Online sequential, outlier robust, and parallel layer perceptron extreme learning machine models for sediment transport in sewer pipes.

Sediment transport is a noteworthy task in the design and operation of sewer pipes. Decreasing sewer pipe hydraulic capacity and transport of pollution are the main consequences of continuous sedimentation. Among different design approaches, the non-deposition with deposited bed (NDB) method can be used for the design of large sewer pipes; however, existing models are established on limited data ranges and mostly applied conventional regression methods. The current study improves the NDB sediment transport modeling by utilizing wide data ranges, and furthermore, applying robust machine learning techniques. In the present study, the conventional extreme learning machine (ELM) technique and its advanced versions, namely the online sequential-extreme learning machine (OS-ELM), outlier robust-extreme learning machine (OR-ELM), and parallel layer perceptron-extreme learning machine (PLP-ELM) are used for the modeling. In the studies conducted in the literature, sediment deposited bed thickness (t s ) or deposited bed width (W b ) was used in the model structure as a deposited sediment variable, and therefore, different parameters in terms of t s and W b can be incorporated into the model structure. However, an uncertainty arises in the selection of the appropriate parameter among W b /Y, t s /Y, W b /D, and t s /D (Y is flow depth and D circular pipe diameter). In order to define the most appropriate parameter to best describe the impact of deposited sediment at the channel bottom in the modeling procedure, four various scenarios using four different parameters that incorporate deposited sediment variables at their structures as W b /Y, t s /Y, W/D, and t s /D are considered for model development. It is found that models that incorporate sediment bed thickness (t s ) provide better results than those which use deposited bed width (W b ) in their structures. Among four different scenarios, models that utilized t s /D dimensionless parameter, give superior results in contrast to their alternatives. Based on the outcomes, the OR-ELM approach outperformed ELM, OS-ELM, and PLP-ELM techniques. The results obtained from applied methods are compared to their corresponding models in the literature, indicating the superiority of the OR-ELM model. It is figured out that the thickness of the deposited bed is an effective variable in modeling NDB sediment transport in sewer pipes.