# An Improved LSSVM Model for Intelligent Prediction of the Daily Water Level

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Data Source

_{c}(subscript c denotes conventional LSSVM model) and LSSVM

_{i}(subscript i denotes improved LSSVM).

## 3. Methodology

#### 3.1. Conventional LSSVM Model

_{c}are written as Equation (2).

_{i}is the slack variable, Y

_{i}is binary target, w is the weight matrix, b is the bias, ξ

_{i}is the slack variable, and e

_{i}is the error variable; γ denotes a regularization constant; φ(X

_{i}) is the kernel function.

#### 3.2. Improved LSSVM Model

_{i}and the aforementioned Equation (2) is re-organized as follows:

_{i}are Lagrangian multipliers. By taking derivatives of w, b, e, α respectively and setting all derivatives as zero (i.e., Equation (5)), the following equations are thus derived.

_{c}and LSSVM

_{i}are trained by using historical daily water level data (Year 2010–2015), on the basis of which short-term forecasting is achieved for the year 2016. The training results for stations Jianli and Chenglingji have been presented in Figure 3. The error rate of model training is further presented and discussed in Section 4.

#### 3.3. Model Performace Metrics

_{c}and LSSVM

_{i}, three metrics were employed as the root mean square error (RMSE, Equation (13)), the mean absolute percentage error (MAPE, Equation (14)), and the index of agreement (d, Equation (15) by Willmott, [26]). RMSE is a frequently used estimator of the difference between observations and model predictions. Meanwhile, MAPE quantifies the ratio between the deviation and observations, thus being scale independent. The index of agreement (d) was developed as a standardized measure of the model forecasting error and varies between 0 (no agreement at all) and 1 (perfect match). Suppose the water level observation is $\left\{{X}_{o1},{X}_{o2},\dots {X}_{on}\right\}$ and the corresponding model prediction is $\left\{{X}_{p1},{X}_{p2},\dots {X}_{pn}\right\}$. $\overline{{X}_{o}}$ is the mean value of the observed time sequence. All metrics are calculated as follows:

## 4. Result and Discussion

#### 4.1. LSSVM_{i} Forecasting of Daily Water Level

_{i}is presented for different stations together with field observations and LSSVM

_{c}predictions (Figure 4 and Figure 5). It was found that the model forecasting is overall satisfactory. Some minor deviations were noted in the June and October for the station Shashi, which locates downstream of the Three Gorge Dam and Gezhou Dam. This could be attributed to the joint operations of multi-reservoir system, especially during the summer seasons when the rainfall generally increases. Besides, the influence of the river confluence was evident, e.g., Chenglingji, which is situated downstream of the Yangtze River–Dongting Lake confluence reaches. The majority of the discrepancies between LSSVM

_{i}predictions and field observations appear in the summer seasons (e.g., June–August).

#### 4.2. Model Performance Evaluation

_{i}are determined by using the cross-validation method (Table 1). By adopting the performance metrics introduced in Section 3.3, the model performance was investigated. Generally, three metrics are computed and tabulated (Table 2). It was found that the LSSVM

_{i}provides more accurate forecasting of daily water level although the improvement is generally moderate. Moreover, RMSE has been calculated for model training results and the comparison is shown in Figure 6. The model residual is comparable for both training and testing stages, indicating the LSSVM

_{i}does not suffer from an over-fitting problem.

_{i}. Similar temporal variation patterns are observed at Chenglingji while it is quite different at Jianli station.

_{i}and LSSVM

_{c}(Table 3). The results show clear increases of qualified rate for the stations of Yichang, Shashi and Jianli, while full qualified forecasting is obtained for Chenglingji and Hankou.

#### 4.3. Influence of Forecast Lead Time

_{i}. Computations of RMSE, MAPE and d are also presented and compared in Table 4. The model accuracy is overall acceptable. Although it decreases gradually as the forecast lead time increases, the LSSVM

_{i}model results in relatively high accuracy. This also implies that the proposed LSSVM

_{i}model should be further improved in order to yield reliable and effective forecast of the daily water level in the Yangtze River, such as alternative types of kernel functions (e.g., RBF: radial basis function) or integrated algorithm (e.g., Wavelet-LSSVM).

