A Comparison of Time Domain and Frequency Domain Approaches for the Fully Coupled Analysis of Deepwater Floating Systems

2006 ◽  
Author(s):  
Ying Min Low ◽  
Robin S. Langley
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Coupled Analysis ◽  
Integration Scheme ◽  
Global Coordinate System ◽  
Mooring Lines ◽  
Frequency Domain Methods ◽  
The Time Domain ◽  
Fully Coupled ◽  
Fully Coupled Analysis

The recognition of the need for a fully coupled analysis of deepwater floating production systems has led to the research and development of several coupled analysis tools in recent years. Barring a handful of exceptions, these tools and available commercial packages are invariably in the time domain. This has resulted in a much better understanding and confidence in time domain coupled analysis, but less so for the frequency domain approach. In this paper, the viability of frequency domain coupled analysis is explored by performing a systematic comparison of time and frequency domain methods using computer programs developed in-house. In both methods, a global coordinate system is employed where the vessel is modeled with six degrees-of-freedom, while the mooring lines and risers are discretized as lumped masses connected by extensional and rotational springs. Coupling between the vessel and the mooring lines is achieved by stiff springs, and the influence of inertia and damping from the lines are directly accounted for without the need for prior assumptions. First and second order wave forces generated from a random environment are applied on the vessel, as well as drag and inertia loading on the lines. For the time domain simulation, the Wilson-theta implicit integration scheme is employed to permit the use of relatively large time steps. The frequency domain analysis is highly efficient despite being formulated in global coordinates, owing to the banded characteristics of the mass, damping and stiffness matrices. The nonlinear drag forces are stochastically linearized iteratively. As both the time and frequency domain models of the coupled system are identical, a consistent assessment of the error induced by stochastic linearization can be made.

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.

Understanding the Dynamic Coupling Effects in Deep Water Floating Structures Using a Simplified Model

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Ying Min Low ◽  
Robin S. Langley
Keyword(s):  
Frequency Domain ◽  
Deep Water ◽  
Time Domain ◽  
Low Frequency ◽  
Wave Frequency ◽  
Computational Time ◽  
Coupled Analysis ◽  
Floating Platform ◽  
Coupling Effects ◽  
Mooring Lines

The global dynamic response of a deep water floating production system needs to be predicted with coupled analysis methods to ensure accuracy and reliability. Two types of coupling can be identified: one is between the floating platform and the mooring lines/risers, while the other is between the mean offset, the wave frequency, and the low frequency motions of the system. At present, it is unfeasible to employ fully coupled time domain analysis on a routine basis due to the prohibitive computational time. This has spurred the development of more efficient methods, including frequency domain approaches. A good understanding of the intricate coupling mechanisms is paramount for making appropriate approximations in an efficient method. To this end, a simplified two degree-of-freedom system representing the surge motion of a vessel and the fundamental vibration mode of the lines is studied for physical insight. Within this framework, the frequency domain equations are rigorously formulated, and the nonlinearities in the restoring forces and drag are statistically linearized. The model allows key coupling effects to be understood; among other things, the equations demonstrate how the wave frequency dynamics of the mooring lines are coupled to the low frequency motions of the vessel. Subsequently, the effects of making certain simplifications are investigated through a series of frequency domain analyses, and comparisons are made to simulations in the time domain. The work highlights the effect of some common approximations, and recommendations are made regarding the development of efficient modeling techniques.

Hydrodynamic Interactions and Relative Motions Analysis for Installation of an Extendable Draft Platform

2009 ◽  
Author(s):  
Bonjun Koo ◽  
Jang Whan Kim
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Domain Analysis ◽  
Frequency Domain Analysis ◽  
Hydrodynamic Interactions ◽  
Coupled Analysis ◽  
Heave Plate ◽  
The Time Domain ◽  
Stabilized Platform ◽  
Relative Motions

The Extendable Draft Platform (EDP) is a deep draft, column stabilized platform with a deck box support for topsides and a single, deep draft heave plate that provides suitable motion characteristics to enable the use of dry tree top tensioned risers. The EDP can be fabricated with topsides installed on the deck box and commissioned quayside in a typical construction yard. With the columns in the retracted position, the EDP floats on its deck box and can be towed, in this configuration, to the location of interest. Once the EDP is transported to its final site, the columns and heave plate are lowered to their final operating draft. During the lowering sequence, the deck box and the lower hull become two relatively independent bodies, mechanically connected by chains that control the lowering of the columns and heave plate, and the guides between the deck box and the columns. This multi-body system is hydrodynamically coupled because of radiated and diffracted waves. The global performance analyses of the installation process (lowering of the lower hull) are carried out by three different methods. The first method is frequency-domain analysis by WAMIT and a frequency domain motion solver. In the frequency domain analysis, all the mechanical connections are modeled as linear springs. The second method is time-domain, partially coupled analysis using HARP/WINPOST. In this analysis, the off diagonal 6×6 hydrodynamic interactions are ignored. The last method is a time domain, fully coupled analysis using HARP/WINPOST. In this analysis, full 12×12 hydrodynamic interactions are considered. In the time domain analyses, the mechanical couplings between each column and deck box are modeled with linear springs and the chain connections are modeled with slender rods by using the nonlinear finite element method. This paper presents and compares analysis results based on the three methods for relative motions and loads between the deck box and the lower hull during the lowering of the columns and heave plate.

