honshu. More details about JAMSTEC's activities may be found in (JAMSTEC, 2012). Water depth in Nankai Trough is close to 2000 m. One of the major environmental forces on the drilling riser comes from the Kuroshio current that flows through this site with relatively high speeds. Such strong currents can cause fatigue damage of the drilling riser due to vortex-induced-vibrations.