pith. sign in

arxiv: 2604.19326 · v1 · submitted 2026-04-21 · ⚛️ physics.flu-dyn

Experimental Demonstration of SDRL Controller for TS Wave Suppression with DBD Actuator

Babak Mohammadikalakoo , Sergio Garcia Villasol , Gabriele Salomone , Marios Kotsonis , Nguyen Anh Khoa Doan This is my paper

Pith reviewed 2026-05-10 02:16 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords TS wave suppressionSDRL controllerDBD actuatorboundary layer controlonline reinforcement learningfeedforward controlwind tunnel experimenttransition delay
0
0 comments X

The pith

A model-free reinforcement learning controller reduces downstream TS wave disturbances by updating an FIR filter online from a single error signal.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows an experimental wind-tunnel setup where a single-step deep reinforcement learning controller suppresses Tollmien-Schlichting waves in a flat-plate boundary layer. The controller sits in a feedforward arrangement between an upstream reference microphone and a downstream error microphone, commanding a DBD plasma actuator by continuously revising the coefficients of a finite-impulse-response filter. Tests with single-frequency, multi-frequency, and broadband disturbances all produce lower second-order statistics and spectral content at the error sensor. The same controller stays effective when freestream speed changes moderately or when the incoming wave spectrum shifts, without any pre-built model of the flow or actuator. These outcomes point toward data-driven, adaptable methods for delaying boundary-layer transition.

Core claim

The SDRL controller updates its policy in real time solely from the downstream error microphone, revising FIR filter coefficients that map the upstream reference signal to the actuator voltage, and thereby attenuates the artificially generated TS waves as measured by reduced disturbance energy and spectral peaks in both microphone records and planar PIV fields across all examined input types and flow speeds.

What carries the argument

The single-step deep reinforcement learning policy that performs online coefficient updates to a finite-impulse-response filter driven only by the downstream error signal to generate the actuation command.

If this is right

  • Downstream disturbance levels drop consistently for single-tone, multi-tone, and broadband TS-wave inputs.
  • Performance holds when freestream velocity varies within the moderate range tested.
  • The feedforward layout with reference and error sensors plus intervening actuator achieves measurable spectral attenuation.
  • The model-free approach supports strategies for active control aimed at boundary-layer transition delay.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same online learning structure could be applied to suppress other convective instabilities without deriving new plant models.
  • Compact microphone-actuator pairs might enable distributed active control along an airfoil surface.
  • Adaptation during operation suggests the method could handle slowly changing conditions such as varying angle of attack.
  • Extension to higher Reynolds numbers would test whether the FIR-update rate remains sufficient for natural transition scenarios.

Load-bearing premise

Real-time updates to the FIR filter coefficients drawn solely from the downstream error microphone will produce stable and effective wave cancellation without any prior model of the flow dynamics or actuator response.

What would settle it

An experiment in which the controller is switched on yet the downstream error-microphone variance or the integrated TS-wave spectral energy in PIV fields fails to decrease relative to the uncontrolled baseline, or the system becomes unstable.

Figures

Figures reproduced from arXiv: 2604.19326 by Babak Mohammadikalakoo, Gabriele Salomone, Marios Kotsonis, Nguyen Anh Khoa Doan, Sergio Garcia Villasol.

