Prediction model of interval grey number based on DGM(1,1)

In grey system theory,the studies in the field of grey prediction model are focused on real number sequences,rather than grey number ones.Hereby,a prediction model based on interval grey number sequences is proposed.By mining the geometric features of interval grey number sequences on a two-dimensional surface,all the interval grey numbers are converted into real numbers by means of certain algorithm,and then the prediction model is established based on those real number sequences.The entire process avoids the algebraic operations of grey number,and the prediction problem of interval grey number is usefully solved.Ultimately,through an example＇s program simulation,the validity and practicability of this novel model are verified.

A New Modified GM (1,1) Model: Grey Optimization Model

Based on the optimization method, a new modified GM (1,1) model is presented, which is characterized by more accuracy prediction for the grey modeling.

Grey GM(1,1) Model with Function-Transfer Method for Wear Trend Prediction and its Application

Trend forecasting is an important aspect in fault diagnosis and work state supervision. The principle, where Grey theory is applied in fault forecasting, is that the forecast system is considered as a Grey system; the existing known information is used to infer the unknown information's character, state and development trend in a fault pattern, and to make possible forecasting and decisions for future development. It involves the whitenization of a Grey process. But the traditional equal time interval Grey GM (1,1) model requires equal interval data and needs to bring about accumulating addition generation and reversion calculations. Its calculation is very complex. However, the non equal interval Grey GM (1,1) model decreases the condition of the primitive data when establishing a model, but its requirement is still higher and the data were pre processed. The abrasion primitive data of plant could not always satisfy these modeling requirements. Therefore, it establishes a division method suited for general data modeling and estimating parameters of GM (1,1), the standard error coefficient that was applied to judge accuracy height of the model was put forward; further, the function transform to forecast plant abrasion trend and assess GM (1,1) parameter was established. These two models need not pre process the primitive data. It is not only suited for equal interval data modeling, but also for non equal interval data modeling. Its calculation is simple and convenient to use. The oil spectrum analysis acted as an example. The two GM (1,1) models put forward in this paper and the new information model and its comprehensive usage were investigated. The example shows that the two models are simple and practical, and worth expanding and applying in plant fault diagnosis.

Application of Grey System GM (1,1) model and unary linear regression model in coal consumption of Jilin Province

The data on the coal production and consumption in Jilin Province for the last ten years were collected,and the Grey System GM( 1,1) model and unary linear regression model were applied to predict the coal consumption of Jilin Production in 2014 and 2015. Through calculation,the predictive value on the coal consumption of Jilin Province was attained,namely consumption of 2014 is 114. 84 × 106 t and of 2015 is 117. 98 ×106t,respectively. Analysis of error data indicated that the predicted accuracy of Grey System GM( 1,1) model on the coal consumption in Jilin Province improved 0. 21% in comparison to unary linear regression model.

The Modified GM( 1 , 1) Grey Forecast Model

Because the impacts of the factors such as some disturbances are graduallyadded into the system, the grey forecast results will deviate from the systemtrue value. To improve the forecast precision, Pro-Dens Julons provided twomethfor-But they had not consider the impact of artificial disturbance. LiZhihua et al. of Qinghua Univ. presented another method. This paper revisesthe method and make it be a spocial case.

Study on the Prediction of Rice Blast Based on the Unbiased GM (1,1) Model

To create a new prediction model, the unbiased GM （1,1） model is optimized by the five-point slide method in this paper. Then, based on the occurrence areas of dce blast in Enshi District during 1995 -2004, the new model and unbiased GM （1, 1 ） model are applied to predict the occurrence areas of rice blast during 2005 -2010. Predicting outcomes show that the prediction accuracy of five-point unbiased sliding optimized GM （1, 1 ） model is higher than the unbiased GM （1,1） model. Finally, combined with the prediction results, the author provides some suggestion for Enshi District in the prevention and control of rice blast in 2010.

Improvement and application of GM(1,1) model based on multivariable dynamic optimization

For the classical GM(1,1)model,the prediction accuracy is not high,and the optimization of the initial and background values is one-sided.In this paper,the Lagrange mean value theorem is used to construct the background value as a variable related to k.At the same time,the initial value is set as a variable,and the corresponding optimal parameter and the time response formula are determined according to the minimum value of mean relative error(MRE).Combined with the domestic natural gas annual consumption data,the classical model and the improved GM(1,1)model are applied to the calculation and error comparison respectively.It proves that the improved model is better than any other models.

