Extreme Vertical Bending Moment Research Articles

Sequential sampling method using Gaussian process regression for estimating extreme structural response

A methodology for estimating extreme response statistics for marine structures, that takes both the long-term variability of the metocean environment and the short-term variability of response into account is presented. The proposed methodology uses Gaussian process regression to estimate parameters of the short-term response distribution, based on output from computationally expensive hydrodynamic simulations. We present an adaptive design strategy for sequential updating of the model, focusing on the metocean conditions that contribute the most to the long-term extreme. With this approach, only a limited number of hydrodynamic simulations are needed.The suggested approach is demonstrated on the problem of estimating the 25-year extreme vertical bending moment on a ship. We show that a relatively small number of iterations (full hydrodynamic simulations) are needed to converge toward the “exact” results obtained by running a large number of simulations covering the entire range of sea states.The results suggest that the proposed method can be used as an alternative to contour-based methods or other methods that consider a few sea states using accurate numerical simulations, with little or no added complexity or computational effort.

Comparing different contour methods with response-based methods for extreme ship response analysis

Environmental contours are often applied in probabilistic structural reliability analysis to identify extreme environmental conditions that may give rise to extreme loads and responses. They facilitate approximate long term analysis of critical structural responses in situations where computationally heavy and time-consuming response calculations makes full long-term analysis infeasible. The environmental contour method identifies extreme environmental conditions that are expected to give rise to extreme structural response of marine structures. The extreme responses can then be estimated by performing response calculations for environmental conditions along the contours.Response-based analysis is an alternative, where extreme value analysis is performed on the actual response rather than on the environmental conditions. For complex structures, this is often not practical due to computationally heavy response calculations. However, by establishing statistical emulators of the response, using machine learning techniques, one may obtain long time-series of the structural response and use this to estimate extreme responses.In this paper, various contour methods will be compared to response-based estimation of extreme vertical bending moment for a tanker. A response emulator based on Gaussian processes regression with adaptive sampling has been established based on response calculations from a hydrodynamic model. Long time-series of sea-state parameters such as significant wave height and wave period are used to construct N-year environmental contours and the extreme N-year response is estimated from numerical calculations for identified sea states. At the same time, the response emulator is applied on the time series to provide long time-series of structural response, in this case vertical bending moment of a tanker. Extreme value analysis is then performed directly on the responses to estimate the N-year extreme response. The results from either method will then be compared, and it is possible to evaluate the accuracy of the environmental contour method in estimating the response. Moreover, different contour methods will be compared.

Effects of Weather Routing on Maximum Vertical Bending Moment in a Ship Taking Account of Wave-Induced Vibrations

In this paper, the effect of weather routing and ship operations on the extreme vertical bending moment (VBM) in a 6000TEU class large container ship which is operated in North Atlantic Ocean is addressed. A direct time-domain nonlinear response simulation method taking account of the wave-induced vibrations is combined with a voyage simulation based on 10 years of meteorological data in the area. The probability distribution of the ship's operational parameters conditional upon the meteorological conditions is considered. It is clarified that the most severe wave condition with the significant wave height over 16 m in the area may not be encountered by the ship due to the weather routing and the extreme value is determined mostly by the wave condition much milder than the most severe in the area. It is also found out that the ship speed assumed in the most contributing sea state strongly affects the extreme value of the total VBM. It is explained by the fact that the wave-induced vibrations in the ship tend to be excited at faster speed.

Analytical formula for collapse extent of VLFS under extreme vertical bending moment

A very large floating structure (VLFS) may undergo buckling and yielding under rare and extreme waves. Then, the cross section of the VLFS collapses completely. The evaluation of the consequence of collapse is critical in view of the risk analysis. In this paper, the parametric dependencies of the collapse extent of a VLFS under extreme vertical bending moments are investigated. A mathematical equation to describe the collapse behavior of the VLFS is developed taking account of the hydroelastic deformation. The whole VLFS is modeled by a segmented beam on an elastic foundation with infinite length connected via a nonlinear rotational spring assuming that a plastic hinge is formed at the collapsing section of the VLFS under the extreme vertical bending moment. By solving the equation in an analytical manner, a simple formula to predict the extent of collapse of the VLFS is developed. The results by the formula are well correlated with those by numerical simulation that has been developed by the present authors. It is shown that the characteristic length defined for a VLFS plays a key role in the collapse behavior.