Comparing Frequency and Time Domain Simulations for Geometry Optimization of a Floating Offshore Wind Turbine Mooring System

2018 ◽  
Author(s):  
Ajit C. Pillai ◽  
Philipp R. Thies ◽  
Lars Johanning
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Pareto Front ◽  
Geometry Optimization ◽  
Offshore Wind ◽  
Offshore Wind Turbine ◽  
Mooring System ◽  
Efficient Design ◽  
Frequency Domain Methods ◽  
The Time Domain

This paper explores geometry optimization of an offshore wind turbine’s mooring system considering the minimization of the material cost and the cumulative fatigue damage. A comparison of time domain simulations against frequency domain simulations is made to explore the suitability of these methods to the design process. The efficient design options, the Pareto front, from the frequency domain study are also re-evaluated using time domain simulations and compared against the time domain Pareto front. Both the time and frequency domain results show optimal results utilizing similar design philosophies, however, the frequency domain methods severely under predict the fatigue loads in the mooring system and incorrectly class infeasible solutions as feasible. The frequency domain is therefore not suitable for optimization use without some external means of applying engineering constraints. Furthermore, re-evaluation of the frequency domain solutions provides guidance to the uncertainty and the necessary design fatigue factors required if implementing frequency domain methods in design.

A Simplified Model for the Study of Dynamic Coupling Effects in Deepwater Floating Structures

2005 ◽  
Author(s):  
Ying Min Low ◽  
Robin S. Langley
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Low Frequency ◽  
Wave Frequency ◽  
Computational Time ◽  
Coupled Analysis ◽  
Floating Platform ◽  
Coupling Effects ◽  
Fundamental Vibration ◽  
Mooring Lines

As the exploitation of hydrocarbon moves towards deeper waters, the global dynamic response of a floating production system needs to be predicted with coupled analysis methods to ensure accuracy and reliability. Two types of coupling can be identified: one is between the floating platform and the mooring lines/risers, while the other is between the mean offset, the wave frequency and the low frequency motions of the system. At present, it is unfeasible to employ fully coupled time domain analysis on a routine basis due to prohibitive computational time. This has spurred the development of more efficient methods that account for the various couplings, including frequency domain approaches. It is paramount for the complex coupling mechanisms to be well understood before appropriate simplifications and assumptions can be made. In this paper, a simplified two degree-of-freedom system representing the surge motion of a vessel and the fundamental vibration mode of the lines is examined which captures the important underlying physics. Within this framework, the frequency domain equations are rigorously formulated, and the nonlinearities in the restoring forces and drag are stochastically linearized. The model allows key coupling effects to be identified: among other things, the equations demonstrate how the wave frequency dynamics of the mooring lines are coupled to the low frequency motions of the vessel. Subsequently, the effects of making certain simplifications are investigated through a series of frequency domain spectral analyses, and comparisons are made to simulations in the time domain. The work highlights the effect of certain common approximations, and recommendations are made regarding the development of efficient modeling techniques.

scholarly journals Filters, Waves and Spectra

Econometrics ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 35 ◽  
Author(s):  
D. Pollock
Keyword(s):  
Frequency Response ◽  
Frequency Domain ◽  
Time Domain ◽  
Econometric Analysis ◽  
Frequency Domain Methods ◽  
The Time Domain ◽  
Filtering Techniques

Econometric analysis requires filtering techniques that are adapted to cater to data sequences that are short and that have strong trends. Whereas the economists have tended to conduct their analyses in the time domain, the engineers have emphasised the frequency domain. This paper places its emphasis in the frequency domain; and it shows how the frequency-domain methods can be adapted to cater to short trended sequences. Working in the frequency domain allows an unrestricted choice to be made of the frequency response of a filter. It also requires that the data should be free of trends. Methods for extracting the trends prior to filtering and for restoring them thereafter are described.

scholarly journals Modeling the Gas price data Using Periodogram and Fourier Series Analysis: استخدام التحليل في مجال التردد لنمذجة بيانات مبيعات الغاز الطبيعي في الولايات المتحدة الأمريكية بواسطة شكل الدورة وتحليل سلسلة فورير

2019 ◽  
Vol 3 (1) ◽  
Author(s):  
Safia Abdullah Al Fadhel, Amal Al-Ser Al-khadir, Obeid Mahmo
Keyword(s):  
Fourier Series ◽  
Frequency Domain ◽  
Time Domain ◽  
Domain Analysis ◽  
The United States ◽  
Frequency Domain Method ◽  
Series Analysis ◽  
Frequency Domain Methods ◽  
The Time Domain ◽  
Fourier Series Analysis

:   This paper takes into account the application of the Periodogram and the Fourier Series Analysis. It is one of the non-parametric methods of Frequency domain analysis or spectral analysis of time series using Gas sales data in the United States of America from 1993-2014. In order to achieve these objectives، the data were obtained and then the Periodogram and the Fourier series methods were used to analyze the data. Based on the analysis، the cycle of variability within the period under study was 135 months، and a high Accuracy data model was estimated for the Fourier series which included trend، seasonal and error components. The RMSE، MASE and MAE standards were used to confirm the efficiency of the model and the model was then used to predict gas sales for six months، and we have 90% 95% confidence intervals for predictions. In addition، a time domain analysis was provided for the data series using Bok Jenkins method to obtain the appropriate ARMA model and to generate Predictions. Finally، a comparison was made between the accuracy measures of the time domain and frequency domain methods The frequency domain method competed with the time domain and the slight difference in efficiency.

