Classification Tree Analysis and Manifold Alignment of Manifold Learning-Based Turbulent Flow Abundances for Flow Characterization

Turbulent drag on flow structures, whether in air or water, represents a serious impediment to realizing flow efficiency for atmospheric and oceanic structures where there is a serious need to optimize energy expenditures.New research and technology have sought to go beyond mere understanding and characterization of flow structure boundary layers towards actual manipulation of them.Such state-of-the-art flow technology relies on high-resolution models which allow prediction and understanding of boundary layer spatio-temporal eddy structure.Machine learning modeling based on classification tree modeling and manifold alignment is performed as a statistical way of providing insight into flow similarity over both small and large-time scales for the time varying boundary layer eddy structure.Flow abundance values for velocity fluctuations in the mean flow direction and particle concentration are estimated for a sinusoidally forced flow field containing medium size particles of size 280 microns.This is done use large eddy simulation data cubes which capture the boundary layer and upper free stream turbulent structure over a single sinusoidal phase at 15• increments.The t-distributed stochastic neighbor embedding, locality preservation projection mapping, and multidimensional scaling are used to estimate low rank embeddings for velocity and concentration depth profiles over the boundary layer in the simulation data cubes.Consecutive two-dimensional latent space embeddings or manifolds of consecutively occurring velocity and concentration data sub-cubes demonstrate topologies which can be compared via Procrustes analysis, a form of manifold alignment.Rotation, translation, and size scaling of one data cube manifold is performed with respect to the data cube manifold occurring right after it in time with a mean square-based dissimilarity value calculated for the pair.Initial results show that the velocity abundances from all decompositions have high dissimilarity values throughout the wave cycle.The multidimensional scaling and locality preserving projection velocity abundances demonstrate small dips in dissimilarity at 0-15• and 180-195• phase transition intervals which are time periods of low sinusoidal turbulent shear stress.The dissimilarity curves for the t-distributed stochastic neighbor embedding velocity abundances are noisy and do not demonstrate strong evidence of local minimum values at this point, suggesting a lack of sensitivity to wave cycle turbulent dynamical changes.The locality preservation projection and multidimensional scaling based-concentration abundances carry high dissimilarity values throughout the sinusoidal phase cycle except at two temporal phases of 0-15• and 180-195•.The low dissimilarity is thought to be due to extremely low stress occurring during the beginning of the wave cycle and flow reversal which fosters topological similarity over the small 15• phase time scale.The two low dissimilarity curve values occurring over the first 180• of the complete wave cycle suggests a phase asymmetrical turbulent response, with the second part of the complete 360• degree cycle being less dissimilar than the first part.Classification tree analysis of manifold learning abundance values for concentration and velocity in the mean flow direction provide comprehension of the nonlinear relationship of latent space abundance values to 12 distinct time phase intervals equally dividing the 360• phase time scale.Mode classification trees show how segmented areas of manifold learning based-latent space are related to one another via the tree graph, ultimately leading to associations with specific flow forcing phase time intervals.Preliminary results suggest that different manifold learning decompositions have different tree graph structures with a tendency for the t-distributed stochastic neighbor embedding and locality preservation projection to possess a concentration-based root node, while the multidimensional scaling always produces a velocity abundance-based 012-2 root node.The second order bifurcation for the tree graph for the locality preserving projection and t-distributed stochastic neighbor embedding tends to have only velocity abundance-based nodes while the same bifurcation for multidimensional scaling has both velocity and concentration abundance nodes.Preliminary results also suggest that the t-distributed stochastic neighbor embedding maps continual maximum values of concentration and velocity abundances toward the first 180• part of the 360• phase cycle.On the other hand, the locality preserving projection tends to map continual maximum and minimum values of concentration and velocity abundances toward the second 180• part of the 360• phase cycle.This is irrespective of the type of root node.Multidimensional scalingbased decision trees, on the other hand, tend to map continual maximum values of concentration and velocity abundances toward the second 180• part of the 360• phase cycle and continual minimum values of both abundances to the first 180• part of the 360• phase cycle.These results suggest that the locality preservation projection is not sensitive to the asymmetrical turbulent sediment-flow physics while multidimensional scaling is sensitive to such dynamics.

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