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Research Papers: Structures and Safety Reliability

Long-Term Extreme Response and Reliability of a Vessel Rolling in Random Beam Seas

[+] Author and Article Information
Wei Chai, Bernt J. Leira

Department of Marine Technology,
Norwegian University of Science and
Technology,
Trondheim 7491, Norway

Arvid Naess

Centre for Ships and Ocean Structures;
Department of Mathematical Sciences,
Norwegian University of Science and
Technology,
Trondheim 7491, Norway

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received June 30, 2016; final manuscript received August 14, 2017; published online September 14, 2017. Assoc. Editor: Wei Qiu.

J. Offshore Mech. Arct. Eng 140(1), 011601 (Sep 14, 2017) (9 pages) Paper No: OMAE-16-1075; doi: 10.1115/1.4037789 History: Received June 30, 2016; Revised August 14, 2017

In this paper, the long-term extreme response of a vessel rolling in random beam seas and the associated reliability evaluation are addressed. The long-term response analysis is based on the upcrossing rates of the roll motion under different sea states. Generally, for nonlinear roll motion in random seas, the high-level roll response is sensitive and closely related to the nonlinear effects associated with the restoring and damping terms. Therefore, assessing the corresponding statistics of the random roll motion with low probability levels is difficult and time-consuming. In this work, the Markov theory is introduced in order to tackle this problem. Specifically, for the dead ship condition, the random roll excitation moment is approximated as a filtered white noise process by applying a second-order linear filter and an efficient four-dimensional (4D) path integration (PI) technique is applied in order to calculate the response statistics. Furthermore, the reliability evaluation is based on the well-known Poisson estimate as well as on the upcrossing rate calculated by the 4D PI method. The long-term analysis and reliability evaluation of the nonlinear roll motion in random seas, which consider the variation of the sea states could be a valuable reference for ship stability research.

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References

Figures

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Fig. 1

GZ curve for the selected ship model

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Fig. 2

Wave energy spectra for two different sea states and the roll excitation moment per unit wave height |Froll(ω)|

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Fig. 3

Mean upcrossing rates obtained by the 4D PI method and MCS for the sea state with Hs = 3.5 m, Tp = 8.5 s

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Fig. 4

Mean upcrossing rates obtained by the 4D PI method and MCS for the sea state with Hs = 2.5 m, Tp = 9.5 s

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Fig. 5

Site of the buoy, No. 42058 in the Caribbean Sea

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Fig. 6

Fitted significant wave height by Weibull model based on the 9 year WSD, as plotted on Weibull paper

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Fig. 7

Fitted mean value of ln(Tp) as a function of Hs based on the 9 year WSD

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Fig. 8

Fitted variance of ln(Tp) as a function of Hs based on the 9 year WSD

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Fig. 9

Fitted joint PDF of Hs and Tp at the site of the NDBC buoy No. 42058 based on the 9 year WSD

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Fig. 10

Long-term upcrossing rates based on the empirical distribution of sea states (Table 2) and the fitted distribution of sea states (Table 3)

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Fig. 11

Exceedance probability of high level responses for the vessel under the sea state with Hs = 3.5 m, Tp = 8.5 s, exposure time T = 1 h, and Nt = 1000

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Fig. 12

Exceedance probability of high level responses for the vessel under the sea state with Hs = 2.5 m, Tp = 9.5 s, exposure time T = 1 h, and Nt = 5000

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Fig. 13

Long-term exceedance probabilities based on the long-term upcrossing rate (Eq. (17)) and based on the exceedance probability of the high levels for each short-term sea state (Eq. (20)), exposure time T = 1 h.

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