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.

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.

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.

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。

G(1,1)灰色模型与灰色线性模型预测法比较及应用——以商洛市房地产发展现状为例

运用实例和统计分析的方法,对统计预测中常用的G(1,1)灰色模型预测法和灰色线性模型预测法进行比较,得到了两种模型在实际预测中的精确度.并通过检验分析,得到了在什么情况下用G(1,1)灰色模型预测,在什么情况下用灰色线性模型预测.

新陈代谢GM(1,1)模型在火灾预测中的应用

灰色模型具有所需数据少、预测精度高和无需先验信息的特点。据此,可以应用新陈代谢的灰色预测GM(1,1)模型对我国近年发生的火灾统计数据进行分析预测。而预测结果表明,该模型简单实用,精度较高,在短期预测中有广阔的应用前景。

灰色GM(1,l)和Verhulst模型在吹填土地基沉降中的应用

在利用灰色GM(1,l)和Verhulst模型预测真空预压加固吹填土地基的最终沉降量时,建模序列直接影响预测结果的精度。结合某吹填土地基加固工程的沉降监测数据,探讨监测序列长度、建模序列长度对上述2种模型最终沉降量预测值及预测精度的影响,总结出不同模型预测地基最终沉降量时建模序列的选取规律。研究结果表明,上述2种模型预测地基最终沉降量的误差均小于1.0%,灰色GM(1,l)模型的适应性更好。

基于改进的GM(1,1)模型的上海市垃圾产量的预测

GM（1,1）模型是上海市垃圾产量预测的一种有效的方法,但序列的随机波动性难以在GM（1,1）模型得到反映。利用灰色震荡序列GM{1,1}模型,对上海市2000年~2008年垃圾产量进行预测,预测结果表明,此方法能够反映出上海市垃圾产量所具有的波动性特性,得到更高的预测精度。

Hybrid grey model to forecast monitoring series with seasonality

The grey forecasting model has been successfully applied to many fields. However, the precision of GM(1,1) model is not high. In order to remove the seasonal fluctuations in monitoring series before building GM(1,1) model, the forecasting series of GM(1,1) was built, and an inverse process was used to resume the seasonal fluctuations. Two deseasonalization methods were presented , i.e., seasonal index-based deseasonalization and standard normal distribution-based deseasonalization. They were combined with the GM(1,1) model to form hybrid grey models. A simple but practical method to further improve the forecasting results was also suggested. For comparison, a conventional periodic function model was investigated. The concept and algorithms were tested with four years monthly monitoring data. The results show that on the whole the seasonal index-GM(1,1) model outperform the conventional periodic function model and the conventional periodic function model outperform the SND-GM(1,1) model. The mean Absolute error and mean square error of seasonal index-GM(1,1) are 30.69% and 54.53% smaller than that of conventional periodic function model, respectively. The high accuracy, straightforward and easy implementation natures of the proposed hybrid seasonal index-grey model make it a powerful analysis technique for seasonal monitoring series.

应用灰色动态GM(1,1)数学模型进行临床血液采集量预测

目的探讨应用灰色动态 GM（1，1）模型，分析和预测常态下承德市中心血站血液品种采集数量的动态发展变化趋势，根据模型的应用效果做出定量预测。方法根据承德市中心血站2004年1月～2013年12月的全血（400 ml）（人次）、单采少白血小板（人份）血液品种年采集数据，将2013年预测值与实际值比较，检验模型的预测能力，同时分析2014～2016年血液采集数量。结果以上两类血液采集品种数量灰色动态 GM（1，1）模型的 Y（t）后验差比（均方差）C均＜0.35，小误差概率P值均为1。精度均为优，用于血液采集量预测的效果好。结论承德市中心血站以上两类血液采集品种数量呈逐渐增高趋势。灰色系统一阶模型 GM（1，1）作为一种新型预测模型，能够在常态下合理预测采供血系统血液采集量。

A self-adaptive grey forecasting model and its application

GM(1,1)models have been widely used in various fields due to their high performance in time series prediction.However,some hypotheses of the existing GM(1,1)model family may reduce their prediction performance in some cases.To solve this problem,this paper proposes a self-adaptive GM(1,1)model,termed as SAGM(1,1)model,which aims to solve the defects of the existing GM(1,1)model family by deleting their modeling hypothesis.Moreover,a novel multi-parameter simultaneous optimization scheme based on firefly algorithm is proposed,the proposed multi-parameter optimization scheme adopts machine learning ideas,takes all adjustable parameters of SAGM(1,1)model as input variables,and trains it with firefly algorithm.And Sobol’sensitivity indices are applied to study global sensitivity of SAGM(1,1)model parameters,which provides an important reference for model parameter calibration.Finally,forecasting capability of SAGM(1,1)model is illustrated by Anhui electricity consumption dataset.Results show that prediction accuracy of SAGM(1,1)model is significantly better than other models,and it is shown that the proposed approach enhances the prediction performance of GM(1,1)model significantly.

Application of the Grey topological method to predict the effects of ship pitching

Ship motion,with six degrees of freedom,is a complex stochastic process.Sea wind and waves are the primary influencing factors.Prediction of ship motion is significant for ship navigation.To eliminate errors,a path prediction model incorporating ship pitching was developed using the Gray topological method,after analyzing ship pitching motions.With the help of simple introduction to Gray system theory,we selected a group of threshold values.Based on an analysis of ship pitch angle sequences over 40 second intervals,a Grey metabolism GM(1,1) model was established according to the time-series which every threshold corresponded to.Forecasting future ship motion with the GM(1,1) model allowed drawing of the forecast curve with effective forecasting points.The precision of the test results show that the model is accurate,and the forecast results are reliable.

