GENETIC ALGORITHM TO PREDICT THE LONGITUDINAL DISPERSION COEFFICIENT IN NATURAL RIVERS 1
BEHZADGHIASI, 2AMIN SARANG, 3HOSSEINSHEIKHIAN, 4MOSTAFARAMEZANI, 5 ROOHOLLAHNOORI 1,2,4,5
Environmental EngineeringDepartment, University of Tehran, Iran 3 GISDepartment, University of Tehran, Iran 1 E-mail:
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Abstract- Although different studies have been carried out on estimating Longitudinal Dispersion Coefficient (LDC) in natural rivers, the inaccuracy and less user-friendliness of the provided models to predict LDC requires more research to focus on. Thus, the main objective of this study is to develop an empirical model by means of genetic algorithm. For this purpose, a set of patterns containing hydraulic and geometric characteristics of 30 rivers in United States was used for calibration of the model and testing the acquired results. Results show that the pattern including the river curvature parameter has the best performance for LDC prediction model. The best model resulted in 0.9435 and 0.9419 for the coefficient of determination (R2) in calibration and test data sets, respectively. Detailed comparison of the implemented model respect to the precedent studies confirmed the genetic algorithm as an accurate estimator for LDC. Keywords- Genetic Algorithm, Longitudinal Dispersion Coefficient, Natural Rivers, Empirical Models
used. These datasets contain hydraulic parameters including mean velocity of river (U) and shear velocity (u*) and geometric data including depth (H), width (W), and curvature (σ). 70% (43 datasets) of the data was used for calibration of the model and the rest was used for testing the results. Table (1) indicates considerable distance between the mean and median values of the parameters, especially for LDC. Being asymmetric respect to the mean for LDC, thus having a high value of skewness, complicates prediction of LDC. Much research effort focused on obviating this complexity and providing an accurate estimation of LDC. 2.2. Genetic Algorithm GA applications include a vast scope in many scientific and engineering works. While the technology and science progress, their applications grow further as well. GA is a search heuristic (also sometimes called a metaheuristic) algorithm which simulates the process of natural selection in order to generate appropriate solutions for optimization and search problems. In this paper each binary chromosome has 40 genomes. In each chromosome, from left to right, equal sets of genomes assigned to coefficients a, b, c and d, allocating 10 genomes to indicate each coefficient.
I. INTRODUCTION Prediction and analysis of dispersion mechanism of discharged pollution in surface water is one of the most challenging areas in water body and river quality management studies. This procedure requires solving the advection/dispersion equation. Whether the model is multi dimension or not, and regardless of adopting analytical or numerical approach in solving the main equation, the principal parameter to be determined is LDC. In fact, quality and quantity of the discharged materials could be modeled mathematically as a function of LDC. Therefore, determining an accurate and reliable formula to predict LDC has become an important subject across the recent decades, leading to a bunch of different solutions such as: lab based approaches, empirical formulas and soft-computing methods lacking cost efficiency, appropriate accuracy and user-friendly interface, respectively. In this paper, the empirical approach is employed because of inherent user friendly benefits of it. To improve the accuracy, a genetic algorithm used to predict the unknown coefficients in the final LDC formula. II. MATERIALS AND PROCEDURE 2.1. Data To calibrate and validate the results, 61 datasets, collected from 30 rivers across United States, were
Table (1) Statistical information of hydraulic and geometric parameters of river datasets
Proceedings of The IRES 22nd International Conference, Toronto, Canada, 1 st January 2016, ISBN: 978-93-85832-86-4 50
Genetic Algorithm To Predict The Longitudinal Dispersion Coefficient In Natural Rivers
III. RESULTS AND DISCUSSIONS R² = 0.8501
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Predicted
According to the literature, the following model was developed for LDC estimation:
Based on the Eq.(2), Deng et al. (2002) used curvature to improve the LDC estimation. Here the Eq.(2) was improved by embedding the curvature (Eq.(3)):
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Measured a)Calibration data set b) Test data set Fig.1: predicted values by GA-1 versus measured values
Unknown coefficients were determined by GA. Eq. (4) and Eq. (5) indicate the GA-1 and GA-2 models. GA-2 model considers the effect of the curvature while the GA-1 ignores it.
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R² = 0.9435 Predicted
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Fig.1 and Fig.2 illustrates the GA-1 and GA-2 predicted values against the measured values for both calibration and test data sets ,respectively, confirming the acquired results by GA. Fig.3 shows the variations of the predicted values by GA respect to the measured values. As can be seen, predicted values closely confirm the measured values. Table (2) describes the detailed comparison among the developed models and the precedent empirical methods. As can be interpreted from the Table (2), Etemad-Shahidi and Taghipour (2012) acquired the best results among the empirical models. However, the GA-2 model obtained the best results among the rest of implemented models and empirical methods. Due to unsatisfactory results by GA-1, only GA-2 andEtemad-Shahidi and Taghipour (2012) model are compared. To go further in detail,Developed Discrepancy Ratio(DDR) diagramwas used. GA apparently outperformed the Etemad-Shahidi and Taghipour (2012) methold (Fig.(4)).
