Probabilistic Analysis of Nonlinear Wave Loads on Ships Using Weibull, Generalized Gamma, and Pareto Distributions

The statistics of nonlinear wave- induced bending moment in ship hull girders in a short-term period is studied. Systematic probabilistic analysis is performed directly on wave load time histories for different ship types under various sea state and ship speed conditions. The order statistics concept and peak-over-threshold method are used for estimation of the extreme wave loads. The generalized gamma, generalized Pareto, and Weibull distributions are utilized for describing wave load peak values. The three distributions are evaluated and compared with respect to the shape parameters, goodness of fit of the models to the wave load data, and statistical uncertainty in the extreme estimates. Important features of the wave load statistics are also revealed.

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A Method for Designing the Backbone for the Segmented Model of an Ultra-Large Container Carrier

Volume 7B: Ocean Engineering ◽

10.1115/omae2019-96136 ◽

2019 ◽

Author(s):

Hui Li ◽

Jian Zou ◽

Weijia Sheng ◽

Xuecong Hu ◽

Wenjia Hu

Keyword(s):

Experimental Studies ◽

Complex Form ◽

Bending Moment ◽

Torsional Stiffness ◽

Mode Shapes ◽

Wave Loads ◽

Torsional Moment ◽

Wave Load ◽

Segmented Model ◽

Vertical Bending Moment

Abstract The segmented model test is often used to study the wave load characteristics of large ships as it can account for the hydroealstic effect. The vertical bending moment (VBM) is of crucial importance in ensuring the safety of ocean-going vessels in rough seas, and there exists in the literature a large number of experimental studies of the VBM. For ships with large openings in the deck, for instance, container ships, the lateral wave loads, such as horizontal bending moment (HBM) and torsional moment (TM) in quartering seas, are as important as VBM. There are, however, few studies on the measurement of the coupled horizontal-torsional vibrations of such ships in model tests. In the paper, a method is proposed for designing flexible backbone models that satisfy the similarities of vertical and horizontal bending stiffness as well as the torsional stiffness, and the measurement of the wave load components is also described. In order to meet the similarity of the hull girder stiffness, the backbone cross-section of a complex form is designed. Finite element method (FEM) is used to calculate the natural frequencies and mode shapes of the segmented model. Measurement of the vertical bending moment, horizontal bending moment and torsional moment are calibrated by applying various combinations of loads.

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Assessment of Load Extrapolation Methods for Wind Turbines

Journal of Solar Energy Engineering ◽

10.1115/1.4003416 ◽

2011 ◽

Vol 133 (2) ◽

Cited By ~ 13

Author(s):

Henrik Stensgaard Toft ◽

John Dalsgaard Sørensen ◽

Dick Veldkamp

Keyword(s):

Analytical Solution ◽

Gaussian Process ◽

Wind Turbine ◽

Process Model ◽

Goodness Of Fit ◽

Bending Moment ◽

Threshold Value ◽

Threshold Method ◽

Peak Over Threshold ◽

Peak Over Threshold Method

In the present paper, methods for statistical load extrapolation of wind-turbine response are studied using a stationary Gaussian process model, which has approximately the same spectral properties as the response for the out-of-plane bending moment of a wind-turbine blade. For a Gaussian process, an approximate analytical solution for the distribution of the peaks is given by Rice. In the present paper, three different methods for statistical load extrapolation are compared with the analytical solution for one mean wind speed. The methods considered are global maxima, block maxima, and the peak over threshold method with two different threshold values. The comparisons show that the goodness of fit for the local distribution has a significant influence on the results, but the peak over threshold method with a threshold value on the mean plus 1.4 standard deviations generally gives the best results. By considering Gaussian processes for 12 mean wind speeds, the “fitting before aggregation” and “aggregation before fitting” approaches are studied. The results show that the fitting before aggregation approach gives the best results.

