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.

     

Estimation of current-induced scour depth around pile groups using neural network and adaptive neuro-fuzzy inference system

The process of local scour around bridge piers is fundamentally complex due to the three-dimensional flow patterns interacting with bed materials. For geotechnical and economical reasons, multiple pile bridge piers have become more and more popular in bridge design. Although many studies have been carried out to develop relationships for the maximum scour depth at pile groups under clear-water scour condition, existing methods do not always produce reasonable results for scour predictions. It is partly due to the complexity of the phenomenon involved and partly because of limitations of the traditional analytical tool of statistical regression. This paper addresses the latter part and presents an alternative to the regression in the form of artificial neural networks, ANNs, and adaptive neuro-fuzzy inference system, ANFIS. Two ANNs model, feed forward back propagation, FFBP, and radial basis function, RBF, were utilized to predict the depth of the scour hole. Two combinations of input data were used for network training; the first input combination contains six-dimensional variables, which are flow depth, mean velocity, critical flow velocity, grain mean diameter, pile diameter, distance between the piles (gap), besides the number of piles normal to the flow and the number of piles in-line with flow, while the second combination contains seven non-dimensional parameters which is a composition of dimensional parameters. The training and testing experimental data on local scour at pile groups are selected from several precious references. Networks’ results have been compared with the results of empirical methods that are already considered in this study. Numerical tests indicate that FFBP-NN model provides a better prediction than the other models. Also a sensitivity analysis showed that the pile diameter in dimensional variables and ratio of pile spacing to pile diameter in non-dimensional parameters are the most significant parameters on scour depth.     

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.     

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.     

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.     

Predictions of bridge scour: Application of a feed-forward neural network with an adaptive activation function

In this study, a new procedure to determine the optimum activation function for a neural network is proposed. Unlike previous methods of optimising activation functions, the proposed approach regards selection of the most suitable activation function as a discrete optimisation problem, which involves generating various combinations of function then evaluating their performance as activation functions in a neural network, returning the function or combination of functions which yields best result as the optimum. The efficacy of the proposed optimisation method is compared with conventional approaches using the data generated from several synthetic functions. Numerical results indicate that the network produced using the proposed method achieves a better accuracy with a smaller network size, compared to other approaches.Bridge scour problem is used to further demonstrate the performance of the proposed algorithm. Based on the training and validation results, a better estimation of both equilibrium and time dependent scour depth is produced by the neural network developed using the proposed optimisation method, compared to networks with a priori chosen activation functions. Furthermore, the performance of the proposed model is compared with predictions of empirical methods, with the former making more accurate predictions.     

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.

     

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.     

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.     

Application of support vector machines in scour prediction on grade-control structures

Research into the problem of predicting the maximum depth of scour on grade-control structures like sluice gates, weirs and check dams, etc., has been mainly of an experimental nature and several investigators have proposed a number of empirical relations for a particular situation. These traditional scour prediction equations, although offer some guidance on the likely magnitude of maximum scour depth, yet applicable to a limited range of the situations. It appears from the literature review that a regression mathematical model for predicting maximum depth of scour under all circumstances is not currently available. This paper explores the potential of support vector machines in modeling the scour from the available laboratory and field data obtained form the earlier published studies. To compare the results, a recently proposed empirical relation and a feed forward back propagation neural network model are also used in the present study. The outcome from the support vector machines-based modeling approach suggests a better performance in comparison to both the empirical relation and back propagation neural network approach with the laboratory data. The results also suggest an encouraging performance by the support vector machines learning technique in comparison to both empirical relation as well as neural network approach in scaling up the results from laboratory to field conditions for the purpose of scour prediction.     

单脉冲雷达天线方向图的BP神经网络建模

为了提高单脉冲雷达仿真速度,提出了应用BP神经网络对单脉冲雷达天线方向图进行建模的方法,并根据这一方法建立了某型单脉冲雷达天线方向图的BP神经网络模型.通过对比BP神经网络建模得到的单脉冲雷达天线方向图和实际单脉冲雷达天线方向图,并考虑到较小的BP神经网络训练均方误差,验证了该方法的有效性.实际的某型单脉冲雷达系统仿真试验表明利用建立的BP神经网络模型能大大地提高雷达仿真速度.     

基于多模型的非线性系统自适应最小方差控制

对于一类典型的离散时间非线性系统, 提出了一种基于多模型的自适应最小方差控制方法. 通过在平衡点附近建立线性模型, 用径向基函数神经元网络来补偿建模误差和未建模动态, 形成了非线性系统的多模型表示. 采用了具有积分性质的切换指标函数作为切换法则和最小方差的控制方法构成了多模型自适应控制器. 仿真实验的结果表明了这种方法的有效性.     

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.     

