Abstract
The study of water surface profiles is beneficial to various applications in water resources management. In this study, two artificial intelligence (AI) models named the artificial neural network (ANN) and genetic programming (GP) were employed to estimate the length of six steady GVF profiles for the first time. The AI models were trained using a database consisting of 5154 dimensionless cases. A comparison was carried out to assess the performances of the AI techniques for estimating lengths of 330 GVF profiles in both mild and steep slopes in trapezoidal channels. The corresponding GVF lengths were also calculated by 1-step, 3-step, and 5-step direct step methods for comparison purposes. Based on six metrics used for the comparative analysis, GP and the ANN improve five out of six metrics computed by the 1-step direct step method for both mild and steep slopes. Moreover, GP enhanced GVF lengths estimated by the 3-step direct step method based on three out of six accuracy indices when the channel slope is higher and lower than the critical slope. Additionally, the performances of the AI techniques were also investigated depending on comparing the water depth of each case and the corresponding normal and critical grade lines. Furthermore, the results show that the more the number of subreaches considered in the direct method, the better the results will be achieved with the compensation of much more computational efforts. The achieved improvements can be used in further studies to improve modeling water surface profiles in channel networks and hydraulic structure designs.
Highlights
Varied flow (GVF) is a nonuniform flow in natural and man-made canals. e study of Gradually varied flow (GVF) is crucial to water resources management as it may be categorized as one of the most common flow conditions in an open channel and play a key role in various hydraulic projects
Results and Discussion e artificial neural network (ANN), genetic programming (GP), varied flow function, and 1-step direct method compute the length of GVF profile between y1 and y2 by considering one channel reach
3-step and 5step direct methods divided the channel reach into 3 and 5 subreaches, respectively. ese methods were used for estimation of GVF profile length between two specified water depths
Summary
Varied flow (GVF) is a nonuniform flow in natural and man-made canals. e study of GVF is crucial to water resources management as it may be categorized as one of the most common flow conditions in an open channel and play a key role in various hydraulic projects. Some examples of the occurrence of GVF include flow through a change in channel bottom slope, canal constrictions and transitions, a variation of channel geometries, flow under the infection of hydraulic structures, and flow from a large reservoir to a canal. In such situations, flow variables, i.e., water depth and flow velocity, vary gradually in each crosssection along a channel. E former presents the spatial variation of water depth in GVF profiles, while the latter relates friction slope (Sf) with flow and channel geometries of the canal under consideration: dy dx S011 − − yycn//yyMN , (1). Water depths at two cross-sections of the same profile are given while the distance between these
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