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利用替代数据法检验了摇摆条件下自然循环系统不规则复合型脉动的混沌特性, 并在此基础上进行混沌预测. 关联维数、最大Lyapunov指数等几何不变量计算结果表明不规则复合型脉动具有混沌特性, 但是由于计算结果受实验时间序列长度的限制和噪声的影响, 可能会出现错误的判断结果. 为了避免出现误判, 在提取流量脉动的非线性特征的同时, 需要用替代数据法进一步检验混沌特性是否来自于确定性的非线性系统. 本文用迭代的幅度调节Fourier 算法进行混沌检验, 在此基础上用加权一阶局域法进行混沌脉动的预测. 计算结果表明: 不规则复合型脉动是来自于确定性系统的混沌脉动, 加权一阶局域法对流量脉动进行混沌预测效果较好, 并提出动态预测方法.Chaos identification and forecasting of the irregular complex flow oscillations in a two-phase natural circulation system under the rolling motion are performed. The irregular complex flow oscillation has chaotic characteristics by calculating the geometric invariants such as the correlation dimension, Kolmogorov entropy and the largest Lyapunov exponent. But the reliability of calculation result is liable to be influenced by data length and the interference of measurement noise, false judgment results may exist in the direct method. To avoid misjudgment for chaos flow oscillation, both the geometric invariants and chaos identification need to be calculated by surrogate-data method. The chaos is identified by the iterated-amplitude adjusted Fourier transform method. Chaotic forecasting for the irregular complex flow oscillation is carried out by adding weight one-rank local region method. By surrogate-data method, we can confirm that the irregular complex flow oscillation is chaotic oscillation from the deterministic system. Comparisons between the prediction results and experimental data indicate that the chaos forecasting based on adding weight one-rank local region method is an effective way for two-phase natural circulation flow instabilities, and a way of dynamical forecast to monitor flow oscillation is presented.
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Keywords:
- chaotic time series /
- surrogate-data method /
- prediction real-time /
- two-phase flow instabilities
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[28] Takens F 1981 Lecture Notes in Math. 898 361
[29] L J H, Lu J A, Chen S H 2002 Chaotic Time Series Analysis and Application (Wuhan: Wuhan University Press) pp59, 60, 102 (in Chinese) [吕金虎, 陆君安, 陈士华 2002 混沌时间序列分析及其应用 (武汉: 武汉大学出版) 第59, 60, 102 页]
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[1] L J H, Murali K, Sinha S, Leung H, Aziz-Alaoui M A 2008 Phys. Lett. A 372 3234
[2] L J H, Chen G R 2006 Int. J. Bifur. Chaos 16 775
[3] Deng W H, L J H 2007 Phys. Lett. A 369 438
[4] L J H 2008 Adv. in Mech. 38 713 (in Chinese) [吕金虎 2008 力学进展 38 713]
[5] L J H, Chen G R 2005 IEEE Trans. Auto. Contr. 50 841
[6] L J H, Yu X H, Chen G R, Cheng D 2004 IEEE Trans. Circ. Syst. I 51 787
[7] Zhou J, Lu J A, L J H 2006 IEEE Trans. Automat. Contr. 51 652
[8] Sachin B 2013 IEEE Trans. Circuits Syst. I 60 199
[9] Chen Y, L J H, Lin Z L Automatica (in press)
[10] Wu C Y, Wang S B, Pan C 1996 Nucl. Eng. Des. 162 223
[11] Chang C J, Richard T, Lahey J 1997 Nucl. Eng. Des. 167 307
[12] Kuang B, Chen H, Hu Z H, Lu L L, Xu J J 2005 J. Eng. Thermoph. 26 88 (in Chinese) [匡波, 陈宏, 胡志华, 陆柳柳, 徐济鋆 2005工程热 26 88]
[13] Sun B, Zhou Y L 2006 J. Harb. Inst. Tech. 38 1963 (in Chinese) [孙斌, 周云龙 2006 哈尔滨工业大学学报 38 1963]
[14] Xiao N, Jin N D 2007 Acta Phys. Sin. 56 5149 (in Chinese) [肖楠, 金宁德 2007 56 5149]
[15] Guo Y, Qiu S Z, Su G H, Jia D N 2008 Ann. Nucl. Energy 35 1598
[16] Tan S, Su G H, Gao P Z 2009 Ann. Nucl. Energy 36 103
[17] Tan S C, Pang F G 2005 Nuclear Power Engineering 26 140 (in Chinese) [谭思超, 庞凤阁 2005核动力工程 26 140]
[18] Tan S C, Gao P Z, Su G H 2008 Atom. Energy. Sci. Tech. 42 1007 (in Chinese) [谭思超, 高璞珍, 苏光辉 2008原子能科学技术 42 1007]
[19] Zhang W C, Tan S C, Gao P Z, Zhang H, Zhang H Y 2012 Atom. Energy Sci. Tech. 46 705 (in Chinese) [张文超, 谭思超, 高璞珍, 张虹, 张红岩 2012 原子能科学技术 46 705]
[20] Theiler J, Euhank S, Longtin A, Caldrikian B, Farmer J D 1992 Physica D: Nonlinear Phenomena 58 77
[21] Liu Y Z, Wen X S, Hu N Q 2001 Acta Phys. Sin. 50 1241 (in Chinese) [刘耀宗, 温熙森, 胡茑庆 2001 50 1241]
[22] Wu Y D, Xie H B 2007 Acta Phys. Sin. 56 6294 (in Chinese) [吴延东, 谢洪波 2007 56 6294]
[23] Ma W C, Jin N D, Gao Z K 2012 Acta Phys. Sin. 61 170510 (in Chinese) [马文聪, 金宁德, 高忠科 2012 61 170510]
[24] L J H, Zhang S C 2002 Control Theory and Application 19 767 (in Chinese) [吕金虎, 张锁春 2002 控制理论与应用 19 767]
[25] Chen Y F, L J H, Zhou C B 2001 Chin. J. Rock Mech. Engin. 20 671 (in Chinese) [陈益峰, 吕金虎, 周创兵 2001 岩石力学与工程学报 20 671]
[26] Yang Y F, Ren X M, Qin W Y, Wu Y F, Zhi X Z 2008 Acta Phys. Sin. 57 6139 (in Chinese) [杨永锋, 任兴民, 秦卫阳, 吴亚锋, 支希哲 2008 57 6139]
[27] Tan S C, Su G H, Gao P Z 2009 Appl. Therm. Eng. 29 3160
[28] Takens F 1981 Lecture Notes in Math. 898 361
[29] L J H, Lu J A, Chen S H 2002 Chaotic Time Series Analysis and Application (Wuhan: Wuhan University Press) pp59, 60, 102 (in Chinese) [吕金虎, 陆君安, 陈士华 2002 混沌时间序列分析及其应用 (武汉: 武汉大学出版) 第59, 60, 102 页]
[30] Grassberger P, Procaccia I 1983 Physica D 9 189
[31] Wang H Y, Lu S 2006 Nonlinear Time Scries Analysis and its Application (Beijing: Science Press) p30 (in Chinese) [王海燕, 卢山 2006非线性时间序列分析及其应用 (北京: 科学出版社) 第30页]
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