Tension leg platform system

Model description: 

The present study of tension leg platform is the first commercial application of a revolutionary design of offshore production platform developed by well-known oil company. Intended for oil and gas production in water depths beyond the reach of traditional fixed structures, the tension leg platform was designed as a rectangular shaped floating platform which was connected to the ocean floor by 16 vertical steel tethers or legs, four per corner. The legs were kept in tension so that vertical movement was suppressed, while limited horizontal movement may occur.

The estimation model is:

$$\begin{align*} y(k) &= 0.590y(k − 3)+1.0598y(k − 1) − 1.0931y(k − 2) + 121.13u(k − 1)u(k− 1)u(k − 9) \\ &− 116.54u(k − 6)u(k − 6)u(k− 6) − 19.797u(k − 4)u(k − 8)u(k − 8) \\ &+ 214.04u(k − 5)u(k − 9) − 34.877u(k− 1)u(k − 1)u(k − 1) − 3.7983u(k − 1)u(k− 2)u(k − 7) \\ &− 25.04u(k − 4)u(k − 8)u(k− 11) + 165.93u(k − 2)u(k − 3)u(k − 4) \\ &− 173.85u(k − 6)u(k − 7) − 69.693u(k− 4)u(k − 12) + 203.12u(k − 5)u(k − 6)u(k − 6) \\ &+ 727.86u(k − 2)u(k − 3)u(k − 5) − 11.107u(k− 3)u(k − 10)u(k − 11) \\ &+ 11.506u(k − 6)u(k− 6)u(k − 12) − 68.607u(k − 2)u(k − 4)u(k− 6) \\ &− 366.75u(k − 3)u(k − 5)u(k − 6)− 25.696u(k − 4)u(k − 8)u(k − 12) \\ &+ 137.86u(k − 1)u(k − 2)u(k − 5)− 142.24u(k − 2)u(k − 2)u(k − 9) \\ &+ 101.44u(k− 1)u(k − 6)u(k − 9) − 9.0283u(k − 3)u(k− 3)u(k − 12) \\ &− 168.30u(k − 2)u(k − 5)u(k − 6)+ 30.295u(k − 5)u(k − 6)u(k − 8) \\ &− 0.158u(k− 1)u(k − 2)u(k − 2) − 433.21u(k − 2)u(k− 2)u(k − 4) \\ &+ 39.88u(k − 3)u(k − 8)u(k − 11)− 162.26u(k − 1)u(k − 4)u(k − 11) \\ &− 212.08u(k− 1)u(k − 1)u(k − 5) − 438.7u(k − 3)u(k− 3)u(k − 5) \\ &+ 162.15u(k − 2)u(k − 4)u(k − 11)− 3.607u(k − 4)u(k − 4)u(k − 11) \\ &+ 13.262u(k− 6)u(k − 9)u(k − 9)+448.4u(k − 3)u(k − 4)u(k− 6) \\ &− 46.475u(k − 4)u(k − 4)u(k − 9) + 119.95u(k − 1)u(k − 1)u(k − 2) + noise \:terms. \end{align*}$$

Here, the input is the wave, and the output is the pitch. Sample rate is 2.2473 Hz

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Publication details: 

TitleNon-linear pitch motion identification and interpretation of a tension leg platform
Publication TypeJournal Article
Year of Publication2004
AuthorsLiu, Jui-Jung, Huang Yun-Fu, and Lin Hung-Wei
JournalJournal of Marine Science and Technology
Volume12
Issue4
Start Page309
Pagination309-318
Date Published01/2004
ISSN0948-4280
AbstractThe present study is concerned with the identification of the non-linear wave force effects known as 'ringing' on an offshore structure. Ringing is a highly non-linear behaviour in which the motion resonances are outside the region of dominating wave energy. The purpose of this paper is to provide a better prediction of the higher frequency responses of wave forces on the cylinder and to interpret the non-linear effects of 'ringing' using the NARMAX method and the higher order frequency response functions.
URLhttp://jmst.ntou.edu.tw/marine/12-4/309-318.pdf