×

Blind disturbance separation and identification in a transitional boundary layer using minimal sensing. (English) Zbl 1476.76032

Summary: A novel approach is presented for identifying disturbance sources in wall-bounded shear flows. The underlying approach models the flow state, as measured by sensors embedded in the flow, as a mixture of disturbance sources. The degenerate unmixing estimation technique is adopted as a blind source separation technique to recover the separate sources and their unknown mixing process. The efficiency of this approach stems from its ability to isolate any, a priori unknown, number of sources, using two sensors only. Furthermore, by adding a single additional sensor, the method is expanded to also determine the propagation velocity vector of each of the isolated sources, based on sensor readings from three sensors appropriately located in the flow field. Theoretical guidelines for locating the sensors are provided. The power of the method is demonstrated via computer simulations and wind-tunnel experiments. The numerical study considers disturbances comprising discrete Tollmien-Schlichting waves and wave packets. Linear stability theory is used to model source mixtures acquired by sensors placed in a Blasius boundary layer. The experimental study investigates the flow over a flat plate, with hot wires as sensors, and a loudspeaker and plasma actuators as source generators. Based on numerical and experimental demonstrations, it is believed that the new approach should prove useful in various applications, including active control of boundary layer transition from laminar to turbulent flow.

MSC:

76D55 Flow control and optimization for incompressible viscous fluids
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76E05 Parallel shear flows in hydrodynamic stability
76F06 Transition to turbulence
76F10 Shear flows and turbulence
76-05 Experimental work for problems pertaining to fluid mechanics

References:

