Predictions of multi-scale vortex-induced vibrations based on a multi-fidelity data assimilation method

Abstract

This paper presents a data assimilation method based on the POD-DeepONet structure to fuse two types of fidelity data from vortex-induced vibration (VIV) problems. The data is mainly focused on amplitude response in different oncoming flow cases from cross-flow (CF) and inline (IL) directions for new flow speed predictions. The low-fidelity data in this paper is calculated from a semi-empirical code called DAVIV, while the high-fidelity data is measured from laboratory experiments. For a complex nonlinear correlation in amplitude and phase error between low and high-fidelity data, the POD-DeepONet structure receives better accuracy and more stable predictions than Neural Network with few training cases. It can successfully reconstruct the amplitude response along the marine riser and capture the changing trend with the oncoming flow speed. The POD-DeepONet is then applied to predict the VIV cross-flow and inline responses with different datasets. The prediction of mean square error (MSE) shows an exponential decline trend with the increasing case number for training. With the exponentially fitted MSE formula, the required case number under the expected error can be quickly obtained, which may provide a reference for efficient and high-fidelity VIV response prediction in engineering.