甲型H1N1流感传染人数的灰色预测模型研究

就我国甲型H1N1流感传染人数的预测运用灰色系统理论建立了GM(1,1)模型和1阶残差修正模型GMε(1,1),并分别作了精度分析研究了GMε(1,1)的变化趋势,提出了临界值和有效域概念.用MATLAB确定了模型参数及模型预测值.     

The deterministic grey dynamic model with convolution integral DGDMC(1, n)

Although the grey forecasting models have been successfully utilized in many fields and demonstrated promising results, literatures show their performance still could be improved. The grey prediction theory is methodology and it is necessary to constantly present new models or algorithm based on the theory to improve its performance, prediction accuracy especially. For this purpose, this paper proposes a new prediction model called the deterministic grey dynamic model with convolution integral, abbreviated as DGDMC(1, n). Improvements upon the existing grey prediction model GM(1, n) are made to a large extent and the messages for a system can be inserted sufficiently. The major improvements include determining the unbiased estimates of the system parameters by the deterministic convergence scheme, introducing the first derivative of the 1-AGO data of each associated series into the DGDMC(1, n) model to strengthen the indicative significance and evaluating the modelling 1-AGO data of the predicted series by the convolution integral. The indirect measurement of the tensile strength of a material for a higher temperature is adpoted for demonstration. The results show that the accuracy of indirect measurement is higher by the DGDMC(1, n) model than by the existing GM(1, n) model.     

基于MGM(1,n)模型的多元核支持向量回归预测

根据灰色系统和支持向量机相结合的方法,采用多变量灰色模型MGM(1,n)对相互影响、相互制约的多变量时间序列进行模拟,获取残差序列后运用多元核支持向量回归机(MSVR)对残差进行回归以修正原模型,得到多变量灰色支持向量回归复合模型(MGM-MSVR).实证结论表明:复合模型具有比原模型更高的精度.     

灰色预测GM(1,1)模型的改进及应用

应用自动寻优定权的方法和最小二乘法,研究了灰色系统理论中灰色预测GM(1,1)模型的预测公式的形成过程,发现灰色预测GM(1,1)模型在形成预测公式时对背景值和初始值的规定是不尽合理的,且现有的改进方法对灰色预测GM(1,1)模型的改进还不尽完善.为了提高灰色预测GM(1,1)模型的预测精度,提出并使用自动寻优定权对背景值进行选择,基于最小二乘法原理对灰色预测GM(1,1)模型的初始值进行改进.实例结果表明,提出的改进方法是有效和完善的,对灰色预测GM(1,1)模型的预测精度也有较大的提高.     

组合GM(1,1)幂模型及其应用

GM(1,1)幂模型是灰色Verhulst模型的推广.由于初始条件选取影响GM(1,1)幂模型的精度,将平均相对误差函数分别看成是幂指数、发展系数、灰作用量的函数,利用蚁群算法进行参数辨识,从而建立多个单项GM(1,1)幂模型.利用这些单项模型建立了线性组合GM(1,1)幂模型,组合权系数利用最大相对误差最小化原则采用粒子群算法确定.实例表明,组合GM(1,1)幂模型的建模精度高于传统GM(1,1)幂模型,同时也说明方法是有效的和可行的,具有重要的理论意义.     

灰色预测GM(1,1)模型的一点改进

讨论了灰色预测GM(1,1)模型理论上存在的一些问题,认为在解微分方程dXdt(1)+aX(1)=b进行预测公式推导时,把-X1(1)=X11作为已知条件来确定微分方程的解是不合理的,而应根据实际情况,不局限于{X(1)(k)}序列,直接从最后的平均相对误差ε-=n1∑k=n1ε(k)入手,将-ε看作是常数cm的函数,求出满足Min{-ε(cm)}的cm值即可,并在此基础上推导出cm的计算公式,形成新的灰色预测公式,从而进一步提高预测精度,最后经过实例验证新的预测公式的正确性及可行性.     