Prediction of efficient outputs based on GM(1,N) model and weak DEA efficiency

This paper expresses the efficient outputs of decisionmaking unit（DMU） as the sum of ＂average outputs＂ forecasted by a GM（1,N） model and ＂increased outputs＂ which reflect the difficulty to realize efficient outputs.The increased outputs are solved by linear programming using data envelopment analysis efficiency theories,wherein a new sample is introduced whose inputs are equal to the budget in the issue No.n ＋ 1 and outputs are forecasted by the GM（1,N） model.The shortcoming in the existing methods that the forecasted efficient outputs may be less than the possible actual outputs according to developing trends of input-output rate in the periods of pre-n is overcome.The new prediction method provides decision-makers with more decisionmaking information,and the initial conditions are easy to be given.

Forecast Grain “Three Quantities” Based on Grey GM (1, 1) and Promote the Structural Reform of Grain Supply Side

As a special product, the cultivation and production of grain directly affect the consumption of people, which has an important influence on the development of social economy and the national economy and people’s livelihood. Firstly, the present situation of grain production is analyzed, and the problems facing the structural reform of grain supply side in China are analyzed from grain output and its import and export volume. Secondly, we use grey GM (1, 1) model to predict grain output and consumption, grain import and export volume and all kinds of grain crops output in China, and then analyze the future trend of grain production in China. Finally, we put forward construction of grain branding, rational allocation of grain planting varieties, construction of traceability system for grain production, further grain processing and development of “Internet agriculture” industrial model to promote structural reform of grain supply side.

Application of Renewal Gray GM (1,1) Model to Prediction of Landslide Deformation

The gray renewal GM (1,1) landslide prediction model was established by improving the gray model. Based on the established model, the author has made prediction of landslide deformation to the Xiangjiapo landslide and the Lianziya dangerous rock body. The results show that the gray renewal GM (1,1) model can supplement the new information in time and remove the old information which reduces the meaning of the information because of time lapse. Therefore, the model is closer to reality.

The Non-Equidistant Grey GRM (1, 1) Model and Its Application

Applying the modeling method of Grey system and accumulated generating operation of reciprocal number for the problem of lower precision as well as lower adaptability in non-equidistant GM (1, 1) model, the calculation formulas were deduced and a non-equidistant GRM (1, 1) model generated by accumulated generating operation of reciprocal number was put forward .The grey GRM (1, 1) model can be used in non-equal interval & equal interval time series and has the characteristic of high precision as well as high adaptability. Example validates the practicability and reliability of the proposed model.

Application of Gray Metabolic GM (1,1) Model in Prediction of Annual Total Yields of Chinese Aquatic Products

To predict the annual total yields of Chinese aquatic products in future five years ( 2011-2015) ,based on the theory and method of gray system,this paper firstly establishes a conventional GM ( 1,1) model and a gray metabolic GM ( 1,1) model respectively to predict the annual total yields of Chinese aquatic products in 2006-2009 and compare the prediction accuracy between these two models. Then,it selects the model with higher accuracy to predict the annual total yields of Chinese aquatic products in future five years. The comparison indicates that gray metabolic GM ( 1,1) model has higher prediction accuracy and smaller error,thus it is more suitable for prediction of annual total yields of aquatic products. Therefore,it adopts the gray metabolic GM ( 1,1) model to predict annual total yields of Chinese aquatic products in 2011-2015. The prediction results of annual total yields are 55. 32,57. 46,59. 72,62. 02 and 64. 43 million tons respectively in future five years with annual average increase rate of about 3. 7% ,much higher than the objective of 2. 2% specified in the Twelfth Five-Year Plan of the National Fishery Development ( 2011 to 2015) . The results of this research show that the gray metabolic GM ( 1,1) model is suitable for prediction of yields of aquatic products and the total yields of Chinese aquatic products in 2011-2015 will totally be able to realize the objective of the Twelfth Five-Year Plan.

Construction of GM(2,1)Model for Oscillating Pitch Angle Series

GM(1, 1) is generally used in Grey System Theory which constructs an Ordinary Differential Equation for given se-ries. It is effective for monotone series, and its simulating effect is good and error is small. However, If the series dosen’ t havea property of monotone, the simulating effect of GM(1,1) is not fine, and its error gets bigger. In this paper, we use GM(2,1) to handle the oxcillation series, which uses the Method of Minimum Squares in determining the uncertain parameters.

Application of GM（1,1） Prediction Model in Science and Technology Novelty Search Work

Grey system theory has been widely applied to many domains such as economy, agriculture, management, Social Sciences and so on. Based on the theory of grey system, this paper established GM（1,1） grey predict model for the first time to forecast The number of Scitech novelty search item and The staff number of Sci-Tech Novelty Search. The predicting results are almost close to the actual values, which shows that the model is reliable so that the models could be used to forecast the two factors in the future years. The study will help the scientific management of Sci-Tech Novelty search work for Novelty search organizations.