Hydro-elastoplastic behaviour of VLFS under extreme vertical bending moment by segmented beam approach

This paper addresses collapse behaviour of Very Large Floating Structure (VLFS) under extreme vertical bending moment. The study is performed as part of risk analysis to evaluate the consequence of a rare collapse event. Elastic and plastic deformation of VLFS develops under the extreme vertical bending moment while the deformation interacts with the fluid around VLFS. Therefore, hydro-elastoplasticity analysis need be developed taking account of these effects. In this study, the whole VLFS structure is modeled as two elastic beams with an elasto-plastic hinge embedded at the connection. The structural deformation is formulated by using finite element method (FEM). The hydrodynamic behaviour is modeled by using Rankine source panel method in time domain based on two-dimensional potential theory. The two models are coupled. A series of scaled model tests is performed for validation. Simulation and tank test results for the basic collapse behaviour of VLFS are presented and discussed. The numerical method is applied further to a realistic VLFS design to clarify its collapse behaviour.

Statistical analysis of wave-induced extreme nonlinear load effects using time-domain simulations

A new hybrid method for the time-domain nonlinear simulation of the hydroelastic load effects and the peak-over-threshold (POT) method for the calculation of the short-term extreme responses are briefly described and applied to a flexible containership of the latest design. Statistical analysis has been carried out to study the sensitivity of the predicted extreme vertical bending moments and vertical shear forces to the changes in the threshold of the POT method, as well as the statistical uncertainty in the prediction due to the limited duration of the nonlinear simulation. It is recommended that 90%–95% quantile should be used as the threshold in the POT method and more than 100 h of time-domain simulation should be carried out in order to obtain satisfactory predictions of the short-term extreme nonlinear load effects.

Analysis of Design Wave Loads on an FPSO Accounting for Abnormal Waves

The paper presents an analysis of structural design wave loads on an FPSO. The vertical bending moment at midship induced by rogue waves are compared with rule values. The loads induced by deterministic rogue waves were both measured in a seakeeping tank and calculated by an advanced time domain method. Two procedures are used to calculate the expected extreme vertical bending moment during the operational lifetime of the ship. The first one relies on a standard linear long term prediction method, which results from the summation of short term distribution of maxima weighted by their probability of occurrence. The short term stationary seastates are represented by energy spectra and the ship responses by linear transfer functions. The second one is a generalization of the former and it accounts for the nonlinearity of the vertical bending moment, by using nonlinear transfer functions of the bending moment sagging peaks which depend of the wave height.

Reassessment of the M.V. Derbyshire Sinking With the Focus on Hull-Girder Collapse

During the last two decades, extensive investigations into the possible causes of the loss of the Capesize bulk carrier M.V. Derbyshire have been made. A total of 13 risk components were considered within the framework of a formal safety assessment. The prime concern was with abnormal wave effects on hatch cover failure and subsequent flooding into forward cargo holds. No serious speculation on hull-girder collapse was raised in the previous investigations. The present paper studies this possible cause, which involves the vessel's sinking due to structural progressive collapse from extreme wave bending actions. The safety measure of the vessel is defined as a ratio of the ultimate hull-girder strength to the applied extreme vertical bending moment. The computed safety measure is found to be quite marginal while the vessel was trapped in typhoon Orchid, indicating that the M.V. Derbyshire could have sunk by hull-girder collapse with or even without hatch cover failure and subsequent water ingress into the forward cargo holds. The results and insights developed from the present study are summarized. Important recommendations for improved ship safety are made.