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## Optimization of sediment rating curve coefficients using evolutionary algorithms and unsupervised artificial neural network | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Caspian Journal of Environmental Sciences | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

مقاله 8، دوره 15، شماره 4، زمستان 2017، صفحه 387-401
اصل مقاله (832 K)
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نوع مقاله: Research Paper | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

شناسه دیجیتال (DOI): 10.22124/cjes.2017.2665 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

نویسندگان | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

M Tabatabaei؛ A Salehpour Jam | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

^{}Agricultural Research, Education and Extension Organization Tehran | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

چکیده | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Sediment rating curve (SRC) is a conventional and a common regression model in estimating suspended sediment load (SSL) of flow discharge. However, in most cases the data log-transformation in SRC models causing a bias which underestimates SSL prediction. In this study, using the daily stream flow and suspended sediment load data from Shalman hydrometric station on Shalmanroud River, Guilan Province, Iran, SRC equation was derived, and then, using evolutionary algorithms (genetic algorithm and particle swarm optimization algorithm) it was calibrated again. Worth mentioning, before model calibration, to increase the generalization power of the models, using self-organizing map (an unsupervised artificial neural network for data clustering), the data were clustered and then by data sampling, they were classified into two homogeneous groups (calibration and test data set). The results showed that evolutionary algorithms are appropriate methods for optimizing coefficients of SRC model and their results are much more favorable than those of the conventional SRC models or SRC models corrected by correction factors. So that, the sediment rating curve models calibrated with evolutionary algorithms, by reducing the RMSE of the test data set of 5754.02 ton/day (in the initial SRC model) to 1681.21 ton.day^{-1} (in the calibrated models by evolutionary algorithms) increased the accuracy of suspended sediment load estimation at a rate of 4072.81 ton.day^{-1}. In total, using evolutionary algorithms in calibrating SRC models prevents data log-transformation and use of correction factors along with increasing in the accuracy of molding results. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

کلیدواژهها | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Clustering؛ Genetic and PSO Algorithms؛ Sediment Rating Curve؛ Self-Organizing Map؛ Suspended Sediment Load | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

