Parametric Interpolants for Frequency-Domain Models of Marine Structures in the Loewner Framework

Traditionally, the dynamic analysis of marine structures is based on linear potential flow theory assumptions, in which a frequency-domain-based characterisation is seemingly computed using hydrodynamic codes. To circumvent the non-parametric nature of such models, this paper proposes the construction of parametric interpolants for marine structures, based on the Loewner framework. The Loewner approach to interpolation utilises pure frequency-based responses only, producing interpolants (dynamical models) in terms of descriptor systems employing simple projections, avoiding altogether the use of optimisation routines. Furthermore, since Loewner interpolants are, in general, not guaranteed to be input-output stable, we employ an algorithm to achieve optimal stability enforcement in <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{R} \mathcal{H}_{\infty}$</tex>, by solving an associated Nehari problem. The overall performance of the proposed interpolants is assessed in detail, considering a numerical case study featuring a benchmark offshore structure.