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A machine learning control (MLC) is proposed based on the explorative gradient method (EGM) for the optimization and sensitivity analysis of actuation parameters. This technique is applied to reduce the drag of a square-back Ahmed body at a Reynolds number Re = 1.7 × 105. The MLC system consists of pulsed blowing along the periphery of the base, 25 pressure taps distributed on the vertical base of the body, and an EGM controller for unsupervised searching for the best control law. The parameter search space contains the excitation frequency fe, duty cycle α, and flow rate blowing coefficient Cm. It is demonstrated that the MLC may cut short the searching process significantly, requiring only about 100 test runs and achieving 13% base pressure recovery with a drag reduction of 11%. Extensive flow measurements are performed with and without control to understand the underlying flow physics. The converged control law achieves fluidic boat tailing and, meanwhile, eliminates the wake bistability. Such simultaneous achievements have never been reported before. A machine-learned response model is proposed to link the control parameters with the cost function. A sensitivity analysis based on this model unveils that the control performance is sensitive to fe and α but less so to Cm. The result suggests that a small sacrifice on performance will give a huge return on actuation power saving, which may provide important guidance on future drag reduction studies as well as engineering applications.

We experimentally optimize mixing of a turbulent round jet using machine learning control (MLC) following Li et al (2017). The jet is manipulated with one unsteady minijet blowing in wall-normal direction close to the nozzle exit. The flow is monitored with two hotwire sensors. The first sensor is positioned on the centerline 5 jet diameters downstream of the nozzle exit, i.e. the end of the potential core, while the second is located 3 jet diameters downstream and displaced towards the shear-layer. The mixing performance is monitored with mean velocity at the first sensor. A reduction of this velocity correlates with increased entrainment near the potential core. Machine Learning Control (MLC) is employed to optimize sensor feedback, a general open-loop broadband frequency actuation and combinations of both. MLC has identified the optimal periodic forcing with small duty cycle as the best control policy employing only 400 actuation measurements, each lasting for 5 seconds. This learning rate is comparable if not faster than typical optimization of periodic forcing with two free parameters (frequency and duty cycle). In addition, MLC re-sults indicate that neither new frequencies nor sensor feedback improves mixing further-contrary to many of other turbulence control experiments. The optimality of pure periodic actuation may be attributed to the simple jet flapping mechanism in the minijet plane. The performance of sensor feedback is shown to face a challenge for small duty cycles. The jet mixing results demonstrate the untapped potential of MLC in quickly learning optimal general control policies, even deciding between open-and closed-loop control.

A key question in flow control is that of the design of optimal controllers when the control space is high-dimensional and the experimental or computational budget is limited. We address this formidable challenge using a particular flavor of machine learning and present the first application of Bayesian optimization to the design of open-loop controllers for fluid flows. We consider a range of acquisition functions, including the recently introduced output-informed criteria of Blanchard and Sapsis (2021), and evaluate performance of the Bayesian algorithm in two iconic configurations for active flow control: computationally, with drag reduction in the fluidic pinball; and experimentally, with mixing enhancement in a turbulent jet. For these flows, we find that Bayesian optimization identifies optimal controllers at a fraction of the cost of other optimization strategies considered in previous studies. Bayesian optimization also provides, as a by-product of the optimization, a surrogate model for the latent cost function, which can be leveraged to paint a complete picture of the control landscape. The proposed methodology can be used to design open-loop controllers

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