Abstract
Random noise removal from particle image velocimetry (PIV) data and spectra is of paramount importance, especially for the computation of derivative quantities and spectra. Data filtering is critical, as a trade-off between filter effectiveness and spatial resolution penalty should be found. In this paper, a filtering method based on proper orthogonal decomposition and low-order reconstruction (LOR) is proposed. The existence of an optimal number of modes based on the minimization of both reconstruction error and signal withdrawal is demonstrated. A criterion to perform the choice of the optimal number of modes is proposed. The method is validated via synthetic and real experiments. As prototype problems, we consider PIV vector fields obtained from channel flow DNS data and from PIV measurement in the wake of a circular cylinder. We determine the optimal number of modes to be used for the LOR in order to minimize the statistical random error. The results highlight a significant reduction in the measurement error. Dynamic velocity range is enhanced, enabling to correctly capture spectral information of small turbulent scales down to the half of the cutoff wavelength of original data. In addition to this, the capability of detecting coherent structures is improved. The robustness of the method is proved, both for low signal-to-noise ratios and for small-sized ensembles. The proposed method can significantly improve the physical insight into the investigation of turbulent flows.
Similar content being viewed by others
References
Adrian RJ (1991) Particle-image techniques for experimental fluid mechanics. Annu Rev Fluid Mech 23:261–304
Adrian RJ, Westerweel J (2011) Particle image velocimetry, vol 30. Cambridge University Press, Cambridge
Adrian RJ, Christensen KT, Liu ZC (2000) Analysis and interpretation of instantaneous turbulent velocity fields. Exp Fluids 29:275–290
Astarita T (2006) Analysis of interpolation schemes for image deformation methods in PIV: effect of noise on the accuracy and spatial resolution. Exp Fluids 40:977–987
Astarita T (2007) Analysis of weighting windows for image deformation methods in PIV. Exp Fluids 43:859–871
Bergmann M, Cordier L, Brancher JP (2005) Optimal rotary control of the cylinder wake using proper orthogonal decomposition reduced-order model. Phys Fluids 17:097101. doi:10.1063/1.2033624
Berkooz G, Holmes P, Lumley JL (1993) The proper orthogonal decomposition in the analysis of turbulent flows. Annu Rev Fluid Mech 25:539–575
Cattell RB (1966) The scree test for the number of factors. Multivar Behav Res 1:245–276
Ceglia G, Discetti S, Ianiro A, Michaelis D, Astarita T, Cardone G (2014) Three-dimensional organization of the flow structure in a non-reactive model aero engine lean burn injection system. Exp Therm Fluid Sci 52:164–173
Cierpka C, Lütke B, Kähler CJ (2013) Higher order multi-frame particle tracking velocimetry. Exp Fluids 54:1–12. doi:10.1007/s00348-013-1533-3
Everson R, Sirovich L (1995) Karhunenloeve procedure for gappy data. J Opt Soc Am 12:165764
Fahl M (2000) Trust-region methods for flow controlbased on reduced order modeling. PhD dissertation, Trier University, Trier, Germany
Giordano R, Ianiro A, Astarita T, Carlomagno GM (2012) Flow field and heat transfer on the base surface of a finite circular cylinder in crossflow. Appl Therm Eng 49:79–88
Graham J, Lee M, Malaya N, Moser R, Eyink G, Meneveau C, Kanov K, Burns R, Szalay A (2013) Turbulent channel flow data set, http://turbulence.pha.jhu.edu/docs/README-CHANNEL.pdf
Guo S, Wu X, Li Y (2006) On the lower bound of reconstruction error for spectral filtering based privacy preserving data mining. In: Proceedings of the 10th European conference on principles and practice of knowledge discovery in databases, Berlin, Germany
Heikkila J (2000) Geometric camera calibration using circular control points. IEEE Trans Pattern Anal Mach Intell 22(10):1066–1077
Hong J, Katz J, Meneveau C, Schultz M (2012) Coherent structures and associated subgrid-scale energy transfer in a rough-wall turbulent channel flow. J Fluid Mech 712:92–128. doi:10.1017/jfm.2012.403
Huang HT, Dabiri D, Gharib M (1997) On errors of digital particle image velocimetry. Meas Sci Technol 8:142740
