Sparse Sensing and DMD-Based Identification of Flow Regimes and Bifurcations in Complex Flows

We present a sparse sensing framework based on dynamic mode decomposition (DMD) to identify flow regimes and bifurcations in large-scale thermofluid systems. Motivated by real-time sensing and control of thermal-fluid flows in buildings and equipment, we apply this method to a direct numerical simulation (DNS) data set of a two-dimensional laterally heated cavity. The resulting flow solutions can be divided into several regimes, ranging from steady to chaotic flow. The DMD modes and eigenvalues capture the main temporal and spatial scales in the dynamics belonging to different regimes. Our proposed classification method is data driven, robust w.r.t. measurement noise, and exploits the dynamics extracted from the DMD method. Namely, we construct an augmented DMD basis, with "built-in" dynamics, given by the DMD eigenvalues. This allows us to employ a short time series of data from sensors, to more robustly classify flow regimes, particularly in the presence of measurement noise. We also exploit the incoherence exhibited among the data generated by different regimes, which persists even if the number of measurements is small compared to the dimension of the DNS data. The data-driven regime identification algorithm can enable robust low-order modeling of flows for state estimation and control.