Hybrid frequency-time domain models for dynamic response analysis of marine structures

Time-domain models of marine structures based on frequency domain data are usually built upon the Cummins equation. This type of model is a vector integro-differential equation which involves convolution terms. These convolution terms are not convenient for analysis and design of motion control systems. In addition, these models are not efficient with respect to simulation time, and ease of implementation in standard simulation packages. For these reasons, different methods have been proposed in the literature as approximate alternative representations of the convolutions. Because the convolution is a linear operation, different approaches can be followed to obtain an approximately equivalent linear system in the form of either transfer function or state-space models. This process involves the use of system identification, and several options are available depending on how the identification problem is posed. This raises the question whether one method is better than the others. This paper therefore has three objectives. The first objective is to revisit some of the methods for replacing the convolutions, which have been reported in different areas of analysis of marine systems: hydrodynamics, wave energy conversion, and motion control systems. The second objective is to compare the different methods in terms of complexity and performance. For this purpose, a model for the response in the vertical plane of a modern containership is considered. The third objective is to describe the implementation of the resulting model in the standard simulation environment Matlab/Simulink.

[1]  E. R. Jefferys.  Simulation of wave power devices , 1984 .

[2]  Β. L. HO,et al.  Editorial: Effective construction of linear state-variable models from input/output functions , 1966 .

[3]  Jørgen Juncher Jensen,et al.  Non-linear wave loads and ship responses by a time-domain strip theory , 1998 .

[4]  Sun-Yuan Kung,et al.  A new identification and model reduction algorithm via singular value decomposition , 1978 .

[5]  Masashi Kashiwagi,et al.  Transient responses of a VLFS during landing and take-off of an airplane , 2004 .

[6]  L. Tick.  Differential Equations With Frequency-Dependent Coefficients , 1959 .

[7]  Alain H. Clément,et al.  Absorption of outgoing waves in a numerical wave tank using a self-adaptive boundary condition , 2000 .

[8]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[9]  C. Guedes Soares,et al.  An implementation of the method of auxiliary state variables for solving seakeeping problems , 2005 .

[10]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[11]  Tristan Perez,et al.  MIMO and SISO identification of radiation force terms for models of marine structures in waves , 2007 .

[12]  Paul Golovato.  A Study of the Transient Pitching Oscillations of a Ship , 1959 .

[13]  O. Egeland,et al.  State-space representation of radiation forces in time-domain vessel models , 2005 .

[14]  Jeffrey M. Falzarano,et al.  Application of extended state space to nonlinear ship rolling , 1998 .

[15]  Jan Tommy Gravdahl,et al.  Modeling and simulation for automatic control , 2002 .

[16]  O. Egeland,et al.  Comparative study of algorithms for obtaining reduced order state-space form of radiation forces , 2005, Proceedings of OCEANS 2005 MTS/IEEE.

[17]  Heinrich Söding,et al.  Leckstabilität im Seegang , 1982 .

[18]  Chi-Tsong Chen,et al.  Linear System Theory and Design , 1995 .

[19]  J. Falnes,et al.  STATE-SPACE MODELLING OF A VERTICAL CYLINDER IN HEAVE , 1995 .

[20]  E. C. Levy.  Complex-curve fitting , 1959, IRE Transactions on Automatic Control.

[21]  JohannesFalnes.  STATE-SPACE MODELLING OF DYNAMIC SYSTEMS IN OCEAN ENGINEERING , 1998 .

[22]  C. Sanathanan,et al.  Transfer function synthesis as a ratio of two complex polynomials , 1963 .

[23]  John V. Wehausen,et al.  Initial-value problem for the motion in an undulating sea of a body with fixed equilibrium position , 1967 .

[24]  Christopher J. Damaren,et al.  Time-domain floating body dynamics by rational approximation of the radiation impedance and diffraction mapping , 2000 .

[25]  F. Ursell,et al.  The decay of the free motion of a floating body , 1964, Journal of Fluid Mechanics.

[26]  K. R. Goheen,et al.  Time Domain Models from Frequency Domain Descriptions: Application to Marine Dynamics , 1992 .

[27]  Paul Van Dooren,et al.  Low order potential damping models for surface vessels , 2006 .

[28]  Thomas Kailath,et al.  Linear Systems , 1980 .

[29]  W. Cummins.  THE IMPULSE RESPONSE FUNCTION AND SHIP MOTIONS , 2010 .

[30]  W. E. Cummins,et al.  The Impulse Response Function and Ship Motion , 1962 .

[31]  Torgeir Moan,et al.  LINEAR AND NONLINEAR HYDROELASTIC ANALYSIS OF HIGH-SPEED VESSELS , 1996 .

[32]  Olav Egeland,et al.  Frequency-Dependent Added Mass in Models for Controller Design for Wave Motion Damping , 2003 .

[33]  Thor I. Fossen.  A Nonlinear Unified State-Space Model for Ship Maneuvering and Control in a Seaway , 2005, Int. J. Bifurc. Chaos.

[34]  Torgeir Moan,et al.  Time Domain Hydroelastic Analysis of a Flexible Marine Structure Using State-Space Models , 2007 .

[35]  Gene F. Franklin,et al.  An error bound for a discrete reduced order model of a linear multivariable system , 1987 .

[36]  Torgeir Moan,et al.  Dynamics of A Force-Compensated Two-Body Wave Energy Converter in Heave with Hydraulic Power Take-Off Subject To Phase Control , 2007 .

[37]  Odd M. Faltinsen,et al.  Sea loads on ships and offshore structures , 1990 .

[38]  Mario A. Jordán,et al.  Optimal identification of potential-radiation hydrodynamics for moored floating structures—a new general approach in state space , 2004 .

[39]  Thor I. Fossen,et al.  Marine Control Systems Guidance, Navigation, and Control of Ships, Rigs and Underwater Vehicles , 2002 .