灰色离散序列增量动态GML(n,1)模型的参数辩识方法及应用

基于灰色 GM( n,1 )微分动态建模原理 ,按离散数据序列特点 ,提出灰色离散时间序列增量动态GML( n,1 )模型及初次、二次参数辩识方法 .GML( n,1 )模型的信息包容量丰富 ,适用范围广泛 .     

基于蚁群算法的灰色组合预测模型

分别利用灰色GM(1,1)模型、GM(1,1)优化模型和新息GM(1,1)模型建立三个单项预测模型,进一步建立了组合灰色预测模型,组合模型的权系数利用蚁群算法确定.最后给出了一个我国人口数量组合预测模型,计算结果表明,基于蚁群算法的灰色组合预测模型的拟合和预测精度要优于传统组合预测模型.     

Discrete grey forecasting model and its optimization

Although the grey forecasting model has been successfully adopted in various fields and demonstrated promising results, the literatures show its performance could be further improved. For this purpose, this paper proposes a novel discrete grey forecasting model termed DGM model and a series of optimized models of DGM. This paper modifies the algorithm of GM(1, 1) model to enhance the tendency catching ability. The relationship between the two models and the forecasting precision of DGM model based on the pure index sequence is discussed. And further studies on three basic forms and three optimized forms of DGM model are also discussed. As shown in the results, the proposed model and its optimized models can increase the prediction accuracy. When the system is stable approximately, DGM model and the optimized models can effectively predict the developing system. This work contributes significantly to improve grey forecasting theory and proposes more novel grey forecasting models.     

灰色GM(1,1)模型的改进模型在房地产价格指数预测中的应用

提出了一种结合非线性回归技术的灰色GM(1,1)模型的改进模型.利用我国的房地产价格指数预测作为研究对象,用以验证所提方法的有效性和准确性.根据实证结果,说明了新的改进模型有效提高了经典灰色模型的预测精度.     

基于信息再利用的灰色系统GM(1.1)模型建模方法及应用

目的:寻找新的灰色系统GM(1.1)模型建模方法,建立拟合精度与预测精度较高的GM(1.1)模型.方法:在邓聚龙教授建模方法的基础上,用基于信息再利用的方法,建立新的灰色系统GM(1.1)模型.结果:用基于信息再利用的灰色系统GM(1.1)模型建模方法建立的GM(1.1)模型,其拟合精度与预测精度不但优于传统方法建立的GM(1.1)模型,而且优于其他改进方法建立的GM(1.1)模型.结论:基于信息再利用的灰色系统GM(1.1)模型建模方法不但建模过程简单适用,而且其建立的GM(1.1)模型拟合精度与预测精度优于其他改进方法建立的GM(1.1)模型,因而具有广泛的应用价值.     

基于改进的GM(1,1)-Markov链组合模型广东省单位GDP能耗预测

本文以灰色系统理论的GM(1,1)模型和随机过程理论的Markov链模型为基础构建了一个动态GM(1,1)-Markov链组合预测模型。该模型同时利用了GM(1,1)模型对序列趋势因素良好的拟合能力和Markov链模型对残差序列信息的提取能力。为进一步提高该模型的预测精度,用泰勒(Taylor)近似方法和新信息优先的思想对该模型进行了改进。最后,以1991-2014年广东省单位GDP能耗数据实证了该模型的预测效果。     

Generalized GM (1, 1) model and its application in forecasting of fuel production

Grey theory is one approach that can be used to construct a model with limited samples to provide better forecasting advantage for short-term problems. Generally, the GM (1, 1) and Discrete GM (1, 1) models are two typical grey forecasting models in grey theory. However, there are two shortcomings in the above grey models respectively, i.e., the homogeneous-exponent simulative deviation in GM (1, 1) model, and the unequal conversion between the original and white equations in DGM (1, 1) model. In this paper, we firstly propose a novel Generalized GM (1, 1) model termed GGM (1, 1) model, based on GM (1, 1) and DGM (1, 1) models, to overcome the above shortcomings. Then, we detailedly study four important properties in this new grey model. Four estimative approaches of stepwise ratio in GGM (1, 1) model context is also covered. In the end, we simulate and forecast the fuel production in China during the period 2003–2010 using three GM (1, 1) models. The empirical results show that GGM (1, 1) model has higher simulative and predictive accuracy than GM (1, 1) and DGM (1, 1) models. This work contributes significantly to improve grey forecasting theory and proposes a optimized GM (1, 1) model.     