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Offshore Wind Turbine Nonlinear Wave Loads and Their Statistics

Journal of Offshore Mechanics and Arctic Engineering ◽

10.1115/1.4042264 ◽

2019 ◽

Vol 141 (3) ◽

Cited By ~ 2

Author(s):

Paul D. Sclavounos ◽

Yu Zhang ◽

Yu Ma ◽

David F. Larson

Keyword(s):

Nonlinear Wave ◽

Machine Learning Algorithms ◽

Offshore Wind ◽

Support Vector ◽

Offshore Wind Turbine ◽

Wave Loads ◽

Wave Load ◽

Support Structure ◽

Nonlinear Load ◽

Floating Offshore Wind Turbines

The development of an analytical model for the prediction of the stochastic nonlinear wave loads on the support structure of bottom mounted and floating offshore wind turbines is presented. Explicit expressions are derived for the time-domain nonlinear exciting forces in a sea state with significant wave height comparable to the diameter of the support structure based on the fluid impulse theory (FIT). The method is validated against experimental measurements with good agreement. The higher order moments of the nonlinear load are evaluated from simulated force records and the derivation of analytical expressions for the nonlinear load statistics for their efficient use in design is addressed. The identification of the inertia and drag coefficients of a generalized nonlinear wave load model trained against experiments using support vector machine learning algorithms is discussed.

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Offshore Wind Turbine Nonlinear Wave Loads and Their Statistics

Volume 9: Offshore Geotechnics; Torgeir Moan Honoring Symposium ◽

10.1115/omae2017-61184 ◽

2017 ◽

Cited By ~ 2

Author(s):

Paul D. Sclavounos ◽

Yu Zhang ◽

Yu Ma ◽

David F. Larson

Keyword(s):

Nonlinear Wave ◽

Machine Learning Algorithms ◽

Offshore Wind ◽

Support Vector ◽

Offshore Wind Turbine ◽

Wave Loads ◽

Wave Load ◽

Support Structure ◽

Nonlinear Load ◽

Floating Offshore Wind Turbines

The development is presented of an analytical model for the prediction of the stochastic nonlinear wave loads on the support structure of bottom mounted and floating offshore wind turbines. Explicit expressions are derived for the time-domain nonlinear exciting forces in a seastate with significant wave height comparable to the diameter of the support structure based on the fluid impulse theory. The method is validated against experimental measurements with good agreement. The higher order moments of the nonlinear load are evaluated from simulated force records and the derivation of analytical expressions for the nonlinear load statistics for their efficient use in design is addressed. The identification of the inertia and drag coefficients of a generalized nonlinear wave load model trained against experiments using Support Vector Machine learning algorithms is discussed.

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Fluctuation of magnitude of wave loads for a long array of bottom-mounted cylinders

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.195 ◽

2019 ◽

Vol 868 ◽

pp. 244-285 ◽

Cited By ~ 1

Author(s):

Xiaohui Zeng ◽

Fajun Yu ◽

Min Shi ◽

Qi Wang

Keyword(s):

Incidence Angle ◽

Local Maximum ◽

Destructive Interference ◽

Horizontal Distance ◽

Wave Loads ◽

Wave Load ◽

Intrinsic Mechanism ◽

Fluctuation Phenomenon ◽

Analytical Formulae ◽

Incident Waves

For wave loads on cylinders constituting a long but finite array in the presence of incident waves, variations in the magnitude of the load with the non-dimensional wavenumber exhibit interesting features. Towering spikes and nearby secondary peaks (troughs) associated with trapped modes have been studied extensively. Larger non-trapped regions other than these two are termed Region III in this study. Studies of Region III are rare. We find that fluctuations in Region III are regular; the horizontal distance between two adjacent local maximum/minimum points, termed fluctuation spacing, is constant and does not change with non-dimensional wavenumbers. Fluctuation spacing is related only to the total number of cylinders in the array, identification serial number of the cylinder concerned and wave incidence angle. Based on the interaction theory and constructive/destructive interference, we demonstrate that the fluctuation characteristics can be predicted using simple analytical formulae. The formulae for predicting fluctuation spacing and the abscissae of every peak and trough in Region III are proposed. We reveal the intrinsic mechanism of the fluctuation phenomenon. When the diffraction waves emitted from the cylinders at the ends of the array and the cylinder concerned interfere constructively/destructively, peaks/troughs are formed. The fluctuation phenomenon in Region III is related to solutions of inhomogeneous equations. By contrast, spikes and secondary peaks are associated with solutions of the eigenvalue problem. This study of Region III complements existing understanding of the characteristics of the magnitude of wave load. The engineering significances of the results are discussed as well.

