Forward Prediction of Runoff Data in Data-Scarce Basins with an Improved Ensemble Empirical Mode Decomposition (EEMD) Model
Abstract
:1. Introduction
2. Materials and Methods
2.1. Empirical Mode Decomposition (EMD)
- Step 1: Identify all local maxima and minima in the original time series X(t). The upper and lower envelopes of the time series are obtained by cubic spline interpolation. The mean of the upper and lower enveloping lines is m(t):
- Step 2: A new series h(t) is calculated by subtracting the mean m(t) from the original series X(t):
- Step 3: The EMD sifting stopping criteria determines whether sifting should stop. If the stopping condition is met, h(t) is the IMF, and the next step is executed. If the stopping condition is not met, then h(t) is used as the original series, steps 1 and 2 are repeated until the stopping condition is met, and the first IMF, IMF1 c1(t), is calculated.
- Step 4: The residual series r1(t) is obtained by subtracting the IMF c1(t) from the original series X(t):
- Step 5: The residual series r1(t) is used as the new original series, and steps 1–4 are repeated. All the IMFs, c1(t), c2(t), …, cn(t), are decomposed until cn(t) is a monotonic or single-extreme-point residual.
2.2. EEMD
- Step 1: White noise ni(t) with a mean of 0 and standard deviation constant is added to the original signal X(t) multiple times. The standard deviation of the white noise is set to 0.1–0.4 times the standard deviation of the original signal (0.2 in this study):
- Step 2: Each Xi(t) undergoes the EMD procedure. The IMF component obtained is denoted by cij(t), and the residual term is denoted by ri(t). Among them, cij(t) represents the j-th IMF from the decomposition of the signal after the i-th addition of Gaussian white noise.
- Step 3: Steps l and 2 are repeated N times. Based on the principle that the statistical mean of an uncorrelated random series is 0, the IMFs are subjected to an overall averaging operation to eliminate the impact of adding Gaussian white noise to the actual IMF multiple times. Finally, the IMF obtained from EEMD is as follows:
2.3. Improved Ensemble Empirical Mode Decomposition (EEMD)
2.4. Improved EEMD-Based Decomposition-Prediction-Reconstruction Model
3. Results and Discussion
3.1. Case Selection
3.2. Calculation and Analysis
3.2.1. Improved EEMD
3.2.2. Radial Basis Function (RBF) Neural Network and Autoregression (AR) Model Prediction
3.3. Result Verification
4. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Orthogonality Index | Zhaoshiyao Station | Suide Station | ||||
---|---|---|---|---|---|---|
SD Criteria | GR Criteria | MTED | SD Criteria | GR Criteria | MTED | |
Without residual | −0.10 | −0.10 | −0.08 | −1.24 | −0.95 | −0.23 |
With residual | −1.72 | −3.57 | −0.66 | −8.63 | −9.86 | −5.64 |
Error Evaluation Index | Zhaoshiyao Station | Suide Station | ||||
---|---|---|---|---|---|---|
SD Criteria | GR Criteria | MTED | SD Criteria | GR Criteria | MTED | |
Relative average deviation (RAD)/% | 9.45 | 9.39 | 6.86 | 25.24 | 25.60 | 11.10 |
Nash–Sutcliffe efficiency (NSE) | 0.19 | −0.24 | 0.40 | 0.34 | 0.29 | 0.89 |
Error Evaluation Index | Zhaoshiyao Station | Suide Station | ||||
---|---|---|---|---|---|---|
AR Model Method | Rainfall-Runoff Method | Improved EEMD Prediction Model | AR Model Method | Rainfall-Runoff Method | Improved EEMD Prediction Model | |
RAD/% | 11.03 | 15.13 | 6.86 | 27.76 | 19.67 | 11.10 |
NSE | −0.87 | −1.54 | 0.40 | −0.02 | −0.11 | 0.89 |
Statistical Parameters | Zhaoshiyao Station | Suide Station | ||||
---|---|---|---|---|---|---|
Mean | Mean Square Error | Coefficient of Variation | Mean | Mean Square Error | Coefficient of Variation | |
Original sequence | 3.86 | 0.51 | 0.13 | 1.28 | 0.40 | 0.31 |
Improved EEMD prediction model | 3.84 | 0.44 | 0.11 | 1.29 | 0.39 | 0.30 |
Rainfall-runoff method | 3.70 | 0.38 | 0.10 | 1.22 | 0.33 | 0.27 |
AR model | 3.75 | 0.37 | 0.10 | 1.26 | 0.33 | 0.26 |
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Yu, Y.; Zhang, H.; Singh, V.P. Forward Prediction of Runoff Data in Data-Scarce Basins with an Improved Ensemble Empirical Mode Decomposition (EEMD) Model. Water 2018, 10, 388. https://doi.org/10.3390/w10040388
Yu Y, Zhang H, Singh VP. Forward Prediction of Runoff Data in Data-Scarce Basins with an Improved Ensemble Empirical Mode Decomposition (EEMD) Model. Water. 2018; 10(4):388. https://doi.org/10.3390/w10040388
Chicago/Turabian StyleYu, Yinghao, Hongbo Zhang, and Vijay P. Singh. 2018. "Forward Prediction of Runoff Data in Data-Scarce Basins with an Improved Ensemble Empirical Mode Decomposition (EEMD) Model" Water 10, no. 4: 388. https://doi.org/10.3390/w10040388
APA StyleYu, Y., Zhang, H., & Singh, V. P. (2018). Forward Prediction of Runoff Data in Data-Scarce Basins with an Improved Ensemble Empirical Mode Decomposition (EEMD) Model. Water, 10(4), 388. https://doi.org/10.3390/w10040388