# Comparative Analysis of ANN and SVM Models Combined with Wavelet Preprocess for Groundwater Depth Prediction

^{1}

^{2}

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^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area and Data

^{2}, comprising 318 km

^{2}(15%) urban land and 1773 km

^{2}(85%) of agriculture land, so water is of vital importance for this agrarian county.

## 3. Model Development

#### 3.1. Model Configuration

- (1)
- Divide overall groundwater depth into two sets: training set and test set. Sample sizes of both sets should be adjusted. Usually the training set size should be larger than test set size to guarantee the objectivity of model.
- (2)
- Build an ANN/SVM training model with parameter calibration using training set data, and apply the model to test set, which generates prediction results of ANN/SVM model.
- (3)
- In parallel with step (2), construct a multi-level wavelet transform model to decompose original groundwater depth time series to several subseries.
- (4)
- Build ANN/SVM training model with parameter calibration for each subseries, and apply each model to corresponding subseries of test set.
- (5)
- Integrate the results of each subseries in chronological order to generate prediction results of WANN/WSVM model.
- (6)
- Compare four models results in step (2) and (5), and analyze the effect of each module in the hybrid model.

#### 3.2. Determination of Lag Time

#### 3.3. ANN Training Model

#### 3.4. SVM Training Model

#### 3.4.1. SVM Algorithm

#### 3.4.2. PSO Parameter Calibration Method

^{−4}, 10

^{−1}].

^{−5}, 2

^{−4}, 2

^{−3},… 2

^{5}} and g in set {2

^{−7}, 2

^{−6}, 2

^{−5},… 2}. Each combination was enumerated to determine the best parameter set. The training and test results of grid search based SVM and WSVM are shown in Figure 7. It is obvious that the PSO based SVM/WSVM simulation accuracy (shown in Section 4.1) bested the grid search based SVM/WSVM model.

#### 3.4.3. Cross Validation

#### 3.5. Wavelet Based Preprocess Analysis

#### 3.6. Model Verification

## 4. Results and Discussion

#### 4.1. Model Fitting and Test Results

#### 4.2. Comparative Discussion of Model Results

- From theoretical point of view, the SVM model has better performance than the ANN model in this case. Models with SVM theory, for both raw data and wavelet preprocessed data, have more accurate precision than that with ANN theory. The focus on generalization ability of SVM model, as explained in 3.5, is a critical issue for overcoming the ANN model. The PSO parameter calibration and cross validation mechanism further guaranteed its prediction performance.
- From model architecture point of view, the wavelet based preprocess profoundly improves model performance. The essential improvement of WANN and WSVM is attributed to the wavelet based preprocess of raw groundwater depth data. The wavelet based preprocess filters the original groundwater depth series into regulated subseries (Figure 10). The partition of raw data makes hybrid models (both WSVM and WANN) more capable of extracting those unknown patterns hidden in the groundwater fluctuations, which leads to more accurate prediction results. This is the reason for the substantial improvement of WANN and WSVM models. Although SVM theory is more efficient than ANN theory, the WANN model performs much better than SVM model. This illustrates that data preprocessing may be more important than the model itself in this case.

