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We propose a multivariate graph centrobaric trajectory-based method for characterizing nonlinear dynamics from high-dimensional chaotic time series. After the optimal selecting of the embedding dimension and time delay, we map the high-dimensional vector point into the two-dimensional radial plane graph, i.e., the high-dimensional vector point is transformed correspondingly to a geometric polygon. By extracting the geometric location of the polygon barycenters, we can obtain the evolving feature of the barycenter dynamical trajectory. Then we use the moment quantity of the barycenter trajectory to distinguish different chaotic time series. Finally, we apply our method to the fluctuating signals measured from gas-liquid two-phase flow experiments. The results suggest that our method can be a powerful tool for not only distinguishing the different flow patterns but also investigating the dynamical evolving mechanism of flow patterns.
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Keywords:
- two-phase flow /
- high-dimentional phase space /
- centrobaric trajectory /
- flow pattern dynamics
[1] Daw C S, Lawkins W F, Downing D J, Clapp N E 1990 Phys. Rev. A 41 1179
[2] Lawkins W F, Daw C S, Downing D J, Clapp N E 1993 Phys Rev. E 47 2520
[3] Daw C S, Finney C E A, Vasudevan M, vanGoor N A, Nguyen K, Bruns D D, Kostelich E J, Grebogi C, Ott E, Yorke J A 1995 Phys. Rev. Lett. 75 2308
[4] Lahey R T 1991 Heat Mass Transfer. 26 351
[5] Letzel H M, Schouten J C, Krishna R, van den Bleek C M 1997 Chem. Eng. Sci. 52 4447
[6] Ji H, Ohara H, Kuramoto K, Tsutsumi A, Yoshida K, Hirama T 2000 Chem. Eng. Sci. 55 403
[7] Llauro F X, Llop M F 2006 Int. J. Multiphase Flow 32 1397
[8] Xiao N, Jin N D 2007 Acta Phys. Sin. 56 5149 (in Chinese) [肖楠, 金宁德 2007 56 5149]
[9] Zhao G B, Yang Y R 2003 AIChE J. 49 869
[10] Li H W, Zhou Y L, Sun B, Yang Y 2010 Chin. J. Chem. Eng. 18 880
[11] Yu H, Chen Y S 2009 Advance in Mechanics 39 154 (in Chinese) [于海, 陈予恕 2009 力学进展 39 154]
[12] Zoldi S M, Greenside H S 1997 Phys. Rev. Lett. 78 1687
[13] Meng D Y, Xu C, Xu Z B 2010 Chin. J. Comput. 33 545 (in Chinese) [孟德宇, 徐晨, 徐宗本 2010 计算机学报 33 545]
[14] Liu Y, Liu Y, Keith C.C.Chan 2010 Signal Processing 90 2375
[15] Auerbach D, Cvitanovic P, Eckmann J P, Gunaratne G, Procaccia I 1987 Phys. Rev. Lett. 58 2387
[16] Saiki Y, Yamada M 2008 Nonlinear Processes in Geophysics 15 675
[17] Cong R, Liu S L, Ma R 2008 Acta Phys. Sin. 57 7487 (in Chinese) [丛蕊, 刘树林, 马瑞 2008 57 7487]
[18] Zhang C T, Ma Q L, Peng H 2010 Acta Phys. Sin. 59 7623 (in Chinese) [张春涛, 马千里, 彭宏 2010 59 7623]
[19] You R Y, Huang X J 2011 Chin. Phys. B 20 020505
[20] Hong W X, Li X, Xu Y H, Wang J J, Song J L 2008 Information fusion and pattern recognition based on the principle of multidimensional chart expression (Beijing: National Defense Industry Press) p193 (In Chinese) [洪文学, 李昕, 徐永红, 王金甲, 宋佳霖 2008 基于多元统计图表示原理的信息融合和模式识别技术 (北京:国防工业出版社)第193页]
