Figure 1.
The architecture of the RBFNN.
It gives the topological structure of the radial basis function neural network (RBFNN).
Figure 2.
The architecture of the linear neural network.
Figure 3.
The structure of the proposed EMD-EEMD-RBFNN-LNN model.
The proposed model has four stages, i.e., denoising, decomposition, component prediction and ensemble. The methods used in the four stages are empirical mode decomposition (EMD), ensemble empirical mode decomposition (EEMD), radial basis function neural network (RBFNN) and linear neural network (LNN), respectively.
Table 1.
Six cases studied in this paper.
Figure 4.
The selected stations of the Haihe River Basin.
This figure shows the locations of the 3 hydrological stations (Guantai, Xiangshuibao, Miyun Reservoir) and 44 meteorological stations (including Beijing). The precipitation data of the 44 meteorological stations are used to compute the annual mean precipitation of HRB.
Table 2.
Four types of comparison models.
Table 3.
Data used in the forecasting processes.
Figure 5.
The denoised series of the six hydrological time series.
This figure gives the denoising result obtained by the EMD-based method (in red color), as a comparison, the denoising result by the wavelet analysis (in blue color) is also given. It shows much better performances of the EMD-based method in denoising.
Table 4.
Statistical characters of the denoising results of the six hydrological time series.
Figure 6.
The decomposition results of the six denoised hydrological time series.
The six series are decomposed into several IMFs and one residue. The IMFs are listed in the order from the highest frequency to the lowest frequency.
Figure 7.
The Lempel-Ziv complexity of the six hydrological time series.
It shows the Lempel-Ziv complexity (LZC) of the six original series, denoised series and the IMFs.
Table 5.
The prediction model structure of IMFs of the case 2.
Table 6.
The prediction model structure of IMFs of the case 5.
Figure 8.
Prediction results of the six series by using the proposed four-stage hybrid forecasting model and its three comparison methods.
The proposed four-stage model has the form ‘denoising-decomposition-component prediction-ensemble’. This study utilizes EMD-based denoising method to denoise and decompose the denoised time series by EEMD, then predicts the IMFs by RBFNN and integrates the predicted results by LNN i.e. it has the form ‘EMD-EEMD-RBFNN-LNN’. As a comparison, the prediction results of its three comparison models (in different colors) are also given in this figure.
Table 7.
Evaluation of the forecasting of the six cases.