#### 4.3. Discussion of WSVM Model

#### 4.3.1. WSVM Model Performance

#### 4.3.2. Stability Test of WSVM Model

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Ebrahimi, H.; Rajaee, T. Simulation of groundwater level variations using wavelet combined with neural network, linear regression and support vector machine. Glob. Planet. Chang.
**2017**, 148, 181–191. [Google Scholar] [CrossRef] - Chitsazan, N.; Tsai, F.T.C. A Hierarchical Bayesian Model Averaging Framework for Groundwater Prediction under Uncertainty. Groundwater
**2015**, 53, 305–316. [Google Scholar] [CrossRef] [PubMed] - Lo, M.-H.; Famiglietti, J.S.; Yeh, P.J.F.; Syed, T.H. Improving parameter estimation and water table depth simulation in a land surface model using GRACE water storage and estimated base flow data. Water Resour. Res.
**2010**, 46, 1–15. [Google Scholar] [CrossRef] - Chang, F.J.; Chang, L.C.; Huang, C.W.; Kao, I.F. Prediction of monthly regional groundwater levels through hybrid soft-computing techniques. J. Hydrol.
**2016**, 541, 965–976. [Google Scholar] [CrossRef] - Yan, Q.; Ma, C. Application of integrated ARIMA and RBF network for groundwater level forecasting. Environ. Earth Sci.
**2016**, 75, 1–13. [Google Scholar] [CrossRef] - Adamowski, J.; Chan, H.F.; Prasher, S.O.; Ozga-Zielinski, B.; Sliusarieva, A. Comparison of multiple linear and nonlinear regression, autoregressive integrated moving average, artificial neural network, and wavelet artificial neural network methods for urban water demand forecasting in Montreal, Canada. Water Resour. Res.
**2012**, 48, 273–279. [Google Scholar] [CrossRef] - Bourennane, H.; King, D.; Couturier, A. Comparison of kriging with external drift and simple linear regression for predicting soil horizon thickness with different sample densities. Geoderma
**2000**, 97, 255–271. [Google Scholar] [CrossRef] - Sahoo, S.; Jha, M.K. Groundwater-level prediction using multiple linear regression and artificial neural network techniques, a comparative assessment. Hydrogeol. J.
**2013**, 21, 1865–1887. [Google Scholar] [CrossRef] - Mirzavand, M.; Ghazavi, R. A Stochastic Modelling Technique for Groundwater Level Forecasting in an Arid Environment Using Time Series Methods. Water Resour. Manag.
**2015**, 29, 1315–1328. [Google Scholar] [CrossRef] - Mogaji, K.A.; Lim, H.S.; Abdullah, K. Modeling of groundwater recharge using a multiple linear regression (MLR) recharge model developed from geophysical parameters, a case of groundwater resources management. Environ. Earth Sci.
**2015**, 73, 1217–1230. [Google Scholar] [CrossRef] - Patle, G.T.; Singh, D.K.; Sarangi, A.; Rai, A.; Khanna, M.; Sahoo, R.N. Time series analysis of groundwater levels and projection of future trend. J. Geol. Soc. India
**2015**, 85, 232–242. [Google Scholar] [CrossRef] - Kumar, A.R.S.; Sudheer, K.P.; Jain, S.K.; Agarwal, P.K. Rainfall-runoff modelling using artificial neural networks comparison of network types. Hydrol. Process.
**2005**, 19, 1277–1291. [Google Scholar] [CrossRef] - Emamgholizadeh, S.; Moslemi, K.; Karami, G. Prediction the Groundwater Level of Bastam Plain (Iran) by Artificial Neural Network (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS). Water Resour. Manag.
**2014**, 15, 5433–5446. [Google Scholar] [CrossRef] - Dogan, A.; Demirpence, H.; Cobaner, M. Prediction of groundwater levels from lake levels and climate data using ANN approach. Water SA.
**2008**, 34, 199–208. [Google Scholar] - Reuter, U.; Möller, B. Artificial Neural Networks for Forecasting of Fuzzy Time Series. Comput.-Aided Civ. Infrastruct. Eng.
**2010**, 25, 363–374. [Google Scholar] [CrossRef] - Wood, D.; Dasgupta, B. An Innovative Tool for Financial Decision Making the Case of Artificial Neural Networks. Creat. Innov. Manag.
**1995**, 4, 172–183. [Google Scholar] [CrossRef] - Krishna, B.; Rao, Y.R.S.; Vijaya, T. Modelling groundwater levels in an urban coastal aquifer using artificial neural networks. Hydrol. Process.
**2008**, 22, 1180–1188. [Google Scholar] [CrossRef] - Katherasan, D.; Elias, J.V.; Sathiya, P.; Haq, A.N. Simulation and parameter optimization of flux cored arc welding using artificial neural network and particle swarm optimization algorithm. J. Intell. Manuf.
**2014**, 25, 67–76. [Google Scholar] [CrossRef] - Mehdi, K.; Mehdi, B. A novel hybridization of artificial neural networks and ARIMA models for time series forecasting. Appl. Soft Comput.
**2011**, 11, 2664–2675. [Google Scholar] - Sonmez, M.; Akgüngör, A.P.; Bektaş, S. Estimating transportation energy demand in Turkey using the artificial bee colony algorithm. Energy
**2017**, 122, 301–310. [Google Scholar] [CrossRef] - Leung, F.; Lam, H.; Ling, S.; Tam, P.K.S. Tuning of the structure and parameters of a neural network using an improved genetic algorithm. IEEE Trans. Neural Netw.
**2003**, 14, 79–88. [Google Scholar] [CrossRef] [PubMed] - Vapnik, V.N. Statistical Learning Theory; John Wiley & Sons: New York, NY, USA, 1998. [Google Scholar]
- Sudheer, C.; Maheswaran, R.; Panigrahi, B.K.; Mathur, S. A hybrid SVM-PSO model for forecasting monthly streamflow. Neural Comput. Appl.
