Extreme Value Estimation of Mooring Lines Top Tension

2019 ◽  
Author(s):  
Marina Leivas Simão ◽  
Paulo Mauricio Videiro ◽  
Mauro Costa Oliveira ◽  
Luís Volnei Sudati Sagrilo
Keyword(s):  
Probability Distribution ◽  
Weibull Distribution ◽  
Time Domain ◽  
Extreme Values ◽  
Wave Spectrum ◽  
Line Tension ◽  
Short Term ◽  
Mooring Lines ◽  
Tension Time ◽  
The One

Abstract It is known that the mooring system of floating platforms responds non-linearly to environmental loads. Even though the wave-frequency excitation can be assumed as a Gaussian process, the line tension generally is not a Gaussian process due to the second-order slow-drift floater motions and the nonlinearities of the system itself. Distinct short-term time-domain analyses with the same wave spectrum excitation, i.e., distinct realizations of the response process, lead to a set of distinct values for the simulated individual maximum observed line tensions. Therefore, the ideal practice for estimating extreme tension values should be to perform a sufficiently large number of independent simulations along with an extreme statistical analysis considering the sample of the maximum line tension identified in each simulation. However, this process can be very time-consuming and cumbersome for everyday design applications. In this paper, the short-term line tension is assumed to be a non-Gaussian ergodic process. The extreme tension is then estimated based on the peaks sample of just a single simulated tension time-history. A number of known probability distributions are fitted to the peaks of the time series and classic order statistics theory is applied to determine the most probable extreme line tension corresponding to a specified short-time period (3-h) in order to identify the one with best performance. The proposed probability distribution models for the tension peaks are the 3-parameter Weibull distribution, the Weibull distribution fitted to the tail of the data (Weibull-tail) and the Shifted Generalized Lognormal Distribution (SGLD). The estimated extreme values are also prone to uncertainties due to time-domain simulation details. The effects of the major parameters in the dynamic analysis, such as simulation length and discretization level of the wave spectrum, are therefore investigated using several simulated mooring line tension time-histories. Furthermore, the effect of correlation between consecutive line tension peaks in the extreme values estimation is investigated through a Nataf transformation-based model for joint probability distribution for the peaks and the one step Markov chain condition. It is shown that this latter consideration leads to extreme value estimates that are invariably smaller than those obtained by standard order statistics. These estimates are also shown to be closer to the extreme estimates directly obtained from a sample of largest values taken from several distinct numerical simulations. Numerical examples cover two study cases for mooring lines belonging to FPSO (Floating, Production, Storage and Offloading) units to be installed in Brazilian waters.

Comparative Study of Extreme Value Estimation Approaches for Mooring Lines Top Tension Responses

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Marina Leivas Simão ◽  
Luis Volnei Sudati Sagrilo ◽  
Paulo Maurício Videiro ◽  
Mauro Costa de Oliveira ◽  
Arvid Naess
Keyword(s):  
Probability Distributions ◽  
Wave Spectrum ◽  
Line Tension ◽  
Chain Condition ◽  
System Response ◽  
Short Term ◽  
Mooring Lines ◽  
Time Histories ◽  
The One ◽  
Nataf Transformation

Abstract It is known that the mooring system response of floating production units subjected to environmental loads is nonlinear. Even though wave elevations can be assumed as Gaussian processes for short-term periods, corresponding line tension responses generally are not, due to second-order slow-drift floater motions and intrinsic nonlinearities of the system. In this work, short-term extreme responses are estimated based on two different approaches. In the first one, a number of probability distributions are fitted to the tension time histories’ peaks samples and classic order statistics is applied to determine the most probable extreme line tension corresponding to a short-time period (3-h) in order to identify the one with best performance. The effect of correlation between consecutive peaks in the extremes estimation is investigated through the one-step Markov chain condition by using a Nataf transformation-based model. In the second approach, a more robust and recently developed method named average conditional exceedance rate (ACER) is investigated, where dependencies between maxima can be easily taken into account. Additionally, effects of major parameters in dynamic analyses, such as simulation length and discretization level of the wave spectrum, are evaluated. All time-series-based extreme estimates are compared with the estimates directly obtained from a sample of epochal maxima (Gumbel method). Numerical examples cover two study cases for mooring lines belonging to Floating Production Storage and Offloading (FPSO) units installed offshore Brazil. It is shown that the consideration of dependence between peaks leads to lower extreme estimates and that both approaches return accurate results.

