Interval grey number sequence prediction by using non-homogenous exponential discrete grey forecasting model

This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on the traditional nonhomogenous discrete grey forecasting model（NDGM）, the interval grey number and its algebra operations are redefined and combined with the NDGM model to construct a new interval grey number sequence prediction approach. The solving principle of the model is analyzed, the new accuracy evaluation indices, i.e. mean absolute percentage error of mean value sequence（MAPEM） and mean percent of interval sequence simulating value set covered（MPSVSC）, are defined and, the procedure of the interval grey number sequence based the NDGM（IG-NDGM） is given out. Finally, a numerical case is used to test the modelling accuracy of the proposed model. Results show that the proposed approach could solve the interval grey number sequence prediction problem and it is much better than the traditional DGM（1,1） model and GM（1,1） model.

A new grey forecasting model based on BP neural network and Markov chain

A new grey forecasting model based on BP neural network and Markov chain was proposed. In order to combine the grey forecasting model with neural network, an important theorem that the grey differential equation is equivalent to the time response model, was proved by analyzing the features of grey forecasting model（GM（1,1））. Based on this, the differential equation parameters were included in the network when the BP neural network was constructed, and the neural network was trained by extracting samples from grey system＇s known data. When BP network was converged, the whitened grey differential equation parameters were extracted and then the grey neural network forecasting model （GNNM（1,1）） was built. In order to reduce stochastic phenomenon in GNNM（1,1）, the state transition probability between two states was defined and the Markov transition matrix was established by building the residual sequences between grey forecasting and actual value. Thus, the new grey forecasting model（MNNGM（1,1）） was proposed by combining Markov chain with GNNM（1,1）. Based on the above discussion, three different approaches were put forward for forecasting China electricity demands. By comparing GM（1, 1） and GNNM（1,1） with the proposed model, the results indicate that the absolute mean error of MNNGM（1,1） is about 0.4 times of GNNM（1,1） and 0.2 times of GM（I, 1）, and the mean square error of MNNGM（1,1） is about 0.25 times of GNNM（1,1） and 0.1 times of GM（1,1）.

STUDY ON GREY FORECASTING MODEL OF COPPER EXTRACTION RATE WITH BIOLEACHING OF PRIMARY SULFIDE ORE

A model GM （grey model） （1,1） for forecasting the rate of copper extraction during the bioleaching of primary sulphide ore was established on the basis of the mathematical theory and the modeling process of grey system theory. It was used for forecasting the rate of copper extraction from the primary sulfide ore during a laboratory microbial column leaching experiment. The precision of the forecasted results were examined and modified via ＂posterior variance examination＂. The results show that the forecasted values coincide with the experimental values. GM （1,1） model has high forecast accuracy; and it is suitable for simulation control and prediction analysis of the original data series of the processes that have grey characteristics, such as mining, metallurgical and mineral processing, etc. The leaching rate of such copper sulphide ore is low. The grey forecasting result indicates that the rate of copper extraction is approximately 20% even after leaching for six months.

The Application of a Grey Markov Model to Forecasting Annual Maximum Water Levels at Hydrological Stations

Compared with traditional real-time forecasting,this paper proposes a Grey Markov Model(GMM) to forecast the maximum water levels at hydrological stations in the estuary area.The GMM combines the Grey System and Markov theory into a higher precision model.The GMM takes advantage of the Grey System to predict the trend values and uses the Markov theory to forecast fluctuation values,and thus gives forecast results involving two aspects of information.The procedure for forecasting annul maximum water levels with the GMM contains five main steps:1) establish the GM(1,1) model based on the data series;2) estimate the trend values;3) establish a Markov Model based on relative error series;4) modify the relative errors caused in step 2,and then obtain the relative errors of the second order estimation;5) compare the results with measured data and estimate the accuracy.The historical water level records(from 1960 to 1992) at Yuqiao Hydrological Station in the estuary area of the Haihe River near Tianjin,China are utilized to calibrate and verify the proposed model according to the above steps.Every 25 years' data are regarded as a hydro-sequence.Eight groups of simulated results show reasonable agreement between the predicted values and the measured data.The GMM is also applied to the 10 other hydrological stations in the same estuary.The forecast results for all of the hydrological stations are good or acceptable.The feasibility and effectiveness of this new forecasting model have been proved in this paper.

Multi-factor high-order intuitionistic fuzzy timeseries forecasting model

Fuzzy sets theory cannot describe the neutrality degreeof data, which has largely limited the objectivity of fuzzy time seriesin uncertain data forecasting. With this regard, a multi-factor highorderintuitionistic fuzzy time series forecasting model is built. Inthe new model, a fuzzy clustering algorithm is used to get unequalintervals, and a more objective technique for ascertaining membershipand non-membership functions of the intuitionistic fuzzy setis proposed. On these bases, forecast rules based on multidimensionalintuitionistic fuzzy modus ponens inference are established.Finally, contrast experiments on the daily mean temperature ofBeijing are carried out, which show that the novel model has aclear advantage of improving the forecast accuracy.

