School of Environment, College of Engineering, University of Tehran, Iran.
School of Electrical & Computer Engineering, College of Engineering, University of Tehran, Iran.
J Contam Hydrol. 2021 Jun;240:103798. doi: 10.1016/j.jconhyd.2021.103798. Epub 2021 Mar 19.
Given the interest in accurately predicting the Longitudinal Dispersion Coefficient (D) within the fields of hydraulic and water quality modeling, a wide range of methods have been used to estimate this parameter. In order to improve the accuracy of D predictions, this paper proposes the use of a Deep Convolutional Network (DCN), a sub-field of machine learning. The proposed deep neural network architecture consists of two parts; first, a one-dimensional convolutional neural network (CNN) to build informative feature maps, and second, a stack of deep, fully connected layers to estimate pollution dispersion (as D) in streams. To accurately predict D the developed model draws upon a large and diverse array of datasets in the form of three dimensionless parameters: Width/Depth (W/H), Velocity/Shear Velocity (U/u*), and Longitudinal Dispersion Coefficient/(Depth * Shear Velocity) (D /Hu*). The model's accuracy is compared to that of several empirical models using a number of statistical measures. In addition, the DCN model results are compared with artificial neural network (ANN) and support vector machine (SVM) models implemented in this research and also similar studies applying various machine learning models (ML) towards D prediction. The statistical evaluation indicates that the DCN model outperforms the tested empirical, ANN, SVM and ML models with a significant difference. Additionally, five-fold cross-validation is performed to analyze the sensitivity and dependency of the DCN model's results on dataset selection, which shows that the dataset selection process does not significantly affect the model's accuracy. Since both ML and empirical models are, in general, poor predictors of the upper and lower ranges of D values, the DCN model's predictions of D in six different extreme-value ranges are assessed. The DCN model shows excellent accuracy in estimating D over the full possible range of data. In comparison with the empirical and ML models mentioned above, the DCN model more accurately predicts D values from river geometry and hydraulic datasets, with low errors across all ranges of D. The most significant advantage of DCN is that it tries to learn high-level features from data in an incremental manner.
鉴于人们对准确预测水力和水质模型领域内纵向弥散系数（D）的浓厚兴趣，已经使用了多种方法来估计该参数。为了提高 D 预测的准确性，本文提出使用深度学习卷积网络（DCN），这是机器学习的一个子领域。所提出的深度神经网络架构由两部分组成；首先，一维卷积神经网络（CNN）用于构建信息丰富的特征图，其次，堆叠深层全连接层用于估计河流中的污染弥散（即 D）。为了准确预测 D，所开发的模型利用了大量形式多样的数据集，这些数据集的三个无量纲参数为：宽度/深度（W/H）、速度/剪切速度（U/u*）和纵向弥散系数/（深度剪切速度）（D /Hu）。通过使用多个统计指标，将模型的准确性与几个经验模型进行了比较。此外，还将 DCN 模型的结果与本研究中实现的人工神经网络（ANN）和支持向量机（SVM）模型以及应用各种机器学习模型（ML）进行 D 预测的类似研究进行了比较。统计评估表明，DCN 模型优于经过测试的经验、ANN、SVM 和 ML 模型，且差异显著。此外，还进行了五折交叉验证，以分析 DCN 模型结果对数据集选择的敏感性和依赖性，结果表明数据集选择过程不会显著影响模型的准确性。由于一般来说，ML 和经验模型都不能很好地预测 D 值的上下限，因此评估了 DCN 模型在六个不同极值范围内对 D 的预测。DCN 模型在整个数据可能范围内对 D 的估计具有出色的准确性。与上述经验和 ML 模型相比，DCN 模型更准确地预测了河流几何和水力数据集的 D 值，在所有 D 值范围内误差都较低。DCN 的最大优势在于它试图以增量方式从数据中学习高级特征。
