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）.

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.

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.