Polynomial Approximation of Morison Wave Loading

1997 ◽  
Vol 119 (1) ◽  
pp. 30-36 ◽  
Author(s):  
V. Bouyssy ◽  
R. Rackwitz
Keyword(s):  
Polynomial Approximation ◽  
Order Approximation ◽  
Offshore Structures ◽  
Random Wave ◽  
Wave Loads ◽  
Wave Loading ◽  
Gaussian Models ◽  
Response Variance ◽  
Non Gaussian ◽  
Fifth Order

For offshore structures with slender elements, the modeling of random wave loads by the Morison equation yields an equation of motion which has no analytical solution for response moments except in a few limiting cases. If polynomial approximations of the Morison drag loads are introduced, some procedures are available to obtain the stationary moments of the approximate response. If the response process is fitted by non-Gaussian models such as proposed by Winterstein (1988), the first four statistical moments of the response are necessary. The paper investigates how many terms should be included in the polynomial approximation of the Morison drag loading to accurately estimate the first four response moments. It is shown that a cubic approximation of the drag loading is necessary to accurately predict the response variance for any excitation. For the fit of the first four response moments, at least a fifth-order approximation appears necessary.

Extremes of Nonlinear Vibration: Comparing Models Based on Moments, L-Moments, and Maximum Entropy

2013 ◽  
Vol 135 (2) ◽  
Author(s):  
Steven R. Winterstein ◽  
Cameron A. MacKenzie
Keyword(s):  
Maximum Entropy ◽  
Nonlinear Effects ◽  
Offshore Structures ◽  
Sufficient Information ◽  
Wave Loads ◽  
Gaussian Models ◽  
Maximum Entropy Models ◽  
Extreme Response ◽  
L Moments ◽  
Non Gaussian

Wind and wave loads on offshore structures show nonlinear effects, which require non-Gaussian statistical models. Here we critically review the behavior of various non-Gaussian models. We first survey moment-based models; in particular, the four-moment “Hermite” model, a cubic transformation often used in wind and wave applications. We then derive an “L-Hermite” model, an alternative cubic transformation calibrated by the response “L-moments” rather than its ordinary statistical moments. These L-moments have recently found increasing use, in part because they show less sensitivity to distribution tails than ordinary moments. We find here, however, that these L-moments may not convey sufficient information to accurately estimate extreme response statistics. Finally, we show that four-moment maximum entropy models, also applied in the literature, may be inappropriate to model broader-than-Gaussian cases (e.g., responses to wind and wave loads).

Efficient Derivation of the Probability Distribution of Extreme Responses due to Random Wave Loading From the Probability Distribution of Extreme Surface Elevations

2013 ◽  
Author(s):  
H. Mallahzadeh ◽  
Y. Wang ◽  
M. K. Abu Husain ◽  
N. I. Mohd Zaki ◽  
G. Najafian
Keyword(s):  
Probability Distribution ◽  
Extreme Values ◽  
Offshore Structures ◽  
Random Wave ◽  
Wave Loading ◽  
Sampling Variability ◽  
Extreme Surface ◽  
Ocean Environment ◽  
Non Gaussian ◽  
Extreme Responses

Offshore structures are exposed to random wave loading in the ocean environment and hence the probability distribution of the extreme values of their response to wave loading is required for their safe and economical design. Due to nonlinearity of the drag component of Morison’s wave loading and also due to intermittency of wave loading on members in the splash zone, the response is often non-Gaussian; therefore, simple techniques for derivation of the probability distribution of extreme responses are not available. To this end, the conventional Monte Carlo time simulation technique is frequently used for predicting the probability distribution of the extreme responses. However, this technique suffers from excessive sampling variability and hence a large number of simulated response records are required to reduce the sampling variability to acceptable levels. This paper takes advantage of the correlation between extreme responses and their corresponding extreme surface elevations to derive the probability distribution of the extreme responses accurately and efficiently, i.e. without the need for extensive simulations.

A New Method of Moments for Reducing the Sampling Variability of Estimated Values of Probability Distribution Parameters

2007 ◽  
Author(s):  
G. Najafian
Keyword(s):  
Probability Distribution ◽  
Method Of Moments ◽  
Probability Model ◽  
Offshore Structures ◽  
Random Wave ◽  
Wave Loading ◽  
Sampling Variability ◽  
Minimum Requirement ◽  
Distribution Parameters ◽  
Non Gaussian

Offshore structures are exposed to random wave loading in the ocean environment and hence the probability distribution of their response to wave loading is the minimum requirement for probabilistic analysis of these structures. Even if the structural system can be assumed to be linear, due to nonlinearity of the wave loading mechanism and also due to the intermittency of wave loading on members in the splash zone, the response is often non-Gaussian. The method of moments is frequently used to determine the parameters of an adopted probability model from a simulated or measured record of response. However, when higher order moments (e.g. 3rd or 4th order moments) are required for estimation of the distribution parameters, the estimated values show considerable scatter due to high sampling variability. In this paper, a more efficient form of the method of moments is introduced, which will lead to more accurate estimates of the distribution parameters by reducing their sampling variability.