Predicting the Number of Beijing Science and Technology Personnel Based on GM(1,N) Model

In this paper, based on the Science and Technology Statistics in Beijing Statistical Yearbook, grey theory is used to study the relationship among S&T (Science and Technology) activities personnel, R&D (research and development) personnel FTE (Full Time Equivalent), intramural expenditure for R&D and Patent Application Amount. According to the grey correlation coefficient, screening of grey GM(1,N) prediction variables, the grey prediction model is established. Meanwhile, time series model and GM(1,1) model are established for patent applications and R&D personnel equivalent FTE. By comparing the simulating results with the real data, the absolute relative error of prediction models is less than 10%. The results of the prediction model are tested. In order to improve the prediction accuracy, the mean values of the predicted values of the two models are brought into the GM(1,N) model to predict the number of scientific and technical personnel in Beijing during 2015-2025. Forecast results show that the number of science and technology personnel in Beijing will grow with exponential growth trend in the next ten years, which has a certain reference value for predicting the science and technology activities and formulating the policy in Beijing.

无线传感器网络中基于压缩感知和GM(1,1)的异常检测方案

针对现有的异常事件检测算法准确率低和能量开销较大等问题,该文提出一种基于压缩感知(CS)和GM(1,1)的异常事件检测方案。首先,基于分簇的思想将传感器节点的数据进行压缩采样后传输至Sink,针对传感器网络中数据稀疏度未知的特点,提出一种基于步长自适应的块稀疏信号重构算法。然后,Sink基于GM(1,1)对节点发生的异常进行预测,并对节点的工作状态进行自适应调整。仿真实验结果表明,相比于其它异常检测算法,该算法的误警率和漏检率较低,在保证异常事件检测可靠性的同时,有效地节省了节点能量。

基于PSR和无偏GM(1,1)模型的福建省耕地生态安全评价与预测

研究目的:对福建省2004—2015年的耕地生态安全状况进行评价,并对2016—2025年的安全状况进行预测,以指导区域耕地合理、可持续利用。研究方法:运用PSR评价模型建立评价指标体系、熵权法确定权重,采用无偏GM(1,1)模型进行预测,通过障碍度模型确定障碍因子。研究结果:(1)2004—2015年福建省耕地生态安全值呈曲折上升趋势,安全级别从较安全级上升为安全级;(2)预测结果显示,2016—2025年福建省耕地生态安全状况维持在安全状态,但安全值呈直线下降趋势;(3)通过障碍度模型得出未来10年福建省耕地生态安全的障碍因素主要集中在经济发展状况及农业生产活动方面。研究结论:2004—2015年,福建省的耕地生态安全状况总体较好,未来10年的耕地安全状况还需通过出台惠农政策、大力开展土地整治及宣传耕地生态安全知识等措施加强。

GM(1，1)模型在铝电解氧化铝浓度估计中的应用研究

详细介绍了灰色GM(1,1)模型的原理及建立步骤。将GM(1,1)模型引入到铝电解氧化铝浓度估算中,对基于Kalman滤波的氧化铝浓度自适应估算模型进行修正。灰色模型建模维度为5,对采用浓度自适应估算模型得到的浓度与实际浓度的偏差序列进行预测,将预测值反馈到浓度自适应估算模型中,形成新的浓度估算值。通过对电解生产中的30余组氧化铝浓度工艺数据进行估算,结果表明,经修正后,浓度估算值与实际值变化趋势保持一致,基本能满足铝电解工业现场的应用要求。

区间灰数表征与算法改进及其GM(1,1)模型应用研究

针对目前区间灰数的表征和运算过程中存在着较为严重的问题 ,即 :运算结果对灰数的灰度进行不必要的放大 ,造成信息的严重失真 ,笔者定义了标准区间灰数与第一和第二标准区间灰数的概念 ,分析了第一和第二标准区间灰数之间的关系 ,进一步设计了普通区间灰数与标准区间灰数之间的转换规则 ,提供了标准区间灰数之间的比较与运算法则 ,较好地解决了区间灰数之间的大小比较与运算问题。最后 ,将这一研究成果应用于基于区间数的GM (1,1)模型预测问题 ,取得了良好的效果。

灰色新陈代谢GM(1,1)模型在参考作物腾发量预测中的应用研究

随着时间的发展,任何一个灰系统都会加入一些未来的扰动因素,对系统的发展产生影响。而常规灰色GM(1,1)预测模型在建模时,采用的是现实时刻t=n为止的过去的数据,没有考虑这些扰动因素。故离现实时刻越远,该模型的预测精度就越低。针对这种情况,提出了灰色新陈代谢GM(1,1)预测模型。并尝试用灰色新陈代谢GM(1,1)预测模型对阜新市参考作物腾发量进行预测。结果表明:灰色新陈代谢GM(1,1)预测模型的预测精度较常规灰色GM(1,1)预测模型有了明显的提高。该模型建模过程简单、适用性强,为参考作物腾发量的预测提供了新的方法。