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Nonlinear Wave Load Effects On The Stochastic Behavior Of Fixed Offshore Platforms

10.4043/5139-ms ◽

1986 ◽

Cited By ~ 1

Author(s):

J.M. Niedzwecki ◽

E.W. Sandt

Keyword(s):

Nonlinear Wave ◽

Offshore Platforms ◽

Wave Load ◽

Stochastic Behavior ◽

Load Effects

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Wave Loads on Floaters of Aquaculture Plants

Volume 6: Nick Newman Symposium on Marine Hydrodynamics; Yoshida and Maeda Special Symposium on Ocean Space Utilization; Special Symposium on Offshore Renewable Energy ◽

10.1115/omae2008-57084 ◽

2008 ◽

Cited By ~ 1

Author(s):

David Kristiansen ◽

Odd M. Faltinsen

Keyword(s):

Stokes Equations ◽

Model Tests ◽

Staggered Grid ◽

Physical Parameters ◽

Surface Zone ◽

Two Dimensional ◽

Wave Loads ◽

Wave Load ◽

Constrained Interpolation ◽

Advection Term

This paper addresses wave loads on horizontal cylinders in the free surface zone by means of model tests and numerical simulations. This has relevance for the design of floating fish farms at exposed locations. Two model geometries were tested, where two-dimensional flow conditions were sought. The cylinders were fixed and exposed to regular wave trains. Wave overtopping the models were observed. A two-dimensional Numerical Wave Tank (NWT) for wave load computations is described. The NWT is based on the finite difference method and solves the incompressible Navier-Stokes equations on a non-uniform Cartesian staggered grid. The advection term is treated separately by the CIP (Constrained Interpolation Profile) method. A fractional and validation of the NWT is emphasized. Numerical results from simulations with the same physical parameters as in the model tests are performed for comparison. Deviations are discussed.

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Wave Loads Computation for Offshore Floating Hose Based on Partially Immersed Cylinder Model of Improved Morison Formula

The Open Petroleum Engineering Journal ◽

10.2174/1874834101508010130 ◽

2015 ◽

Vol 8 (1) ◽

pp. 130-137 ◽

Cited By ~ 1

Author(s):

Shi-fu Zhang ◽

Chang Chen ◽

Qi-xin Zhang ◽

Dong-mei Zhang ◽

Fan Zhang

Keyword(s):

Mechanical Characteristics ◽

Water Area ◽

Wave Loads ◽

Wave Load ◽

Mechanic Analysis ◽

Morison Equation ◽

Offshore Pipeline ◽

Cylinder Model ◽

Calculation Results

Aimed at wave load computation of floating hose, the paper analyzes the morphologic and mechanical characteristics of offshore hose by establishing the partially immersed cylender model, and points out that the results of existing Morison equation to calculate the wave loads of floating hose is not precise enough. Consequently, the improved Morison equation has been put forward based on its principle. Classical series offshore pipeline has been taken as example which applied in the water area of different depth. The wave loads of pipeline by using the improved Morison equation and compared the calculation results with the existing Morison equation. Calculations for wave loads on pipelines in different depth were accomplished and compared by the improved Morison equation and the existing Morison equation. Results show that the improved Morison equation optimizes the accuracy of the computation of wave load on floating hose. Thus it is more suitable for analyzing the effects of wave loads on floating hose and useful for mechanic analysis of offshore pipeline.

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