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(Received: July 05. 2017 Accepted: Nov. 28. 2017)
Sediment rating curve (SRC) is a conventional and a common regression model in estimating suspended sediment load (SSL) of flow discharge. However, in most cases the data log-transformation in SRC models causing a bias which underestimates SSL prediction. In this study, using the daily stream flow and suspended sediment load data from Shalman hydrometric station on Shalmanroud River, Guilan Province, Iran, SRC equation was derived, and then, using evolutionary algorithms (genetic algorithm and particle swarm optimization algorithm) it was calibrated again. Worth mentioning, before model calibration, to increase the generalization power of the models, using self-organizing map (an unsupervised artificial neural network for data clustering), the data were clustered and then by data sampling, they were classified into two homogeneous groups (calibration and test data set). The results showed that evolutionary algorithms are appropriate methods for optimizing coefficients of SRC model and their results are much more favorable than those of the conventional SRC models or SRC models corrected by correction factors. So that, the sediment rating curve models calibrated with evolutionary algorithms, by reducing the RMSE of the test data set of 5754.02 ton/day (in the initial SRC model) to 1681.21 ton.day
It is necessary to have adequate up-to-date information about the suspended sediment load (SSL) of rivers and monitor them continually in order to be aware of the watershed sediment yield condition, the amount of erosion as well as changes in the river bed and river bank, the quality of water, along with optimum design and favorable performance of water resource structures (Tayfur 2012; Nourani (1) Where, Q A. Estimation of daily SSL of Shalman River using the traditional SRC model and the SRC model modified by traditional correction factors. B. Optimization of SRC model's coefficients using evolutionary algorithms (GA and PSO algorithm) and re-estimation of SSL. C. Comparison of traditional SRC models (part A) with optimized models (part B) in terms of SSL estimation as accurate as possible.
In this study, MATLAB 7.11 software was used to implement GA and PSO algorithms, cluster the data, and calculate the cluster validity index. The data were statistically analyzed using SPSS19 and MATLAB software programs.
The present study was performed in the Shalman watershed at Shalman hydrometric station, which is located between longitude 49°56'-50°18' E and latitude 36°54'- 37°14' N in Guilan Province, Iran (Fig. 1). The watershed has the area of 48021 hectares and mean elevation of 522 m above sea level. The data used in this study included 841information records of hydrometric data of instantaneous flow discharge and sediment discharge in Shalman Hydrometric Station during the 34 years (1972-2006). The statistical parameters [mean ( ), standard deviation (S According to the statistical data in Table 1, the sediment discharge has a high skewness and coefficient of variation, as the variation between its maximum and minimum is very high. This result along with other calculated statistics revealed the complexity of SSL modeling of the river.
To build the SRC models as accurate as possible, the calibration data of the models should represent the data of the entire statistical period. Moreover, to evaluate the models and its results, the test data should be similar to those of calibration (in terms of statistical parameters) and have the same distribution. To do so, the SOM clustering method was used to cluster the data, and proportional allocation method was used to sample the clusters to prepare two homogenous and similar sets of data (calibration and test data sets). The number of optimal clusters was determined using Davies-Bouldin index. To analyze the results of clustering, besides comparing the statistical parameters (mean, standard deviation, skewness, etc.) together, the similarity of data distribution (in calibration and evaluation) was examined using Two-Sample Kolmogorov-Smirnov Test (KS). All these stages are briefly described below:
Data clustering is a common method in analysis of statistical data in which similar data are classified into different clusters in a way that the samples in each cluster are similar to one another but different from samples of other clusters (Yar Kiani 2009).
The self-organizing map (SOM) is an unsupervised artificial neural network proposed by Kohonen (1982). One of the most important application of the SOM is its ability in the clustering of data. Generally, SOM networks learn to cluster groups of similar input data from a high dimensional input space in a non-linear fashion onto a low dimensional (most commonly two-dimensional) discrete lattice of neurons in an output layer (Kohonen 2001). The typical structure of an SOM consists of two layers: an input layer and a Kohonen or output layer (Fig. 2).
In the SOM structure, input layer contains one neuron for each variable ( I = 1,2,..., n) (e.g., flow discharge, suspended sediment load, etc.) in the data set and it is fully connected to the Kohonen layer through adjustable weights (wfor _{ji} j = 1,2, ..., m).The process of network learning is formed of three phases of the competition, co-operation and adaptation. In competitive phase, by introducing a data pattern (an input vector) to the SOM network, the Euclidean distances of the data to the neurons of output layer are calculated and each neuron of the output layer that has the least distance is selected as a winner neuron or neuron which is the closest neuron to the input vector.
This neuron is also called best matching unit (BMU). Notably, at the first, the weight of neurons in the output layer is randomly defined, but during the process of learning, it is more similar to the vector values of input variables. The Euclidean distance is calculated according to the following equation (Bowden , (2) Where: D
