The Muskingum model is a hydrologic flood routing method in which the accuracy of the parameter estimation affects the routed hydrograph, especially in both the value and time of the flood peak. Meta-heuristic algorithms are good candidates to determine optimal/near-optimal parameters in the Muskingum model. In this paper, two metaheuristic algorithms -the simulated annealing (SA) algorithm and the shuffled frog leaping algorithm (SFLA) -are applied and compared in two benchmark and real case studies, considering the sum of the squared deviation (SSQ) between observed and routed outflows and the sum of the absolute value of deviation (SAD) between observed and routed outflow as the objective functions, and deviation of value and occurrence time of the routed flood peak (DPO and DPOT) as the important parameters on the routed flood hydrograph. Results show that the SFLA improves (decreases) the SSQ and SAD by 0 . 03% and 0 . 39% in the benchmark problem, and by 3 . 59% and 2 . 03% in the real case study, respectively, compared to reported results using various optimisation algorithms. In addition, the SFLA improves (decreases) the DPO of the routed hydrograph in the benchmark problem by 56 . 67% compared to the best (minimum) result using the Tung method.
Two new mathematical forms of the nonlinear Muskingum model called NL4 and NL5, involving four and five parameters, respectively, can be used in river flood routing. The accuracy of the estimation of the Muskingum model parameters is essential for flood routing. This paper proposes a novel hybrid algorithm, based on the shuffled frog leaping algorithm (SFLA) and Nelder-Mead simplex (NMS), for the estimation of parameters of two new nonlinear Muskingum models. The proposed methodology is applied by considering minimization of the sum of the square deviation (SSD) between observed and routed outflows in (1) experimental, (2) real, and (3) multimodal examples. Results show that the SSD is 0.91, 3.97, and 4.44% smaller (better) than pertinent values obtained by the genetic algorithmgeneralized reduced gradient (GA-GRG) method in experimental, real, and multimodal examples, respectively.
Water has a considerable role in all aspects of human life. Thus, evaluation of water characteristics in general and water quality in particular are necessary to enhance the health of humans and ecosystems. Data-driven models are computing methods that are capable of extracting different system states without using complex relationships. Prediction and simulation are two branches of data-driven modeling that use previous and previous-current data sets to fill gaps in time series. This paper investigates the capability of an adaptive neural fuzzy inference system (ANFIS) and genetic programming (GP) as two data-driven models to predict and simulate water quality parameters (e.g., sodium, potassium, magnesium, sulfates, chloride, pH, electrical conductivity, and total dissolved solids) at the Astane station in Sefidrood River, Iran. The writers considered six combinations of data sets, including the previously noted water quality parameters and river discharge in the previous and previous-current months, as input data. Implementation of the ANFIS and GP models in this paper illustrates the flexibility of GP in time series modeling relative to ANFIS, especially in the testing data set. Accordingly, the writers calculated the coefficient of variation of root mean squared error as the error criterion in different ANFIS and GP models (for assigning achievement probability to an appropriate solution) for each quality parameter. The average of the previously noted values for the six combinations of data sets improved (decreased) 80.51 and 80.89%, respectively, in the training and testing data sets with GP relative to ANFIS. These results indicate that the writers' proposed modeling, based on GP, is an effective tool for determining water quality parameters.
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