[21] Takens F, 1981 Dynamical Systems and Turbulence (Berlin: Spring Verlag) p366
[22] Saary M J 2008 Journal of Clinical Epidemiology 60 311
[23] Hubert M, Rousseeuw P J, Verboven S 2002 Chemometrics and Intelligent Laboratory Systems 60 100
[24] Kim H S, Eykholt R, Salas J D 1999 Physica D 127 48
[25] Zheng G B, Jin N D 2009 Acta Phys. Sin. 58 4485 (in Chinese) [郑桂波, 金宁德 2009 58 4485]
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[1] Daw C S, Lawkins W F, Downing D J, Clapp N E 1990 Phys. Rev. A 41 1179
[2] Lawkins W F, Daw C S, Downing D J, Clapp N E 1993 Phys Rev. E 47 2520
[3] Daw C S, Finney C E A, Vasudevan M, vanGoor N A, Nguyen K, Bruns D D, Kostelich E J, Grebogi C, Ott E, Yorke J A 1995 Phys. Rev. Lett. 75 2308
[4] Lahey R T 1991 Heat Mass Transfer. 26 351
[5] Letzel H M, Schouten J C, Krishna R, van den Bleek C M 1997 Chem. Eng. Sci. 52 4447
[6] Ji H, Ohara H, Kuramoto K, Tsutsumi A, Yoshida K, Hirama T 2000 Chem. Eng. Sci. 55 403
[7] Llauro F X, Llop M F 2006 Int. J. Multiphase Flow 32 1397
[8] Xiao N, Jin N D 2007 Acta Phys. Sin. 56 5149 (in Chinese) [肖楠, 金宁德 2007 56 5149]
[9] Zhao G B, Yang Y R 2003 AIChE J. 49 869
[10] Li H W, Zhou Y L, Sun B, Yang Y 2010 Chin. J. Chem. Eng. 18 880
[11] Yu H, Chen Y S 2009 Advance in Mechanics 39 154 (in Chinese) [于海, 陈予恕 2009 力学进展 39 154]
[12] Zoldi S M, Greenside H S 1997 Phys. Rev. Lett. 78 1687
[13] Meng D Y, Xu C, Xu Z B 2010 Chin. J. Comput. 33 545 (in Chinese) [孟德宇, 徐晨, 徐宗本 2010 计算机学报 33 545]
[14] Liu Y, Liu Y, Keith C.C.Chan 2010 Signal Processing 90 2375
[15] Auerbach D, Cvitanovic P, Eckmann J P, Gunaratne G, Procaccia I 1987 Phys. Rev. Lett. 58 2387
[16] Saiki Y, Yamada M 2008 Nonlinear Processes in Geophysics 15 675
[17] Cong R, Liu S L, Ma R 2008 Acta Phys. Sin. 57 7487 (in Chinese) [丛蕊, 刘树林, 马瑞 2008 57 7487]
[18] Zhang C T, Ma Q L, Peng H 2010 Acta Phys. Sin. 59 7623 (in Chinese) [张春涛, 马千里, 彭宏 2010 59 7623]
[19] You R Y, Huang X J 2011 Chin. Phys. B 20 020505
[20] Hong W X, Li X, Xu Y H, Wang J J, Song J L 2008 Information fusion and pattern recognition based on the principle of multidimensional chart expression (Beijing: National Defense Industry Press) p193 (In Chinese) [洪文学, 李昕, 徐永红, 王金甲, 宋佳霖 2008 基于多元统计图表示原理的信息融合和模式识别技术 (北京:国防工业出版社)第193页]
[21] Takens F, 1981 Dynamical Systems and Turbulence (Berlin: Spring Verlag) p366
[22] Saary M J 2008 Journal of Clinical Epidemiology 60 311
[23] Hubert M, Rousseeuw P J, Verboven S 2002 Chemometrics and Intelligent Laboratory Systems 60 100
[24] Kim H S, Eykholt R, Salas J D 1999 Physica D 127 48
[25] Zheng G B, Jin N D 2009 Acta Phys. Sin. 58 4485 (in Chinese) [郑桂波, 金宁德 2009 58 4485]
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