Original ResearchMultigene genetic programming for sediment transport modeling in sewers for conditions of non-deposition with a bed deposit
Introduction
Sewer system design considering sedimentation problems is an essential issue in urban hydrology and hydraulic engineering practice. Deposition of sediment significantly impacts the hydraulic capacity of the sewer systems. In order to prevent such problems, sewers and drainage systems must be designed to be self-cleansing. A self-cleansing channel has capability to convey sediment particles with the flow and remove deposited sediment from the channel bed. There are variety of self-cleansing design criteria such as; incipient motion (Bong et al., 2013, Bong et al., 2016, Novak and Nalluri, 1984, Safari, 2016, Safari et al., 2017a), incipient deposition (Aksoy et al., 2017, Loveless, 1992, Safari et al., 2014, Safari et al., 2015, Safari et al., 2016) and non-deposition (May et al., 1996, Ota and Nalluri, 2003, Ota and Perrusquia, 2013, Safari et al., 2017b). As reported by Ackers et al. (1996), May et al. (1996), and Butler et al. (1996, 2003) the non-deposition concept is the most reliable method for sewer system design. It has to be emphasized that the non-deposition concept can be divided into two criteria of non-deposition without a bed deposit and non-deposition with a bed deposit. In the former, sediment particles are transported with the flow, while in the later, a small depth of deposited sediment exists at the channel bed. The justification of this method comes from the finding of Ab Ghani (1993), May (1993), and Ota and Nalluri (2003) who confirmed that large sewers require higher self-cleansing velocity, and therefore, sewer design based on non-deposition without considering the sediment deposited on the bed considers an uneconomical (steeper) channel bed slope. It is concluded that large sewers must be designed based on non-deposition with a bed deposit criterion.
Self-cleansing models available in the literature mostly are developed using multiple non-linear regression analysis such as: Alvarez (1990), El-Zaemey (1991), Perrusquia (1992), Ab Ghani (1993), and Nalluri et al. (1997). Regression models have a simple structure and are valuable for defining the effective variables in the sediment transport in sewer systems, however, their computational ability is not as high as artificial intelligence (AI) techniques. Recently, application of AI techniques has attracted the interest of many researchers for variety of water resources engineering problems (Chang et al., 2016, Chang and Tsai, 2016, Nourani et al., 2014a, Yaseen et al., 2015). Although, there are a few studies in the literature applying AI techniques to model sediment transport in drainage systems for non-deposition without a bed deposit and incipient deposition conditions (e.g., Ab Ghani & Azamathulla, 2011; Azamathulla et al., 2012; Ebtehaj & Bonakdari, 2014; Mohammadi et al., 2015; Roushangar & Ghasempour, 2016; Safari et al., 2016), to the best of the authors knowledge no study on application of AI techniques has been done for modeling sediment transport in sewers with bed deposits.
Genetic programming (GP) (Koza, 1992) is an AI technique that evolves computer programs to automatically solve problems using Darwinian natural selection. In hydrological applications, GP and its advancements are commonly used to infer the underlying structure of either natural (Al-Juboori and Guven, 2016, Danandeh Mehr et al., 2013, Ghorbani et al., 2010, Kisi et al., 2012, Meshgi et al., 2015, Nourani et al., 2014b, Olyaie et al., 2017) or experimental processes (Khan et al., 2012, Sattar, 2014, Uyumaz et al., 2014, Zahiri et al., 2014, Zahiri et al., 2015). In such applications, GP generates some possible programs (solutions) to identify the process mathematically. When the task is to build an empirical model of data acquired from a set of experiments, GP is known as symbolic regression (Searson, 2015), which is a self-structuring technique without requiring the user to know or specify the form of the solution in advance. It differs from either conventional regression analysis or other AI techniques, in which modelers must specify the structure of the process of the interest.
This study, for the first time, investigates the ability of one of the most recent advancements of the GP technique, namely multigene GP (MGGP, Searson, 2009), for sediment transport modeling in sewers with bed deposit. To this end, four experimental data sets including wide ranges of sediment size and concentration, deposit thickness, and pipe size are used. The new models are compared with conventional regression models available in the literature to evaluate how the MGGP technique is beneficial to formulate sediment transport over bed deposit in sewers.
Section snippets
Sediment transport over a bed deposit in sewers
Self-cleansing design for non-deposition with a bed deposit is recommended for designing large sewers. The primarily studies of sediment transport over a bed deposit were done by Ambrose (1953) and Craven (1953) who found that the bed deposit thickness affects the sediment transport capacity of the pipe channels. After decades, May (1982) and May et al. (1989) started again to investigate the effects of a sediment deposit on sediment transport in sewers. Similar to May et al. (1989), in a
Experimental data
Experimental data for non-deposition conditions with a bed deposit collected by El-Zaemey (1991), Perrusquia, 1992, Perrusquia, 1993, May (1993), and Ab Ghani (1993) are used in this study. All the experiments were done in circular channels with a variety of sizes. El-Zaemey (1991) and Perrusquia, 1992, Perrusquia, 1993 did experiments in pipes having 305 and 225 mm diameters, respectively, while May (1993) and Ab Ghani (1993) did experiments in a larger pipe having a 450 mm diameter. The
Data preparation
The characteristics of flow, fluid, sediment, and channel must be considered for determination of the sediment transport process in sewers. In this study, flow velocity (V), hydraulic radius (R), and gravitational acceleration (g) are the flow characteristics; fluid kinematic viscosity (ν) and density (ρ) are the fluid characteristics; sediment density (ρs), median sediment size (d), and volumetric sediment concentration (Cv) are the sediment characteristics; and channel friction factor (λ) is
Results and discussion
In order to develop the MGGP-based model for sediment transport in sewers for non-deposition with a bed deposit condition, an open-source software platform for symbolic regression in MATLAB®, namely GPTIPS2 (Searson, 2015) is used in the current study. Using the experimental data listed in Table 1 and MGGP setting attributes mentioned earlier, GPTIPS2 was executed. Fig. 2 illustrates the summary of runs that were configured to minimize the error metric (RMSE) over the training data. The upper
Conclusions
The estimation accuracy of an experimental model depends on the data features (type, range) and the regression technique used for model development. Moreover, the complexity of a model is another important criterion since, in general, engineers prefer not only accurate but also simple, i.e. parsimonious, models for practical applications. With respect to these issues, this study proposed a new model, namely Pareto-optimal MGGP, to calculate Frp in non-deposition with a bed deposit condition in
Acknowledgments
The first author would like to thank to International Affairs of Iran's National Elites Foundation of Iran (BMN) for financial support of this study under the contract no. 102/2716, which was done during his stay as Post-doctoral Research Fellow at Urmia University and University of Tabriz, Iran. Very special gratitude goes to Prof. Maghsud Solimanpur, Vice Chancellor for Research and Technology of Urmia University and Dr. Behnam Mohammadi-Ivatloo from Technology Affairs Management (TAM) of
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