Improvement on the Existing Equations for Predicting Longitudinal Dispersion Coefficient

Abstract

Accurate prediction of longitudinal dispersion coefficient (K) is a key element in studying of pollutant transport in rivers when the full cross sectional mixing has occurred. In this regard, several research studies have been carried out and different equations have been proposed. The predicted values of K obtained by different equations showed a great amount of uncertainty due to the complexity of the phenomenon. Therefore, there is still a need to make an improvement on the existing predictive models. In this study, a multi-objective particle swarm optimization (PSO) technique was used to derive new equations for predicting longitudinal dispersion coefficient in natural rivers. To do this, extensive field data, including hydraulic and geometrical characteristics of different rivers were applied. The results of this study were compared with those of the previous studies using the statistical error measures. The comparison revealed that the proposed model is superior to the previous ones. According to this study, PSO algorithm can be applied to improve the performance of the predictive equations by finding optimum values of the coefficients. The proposed model can be successfully applied to estimate the longitudinal dispersion coefficient for a wide range of rivers' characteristics.

Improvements in the Explicit Estimation of Pollutant Dispersion Coefficient in Rivers by Subset Selection of Maximum Dissimilarity Hybridized With ANFIS-Firefly Algorithm (FFA)

“…Indeed, these tables present the values of the statistical indices used to validate the applicability of published existing equations in estimating K x for extended data from small to large rivers. The best results that are presented in Tables 7 and 8 are for equation Alizadeh et al [41] with R 2 = 0.20, NSE=0.17 in test data and R 2 = 0.16, NSE = −0.02 over all of the data, respectively in dimensional results. In the Non-dimensional values, the best results are derived by the Seo and Cheong [11], equation with R 2 = 0.37 and NSE = −0.32 in the test set and R 2 = 0.24 and NSE = −0.38 over all of the data.…”

“…Data-driven techniques for over a decade have been used to evaluate many hydraulic and hydrologic problems. Regarding the K x estimation, the most frequently data-driven tools are ANN [17], [34], [35], ANFIS [15], [23], [36], genetic programming [37]- [39], SVM [36], [40], particle swarm optimization [41], differential evolution [42], Granular Computing Model [43], Polynomial regression [44] and regression kriging [18]. These studies are some of the recently published researches that have been widely carried out to estimate K x based on a limited number of data and a small range of applicability.…”

Derivation of Optimized Equations for Estimation of Dispersion Coefficient in Natural Streams Using Hybridized ANN With PSO and CSO Algorithms

“…At a distance downward from the source injection, the longitudinal dispersion becomes the essential mechanism and quantified by the longitudinal dispersion coefficient (Kx) [3].Kx is a crucial factor in studying the environmental hydraulics of water quality in rivers [4,5]. In applied aspects of river engineering such as pollutant transport, the dominant process is one-dimensional [6], and the longitudinal dispersion acts as the most crucial parameter in modeling the fate of contaminants chemicals, nutrients, sediments and river water quality [1,7,8,9]. The longitudinal dispersion process as the primary mechanism in applied river quality studies is simulated by the conventional advectiondispersion equation [10]:…”

“…According to the previous studies, the flow depth (H), section width (B), mean flow velocity (U), bed shear velocity (U*), river shape parameter (b), channel sinuosity (s) in river sections and the combinations of them (e.g., the flow discharge, Q) are the most influential parameters for determination of the Kx [17,18,19,20,21]. Based on these hydraulic and hydrodynamic parameters, several researches were carried out to develop a formula for estimation of the Kx based on the following representation For this purpose, several methods including empirical/mathematical based equations [22,23,24,25], statistical and regression-based equations [14,17,26,27] and in recent years different models of soft computing such as adaptive neuro fuzzy inference system (ANFIS), support vector machine (SVM), Gene expression programming (GEP) and ANN [3,6,9,11,12,28,29,30,31] were used to predict and develop a formula that can be used in the estimation of Kx in natural rivers. Most of the recent studies discussed that new flexible structure-based models such as ANN outperformed the older rigid structure but simple models [11,12,13,15].…”

“…In recent years, nature-inspired optimization algorithms are proposed to find the global optimum in optimization problems. For estimation of the Kx, different optimization algorithms,including genetic algorithm (GA) [20,28,44,45,46], PSO [6], Differential Evolution (DE) [30,44], and Genetic Programming (GP) [9,31,48,11] were used. All of these studies come in with major drawbacks.…”