Hammerstein-Wiener based reduced-order model for vortex-induced non-linear fluid-structure interaction

Fluid-structure interaction (FSI) phenomena are of interest in several engineering fields. It is highly desirable to develop computationally efficient models to predict the dynamics of FSI. The complexity of modeling lies in the highly non-linear response of both the fluid and structure. The current study proposes an overall model containing two blocks corresponding to a force model and a structural model. The force model consists of two submodels: one for the amplitude and one for the frequency, where the latter is composed of an input/output linear model and a non-linear corrector. The amplitude submodel and the non-linear corrector term in the frequency submodel are modeled using an Hammerstein-Wiener modeling technique in which the non-linear input and output functions are determined by training neural networks using a training dataset. The current model is tested on a well-known fluid-structure interaction problem: a suspended rigid cylinder immersed in a flow at a low Reynolds number regime that exhibits a non-linear behavior. First, a training dataset is generated for a given input profile using a high-fidelity numerical simulation and it is used to train the reduced-order model. Subsequently, the trained model is given a different input profile (i.e., a validation profile) to compare its predictive capability against the high-fidelity numerical simulation. The validation profile is significantly different from the one used for training. The predictive performance of the current reduced-order model is further compared with the results obtained from a reduced-order model that uses polynomial fitting. We demonstrate that the current model provides a superior performance for the validation profile, i.e., it results in a better prediction.