Prediction of Offshore Structural Response Extreme Values by Modified Finite-Memory Nonlinear System Modeling

2016 ◽  
Author(s):  
N. I. Mohd Zaki ◽  
M. K. Abu Husain ◽  
N. A. Mukhlas ◽  
G. Najafian
Keyword(s):  
Nonlinear System ◽  
Probability Distribution ◽  
Extreme Values ◽  
Offshore Structures ◽  
Horizontal Distance ◽  
Wave Loading ◽  
Offshore Structure ◽  
Short Term ◽  
Finite Memory ◽  
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 of great value in the design of these structures. 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. However, it has recently been shown that the short-term response of an offshore structure exposed to Morison wave loading can be approximated by the response of an equivalent finite-memory nonlinear system (FMNS). Previous investigation has shown that the developed FMNS models perform better for high Hs values and that their performance for low Hs value is not particularly good. In this paper, MFMNS technique, a modified version of FMNS models is discussed. The improvement in MFMNS model is simply achieved by dividing the structure into two zones (Zones 1 and 2) so that the horizontal distance between the nodes in each zone is relatively small compared to the wavelengths. It is shown that MFMNS technique can be used to determine the short-term probability distribution of the extreme responses accurately with great efficiency.

Short-Term Distribution of the Extreme Values of Offshore Structural Response by Modified Finite-Memory Nonlinear System Modeling

2013 ◽  
Author(s):  
N. I. Mohd Zaki ◽  
M. K. Abu Husain ◽  
Y. Wang ◽  
G. Najafian
Keyword(s):  
Nonlinear System ◽  
Probability Distribution ◽  
Extreme Values ◽  
Offshore Structures ◽  
Random Wave ◽  
Horizontal Distance ◽  
Wave Loading ◽  
Offshore Structure ◽  
Short Term ◽  
Finite Memory

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 of great value in the design of these structures. 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. However, it has recently been shown that the short-term response of an offshore structure exposed to Morison wave loading can be approximated by the response of an equivalent finite-memory nonlinear system (FMNS). Previous investigation shows that the developed FMNS models perform better for high Hs values and their performance for low Hs value is not particularly good. In this paper, the modified version of FMNS models is referred to as MFMNS models is discussed. The improvement of MFMNS model is simply by dividing the structure into two zones (Zones 1 and 2) so that the horizontal distance between the nodes in each zone is relatively small compared to the wavelength. The modified version of MFMNS is used to determine the short-term probability distribution of the response extreme values with great efficiency.

Mooring Line Damping Estimation by a Simplified Dynamic Model

2007 ◽  
Author(s):  
Halvor Lie ◽  
Zhen Gao ◽  
Torgeir Moan
Keyword(s):  
Dynamic Model ◽  
Time Domain ◽  
Low Frequency ◽  
Line Tension ◽  
Mooring Line ◽  
Short Term ◽  
Simplified Method ◽  
On Line ◽  
Simulation Results ◽  
Frequency Domain Approach

When predicting slowly varying resonant vessel motions, a realistic estimate of the motion damping is crucial. Mooring line damping, which is mainly induced by the drag force on line, can dominate the total damping of catenary moored systems and methods for predicting mooring line damping are therefore required. Based on a simplified dynamic model of mooring line tension, an approach to estimate the corresponding damping is presented in this paper. Short-term time domain simulations of dynamic line tension are carried out to verify the accuracy of the simplified frequency domain approach. Compared with the simulation results, the practical simplified method proposed herein gives a maximum 30% lower prediction of the damping coefficient of each mooring line and an about 20% smaller estimate of the total line damping and therefore yields conservative estimates of the low frequency vessel motions.

