Elsevier

Applied Mathematics and Computation

Volume 270, 1 November 2015, Pages 731-743
Applied Mathematics and Computation

A survey of water level fluctuation predicting in Urmia Lake using support vector machine with firefly algorithm

https://doi.org/10.1016/j.amc.2015.08.085Get rights and content

Highlights

  • Forecasting lake level at various horizons is reported here.

  • SVM coupled with FA was used to forecast lake level.

  • Results demonstrate the SVM–FA superiority.

Abstract

Forecasting lake level at various horizons is a critical issue in navigation, water resource planning and catchment management. In this article, multistep ahead predictive models of predicting daily lake levels for three prediction horizons were created. The models were developed using a novel method based on support vector machine (SVM) coupled with firefly algorithm (FA). The FA was applied to estimate the optimal SVM parameters. Daily water-level data from Urmia Lake in northwestern Iran were used to train, test and validate the used technique. The prediction results of the SVM–FA models were compared to the genetic programming (GP) and artificial neural networks (ANNs) models. The experimental results showed that an improvement in the predictive accuracy and capability of generalization can be achieved by the SVM–FA approach in comparison to the GP and ANN in 1 day ahead lake level forecast. Moreover, the findings indicated that the developed SVM–FA models can be used with confidence for further work on formulating a novel model of predictive strategy for lake level prediction.

Introduction

Lakes provide water for various domestic, industrial and agricultural applications [1]. Forecasting level of lake water using the previously recorded levels is an interesting approach in water resource planning, lake navigation, management of tidal irrigation as well as drainage canals. Level of lake water is affected by the natural water exchange between the lake and its watershed; thus, the water level reflects the climate changes within the region [2]. For many research and practical applications, it would be beneficial to have a model capable of simulating (and predicting) water level variations based solely on the previously recorded values [2]. So far, numerous studies have been carried out for predicting fluctuations of sea/lake water level using several models, including the neural networks, neuro-fuzzy and genetic programming [2], [3], [4], [5].

In this article, we introduce prediction models of daily lake levels for different prediction horizons using the data acquired from Urmia Lake in northwestern Iran. The proposed models were developed using the soft computing approach, namely the support vector machine (SVM) with firefly algorithm (FA).

The SVM is an intelligent technique, which is employed in several engineering disciplines [6], [7]. The prediction accuracy of an SVM model highly depends on proper selection of parameters. Various optimization algorithms have been used for selection of these parameters [8], [9], [10], such as the grid search algorithm [11] and gradient decent algorithm [12], but the success rate has been minimal. Computational complexity seems to be the main disadvantage of the grid method, which restricts its applicability to simple cases. The grid search algorithm is also prone to local minima. Multiple local solutions exist for most of the optimization problems and evolutionary algorithms seem to be the best, because they are capable of providing global solution to such problems.

Nature-inspired metaheuristic optimization algorithms, such as the ant colony optimization (ACO), genetic algorithm (GA), particle swarm optimization (PSO) and cuckoo search (CS) have found wide applications in different fields of science for several hybrid algorithms [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24]. The basis of these algorithms is the selection of the most appropriate in natural systems [25]. The latest algorithm among the nature-inspired metaheuristic optimization algorithms is the firefly algorithm (FA) [26]. The FA is believed to be more robust and efficient in finding both global and local optima compared to others [27], [28], [29], [30], [31], [32], [33]. The prediction accuracy of the SVM model highly depends on proper choice of model parameters. Even though prearranged approaches for parameter selection are essential, alignment of the model parameter is also important. In this study, the FA was used for determination of the SVM parameters.

A short-term predictive model of daily lake levels was developed using the SVM method, while the model parameters were obtained by the FA. The SVM–FA results were also compared to the genetic programing (GP) and artificial neural networks (ANNs) results.

The organization of the remaining parts of this paper is as follows: Section 2 explains the lake level data and prediction models for different prediction horizons. Section 3 describes the SVM–FA method, as well as GP and ANN as benchmark methods. The comparative results and discussion are put forward in Section 4. Finally, the conclusions are presented in Section 5.

Section snippets

Region and data description

Daily records of water level from Urmia Lake (North-Western Iran) were used in the present study. This lake is the world's second largest saline lake. It has started drying out, which has a dramatic impact on the environmental conditions of the neighbor regions. Table 1 presents statistics of the daily water level X, in which Csx, CV, Xmax, SD, Xmean, and Xmin represent the skewness coefficient, coefficient of variation, maximum, standard deviation, mean and, minimum, respectively. It can be

Soft computing prediction algorithms

This section describes the soft computing prediction algorithms used in this study. In this view, Section 3.1 elaborates on the support vector machine theory. Section 3.1.1 introduces the firefly searching algorithm. Section 3.2 presents artificial neural network with all used parameters. Finally Section 3.3 gives the main details of applied genetic programming method.

Results and discussion

Predictive models of lake's water levels were developed for 1 and 7 days ahead. As the inputs, we used previous water levels from one to five days in the past. When developing multistep ahead prediction models, two approaches are possible: (a) iterated prediction approach, and (b) direct prediction approach.