Figure 1
Figure 1. Figure 1: Side and top views of the experimental setup. The signals [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Pressure coefficient distribution for two arrays of press [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Linear stability diagram at Reδ ∗,ref ≈ 1.7 × 103 (U∞ = 20 m/s), showing the amplification factor (N) as blue contours. The neutral stability curve (αi = 0) (black dashed lines). The T-DBD and C-DBD at x = −279 and x = 0, respectively (red dotted lines). The TS wave excitation frequencies triggered by the T-DBD actuator (bold black markers). The boundary conditions impose zero velocity perturbations (u ′ =… view at source ↗
Figure 4
Figure 4. Figure 4: T-DBD voltage signals (a − e) and their fast Fourier transform (FFT) (f − g) for cases: (a) A, (b) B1, (c) B2, (d) C1, (e) C2 [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Schematic of the control unit. xs(k), ys(k), and es(k) refer to reference, actuator, and error signals, respectively. Figure is adjusted from Mohammadikalakoo et al. (2025). The control framework couples the SDRL agent with the physical system through a real-time simulation and testing platform. The framework performs signal acquisition, digital filtering, reward evaluation, and high-voltage actuation synt… view at source ↗
Figure 6
Figure 6. Figure 6: Reward moving average (solid orange line) and moving maximu [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Frequency response of the best-performing FIR filter o [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Fourier transform of the plasma controller signal (blue) a [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Error signal (es) time series corresponding to the best-performing FIR filter obtained for (a) A, (b) B1, and (c) C1 control cases [PITH_FULL_IMAGE:figures/full_fig_p019_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Error signal (es) Fourier transform corresponding to the best-performing FIR filter obtained for (a) A , (b) B1, and (c) C1 control cases. In case A ( [PITH_FULL_IMAGE:figures/full_fig_p020_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Representative PIV fluctuation statistics: normalized w [PITH_FULL_IMAGE:figures/full_fig_p023_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Normalized streamwise velocity fluctuation field based on t [PITH_FULL_IMAGE:figures/full_fig_p024_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Fourier transforms of the downstream microphone sign [PITH_FULL_IMAGE:figures/full_fig_p025_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Perturbation velocity statistics for case [PITH_FULL_IMAGE:figures/full_fig_p031_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Normalized standard deviation fields of the perturbation [PITH_FULL_IMAGE:figures/full_fig_p031_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: shows the time traces of the error signal (es) for both velocities. The amplitude of the pressure fluctuations is notably reduced when control is active, with the oscillations at U∞ = 22.5 m/s following a similar decay trend as those observed at 20 m/s. The controller continues to produce a stable and phase-aligned response despite the shorter convective timescale. The corresponding frequency-domain repre… view at source ↗
Figure 17
Figure 17. Figure 17: Error signal (es) Fourier transform corresponding to the best-performing FIR filter obtained for cases (a) B1 at Reδ ∗,ref ≈ 1700 (U∞ = 20 m/s) and (b) B2 at Reδ ∗,ref ≈ 1912 (U∞ = 22.5 m/s). Similar behavior is observed for cases C1 − C2 in these two freestream velocities as shown in Tables 4 and 5. It must be emphasized that these results are based on only two test velocities and, therefore cannot be in… view at source ↗
read the original abstract

An experimental wind-tunnel implementation of a model-free single-step deep reinforcement learning (SDRL) controller is presented for TS wave suppression in a flat plate boundary layer. The controller is deployed in a feedforward layout. The arrangement comprises an upstream reference microphone, a downstream error microphone, and a DBD plasma actuator located between them. The controller updates its policy online from the measured error signal and, in real time, adjusts the coefficients of a finite-impulse-response (FIR) filter that maps the reference signal to the actuation command. TS waves are artificially introduced by a second, upstream-located DBD trigger actuator identical in specification to the control actuator. The trigger actuator is driven with single-frequency, multi-frequency, or broadband white-noise inputs depending on the control cases. Experiments were carried out in an anechoic wind tunnel facility using flush-mounted pressure microphones for sensing and controller feedback, together with two-component planar particle image velocimetry~(PIV) for flow-field verification. The controller performance is assessed via second-order statistics of the error signal and the spectral attenuation of the TS wave content. Across all tested scenarios, the SDRL-based controller consistently reduces the downstream disturbance level and exhibits robustness to moderate variations in freestream velocity and in the incoming TS wave disturbance spectrum. These results provide an experimental step toward adaptable, data-driven TS wave suppression with compact sensing and actuation, supporting practical strategies for boundary layer transition delay.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper describes an experimental wind-tunnel demonstration of a model-free single-step deep reinforcement learning (SDRL) controller for suppressing Tollmien-Schlichting (TS) waves in a flat-plate boundary layer. The feedforward setup uses an upstream reference microphone, a DBD plasma actuator, and a downstream error microphone; the controller updates FIR filter coefficients online from the error signal alone to generate the actuation command. Artificial TS waves are introduced via a second upstream DBD actuator driven by single-frequency, multi-frequency, or broadband inputs. Performance is assessed through second-order statistics of the error signal, spectral attenuation, and two-component PIV, with claims of consistent downstream disturbance reduction and robustness to moderate freestream velocity and spectrum variations.

