Publications Details

Feature selection, clustering, and prototype placement for turbulence data sets

Barone, Matthew F.; Ray, Jaideep R.; Domino, Stefan P.

This paper explores unsupervised learning approaches for analysis and categorization of turbulent flow data. Single point statistics from several high-fidelity turbulent flow simulation data sets are classified using a Gaussian mixture model clustering algorithm. Candidate features are proposed, which include barycentric coordinates of the Reynolds stress anisotropy tensor, as well as scalar and angular invariants of the Reynolds stress and mean strain rate tensors. A feature selection algorithm is applied to the data in a sequential fashion, flow by flow, to identify a good feature set and an optimal number of clusters for each data set. The algorithm is first applied to Direct Numerical Simulation data for plane channel flow, and produces clusters that are consistent with turbulent flow theory and empirical results that divide the channel flow into a number of regions (viscous sub-layer, log layer, etc). Clusters are then identified for flow over a wavy-walled channel, flow over a bump in a channel, and flow past a square cylinder. Some clusters are closely identified with the anisotropy state of the turbulence, as indicated by the location within the barycentric map of the Reynolds stress tensor. Other clusters can be connected to physical phenomena, such as boundary layer separation and free shear layers. Exemplar points from the clusters, or prototypes, are then identified using a prototype selection method. These exemplars summarize the dataset by a factor of 10 to 1000. The clustering and prototype selection algorithms provide a foundation for physics-based, semi-automated classification of turbulent flow states and extraction of a subset of data points that can serve as the basis for the development of explainable machine-learned turbulence models.