Coupled Dynamic Analysis of a Moored Spar in Random Waves and Currents (Time-Domain Versus Frequency-Domain Analysis)

1999 ◽  
Vol 121 (3) ◽  
pp. 194-200 ◽  
Author(s):  
Z. Ran ◽  
M. H. Kim ◽  
W. Zheng
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Software Package ◽  
Volterra Series ◽  
Domain Analysis ◽  
Frequency Domain Analysis ◽  
Random Waves ◽  
Mooring Lines ◽  
Drag Forces ◽  
The Time Domain

Nonlinear coupled responses of a moored spar in random waves with and without colinear currents are investigated in both time and frequency domains. The first and second-order wave forces, added mass and radiation damping, and wave drift damping are calculated from a hydrodynamics software package called WINTCOL. The total wave force time series (or spectra) are then generated in the time (or frequency) domain based on a two-term Volterra series model. The mooring dynamics are solved using the software package WINPOST, which is based on a generalized-coordinate-based finite element method. The mooring lines are attached to the platform through linear and rotational springs and dampers so that various boundary conditions can be modeled using proper spring and damping values. In the time-domain analysis, the nonlinear drag forces on the hull and mooring lines are applied at the instantaneous position. In the frequency-domain analysis, nonlinear drag forces are stochastically linearized, and solutions are obtained by an iterative procedure. The time-domain results are systematically compared with the frequency-domain results.

Extreme Response Analysis of Floating Structures Using Coupled Frequency Domain Analysis

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Ying Min Low ◽  
Andrew J. Grime
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Low Frequency ◽  
Domain Analysis ◽  
Frequency Domain Analysis ◽  
Coupled Analysis ◽  
Statistical Techniques ◽  
Frequency Domain Methods ◽  
Extreme Response ◽  
The Mean

In the dynamic analysis of a floating structure, coupled analysis refers to a procedure in which the vessel, moorings, and risers are modeled as a whole system, thus allowing for interactions between various system components. Because coupled analysis in the time domain is impractical owing to prohibitive computational costs, a highly efficient frequency domain approach was developed in a previous work, wherein the drag forces are linearized. The study showed that provided the geometric nonlinearity of the moorings/risers is insignificant, which often holds for ultradeepwater systems, the mean-squared responses yielded by the time and frequency domain methods are in close agreement. Practical design is concerned with the extreme response, for which the mean upcrossing rate is a key parameter. Crossing rate analysis based on statistical techniques is complicated as the total response occurs at two timescales, with the low frequency contribution being notably non-Gaussian. Many studies have been devoted to this problem, mainly relying on a technique originating from Kac and Siegert; however, these studies have mostly been confined to a single-degree-of-freedom system. The aim of this work is to apply statistical techniques in conjunction with frequency domain analysis to predict the extreme responses of the coupled system, in particular the modes with a prominent low frequency component. It is found that the crossing rates for surge, sway and yaw thus obtained agree well with those extracted from time domain simulation, whereas the result for roll is less favorable, and the reasons are discussed.

Investigation of Transient Thermal Analysis Computational Efficiency Improvements via Frequency Domain Methods

2012 ◽  
Author(s):  
Gregory A. Banyay ◽  
John C. Brigham ◽  
Evgenii Rudnyi
Keyword(s):  
Thermal Analysis ◽  
Frequency Domain ◽  
Time Domain ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Model Order ◽  
Frequency Domain Methods ◽  
Thermal Transient ◽  
The Time Domain ◽  
Transient Thermal

During the operation of a Nuclear Steam Supply System (NSSS), the possibility exists for certain thermal transients to occur in the Reactor Coolant System (RCS). These transients exhibit some amount of periodicity in terms of temperature versus time. The current method of solving for temperature or thermal-mechanical stress states in the nuclear pressure vessel industry is by solving the governing equations in the time domain. For some analytical situations, significant computational savings could be realized by solving the thermal transient problem in the frequency domain. That is, the time, memory, and disk space required to solve the analysis is much less in the frequency domain than in the time domain. Two frequency domain methods are discussed in this paper. First, a Laplace-based model order reduction approach is applied to a reactor vessel component subjected to a representative thermal transient. Second, the feasibility of a Fourier-based spectral approach is discussed. For transient thermal analysis, it is shown that by employing model order reduction, significant computational savings can be realized with insignificant compromise in the accuracy of results.

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