【作者】 汪金菊；

【导师】 朱功勤；

【作者基本信息】 合肥工业大学 ， 计算机应用技术， 2008， 博士

【摘要】 实际测量得到的混沌时间序列不可避免地存在噪声,极大地影响了其参数计算和下一步的预测精度。鉴于此,本文深入研究了贝叶斯的理论与方法,并且把它与其他模型相结合构造了含加性高斯噪声的混沌时间序列的降噪和预测模型。主要研究工作及成果如下:(1)基于马尔可夫模型及经验贝叶斯的思想,提出了一种混沌时间序列的小波域统计降噪方法。对含加性高斯噪声的混沌时间序列进行对偶树复小波变换,得到小波系数的实部和虚部;对该实部和虚部数据分别建立隐马尔科夫树模型,再结合经验贝叶斯方法估计加噪前源混沌时间序列所对应的小波系数的实部和虚部;最后采用对偶树复小波逆变换得到降噪后的混沌时间序列。仿真结果表明该方法能够有效地对混沌时间序列进行降噪,且能够较好地校正混沌时间序列相空间中点的位置,逼近真实的混沌吸引子轨迹。(2)运用RBF神经网络模型及分层贝叶斯的思想,建立了一种含噪混沌时间序列的相空间域预测方法。分层贝叶斯算法把RBF神经网络模型中的径向基函数个数、模型参数、以及噪声参数都视为随机变量需要进行估计。对其中必要的计算,采用可逆跳跃马尔可夫链蒙特卡罗方法。仿真结果表明该方法具有较强的抗噪能力以及有效地抑制了过拟和现象,且预测精度对重构相空间的嵌入维数和时延参数的变化不敏感。(3)基于变分贝叶斯及相空间重构理论,构造了含噪混沌时间序列相空间域线性回归预测模型。对序列进行相空间重构,在相空间中用变分贝叶斯推断方法估计线性回归系数。仿真结果表明该模型具有较强的抗噪能力以及有效地抑制了过拟和现象,且预测精度对重构相空间的嵌入维数和时延参数的变化不敏感。(4)借鉴Kriging模型及相空间重构理论建立了含噪混沌时间序列相空间域Kriging预测方法。仿真结果表明该方法能够有效地预测含噪混沌时间序列,且具有较强的抗噪能力以及有效地抑制了过拟和现象。同时预测精度对重构相空间的嵌入维数和时延参数的变化不敏感。(5)基于Kriging模型及变分贝叶斯方法.建立了一种含噪混沌时间序列相空间域预测模型。仿真结果表明该方法能够有效地预测含噪混沌时间序列,且具有较强的抗噪能力以及有效地抑制了过拟和现象。同时预测精度对重构相空间的嵌入维数和时延参数的变化不敏感。更多还原

【Abstract】 Chaotic time series have noise arrived from practical measure,which affect parameters calculation and the next prediction precision.The dissertatior studies bayesian theory and method.And we integrate bayesian method with the other models to construct denoising models and prediting models of noisy chaotic time series. The main results in this dissertation are outlined as follows.(1)We presented a chaotic time series statistical denoising method in wavelet domain based on the idea of markov model and experiential bayes. The dual-tree complex wavelet decomposed chaotic time series with additive gaussian noise to obtain real part and imaginary part of wavelet coefficients. We modeled the real part and imaginary part data as hidden markov trees model. Empirical Bayesian method was used to estimate wavelet coefficients real part and imaginary part of source chaotic time series. Finally using dual-tree complex wavelet inverse transform, we can get the denoised chaotic time series. The numerical experiments results show that the proposed method is efficient. It can better correct the position of data points in phase space and approximate the real chaotic attractor trajectories more closely.(2) Using RBF neural networks and hierarchical bayesian algorithm,a phase space domain prediction method of noisy chaotic time series was constructed. The hierarchical bayesian algorithm treated the numbers of radial function,model parameters,and noise parameters as random variables that need to be estimated in the RBF neural networks. we used the reversible jumping Markov Chain Monte Carlo (rjMCMC) method to perform the necessary computations. The numerical experiment results show our method can predict noisy chaotic time series effectively .The model is robust to noise and control the overfitting effectively.The prediction effect is not sensitive to the change of embedding dimension and time delay.(3) Based on variational bayesian and phase spa;e reconstructive theory we constructed a linearly regressive prediction model in noisy chaotic time series phase space.Time series phase space was constructed.Variational bayesian method estimated the linealy regressive coefficients. The numerical experiment results show the model is robust to noise and control the overfitting effectively.The prediction effect is not sensitive to the change of embedding dimension and time delay. (4) We constructed a prediction model of the chaotic time series with additive gaussian noise based on Kriging model in the phase space. The numerical experiment results show the model is robust to noise and control the overfitting effectively.The prediction effect is not sensitive to the change of embedding dimension and time delay.(5) Based on the variational bayesian method and Kriging mathematical idea we constructed a noisy chaotic time series phase space domain prediction model. The numerical experiment results show our method can predict noisy chaotic time series effectively .The model is robust to noise and control the overfitting effectively.The prediction effect is not sensitive to the change of embedding dimension and time delay.更多还原