Grey relationship analysis and grey forecasting modeling on thermal stability of synthetic single diamond

Through analyzing 7 Ib-type samples of synthetic single diamonds by their DTA and TG in air, we ascertained the extrapolated onset temperature on the curves of DTA as the characteristic temperature of their thermal stabilities. Based on the grey system theory, we analyzed 4 factors influential in the thermal stability by the grey relationship analysis, a quantitative method, and derived the grey relationship sequence, that is, the rank of the influence extent of 4 factors on the thermal stability. Furthermore, we established the grey forecasting model, namely GM(1,5), for predicting the thermal stability of single diamonds with their intrinsic properties, which was then examined by a deviation-probability examination. The results illustrate that it is reasonable to take the Extrapolated Onset Temperature in DTA as the characteristic temperature for thermal stability (TS) of Ib-type synthetic single diamonds. The nitrogen content and grain shape regularity of diamonds are dominating factors. Likewise, grain size and compressive strength are minor factors. In addition, GM(1,5) can be used to predict the thermal stability of Ib-type synthetic single diamonds available. The precision rank of GM(1,5) is ‘GOOD’.

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.

Expansion modelling of discrete grey model based on multi-factor information aggregation

This paper aims to study a novel expansion discrete grey forecasting model, which could aggregate input information more effectively. In general, existing multi-factor grey forecasting models, such as one order and h variables grey forecasting model （GM （1, h））, always aggregate the main system variable and independent variables in a linear form rather than a nonlinear form, while a nonlinear form could be used in more cases than the linear form. And the nonlinear form could aggregate collinear independent factors, which widely lie in many multi-factor forecasting problems. To overcome this problem, a new approach, named as the Solow residual method, is proposed to aggregate independent factors. And a new expansion model, feedback multi-factor discrete grey forecasting model based on the Solow residual method （abbreviated as FDGM （1, h））, is proposed accordingly. Then the feedback control equation and the parameters＇ solution of the FDGM （1, h） model are given. Finally, a real application is used to test the modelling accuracy of the FDGM （1, h） model. Results show that the FDGM （1, h） model is much better than the nonhomogeneous discrete grey forecasting model （NDGM） and the GM （1, h） model.

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.

Novel grey forecast model and its application

The advancement of grey system theory provides an effective analytic tool for power system load fore-cast. All kinds of presently available grey forecast models can be well used to deal with the short-term load fore-cast. However, they make big errors for medium or long-term load forecasts, and the load that does not satisfythe approximate exponential increasing law in particular. A novel grey forecast model that is capable of distin-guishing the increasing law of load is adopted to forecast electric power consumption (EPC) of Shanghai. Theresults show that this model can be used to greatly improve the forecast precision of EPC for a secondary industryor the whole society.

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.

Improved grey prediction model based on exponential grey action quantity

With the passage of time, it has become important to investigate new methods for updating data to better fit the trends of the grey prediction model. The traditional GM（1,1） usually sets the grey action quantity as a constant. Therefore, it cannot effectively fit the dynamic characteristics of the sequence, which results in the grey model having a low precision. The linear grey action quantity model cannot represent the index change law. This paper presents a grey action quantity model, the exponential optimization grey model（EOGM（1,1））, based on the exponential type of grey action quantity; it is constructed based on the exponential characteristics of the grey prediction model. The model can fully reflect the exponential characteristics of the simulation series with time. The exponential sequence has a higher fitting accuracy. The optimized result is verified using a numerical example for the fluctuating sequence and a case study for the index of the tertiary industry＇s GDP. The results show that the model improves the precision of the grey forecasting model and reduces the prediction error.

Prediction Model Based on the Grey Theory for Tackling Wax Deposition in Oil Pipelines

Problems involving wax deposition threaten seriously crude pipelines both economically and operationally. Wax deposition in oil pipelines is a complicated problem having a number of uncertainties and indeterminations. The Grey System Theory is a suitable theory for coping with systems in which some information is clear and some is not, so it is an adequate model for studying the process of wax deposition. In order to predict accurately wax deposition along a pipeline, the Grey Model was applied to fit the data of wax deposition rate and the thickness of the deposited wax layer on the pipe-wall, and to give accurate forecast on wax deposition in oil pipelines. The results showed that the average residential error of the Grey Prediction Model is smaller than 2%. They further showed that this model exhibited high prediction accuracy. Our investigation proved that the Grey Model is a viable means for forecasting wax deposition. These findings offer valuable references for the oil industry and for firms dealing with wax cleaning in oil pipelines.