**2014**, 24, 1381–1389. [Google Scholar] [CrossRef] - Wang, W.C.; Xu, D.M.; Chau, K.W.; Chen, S. Improved annual rainfall-runoff forecasting using PSO–SVM model based on EEMD. J. Hydroinform.
**2013**, 15, 1377–1390. [Google Scholar] [CrossRef] - Kisi, O.; Cimen, M. Precipitation forecasting by using wavelet-support vector machine conjunction model. Eng. Appl. Artif. Intell.
**2012**, 25, 783–792. [Google Scholar] [CrossRef] - Hou, Y.K.; Chen, H.; Xu, C.Y.; Chen, J.; Guo, S.L. Coupling a Markov Chain and Support Vector Machine for at-site downscaling of daily precipitation. J. Hydrometeorol.
**2017**, 18, 2385–2406. [Google Scholar] [CrossRef] - Misra, D.; Oommen, T.; Agarwal, A.; Mishra, S.K.; Thompson, A.M. Application and analysis of support vector machine based simulation for runoff and sediment yield. Biol. Syst. Eng.
**2009**, 103, 527–535. [Google Scholar] [CrossRef] - Yoon, H.; Jun, S.-C.; Hyun, Y.; Bae, G.-O.; Lee, K.-K. A comparative study of artificial neural networks and support vector machines for predicting groundwater levels in a coastal aquifer. J. Hydrol.
**2011**, 396, 128–138. [Google Scholar] [CrossRef] - Shiri, J.; Kisi, O.; Yoon, H.; Lee, K.-K.; Hossein Nazemi, A. Predicting groundwater level fluctuations with meteorological effect implications—A comparative study among soft computing techniques. Comput. Geosci.
**2013**, 56, 32–44. [Google Scholar] [CrossRef] - Amid, S.; Gundoshmian, T.M. Prediction of output energies for broiler production using linear regression, ANN (MLP, RBF), and ANFIS models. Environ. Prog. Sustain. Energy
**2017**, 36, 577–585. [Google Scholar] [CrossRef] - Asnaashari, M.; Farhoosh, R.; Farahmandfar, R. Prediction of oxidation parameters of purified Kilka fish oil including gallic acid and methyl gallate by adaptive neuro-fuzzy inference system (ANFIS) and artificial neural network. J. Sci. Food Agric.
**2016**, 96, 4594–4602. [Google Scholar] [CrossRef] [PubMed] - Suryanarayana, C.; Sudheer, C.; Mahammood, V.; Panigrahi, B.K. An integrated wavelet-support vector machine for groundwater level prediction in Visakhapatnam, India. Neurocomputing
**2014**, 145, 324–335. [Google Scholar] [CrossRef] - Rathinasamy, M.; Rakesh, K.; Jan, A.; Sudheer, C.; Partheepan, G.; Jatin, A.; Boini, N. Wavelet-based multiscale performance analysis: An approach to assess and improve hydrological models. Water Resour. Res.
**2014**, 50, 9721–9737. [Google Scholar] [CrossRef] - Maheswaran, R.; Khosa, R. Wavelet-Volterra coupled model for monthly streamflow forecasting. J. Hydrol.
**2012**, 450–451, 320–335. [Google Scholar] [CrossRef] - Moosavi, V.; Vafakhah, M.; Shirmohammadi, B.; Behnia, N. A Wavelet-ANFIS Hybrid Model for Groundwater Level Forecasting for Different Prediction Periods. Water Resour. Manag.
**2013**, 27, 1301–1321. [Google Scholar] [CrossRef] - Nourani, V.; Hosseini Baghanam, A.; Adamowski, J.; Kisi, O. Applications of hybrid wavelet–Artificial Intelligence models in hydrology, A review. J. Hydrol.
**2014**, 514, 358–377. [Google Scholar] [CrossRef] - Janacek, G. Time series analysis forecasting and control. J. Time Ser. Anal.
**2010**, 31, 303. [Google Scholar] [CrossRef] - Yao, C.; Wu, F.; Chen, H.J.; Hao, X.L.; Shen, Y. Traffic sign recognition using HOG-SVM and grid search. In Proceedings of the 12th International Conference on Signal Processing (ICSP), Hangzhou, China, 19–23 October 2014; pp. 962–965. [Google Scholar]
- Mallat, S. A theory for multiresolution signal decomposition: The Wavelet representation. IEEE Trans. Pattern Anal. Mach. Intell.
**1989**, 11, 674–693. [Google Scholar] [CrossRef] - Panagoulia, D.; Tsekouras, G.J.; Kousiouris, G. A multi-stage methodology for selecting input variables in ANN forecasting of river flows. Glob. NEST J.
**2017**, 19, 49–57. [Google Scholar] - Panagoulia, D. Artificial neural networks and high and low flows in various climate regimes. Hydrol. Sci. J.
**2006**, 4, 563–587. [Google Scholar] [CrossRef]

