EMD-RBFNN Coupling Prediction Model of Complex Regional Groundwater Depth Series: A Case Study of the Jiansanjiang Administration of Heilongjiang Land Reclamation in China
Abstract
:1. Introduction
2. Study Area and Data Description
2.1. Study Area
2.2. Data Description
3. Methods
3.1. The Diagnosis Method of the Complexity of Hydrological Series
3.2. EMD
3.2.1. Basic Concepts
- (1)
- In the total data range, the number of extreme value points is equal to or no greater than one different from the number of zero-crossing points;
- (2)
- At any point, the average value of upper and lower limits made by the maximum points and minimum points, which are equal to zero.
3.2.2. Concrete Steps
- (1)
- Determine all maximum and minimum points in a sequence f(t), and then fit them into the up envelope ea(t) and down envelope eb(t) of the sequence f(t), respectively, with the cubic spline function.
- (2)
- Calculate the mean value m1(t) of the up and down envelopesm1(t) = [ea(t) + eb(t)]/2
- (3)
- Calculate the interpolating sequence h1(t)h1(t) = f (t) − m1(t)
- (4)
- Take h1(t) as a new sequence, repeat steps (1) to (3), and apply k iterations of screening to h1(t); namely,
- (5)
- Calculate the remaining sequence r1(t)r1(t) = f (t) − IMF1(t)
- (6)
- Take r1(t) as the new sequence to be decomposed, and repeat steps (1) to (5), resulting in
3.2.3. End Effect
3.3. Radial Basis Function Neural Network
3.3.1. The Network Structure
3.3.2. Basic Concepts
3.4. EMD-RBFNN Coupling Forecast Model
4. Results and Discussion
4.1. The Complexity Measure of the Groundwater Depth Sequence
4.2. EMD-RBFNN Coupling Predictive Model of Groundwater Depth
4.2.1. Empirical Mode Decomposition of Monthly Groundwater Depth Sequence
4.2.2. Monthly Groundwater Depth Prediction
Determinate Input and Output Samples
Determine the Network Training Parameters
The Fitting and Forecasting of Model
Testing of Model Accuracy
Groundwater Depth Prediction
4.3. Management Countermeasures of Groundwater Resources
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
- Li, Z.W. Temporal Scaling and Complexity Analyses of Dynamic Groundwater Systems. Ph.D. Thesis, The University of Iowa, Iowa City, IA, USA, 2006. [Google Scholar]
- Cantone, J.; Schmidt, A. Improved understanding and prediction of the hydrologic response of highly urbanized catchments through development of the Illinois Urban Hydrologic Model. Water Resour. Res. 2011, 47, 427–438. [Google Scholar] [CrossRef]
- Březková, L.; Šálek, M.; Soukalová, E.; Starý, M. Predictability of Flood Events in View of Current Meteorology and Hydrology in the Conditions of the Czech Republic. Soil Water Res. 2007, 2, 156–168. [Google Scholar]
- Daliakopoulosa, I.N.; Coulibalya, P.; Tsanis, I.K. Groundwater level forecasting using artificial neural networks. J. Hydrol. 2005, 309, 229–240. [Google Scholar] [CrossRef]
- Adamowski, J.; Chan, H.F. A wavelet neural network conjunction model for groundwater level forecasting. J. Hydrol. 2011, 407, 28–40. [Google Scholar] [CrossRef]
- Affandi, A.K.; Watanabe, K. Daily groundwater level fluctuation forecasting using soft computing technique. Nat. Sci. 2007, 5, 1–10. [Google Scholar]
- Lin, G.F.; Chen, L.H. Time series forecasting by combining the radial basis function network and the self-organizing map. Hydrol. Process. 2005, 19, 1925–1937. [Google Scholar] [CrossRef]
- Dash, N.B.; Panda, S.N.; Remesan, R.; Sahoo, N. Hybrid neural modeling for groundwater level prediction. Neural Comput. Appl. 2010, 19, 1251–1263. [Google Scholar] [CrossRef]
- Bidwell, V.J. Realistic forecasting of groundwater level, based on the eigen structure of aquifer dynamics. Math. Comput. Simul. 2005, 69, 12–20. [Google Scholar] [CrossRef]
- Hong, Y.M.; Wan, S. Forecasting groundwater level fluctuations for rainfall-induced landslide. Nat. Hazards 2011, 57, 167–184. [Google Scholar] [CrossRef]
- Izady, A.; Davary, K.; Alizadeh, A.; Ghahraman, B.; Sadeghi, M.; Moghaddamnia, A. Application of “panel-data” modeling to predict groundwater levels in the Neishaboor Plain, Iran. Hydrogeol. J. 2011, 20, 435–447. [Google Scholar] [CrossRef]
- Chebud, Y.; Melesse, A. Operational Prediction of Groundwater Fluctuation in South Florida Using Sequence Based Markovian Stochastic Model. Water Resour. Manag. 2011, 25, 2279–2294. [Google Scholar] [CrossRef]
