Estimation of Fuzzy Parameters in the Linear Muskingum Model with the Aid of Particle Swarm Optimization

Mike Spiliotis, Alvaro Sordo-Ward and Luis Garrote
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Mike Spiliotis: Department of Civil Engineering, School of Engineering, Democritus University of Thrace, 671 00 Xanthi, Greece
Alvaro Sordo-Ward: Department of Civil Engineering: Hydraulics, Energy and Environment, Universidad Politécnica de Madrid, 28040 Madrid, Spain
Luis Garrote: Department of Civil Engineering: Hydraulics, Energy and Environment, Universidad Politécnica de Madrid, 28040 Madrid, Spain

Sustainability, 2021, vol. 13, issue 13, 1-26

Abstract: The Muskingum method is one of the widely used methods for lumped flood routing in natural rivers. Calibration of its parameters remains an active challenge for the researchers. The task has been mostly addressed by using crisp numbers, but fuzzy seems a reasonable alternative to account for parameter uncertainty. In this work, a fuzzy Muskingum model is proposed where the assessment of the outflow as a fuzzy quantity is based on the crisp linear Muskingum method but with fuzzy parameters as inputs. This calculation can be achieved based on the extension principle of the fuzzy sets and logic. The critical point is the calibration of the proposed fuzzy extension of the Muskingum method. Due to complexity of the model, the particle swarm optimization (PSO) method is used to enable the use of a simulation process for each possible solution that composes the swarm. A weighted sum of several performance criteria is used as the fitness function of the PSO. The function accounts for the inclusive constraints (the property that the data must be included within the produced fuzzy band) and for the magnitude of the fuzzy band, since large uncertainty may render the model non-functional. Four case studies from the references are used to benchmark the proposed method, including smooth, double, and non-smooth data and a complex, real case study that shows the advantages of the approach. The use of fuzzy parameters is closer to the uncertain nature of the problem. The new methodology increases the reliability of the prediction. Furthermore, the produced fuzzy band can include, to a significant degree, the observed data and the output of the existent crisp methodologies even if they include more complex assumptions.

Keywords: flood routing; Muskingum method; extension principle; calibration; fuzzy sets and systems; particle swarm optimization (search for similar items in EconPapers)
JEL-codes: O13 Q Q0 Q2 Q3 Q5 Q56 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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