[1] Amitay, M., Tuna, B.A & Dell’Orso, H.2016Identification and mitigation of TS waves using localized dynamic surface modification. Phys. Fluids28 (6), 064103.
[2] Antoni, J.2005Blind separation of vibration components: principles and demonstrations. Mech. Syst. Signal Process.19 (6), 1166-1180.
[3] Boiko, A.V., Dovgal, A.V., Grek, G.R. & Kozlov, V.V.2011Physics of Transitional Shear Flows: Instability and Laminar-Turbulent Transition in Incompressible Near-Wall Shear Layers, vol. 98. Springer.
[4] Brunton, S.L., Rowley, C.W & Williams, D.R.2013Reduced-order unsteady aerodynamic models at low Reynolds numbers. J. Fluid Mech.724, 203-233. · Zbl 1287.76078
[5] Cherry, E.C.1953Some experiments on the recognition of speech, with one and with two ears. J. Acoust. Soc. Am.25 (5), 975-979.
[6] Cichocki, A., Zdunek, R. & Amari, S.-I.2007Hierarchical ALS algorithms for nonnegative matrix and 3D tensor factorization. Lect. Notes Comput. Sci.4666, 169-176. · Zbl 1172.94390
[7] Cichocki, A., Zdunek, R., Phan, A.H. & Amari, S.-I.2009Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-Way Data Analysis and Blind Source Separation. John Wiley & Sons.
[8] Cohen, J.1994The initial evolution of a wave packet in a laminar boundary layer. Phys. Fluids6 (3), 1133-1143. · Zbl 0866.76028
[9] Corke, T.C., Post, M.L. & Orlov, D.M.2009Single dielectric barrier discharge plasma enhanced aerodynamics: physics, modeling and applications. Exp. Fluids46 (1), 1-26.
[10] Fabbiane, N., Simon, B., Fischer, F., Grundmann, S., Bagheri, S. & Henningson, D.S.2015On the role of adaptivity for robust laminar flow control. J. Fluid Mech.767, R1.
[11] Fransson, J.H.M.2004Leading edge design process using a commercial flow solver. Exp. Fluids37 (6), 929-932.
[12] Gao, B., Lu, P., Woo, W.L., Tian, G.Y., Zhu, Y. & Johnston, M.2018Variational Bayesian subgroup adaptive sparse component extraction for diagnostic imaging system. IEEE Trans. Ind. Electron.65 (10), 8142-8152.
[13] Gaster, M.1975A theoretical model of a wave packet in the boundary layer on a flat plate. Proc. R. Soc. Lond. A347 (1649), 271-289.
[14] Gaster, M. & Grant, I.1975An experimental investigation of the formation and development of a wave packet in a laminar boundary layer. Proc. R. Soc. Lond. A347 (1649), 253-269.
[15] Gluzman, I., Oshman, Y. & Cohen, J.2020Detection and isolation of Tollmien-Schlichting waves in shear flows using blind source separation. Mech. Syst. Signal Process.136, 106485.
[16] Greenblatt, D., Goeksel, B., Rechenberg, I., Schüle, C.Y., Romann, D. & Paschereit, C.O.2008Dielectric barrier discharge flow control at very low flight Reynolds numbers. AIAA J.46 (6), 1528-1541.
[17] Haykin, S. & Chen, Z.2005The cocktail party problem. Neural Comput.17 (9), 1875-1902.
[18] Hyvärinen, A. & Oja, E.2000Independent component analysis: algorithms and applications. Neural Netw.13 (4), 411-430.
[19] Jordinson, R1970The flat plate boundary layer. Part 1. Numerical integration of the Orr-Sommerfeld equation. J. Fluid Mech.43 (04), 801-811. · Zbl 0216.52402
[20] Kim, J. & Bewley, T.R.2007A linear systems approach to flow control. Annu. Rev. Fluid Mech.39, 383-417. · Zbl 1296.76074
[21] Kim, K.J., Jang, C.S., Jeong, J.-M. & Nam, S.W.2006 Acoustic echo cancellation using the duet algorithm based blind separation in a noisy environment. In TENCON 2006 - 2006 IEEE Region 10 Conference, pp. 1-4. IEEE.
[22] Kriegseis, J., Simon, B. & Grundmann, S.2016Towards in-flight applications? A review on dielectric barrier discharge-based boundary-layer control. Appl. Mech. Rev.68 (2), 020802.
[23] Li, Y. & Gaster, M.2006Active control of boundary-layer instabilities. J. Fluid Mech.550, 185-205. · Zbl 1222.76044
[24] Moreau, E.2007Airflow control by non-thermal plasma actuators. J. Phys. D: Appl. Phys.40 (3), 605.
[25] Nogueira, L.C.F. & Petraglia, M.R.2015 Robust localization of multiple sound sources based on BSS algorithms. In 2015 IEEE 24th International Symposium on Industrial Electronics (ISIE), pp. 579-583. IEEE.
[26] Opfer, H., Evert, F., Ronneberger, D. & Grosche, F.R.2004 On the potential and the limitations of boundary-layer stabilization via active wave cancellation. In Recent Results in Laminar-Turbulent Transition (ed. S. Wagner, M. Kloker, U. Rist), Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol. 86. pp. 219-230. Springer. · Zbl 1067.76003
