Abstract

This work proposes a special type of Finite Element (FE) technology – the Empirical Interscale FE method – for modeling heterogeneous structures in the small strain regime, for both dynamic and static analyses. The method combines a domain decomposition framework, where interface conditions are established through “fictitious” frames, with dimensional hyperreduction at subdomain level. Similar to other multiscale FE methods, the structure is assumed to be partitioned into coarse-scale elements, each of these elements is equipped with a fine-scale subgrid, and the displacements of the boundaries of the coarse-scale elements are described by standard polynomial FE shape functions. The distinguishing feature of the proposed method is the employed “interscale” variational formulation, which directly relates coarse-scale nodal internal forces with fine-scale stresses, thereby avoiding the typical nested local/global problems that appear, in the nonlinear regime, in other multiscale methods. This distinctive feature, along with hyperreduction schemes for nodal internal and external body forces , greatly facilitate the implementation of the proposed formulation in existing FE codes for solid elements. Indeed, one only has to change the location and weights of the integration points, and to replace a few polynomial-based FE matrices with “empirical” operators, i.e., derived from the information obtained in appropriately chosen computational experiments. We demonstrate that the elements resulting from this formulation are not afflicted by volumetric locking when dealing with nearly-incompressible materials, and that they can handle non-matching fine-scale grids as well as curved structures. Last but not least, we show that, for periodic structures, this method converges upon mesh refinement to the solution delivered by classical first-order computational homogenization. Thus, although the method does not presuppose scale separation, it can represent solutions in this limiting case by taking sufficiently small coarse-scale elements.

Abstract

Digital twins (DTs) offer significant promise for condition-based maintenance of floating offshore wind turbines (FOWTs); however, existing solutions typically compromise either on physical rigor or real-time computational performance. This paper presents a real-time DT framework that resolves this trade-off by embedding a hydro-elastic reduced-order model (ROM) that accurately captures structural dynamics and fluid–structure interaction. Integrated in a cloud-ready Internet of Things architecture, the ROM reconstructs full-field displacements, von Mises stresses, and fatigue metrics with near real-time responsiveness. Validation on the 5 MW OC4-DeepCWind semi-submersible platform shows that the ROM reproduces finite-element (FEM) displacements and stresses with relative errors below 1%. A three-hour load case is solved in 0.69 min for displacements and 3.81 min for stresses on a consumer-grade NVIDIA RTX 4070 Ti GPU—over two orders of magnitude faster than the full FEM model—while one million fatigue stress histories (1000 hotspots×1000 operating scenarios) are processed in 37 min. This efficiency enables continuous structural monitoring, rapid *what-if* assessments and timely decision-making for targeted inspections and adaptive control. By effectively combining physics-based reduced-order modeling with high-throughput computation, the proposed framework overcomes key barriers to DT deployment: computational overhead, physical fidelity and scalability. Although demonstrated on a steel platform, the approach is readily extensible to composite structures and multi-turbine arrays, providing a robust foundation for cost-effective and reliable deep-water wind-energy operations.