Bayesian neural networks for prediction of equilibrium and time-dependent scour depth around bridge piers

The physical process of scour around bridge piers is complicated. Despite various models presented to predict the equilibrium scour depth and its time variation from the characteristics of the current and sediment, scope exists to improve the existing models or to provide alternatives to them. In this paper, a neural network technique within a Bayesian framework, is presented for the prediction of equilibrium scour depth around a bridge pier and the time variation of scour depth. The equilibrium scour depth was modeled as a function of five variables; flow depth and mean velocity, critical flow velocity, median grain diameter and pier diameter. The time variation of scour depth was also modeled in terms of equilibrium scour depth, equilibrium scour time, scour time, mean flow velocity and critical flow velocity. The Bayesian network predicted equilibrium and time-dependent scour depth much better when it was trained with the original (dimensional) scour data, rather than using a non-dimensional form of the data. The selection of water, sediment and time variables used in the models was based on conventional scour depth data analysis. The new models estimate equilibrium and time-dependent scour depth more accurately than the existing expressions. A committee model, developed by averaging the predictions of a number of individual neural network models, increased the reliability and accuracy of the predictions. A sensitivity analysis showed that pier diameter has a greater influence on equilibrium scour depth than the other independent parameters.     

Generalized Regression Neural Networks and Feed Forward Neural Networks for prediction of scour depth around bridge piers

In this study, Generalized Regression Neural Networks (GRNN) and Feed Forward Neural Networks (FFNN) approaches are used to predict the scour depth around circular bridge piers. Hundred and sixty five data collected from various experimental studies, are used to predict equilibrium scour depth. The model consisting of the combination of dimensional data involving the input variables is constructed. The performance of the models in training and testing sets are compared with observations. Then, the model is also tested by Multiple Linear Regression (MLR) and empirical formula. The results of all approaches are compared in order to get more reliable comparison. The results indicated that GRNN can be applied successfully for prediction of scour depth around circular bridge piers.     

Neural network and neuro-fuzzy assessments for scour depth around bridge piers

The mechanism of flow around a pier structure is so complicated that it is difficult to establish a general empirical model to provide accurate estimation for scour. Interestingly, each of the proposed empirical formula yields good results for a particular data set. Hence, in this study, alternative approaches, artificial neural networks (ANNs) and adaptive neuro-fuzzy inference system (ANFIS), are proposed to estimate the equilibrium and time-dependent scour depth with numerous reliable data base. Two ANN models, multi-layer perception using back-propagation algorithm (MLP/BP) and radial basis using orthogonal least-squares algorithm (RBF/OLS), were used. The equilibrium scour depth was modeled as a function of five variables; flow depth, mean velocity, critical flow velocity, mean grain diameter and pier diameter. The time variation of scour depth was also modeled in terms of equilibrium scour depth, equilibrium scour time, scour time, mean flow velocity and critical flow velocity. The training and testing data are selected from the experimental data of several valuable references. Numerical tests indicate that MLP/BP model provide a better prediction of scour depth than RBF/OLS and ANFIS models as well as the previous empirical approaches. Finally, sensitivity analysis shows that pier diameter has a greater influence on equilibrium scour depth than the other independent parameters.     

Prediction of local scour around bridge piers using the ANFIS method

Local scour around bridge piers is a complicated physical process and involves highly three-dimensional flows. Thus, the scour depth, which is directly related to the safety of a bridge, cannot be given in the form of the exact relationship of dependent variables via an analytical method. This paper proposes the use of the adaptive neuro-fuzzy inference system (ANFIS) method for predicting the scour depth around a bridge pier. Five variables including mean velocity, flow depth, size of sediment particles, critical velocity for particles’ initiation of motion, and pier width were used for the scour depth. For comparison, predictions by the artificial neural network (ANN) model were also provided. Both the ANN model and ANFIS method were trained and validated. The findings indicate that the modeling with dimensional variables yields better predictions than when normalized variables are used. The ANN model was applied to a field-scale dataset. Prediction results indicated that the errors are much larger compared to the case of a laboratory-scale dataset. The MAPE by the ANN model trained with part of the field data was not seriously different from that by the model trained with the laboratory data. However, the application of the ANFIS method improved the predictions significantly, reducing the MAPE to the half of that by the ANN model. Five selected empirical formulas were also applied to the same dataset, and Sheppard and Melville’s formula was found to provide the best prediction. However, the MAPEs for the scour depths predicted by empirical formulas are much larger than MAPEs by either the ANN or the ANFIS method. The ANFIS method predicts much better if the range of the training dataset is sufficiently wide to cover the range of the application dataset.