Significance. If the reported reductions are substantial and the online learning proves stable, the work would constitute a meaningful experimental step toward compact, data-driven active flow control for boundary-layer transition delay. The model-free online adaptation, use of standard DBD actuators and microphones, and PIV verification are strengths that could support practical strategies without requiring detailed plant models.

major comments (2)
  1. [Results] The central claim that the SDRL controller 'consistently reduces the downstream disturbance level' across single-frequency, multi-frequency, and broadband cases is not supported by any numerical attenuation values, error bars, or statistical significance tests. This absence prevents verification of the magnitude and reliability of the suppression.
  2. [Controller Description] The robustness claim requires that real-time FIR coefficient updates from the error microphone alone remain stable and effective despite unknown convective delays, nonlinear DBD response, and varying spectra. No coefficient trajectories, learning-rate bounds, or failure-mode tests under untested conditions are provided to substantiate this.
minor comments (2)
  1. [Abstract] The abstract states that performance is assessed via 'second-order statistics of the error signal and the spectral attenuation' but supplies no details on windowing, normalization, or how the spectra were computed.
  2. [Experimental Setup] Reproducibility would benefit from explicit values for FIR filter length, sampling frequency, and the precise form of the single-step RL update rule.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and positive overall assessment. We address the two major comments point by point below.

read point-by-point responses

  1. Referee: The central claim that the SDRL controller 'consistently reduces the downstream disturbance level' across single-frequency, multi-frequency, and broadband cases is not supported by any numerical attenuation values, error bars, or statistical significance tests. This absence prevents verification of the magnitude and reliability of the suppression.

    Authors: We agree that explicit numerical values would strengthen the presentation. The original manuscript reports performance through second-order statistics and spectral plots but does not tabulate attenuation in dB or include error bars. In the revision we will add a table (or inline values) giving the measured attenuation in dB for each case, together with standard deviations obtained from repeated runs, and a short statement on statistical consistency. revision: yes

  2. Referee: The robustness claim requires that real-time FIR coefficient updates from the error microphone alone remain stable and effective despite unknown convective delays, nonlinear DBD response, and varying spectra. No coefficient trajectories, learning-rate bounds, or failure-mode tests under untested conditions are provided to substantiate this.

    Authors: The experimental results already demonstrate successful online adaptation for moderate freestream-velocity changes and for single-frequency through broadband spectra, which implicitly shows that the error-driven FIR update remains stable under the tested convective delays and actuator nonlinearities. We will add the numerical learning-rate value used and, space permitting, one representative plot of coefficient evolution. Explicit failure-mode tests outside the moderate range examined would require additional experiments that lie beyond the scope of the present study. revision: partial

Circularity Check

0 steps flagged

No circularity: pure experimental demonstration with no derivations or predictions

full rationale

The manuscript is an experimental wind-tunnel study reporting measured performance of an online-updated FIR filter under SDRL control. No equations, first-principles derivations, fitted parameters, or predictive claims appear in the abstract or described content. All reported outcomes (disturbance reduction, robustness to velocity/spectrum changes) are direct empirical observations from microphones and PIV, not outputs of any model that could loop back to its own inputs. The reader's assessment of zero circularity is therefore confirmed; the work contains no load-bearing mathematical steps to inspect.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The paper is an experimental demonstration and introduces no new theoretical axioms, free parameters, or invented entities beyond standard RL hyperparameters that are not specified in the abstract.

pith-pipeline@v0.9.0 · 5575 in / 1066 out tokens · 44568 ms · 2026-05-10T02:16:22.089777+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

21 extracted references · 21 canonical work pages

  1. [1]

    & Gerbeth, G

    Albrecht, T., Grundmann, R., Mutschke, G. & Gerbeth, G. 2006 On the stability of the boundary layer subject to a wall-parallel Lorentz force. Physics of Fluids 18 (9), 098103. Bagheri, Shervin, Brandt, Luca & Henningson, Dan S. 2009 Input-output analysis, model reduction and control of the flat-plate boundary layer. Journal of Fluid Mechanics 620, 263–298....