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R² = 0.9419 Predicted
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Measured a) Calibration data set b) Test data set Fig.2: predicted values by GA-2 versus measured values
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R² = 0.9195 600 LDC
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Fig.3: Variations between the predicted and measured values
Proceedings of The IRES 22nd International Conference, Toronto, Canada, 1 st January 2016, ISBN: 978-93-85832-86-4 51
Genetic Algorithm To Predict The Longitudinal Dispersion Coefficient In Natural Rivers Table (2): Detailed comparison among the developed models and the precedent empirical methods
Standardized Gussian function values (QDDR)
-4
GA provides reliable and accurate results in obtaining unknown coefficients of the empirical models. GA-2 acquired the best results in comparison to precedent research, respect to the selected performance measures. Using the GA along with determining appropriate set of input parameters concluded to best results respect to precedent empirical models.
GA-2 Etemad-Shahidi and Taghipour (2012)
REFRENCES
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Standardized DDR values (ZDDR)
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[1]. Deng Z, Singh V P and Bengtsson L. (2001). “Longitudinal dispersion coefficient in straight rivers”. J HydraulEng ASCE. 127(11): 919-927. [2]. Deng Z, Bengtsson L, Singh V P and Adrian D D. (2002). “Longitudianl dispersion coefficient in singlechannel streams”. J HydraulEng ASCE. 128(10): 901-916. [3]. Disley T, Gharabaghi B, Mahboubi A and McBean A. (2015). “Predictive equation for longitudinal dispersion coefficient”. Hydrol Process. 29: 161–172. [4]. Etemad-Shahidi A and Taghipour M. (2012). “Predicting longitudinal dispersion coefficient in natural streams using M5’ Model Tree”. J Hydraul Eng. 138 (6): 542–554. [5]. Fischer H B, List E J, Koh R C Y, Imberger J and Brooks N H. (1979). Mixing in inland and coastal waters, Academic, New York. [6]. Fischer H B. (1975). “Discussion of ‘Simple method for predicting dispersion in stream’ by R. S. McQuivey and T. N. Keefer”. J Environ EngDiv ASCE. 101(3): 453-455. [7]. Guymer I. (1998). “Longitudinal dispersion in sinuous channel with changes in shape”. J HydraulEng 124 (1): 3340. [8]. Kashefipour M S and Falconer RA. (2002). “Longitudinal dispersion coefficients in natural channels”. Water Res. 36(6): 1596-1608. [9]. Koussis A D and Rodriguez-Mirasol J. (1998). “Hydraulic estimation of dispersion coefficient for streams”. J HydraulEng ASCE. 124(3): 317-320. [10]. Noori R, Karbassi A R, Mehdizadeh H, Vesali-Naseh M and Sabahi M S. (2011). “A framework development for predicting the longitudinal dispersion coefficient in natural streams using an artificial neural network”. Environ. Prog Sustain. 30(3): 439-449. [11]. Noori R, Karbassi A R, Farokhnia A and Dehghani M. (2009). “Predicting the longitudinal dispersion coefficient
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Fig.4: DDR measure for GA and Etemad-Shahidi and Taghipour (2012)
CONCLUSIONS Much research effort is dedicated to LDC estimation and various methods are proposed. Among the proposed models, Eq.(2) is the simplest method. Another contribution of the research was investigating the curvature parameter which was supposed to influence the LDC estimation. In this regard, a new model, called GA-2, was proposed by embedding the curvature into the Eq.(2). Main conclusions of the research are as follows: Considering the curvature improves the accuracy of empirical models in LDC estimation. The only model to compete the proposed model of this research was Etemad-Shahidi and Taghipour (2012), which also considered the curvature. This confirms the importance of curvature in LDC estimation.
Proceedings of The IRES 22nd International Conference, Toronto, Canada, 1 st January 2016, ISBN: 978-93-85832-86-4 52
Genetic Algorithm To Predict The Longitudinal Dispersion Coefficient In Natural Rivers using support vector machine and adaptive neuro-fuzzy inference system techniques”. EnviroEng Sci. 26(10): 15031510. [12]. Rutherford, J C. (1994). River Mixing. John Wiley & Sons, Chichester, U K, 347 pp. [13]. Sattar A and Gharabaghi B. (2015). “Gene expression models for prediction of longitudinal dispersion coefficient in streams”. Journal of Hydrology. 524: 587-596.
[14]. Seo I W and Cheong T S. (1998). “Predicting dispersion coefficient in natural Streams”. J ASCE. 124(1): 25-32. [15]. Zeng Y and Huai W. (2014). “Estimation of dispersion coefficient in rivers”. Journal environment Research. 8(1) :2-8.
longitudinal HydraulEng longitudinal of Hydro-
Proceedings of The IRES 22nd International Conference, Toronto, Canada, 1 st January 2016, ISBN: 978-93-85832-86-4 53