Forecasting freight volume based on wavelet denoising and FG-Markov

To eliminate the grey bias and improve ant-jamming performance of the standard grey-Markov forecasting model,a forecasting model based on wavelet packet decomposition and fuzzy grey Markov(FG-Markov)is proposed considering the characteristics of randomness and nonlinearility of freight volume forecasting.Firstly,based on the data analysis ability of wavelet packet to non-stationary random signal,wavelet packet decomposition is used to improve the analysis ability of data signal by decomposing historical freight volume data into wavelet packet component.On this basis,FG-Markov chain is proposed to obtain the transfer probability matrix of wavelet packet coefficients by introducing fuzzy grey variables,and forecast the freight volume by reconstructing wavelet packet coefficients.Finally,an example of Lanzhou railroad hub is carried out in order to testify the validity and applicability of this forecasting model.Compared with neural network model and other forecasting models,the proposed forecasting model can improve the forecasting accuracy under the same conditions.The forecasting accuracy of wavelet packet decomposition and FG-Markov is not only greater than that of any other single forecasting models,but also superior to that of other traditional combinational forecasting models,which can meet the actual requirements of freight volume forecasting.

Using Grey System Theory for Earthquake Forecast

By combining conventional grey correlation analysis, grey clustering method and grey forecasting methods with our multi-goal forecast thoughts and the techniques of grey time series processing, we develop six different grey earthquake forecast models in this paper. Using the record of major earthquakes in Japan from 1872 to 1995, we forecast future earthquakes in Japan. We develop an earthquake forecast model. By using the major earthquakes in Japan from 1872 to 1984, we forecast earthquakes from 1985 to 1995 and check the precision of the grey earthquake models. We find that the grey system theory can be applied to earthquake forecast. We introduce the above analysis methods and give a real example to evaluate and forecast. We also further discuss the problems of how to improve the precision of earthquake forecast and how to strengthen the forecast models in future research.

Prediction of Total Output Value of Construction Industry in Jiangxi Province Based on Grey Prediction Model

In order to realize the accurate prediction of the total output value of construction industry in the future,the grey prediction model is used to compare the measured value with the predicted value from 2012 to 2021,and based on the existing data,the total output value of construction industry in Jiangxi Province in the next five years is predicted.The results show that the grey prediction model has a good prediction effect,and the error between the predicted value and the measured value is within 14%,which provides a basis for policy adjustment and resource optimization.

Analysis of Air Pollutants in Xiong’an New Area Based on MATLAB Grey Model

The purpose of this paper is to study the air pollutants in Xiong’an New Area based on MATLAB grey model [1]. From 2011 to 2016, the results of sulfur dioxide (SO2), nitrogen dioxide (NO2) and inhalable particulate matter (PM1O) detected at monitoring points in the three counties of Xiong’an were analyzed. According to the national environmental air quality standard [2], the air quality in Xiong’an New Area was reasonably evaluated based on grey model in MATLAB. Judging from the weight of pollution factors in the model, sulfur dioxide (SO2) is the controlling factor of air quality in Xiong’an New Area, and the weight of nitrogen dioxide (NO2) gradually increases. The main sources of the three pollutants were obtained by comprehensive data analysis, and a grey model was established according to the mass concentration of the main air pollutants, and the grey forecasting model was tested. The experimental results show that the model can be effectively applied to the forecasting of ambient air quality. On this basis, the present situation of atmospheric environmental quality in Xiong’an New Area and suggestions for improvement are obtained.

Differential Hydrological Grey Model (DHGM) with self-memory function and its application to flood forecasting

This paper addresses a problem of flood forecasting with the self-memory function. Considering flood forecasting’s uncertainty and updating demand, a hybrid hydrological model, namely Differential Hy- drological Grey Model with self-memory function (DHGM-SM), is developed. The model has two fold features. One is to establish a self-memorization equation linked with DHGM, that could extract useful information from past data series and realize updating of hydrological dynamic process. The other is that this model has higher efficiency relative to original hydrological model without self-memory func- tion. This approach was applied to river flow forecasting of two representative basins in Tunxi of South China and Daqinggou of North China. It is shown that this hybrid method has satisfactory forecasting accuracy by examination of both calibration and validation.

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.

Research on the Forecast of Grain Production in Henan Province from 2010 to 2015

According to the latest amended agricultural economic statistical data from 1996 to 2009 in Henan Statistical Yearbook-2010,by selecting and establishing the optimized grey model of logarithmic new developed coefficient, we conduct the empirical analysis and forecast research on the grain output and the relevant main economic indices in Henan Province from 2010 to 2015. The results show that the grain output of Henan Province in 2010 will reach 54.896 9 million tons, and it will break through 60 million tons at 60.17 million tons in 2015. In years ahead, the grain output of Henan Province will develop to a new stage steadily, which guarantees the national grain supply and socio-economic sustainable development forcibly.