عنوان مقاله [English]
In this study, the discharge coefficient of rectangular and circular side orifices was estimated using the extreme learning machine method. Furthermore, in this study for evaluating the ability of different ELM models the Monte Carlo simulations are used. The Monte Carlo simulation is a comprehensive classification of computational algorithms which uses the random sampling procedure for calculating numerical results. The main idea of this method is based on solving problems which might be actual in nature using random decision-making processes. The Monte Carlo methods are usually used for simulating physical and mathematical systems not solvable with other methods. The Monte Carlo simulation is generally used by probability distribution to solve various problems such as numerical optimization and numerical integration. The k-fold cross validation method is also used for examining the performance of the above models. In this method, the main sample is randomly divided into k sub-samples with the same size. Among k sub-samples, a sub-sample is used as the validation data and the remaining as the test data of the model. Then, the validation process repeats k times (equal to the number of layers) and each of k sub-samples is used exactly once as validation data. In this study, the experimental values obtained by Hussein et al. (2010) and Hussein et al. (2011) are used for validating the results of the numerical models. Their experimental model consisted of a rectangular channel with the length, the width and the height of 9.15m, 0.5m and 0.6m, respectively. They installed the circular and rectangular orifices at a distance of 5m from the inlet of the main channel on the side wall. In the next stage, the most
optimized number of hidden neurons was chosen equal to 30 and the results of
all activation functions of the extreme learning machine were examined and the
sigmoid activation function is selected for simulating the discharge coefficient. Subsequently, two modeling combinations were introduced using the input parameters as well as five different extreme learning machine models were
developed. The analysis of the modeling results showed that the model with the
shape coefficient has more accuracy. The superior model is a function of all
input parameters and reasonably estimates values of the discharge coefficient.
For example, the values of R and MAPE for this model are estimated 0.990 and
0.223, respectively. The results of the superior model were also compared with
the empirical equations and it was shown that this model has more accuracy.
Also, the partial derivative sensitivity analysis (PDSA) was run for all input