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.
Azam Akhbari; Amir Hossein Zaji; Hamed Azimi; Mohsen Vafaeifard
Abstract
Weirs are installed on open channels to adjust and measure the flow. Also, discharge coefficient is considered as the most important hydraulic parameter of a weir. In this study, using the Radial Base Neural Networks (RBNN) and M5' methods, the discharge coefficient of triangular plan form weirs is modeled. ...
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Weirs are installed on open channels to adjust and measure the flow. Also, discharge coefficient is considered as the most important hydraulic parameter of a weir. In this study, using the Radial Base Neural Networks (RBNN) and M5' methods, the discharge coefficient of triangular plan form weirs is modeled. At first, the effective parameters in the prediction of the discharge coefficient are identified. Then, by combining the input parameters, for each of the RBNN and M5' methods, six different models are introduced. By analyzing the modeling results for all models, it was shown that the M5' model is capable of modeling the discharge coefficient more accurately. Also, based on the modeling results, a model that considered the impact of all input parameters was introduced as a superior model. The mean absolute percentage error (MAPE) and correlation coefficients (R2) values for the preferred model in the test mode were calculated 2.774 and 0.831, respectively. Also, for each of the M5' models, some relationships were proposed to estimate the triangular plan form weirs. The evaluation of these relationships showed that the parameters of the ratio of head over the weir to channel width (h/B) and Froude number (Fr) were the most effective parameters in the prediction of the discharge coefficient.
