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

We propose an automated analysis of the flow control behavior from an ensemble of control laws and associated time-resolved flow snapshots. The input may be the rich database of machine learning control 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. The algorithm picks up the most effective sensors s7′ and s22′ from 25 sensors. The best control law exhibits a net upward force with high frequency. The learning curve shows the difficulty to stabilize the mixing layer with only a few individuals distributed below Jsn=1. This is also verified in the control landscape exhibiting a pretty small distance with the unforced case. The fluctuation contribution of each centroid tends to be lower with the increasing performance of the control law. 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.