Optimum Design of Straight Circular Channels Incorporating Constant and Variable Roughness Scenarios: Assessment of Machine Learning Models

Majid Niazkar,Samuel Yousefi

doi:10.1155/2021/9984934

Abstract

In this study, two machine learning (ML) models named as artificial neural network (ANN) and genetic programming (GP) were applied to design optimum canals with circular shapes. In this application, the earthwork and lining costs were considered as the objective function, while Manning’s equation was utilized as the hydraulic constraint. In this design problem, two different scenarios were considered for Manning’s coefficient: (1) constant Manning’s coefficient and (2) the experimentally proved variation of Manning’s coefficient with water depth. The defined design problem was solved for a wide range of different dimensionless variables involved to produce a large enough database. The first part of these data was used to train the ML models, while the second part was utilized to compare the performances of ANN and GP in optimum design of circular channels with those of explicit design relations available in the literature. The comparison obviously indicated that the ML models improved the accuracy of the circular channel design from 55% to 91% based on two performance evaluation criteria. Finally, application of the ML models to optimum design of circular channels demonstrates a considerable improvement over the explicit design equations available in the literature.

Highlights

Among various studies on optimum channel design, design of circular channels, as one of conventional sections, was considered among the earliest attempts
artificial neural network (ANN) and genetic programming (GP) have quite similar performances in calculating r∗ for the variable roughness scenario. e performances of the machine learning (ML) models are compared with those of explicit equations in Figure 4(d) for estimating y∗ for the test data. e results indicate that both ML models achieved much closer values to the optimum solutions, while GP obtained slightly better results than ANN for calculating optimum y∗ for variable n
root mean square error (RMSE) and mean absolute relative error (MARE) by the ML models in estimating y∗ in comparison with the explicit equations. erefore, Figure 4 clearly demonstrates that the ML models reached much closer results to the optimum solutions in design of a lined circular channel for flow-dependent n

Summary

Introduction

Among various studies on optimum channel design, design of circular channels, as one of conventional sections, was considered among the earliest attempts. Swamee et al [9] presented explicit relations for the optimum design of canals with circular shapes by minimizing earthwork cost of channel construction. Aksoy and Altan-Sakarya [3] proposed two models for calculating the optimal section variables of circular channels by minimizing earthwork and lining costs, while Manning’s equation was the hydraulic constraint. The optimum design of lined canals with circular shapes is tackled by applying two ML methods (artificial neural network (ANN) and genetic programming (GP)) for estimating channel properties in for two scenarios: (1) constant and (2) variable Manning’s coefficients. E performances of these ML models were compared with those of the explicit design equations present in the literature In this regard, the problem statement of the circular channel design is introduced . Afterwards, the results of applying ML to the channel design with circular shapes are presented and discussed for constant and variable roughness scenarios

Objectives

Methods

Results

Conclusion