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Top1. Introduction
The insertion of artifacts within watercourses has always constituted a point of discontinuity in the morphology of rivers. Local scour is the flow-induced erosion of soil material happens around such discontinuities in the rivers and water channels. This is caused by an accelerated flow around the structures like bridge piers, abutments, dykes, weirs, etc. Proper design of equilibrium scour depth around bridge piers is a prime concern for safety and economic design in hydraulic engineering. Topczewski et al. (2016) presented the principles of scour monitoring near bridge support. Numerous investigations (Karimi et al., 2017; Hoffmans and Verheij, 1997) have been carried out to predict the scour depth around bridge piers. It is a tedious task to determine and formulate mathematical models for equilibrium scour depth under the influence of flow, bed materials and different pier size (Firat and Gungor, 2009). Hung and Yau (2014) developed a nonlinear three-dimensional finite element model to investigate the behavior of scoured piers on floods. Dey and Raikar (2005) developed an empirical model to determine the maximum scour depth using experimental data in clear water and later extended (Dey and Raikar, 2007) their model to live bed scour condition. Briaud et al. (2005) proposed another model to predict the scour in cohesive soils in a contracted channel. However, there is a lack of reliable models for predicting scour depth to cover all possible ranges from the above methods (Lee et al., 2007). Moreover, the aforementioned models are time consuming and costly. Reviewing these difficulties, number of researchers has been involved in exploring refining methods for enhancing the conventional methods.
In recent times, numerous approaches related to soft computing are widely used in solving nonlinear relationships. Artificial neural networks (ANN) have been recently and widely accepted modeling tool in all hydraulic (Cigizoglu and Kisi, 2006; Lee et al., 2007) and hydrologic problems (Jeong and Kim, 2005; Sudheer and Jain, 2004; Jain and Kumar, 2007). As the estimation of scour depth is a very tedious task, many researchers have presented studies on scour depth prediction by using ANN. Some specific applications of neural network to scour depth prediction around bridge piers are mentioned below. In their work of Kambekar and Deo (2003), an alternative solution for pile scour analysis by feedforward back propagation and cascade correlation algorithm is proposed. The proposed model predicts depth of scour more accurately than its width. Efficacy of back-propagation neural network in predicting the scour depth by considering the inputs as flow depth, mean velocity, grain diameter, geometric standard deviation and critical velocity is detailed in Lee et al. (2007). Application of ANN and genetic algorithm (GA) in scour depth predictions within channel contractions are given by Raikar et al. (2016). Azamathulla et al. (2010) reported the performance of ANN and genetic programming (GP) models to predict the scour depth around bridge pier and found the outperformance of GP models. Firat and Gungor (2009) tested the performance of generalized regression neural networks (GRNN) and Feedforward neural networks with that of multiple linear regression models and other empirical formulas. The results indicated the successful application of GRNN in predicting scour depth around circular bridge piers. Application of support vector machine in the prediction of scour is shown in Pal et al. (2011). The comparison studies of ANFIS model and linear regression models in predicting the pier scour depth values provides precise result for ANFIS model. Similarly, many researchers have given pier scour estimation studies by soft computing methods.