Receiving More Accurate Predictions for Longitudinal Dispersion Coefficients in Water Pipelines: Training Group Method of Data Handling Using Extreme Learning Machine Conceptions

Abstract

Longitudinal dispersion coefficient (LDC) is known as the most remarkable environmental variables which plays a key role in evaluation of pollution profiles in water pipelines. Even though, there is a wide range of numerical models to estimate coefficient of longitudinal dispersion, these mathematical techniques may often come in quite few inaccuracies due to complex mechanism of convection-diffusion processes in pollutant transition in water pipelines. In this research work, to obtain more accurate prediction of LDC, general structure of group method of data handling (GMDH) is modified by means of extreme learning machine (ELM) conceptions. In fact, with getting inspiration from ELM, a novel GMDH method, called GMDH network based on using extreme learning machine (GMDH-ELM), is proposed in which weighting coefficients of quadratic polynomials applied in conventional GMDH are no longer required to be updated either using back propagation technique or other evolutionary algorithms through training stage. In fact, an intermediate parameter is employed to establish a relationship between the input and output in each neuron of the GMDH model. In this way, a well-known and reliable dataset (233 experimental data) related to LDC in water network pipelines, as output vector, is applied to conduct training and testing phases. Through datasets, the Re number, the average longitudinal flow velocity, the friction factor of pipeline and the diameter of pipe are considered as inputs of the proposed approach. The results of GMDH-ELM model indicate a highly satisfying level of precision in both training and testing phases. Furthermore, feed forward structure of GMDH model was improved by particle swarm optimization (PSO) and gravitational search algorithm (GSA) to predict LDC. Through a sound judgment, a comparison is drawn between the performance of GMDH-ELM and other developed GMDH models. Moreover, several empirical equations existing in literature have been applied for comparisons. Overall, results of GMDH-ELM have permissible superiority over the other soft computing tools and conventional predictive models.