(3)
Where: t, time, a function transforming the distance between neighboring neurons of the BMU to a ratio of the neighborhood and η (t) is
the learning rate. The process of learning the SOM network is continued by presenting new input data vectors to the SOM network, and during this process the connection weights are adjusted until they remain unchanged. A full description of the self-organizing map process was proposed by Kohonen (1982).
The indexes evaluating the quality of clustering, regardless of the algorithm used in them, examine the clusters in terms of two parameters: 1- Intra-cluster Similarity (Cluster Compactness) and 2- Inter-cluster Dissimilarity (Cluster Separation). A suitable clustering method (in which number of clusters are optimum) is that in which the value of the two parameters is high (Kaufman There are various methods to determine the optimal number of clusters (Dunn index, silhouette index, Davies-Bouldin index, validation index, etc.) of which Davies-Bouldin index was used in this study due to its efficiency and easy implementation in MATLAB software. The index is briefly described below: Davies-Bouldin index: It calculates mean similarity between two clusters that are most similar (Yar Kiani 2009). The lower calculated value of the index increases the quality of clustering. The index uses the inter-cluster similarity that is defined based on the dispersion of a cluster and inter-cluster dissimilarity. Equation 4 (Yar Kiani 2009): (4) Where, R (5) Where, d (6) Where, is the number of data in the i (7) Where, DB: Davies-Bouldin index; n , (8)
To prepare two sets that were as homogenous and similar as possible (calibration and test data sets), the proportional allocation method was used for sampling the clusters. In this method, the number of samples varies with the size of the cluster, as the size of a cluster increases, the number of samples increases too, and vice versa (May (9) Where, nh: number of samples drawn from h cluster; n: number of required data; Nh: number of data in h cluster; and Nj: number of data in other clusters. In the present study, 80% of the data were used for making the calibration set, and the remaining 20% of the data were used for making the test sets.
Besides, comparison of statistical data (mean, standard deviation, skewness, etc.), the nonparametric two-sample Kolmogorov-Smirnov test (due to the abnormal distribution of data) was used to examine and compare homogeneity and the similarity of the data in calibration and test data sets. The KS test was performed at error level of 1% (α = 1%) using Equation 10 and MATLAB software (Mansourfar 2009): (10) Where, F(ni
The sediment rating curve model (SRC model) was prepared on the basis of Equation 1 and least square method using homogenized data of the calibration data set. Moreover, the FAO correction factor was used to modify the SRC model (SRC-FAO model). The FAO correction factor introduced by Jones (11) Where, CF: FAO correction factor; : mean sediment discharge of observational samples (mg.l
The GA is a nonlinear search and optimization method inspired by biological processes of natural selection and survival of the fittest species. This searching method has relatively few assumptions and do not rely on any mathematic properties of function (continuity and differentiability) (Tayfur 2012). In this method, a population of potential responses is obtained through selecting a random set out of initial solutions, which are actually a set of initial responses of the problem (initial population). Thereafter, individuals of the population compete with each other to survive and make better responses based on the objective function (Equation 12); consequently, the quality and quantity of the appropriate responses increase in next generations using three genetic operators, including selection, reproduction, and mutation; and this process continues up to the convergence of the algorithm and finding the optimal final response (here a and b coefficients in the SRC regression model). (12) Where, : vector of SRC coefficients (values of a chromosome’s genes); SSL When using GA, roulette wheel selection method (weighting method based on the cost of the chromosome) was used to select parents for reproduction; the blending method was used to reproduce; and uniform random number generation method was used for genetic mutations. Noteworthy, GA was used with calibration data, and SRC model coefficients after optimization were used in the SSL estimation of the test data set. In total, to use a continuous genetic algorithm in this study, we determined an initial population of 50, reproduction of 75%, mutation of 15%, and maximum number of reproductions of 500.
PSO consists of a group of particles (individuals) which refine their knowledge of the search space (Kisi In PSO algorithm, particles cooperate with one another to reach a common goal, and thus, this method is more effective than that in which particles act separately (Shahriar In this method, the collective behavior does not only depend on individuals’ behavior in the society, but also associates with the manner of interaction among individuals in a group in a way that particles scatter in the searching space and then gradually moves toward successful areas (optimum solutions) to achieve the best solutions under the influence of their own knowledge and their neighbors’ knowledge. In PSO algorithm, firstly, some particles with random location and speed are created; then, these particles modify their movement toward the goal based on the best previous location of themselves and their neighbors in each repetition. After consequent repetitions, the problem converges to the optimum solution. The speed (V) and location (X) of each particle are modified through equations 13 and 14, respectively (Shahriar Shahhoseini
(13) (14)