## 5. Conclusions

_{i}model was proposed through a bias error control scheme.

_{i}in short term forecasting of the daily water level was evaluated and compared with the conventional LSSVM

_{c}model. Both models were trained by using historical hydrological data (Year 2010–2015) to provide forecasting results of Year 2016. It was found that the result yielded by the LSSVM

_{i}model is generally satisfactory, although the precision is inevitably affected by the seasonality and forecast lead time. Meanwhile, the influence of joint operations of the multi-reservoir system and river confluence was noted at Shashi station and Chenglingji station respectively. Although the forecasting accuracy decreases gradually as the forecast lead time increases, it is improved most of the time by LSSVM

_{i}. The present study indicates the capability and flexibility of LSSVM-type models in resolving time series problems. The LSSVM

_{i}proves to be a promising alternative in the daily water level forecasting of the Yangtze River (China) while optimization in forecast extrapolation and error control scheme is still required in future research.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Choi, K.H.; Ang, B.W. A time-series analysis of energy-related carbon emissions in Korea. Energy Policy
**2001**, 29, 1155–1161. [Google Scholar] [CrossRef] - Montoya, J.V.; Roelke, D.L.; Winemiller, K.O.; Cotner, J.B.; Snider, J.A. Hydrological seasonality and benthic algal biomass in a Neotropical floodplain river. J. N. Am. Benthol. Soc.
**2006**, 25, 157–170. [Google Scholar] [CrossRef] - Buyukyildiz, M.; Tezel, G.; Yilmaz, V. Estimation of the Change in Lake Water Level by Artificial Intelligence Methods. Water Resour. Manag.
**2014**, 28, 4747–4763. [Google Scholar] [CrossRef] - Kisi, O.; Shiri, J.; Nikoofar, B. Forecasting daily lake levels using artificial intelligence approaches. Comput. Geosci.
**2012**, 41, 169–180. [Google Scholar] [CrossRef] - Sulaiman, M.; El-Shafie, A.; Karim, O.; Basri, H. Improved Water Level Forecasting Performance by Using Optimal Steepness Coefficients in an Artificial Neural Network. Water Resour. Manag.
**2011**, 25, 2525–2541. [Google Scholar] [CrossRef] - Zhong, C.; Jiang, Z.; Chu, X.; Guo, T.; Wen, Q. Water level forecasting using a hybrid algorithm of artificial neural networks and local Kalman filtering. Proc. Inst. Mech. Eng. Part M J. Eng. Marit. Environ.
**2017**. [Google Scholar] [CrossRef] - Alvisi, S.; Mascellani, G.; Franchini, M.; Bardossy, A. Water level forecasting through fuzzy logic and artificial neural network approaches. Hydrol. Earth Syst. Sci. Discuss.
**2005**, 2, 1107–1145. [Google Scholar] [CrossRef] - Palani, S.; Liong, S.Y.; Tkalich, P. An ANN application for water quality forecasting. Mar. Pollut. Bull.
**2008**, 56, 1586–1597. [Google Scholar] [CrossRef] - Nourani, V.; Mogaddam, A.A.; Nadiri, A.O. An ANN-based model for spatiotemporal groundwater level forecasting. Hydrol. Process.
**2010**, 22, 5054–5066. [Google Scholar] [CrossRef] - Ivan, H.; Gilja, G. Time series forecasting of parameters in hydraulic engineering using artificial neural networks. In Proceedings of the International Symposium on Water Management & Hydraulic Engineering, Primošten, Hrvatska, 6–8 September 2017. [Google Scholar]
- Valizadeh, N.; El-Shafie, A.; Mirzaei, M.; Galavi, H.; Mukhlisin, M.; Jaafar, O. Accuracy Enhancement for Forecasting Water Levels of Reservoirs and River Streams Using a Multiple-Input-Pattern Fuzzification Approach. Sci. World J.
