基于智能计算和混沌理论的铀价格预测研究
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摘要
铀矿资源产品被世界各国广泛应用于军事、经济和社会生活等方面，对世界诸多领域产生了革命性的影响。铀资源既是核能发展的物质基础，同时也是一种战略资源，铀资源价格定量预测对核能开发及利用政策和发展规划的制定具有重要的参考价值。由于铀价格具有复杂性、非线性和不确定性等特点，使得传统的时间序列预测技术很难达到满意的效果。随着人工智能技术、混沌动力学和信号处理技术的发展，人们对非线性时间序列表现出的复杂性有了更加深刻的认识，这也为国际市场铀价格时间序列分析和预测提供了新的、科学有效的方法。
本文基于混沌理论和经验模态分解（Empirical Mode Decomposition，EMD）技术，结合若干智能计算方法：最小二乘支持向量机（Least Square Support Vector Machine,LSSVM），动态模糊神经网络（Dynamic Fuzzy Neural Network, DFNN），极限学习机（Extreme Learning Machine, ELM）和相关向量机（Relevance Vector Machine, RVM），针对国际市场铀价格时间序列智能预测建模问题展开较深入的研究，建立了多种混合智能预测模型，为铀价格时间序列预测探索了有效的方法，也为非线性预报建模提供了有效的新途径。主要研究内容如下：
1、简单介绍了相空间重构理论，以及确定相空间重构参数的常用方法。针对实际铀价格时间序列相空间重构的参数选取问题，首先采用互信息法和Cao方法分别确定延迟时间和嵌入维数，然后引入微分熵方法同时确定嵌入维数和延迟时间；
2、对铀价格时间序列进行非线性与混沌特性的识别。一方面，将基于相空间重构的延迟向量方差（Delay Vector Variance，DVV）算法用于判定铀价格序列的非线性特性，通过DVV分布图或DVV散点图对铀价格时间序列信号进行定性描述；另一方面，分别通过定量计算G-P关联维数与最大Lyapunov指数两个特征量来对国际铀资源月价格时间序列的混沌特性进行识别；
3、在相空间重构的基础上，提出了一种基于动态模糊神经网络的铀价格时间序列预测方法，并利用量子行为粒子群算法(Quantum behaved Particle Swarm Optimization，QPSO)优化模型参数。该方法无须领域的专家知识就可以实现对铀价格时间序列预测自动建模及抽取模糊规则，可以实现在线学习，且所得到的模糊规则数不随输入变量的增加而按指数增长；
4、提出一种基于经验模式分解和极限学习机的铀价格时间序列混合预测方法。首先通过EMD分解，将原始非平稳的价格序列分解为若干固有模态分量（Intrinsic ModeFunction，IMF)，根据频率高低将各分量分组叠加得到3个新序列；然后在相空间重构的基础上对各序列分别构建ELM模型进行预测；最后对3个序列的预测值进行合成。仿真实验结果表明了方法的有效性；
5、提出了一种基于集成经验模态分解（Ensemble Empirical Mode Decomposition，EEMD）和相空间重构的铀价格智能预测混合建模方法。首先针对EMD的不足，将EEMD用于铀价格序列分解，接着对分解后的固有模态分量依据频率高低重新组合成高频、低频与余项3个新序列，然后在相空间重构的基础上分别用RVM、LSSVM和ELM预测高频、低频与余项序列，最后对3个序列的预测值进行叠加得到铀价格序列预测值。仿真实验表明，该方法有较高的预测精度；
6、建立一种基于多元线性回归和最小二乘支持向量机的铀价格集成预测模型。首先利用多元线性回归模型获取时间序列的线性信息，然后利用最小二乘支持向量机出色的非线性拟合能力建立混合预测模型；此外，为了提高预测精度，将粒子群优化算法用于LSSVM参数的优化选取。实验结果表明，与其他模型相比该方法的预测性能有较大的提高。
Uranium resource products have been widely used in economics, military, social lives,and so on and have a revolutionary effect on the real world in many areas. Uranium resourceis both the material basis for the development of nuclear energy and a kind of strategicresource.Therefore, more accurate forecasts for international uranium resource prices play anincreasingly important role in the development planning and utilization of nuclear energy.Forecasting the uranium resource prices is one of the most important and challenging tasksdue to its inherent nonlinearity and non-stationary characteristics.
