Data-driven identification of coupling closure equations in vortex-induced vibrations phenomenological models

High-fidelity computational models for describing fluid–structure interaction used in vortex-induced vibrations applications, even providing fine and accurate descriptions of quantities of interest, might not be adequate when multiple code runs are required, like in exploring an input space or synthesizing a controller. Reduced order or simplified models play a crucial role in such context. Here, wake oscillator modeling is adopted, in which, as the interest is devoted to the solid response, the flow, more specifically the action of its vortex shedding, is described by a nonlinear oscillator. This leads to the need to introduce closure models for the fluid–structure interaction. Previous works use suggested functional forms and identify the associated parameters through inverse formulations and available data. A different approach is pursued here. Instead of estimating parameters, the missing term describing the action of the flow on the structure is cast as a model discrepancy to be discovered through the sparse identification of nonlinear dynamics, given a previously chosen library of functions, as identifying a form sheds light on the underlying physics and helps in building a predictive model. An example, dealing with multiple scenarios, is explored from different perspectives, in order to assess the performance of the proposed methodology.