Receiving More Accurate Predictions for Longitudinal Dispersion Coefficients in Water Pipelines: Training Group Method of Data Handling Using Extreme Learning Machine Conceptions
Receiving More Accurate Predictions for Longitudinal Dispersion Coefficients in Water Pipelines: Training Group Method of Data Handling Using Extreme Learning Machine Conceptions
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DOI：
10.1007/s11269-019-02463-w
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发表时间：
2020-01-16
影响因子：
4.3
通讯作者：
Mehrpooya, Adel
中科院分区：
文献类型：
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作者：
Sabed-Movahed, Farid;Najafzadeh, Mohammad;Mehrpooya, Adel
纵向扩散系数（LDC）被认为是最显着的环境变量，在评估输水管道污染状况方面发挥着关键作用。尽管有各种各样的数值模型来估计纵向扩散系数，但由于输水管道中污染物转变的对流扩散过程的复杂机制，这些数学技术通常可能不太准确。在这项研究工作中，为了获得更准确的LDC预测，通过极限学习机（ELM）概念修改了数据处理组方法（GMDH）的一般结构。事实上，受到ELM的启发，提出了一种新的GMDH方法，称为基于极限学习机的GMDH网络（GMDH-ELM），其中传统GMDH中应用的二次多项式的加权系数不再需要在训练阶段使用反向传播技术或其他进化算法进行更新。事实上，GMDH模型的每个神经元中使用中间参数来建立输入和输出之间的关系。这样，应用与水网管道LDC相关的众所周知且可靠的数据集（233个实验数据）作为输出向量来进行训练和测试阶段。通过数据集，Re数、平均纵向流速、管道摩擦系数和管道直径被视为该方法的输入。 GMDH-ELM 模型的结果表明训练和测试阶段的精度都非常令人满意。此外，通过粒子群优化（PSO）和引力搜索算法（GSA）改进GMDH模型的前馈结构来预测LDC。通过合理的判断，对 GMDH-ELM 和其他开发的 GMDH 模型的性能进行了比较。此外，还应用文献中存在的几个经验方程进行比较。总体而言，GMDH-ELM 的结果相对于其他软计算工具和传统预测模型具有可允许的优越性。
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.