The Extended Grey GM(2,1,Σexp(ct))Model and Its Application in the Predictions

The conventional grey GM(2,1)model built for the fast growing time sequence generally has big errors.To improve the modeling precision,the paper improves from the following two aspects:First,the paper transforms the accumulated generating sequence of original time sequence quantitatively to make the transformed time sequence have the better adaptability to the model;second,the paper extends the conventional grey GM(2,1)model’s structure to make the extended model meet the variation law of fast growing sequence better.The extended grey model is called the GM(2,1,Σexp(ct))model.The paper offers the parameter optimization method and the solving method of time response sequence of GM(2,1,Σexp(ct))model.Using the model and methods proposed,the paper builds the GM(2,1,Σexp(ct))models for the natural gas consumption of China and Chongqing City,China,respectively.Results show that the models built have high simulation precision and prediction precision.

Variation in reach-averaged bankfull discharge in the Yellow River Estuary in recent years

The Yellow River Estuary(YRE)alternatively experienced channel aggradation and degradation during the period 1990-2016.To study the variation in flood discharge capacity during the process of river bed evolution,bankfull characteristic parameters were investigated on the basis of measured hydrological data and surveyed cross-sectional profiles,which was crucial for comprehending the processes and the key factors to cause these rapid changes.A reach-averaged method was presented in this study in order to calculate the characteristic bankfull parameters in the YRE,and this method integrated the geometric mean using the logarithmic transformation with a weighted mean based on the distance between the two successive sections.The reach-averaged bankfull parameters in the tail reach of the Yellow River Estuary(the Lijin-Xihekou reach)during the period 1990-2016 were then calculated.Calculated results indicated that the adoption of a concept of reach-averaged bankfull discharge was much more representative than the cross-sectional bankfull discharge,and the results also indicated that bankfull discharges decreased during the process of channel aggradation,and increased during the process of channel degradation.Finally,an empirical formula and a delayed response function were established between the reach-averaged bankfull discharge and the previous 4-year average fluvial erosion intensity during flood seasons,and both of them were adopted to reproduce the reach-averaged bankfull discharges,and calculated results showed high correlations(R^(2)>0.8)of these two methods.

A Novel Simultaneous Grey Model SGM(1,2) and Its Applications in Prediction

The common models used for grey system predictions include the GM(1, 1), the GM(1, N),the GM(N, 1), and so on, but their whitening equations are all single ordinary differential equations.However, objects and factors generally form a whole through mutual restrictions and connections when the objective world is developing and changing continuously. In other words, variables affect each other. The relationship can’t be properly reflected by the single differential equation. Therefore, the paper proposes a novel simultaneous grey model. The paper gives a modeling method of simultaneous grey model SGM(1, 2) with 2 interactive variables. The example proves that the simultaneous grey model has high precision and improves the precision significantly compared with the conventional single grey model. The new method proposed enriches the grey modeling method system and has important significance for the in-depth study, popularization and application of grey models.