TY - GEN
T1 - A nested genetic algorithm for the numerical solution of non-linear coupled equations in water quality modeling
AU - García, Hermes A.
AU - Guerrero-Bolaño, Francisco J.
AU - Obregón-Neira, Nelson
PY - 2010
Y1 - 2010
N2 - Due to both mathematical tractability and efficiency on computational resources, it is very common to find in the realm of numerical modeling in hydro-engineering that regular linearization techniques have been applied to nonlinear partial differential equations properly obtained in environmental flow studies. Sometimes this simplification is also made along with omission of nonlinear terms involved in such equations which in turn diminishes the performance of any implemented approach. This is the case for example, for contaminant transport modeling in streams. Nowadays, a traditional and one of the most common used water quality model such as QUAL2k, preserves its original algorithm, which omits nonlinear terms through linearization techniques, in spite of the continuous algorithmic development and computer power enhancement. For that reason, the main objective of this research was to generate a flexible tool for non-linear water quality modeling. The solution implemented here was based on two genetic algorithms, used in a nested way in order to find two different types of solutions sets: the first set is composed by the concentrations of the physical-chemical variables used in the modeling approach (16 variables), which satisfies the non-linear equation system. The second set, is the typical solution of the inverse problem, the parameters and constants values for the model when it is applied to a particular stream. From a total of sixteen (16) variables, thirteen (13) was modeled by using non-linear coupled equation systems and three (3) was modeled in an independent way. The model used here had a requirement of fifty (50) parameters. The nested genetic algorithm used for the numerical solution of a non-linear equation system proved to serve as a flexible tool to handle with the intrinsic non-linearity that emerges from the interactions occurring between multiple variables involved in water quality studies. However because there is a strong data limitation in local assessment studies, further work is necessary to develop a strong validation scheme for this modeling approach.
AB - Due to both mathematical tractability and efficiency on computational resources, it is very common to find in the realm of numerical modeling in hydro-engineering that regular linearization techniques have been applied to nonlinear partial differential equations properly obtained in environmental flow studies. Sometimes this simplification is also made along with omission of nonlinear terms involved in such equations which in turn diminishes the performance of any implemented approach. This is the case for example, for contaminant transport modeling in streams. Nowadays, a traditional and one of the most common used water quality model such as QUAL2k, preserves its original algorithm, which omits nonlinear terms through linearization techniques, in spite of the continuous algorithmic development and computer power enhancement. For that reason, the main objective of this research was to generate a flexible tool for non-linear water quality modeling. The solution implemented here was based on two genetic algorithms, used in a nested way in order to find two different types of solutions sets: the first set is composed by the concentrations of the physical-chemical variables used in the modeling approach (16 variables), which satisfies the non-linear equation system. The second set, is the typical solution of the inverse problem, the parameters and constants values for the model when it is applied to a particular stream. From a total of sixteen (16) variables, thirteen (13) was modeled by using non-linear coupled equation systems and three (3) was modeled in an independent way. The model used here had a requirement of fifty (50) parameters. The nested genetic algorithm used for the numerical solution of a non-linear equation system proved to serve as a flexible tool to handle with the intrinsic non-linearity that emerges from the interactions occurring between multiple variables involved in water quality studies. However because there is a strong data limitation in local assessment studies, further work is necessary to develop a strong validation scheme for this modeling approach.
KW - Genetic algorithms
KW - non-linear systems
KW - water quality
UR - https://www.scopus.com/pages/publications/77955759476
U2 - 10.1063/1.3452081
DO - 10.1063/1.3452081
M3 - Conference contribution
AN - SCOPUS:77955759476
SN - 9780735407787
T3 - AIP Conference Proceedings
SP - 1243
EP - 1248
BT - ISCM II and EPMESC XII - Proc. of the 2nd Int. Symposium on Computational Mechanics and the 12th Int. Conf. on the Enhancement and Promotion of Computational Methods in Engineering and Science
T2 - 2nd International Symposium on Computational Mechanics, ISCM II, and the 12th International Conference on the Enhancement and Promotion of Computational Methods in Engineering and Science, EPMESC XII
Y2 - 30 November 2009 through 3 December 2009
ER -