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Structure of multi layer perceptron with feed forward back propagation (Hornik et al. 1989). 

Structure of multi layer perceptron with feed forward back propagation (Hornik et al. 1989). 

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Conference Paper
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Local scouring around hydraulic structures such as bridge piers is the consequence of the erosive process of stream flows on alluvial beds. Since, the local scouring around real scaled bridge piers endangers the safety and stability of bridges, it is essential to evaluate the maximum local scour depth. Wide variety of physical parameters (i.e. flow...

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... is the process of removal of material from a stream bed by the erosive action of flowing water. The process of scour around bridge piers involves complexities of both the three dimensional flow and the sediment transport. When flow occurs past a bridge pier, it undergoes a three-dimensional separation and this separated shear layer rolls up to form a vortex system which is swept downstream by the flow. When viewed from the top, this vortex system has the characteristic shape of a horseshoe and it thus called a horseshoe vortex. (Kothyari et al. 1992). Consequently, significant change in the bed shear stress distribution results in formation of a local scour hole in the vicinity of a bridge pier. The most Common cause of bridge failure is scouring at bridge piers and abutments mainly during flood events. (Cardoso & Bettess 1999). The local scour depth develops in high flows and if is not predicted correctly, the bottom level of local scour hole will exceed the original level of the pier foundation (Esmaeili et al. 2011). For a long time, the local scour at bridge foundations was one of the major concerns for engineers. However, the complexities of three dimensional (3D) separated flows, its interaction with the transport of sediment and the changing mobile boundary, present great difficulties in analyzing the problem theoretically (Ahmed & Rajaratnam 1998). Many studies carried out for developing empirical formulas to estimate the local scour depth around bridge piers however, most of them were obtained based on dimensional analysis and data correlation of simplified laboratory experiments. Usually, these empirical formulas are not accurately adapted to the real prototype environment and just could provide good results for a particular type of experimental data. This is because the conventional analysis of data can not include the correct influence of the set of influential parameters on scour depth (Ettema et al. 1998). Recognizing these issues besides the necessity to have a capability to predict the local scour depth more precisely especially for real scaled bridge piers, it will be helpful to employ new methods for improving the traditional physical-based analysis. As for the prediction of local scour depth, the new methods will be more practical and flexible if they can provide promising results based on the limitations of the field observed data. Recently, artificial intelligence is being used extensively for modeling the complex issues in civil engineering related works as an appropriate alternative method. The advantage of artificial intelligence can be attributed to the flexible mathematical structure that will enable this method to identify the complex and non-linear relationship between the input and the output data. The Artificial Neural Networks (ANNs) is a mathematical tool to represent low-level intelligence in natural organisms and it is a flexible structure, capable of making a non-linear mapping between input and output space (Gorzalczany, 2002). Artificial neural networks have been used extensively in different hydrologic, water resources, hydraulic, ocean and coastal engineering works and presents proper results. In the past few years, the Fuzzy-Inference System (FIS) that is based on the human thinking way in a mathematical framework has been combined with ANNs and leads to the Adaptive Neuro-Fuzzy Inference System (ANFIS). ANFIS also has been used in reservoir operation, modeling the hydrological time series and wave prediction studies and other related fields (Bateni et al. 2007a). The vast majority of works which used ANNs-FFBP and ANFIS for estimating the local scour depth, employed the experimental data and simulations based on field measured data is scarce. While the work based on the field measured data may include much more uncertainties and limitations in comparison to that use the experimental data, application of artificial intelligence based on field measured data would be an important target for practical purposes. This study aimed to evaluate the capability of ANNs-FFBP and ANFIS for predicting the local scour depth around real scaled bridge piers, based on a reliable field measured data. Besides the conventional input parameters for evaluating the local scour depth, the qualitative parameters represents the pier shape, sediment transport and debris effect were used for predicting the local scour depth by the Artificial Intelligence. Artificial Neural Networks (ANNs) is based on the performance of simple units called neurons, cell and nodes. Each neuron in each layer has a connection to all elements in the previous and next layer through links with a weight. If the X=[x 1 , x 2 ,... x n ] and W=[w 1 , w 2 ,... w n ] are input and weight vectors respectively and f(x) is the goal multivariate function, the training procedure would be find the most appropriate weights for the best approximation of f(x). One of the most popular configurations for ANNs is the feed forward back propagation as a sub-set of multi-layer perceptron. The structure of Multi-layer perceptron is shown in Figure 1. It resembles a model, where a set of data (x 1 , x 2 ,... x n ) are fed directly the network through the input layer and then the multi-layer perceptron will present the target value in the output layer. Increasing the number of hidden layer will increase the complexity of the network because of the higher number of connections in the ANNs. Number of optimum hidden layer and the nodes in each layer can be determined by trial and error. There are two main processes in back propagation algorithm (BP) namely forward and backward passes. In the forward pass, an output pattern presents to the network and its effects propagate through the network, layer by layer. In the present study the BP algorithm supported by the generalized delta rule proposed by Rumelhart et al. (1986) was used. Briefly, each node multiplies every input by its interconnection weight, sums the product together and then passes the sum through a transfer function to produce the target results. The common transfer function is an S shaped sigmoid function that is presented as ...

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