Bayesian optimization of a cost function in suboptimal control for reducing skin friction drag in wall turbulence

TL;DR

This paper introduces a Bayesian optimization framework integrated with suboptimal control theory to systematically identify effective cost functions for reducing skin friction drag in turbulent channel flows, achieving significant drag reduction.

Contribution

It presents a novel automated method combining Bayesian optimization with suboptimal control to optimize cost functions for flow control, demonstrating improved drag reduction in turbulence.

Findings

Achieved approximately 20% drag reduction.

Successfully rediscovered effective cost functions from previous studies.

Demonstrated the method's potential for advancing active flow control strategies.

Abstract

A systematic and automated framework for developing closed-loop flow control strategies is proposed, integrating suboptimal control theory [Lee et al., J. Fluid Mech. 358, 245 (1998)] with Bayesian optimization. The approach is demonstrated in the context of reducing skin friction drag in a low-Reynolds-number turbulent channel flow. A cost function in the suboptimal control framework is formulated as a linear combination of various wall quantities, with the corresponding weight coefficients optimized via Bayesian optimization to maximize a drag reduction rate. The proposed method successfully identifies effective cost functions, achieving approximately 20% drag reduction, which is comparable to or even higher than those reported in previous studies. Additionally, some cost functions proposed in previous studies are rediscovered. The present approach offers novel perspectives on the decision of the cost function, highlighting its potential for advancing active control strategies in turbulent flows.