Abstract
Vortex identification and visualization are important for understanding the underlying physical mechanism of the flow field and have been intensively studied recently. Local vortex identification methods could provide results in a rapid way, but they require the choice of a suitable criterion and threshold, which leads to poor robustness. Global vortex identification methods could obtain reliable results, while they require considerable user input and are computationally intractable for large-scale data sets. To address the problems described above, we present a novel vortex identification method based on the convolutional neural network (CNN). The proposed method integrates the advantages of both the local and global vortex identification methods to achieve higher precision and recall efficiently. In specific, the proposed method firstly obtains the labels of all grid points using a global and objective vortex identification method and then samples local patches around each point in the velocity field as the inputs of CNN. After that it trains the CNN to decide whether the central points of these patches belong to vortices. By this way, our method converts the vortex identification task to a binary classification problem, which could detect vortices quickly from the flow field in an objective and robust way. Extensive experimental results demonstrate the efficacy of our proposed method, and we expect this method can replace or supplement existing traditional methods.
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Bin T, Yi L (2018) CNN based flow field feature visualization method. Int J Perform Eng 14(3):434–444. https://doi.org/10.23940/ijpe.18.03
Biswas A, Thompson D, He W, Deng Q, Chen C-M, Shen H-W, Machiraju R, Rangarajan A (2015) An uncertainty-driven approach to vortex analysis using oracle consensus and spatial proximity. In: IEEE pacific visualization symposium, IEEE Computer Society, Los Alamitos, pp 1–8. https://doi.org/10.1109/PACIFICVIS.2015.715638
Chakraborty P, Balachandar S, Adrian RJ (2005) On the relationships between local vortex identification schemes. J Fluid Mech 535(4):189–214. https://doi.org/10.1017/S0022112005004726
Chong MS, Perry AE, Cantwell BJ (1990) A general classification of three-dimensional flow fields. Phys Fluids A 2(5):765–777. https://doi.org/10.1063/1.857730
Cover T, Hart P (1967) Nearest neighbor pattern classification. IEEE Trans Inf Theory 13(1):21–27. https://doi.org/10.1109/TIT.1967.1053964
Franz K, Roscher R, Milioto A, Wenzel S, Kusche J (2018) Ocean eddy identification and tracking using neural networks. In: Computer vision and pattern recognition
Freund Y, Schapire RE (1997) A decision-theoretic generalization of on-line learning and an application to boosting. J Comput Syst Sci 55(1):119–139. https://doi.org/10.1006/jcss.1997.1504
Girshick RB, Donahue J, Darrell T, Malik J (2014) Rich feature hierarchies for accurate object detection and semantic segmentation. In: IEEE conference on computer vision and pattern recognition proceedings of the 2014 CVPR ’14. IEEE Computer Society, Los Alamitos, pp 580–587
Günther T, Theiselr H (2018) The state of the art in vortex extraction. Comput Graph Forum 1:1–24. https://doi.org/10.1111/cgf.13319
Haller G, Hadjighasem A, Farazmand M, Huhn F (2015) Defining coherent vortices objectively from the vorticity. J Fluid Mech 795(7):136–173. https://doi.org/10.1017/jfm.2016.151
Hunt JCR (1987) Vorticity and vortex dynamics in complex turbulent flows. Trans Can Soc Mech Eng 11(1):21–35. https://doi.org/10.1139/tcsme-1987-0004
Jeong J, Hussain F (1995) On the identification of a vortex. J Fluid Mech 285(1):69–94. https://doi.org/10.1017/S0022112095000462
Jiang M, Machiraju R, Thompson D (2005) Detection and visualization of vortices. In: Visualization handbook, pp 295–309. https://doi.org/10.1016/B978-012387582-2/50016-2
Kingma DP, Ba J (2014) Adam: a method for stochastic optimization. In: Computer sciences
Lguensat R, Sun M, Fablet R, Mason E, Tandeo P, Chen G (2017) Eddynet: a deep neural network for pixel-wise classification of oceanic eddies. In: Computer vision and pattern recognition
Liu CQ, Wang YQ, Yang Y, Duan ZW (2016) New omega vortex identification method. Sci China Phys Mech Astron 59(8):684–711. https://doi.org/10.1007/s11433-016-0022-6
Lucas BD, Kanade T (1981) An iterative image registration technique with an application to stereo vision. In: International joint conference on artificial intelligence. Elsevier, Amsterdam, pp 674–679
Mattia S, George H (2016) Forecasting long-lived lagrangian vortices from their objective eulerian footprints. J Fluid Mech 813:436–457. https://doi.org/10.1017/jfm.2016.865
Ren S, Girshick R, Girshick R, Sun J (2015) Faster r-cnn: towards real-time object detection with region proposal networks. IEEE Trans Pattern Anal Mach Intell 39(6):1137–1149. https://doi.org/10.1109/TPAMI.2016.2577031
Sadarjoen A, Post FH, Ma B, Banks DC, Pagendarm HG (2002) Selective visualization of vortices in hydrodynamic flows. In: Proceedings of visualization. IEEE Computer Society, Los Alamitos. pp 419–422, https://doi.org/10.1109/VISUAL.1998.745333
Schafhitzel T, Vollrath J, Gois J, Weiskopf D, Castelo A, Ertl T (2008) Topology-preserving \(\lambda _2\)-based vortex core line detection for flow visualization. Comput Graph Forum 27:1023–1030. https://doi.org/10.1111/j.1467-8659.2008.01238.x
Serra M, Haller G (2016) Efficient computation of null-geodesic with applications to coherent vortex detection. Proc R Soc A: Math Phys Eng Sci 473:1–18. https://doi.org/10.1098/rspa.2016.0807
Serra M, Haller G (2016) Objective eulerian coherent structures. Chaos Interdiscip J Nonlinear Sci 26(5):95–105. https://doi.org/10.1063/1.4951720
Simard PY, Steinkraus D, Platt JC (2003) Best practices for convolutional neural networks applied to visual document analysis. In: International conference on document analysis and recognition. IEEE Computer Society, Los Alamitos, pp 958–963, https://doi.org/10.1109/ICDAR.2003.1227801
Ströfer CM, Wu J, Xiao H, Paterson E (2018) Data-driven, physics-based feature extraction from fluid flow fields. In: Fluid dynamics
Wu JZ, Xiong AK, Yang YT (2005) Axial stretching and vortex definition. Phys Fluids 17(3):69–78. https://doi.org/10.1063/1.1863284
Zhang L, Deng Q, Machiraju R, Rangarajan A, Thompson D, Walters DK, Shen H (2014) Boosting techniques for physics-based vortex detection. Comput Graph Forum 33:1–12. https://doi.org/10.1111/cgf.12275
Zhang S, Zhang H, Shu CW (2009) Topological structure of shock induced vortex breakdown. J Fluid Mech 1(639):343–372. https://doi.org/10.1017/S002211200999108X
Acknowledgements
This work was supported in part by the National Key Research and Development Program of China (# 2016YFB0200701) and the National Natural Science Foundation of China (# 61806205, # 91530324 and # 91430218).
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Deng, L., Wang, Y., Liu, Y. et al. A CNN-based vortex identification method. J Vis 22, 65–78 (2019). https://doi.org/10.1007/s12650-018-0523-1
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DOI: https://doi.org/10.1007/s12650-018-0523-1