- He, B.; Takase, K.; Wang, Y. Regional groundwater prediction model using automatic parameter calibration SCE method for a coastal plain of Seto Inland Sea. Water Resour. Manag. 2007, 21, 947–959. [Google Scholar] [CrossRef]
- Huang, N.E.; Shen, Z.; Long, S.R.; Wu, M.C.; Shih, H.H.; Zheng, Q.; Yen, N.-C.; Tung, C.C.; Liu, H.H. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. Lond. A Math. Phys. Eng. Sci. 1998, 454, 903–995. [Google Scholar] [CrossRef]
- Blanco-Velasco, M.; Weng, B.; Barner, K.E. ECG signal denoising and baseline wander correction based on the empirical mode decomposition. Comput. Biol. Med. 2008, 38, 1–13. [Google Scholar] [CrossRef] [PubMed]
- Guhathakurta, K.; Mukherjee, I.; Chowdhury, A.R. Empirical mode decomposition analysis of two different financial time series and their comparison. Chaos Solitons Fractals 2008, 37, 1214–1227. [Google Scholar] [CrossRef]
- Coughlin, K.T.; Tung, K.K. 11-Year solar cycle in the stratosphere extracted by the empirical mode decomposition method. Adv. Space Res. 2004, 34, 323–329. [Google Scholar] [CrossRef]
- Bassiuny, A.M.; Li, X.; Du, R. Fault diagnosis of stamping process based on empirical mode decomposition and learning vector quantization. Int. J. Mach. Tools Manuf. 2007, 47, 2298–2306. [Google Scholar] [CrossRef]
- Sinclair, S.; Pegram, G.G.S. Empirical Mode Decomposition in 2-D space and time: A tool for space-time rainfall analysis and nowcasting. Hydrol. Earth Syst. Sci. 2005, 9, 127–137. [Google Scholar] [CrossRef]
- Iyengar, R.N.; Kanth, S.T.G.R. Intrinsic mode functions and a strategy for forecasting Indian monsoon rainfall. Meteorol. Atmos. Phys. 2005, 90, 17–36. [Google Scholar] [CrossRef]
- Huang, Y.; Schmitt, F.G.; Lu, Z.; Liu, Y. Analysis of daily river flow fluctuations using empirical mode decomposition and arbitrary order Hilbert spectral analysis. J. Hydrol. 2009, 373, 103–111. [Google Scholar] [CrossRef]
- Mcmahon, T.A.; Vogel, R.M.; Peel, M.C.; Pegram, G.G.S. Global streamflows—Part 1: Characteristics of annual streamflows. J. Hydrol. 2007, 347, 243–259. [Google Scholar] [CrossRef]
- Lin, G.F.; Chen, L.H. A non-linear rainfall-runoff model using radial basis function network. J. Hydrol. 2004, 289, 1–8. [Google Scholar] [CrossRef]
- Chen, H.; Kim, A.S. Prediction of permeate flux decline in crossflow membrane filtration of colloidal suspension: A radial basis function neural network approach. Desalination 2006, 192, 415–428. [Google Scholar] [CrossRef]
- Liu, D.; Zhou, M.; Meng, J. Application of Approximate Entropy for Analyzing Complexity of Groundwater Depth Series in Sanjiang Plain. J. Nat. Resour. 2012, 27, 115–121. (In Chinese) [Google Scholar]
- He, Z.; Gao, S.; Chen, X.; Zhang, J.; Bo, Z.; Qian, Q. Study of a new method for power system transients classification based on wavelet entropy and neural network. Int. J. Electr. Power Energy Syst. 2011, 33, 402–410. [Google Scholar]
- Pincus, S.M. Approximate entropy as a measure of system complexity. Proc. Natl. Acad. Sci. USA 1991, 88, 2297–2301. [Google Scholar] [CrossRef] [PubMed]
- Zhao, H.; Wang, G.; Xu, C.; Yu, F. Voice Activity Detection Method Based on Multivalued Coarse-Graining Lempel-Ziv Complexity. Comput. Sci. Inf. Syst. 2011, 8, 869–888. [Google Scholar] [CrossRef]
- Duarte, M.; Zatsiorsky, V.M. On the fractal properties of natural human standing. Neurosci. Lett. 2000, 283, 173–176. [Google Scholar] [CrossRef]
- Planinšič, P.; Petek, A. Characterization of corrosion processes by current noise wavelet-based fractal and correlation analysis. Electrochim. Acta 2008, 53, 5206–5214. [Google Scholar] [CrossRef]
- Wang, W.S.; Xiang, H.L.; Huang, W.J.; Ding, J. Study on fractal dimension of runoff sequence based on successive wavelet transform. J. Hydraul. Eng. 2005, 36, 598–601. [Google Scholar]
- Wu, F.; Qu, L. An improved method for restraining the end effect in empirical mode decomposition and its applications to the fault diagnosis of large rotating machinery. J. Sound Vib. 2008, 314, 586–602. [Google Scholar] [CrossRef]
- Peel, M.C.; Amirthanathan, G.E.; Pegram, G.G.S.; McMahon, T.A.; Chiew, F.H.S. Issues with the Application of Empirical Mode Decomposition Analysis. In Proceedings of the International Congress on Modelling and Simulation, Melbourne, Australia, 12–15 December 2005; pp. 1681–1687.
