边坡演化的非线性时间序列多元混沌判别

周翠英; 陈恒; 朱凤贤

Volume 33 Issue 3

May 2008

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Article Navigation > Earth Science > 2008 > 33(3): 393-398

ZHOU Cui-ying, CHEN Heng, ZHU Feng-xian, 2008. Multivariable Chaotic Discrimination for Slope Evaluation According to Their Nonlinear Displacement-Time Sequence. Earth Science, 33(3): 393-398.

Citation:

ZHOU Cui-ying, CHEN Heng, ZHU Feng-xian, 2008. Multivariable Chaotic Discrimination for Slope Evaluation According to Their Nonlinear Displacement-Time Sequence. Earth Science, 33(3): 393-398.

ZHOU Cui-ying, CHEN Heng, ZHU Feng-xian, 2008. Multivariable Chaotic Discrimination for Slope Evaluation According to Their Nonlinear Displacement-Time Sequence. Earth Science, 33(3): 393-398.

Citation:

ZHOU Cui-ying, CHEN Heng, ZHU Feng-xian, 2008. Multivariable Chaotic Discrimination for Slope Evaluation According to Their Nonlinear Displacement-Time Sequence. Earth Science, 33(3): 393-398.

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Multivariable Chaotic Discrimination for Slope Evaluation According to Their Nonlinear Displacement-Time Sequence

Research Centre for Geotechnical Engineering and Information Technology, School of Engineering, Sun Yat-sen University, Guangzhou 510275, China

Received Date: 2008-03-30
Publish Date: 2008-05-25

Abstract

Abstract

According to the displacement-time sequence data of several slopes, the multivariable chaotic features of slope evaluation process are discussed, including reconstruction for their phase-space by the estimation of delayed time and embedded dimension method, calculation for the correlation dimension D2 of the slope system by eliminating the time correlative points.Then, the multivariable chaotic features of the slopes are studied by calculating their maximum Lyapunov index using the improved Kantz method and taking K₂ as the similar one of Kolmogorov entropy, and by introducing the approximation entropy-ApEn and the chaotic feature index describing the complexity degree of the system.Example analysis shows that the correlation dimension D₂ is a non-integral number for most of slope systems, the maximum Lyapunov index and the entropy value are all bigger than 0, and the complexity degree of the system is located on the interval of (0, 1).By comparing the calculated data with the actual characteristic value of the slope systems, the chaotic features of the slope system are revealed and the chaotic features are clearer in the time period closed to sliding.
- slope evaluation,
- nonlinear displacement-time sequence,
- displacement-phase space reconstruction,
- multivariable chaotic discrimination

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References

Cheng, Q. M., 2006. Singularity-generalized self-similarity-fractal spectrum (3S) models. Earth Science-Journal of China University of Geosciences, 31(3): 337-348(in Chinese with English abstract).

Grassberger, P., Procaccia, I., 1983. Measuring the strangeness of strange attractors. Physica D, 9: 189-208. doi: 10.1016/0167-2789(83)90298-1

Huang, R. Q., Xu, Q., 1996. The application of nonlinear theory in engineering geology. Bulletin of National Natural Science Foundation of China, 2: 79-84(in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTOTAL-ZKJJ199602000.htm

Huang, S. W., 2002. Study on chaotic vibration of engineering structures, algorithms of chaotic maximum optimization and its application [Dissertation]. Hehai University, Nanjing (in Chinese with English abstract).

Kautz, H., Schreiber, T., 1997. Nonliear time series analysis. Cambridge University Press, Cambridge.

Kim, H. S., Eykholt, R., Salas, J. D., 1999. Nonlinear dynamic, delay times, and embedding windows. Physica D, 127: 48-60. doi: 10.1016/S0167-2789(98)00240-1

Liu, B. Z., Pen, J. H., 2004. Nonlinear dynamic mechanics. Higher Education Press, Beijing (in Chinese).

Lopez-Ruiz, R., Manclni, H. L., Calet, X. A., 1995. A statistical measure of complexity. Phys. Lett. , 209(5-6) 321-326. doi: 10.1016/0375-9601(95)00867-5

Lü, J. H., Chen, J. A., Chen, S. H., 2002. Chaotic time sequence analysis and application. Wuhan University Press, Wuhan (in Chinese).

Pincus, S. M., 1995. Approximate entropy (ApEn) as a complexity measure. Chaos, 5(1): 110-117. doi: 10.1063/1.166092

Provenzale, A., Smith, L. A., Vio, R., et al., 1994. Distinguishing between low-dimensional dynamics and randomness in measured time series. Physica D, 58: 31-49.

Qin, S. Q., Jiao, J. J., Wang, S. J., et al., 2001. A nonlinear catastrophe model of instability of planar-slip slope and chaotic dynamical mechanisms of its evolutionary process. International Journal of Solids and Structures, 38: 8093-8109. doi: 10.1016/S0020-7683(01)00060-9

Takens, F., 1981. Detecting strange attractors in turbulence. In: Dynamical systems and turbulence. Lecture Notes in Mathematics, 898: 366-381.

Theiler, J., 1986. Spurious dimension from correlation algorithms applied to limited time series data. Phys. Rev. A, 34(3): 2427-2432. doi: 10.1103/PhysRevA.34.2427

Wolf, A., Swift, J. B., Swinney, H. L., et al., 1985. Determining Lyapunov exponents froma time series. Physica D, 16(3): 285-317. doi: 10.1016/0167-2789(85)90011-9

Yu, C. W., 2002. Complexity of geosystems: Basic issues of geological science (Ⅰ). Earth Science-Journal of China University of Geosciences, 27(5): 509-519(in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTOTAL-DQKX200205005.htm

Zhou, C. Y., 2000. Nonlinear features and prognosis of landslides, landslides in research, theory and practice. Thomas Telford, London, 1(1): 267-272.

成秋明, 2006. 非线性成矿预测理论: 多重分形奇异性-广义自相似性-分形谱系模型与方法. 地球科学——中国地质大学学报, 31(3): 337-348. https://www.cnki.com.cn/Article/CJFDTOTAL-DQKX200603008.htm

黄润秋, 许强, 1996. 非线性理论在工程地质中的应用. 中国科学基金, 2: 79-84. https://www.cnki.com.cn/Article/CJFDTOTAL-ZKJJ199602000.htm

黄胜伟, 2002. 工程结构混沌振动、混沌最优化算法及其应用[博士论文]. 南京: 河海大学.

刘秉正, 彭建华, 2004. 非线性动力学. 北京: 高等教育出版社.

吕金虎, 陈君安, 陈士华, 2002. 混沌时间序列分析及其应用. 武汉: 武汉大学出版.

於崇文, 2002. 地质系统的复杂性——地质科学的基本问题(Ⅰ). 地球科学——中国地质大学学报, 27(5): 509-519. https://www.cnki.com.cn/Article/CJFDTOTAL-DQKX200205005.htm

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