**Figure 7.**Scatter plot of simulated data and observed data for each model (

**a**) SVM-GS training stage; (

**b**) SVM-GS test stage; (

**c**) WSVM-GS training stage; (

**d**) WSVM-GS test stage.

**Figure 8.**SVM training principle combined with PSO parameter optimization and k-fold cross validation.

**Figure 12.**Scatter plot of simulated data and observed data for each model (

**a**) ANN training stage; (

**b**) ANN test stage; (

**c**) SVM training stage; (

**d**) SVM test stage; (

**e**) WANN training stage; (

**f**) WANN test stage; (

**g**) WSVM training stage; (

**h**) WSVM test stage.

**Figure 14.**Scatter plot of simulated data and observed data for each subseries in WSVM model (

**a**) low frequency subseries a3 training stage; (

**b**) low frequency subseries a3 test stage; (

**c**) high frequency subseries d3 training stage; (

**d**) high frequency subseries d3 test stage; (

**e**) high frequency subseries d2 training stage; (

**f**) high frequency subseries d2 test stage; (

**g**) high frequency subseries d1 training stage; (

**h**) high frequency subseries d1 test stage.

No. | Name | East Longitude | North Latitude | Start Time | End Time | Maximum Depth (m) | Minimum Depth (m) | Mean Depth (m) | Standard Deviation |
---|---|---|---|---|---|---|---|---|---|

1 | Banqiaoji | 116.6944444 | 33.3272222 | 1974/8 | 2010/12 | 4.99 | 0.27 | 2.56 | 0.97 |

2 | Mengcheng south | 116.5736111 | 33.2469444 | 1974/8 | 2010/12 | 10.29 | 0.37 | 2.68 | 1.92 |

3 | Guoji | 116.4722222 | 33.0430556 | 1974/8 | 2010/12 | 5.64 | 0.06 | 2.14 | 0.90 |

4 | Lvwangji | 116.4850000 | 33.1658333 | 1974/8 | 2010/12 | 4.12 | 0.43 | 2.68 | 0.79 |

5 | Shunheji | 116.6433333 | 33.0191667 | 1974/1 | 2010/12 | 7.15 | 0.06 | 2.13 | 0.77 |

6 | Maji | 116.3252778 | 33.3269444 | 1979/3 | 2010/12 | 4.53 | 0.37 | 2.09 | 0.78 |