Based on chaos theory and empirical mode decomposition technique, several hybridintelligence prediction models for international uranium resource prices forecasting have beenestablished combining with some intelligent computation methods such as Least SquareSupport Vector Machine(LSSVM), Dynamic Fuzzy Neural Network(DFNN), ExtremeLearning Machine(ELM) and Relevance Vector Machine(RVM). The main contents discussedin this thesis are described as follows:
1、The influence of phase space parameters on phase space quality and the commonmethods for determining delay time and embedding dimension are discussed based on thereconstruction theory. In view of parameter selection problem of phase space reconstructionfor the actual uranium price time series, a novel method for determining the set of parametersfor a phase space representation of a time series named as the entropy ratio(ER) method isintroduced. Based upon the differential entropy, both the optimal embedding dimension andtime lag are simultaneously determined.
2、 Nonlinearity and chaotic characteristic for uranium price series have beenidentification. On the one hand, nonlinear nature of the time series is examined by performingdelay vector variance (DVV) analyses on both the original and a number of surrogate timeseries, using the optimal embedding dimension of the original time series. On the other hand,quantitative calculation about saturation correlation dimension and the largest Lyapunovexponent of uranium price series is used to identity their chaotic characteristics.
3、Based on the phase reconstruction, a prediction model for international uraniumresource prices based on DFNN combined with Quantum-behaved Particle SwarmOptimization(QPSO) were proposed. The salient characteristics of the method are:1)hierarchical on-line self-organizing learning is used;2)neurons can be recruited or deleteddynamically according to their significance to the system’s performance; and3)fast learningspeed can be achieved.
4、A hybrid forecasting approach combining empirical mode decomposition(EMD),phase space reconstruction(PSR), and ELM for international uranium resource prices isproposed. In the first stage, the original uranium resource price series are first decomposedinto a finite number of independent intrinsic mode functions(IMFs), with different frequencies.In the second stage, the IMFs are composed into three subseries based on the fine-to-coarsereconstruction rule. In the third stage, based on phase space reconstruction, different ELMmodels are used to model and forecast the three subseries, respectively, according to the intrinsic characteristic time scales. Finally, in the fourth stage, these forecasting results arecombined to output the ultimate forecasting result. Experimental results from real uraniumresource price data demonstrate that the proposed hybrid forecasting method outperformsRBF neuralnetwork(RBFNN) and single ELM in terms of RMSE, MAE, and DS.
5、A novel hybrid ensemble modeling approach integrating ensemble empirical modedecomposition(EEMD) and multiple intelligent computation methods such as RVM, LSSVMand ELM is proposed for international uranium resource prices forecasting, based on thephase reconstruction. This hybrid approach is formulated specifcally to address difficulties inmodeling uranium resource prices forecasting, which has inherently complexity andirregularity. In the proposed hybrid ensemble learning paradigm, EEMD, as a competitivedecomposition method in stead of EMD, is first applied to decompose original data ofinternational uranium resource prices into a number of independent intrinsic modefunctions(IMFs) of original data. Then the IMFs are composed into three subseries based onthe fine-to-coarse reconstruction rule. Based on phase space reconstruction, different modelsincluding RVM, LSSVM, ELM are used to model and forecast the three subseries,respectively, according to the intrinsic characteristic time scales. Finally, these predictedsubseries are aggregated into an ensemble result as final prediction. Empirical resultsdemonstrate that the hybrid modeling approach can outperform some other popularforecasting models in both level prediction and directional forecasting.