- Su, Y.; Liu, Z.; Li, K.; Huo, B. A new method for end effect of EMD and its application to harmonic analysis. Adv. Technol. Electr. Eng. Energy 2008, 27, 33–37. [Google Scholar]
- Parey, A.; Pachori, R.B. Variable cosine windowing of intrinsic mode functions: Application to gear fault diagnosis. Measurement 2012, 45, 415–426. [Google Scholar] [CrossRef]
- Yang, Z.; Yang, L.; Qing, C. An oblique-extrema-based approach for empirical mode decomposition. Digit Signal Process. 2010, 20, 699–714. [Google Scholar] [CrossRef]
- Lu, W.C.; Xue, H.; Liu, C.W.; Gao, N. Study of forecasting model of customer retention for supermarket based on RBF neural network. J. Beijing Technol. Bus. Univ. Nat. Sci. Ed. 2009, 27, 45–48. (In Chinese) [Google Scholar]
- Moradkhani, H.; Hsu, K.L.; Gupta, H.V.; Sorooshian, S. Improved stream flow forecasting using self-organizing radial basis function artificial neural networks. J. Hydrol. 2004, 295, 246–262. [Google Scholar] [CrossRef]
- Rakhshandehroo, G.R.; Shaghaghian, M.R.; Keshavarzi, A.R.; Talebbeydokhti, N. Temporal variation of velocity components in a turbulent open channel flow: Identification of fractal dimensions. Appl. Math. Model. 2009, 33, 3815–3824. [Google Scholar] [CrossRef]
- Klionsky, D.M.; Oreshko, N.I.; Geppener, V.V. Empirical Mode Decomposition in Segmentation and Clustering of Slowly and Fast Changing Non-Stationary Signals. Pattern Recognit. Image Anal. 2009, 19, 14–29. [Google Scholar] [CrossRef]
- Erdoğan, H.; Gülal, E. The application of time series analysis to describe the dynamic movements of suspension bridges. Nonlinear Anal. Real World Appl. 2009, 10, 910–927. [Google Scholar] [CrossRef]
- Luan, Z.Q.; Liu, G.H.; Yan, B.X. Application of Time-Series Model to Predict Groundwater Dynamic in Sanjiang Plain, Northeast China. Wetl. Sci. 2011, 9, 47–51. (In Chinese) [Google Scholar]
The Location of Long-Term Monitoring Wells | The Number of Long-Term Monitoring Wells | Average Groundwater Depth (m) | Annual Average Increase (m) | |
---|---|---|---|---|
1997 | 2007 | |||
Subarea 1 of Farm 859 | 01 | 3.12 | 7.14 | 0.40 |
Subarea 69 of Farm Qixing | 02 | 4.92 | 9.15 | 0.42 |
Subarea 22 of Farm Qianjin | 03 | 6.09 | 9.81 | 0.37 |
Subarea 24 of Farm Chuangye | 04 | 8.14 | 13.47 | 0.53 |
District 5 of Farm Yalvhe | 05 | 6.26 | 7.77 | 0.15 |
Subarea 28 of Farm Hongwei | 06 | 8.35 | 12.34 | 0.40 |
District 8 of Farm Nongjiang | 07 | 5.31 | 10.84 | 0.55 |
Subarea 17 of Farm Qinglongshan | 08 | 5.69 | 7.44 | 0.18 |
Subarea 36 of Farm Qindeli | 09 | 10.35 | 11.90 | 0.16 |
Ministry of Farm Qianfeng | 10 | 6.80 | 9.91 | 0.31 |
District 6 of Farm Honghe | 11 | 5.81 | 9.34 | 0.35 |
District 5 of Farm Erdaohe | 12 | 8.73 | 10.04 | 0.13 |
Subarea 11 of Farm Daxing | 13 | 4.06 | 8.51 | 0.45 |
Subarea 31 of Farm Shengli | 14 | 9.55 | 13.47 | 0.39 |
Subarea 12 of Farm Qianshao | 15 | 9.35 | 10.03 | 0.07 |