Efficient Derivation of the Probability Distribution of the Extreme Values of Offshore Structural Response: Comparison of Three Different Methods

2013 ◽  
Author(s):  
M. K. Abu Husain ◽  
N. I. Mohd Zaki ◽  
G. Najafian
Keyword(s):  
Probability Distribution ◽  
Extreme Values ◽  
Structural Response ◽  
Offshore Structures ◽  
Simulation Technique ◽  
Random Wave ◽  
Wave Loading ◽  
Sampling Variability ◽  
Time Simulation ◽  
Extreme Responses

Offshore structures are exposed to random wave loading in the ocean environment and hence the probability distribution of the extreme values of their response to wave loading is required for their safe and economical design. To this end, the conventional (Monte Carlo) time simulation technique (CTS) is frequently used for predicting the probability distribution of the extreme values of response. However, this technique suffers from excessive sampling variability and hence a large number of simulated extreme responses (hundreds of simulated response records) are required to reduce the sampling variability to acceptable levels. In this paper, three different versions of a more efficient time simulation technique (ETS) are compared by exposing a test structure to sea states of different intensity. The three different versions of the ETS technique take advantage of the good correlation between extreme responses and their corresponding surface elevation extreme values, or quasi-static and dynamic linear extreme responses.

The Influence of Alternative Wave Loading and Support Modeling Assumptions on Jack-Up Rig Response Extremes

1996 ◽  
Vol 118 (2) ◽  
pp. 109-114 ◽  
Author(s):  
L. Manuel ◽  
C. A. Cornell
Keyword(s):  
Nonlinear Models ◽  
Random Wave ◽  
Force Model ◽  
Wave Loading ◽  
Force Modeling ◽  
Hydrodynamic Damping ◽  
Extreme Response ◽  
The Absolute ◽  
Non Gaussian ◽  
Jack Up

A study is conducted of the response of a jack-up rig to random wave loading. Steady current and wind load effects are also included. The effects of varying the relative motion assumption (in the Morison equation) and of varying the bottom fixity assumptions are investigated. One “fixity” model employs nonlinear soil springs. Time domain simulations are performed using linearized as well as fully nonlinear models for the jack-up rig. Comparisons of response statistics are made for two seastates. Hydrodynamic damping causes the rms response to be lower in the relative Morison case. The absence of this source of damping in the absolute Morison force model gives rise to larger resonance/dynamic effects—this tends to “Gaussianize” the response. Hence, the relative Morison model leads to stronger non-Gaussian behavior than the absolute Morison model. This is reflected in moments as well as extremes. The different support conditions studied are seen to significantly influence extreme response estimates. In general, stiffer models predict smaller rms response estimates, but also exhibit stronger non-Gaussian behavior. The choice of the Morison force modeling assumption (i.e., the relative versus the absolute motion formulation) is seen to have at least a secondary role in influencing response moments and extremes.

System Identification of a Six-Legged Semisubmersible Subjected to Wave Loads through Frequency Domain Analysis

2013 ◽  
Vol 373-375 ◽  
pp. 770-784
Author(s):  
Guo Zheng Yew ◽  
M.S. Liew ◽  
Mohd Shahir Liew ◽  
Cheng Yee Ng
Keyword(s):  
System Identification ◽  
Transfer Function ◽  
Transfer Functions ◽  
Structural Response ◽  
Offshore Structures ◽  
Frequency Domain Analysis ◽  
Random Wave ◽  
Wave Loads ◽  
Sea State ◽  
Wave Heights

Sea state conditions such as wind, wave and current vary in different ocean waters. Two similar offshore structures installed in two different ocean regions will yield different responses. Determining the transfer function of the structure is a system identification exercise that yields the structural response and behaviour given any sea state condition. The transfer function can be determined using available measured sea state data and structural response data. In this paper, a six-legged semisubmersible physical model is developed to a scale of 1:100 and is tested in a wave tank to measure its responses due to simulated random wave loads. The transfer functions of the semisubmersible model are then determined using the measured responses and the measured wave heights.