**2014**, 2014, 432976. [Google Scholar] [CrossRef] [PubMed] - Kang, M.G.; Maeng, S.J. Gray Models for Real-Time Groundwater-Level Forecasting in Irrigated Paddy-Field Districts. J. Irrig. Drain. Eng.
**2015**, 142, 04015036. [Google Scholar] [CrossRef] - Guo, Z.; Bai, G. Application of Least Squares Support Vector Machine for Regression to Reliability Analysis. Chin. J. Aeronaut.
**2009**, 22, 160–166. [Google Scholar] [CrossRef] [Green Version] - Luo, W.L.; Zou, Z.J. Parametric Identification of Ship Maneuvering Models by Using Support Vector Machines. J. Ship Res.
**2009**, 53, 19–30. [Google Scholar] - Sujay Raghavendra, N.; Deka, P.C.; Shukla, S. Forecasting monthly groundwater level fluctuations in coastal aquifers using hybrid Wavelet packet–Support vector regression. Cogent Eng.
**2015**, 2, 999414. [Google Scholar] [CrossRef] - Seo, Y.; Kim, S.; Singh, V.P. Physical Interpretation of River Stage Forecasting Using Soft Computing and Optimization Algorithms. In Harmony Search Algorithm; Springer: Berlin/Heidelberg, Germany, 2016. [Google Scholar]
- Francesco, G.; Rudy, G.; Giovanni, D.M. Support Vector Regression for Rainfall-Runoff Modeling in Urban Drainage: A Comparison with the EPA’s Storm Water Management Model. Water
**2016**, 8, 69. [Google Scholar] [CrossRef] - Noori, R.; Karbassi, A.R.; Moghaddamnia, A.; Han, D.; Zokaei-Ashtiani, M.H.; Farokhnia, A.; Gousheh, M.G. Assessment of input variables determination on the SVM model performance using PCA, Gamma test, and forward selection techniques for monthly stream flow prediction. J. Hydrol. (Amst.)
**2011**, 401, 177–189. [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] - Cheng, M.Y.; Hoang, N.D.; Wu, Y.W. Cash flow prediction for construction project using a novel adaptive time-dependent least squares support vector machine inference model. J. Civ. Eng. Manag.
**2015**, 21, 679–688. [Google Scholar] [CrossRef] - Cong, Y.; Wang, J.; Li, X. Traffic Flow Forecasting by a Least Squares Support Vector Machine with a Fruit Fly Optimization Algorithm. Procedia Eng.
**2016**, 137, 59–68. [Google Scholar] [CrossRef] - Ismail, S.; Shabri, A.; Samsudin, R. A hybrid model of self-organizing maps (SOM) and least square support vector machine (LSSVM) for time-series forecasting. Expert Syst. Appl.
**2011**, 38, 10574–10578. [Google Scholar] [CrossRef] - Li, S.; Xiong, L.; Dong, L.; Zhang, J. Effects of the Three Gorges Reservoir on the hydrological droughts at the downstream Yichang station during 2003–2011. Hydrol. Process.
**2013**, 27, 3981–3993. [Google Scholar] [CrossRef] - Guo, J.; Zhou, J.; Qin, H.; Zou, Q.; Li, Q. Monthly streamflow forecasting based on improved support vector machine model. Expert Syst. Appl.
**2011**, 38, 13073–13081. [Google Scholar] [CrossRef] - Ghorbani, M.A.; Khatibi, R.; Goel, A.; FazeliFard, M.H.; Azani, A. Modeling river discharge time series using support vector machine and artificial neural networks. Environ. Earth Sci.
**2016**, 75, 685. [Google Scholar] [CrossRef] - Willmott, C. On the validation of models. Phys. Geogr.
**1981**, 2, 184–194. [Google Scholar] [CrossRef]

**Figure 2.**Temporal variation of daily water level at Jianli station (top panel) and Chenglingji station (bottom panel).