    work page 2006

  2. [2]

    Carpenter, PW & Garrad, AD 1985 The hydrodynamic stability of flow over kramer-type compliant surfaces. part

    work page 1985

  3. [3]

    Journal of Fluid Mechanics 155, 465–510

    tollmien-schlichting instabi lities. Journal of Fluid Mechanics 155, 465–510. Chen, W., W ang, Q., Yan, L., Hu, G. & Noack, B. R. 2023 Deep reinforcement learning- 28 Mohammadikalakoo et al. based active flow control of vortex-induced vibration of a sq uare cylinder. Physics of Fluids 35 (5). Davies, C. & Carpenter, P. W. 1997 Numerical simulation of the e...

    work page 2023

  4. [4]

    Journal of Fluid Mechanics 810, 60–81

    F abbiane, Nicol`o, Bagheri, Shervin & Henningson, Dan S 2017 Energy efficiency and performance limitations of linear adaptive control for tra nsition delay. Journal of Fluid Mechanics 810, 60–81. F abbiane, Nicolo, Semeraro, Onofrio, Bagheri, Shervin & He nningson, Dan S 2014 Adaptive and model-based control theory applied to convect ively unstable flows. A...

    work page 2017

  5. [5]

    In 3rd Shear Flow Conference , p

    F an, Xuetong, Hofmann, Lorenz & Herbert, Thorw ald 1993 Active flow control with neural networks. In 3rd Shear Flow Conference , p

    work page 1993

  6. [6]

    Nature Communications 16,

    Font, Bernat, Alc ´antara-´Avila, Francisco, Rabault, Jean, Vinuesa, Ricardo & Lehmkuhl, Oriol 2025 Deep reinforcement learning for active flow control in a turbulent separation bubble. Nature Communications 16,

    work page 2025

  7. [7]

    Physical review letters 96 (6), 064501

    Fransson, Jens HM, Talamelli, Alessandro, Brandt, Luca & Co ssu, Carlo 2006 Delaying transition to turbulence by a passive mechanism. Physical review letters 96 (6), 064501. Fransson, J. H. M., Brandt, L., Talamelli, A. & Cossu, C. 2004 Experimental study of the stabilizing effect of streaks on tollmien–schlichting w aves. Physics of Fluids 16 (10), 3627–3...

    work page 2006

  8. [8]

    & Hachem, E

    Ghraieb, H., Viquerat, J., Larcher, A., Meliga, P. & Hachem, E. 2021 Single-step deep reinforcement learning for open-loop control of lamin ar and turbulent flows. Physical Review Fluids

    work page 2021

  9. [9]

    & Hachem, E

    Ghraieb, H., Viquerat, J., Larcher, A., Meliga, P. & Hachem, E. 2022 Single-step deep reinforcement learning for two- and three-dimensional opt imal shape design. AIP Advances

    work page 2022

  10. [10]

    International Journal of Heat and Fluid Flow 30 (3), 394–402

    Grundmann, Sven & Tropea, Cameron 2009 Experimental damping of boundary-layer oscillations using dbd plasma actuators. International Journal of Heat and Fluid Flow 30 (3), 394–402. Guastoni, L., Rabault, J., Schlatter, P., Azizpour, H. & Vin uesa, R. 2023 Deep reinforcement learning for turbulent drag reduction in cha nnel flows. European Physical Journal ...

    work page 2009

  11. [11]

    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471 (2177), 20140928

    Hussein, Mahmoud I, Biringen, Sedat, Bilal, Osama R & Kucala , Alec 2015 Flow stabilization by subsurface phonons. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471 (2177), 20140928. Kotsonis, M., Shukla, Ram Krishan & Pr ¨obsting, Stefan 2015 Control of natural Tollmien-Schlichting waves using dielectric barr ier dis...

    work page 2015

  12. [12]

    & Hendricks, E

    Ladd, D. & Hendricks, E. 1988 Active control of 2-D instability waves on an axisymmet ric body. Exp. Fluids 6, 69–70. Li, J. & Zhang, M. 2022 Reinforcement-learning-based control of confined cyl inder wakes with stability analyses. Journal of Fluid Mechanics

    work page 1988

  13. [13]

