| 摘要: |
| 利用局部非线性直接预测方法及实测值与预测值的相关系数，提出了混沌时间序列及含有噪音（白噪音）混沌时间序列的检测混沌和噪音特征的一种方法。该方法对Logistic映射资料及赤道日SST资料进行了混沌及噪音检测。结果表明，该检测方法优于一般诸方法对混沌资料的检测，在资料含噪信比约为32%时，实测值与预测值的相关系数达0.5，在此可信相关系数范围内可检测资料的混沌特征。同时指出了随着资料噪信比的增加，实测值与预测值的相关系数递减，逐渐表现出噪音特性。此外该方法可用于奇怪吸引子关联维数及Kolmogorov熵初步估计。 |
| 关键词: 非线性预测 混沌 噪音 相关系数 |
| DOI：10.11693/hyhz200001012012 |
| 分类号: |
| 基金项目:国家自然科学基金自助项目，49476254号 |
附件 |
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| APPLICATION OF LOCAL NONLINEAR DIRECT FORECASTING METHOD TO DETECT OCEAN CHAOS AND NOISE |
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WEI En-bo1, SONG Qian2, QIN Zheng-cai2, TIAN Ji-wei2
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1.College of Power Engineering, University of shanghai Science and Technology, Shanghai, 200093;2.Physical Oceanography Laboratory, Ocean University of Qingdao, Qingdao, 266003
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| Abstract: |
| This paper gives a method for detecting chaos and noise in chaotic time series and in time series with white noise by using a local nonlinear direct forecasting method and the coefficient of correlation between predicted and actual values. The method is applied to Logistic map data, the equator day SST data and data with noise. The results of application show that the method is better than general spectral analysis in detecting chaos and noise. When the data is contaminated by additive noise 34% in proportion to that of the signal, the correlation coefficient is about 0.5. Within this creditable correlation coefficient, the chaotic phenomenon of the time series is detected by the method.
When the rates of noise-signal increase, the correlation coefficients decrease and the noise character increases. The correlation dimension and the Kolmogorov entropy can be determined by the method. Our results showed that the correlation dimension and Kolmogorov entropy of equator day SST data were about 5 and 0.14(1/d), respectively.
Use of the above results yielded the main conclusions below.
1) The application of nonlinear direct forecasting to detect the deterministic chaos in natural signals with noise is valid.
2) The time series of the equator day SST is chaotic and contaminated by some additive noises.
3) The higher the noise-signal ratio is, the smaller the corresponding correlation coefficient is. |
| Key words: Nonlinear forecast, Chaos, Noise, Correlation coefficient |