[27] Oshman, Y. & Markley, F.L.1999Spacecraft attitude/rate estimation using vector-aided GPS observations. IEEE T. Aero. Elec. Sys.35 (3), 1019-1032.
[28] Ozerov, A & Fevotte, C.2010Multichannel nonnegative matrix factorization in convolutive mixtures for audio source separation. IEEE Trans. Audio Speech18 (3), 550-563.
[29] Pedersen, M.S., Larsen, J., Kjems, U. & Parra, L.C.2007 A survey of convolutive blind source separation methods. In Multichannel Speech Processing Handbook (ed. J. Benesty, Y. Huang, M. Sondhi), pp. 1065-1084. Springer.
[30] Rickard, S.2007 The DUET blind source separation algorithm. In Blind Speech Separation (ed. S. Makino, H. Sawada, T.W. Lee), pp. 217-241. Springer.
[31] Rowley, C.W.2005Model reduction for fluids, using balanced proper orthogonal decomposition. Intl J. Bifurcation Chaos15 (03), 997-1013. · Zbl 1140.76443
[32] Saric, W.S.2008 Experiments in 2-D boundary-layers: stability and receptivity advances in laminar-turbulent transition modelling, NATO educational notes.
[33] Sawada, H., Araki, S. & Makino, S.2010Underdetermined convolutive blind source separation via frequency bin-wise clustering and permutation alignment. IEEE Trans. Audio Speech19 (3), 516-527.
[34] Schmid, P.J.2010Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech.656, 5-28. · Zbl 1197.76091
[35] Schmid, P.J. & Henningson, D.S.2001 Stability and transition in shear flows, vol. 142. Springer Science & Business Media. · Zbl 0966.76003
[36] Semeraro, O., Bagheri, S., Brandt, L. & Henningson, D.S.2013Transition delay in a boundary layer flow using active control. J. Fluid Mech.731, 288-311. · Zbl 1294.76093
[37] Serviere, C. & Fabry, P.2005Principal component analysis and blind source separation of modulated sources for electro-mechanical systems diagnostic. Mech. Syst. Signal Process.19 (6), 1293-1311.
[38] Silva, M., Figueiredo, E., Costa, J.C.W.A. & Mascare Nas, D.2020Spatio-temporal decomposition of 2d travelling waves from video measurements. Mech. Syst. Signal Process.139, 106599.
[39] Sipp, D. & Schmid, P.J.2016Linear closed-loop control of fluid instabilities and noise-induced perturbations: a review of approaches and tools. Appl. Mech. Rev.68 (2), 020801.
[40] Sturzebecher, D. & Nitsche, W.2003Active cancellation of Tollmien-Schlichting instabilities on a wing using multi-channel sensor actuator systems. Intl J. Heat Fluid Flow24 (4), 572-583.
[41] Taira, K., Brunton, S.L, Dawson, S.T.M., Rowley, C.W., Colonius, T., Mckeon, B.J., Schmidt, O.T, Gordeyev, S., Theofilis, V. & Ukeiley, L.S.2017Modal analysis of fluid flows: an overview. AIAA J.55 (12), 4013-4041.
[42] Taylor, J.A. & Glauser, M.N.2004Towards practical flow sensing and control via pod and lse based low-dimensional tools. Trans. ASME J. Fluids Engng126 (3), 337-345.
[43] Trefethen, L.N.2000Spectral Methods in MATLAB, vol. 10. SIAM. · Zbl 0953.68643
[44] Vadarevu, S.B., Symon, S., Illingworth, S.J. & Marusic, I.2019Coherent structures in the linearized impulse response of turbulent channel flow. J. Fluid Mech.863, 1190-1203. · Zbl 1415.76366
[45] Vigario, R. & Oja, E.2008BSS and ICA in neuroinformatics: from current practices to open challenges. IEEE Rev. Biomed. Engng1, 50-61.
[46] Wang, Y., Yılmaz, Ö. & Zhou, Z.2013Phase aliasing correction for robust blind source separation using duet. Appl. Comput. Harmon. Anal.35 (2), 341-349. · Zbl 1336.94026
[47] Yilmaz, O. & Rickard, S.2004Blind separation of speech mixtures via time-frequency masking. IEEE Trans. Signal Process.52 (7), 1830-1847. · Zbl 1369.94383
[48] Yoshioka, T., Nakatani, T., Miyoshi, M. & Okuno, H.G.2010Blind separation and dereverberation of speech mixtures by joint optimization. IEEE Trans. Audio Speech19 (1), 69-84.
[49] Zhang, J., Gao, H., Liu, Q., Farzadpour, F., Grebe, C. & Tian, Y.2017Adaptive parameter blind source separation technique for wheel condition monitoring. Mech. Syst. Signal Process.90, 208-221.
[50] Zhen, L., Peng, D., Yi, Z., , Xiang, Y. & Chen, P.2017Underdetermined blind source separation using sparse coding. IEEE Trans. Neural Netw. Learn. Syst.28 (12), 3102-3108.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.