**Figure 3.**LSSVMi (least squares support vector machine) model training results at Jianli station (

**top panel**) and Chenglingji station (

**bottom panel**).

**Figure 8.**Effects of forecast lead time on LSSVMi model accuracy at Jianli (

**top panel**) and Chenglingji (

**bottom panel**).

**Table 1.**Parameters of the LSSVM

_{i}(least squares support vector machine) model with regard to different forecast lead times.

Lead Time | Parameter | Yichang | Shashi | Jianli | Chenglingji | Hankou |
---|---|---|---|---|---|---|

1-day | $a$ | 6.655e7 | 5.488e8 | 7.59e8 | 8.43e7 | 8.41e8 |

$\gamma $ | 1.75e6 | 3.489e2 | 2.688e7 | 6.93e2 | 4.85e3 | |

2-day | $a$ | 6.555e7 | 5.889e9 | 6.95e8 | 8.43e7 | 8.43e8 |

$\gamma $ | 2.75e6 | 3.689e2 | 1.388e7 | 5.99e2 | 2.97e5 | |

3-day | $a$ | 6.455e7 | 5.889e6 | 6.59e8 | 8.43e7 | 7.41e9 |

$\gamma $ | 3.75e6 | 1.789e3 | 1.188e7 | 5.95e3 | 3.07e5 |

Stations | RMSE [m] | MAPE [%] [-] | D [-] | |||
---|---|---|---|---|---|---|

LSSVM_{c} | LSSVM_{i} | LSSVM_{c} | LSSVM_{i} | LSSVM_{c} | LSSVM_{i} | |

Yichang | 0.1394 | 0.1384 | 10.0872 | 8.6710 | 0.9848 | 0.9863 |

Shashi | 0.1727 | 0.1740 | 20.7350 | 20.5456 | 0.9796 | 0.9794 |

Jianli | 0.3196 | 0.2222 | 6.1984 | 2.4874 | 0.9552 | 0.9736 |

Chenglingji | 0.1482 | 0.1449 | 1.3801 | 1.3232 | 0.9852 | 0.9857 |

Hankou | 0.1536 | 0.1546 | 1.5315 | 1.4613 | 0.9862 | 0.9865 |

Stations | Yichang | Shashi | Jianli | Chenglingji | Hankou |
---|---|---|---|---|---|

LSSVMi | 0.9726 | 0.9235 | 1.0000 | 1.0000 | 1.0000 |

LSSVMc | 0.9671 | 0.9207 | 0.9644 | 1.0000 | 1.0000 |

Stations | RMSE [m] | MAPE [%] | D [-] | ||||||
---|---|---|---|---|---|---|---|---|---|

1-day | 2-day | 3-day | 1-day | 2-day | 3-day | 1-day | 2-day | 3-day | |

Jianli | 0.2222 | 0.3755 | 0.4175 | 2.4874 | 3.1273 | 4.7808 | 0.9736 | 0.9603 | 0.9489 |

Chenglingji | 0.1448 | 0.3262 | 0.4056 | 1.3232 | 1.9215 | 2.1845 | 0.9857 | 0.9737 | 0.9681 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Guo, T.; He, W.; Jiang, Z.; Chu, X.; Malekian, R.; Li, Z.
An Improved LSSVM Model for Intelligent Prediction of the Daily Water Level. *Energies* **2019**, *12*, 112.
https://doi.org/10.3390/en12010112

**AMA Style**

Guo T, He W, Jiang Z, Chu X, Malekian R, Li Z.
An Improved LSSVM Model for Intelligent Prediction of the Daily Water Level. *Energies*. 2019; 12(1):112.
https://doi.org/10.3390/en12010112

**Chicago/Turabian Style**

Guo, Tao, Wei He, Zhonglian Jiang, Xiumin Chu, Reza Malekian, and Zhixiong Li.
2019. "An Improved LSSVM Model for Intelligent Prediction of the Daily Water Level" *Energies* 12, no. 1: 112.
https://doi.org/10.3390/en12010112