Predicting changes in Bitcoin price using grey system theory

Bitcoin is currently the leading global provider of cryptocurrency.Cryptocurrency allows users to safely and anonymously use the Internet to perform digital currency transfers and storage.In recent years,the Bitcoin network has attracted investors,businesses,and corporations while facilitating services and product deals.Moreover,Bitcoin has made itself the dominant source of decentralized cryptocurrency.While considerable research has been done concerning Bitcoin network analysis,limited research has been conducted on predicting the Bitcoin price.The purpose of this study is to predict the price of Bitcoin and changes therein using the grey system theory.The first order grey model(GM(1,1))is used for this purpose.It uses a firstorder differential equation to model the trend of time series.The results show that the GM(1,1)model predicts Bitcoin’s price accurately and that one can earn a maximum profit confidence level of approximately 98%by choosing the appropriate time frame and by managing investment assets.

Non-equal-interval direct optimizing Verhulst model that x(n) be taken as initial value and its application

To overcome the deficiencies of the existing Verhulst GM(1,1) model, based on the existing grey theory, a non-equal-interval direct optimum Verhulst GM(1,1) model is built which chooses a modified n-th component x(n) of X(0) as the starting condition of the grey differential model. It optimizes a modified β value and the background value, and takes two times fitting optimization. The new model extends equal intervals to non-equal-intervals and is suitable for general data modelling and estimating parameters of the direct Verhulst GM(1,1). The new model does not need to pre-process the primitive data, nor accumulate generating operation (AGO) and inverse accumulated generating operation (IAGO). It is not only suitable for equal interval data modelling, but also for non-equal interval data modelling. As the new information is fully used and two times fitting optimization is taken, the fitting accuracy is the highest in all existing models. The example shows that the new model is simple and practical. The new model is worth expanding on and applying in data processing or on-line monitoring for tests, social sciences and other engineering sciences.

Grey System Judgment on Reliability of Mechanical Equipment

he Grey system theory -was applied in reliability analysis of mechanical equip-ment. It is a new theory and method in reliability engineering of mechanical engineering of mechanical equipment. Through the Grey forecast of reliability parameters and the reliability forecast of parts and systems, decisions were made in the real operative state of e-quipment in real time. It replaced the old method that required mathematics and physical statistics in a large base of test data to obtain a pre-check , and it was used in a practical problem. Because of applying the data of practical operation state in real time, it could much more approach the real condition of equipment; it-was applied to guide the procedure and had rather considerable economic and social benefits.

Industrial Engineering Analysis of Chinese Manufacturing Industry in Transition Period Based on Grey Predictions

In order to explore the characteristics and development strategies of Chinese manufacturing production system, the grey forecasting model GM( 1,1) and the grey verhulst dynamic model were built firstly. The prediction results show that Chinese manufacturing productivity would reach $ 32 806 per person in 2018,which indicates rapid development and lays the foundation for China to become the world's manufacturing power since the reform and opening up. However, it is predicted that Chinese manufacturing productivity would peak in 2018 based on the grey verhulst dynamic model,which reveals the resource configuration mode of Chinese manufacturing system could not prop up its increasing manufacturing capability. Furthermore the main reasons of this phenomenon were explored,which could be summarized as the lack of accumulation,integration of industrial engineering( IE)and information technology( IT), promoting mechanism of IE application as well as integration model of management innovation and technology innovation,etc. Finally,a series of strategies based on IE theory to solve these problems were given. This study provides an effective way to deal with the challenges and opportunities facing the Chinese manufacturing industry,meanwhile,it may contribute to the theoretical system of IE.

A New DGM(1,1)Model with a Grey Parameter and Its Application

In the DGM(1, 1) model modeling process, the influencing factors are uncertain. But the solution of DGM(1, 1) model with uncertain information is unique, which conflicts with the nonuniqueness principle of solution in grey theory. In view of this situation, this paper makes an in-depth analysis of the meaning of grey action quantity β_(2) in DGM(1, 1) model and regards β_(2) as an interval grey number. The maximum possibility whitenization value is given to estimate the kernel of grey number,and the typical possibility function is constructed to describe the possibility of grey number taking different values. A new DGM(1, 1) model with a grey parameter is then proposed, whose simulation results are interval grey numbers. The proposed model is compatible with the DGM(1, 1) model in model structure and simulation results. Finally, the practical example results show the applicability and effectiveness of the proposed model.

A strip thickness prediction method of hot rolling based on D_S information reconstruction

To improve prediction accuracy of strip thickness in hot rolling, a kind of Dempster/Shafer(D_S) information reconstitution prediction method(DSIRPM) was presented. DSIRPM basically consisted of three steps to implement the prediction of strip thickness. Firstly, iba Analyzer was employed to analyze the periodicity of hot rolling and find three sensitive parameters to strip thickness, which were used to undertake polynomial curve fitting prediction based on least square respectively, and preliminary prediction results were obtained. Then, D_S evidence theory was used to reconstruct the prediction results under different parameters, in which basic probability assignment(BPA) was the key and the proposed contribution rate calculated using grey relational degree was regarded as BPA, which realizes BPA selection objectively. Finally, from this distribution, future strip thickness trend was inferred. Experimental results clearly show the improved prediction accuracy and stability compared with other prediction models, such as GM(1,1) and the weighted average prediction model.