Time-domain parametric models for floating structures: A Loewner-based approach

Design, control, and optimisation of offshore floating structures have undergone significant evolution in recent years, driven by cutting-edge technology, including novel marine renewable energy sources and autonomous underwater vehicles. A key cornerstone is the availability of mathematical models capable of providing an accurate (yet computationally tractable) prediction of their behaviour, under different ocean conditions. The most widely adopted approach for capturing fluid–structure interactions is based on linear potential flow theory, where the system’s hydrodynamic behaviour is described through a finite set of frequency-dependent linear coefficients. A well-known limitation of this frequency-domain approach is its inherently non-parametric nature: if not parameterised accordingly, effective time-domain simulation necessitates the numerical solution of a convolution operator, which describes memory effects due to the surrounding fluid, an approach inconvenient for both simulation (computational) and control design (representational compatibility). Not only is a closed-form expression fundamental, but any candidate parametric model also needs to comply with the physical properties characterising a floating structure, including input/output stability, minimum-phase behaviour, and passivity. This paper presents a novel approach to producing physically consistent parametric structures for time-domain modelling of floating systems, utilising a Loewner-based method. The models, capable of providing approximate interpolation of raw frequency-domain data computed with off-the-shelf hydrodynamic solvers, accurately capture the complex behaviour of multi-mode and multi-body offshore structures, while respecting the dynamical properties associated with the system’s physics. The technique is illustrated in detail, using four different offshore structures from various fields of ocean engineering, highlighting the benefits of the proposed time-domain modelling framework.