     

Group method of data handling to predict scour depth around bridge piers

In this study, group method of data handling network with quadratic polynomial was used to predict scour depth around bridge piers. Effective parameters on scour phenomena include sediment size, geometry of bridge pier, and upstream flow conditions. Different shapes of piers have been utilized to develop the GMDH network. Back propagation algorithm was performed to train the GHMD network which updated weighting coefficients of quadratic polynomial in each iteration of the training stage. The GMDH performed with the lowest errors of training and testing stages for cylindrical pier. Also, Richardson and Davis, Johnson’s equations produced relatively good performances for different types of piers. Finally, the results indicated that GMDH could be provided more accurate prediction than those obtained using traditional equations.     

Support vector regression based modeling of pier scour using field data

This paper investigates the potential of support vector machines based regression approach to model the local scour around bridge piers using field data. A dataset of consisting of 232 pier scour measurements taken from BSDMS were used for this analysis. Results obtained by using radial basis function and polynomial kernel based Support vector regression were compared with four empirical relation as well as with a backpropagation neural network and generalized regression neural network. A total of 154 data were used for training different algorithms whereas remaining 78 data were used to test the created model. A coefficient of determination value of 0.897 (root mean square error=0.356) was achieved by radial basis kernel based support vector regression in comparison to 0.880 and 0.835 (root mean square error=0.388 and 0.438) by backpropagation neural and generalized regression neural network. Comparisons of results with four predictive equations suggest an improved performance by support vector regression. Results with dimensionless data using all three algorithms suggest a better performance by dimensional data with this dataset. Sensitivity analysis suggests the importance of depth of flow and pier width in predicting the scour depth when using support vector regression based modeling approach.     

CFD modeling of scale effects on turbulence flow and scour around bridge piers

Sediment scour near bridge piers is a problem of nationwide concern because it has resulted in more bridge failures than all other causes in recent years. The existing bridge scour equation from HEC-18 was developed from laboratory experiments in relatively small scale. Field studies by Mueller [Mueller D, Wagner Chad R. Analysis of pier scour predictions and real-time field measurements. In: Proceedings of ICSF-1 first international conference on scour of foundations, Texas A&M University, College Station, Texas, USA; 2002] indicate that it is difficult to verify the scour equation with field data obtained from large bridge piers. In this study, computational model simulations using a 3D CFD model were conducted to examine scale effects on turbulent flow and sediment scour. For the large-scale model, the physical scale and boundary velocity were set up from the small scale model based on the Froude similarity law. Results of flow and sediment scour were obtained from two different approaches: (a) Froude similarity which is commonly used in physical modeling and (b) full scale 3D CFD modeling. Unlike physical modeling in which the effect of turbulent Reynolds number is ignored, the CFD model employs a 2nd order turbulent model to calculate turbulent velocity and sediment scour. Effects of scale on turbulence flow and sediment scour were investigated by comparing different results obtained from a full scale numerical model to those derived from the Froude similarity method.     

