Towards human-interpretable, automated learning of feedback control for the mixing layer

Abstract

We propose an automated analysis of the flow control behaviour from an ensemble of control laws and associated time-resolved flow snapshots. The input may be the rich data base of machine learning control (MLC) optimizing a feedback law for a cost function in the plant. The proposed methodology provides (1) insights into control landscape which maps control laws to performance including extrema and ridge-lines, (2) a catalogue of representative flow states and their contribution to cost function for investigated control laws and (3) a visualization of the dynamics. Key enablers are classification and feature extraction methods of machine learning. The analysis is successfully applied to the stabilization of a mixing layer with sensor-based feedback driving an upstream actuator. The fluctuation energy is reduced by 26\%. The control replaces unforced Kelvin-Helmholtz vortices with subsequent vortex pairing by higher-frequency Kelvin-Helmholtz structures of lower energy. These efforts target a human interpretable, fully automated analysis of MLC identifying qualitatively different actuation regimes, distilling corresponding coherent structures, and developing a digital twin of the plant.