Data driven techniques for modal decomposition and reduced-order modelling of fluids

Abstract

In this thesis, a number of data-driven techniques are proposed for the analysis and extraction of reduced-order models of fluid flows. Throughout the thesis, there has been an emphasis on the practicality and interpretability of data-driven feature-extraction techniques to aid practitioners in flow-control and estimation. The first contribution uses a graph theoretic approach to analyse the similarity of modes extracted using data-driven modal decomposition algorithms to give a more intuitive understanding of the degrees of freedom in the underlying system. The method extracts clusters of spatially and spectrally similar modes by post-processing the modes extracted using DMD and its variants. The second contribution proposes a method for extracting coherent structures, using snapshots of high dimensional measurements, that can be mapped to a low dimensional output of the system. The importance of finding such coherent structures is that in the context of active flow control and estimation, the practitioner often has to rely on a limited number of measurable outputs to estimate the state of the flow. Therefore, ensuring that the extracted flow features can be mapped to the measured outputs of the system can be beneficial for estimating the state of the flow. The third contribution concentrates on using neural networks for exploiting the nonlinear relationships amongst linearly extracted modal time series to find a reduced order state, which can then be used for modelling the dynamics of the flow. The method utilises recurrent neural networks to find an encoding of a high dimensional set of modal time series, and fully connected neural networks to find a mapping between the encoded state and the physically interpretable modal coefficients. As a result of this architecture, the significantly reduced-order representation maintains an automatically extracted relationship to a higher-dimensional, interpretable state.