scholarly journals A Comparison of Numerical Approaches for the Design of Mooring Systems for Wave Energy Converters

2020 ◽  
Vol 8 (7) ◽  
pp. 523 ◽  
Author(s):  
Imanol Touzon ◽  
Vincenzo Nava ◽  
Borja de Miguel ◽  
Victor Petuya
Keyword(s):  
Frequency Domain ◽  
Wave Energy ◽  
Time Domain ◽  
Linear Time ◽  
Line Tension ◽  
Mooring System ◽  
Mooring Lines ◽  
Viscous Forces ◽  
And Performance ◽  
Inertia Forces

This paper analyses the numerical outcome of applying three different well-known mooring design approaches to a floating wave energy converter, moored by means of four catenary lines. The approaches include: a linearized frequency domain based on a quasistatic model of the mooring lines, a time domain approach coupled with an analytic catenary model of the mooring system, and a fully coupled non-linear time domain approach, considering lines’ drag and inertia forces. Simulations have been carried out based on a set of realistic combinations of lines pretension and linear mass, subject to extreme environmental conditions. Obtained results provide realistic cost and performance indicators, presenting a comparison in terms of total mooring mass and required footprint, as well as the design line tension and structure offset. It has been found that lines’ viscous forces influence significantly the performance of the structure with high pretensions, i.e., >1.2, while there is acceptable agreement between the modelling approaches with lower pretensions. Line tensions are significantly influenced by drag and inertia forces because of the occurrence of snap loads due to the heaving of the floater. However, the frequency domain approach provides an insight towards the optimal design of the mooring system for preliminary designs.

Short-term probability distribution of the extreme values of offshore structural response by an efficient time simulation technique

2014 ◽  
Vol 11 (3) ◽  
pp. 286-299 ◽  
Author(s):  
M.K. Abu Husain ◽  
N.I. Mohd Zaki ◽  
H. Mallahzadeh ◽  
G. Najafian
Keyword(s):  
Probability Distribution ◽  
Extreme Values ◽  
Structural Response ◽  
Simulation Technique ◽  
Short Term ◽  
Time Simulation

Long-Term Distribution of the Extreme Values of Offshore Structural Response by Finite-Memory Nonlinear System Modelling

2011 ◽  
Author(s):  
N. I. Mohd Zaki ◽  
G. Najafian
Keyword(s):  
Nonlinear System ◽  
Probability Distribution ◽  
Extreme Values ◽  
System Modelling ◽  
Wave Loading ◽  
Offshore Structure ◽  
Short Term ◽  
Extreme Response ◽  
Finite Memory

Offshore structures are exposed to random wave loading in the ocean environment and hence the long-term probability distribution of the extreme values of their response to wave loading is of great value in the design of these structures. Due to nonlinearity of the drag component of Morison 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 extreme response probability distributions are not available. However, it has recently been shown that the short-term response of an offshore structure exposed to Morison wave loading can be approximated by the response of an equivalent finite-memory nonlinear system (FMNS). In this paper, the approximate FMNS models are used to determine both the short-term and the long-term probability distribution of the response extreme values with great efficiency.

