Ali Azizpor; Ahmad Rajabi; Fariborz Yosefvand; Saeid Shabanlou
Abstract
In the current study, a new hybrid of the genetic algorithm (GA) and adaptive Neuro-fuzzy inference system (ANFIS) was introduced to model the discharge coefficient (DC) of triangular weirs. The genetic algorithm was implemented for increasing the efficiency of ANFIS by adjusting membership functions ...
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In the current study, a new hybrid of the genetic algorithm (GA) and adaptive Neuro-fuzzy inference system (ANFIS) was introduced to model the discharge coefficient (DC) of triangular weirs. The genetic algorithm was implemented for increasing the efficiency of ANFIS by adjusting membership functions as well as minimizing error values. To evaluate the proficiency of the proposed hybrid method, the Monte Carlo simulations (MCS) and the k-fold validation method (k=5) was applied. The results of developed hybrid model indicate that the weir vortex angle, flow Froude number, the ratio of the weir length to its height, the ratio of the channel width to the weir length and ratio of the flow head to the weir height are the most effective parameters in the DC estimation. The quantitative examination of the proposed hybrid method indicates that the Root Mean Square Error (RMSE) and Mean Absolute Percent Error (MAPE) are as 0.016 and 1.647 (respectively) for the superior model. Besides, the Froude number is found as the most effective variable in DC modeling through the quantitative analysis. A comparison of the developed hybrid ANFIS-GA with the individual ANFIS model in the DC estimation indicates the hybrid model outperformed than the individual one.
Ehsan Yarmohammadi; Fariborz Yosefvand; Ahmad Rajabi; Saeid Shabanlou
Abstract
In this paper, for the first time, the discharge coefficient of triangular plan form weirs is simulated by the extreme learning machine (ELM). ELM is one of the powerful and rapid artificial intelligence methods in modeling complex and non-linear phenomena. Compared to other learning algorithms such ...
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In this paper, for the first time, the discharge coefficient of triangular plan form weirs is simulated by the extreme learning machine (ELM). ELM is one of the powerful and rapid artificial intelligence methods in modeling complex and non-linear phenomena. Compared to other learning algorithms such as back propagation, this model acts rapidly in the learning process and provides a desirable performance in processing generalized functions. In this study, the Monte Carlo simulation is used for examining capabilities of numerical models. Also, the k-fold cross validation method with k=5 is utilized for evaluating abilities of the ELM models. Then, six ELM models are introduced by means of the parameters affecting the discharge coefficient of triangular plan form weirs. After that, the superior model is identified by analyzing the results of the mentioned models. The superior model predicts discharge coefficient values with reasonable accuracy. This model simulates the discharge coefficient as a function of the flow Froude number, vertex angle of the triangular plan form weir, the ratio of weir length to its height, the ratio of flow head to weir height and the ratio of channel width to weir length. For the best model, the Mean Absolute Error, Root Mean Square Error and determination coefficient are computed 1.173, 0.012 and 0.967, respectively. Furthermore, examination of the influence of the input parameters indicates that the flow Froude number is the most influenced factor in modeling the discharge coefficient. Also, the error distribution showed that roughly 86 % of the superior model results had an error less than 2 %. Furthermore, a practical equation was provided to compute the discharge coefficient.
