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