In the iterated prediction scheme, one step ahead prediction is used for building the subsequent predictions (i.e. for p steps ahead). Contrary to this, in the direct prediction approach,

Performance comparison of SVM–FA, ANN and GP

To validate the virtues of the suggested SVM–FA approach on a more tangible and definite basis, the prediction precision of the SVM–FA model was compared to those of the GP and ANN methods. For each of the three aforementioned methods, two different direct predictive models were developed (for different prediction horizons). To compare, R2, RMSE and r were used. The prediction accuracy of each model for training, test and validation datasets is summarized in Table 6.

For the training dataset,

Conclusion

The ability of the SVM–FA model in prediction of daily lake levels was explored. The proposed SVM–FA models were developed by combining the FA and SVM. The SVM implements structural minimization, whereas the FA is applied to determine the optimal SVM parameters.

Observations collected from Urmia Lake (northwestern Iran) during 1972–2003 were used for model development and testing. Two predictive models for different prediction horizons (1 day and 7 days ahead) were created using the SVM–FA.

Acknowledgments

We sincerely thank the editor and the reviewers for their constructive comments. The authors express their sincere thanks for the funding support they received from the HIR-MOHE University of Malaya under grant no. UM.C/HIR/MOHE/ENG/34.

References (70)

  • M. Basu

    Modified particle swarm optimization for nonconvex economic dispatch problems

    Int. J. Electric. Pow. Energ. Syst.

    (2015)
  • Z. Beheshti et al.

    Memetic binary particle swarm optimization for discrete optimization problems

    Inform. Sci.

    (2015)
  • M. Kumar et al.

    Optimal design of FIR fractional order differentiator using cuckoo search algorithm

    Exp. Syst. Appl.

    (2015)
  • A. Teske et al.

    Efficient detection of faulty nodes with cuckoo search in t-diagnosable systems

    Appl. Soft Comput.

    (2015)
  • P.J. García Nieto et al.

    HHybrid PSO—SVM-based method for long-term forecasting of turbidity in the Nalón river basin: a case study in Northern Spain

    Ecol. Eng.

    (2014)
  • P.J. García Nieto et al.

    Hybrid modelling based on support vector regression with genetic algorithms in forecasting the cyanotoxins presence in the Trasona reservoir (Northern Spain)

    Env. Res.

    (2013)
  • I. Fister et al.

    A comprehensive review of firefly algorithms

    Swarm Evolution. Comput.

    (2013)
  • Ch.S. et al.

    A support vector machine-firefly algorithm based forecasting model to determine malaria transmission

    Neurocomputing

    (2014)
  • T. Kanimozhi et al.

    An integrated approach to region based image retrieval using firefly algorithm and support vector machine

    Neurocomputing

    (2015)
  • S.R. Massan et al.

    Wind turbine micrositing by using the firefly algorithm

    Appl. Soft Comput.

    (2015)
  • I. Fister et al.

    A review of chaos-based firefly algorithms: perspectives and research challenges

    Appl. Math. Comput.

    (2015)
  • I. Fister et al.

    Memetic self-adaptive firefly algorithm

    Swarm Intelligence and Bio-Inspired Computation Theory and Applications

    (2013)
  • W.Z. Lu et al.

    Potential assessment of the “support vector machine” method in forecasting ambient air pollutant trends

    Chemosphere

    (2005)
  • T. Asefa et al.

    Multi-time scale stream flow predictions: the support vector machines approach

    J. Hydrol.

    (2006)
  • Y. Ji et al.

    Multitask multiclass support vector machines: model and experiments

    Pattern Recogn.

    (2013)
  • S. Rajasekaran et al.

    Support vector regression methodology for storm surge predictions

    Ocean Eng.

    (2008)
  • H. Yang et al.

    Localized support vector regression for time series prediction

    Neurocomputing

    (2009)
  • K.P. Wu et al.

    Choosing the kernel parameters for support vector machines by the inter-cluster distance in the feature space

    Pattern Recogn.

    (2009)
  • S. Shamshirband et al.

    Wind turbine power coefficient estimation by soft computing methodologies: comparative study

    Energ. Convers. Manage.

    (2014)
  • I. Fister et al.

    A comprehensive review of firefly algorithms

    Swarm Evolution. Comput.

    (2013)
  • S. Ch et al.

    A support vector machine-firefly algorithm based forecasting model to determine malaria transmission

    Neurocomputing

    (2014)
  • M. Casdagli

    Nonlinear prediction of chaotic time series

    Physica D

    (1989)
  • M. Marcellino et al.

    A comparison of direct and iterated multistep AR methods for forecasting macroeconomic time series

    J. Econom.

    (2006)
  • G. Chevillon et al.

    Non-parametric direct multi-step estimation for forecasting economic processes

    Int. J. Forecast.

    (2005)
  • R. Ramanathan et al.

    Short-run forecasts of electricity loads and peaks

    J. Forecast.

    (1997)
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