Kernel Function Definition Completion for Time–Domain State–Space Representations of Radiation Forces: Application to the Hankel Singular Value Decomposition

Type Article
Date 2021-07
Language English
Author(s) Lecuyer-Le Bris RomainORCID1, Le Boulluec Marc1, Charpentier Jean-FrédéricORCID2, Benbouzid MohamedORCID3, 4
Affiliation(s) 1 : Laboratoire Comportement des Structures en Mer, IFREMER, BP 70, 29280 Plouzané, France
2 : Institut de Recherche de l’Ecole Navale (EA 3436 IRENav), French Naval Academy, 29400 Brest, France
3 : Institut de Recherche Dupuy de Lôme (UMR CNRS 6027, IRDL), University of Brest, 29238 Brest, France
4 : Logistics Engineering College, Shanghai Maritime University, Shanghai 201306, China
Source Journal Of Marine Science And Engineering (2077-1312) (MDPI AG), 2021-07 , Vol. 9 , N. 7 , P. 768 (23p.)
DOI 10.3390/jmse9070768
Note This article belongs to the Section Ocean Engineering
Keyword(s) state-space, convolution replacement, Hankel singular value decomposition, discrete model, kernel function
Abstract

This paper focuses on the formulation of state–space representations of radiation forces for marine structures using Hankel Singular Value Decomposition (HSVD), a method used to obtain a state–space realization from a Hankel matrix, with the classical definition of the kernel function and its new definition given in this paper. The first part shows the influence of a term commonly neglected and the resulting improvement by taking this term into account. The second part will focus on the feedthrough matrix to understand why some models have none and why some others, such as HSVD, have one. An exact definition of the kernel function will be given underlying its discontinuity and its causality. This study also shows the interest of extrapolating hydrodynamic coefficients before approaching radiation forces by a state–space model.

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Lecuyer-Le Bris Romain, Le Boulluec Marc, Charpentier Jean-Frédéric, Benbouzid Mohamed (2021). Kernel Function Definition Completion for Time–Domain State–Space Representations of Radiation Forces: Application to the Hankel Singular Value Decomposition. Journal Of Marine Science And Engineering, 9(7), 768 (23p.). Publisher's official version : https://doi.org/10.3390/jmse9070768 , Open Access version : https://archimer.ifremer.fr/doc/00706/81764/