Location of the Long-Term Monitoring Well | WE (0.16) | ApEn (0.16) | LZC (0.16) | D | CIj | Complexity Sort | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
R/S Analysis Method (0.12) | Wavelet Estimator Method | |||||||||||||
DWT (0.16) | CWT (0.24) | |||||||||||||
sort | value | sort | value | sort | value | sort | value | sort | value | sort | value | |||
Subarea 22 of Farm Qianjin | ⑭ | 2 | ③ | 13 | ⑧ | 8 | ⑦ | 9 | ⑧ | 8 | ⑤ | 11 | 8.68 | ⑥ |
District 6 of Farm Honghe | ⑥ | 10 | ④ | 12 | ④ | 12 | ⑨ | 7 | ⑦ | 9 | ⑧ | 8 | 9.64 | ③ |
Ministry of Farm Qianfeng | ② | 14 | ⑥ | 10 | ⑫ | 4 | ③ | 13 | ③ | 13 | ⑪ | 5 | 9.32 | ④ |
District 5 of Farm Erdaohe | ⑪ | 5 | ⑮ | 1 | ⑮ | 1 | ⑧ | 8 | ⑫ | 4 | ⑬ | 3 | 3.44 | ⑮ |
Subarea 12 of Farm Qianshao | ① | 15 | ⑬ | 3 | ⑩ | 6 | ⑩ | 6 | ⑨ | 7 | ⑭ | 2 | 6.16 | ⑬ |
EMD Component | IMF1 | IMF2 | IMF3 | IMF4 | IMF5 | Res |
---|---|---|---|---|---|---|
Variance contribution rate (%) | 9.83 | 19.45 | 1.72 | 3.66 | 7.09 | 58.25 |
Index | EMD-RBFNN Model | Conventional Time Series Model | |
---|---|---|---|
Fitting Effect Index | C | 0.0871 | 0.187 |
p | 1 | 0.9833 | |
E1(%) | 4.43 | 5.14 | |
E2 | 1 | 1 | |
Experiment Forecast Effect Index | E3(%) | 100 | 88.89 |
Year | Month | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | Average | |
2008 | 9.6280 | 9.8348 | 10.0642 | 10.2046 | 10.1804 | 9.9803 | 9.7434 | 9.5877 | 9.4811 | 9.3986 | 9.3727 | 9.4314 | 9.74 |
2009 | 9.5793 | 9.8101 | 10.0876 | 10.3578 | 10.5288 | 10.5490 | 10.4785 | 10.3633 | 10.2127 | 10.0682 | 9.9639 | 9.9127 | 10.16 |
2010 | 9.9172 | 9.9788 | 10.0949 | 10.2261 | 10.2879 | 10.2115 | 10.0410 | 9.8756 | 9.7603 | 9.7153 | 9.7361 | 9.7410 | 9.97 |
2011 | 9.6692 | 9.5768 | 9.5820 | 9.7411 | 9.9698 | 10.1129 | 10.1029 | 9.9980 | 9.8716 | 9.7503 | 9.6714 | 9.6536 | 9.81 |
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Fu, Q.; Liu, D.; Li, T.; Cui, S.; Hu, Y. EMD-RBFNN Coupling Prediction Model of Complex Regional Groundwater Depth Series: A Case Study of the Jiansanjiang Administration of Heilongjiang Land Reclamation in China. Water 2016, 8, 340. https://doi.org/10.3390/w8080340
Fu Q, Liu D, Li T, Cui S, Hu Y. EMD-RBFNN Coupling Prediction Model of Complex Regional Groundwater Depth Series: A Case Study of the Jiansanjiang Administration of Heilongjiang Land Reclamation in China. Water. 2016; 8(8):340. https://doi.org/10.3390/w8080340
Chicago/Turabian StyleFu, Qiang, Dong Liu, Tianxiao Li, Song Cui, and Yuxiang Hu. 2016. "EMD-RBFNN Coupling Prediction Model of Complex Regional Groundwater Depth Series: A Case Study of the Jiansanjiang Administration of Heilongjiang Land Reclamation in China" Water 8, no. 8: 340. https://doi.org/10.3390/w8080340
APA StyleFu, Q., Liu, D., Li, T., Cui, S., & Hu, Y. (2016). EMD-RBFNN Coupling Prediction Model of Complex Regional Groundwater Depth Series: A Case Study of the Jiansanjiang Administration of Heilongjiang Land Reclamation in China. Water, 8(8), 340. https://doi.org/10.3390/w8080340