一类优化灰色作用量的GM(2,1)模型

通过把GM(2,1)模型中的灰色作用量b改进为b_1+b_2k,从而构建了灰色作用量优化的GM(2,1)模型,并改进了相应的边界条件,通过实例验证以及与累积GM(2,1)模型和反向累积GM(2,1)模型对比,发现改进灰作用量后的GM(2,1)模型具有较高的模拟精度.     

GM(1,1)模型适用域讨论及模型的改进

在已有灰色系统理论的基础上,讨论了GM(1,1)模型的适用域,明确界定了GM(1,1)模型的有效区域和禁区,并提出了GM(1,1)模型的一种改进形式——离散灰色预测DGM(1,1)模型.通过对我国经济增长的实证分析说明了该模型的有效性和可靠性.研究结果表明,提出的DGM(1,1)模型可作为灰色预测的一种精确模型,因此,为我国经济增长预测提供了一种新的方法,对当前我国经济的理性增长具有重要的指导意义.     

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.     

基于分数阶累加的GM(2,1)模型及其改进研究

在传统GM(2,1)模型模型的基础上,通过引入分数阶算子得出了基于分数阶累加的GM(2,1)模型的一般形式。为进一步提高预测精度,提出了一种改进形式,并给出了两种不同方式来确定时间响应式的参数。最后以两个实例验证了本文提出的分数阶GM(2,1)模型及其改进模型的有效性和实用性。     

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.     

分数阶反向累加DGM(2,1)模型在低渗透油井产能预测中的应用

针对常见的灰色模型不能很好的解决新信息优先的问题,将分数阶融入到DGM(2,1)模型中,给出改进的分数阶反向累加DGM(2,1)模型(简记为RDGM(2,1)模型).RDGM(2,1)模型能够充分应用最新获得的数据,从中获取最有价值的信息.由于分数阶的灵活性,RDGM(2,1)模型能更好的反映数据中包含的信息,体现灰色模型处理少数据时精度高的优点.将RDGM(2,1)模型运用到油井的产能预测中,并与DGM(2,1)模型等灰色模型做了对比,结果表明RDGM(2,1)模型的模拟精度更高.     

基于小波分析的灰色GM(1,1)模型道路交通事故预测

道路交通事故预测是道路交通安全研究的一项重要内容,针对灰色GM(1,1)预测模型对波动性较大道路交通事故序列预测精度较低的缺点,引入小波分析理论,在小波分析理论的基础上建立灰色GM(1,1)预测模型.通过小波分析将某省2002-2009年道路交通事故起数分解成多层近似平稳的数据序列,然后对低频重构序列建立GM(1,1)模型进行预测.仿真结果表明,方法的预测结果比直接用灰色GM(1,1)模型更拟合原始数据,预测效果更好.预测结果可以为交通部门科学监管和制定决策提供一定的指导.     

残差灰色预测模型在我国老龄人口预测中的应用

利用灰色预测理论,建立了GM(1,1)模型和残差灰色预测模型,经过分析,结果表明:残差灰色预测比GM(1,1)模型预测精度高.于是,利用残差灰色预测模型对2012-2020年我国人口老龄化状况进行了预测,为我国政府制定正确的相关政策提供科学理论依据.     

基于差分方程的灰色DEGM(2,1)建模

传统灰色GM(2,1)模型的定义及参数估计都是以差分方程为基础进行,时间响应函数却是由微分方程解得,从差分方程到微分方程的跳跃,既缺乏严格的理论依据,也会产生跳跃性误差,因而备受争议.本文引入一种基于二阶常系数非齐次线性差分方程的灰色DEGM(2,1)模型,该模型从给出定义,到参数估计,再到预测值求解,都统一使用差分方程来完成,实现了模型从定义到求解的理论一致性、完整性,并且使用该模型时不需要计算时间响应函数、递推函数等,应用更为方便,计算量也更小.实例表明,新提出的DEGM(2,1)模型有较高的预测精度,值得推广使用.     

基于灰色预测模型的广州市城镇生活垃圾清运量预测

基于灰色预测理论,分别用GM(1,1)模型、分数阶GM(1,1)模型和新陈代谢GM (1,1)模型对广州市2015-2019年城镇生活垃圾清运量数据进行建模、检验和比较,结果表明新陈代谢GM(1,1)模型预测精度最高.预测2020-2024年广州市城镇生活垃圾清运量仍呈现长的趋势,在2024年将会突破1000万吨.     

A research on the grey prediction model GM(1,n)

The grey theory can be applied in the research of prediction, decision-making and control, especially in prediction. The primary characteristic of a grey system is the incompleteness of information. A grey system could be whitened by way of inserting more messages in itself and its accuracy of prediction could be raised. The solution to the existing grey prediction model GM(1,n) is inaccurate and then its prediction accuracy cannot be expected. To solve the existing GM(1,n) by assuming step by step the first order accumulated generating operation data of the associated series to be constants is incorrect. The existing model GM(1,n) is seriously wrong even for a system having a nonnegative associated series with constant entries. There are currently only a few wrong papers based on the existing GM(1,n) model to be published. Almost all the improved prediction models based on the existing GM(1,n) model are correct. For example, the improved models are correct by convolution integral or fitting their forcing terms by several elementary functions. The algorithm of GMC(1,n) is applied to explain why the existing GM(1,n) model is incorrect in this article.     

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.     