Probabilistic Modelling of Extreme Offshore Structural Response due to Random Wave Loading

2013 ◽  
Author(s):  
Y. Wang ◽  
H. Mallahzadeh ◽  
M. K. Abu Husain ◽  
N. I. Mohd Zaki ◽  
G. Najafian
Keyword(s):  
Extreme Values ◽  
Structural Response ◽  
Offshore Structures ◽  
Random Wave ◽  
Wave Loading ◽  
Empirical Distributions ◽  
Generalized Pareto ◽  
Economical Design ◽  
Ocean Environment ◽  
Extreme Responses

Offshore structures are exposed to random wave loading in the ocean environment and hence the probability distribution of the extreme values of their response to wave loading is required for their safe and economical design. This paper investigates the suitability of the Gumbel, the Generalized Extreme Value (GEV), and the Generalized Pareto (GP) distributions for modelling of extreme responses by comparing them with empirical distributions derived from extensive Monte Carlo time simulations. It will be shown that none of these distributions can model the extreme values adequately but that a mixed distribution consisting of both GEV and GP distributions seems to be capable of modelling the extreme responses with very good accuracy.

An Efficient Monte Carlo Simulation Technique for Derivation of the Probability Distribution of the Extreme Values of Offshore Structural Response

2010 ◽  
Author(s):  
M. K. Abu Husain ◽  
G. Najafian
Keyword(s):  
Probability Distribution ◽  
Extreme Values ◽  
Structural Response ◽  
Offshore Structures ◽  
Simulation Technique ◽  
Random Wave ◽  
Wave Loading ◽  
Sampling Variability ◽  
Monte Carlo Simulation Technique ◽  
Ocean Environment

Offshore structures are exposed to random wave loading in the ocean environment and hence the probability distribution of the extreme values of their response to wave loading is required for their safe and economical design. To this end, the conventional simulation technique (CTS) is frequently used for predicting the probability distribution of the extreme values of response. However, this technique suffers from excessive sampling variability and hence a large number of simulated response extreme values (hundreds of simulated response records) are required to reduce the sampling variability to acceptable levels. In this paper, a more efficient version of the time simulation technique (ETS) is introduced to derive the probability distribution of response extreme values from a much smaller sample of simulated extreme values.

Estimating Iceberg-Wave Companion Loads Using Probabilistic Methods

2015 ◽  
Author(s):  
Mark Fuglem ◽  
Paul Stuckey ◽  
Somchat Suwan
Keyword(s):  
Hydrodynamic Pressure ◽  
Offshore Structures ◽  
Probabilistic Methods ◽  
Wave Loads ◽  
Wave Loading ◽  
Wave Load ◽  
Sea State ◽  
Load Factors ◽  
Induced Velocity ◽  
The Impact

Many challenges arise when designing offshore structures for iceberg loads in arctic and subarctic regions. To help the designer, the ISO 19906:2010 standard provides guidance for the calculation of design ice loads using both deterministic and probabilistic approaches. In determining design loads for different environmental factors, both principal and companion actions must be taken into account; an example is iceberg actions and companion wave actions. ISO 19906 allows the designer to calculate the companion wave action as a specified fraction (combination factor) of the extreme level (EL) design wave load. Alternatively, the designer can calculate appropriate companion wave loads explicitly. A methodology has been developed at C-CORE in which representative iceberg actions are determined using a software package, the Iceberg Load Software (ILS). This is a probabilistic tool which uses Monte Carlo simulation to obtain a distribution of global impact forces based on the expected range of iceberg and environmental conditions that a structure would likely encounter. The software provides a reasonably accurate representation of the iceberg loading situation, following the provisions of ISO 19906:2010, without introducing unnecessary conservatism in the design load. In the software, the influence of waves on the iceberg actions are considered, but companion wave loads must be calculated and added externally to the software, The software accounts for the probability of different sea state conditions and the influence of the sea state on the probability and severity of iceberg impact, given the correlations between the sea state, iceberg management effectiveness and iceberg drift and wave-induced velocity. The additional hydrodynamic pressure due to the wave during the period of the impact; is not considered. This wave loading will be complicated by the influence that the presence the iceberg and structure have on the local sea state. In this paper, brief descriptions are provided of background studies on companion wave loading and the application of companion load factors in ISO 19906. The companion load factors allow the designer to apply the design wave load, which is calculated for situations with no iceberg present, to the case of iceberg impacts. In this study, a methodology is presented for determining companion wave loads based on the distribution of sea states expected during an iceberg impact. These sea states are significantly less severe than that associated with the design wave load as iceberg impacts are rare events. The companion wave loads are determined without accounting for the influence of the iceberg; this is thought to be quite conservative. An example application of the methodology is presented for a hypothetical platform located on the Grand Banks, off the east coast of Newfoundland. Iceberg actions, wave actions and combined iceberg-wave actions are estimated using the described methodology. Comparisons are provided for the resulting companion loads and those based on ISO 19906:2010 companion load factors applied to the extreme level wave load.

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