    Experimental SDRL-based control of TS waves 29 Liepmann, H. W. & Fila, G. H. 1946 Investigations of effects of surface temperature and si ngle roughness elements on boundary-layer transition. Tech. Rep. Report No

    work page 1946

  14. [14]

    Liepmann, H

    NACA. Liepmann, H. W. & Nosenchuck, D. M. 1982 Active control of laminar-turbulent transition. Journal of Fluid Mechanics 118, 201–204. Lin, N., Reed, H. L. & Saric, W. S. 1992 Effect of leading-edge geometry on boundary-layer receptivity to freestream sound. In Instability, Transition, and Turbulence , pp. 421–440. Springer. Linot, Alexander J., Zeng, Kai...

    work page 1982

  15. [15]

    Mayes, C, Schlichting, H, Krause, E, Oertel, H J & Gersten, K 2003 Boundary-Layer Theory

    AGARD. Mayes, C, Schlichting, H, Krause, E, Oertel, H J & Gersten, K 2003 Boundary-Layer Theory. Springer. Merino-Mart´ınez, R., Carpio, A. Rubio, T ´ercio, L., Pereira, L., van Herk, S., A vallone, F., Ragni, M. & Kotsonis, M. 2020 Aeroacoustic design and characterization of the 3d-printed, open-jet, anechoic wi nd tunnel of delft university of technolog...

    work page 2003

  16. [16]

    Saric, W. S. & Reed, H. L. 1983 Effect of suction and blowing on Boundary-Layer transit ion. In Proceedings of the 21st Aerospace Sciences Meeting . American Institute of Aeronautics and Astronautics (AIAA), Reno, NV, USA, aIAA Paper 83-0043. Schlichting, Hermann & Gersten, Klaus 2017 Boundary-Layer Theory , 9th edn. Berlin/Heidelberg: Springer. Schultz, M...

    work page 1983

  17. [17]

    Measurement Science and Technology 30 (9), 092001

    Sciacchitano, Andrea 2019 Uncertainty quantification in particle image velocime try. Measurement Science and Technology 30 (9), 092001. Sturzebecher, Dana J. & Nitsche, Wolfgang Hartmut 2003 Active cancellation of 30 Mohammadikalakoo et al. Tollmien–Schlichting instabilities on a wing using multi- channel sensor actuator systems. International Journal of H...

    work page 2019

  18. [18]

    Journal of Computational Physics

    Viquerat, Jonathan, Rabault, Jean, Kuhnle, Alexander, Ghr aieb, Hassan, Larcher, Aur´elien & Hachem, Elie 2021 Direct shape optimization through deep reinforcement learning. Journal of Computational Physics

    work page 2021

  19. [19]

    & Bottaro, A

    W alther, S., Airiau, C. & Bottaro, A. 2001 Optimal control of tollmien-schlichting waves in a developing boundary layer. Physics of Fluids 13 (7), 2087–2096. W ang, C., Yu, P. & Huang, H. 2023 Reinforcement-learning-based parameter optimizati on of a splitter plate downstream in cylinder wake with stabili ty analyses. Physical Review Fluids 8 (8). Widman...

    work page 2001

  20. [20]

    The amplitude of the pressure fluctuations is notably reduced when con trol is active, with the oscillations at U∞ = 22

    Figure 16 shows the time traces of the error signal ( es) for both velocities. The amplitude of the pressure fluctuations is notably reduced when con trol is active, with the oscillations at U∞ = 22 . 5 m/s following a similar decay trend as those observed at 20 m/s. The controller continues to produce a stable and phase-alig ned response despite the short...

    work page 1912

  21. [21]

    5 m/s). Experimental SDRL-based control of TS waves 33 Figure 17: Error signal ( es) Fourier transform corresponding to the best-performing FIR filter obtained for cases (a) B1 at Reδ∗ , ref ≈ 1700 ( U∞ = 20 m/s) and (b) B2 at Reδ∗ , ref ≈ 1912 ( U∞ =

    work page 1912