Grey forecasting method of quarterly hydropower production in China based on a data grouping approach

Grey model GM (1,1) has been widely used in short-term prediction of energy production and consumption due to its advantages in data sets with small numbers of samples. However, the existing GM (1,1) modelling method can merely forecast the general trend of a time series but fails to identify and predicts the seasonal fluctuations. In the research, the authors propose a data grouping approach based grey modelling method DGGM (1,1) to predict quarterly hydropower production in China. Firstly, the proposed method is used to divide an entire quarterly time series into four groups, each of which contains only time series data within the same quarter. Afterwards, by using the new series of four quarters, models are established, each of which includes specific seasonal characteristics. Finally, according to the chronological order, the prediction results of four GM (1,1) models are combined into a complete quarterly time series to reflect seasonal differences. The mean absolute percent errors (MAPEs) of the test set 2011Q1–2015Q4 solved using the DGGM (1,1), traditional GM (1,1), and SARIMA models are 16.2%, 22.1%, and 22.2%, respectively; the results indicated that DGGM (1,1) has better adaptability and offers a higher prediction accuracy. It is predicted that China's hydropower production from 2016 to 2020 is supposed to maintain its seasonal growth with the third and first quarters showing the highest and lowest productions, respectively.     

灰色GM(1,1,k,k2)模型背景值及时间响应函数优化

本文提出了一种新的带有时间幂次项的灰色GM(1,1,k,k²)模型,给出了其灰微分方程和白化微分方程基本形式。基于最小二乘法获得了该模型参数估计值,并推导了该模型时间响应函数。鉴于GM(1,1,k,k²)模型灰微分方程与白化微分方程之间存在跳跃关系,首先对灰微分方程的背景值进行了优化,并推导了优化后的背景值计算公式。为了克服初始值的影响,根据误差平方和最小,进一步优化了GM(1,1,k,k²)模型时间响应函数。最后,该优化后的GM(1,1,k,k²)模型被应用于软土地基沉降预测,获得了较好的模拟预测效果,说明模型是可行的。     

累加生成的改进和GM(1,1,t)灰色模型

根据卷积变换可提高变换序列光滑度的特性和累加生成的机理,对灰色建模中的序列生成方式和GM(1,1)模型加以改进,用线性序列对建模序列作卷积变换,建立带线性时间项的灰色模型GM(1,1,t),实例计算结果表明GM(1,1,t)模型的模拟精度较GM(1,1)模型有较大提高且适用范围更广.     

A new grey prediction model FGM(1, 1)

The effectiveness of the first entry of the original series by GM(1, 1) is researched in this paper. The results show that the modelling values and forecasts are independent of the first entry of the original series. The grey prediction model presented in this paper is called first-entry GM(1, 1), abbreviated as FGM(1, 1), which is based on the existing GM(1, 1) but modelled with data including the first-entry’s messages of the original series. A proof concerning this subject has been presented by other authors. However, the algorithm of their direct proof is too complicated. A more compact algorithm is presented in this paper to prove the first entry of the original series ineffective to the modelling values and forecasts by GM(1, 1). Then, an arbitrary number can be inserted in the front of the original series to extract the messages from its first entry. Only a few data (usually fewer than ten) are used for model building. This paper deals with the effectiveness of the first entry of the original series by GM(1, 1).     

北京市水资源利用建模分析研究

以北京市为例,分别应用无偏灰色GM(1,1)模型和非线性模型对北京市2001年-2010年的用水量进行了建模,利用最优化方法,计算了上述两种模型的最优组合模型,通过三种模型分别计算了北京市2001年-2010年的水资源利用量,并与北京市2001年-2010年的实际用水量进行了对比,采用精度检验方法,分别对无偏灰色模型,非线性模型和组合模型进行了精度检验,计算结果表明,加权组合模型是三种模型中精度最高的模型,通过组合模型计算得出的用水量值与实际水资源利用量相比误差最小,由此得出,可以利用组合模型对北京市未来的水资源利用量进行预测,预测结果可为其他相关研究提供参考.     

同时优化背景值和灰导数的新非等间距GM(1,1)模型

结合GM(1,1)的建模过程,提出了以原始序列的一次累加生成序列为背景值的非等间距序列GM(1,1)模型的最原始形式;并基于灰模型的非齐次指数特性和求导的定义,从灰导数在离散点的生成出发,同时优化最原始的非等间距灰微分方程的灰导数和背景值,并建立新非等间距灰模型;新模型不仅提高了灰模型的拟合精度和预测精度,且拓宽了GM(1,1)的适用范围.     

Electricity consumption prediction using a neural-network-based grey forecasting approach

Electricity consumption is an important economic index and plays a significant role in drawing up an energy development policy for each country. Multivariate techniques and time-series analysis have been proposed to deal with electricity consumption forecasting, but a large amount of historical data is required to obtain accurate predictions. The grey forecasting model attracted researchers by its ability to characterize an uncertain system effectively with a limited number of samples. GM(1,1) is the most frequently used grey forecasting model, but its developing coefficient and control variable were dependent on the background value that is not easy to be determined, whereas a neural-network-based GM(1,1) model called NNGM(1,1) has been presented to resolve this troublesome problem. This study has applied NNGM(1,1) to electricity consumption and has examined its forecasting ability on electricity consumption using sample data from the Turkish Ministry of Energy and Natural Resources and the Asia–Pacific Economic Cooperation energy database. Experimental results demonstrate that NNGM(1,1) performs well.