Huang Z, Du W, Chen B (2005) Deriving private information from randomized data. In: Proceeding of the ACM SIGMOD conference of management of data, Baltimore, BA
Kargupta H, Datta S, Wang Q, Sivakumar K (2003) On the privacy preserving properties of random data perturbation techniques. In: Proceedings of the 3rd international conference on data mining, pp 99–193
Li Y, Perlman E, Wan M, Yang Y, Meneveau C, Burns R, Chen S, Szalay A, Eyink G (2008) A public turbulence database cluster and applications to study lagrangian evolution of velocity increments in turbulence. J Turbul 9:N31. doi:10.1080/14685240802376389
Liu Z, Adrian RJ, Hanratty TJ (2001) Large-scale modes of turbulent channel flow: transport and structure. J Fluid Mech 448:53–80. doi:10.1017/S0022112001005808
Marchenko VA, Pastur LA (1967) Distribution of eigenvalues for some sets of random matrices. Mat Sb (NS) 72(114):507–536
Neal DR, Sciacchitano A, Smith BL, Scarano F (2015) Collaborative framework for piv uncertainty quantification: the experimental database. Meas Sci Technol 26
Novara M, Scarano F (2013) A particle-tracking approach for accurate material derivative measurements with tomographic PIV. Exp Fluids 54:1–12. doi:10.1007/s00348-013-1584-5
Raben SG, Charonko J, Vlachos PP (2012) Adaptive gappy proper ortogonal decomposition for particle image velocimetry data reconstruction. Meas Sci Technol 23(025):303
Ravindran S (2000) Reduced-order adaptive controllers for fluid flows using POD. J Sci Comput 15:457–478. doi:10.1023/A:1011184714898
Scarano F (2003) Theory of non-isotropic spatial resolution in PIV. Exp Fluids 35:26877
Schiavazzi D, Coletti F, Iaccarino G, Eaton JK (2014) A matching pursuit approach to solenoidal filtering of three-dimensional velocity measurements. J Comput Phys 263:206–221. doi:10.1016/j.jcp.2013.12.049
Sciacchitano A, Scarano F, Wieneke B (2012) Multi-frame pyramid correlation for time-resolved PIV. Exp Fluids 53:1087105
Sirovich L (1987) Turbulence and the dynamics of coherent structures: I, II, III. Q Appl Math 45:561–590
Stewart G (2001) Matrix algorithms volume 2: eigensystems, vol 2. SIAM, Philadelphia
Venturi D (2006) On proper orthogonal decomposition of randomly perturbed fields with applications to flow past a cylinder and natural convection over a horizontal plate. J Fluid Mech 559:215–254. doi:10.1017/S0022112006000346
Venturi D, Karniadakis GE (2004) Gappy data and reconstruction procedures for flow past a cylinder. J Fluid Mech 519:315–336. doi:10.1017/S0022112004001338
Violato D, Ianiro A, Cardone G, Scarano F (2012) Three-dimensional vortex dynamics and convective heat transfer in circular and chevron impinging jets. Int J Heat Fluid Flow 37:22–36
Westerweel J (1994) Efficient detection of spurious vectors in particle image velocimetry data sets. Exp Fluids 16:23647
Westerweel J (1997) Fundamentals of digital particle image velocimetry. Meas Sci Technol 8:137992
Westerweel J (2000) Theoretical analysis of the measurement precision in particle image velocimetry. Exp Fluids 29:S312
Westerweel J, Scarano F (2005) Universal outlier detection for PIV data. Exp Fluids 39:1096100
Westerweel J, Elsinga GE, Adrian RJ (2013) Particle image velocimetry for complex and turbulent flows. Annu Rev Fluid Mech 45:409–436
Yu H, Kanov K, Perlman E, Graham J, Frederix E, Burns R, Szalay A, Eyink G, Meneveau C (2012) Studying lagrangian dynamics of turbulence using on-demand fluid particle tracking in a public turbulence database. J Turbul 13:N12. doi:10.1080/14685248.2012.674643
Acknowledgments
The authors wish to thank Mr. Carlos Cobos for contributing the realization of the experimental setup, Prof. J. Rodriguez for providing the laser and Lasing S.A. for providing the Andor cameras used in the validation experiment. The authors wish also to thank Dr. A. Sciacchitano for insightful discussions on the validation experiment. This work has been partially supported by grant TRA2013-41103-P of the Spanish Ministry of Economy and Competitiveness. This grant includes FEDER funding.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Raiola, M., Discetti, S. & Ianiro, A. On PIV random error minimization with optimal POD-based low-order reconstruction. Exp Fluids 56, 75 (2015). https://doi.org/10.1007/s00348-015-1940-8
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00348-015-1940-8