Prediction of hydraulic resistance coefficient using an ensemble neural network algorithm

Abstract

This study presents the development and testing of a computational algorithm based on ensemble learning of artificial neural networks for predicting the empirical hydraulic resistance coefficient known as the Chézy roughness coefficient in open channels. The input data for the model include hydrological and hydro-morphological characteristics of the channel: average flow width and depth, hydraulic radius, discharge or flow velocity, water surface slope, bed roughness, and other parameters influencing flow resistance. The target variable is the Chézy coefficient, which must be determined with high accuracy. Ensemble learning methods are based on the principle of combining the predictions of several individual models to obtain a more reliable and accurate result.
This study introduces an ensemble approach using artificial neural networks for estimating the Chézy roughness coefficient. It expands upon previous research focused on empirical estimation of the Chézy coefficient through neural networks, which involved the review of existing computational methods, refinement of input parameters, and the design of a base model with enhanced architectural complexity. The ensemble was implemented, trained, and evaluated using Python programming tools.
A general ensemble model consisting of three homogeneous fully connected neural networks is proposed. An algorithm for distributing data among ensemble models is proposed. Training subsets for each neural network in the ensemble are formed using the Bagging method (Bootstrap Aggregating). A training algorithm for the ensemble is developed, where each neural network is trained in parallel on its bootstrap sample using the backpropagation method. A forecasting algorithm using the trained ensemble is also proposed. Prediction of the empirical Chezy coefficient for new, unseen data is performed by aggregating forecasts from all neural networks, incorporating an inverse problem approach. The implementation of training and prediction algorithms is presented in Python.
For testing the proposed computational algorithm, field hydrological and hydro-morphological data from specific sections of the mountain rivers Tysa, Teresva, Latorytsia, Opir, Rika, and Chornyi Cheremosh were used. The testing procedure involved comparing observed and predicted flow discharges. Performance metrics such as absolute error and Nash–Sutcliffe efficiency coefficient were used to assess model effectiveness. The proposed ensemble model demonstrated higher accuracy and greater prediction stability compared to individual neural networks, confirming a typical advantage of the Bagging method.