6、Based on the phase reconstruction, the time series of uranium resource price isexpanded to multivariate time series, which includes ergodic information, and so that moreabundant information can be found in favor of model training. A hybrid model combiningMLR and LSSVM is established. The proposed hybrid model exploits the unique strength ofMLR and LSSVM models in forecasting uranium resource prices. In addition, particle swarmoptimization (PSO) is used to find the optimal parameters of LSSVM in order to improve theprediction accuracy. Experimental results indicate that the proposed model outperforms sometraditional models, including MLR, RBFNN, LSSVM, the linear combination model, and themodel incorporating MLR and RBFNN.
本文基于混沌理论和经验模态分解（Empirical Mode Decomposition，EMD）技术，结合若干智能计算方法：最小二乘支持向量机（Least Square Support Vector Machine,LSSVM），动态模糊神经网络（Dynamic Fuzzy Neural Network, DFNN），极限学习机（Extreme Learning Machine, ELM）和相关向量机（Relevance Vector Machine, RVM），针对国际市场铀价格时间序列智能预测建模问题展开较深入的研究，建立了多种混合智能预测模型，为铀价格时间序列预测探索了有效的方法，也为非线性预报建模提供了有效的新途径。主要研究内容如下：
1、简单介绍了相空间重构理论，以及确定相空间重构参数的常用方法。针对实际铀价格时间序列相空间重构的参数选取问题，首先采用互信息法和Cao方法分别确定延迟时间和嵌入维数，然后引入微分熵方法同时确定嵌入维数和延迟时间；
2、对铀价格时间序列进行非线性与混沌特性的识别。一方面，将基于相空间重构的延迟向量方差（Delay Vector Variance，DVV）算法用于判定铀价格序列的非线性特性，通过DVV分布图或DVV散点图对铀价格时间序列信号进行定性描述；另一方面，分别通过定量计算G-P关联维数与最大Lyapunov指数两个特征量来对国际铀资源月价格时间序列的混沌特性进行识别；
3、在相空间重构的基础上，提出了一种基于动态模糊神经网络的铀价格时间序列预测方法，并利用量子行为粒子群算法(Quantum behaved Particle Swarm Optimization，QPSO)优化模型参数。该方法无须领域的专家知识就可以实现对铀价格时间序列预测自动建模及抽取模糊规则，可以实现在线学习，且所得到的模糊规则数不随输入变量的增加而按指数增长；
4、提出一种基于经验模式分解和极限学习机的铀价格时间序列混合预测方法。首先通过EMD分解，将原始非平稳的价格序列分解为若干固有模态分量（Intrinsic ModeFunction，IMF)，根据频率高低将各分量分组叠加得到3个新序列；然后在相空间重构的基础上对各序列分别构建ELM模型进行预测；最后对3个序列的预测值进行合成。仿真实验结果表明了方法的有效性；
5、提出了一种基于集成经验模态分解（Ensemble Empirical Mode Decomposition，EEMD）和相空间重构的铀价格智能预测混合建模方法。首先针对EMD的不足，将EEMD用于铀价格序列分解，接着对分解后的固有模态分量依据频率高低重新组合成高频、低频与余项3个新序列，然后在相空间重构的基础上分别用RVM、LSSVM和ELM预测高频、低频与余项序列，最后对3个序列的预测值进行叠加得到铀价格序列预测值。仿真实验表明，该方法有较高的预测精度；
6、建立一种基于多元线性回归和最小二乘支持向量机的铀价格集成预测模型。首先利用多元线性回归模型获取时间序列的线性信息，然后利用最小二乘支持向量机出色的非线性拟合能力建立混合预测模型；此外，为了提高预测精度，将粒子群优化算法用于LSSVM参数的优化选取。实验结果表明，与其他模型相比该方法的预测性能有较大的提高。
Uranium resource products have been widely used in economics, military, social lives,and so on and have a revolutionary effect on the real world in many areas. Uranium resourceis both the material basis for the development of nuclear energy and a kind of strategicresource.Therefore, more accurate forecasts for international uranium resource prices play anincreasingly important role in the development planning and utilization of nuclear energy.Forecasting the uranium resource prices is one of the most important and challenging tasksdue to its inherent nonlinearity and non-stationary characteristics.
