Applying fuzzy grey modification model on inflow forecasting

Abstract

This paper investigates a modified grey model for forecasting the inflow of a reservoir. The integral form of the background value is employed for the original grey model, GM(1,1), to improve accuracy and applicability. Thereafter, the Fourier series is altered to handle extreme values with regard to prediction; exponential smoothing is used to improve the drawbacks of the prediction delay phenomenon. Finally, we are hybridised as the ultimate grey model with outstanding prediction accuracy, namely EFGM(1,1). As a typhoon causes significant changes in the inflow of a reservoir, this paper applies the fuzzy membership function for dealing with it during the flood season to construct the fuzzy grey modification model, FEFGM(1,1). Results of grey models are compared with those of the Autoregressive Integrated Moving Average (ARIMA). By evaluating different indices, the errors of the predicted extreme value of EFGM(1,1) perform better than those of GM(1,1) and ARIMA, however worse than that of FEFGM(1,1). The final FEFGM(1,1) shows high precision with regard to reservoir inflow prediction during typhoons with combined effects of fuzzy, exponential smoothing, Fourier series.

Introduction

Typhoons and extreme rainfall may result in multiple disasters and bring in large amounts of sediment which largely reduce the effective storage of the reservoirs. It is necessary to construct a set of high precision real-time forecast models which cannot only distribute the water resources appropriately but also enhance early warnings against natural disasters. The rainfall and flow of the reservoir are analysed through differential hydrological grey models, time series, and autoregressive integrated moving average methods (Otok and Suhartono, 2009). Additionally, other methods like the Artificial Neural Network (ANN) have been applied (Aguirre et al., 2007, Pan et al., 2007, Lin et al., 2009a, Lin et al., 2009b, Zhang et al., 2009). Studies show that the correlation between the rainfall and the flow is not as high as expected, and suggest the adoption of the concept of auto-regression of flow in predicting the reservoir inflow (Wang and Liao, 2004, Collischonn et al., 2007).

Traditional regression analysis methods require a large number of variables and need a large corpus of data from which to draw conclusions. The grey system uses four datasets to build the grey forecasting model (Deng, 1989). Additionally, the grey model is not only applicable to forecasting the equal interval time series but is also applicable to the non-equal interval time series and the negative number series (He and Hwang, 2007).

Yu et al. (2000) proposed the rainfall forecast model based on the grey model following the fuzzy regression technique. However, the grey model regards the data set applying the Accumulated Generation Operation (AGO) as an exponential function. As a result, the forecasted values for original sequences with unsteady and centralised pattern are not ideal (Li, 1990a, Li, 1990b). Lin (2001) simulated the residual sequence obtained from grey model and combined it with the original predicted value to enhance the forecast accuracy. In order to enhance the forecast accuracy of the grey model, other studies improve upon the background value of the grey model and use superposition models, such as the Fourier series, to correct the periodic residues of the grey model and the exponential smoothing technique to correct the randomness of residuals of the grey model; the results show that the model can achieve higher levels of accuracy than that of the fuzzy forecast technique and ANN (Lin et al., 2001, Lin et al., 2009a, Su et al., 2002, Shi and Ning, 2005, Lin and Lee, 2007, Guo et al., 2008, Hsu et al., 2009).

The fuzzy theory uses the Membership Function to convert the subjective problems into values during the normalisation process, but it also needs to rely on membership functions and experience (Liang et al., 2000, Chen et al., 2002a, Chen et al., 2002b). In contrast, the grey system theory focuses on the study of small sampling data. Its difference from the fuzzy mathematics lies in the context of clear denotation and uncertain connotation (Liu, 2003). Therefore, the fuzzy theory is designed for fuzzy or incomplete information. Without any complicated calculation processes, the theory can still potentially come to the correct conclusions (Chen et al., 2002a, Chen et al., 2002b). In the field of hydraulic engineering, many researchers have conducted numerous studies on fuzzy theory that have elicited excellent performance. For example, Wang (1999) uses fuzzy decision analysis to regulate the reservoir operation during periods of flooding.

This paper investigates the modified grey model for predicting the reservoir's inflow. In the proposed grey model, the background values are modified by integration. Furthermore, the Fourier series and exponential smoothing techniques are utilised to correct periodical residues and random residuals for forecasting. As typhoons cause significant changes in the inflow, we apply the fuzzy membership function in dealing with inflow during the flood season to construct the fuzzy grey modification model.

The grey forecasting model and fuzzy theory is briefly introduced in Section 2. The concept of combining fuzzy and grey models is proposed in Section 3. The case study of 10-day reservoir inflow prediction of the Shimen reservoir and the application of different models, including a comparison among them, are presented in Section 4. Finally, conclusions are given in Section 5.