7 | Sanyiji | 116.4855556 | 33.0958333 | 1974/8 | 2010/12 | 5.64 | 0.06 | 2.14 | 0.90 |

8 | Tancheng | 116.5600000 | 33.4444444 | 1974/1 | 2010/12 | 5.27 | 0.38 | 2.30 | 1.10 |

9 | Wangji | 116.7266667 | 33.2477778 | 1974/1 | 2010/12 | 6.16 | 0.24 | 2.23 | 0.70 |

10 | Yuefang | 116.4177778 | 33.3477778 | 1979/3 | 2010/12 | 3.88 | 0.61 | 1.96 | 0.61 |

Model | Training Stage | Test Stage | Gap | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

RAE | r | RMSE | NSE | RAE | r | RMSE | NSE | RAE | r | RMSE | NSE | |

ANN | 0.55 | 0.82 | 0.43 | 0.64 | 0.64 | 0.72 | 0.60 | 0.44 | 0.09 | 0.10 | 0.17 | 0.20 |

SVM | 0.58 | 0.85 | 0.41 | 0.68 | 0.64 | 0.78 | 0.53 | 0.56 | 0.06 | 0.07 | 0.12 | 0.12 |

WANN | 0.13 | 0.99 | 0.080 | 0.99 | 0.21 | 0.97 | 0.20 | 0.93 | 0.09 | 0.02 | 0.12 | 0.06 |

WSVM | 0.10 | 0.99 | 0.095 | 0.98 | 0.20 | 0.97 | 0.18 | 0.94 | 0.10 | 0.02 | 0.085 | 0.04 |

Subseries | Training Stage | Test Stage | Gap | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

RAE | r | RMSE | NSE | RAE | r | RMSE | NSE | RAE | r | RMSE | NSE | |

a3 | 0.04 | 1.00 | 0.021 | 0.99 | 0.11 | 1.00 | 0.078 | 0.99 | 0.07 | 0.00 | 0.057 | 0.00 |

d3 | 0.14 | 1.00 | 0.037 | 0.99 | 0.24 | 1.00 | 0.081 | 0.98 | 0.10 | 0.00 | 0.044 | 0.01 |

d2 | 0.02 | 0.95 | 0.060 | 0.99 | 0.03 | 0.95 | 0.099 | 0.98 | 0.01 | 0.00 | 0.039 | 0.01 |

d1 | 0.02 | 0.94 | 0.059 | 0.99 | 0.03 | 0.94 | 0.083 | 0.98 | 0.01 | 0.00 | 0.024 | 0.01 |

Scheme | Training Stage | Test Stage | Gap | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

RAE | r | RMSE | NSE | RAE | r | RMSE | NSE | RAE | r | RMSE | NSE | |

1 | 0.13 | 0.99 | 0.11 | 0.98 | 0.16 | 0.99 | 0.10 | 0.95 | 0.03 | 0.00 | 0.01 | 0.03 |

2 | 0.13 | 0.98 | 0.07 | 0.98 | 0.16 | 0.98 | 0.16 | 0.96 | 0.03 | 0.00 | 0.09 | 0.02 |

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## Share and Cite

**MDPI and ACS Style**

Zhou, T.; Wang, F.; Yang, Z.
Comparative Analysis of ANN and SVM Models Combined with Wavelet Preprocess for Groundwater Depth Prediction. *Water* **2017**, *9*, 781.
https://doi.org/10.3390/w9100781

**AMA Style**

Zhou T, Wang F, Yang Z.
Comparative Analysis of ANN and SVM Models Combined with Wavelet Preprocess for Groundwater Depth Prediction. *Water*. 2017; 9(10):781.
https://doi.org/10.3390/w9100781

**Chicago/Turabian Style**

Zhou, Ting, Faxin Wang, and Zhi Yang.
2017. "Comparative Analysis of ANN and SVM Models Combined with Wavelet Preprocess for Groundwater Depth Prediction" *Water* 9, no. 10: 781.
https://doi.org/10.3390/w9100781