Assessment of M5′ model tree and classification and regression trees for prediction of scour depth below free overfall spillways

The scour below spillways can endanger the stability of the dams. Hence, determining the scour depth downstream of spillways is of vital importance. Recently, soft computing models and, in particular, artificial neural networks (ANNs) have been used for scour depth prediction. However, ANNs are not as comprehensible and easy to use as empirical formulas for the estimation of scour depth. Therefore, in this study, two decision-tree methods based on model trees and classification and regression trees were employed for the prediction of scour depth downstream of free overfall spillways. The advantage of model trees and classification and regression trees compared to ANNs is that these models are able to provide practical prediction equations. A comparison between the results obtained in the present study and those obtained using empirical formulas is made. The statistical measures indicate that the proposed soft computing approaches outperform empirical formulas. Results of the present study indicated that model trees were more accurate than classification and regression trees for the estimation of scour depth.     

Prediction of scouring around an arch-shaped bed sill using Neuro-Fuzzy model

In this study, Adaptive Neuro-Fuzzy Inference System (ANFIS) has been used to model local scouring depth and pattern scouring around concave and convex arch shaped circular bed sills. The experimental part of this research study includes seven sets of laboratory test cases which were performed in an experimental flume under different flow conditions. A data set consists of 2754 data points of scouring depth were collected to use in the ANFIS model. The ratio of arch diameter, D, to flume width, W, is used as a non dimensional variables in all test cases. The results from ANFIS model were compared with the results of ANN model obtained by Homayoon et al. [24] and previously presented models. The results indicated that for D/W equal to 1 and 1.2, the ANFIS models produced a good performance for convex and concave bed sills. As a result, the ANFIS models can be used as an alternative to ANN for estimation of scour depth and scour pattern around a concave bed sill installed with a bridge pier.     

Bridge pile damage upon vessel impact

Many piers of bridges that span navigable waters are increasingly subjected to vessel impact. Many of these bridge piers are concrete and are constructed such that the piling system and the bridge pier are one. Depending upon the size and the material of the pile and upon vessel impact there may be a failure within the pile itself or at the pile-pier intersection. If the impact is great enough, the failure or fracture may be a complete one, and the pier moves horizontally and/or vertically. Thus, failure of the bridge may result while the pier is still intact. A new bridge may be built or rehabilated using the existing pier which may now be inadequate. In many cases the amount of piling failure is difficult to assess. Thus, a procedure has been developed to determine the amount of pier movement (failure of the piles) that might occur. The procedure uses a modification of two existing computer programs (a lateral pile program and a pile group program).     

Experimental and numerical investigation of bridge pier scour estimation using ANFIS and teaching–learning-based optimization methods

Studies have shown that the major cause of the bridge failures is the local scour around the pier foundations or their abutments. The local scour around the bridge pier is occurred by changing the flow pattern and creating secondary vortices in the front and rear of the bridge piers. Until now, many researchers have proposed empirical equations to estimate the bridge pier scour based on laboratory and field datasets. However, scale impact, laboratory simplification, natural complexity of rivers and the personal judgement are among the main causes of inaccuracy in the empirical equations. Therefore, due to the deficiencies and disadvantages of existing equations and the complex nature of the local scour phenomenon, in this study, the adaptive network-based fuzzy inference system (ANFIS) and teaching–learning-based optimization (TLBO) method were combined and used. The parameters of the ANFIS were optimized by using TLBO optimization method. To develop the model and validate its performance, two datasets were used including laboratory dataset that consisted of experimental results from the current study and previous ones and the field dataset. In total, 27 scaled experiments of different types of pier groups with different cross sections and side slopes were carried out. To evaluate the model ability in prediction of scour depth, results were compared to the standard ANFIS and empirical equations using evaluation functions including Hec-18, Froehlich and Laursen and Toch equations. The results showed that adding TLBO to the standard ANFIS was efficient and can increase the model capability and reliability. Proposed model achieved better results than Laursen and Toch equation which had the best results among empirical relationships. For instance, proposed model in comparison with the Laursen and Toch equation, based on the RMSE function, yielded 50.4% and 71.8% better results in laboratory and field datasets, respectively.