灰色时序组合模型及其在地下水埋深预测中的应用

地下水埋深的变化过程是一个复杂的非线性过程,这种具有复杂的非线性组合特征的序列,使用某一种模型进行预测,结果往往不理想.在分析了灰色GM(1,1)模型、灰色GM(1,1)周期性修正模型和时序AR(n)模型的优点和缺点基础上,提出了一种新的灰色时序组合预报模型.该方法利用了GM预测所需原始数据少、方法简单的优点,用周期修正方法反映其地下水位埋深周期性波动的特征,用AR(n)模型预报其地下水位埋深的随机变化.实例研究表明,这种方法方便简洁实用且预测结果接近于实际观测值,为其它地区的地下水位埋深和相关时间序列的分析研究提供参考与借鉴作用.     

GM(1,1)模型灰色作用量的优化

通过把GM(1,1)模型中的灰色作用量b改进为动态的b_1+b_2k,从而构建了对灰色作用量优化的GM(1,1)模型.通过实例的验证以及与GM(1,1)模型对比,发现优化的GM(1,1)模型的模拟精度和预测精度均较高.     

基于数据变换的优化GM(1,1)模型

本文研究了提高灰色GM(1,1)模型预测精度的问题.利用复合函数变换对原始数据序列经过一定处理的基础上同时优化模型的背景值和初始值的方法,获得了比改进单个模型条件更高预测精度的GM(1,1)模型,推广了灰色预测模型的适用范围.     

直觉模糊GM(1,1)模型及其在灰色发展决策的应用

研究了以直觉模糊数为对象的GM(1,1)模型并运用到灰色发展决策方法。利用灰色系统理论中核和灰度的内涵,将直觉模糊数的犹豫度和记分函数结合构建了直觉模糊数序列 GM(1,1)预测模型,从而实现了直觉模糊数的预测。在此基础上结合变权原理提出了基于直觉模糊数的灰色发展决策方法。最后,算例分析说明了该方法的合理性和可行性。     

On the properties of small sample of GM(1,1) model

In grey prediction modeling, the more samples selected the more errors. This paper puts forward new explanations of “incomplete information and small sample” of grey systems and expands the suitable range of grey system theory. Based on the geometric sequence, it probes into the influence on the relative errors by selecting the different sample sizes. The research results indicate that to the non-negative increasing monotonous exponential sequence, the more samples selected, the more average relative errors. To the non-negative decreasing monotonous exponential sequence, a proper sample number exists that has the least average relative error. When the initial value of the sequence of raw data of new information GM(1,1) model changes, the development coefficient remains unchanged. The segmental correction new information GM(1,1) model (SNGM) can obviously improve the simulation accuracy. It puts forward the mathematic proofs that the small sample usually has more accuracy than the large sample when establishing GM(1,1) model in theory.     

改进GM(2,1)模型的MATLAB实现及其应用

针对经济预测,根据灰色模型GM(1,1)的应用介绍了灰色模型GM(2,1)的原理,并利用最小二乘法改进GM(2,1)算法及其预测步骤,用MATLAB实现了预测,用中国经济增长率数据做了仿真,对观测时间序列拟合出数学模型.     

The modeling mechanism,extension and optimization of grey GM (1, 1) model

The modeling mechanism of GM (1, 1) model is studied by using the thought of matrix analysis in this paper, the extension form GGM (1, 1) model based on the fractional order accumulated generating is put forward and its theoretical significance is analyzed. Furthermore, the influence of multiple transformation, translation transformation for the initial value and generating series on model parameters and predictive value are researched, then the quantitative relation among them is deduced and an optimization model and corresponding algorithm in practical modeling are presented.