In this contribution, we consider the Dynamic Mode Decomposition (DMD) framework as a purely data-driven tool to investigate both standard and actuated turbulent channel databases via Direct Numerical Simulation (DNS). Both databases have comparable Reynolds number Re ≈ 3600. The actuation consists in the imposition of a streamwise-varying sinusoidal spanwise velocity at the wall, known to lead to drag reduction. Specifically, a composite-based DMD analysis is conducted, with hybrid snapshots composed by skin friction and Reynolds stresses. A small number of dynamic modes (∼3–9) are found to recover accurately the DNS Reynolds stresses near walls. Moreover, the DMD modes retrieved propagate at a range of phase speeds consistent with those reported in the literature. We conclude that composite DMD is an attractive, purely data-driven tool to study turbulent flows. On the one hand, DMD is helpful to identify features associated with the drag, and on the other hand, it reveals the changes in flow structure when actuation is imposed.

Dynamic Mode Decomposition (DMD) techniques have risen as prominent feature identification methods in the field of fluid dynamics. Any of the multiple variables of the DMD method allows to identify meaningful features from either experimental or numerical flow data on a data-driven manner. Performing a DMD analysis requires handling matrices $\mathbf{V}\in {\mathbb{R}}^{n_p\times N}$ , where $n_p$ and N are indicative of the spatial and temporal resolutions. The DMD analysis of a complex flow field requires long temporal sequences of well resolved data, and thus the memory footprint may become prohibitively large. In this contribution, the effect that principled spatial agglomeration (i.e., reduction in $n_p$ via clustering) has on the results derived from the DMD analysis is investigated. We compare twelve different clustering algorithms on three testcases, encompassing different flow regimes: a synthetic flow field, a $R{e}_D=60$ flow around a cylinder cross section, and a $R{e}_{\tau }\approx 200$ turbulent channel flow. The performance of the clustering techniques is thoroughly assessed concerning both the accuracy of the results retrieved and the computational performance. From this assessment, we identify DBSCAN/HDBSCAN as the methods to be used if only relatively high agglomeration levels are affordable. On the contrary, Mini-batch K-means arises as the method of choice whenever high agglomeration $\widetilde{n_p}/n_p\ll 1$ is possible.

Capacity prediction plays a critical role in battery health management. In recent years, the regeneration phenomenon has been considered to increase the accuracy of capacity prediction. Against this background, this method innovates upon the existing hybrid technique by integrating complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and adaptive neuro-fuzzy inference system (ANFIS). The advancement lies in the selective application of variational mode decomposition (VMD) to the intrinsic mode function identified by CEEMDAN, which exhibits regeneration features. This targeted re-decomposition allows the significant fluctuations in these components to be captured more effectively. The effectiveness of the proposed approach has been validated using NASA's lithium-ion battery aging datasets, showcasing an improved prediction accuracy and a better explanation for the capacity regeneration phenomenon. The research presents a significant contribution to the capacity prediction of lithium-ion batteries, providing a robust predictive framework that could be vital for the advancement of battery management systems.

A novel Dynamic Mode Decomposition (DMD) technique capable of handling non–uniformly sampled data is proposed. As it usual in DMD analysis, a Koopman assumption on consecutive snapshots is made. However, the technique here proposed presents two differences with established DMD methods: first, the Koopman assumption is established on the numerically discretized counterpart of a linearized state-equation; and second, a dimensionally–reduced view of the state data is considered. The performance of the new method, which we term θ-DMD, is assessed on three different, increasingly complex datasets: a synthetic flow field, a ReD = 60 flow around a cylinder cross section, and a Reτ = 200 turbulent channel flow. For the three datasets considered, whenever the dataset is uniformly sampled, the θ-DMD method provides comparable results to the original DMD method. Additionally, the θ-DMD is still capable of recovering relevant flow features from non–uniformly sampled databases, whereas DMD cannot. The proposed tool opens the way to conduct DMD analyses for non–uniformly sampled data, and can be useful e.g., when confronted with experimental datasets with missing data, or when facing numerical datasets generated using adaptive time-integration schemes. Keywords: modal decompositions, dynamic mode decomposition, feature detection, non–uniformly sampled datasets.