     

Prediction of pipeline scour depth in clear-water and live-bed conditions using group method of data handling

In the present study, the Group method of data handling (GMDH) network was utilized to predict the scour depth below pipelines. GMDH network was developed using back propagation. Input parameters that were considered as effective parameters on the scour depth included those of sediment size, geometry of pipeline, and approaching flow characteristics. Training and testing performances of the GMDH networks have been carried out using nondimensional data sets that were collected from the literature. These data sets are related to the two main situations of pipelines scour experiments namely clear-water and live-bed conditions. The testing results of performances were compared with the support vector machines (SVM) and existing empirical equations. The GMDH network indicated that using of back propagation produced lower error of scour depth prediction than those obtained using the SVM and empirical equations. Also, the effects of many input parameters on the scour depth have been investigated.     

Experimental investigation and finite element modelling of the effects of flow velocities on a skewed integral bridge

This paper presents finite element modelling of the effects of different flow velocities on the structural behaviour of a skewed integral bridge. Flow velocities affect the scour depths at the piles of a bridge and thus affect its structural behaviour. Laboratory tests on a scaled-down hydraulic model along with numerical modelling were performed to simulate the structural behaviour of the scoured integral bridge. A finite element package was used for the numerical modelling work, and the displacements and strains corresponding to the measured locations on the physical model were extracted. The experimental and numerical results for the case of maximum scour depths were compared.     

Development of a stochastic wave force function on ocean-structures

The wave forces exerted on structures are of vital importance in the design of marine structures.

Circular piles are frequently used to provide most or all of the support for such structures. The forces exerted by waves of similar properties vary greatly. These variations are the result of fluctuations in fluid particle velocities and accelerations as well as by eddies and turbulence around piles caused by rapidly reversing flow. Consequently, a deterministic approach to wave force prediction appears to be impossible. As an alternative, a probabilistic approach was developed in this paper.

The method applied here utilizes a multiple linear regression analysis to develop a relationship between wave parameters which are relatively easy to observe and the parameters used in the Morison force equation. They include the velocity and acceleration of water particles and the drag and mass coefficients and are considered to be random variables. The assumption of their lognormal distribution was reasonably well verified. Using Monte Carlo simulation these regression relations were then utilized to generate the frequency function of the wave forces. The wave force function can best be described as stationary periodic process. It can then be used as an input function for a probabilistic dynamic analysis of offshore structures.     

Review of input determination techniques for neural network models based on mutual information and genetic algorithms

The use of artificial neural networks (ANNs) models has grown considerably over the last decade. One of the difficulties in using ANNs is the fact that in most cases there are several numbers of input variables available. In the past, there was a tendency to use a large number of inputs in ANNs applications. This can have a number of detrimental effects on the network during training and it also requires a greater amount of data to efficiently estimate the connection weights. Additional inputs tend to increase the required time for training and the risk of the training algorithm becoming stuck in a local minimum. A large number of inputs also increases the risk of including spurious variables that merely increase the noise in the forecasts. Consequently, it is important to use an appropriate selection technique of the input variables in order to obtain the smallest number of independent inputs that are useful predictors for the system which is being researched. The aim of this paper is to review techniques that will allow the selection of appropriate model inputs based particularly on mutual information and genetic algorithms.     

Enrollment Management Model: Artificial Neural Networks versus Logistic Regression

This paper presents an enrollment management model by applying artificial neural network (ANN). The aim of the research, which has been presented in this paper, is to show that ANNs are more successful in predicting than the classical statistical method – regression analysis (logistic regression). Both predictive models, no matter whether they are based on ANNs or logistic regression, offer satisfactory predictive results, and they can offer support in the decision-making process. However, the model based on neural networks shows certain advantages. ANNs demand understanding of functional connection between independent and dependent variables in order to evaluate the model. Also, they adapt easily to related independent variables, without the appearance of the problem of multicollinearity. In contrast to logistic regression, neural networks can recognize the appearance of nonlinearity and interactions in input data, and they can react on time.     