Based on chaos theory and empirical mode decomposition technique, several hybridintelligence prediction models for international uranium resource prices forecasting have beenestablished combining with some intelligent computation methods such as Least SquareSupport Vector Machine(LSSVM), Dynamic Fuzzy Neural Network(DFNN), ExtremeLearning Machine(ELM) and Relevance Vector Machine(RVM). The main contents discussedin this thesis are described as follows:
1、The influence of phase space parameters on phase space quality and the commonmethods for determining delay time and embedding dimension are discussed based on thereconstruction theory. In view of parameter selection problem of phase space reconstructionfor the actual uranium price time series, a novel method for determining the set of parametersfor a phase space representation of a time series named as the entropy ratio(ER) method isintroduced. Based upon the differential entropy, both the optimal embedding dimension andtime lag are simultaneously determined.
2、 Nonlinearity and chaotic characteristic for uranium price series have beenidentification. On the one hand, nonlinear nature of the time series is examined by performingdelay vector variance (DVV) analyses on both the original and a number of surrogate timeseries, using the optimal embedding dimension of the original time series. On the other hand,quantitative calculation about saturation correlation dimension and the largest Lyapunovexponent of uranium price series is used to identity their chaotic characteristics.
3、Based on the phase reconstruction, a prediction model for international uraniumresource prices based on DFNN combined with Quantum-behaved Particle SwarmOptimization(QPSO) were proposed. The salient characteristics of the method are:1)hierarchical on-line self-organizing learning is used;2)neurons can be recruited or deleteddynamically according to their significance to the system’s performance; and3)fast learningspeed can be achieved.
4、A hybrid forecasting approach combining empirical mode decomposition(EMD),phase space reconstruction(PSR), and ELM for international uranium resource prices isproposed. In the first stage, the original uranium resource price series are first decomposedinto a finite number of independent intrinsic mode functions(IMFs), with different frequencies.In the second stage, the IMFs are composed into three subseries based on the fine-to-coarsereconstruction rule. In the third stage, based on phase space reconstruction, different ELMmodels are used to model and forecast the three subseries, respectively, according to the intrinsic characteristic time scales. Finally, in the fourth stage, these forecasting results arecombined to output the ultimate forecasting result. Experimental results from real uraniumresource price data demonstrate that the proposed hybrid forecasting method outperformsRBF neuralnetwork(RBFNN) and single ELM in terms of RMSE, MAE, and DS.
5、A novel hybrid ensemble modeling approach integrating ensemble empirical modedecomposition(EEMD) and multiple intelligent computation methods such as RVM, LSSVMand ELM is proposed for international uranium resource prices forecasting, based on thephase reconstruction. This hybrid approach is formulated specifcally to address difficulties inmodeling uranium resource prices forecasting, which has inherently complexity andirregularity. In the proposed hybrid ensemble learning paradigm, EEMD, as a competitivedecomposition method in stead of EMD, is first applied to decompose original data ofinternational uranium resource prices into a number of independent intrinsic modefunctions(IMFs) of original data. Then the IMFs are composed into three subseries based onthe fine-to-coarse reconstruction rule. Based on phase space reconstruction, different modelsincluding RVM, LSSVM, ELM are used to model and forecast the three subseries,respectively, according to the intrinsic characteristic time scales. Finally, these predictedsubseries are aggregated into an ensemble result as final prediction. Empirical resultsdemonstrate that the hybrid modeling approach can outperform some other popularforecasting models in both level prediction and directional forecasting.
6、Based on the phase reconstruction, the time series of uranium resource price isexpanded to multivariate time series, which includes ergodic information, and so that moreabundant information can be found in favor of model training. A hybrid model combiningMLR and LSSVM is established. The proposed hybrid model exploits the unique strength ofMLR and LSSVM models in forecasting uranium resource prices. In addition, particle swarmoptimization (PSO) is used to find the optimal parameters of LSSVM in order to improve theprediction accuracy. Experimental results indicate that the proposed model outperforms sometraditional models, including MLR, RBFNN, LSSVM, the linear combination model, and themodel incorporating MLR and RBFNN.
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