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Estimation of open channels hydraulic parameters with the stochastic particle collision algorithm

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Abstract

In the present work, the 1D flow and transport equations for open channels are numerically solved and coupled to a recently developed global search optimization, the particle collision algorithm (PCA), to estimate two essential parameters present in flow and transport equations, respectively, the bed roughness and the dispersion coefficient. The PCA is inspired in the scattering and absorption phenomena of a given incident nuclear particle by a target nucleus. In this method, if the particle in a given location of the design space reaches a low value of the objective function, it is absorbed, otherwise, it is scattered. This allows the search space to be widely explored, in such a way that the most promising regions are searched through successive scattering and absorption events. Based on real data measured in the Albear channel, Cuba, the bed roughness and longitudinal dispersion coefficient were successfully estimated from two numerical experiments dealing, respectively, with flow and transport equations. The results obtained were supported by the high correlations achieved between simulations and observations, demonstrating the feasibility of the approach here considered.

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Abbreviations

A :

Cross-sectional area (m2)

C :

Substance concentration (kg m−3)

D :

Longitudinal dispersion coefficient (m2 s−1)

D q :

Bulk discharge, seepage, or lateral input (m2 s−1)

g :

Acceleration due to gravity (m s−2)

h :

Local flow depth (m)

k e :

Longitudinal coefficient of expansion or contraction

n :

Roughness coefficient (m1/6)

N T :

Number iterations (–)

q :

Input or lateral discharge (m2 s−1)

q est :

Estimated seepage loss (m3 s−1)

Q :

Flow discharge (m3 S−1)

R :

Hydraulic radius (m)

S 0 :

Longitudinal bed slope (–)

\( \bar{t} \) :

Mean traveling time (s)

T :

Top width (m)

U :

Mean velocity (m s−1)

X Θ :

Sensitivity coefficient (–)

v x :

Velocity component (m s−1)

\( \sigma_{t}^{2} \) :

Concentration variance (kg2 M−6)

τ:

Integration variable (s)

Θ:

Vector of parameters (–)

Ψobs :

Measured values (–)

Ψsim :

Computed values(–)

ψ :

Variable (–)

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Acknowledgments

The authors acknowledge the financial support provided by the Brazilian agency CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior), through the international cooperation program between Brazil and MES (Ministry of Higher Education, Cuba). They are also grateful for the information provided by Aguas de La Habana. Finally, the authors acknowledge Prof. Wagner Sacco for kindly providing all the details related to the implementation of the PCA. AJSN acknowledges also the financial support provided by FAPERJ, Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro, and CNPq, Conselho Nacional de Desenvolvimento Científico e Tecnológico.

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Authors and Affiliations

  1. Instituto Superior Politécnico “José Antonio Echeverría”, Cujae, Calle 114 No 11901 e/. Rotonda y Ciclovía, Marianao, La Habana, Cuba

    Yoel Martínez González & José Bienvenido Martínez Rodríguez

  2. Instituto Politécnico da Universidade do Estado do Rio de Janeiro, Rua Alberto Rangel, s/n, Vila Nova, CEP: 28630-050, Nova Friburgo, Rio de Janeiro, Brazil

    Antônio José da Silva Neto

  3. Department of Computational Modelling, Instituto Politécnico da Universidade do Estado do Rio de Janeiro, Estrada Lumiar-São Pedro, Km 4, São Pedro da Serra, CEP: 28616-970, Nova Friburgo, Rio de Janeiro, Brazil

    Pedro Paulo Gomes Watts Rodrigues

Authors
  1. Yoel Martínez González
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  2. José Bienvenido Martínez Rodríguez
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  3. Antônio José da Silva Neto
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  4. Pedro Paulo Gomes Watts Rodrigues
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Correspondence to Yoel Martínez González.

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Technical Editor: Francisco Cunha.

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Martínez González, Y., Martínez Rodríguez, J.B., da Silva Neto, A.J. et al. Estimation of open channels hydraulic parameters with the stochastic particle collision algorithm. J Braz. Soc. Mech. Sci. Eng. 36, 69–77 (2014). https://doi.org/10.1007/s40430-013-0069-z

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  • DOI: https://doi.org/10.1007/s40430-013-0069-z

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