Using Autoregressive with Exogenous Input Models to Study Pulsatile Flows

The content of this paper shows the first outcomes of a supplementary method to simulate the behavior of a simple design formed by two rectangular leaflets under a pulsatile flow condition. These problems are commonly handled by using Fluid-Structure Interaction (FSI) simulations; however, one of its main limitations are the high computational cost required to conduct short time simulations and the vast number of parameter adjustments to simulate different scenarios. In order to overcome these disadvantages, we propose a system identification method with hereditary computation—AutoRegressive with eXogenous (ARX) input method—to train a model with FSI simulation outcomes and then use this model to simulate the outputs that are commonly measured from this kind of simulation, such as the pressure difference and the opening area of the leaflets. Numerical results of the presented methodology show that our model is able to follow the trend with significant agreement with the FSI results, with an average correlation coefficient R of Rtr=90.14% and Rtr=92.27% in training; whereas for validation, the average R is Rval=93.31% and Rval=83.08% for opening area and pressure difference, respectively. The system identification model is efficiently capable of estimating the outputs of the FSI approach; however, it is not intended to substitute FSI simulations, but to complement them when the requirement is to conduct many repetitions of the phenomena with similar conditions.