In the above equations, gbest shows the best location obtained from the population of particles; pbest is the best location of the particle itself experienced up to now; t is the number of repetitions; rand The value of these two coefficients is determined in the interval [0 and 2], mostly 2 or 1.49 for both coefficients. In the above equations, ω is the inertia coefficient that decreases linearly and is defined in the interval [0 and 1] (Shahriar Shahhoseini To use the PSO algorithm in this study, the number of initial particles, C
To evaluate the results obtained from different models of SRC (the conventional SRC model, SRC-FAO, SRC-GA and SRC-PSO) and compare their results with those of observational sediment data (data of the test set), graphic drawings and error measurements were performed. Moreover, for each model, the scatter plot of the observational data was drawn using calculated data of the model, and we determined the linear regression equation and correlation coefficient (R (15) (16) (17) (18) In the above equations, S
Optimal number of clusters in the studied data were determined as 8 clusters using SOM clustering and Davies-Bouldin index (Fig. 2). Results of statistical parameters and nonparametric two-sample Kolmogorov-Smirnov test in calibration and test data sets (obtained from data clustering through the proportional allocation method) are respectively shown in Tables 2 and 3.
In Table 3, h letter is a statistic for two-sample Kolmogorov-Smirnov test in MATLAB software. When h = 0, it means that it does not reject the null hypothesis (which is that x1 and x2 are from the same continuous distribution) at the significance level of α (α is the desired significance level, e.g. 0.05). The obtained results from the K-S test showed that the distribution of the corresponding data in both data sets (calibration and test data sets) was identical (proof of H
Table 4 shows the results of calibration and evaluation of various models of SRC using data of calibration and test data sets. The obtained results show that hybrid models of SRC (SRC-GA and SRC-PSO models) are more favorable than the SRC model and SRC model modified by an FAO factor (SRC-FAO). Also, among the hybrid models, SRC-GA model was selected as the best model because it had slightly more proper performance than SRC-PSO model. In Fig. 4, the fitness of various models of SRC to observational data [flow discharge (QW) and daily sediment discharge (QS) in calibration data set] has been presented. As well shown in Fig. 4, GA and PSO hybrid models showed better fitness than other models. Furthermore, their difference was very partial, as their curves almost overlay each other.
As shown in Fig. 4, some of the data are far from the regression line. This problem can be explained in two parts. First, one of the problems which is associated with sediment data measured at the hydrometric stations is basically the lack of data samples on flood conditions. So, it is common that the quality of these data does not have enough precision to a perfect model calibration. Second, in the sediment rating curve, there is only one predictor variable which is the flow discharge. According to the Rodríguez-Blanco As can be seen in Fig. 5, the slope of fitness line in the evolutionary models (SRC-GA and SRC-PSO) is better than those of FAO-SRC and SRC models (0.78 against 0.71 in FAO-SRC and 0.07 in SRC models respectively). However, in comparison with PSO-SRC model, the GA-SRC model, by having the less y-intercept and more R
(test data set) from different SRC models.
Accurate suspended sediment load estimation is very essential in planning, designing, operating and favorable performance of water resource structures. The models based on regression methods, such as SRC model, have
restricted assumptions such as normality, linearity and constant variance. These models are able to provide only one solution point (a and b coefficients) for estimation of sediment load. On the other hand, the evolutionary algorithms, such as GAs, PSO and etc. can produce more than one solution points that provide the optimal relation between flow discharge and sediment loads. Also, they are not restricted by regression assumptions. Generally, to optimize the coefficients of the SRC model, data log-transformation and least square error method are used in a form of linear regression.
The data log-transformation results in a bias in the calculation of model coefficients and underestimation of SSL (sediment discharge or sediment concentration). This problem is most obvious in high flood discharges, and the model error increases with an increase in the flow discharge. So far, different correction factors have been introduced to correct the bias. However, these factors sometimes cause another error in the form of an overestimation along with different results. In this study, besides the conventional methods (least square error method and the model modified with FAO factor), the SRC model coefficients were optimized through evolutionary algorithms (GA and PSO) and results were much more favorable than those of the conventional methods. The results of this study conformed to those of the studies conducted by Altunkaynak (2009), Mohammad Rezapour
model and its results, the test data set should be similar to those of calibration data set. This is an important problem and of the fundamental challenges in modeling, as the failure to use similar homogenous data in calibration and test sets may largely affect the results of modeling. So that, the SOM clustering method can be used to provide similar homogeneous data sets for calibration and evaluation of data-driven models (Li
We are grateful for financial support of Soil Conservation and Watershed Management Research Institute (SCWMRI).
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آمار تعداد مشاهده مقاله: 189 تعداد دریافت فایل اصل مقاله: 128 |
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