Catheter-directed foam sclerotherapy treatment of saphenous vein incompetence

VASA ◽  
2012 ◽  
Vol 41 (2) ◽  
pp. 120-124 ◽  
Author(s):  
Asciutto ◽  
Lindblad
Keyword(s):  
Saphenous Vein ◽  
Short Term ◽  
Foam Sclerotherapy ◽  
Results Of Treatment ◽  
Ulcer Healing Rate ◽  
Complete Obliteration ◽  
Ceap Classification ◽  
One Year ◽  
The One

Background: The aim of this study is to report the short-term results of catheter-directed foam sclerotherapy (CDFS) in the treatment of axial saphenous vein incompetence. Patients and methods: Data of all patients undergoing CDFS for symptomatic primary incompetence of the great or small saphenous vein were prospectively collected. Treatment results in terms of occlusion rate and patients’ grade of satisfaction were analysed. All successfully treated patients underwent clinical and duplex follow-up examinations one year postoperatively. Results: Between September 2006 and September 2010, 357 limbs (337 patients) were treated with CDFS at our institution. Based on the CEAP classification, 64 were allocated to clinical class C3 , 128 to class C4, 102 to class C5 and 63 to class C6. Of the 188 patients who completed the one year follow up examination, 67 % had a complete and 14 % a near complete obliteration of the treated vessel. An ulcer-healing rate of 54 % was detected. 92 % of the patients were satisfied with the results of treatment. We registered six cases of thrombophlebitis and two cases of venous thromboembolism, all requiring treatment. Conclusions: The short-term results of CDFS in patients with axial vein incompetence are acceptable in terms of occlusion and complications rates.

Hidden “holes” in the capital of banks and the supply of credit to the real sector of economy

2018 ◽  
pp. 49-68 ◽  
Author(s):  
M. E. Mamonov
Keyword(s):  
Credit Risk ◽  
The Other ◽  
Real Sector ◽  
Capital Management ◽  
Loan Loss ◽  
Short Term ◽  
The Real ◽  
Ex Post ◽  
The One

Our analysis documents that the existence of hidden “holes” in the capital of not yet failed banks - while creating intertemporal pressure on the actual level of capital - leads to changing of maturity of loans supplied rather than to contracting of their volume. Long-term loans decrease, whereas short-term loans rise - and, what is most remarkably, by approximately the same amounts. Standardly, the higher the maturity of loans the higher the credit risk and, thus, the more loan loss reserves (LLP) banks are forced to create, increasing the pressure on capital. Banks that already hide “holes” in the capital, but have not yet faced with license withdrawal, must possess strong incentives to shorten the maturity of supplied loans. On the one hand, it raises the turnovers of LLP and facilitates the flexibility of capital management; on the other hand, it allows increasing the speed of shifting of attracted deposits to loans to related parties in domestic or foreign jurisdictions. This enlarges the potential size of ex post revealed “hole” in the capital and, therefore, allows us to assume that not every loan might be viewed as a good for the economy: excessive short-term and insufficient long-term loans can produce the source for future losses.

scholarly journals Time and Frequency Domain Dynamic Analysis of Offshore Mooring

2021 ◽  
Vol 9 (7) ◽  
pp. 781
Author(s):  
Shi He ◽  
Aijun Wang
Keyword(s):  
Dynamic Analysis ◽  
Frequency Domain ◽  
Time Domain ◽  
Linearization Method ◽  
Euler Method ◽  
Single Component ◽  
Hydrodynamic Drag ◽  
Lumped Mass ◽  
Mooring Lines ◽  
The Time Domain

The numerical procedures for dynamic analysis of mooring lines in the time domain and frequency domain were developed in this work. The lumped mass method was used to model the mooring lines. In the time domain dynamic analysis, the modified Euler method was used to solve the motion equation of mooring lines. The dynamic analyses of mooring lines under horizontal, vertical, and combined harmonic excitations were carried out. The cases of single-component and multicomponent mooring lines under these excitations were studied, respectively. The case considering the seabed contact was also included. The program was validated by comparing with the results from commercial software, Orcaflex. For the frequency domain dynamic analysis, an improved frame invariant stochastic linearization method was applied to the nonlinear hydrodynamic drag term. The cases of single-component and multicomponent mooring lines were studied. The comparison of results shows that frequency domain results agree well with nonlinear time domain results.

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