Knowledge extraction from trained neural network scour model at culvert outlets

Artificial neural networks (ANNs), due to their outstanding capabilities for modeling complex processes, have been successfully applied to a variety of problems in hydraulics. However, one of the major criticisms of ANNs is that they are just black-box models, since a satisfactory explanation of their behavior has not been offered. They, in particular, do not explain easily how the inputs are related to the output and also whether the selected inputs have any significant relationship with an output. In this paper, a perturbation analysis for determining the order of influence of the elements in the input vector on the output vector is discussed. The analyses of the results suggest that each variable in the input vector (d ₅₀/d ₀, F ₀, H/d ₀, σ_g, and W ₀/d ₀) influences the depth of scour in different ways. However, the magnitude of the influence cannot be clearly quantified by this approach. Further it adds that the selection of input vector based on linear measures between the variables of interest, which is commonly employed, may still include certain spurious elements that only increase the model complexity.     

Estimation of heat transfer in oscillating annular flow using artifical neural networks

In this study, the prediction of heat transfer from a surface having constant heat flux subjected to oscillating annular flow is investigated using artificial neural networks (ANNs). An experimental study is carried out to estimate the heat transfer characteristics as a function of some input parameters, namely frequency, amplitude, heat flux and filling heights. In the experiments, a piston cylinder mechanism is used to generate an oscillating flow in a liquid column at certain frequency and amplitude. The cycle-averaged values are considered in the calculation of heat transfer using the control volume approach. An experimentally evaluated data set is prepared to be processed with the use of neural networks. Back propagation algorithm, the most common learning method for ANNs, is used for training and testing the network. Results of the experiments and the ANN are in close agreements with errors less than 5%. The study showed that the ANNs could be used effectively for modeling oscillating flow heat transfer in a vertical annular duct.     

水平单调载荷作用下的桩基桥墩滞回特性

为研究桩基桥墩-地基系统的非线性性能,根据模型与原型的物理相似关系制作1∶5比例的桩基桥墩模型. 采用力-位移混合控制加载的拟静力试验方法,通过在墩顶施加水平单调增加载荷,得到墩顶水平载荷下桩基桥墩的载荷-位移滞回曲线、骨架曲线和滞回特性. 用非线性弹簧单元模拟土体、用梁单元模拟桩和桥墩,建立模型桥墩的计算模型. 计算模型的骨架曲线与试验模型的骨架曲线吻合较好,表明采用非线性弹簧单元和梁单元分别模拟土体和桩是可行的,可以为考虑土-结构相互作用时的桥梁抗震分析提供参考依据.     

Settlement prediction of the rock-socketed piles through a new technique based on gene expression programming

The settlement design of bored piles socketed into rock has received considerable attention. Although many design methods of pile settlement are recommended in the literature, proposing new/practical technique(s) with higher performance prediction is of advantage. A new model based on gene expression programming (GEP) is presented in this paper for predicting the settlement of the rock-socketed pile. To do this, 96 piles socketed in different types of rock (mostly granite) as part of the Klang Valley Mass Rapid Transit project, Malaysia, were studied. In order to propose a predictive model with higher performance prediction, a series of GEP analyses were conducted using the most important factors on pile settlement, i.e. ratio of length in soil layer to length in rock layer, ratio of total length to diameter, uniaxial compressive strength, standard penetration test and ultimate bearing capacity. For comparison purpose, using the same dataset, linear multiple regression (LMR) technique was also performed. After developing the equations, their prediction performances were checked through several performance indices. The results demonstrated the feasibility of GEP-based predictive model of settlement. Coefficients of determination (CoD) values of 0.872 and 0.861 for training and testing datasets of GEP equation, respectively, show superiority of this model in predicting pile settlement while these values were obtained as 0.835 and 0.751 for the LMR model. Moreover, root mean square error (RMSE) values of (1.293 and 1.656 for training and testing) and (1.737 and 1.767 for training and testing) were achieved for the developed GEP and LMR models, respectively.