BIOTURB: A FORTRAN program to simulate the effects of bioturbation on the vertical distribution of sediment

Bioturbation may have serious implications for preservation of original stratigraphic distribution of sediment. Thus, several methods have been developed to model the redistribution of sediment by bioturbation. The program BIOTURB provides a tool to compare and evaluate different models of bioturbation and their effects on sediment distribution. A flexible approach allowing changes in bioturbating fauna with time, fluctuation of sedimentation rate and sediment type deposited, selective sediment transport by organisms, both random and nonrandom mixing processes, and variation in intensity of mixing with depth was taken. This was achieved by using a transition matrix modeled after a bioturbating fauna in conjunction with a Monte Carlo procedure to govern the redistribution of sediment during mixing. The simulation model, FORTRAN program, and an example are described in detail.     

Concrete breakout strength of single anchors in tension using neural networks

A feed forward neural network model for evaluating the concrete breakout strength of single cast-in and post-installed mechanical anchors in tension is presented. The nodes of the neural network input layer represent the embedment depth, anchor head diameter, concrete strength and anchor installation system, and the neural network output is the tensile capacity of anchors as governed by the concrete breakout. Three different techniques have been adopted to represent the anchor installation system in the neural network input layer. The training, validation and testing of the developed networks were based on a database of 451 experimental tests obtained from previous laboratory anchor tests. Testing of the trained neural network indicates good predictions of the concrete breakout strength of cast-in and post-installed mechanical anchors in tension.The relationships between the concrete breakout strength of anchors and different influencing parameters obtained from the trained neural networks were in general agreement with those of the ACI 318-02 for cast-in and post-installed mechanical anchors. It has been shown that the concrete breakout strength of anchors in tension is approximately proportional to the embedment depth of 1.5 power and marginally affected by changing the anchor head diameter.     

Real-time prediction of unsteady aerodynamics: Application foraircraft control and manoeuvrability enhancement

The capability to control unsteady separated flow fields could dramatically enhance aircraft agility. To enable control, however, real-time prediction of these flow fields over a broad parameter range must be realized. The present work describes real-time predictions of three-dimensional unsteady separated flow fields and aerodynamic coefficients using neural networks. Unsteady surface-pressure readings were obtained from an airfoil pitched at a constant rate through the static stall angle. All data sets were comprised of 15 simultaneously acquired pressure records and one pitch angle record. Five such records and the associated pitch angle histories were used to train the neural network using a time-series algorithm. Post-training, the input to the network was the pitch angle (alpha), the angular velocity (dalpha/dt), and the initial 15 recorded surface pressures at time (t (0)). Subsequently, the time (t+Deltat) network predictions, for each of the surface pressures, were fed back as the input to the network throughout the pitch history. The results indicated that the neural network accurately predicted the unsteady separated flow fields as well as the aerodynamic coefficients to within 5% of the experimental data. Consistent results were obtained both for the training set as well as for generalization to both other constant pitch rates and to sinusoidal pitch motions. The results clearly indicated that the neural-network model could predict the unsteady surface-pressure distributions and aerodynamic coefficients based solely on angle of attack information. The capability for real-time prediction of both unsteady separated flow fields and aerodynamic coefficients across a wide range of parameters in turn provides a critical step towards the development of control systems targeted at exploiting unsteady aerodynamics for aircraft manoeuvrability enhancement.     

Bayesian neural networks at scale: a performance analysis and pruning study

Bayesian neural networks (BNNs) are a promising method of obtaining statistical uncertainties for neural network predictions but with a higher computational overhead which can limit their practical usage. This work explores the use of high-performance computing with distributed training to address the challenges of training BNNs at scale. We present a performance and scalability comparison of training the VGG-16 and Resnet-18 models on a Cray-XC40 cluster. We demonstrate that network pruning can speed up inference without accuracy loss and provide an open-source software package, BPrune, to automate this pruning. For certain models we find that pruning up to 80% of the network results in only a 7.0% loss in accuracy. With the development of new hardware accelerators for deep learning, BNNs are of considerable interest for benchmarking performance. This analysis of training a BNN at scale outlines the limitations and benefits compared to a conventional neural network.

     

Reality of virtual damage identification based on neural networks and vibration analysis of a damaged bridge under a moving vehicle

Presented here is a reality of virtual damage detection and vibration behaviour study of a discrete beam-like bridge with one or several non-propagating edge cracks subjected to a moving vehicle. In this model, the simply supported beam elements are replaced by a range of rigid bars, which are connected by transverse and rotational springs, while the mass and rotational moment of inertia may be lumped at various points along the beam. The adopted vehicle model here is a four degrees-of-freedom, two axes half-vehicle model with tires flexibility and linear suspensions. Damage can be modelled by altering the spring stiffness equation at the crack position according to predictions, which allows the inclusion of simple or complex damage. To simplify, damage is represented here by an open crack, and stiffness of a given element with damage is calculated by fracture mechanics. Both the discrete element and finite element methods are used to investigate vibration analysis of a discrete beam model subjected to a moving vehicle to confirm model feasibility in vibration analysis under a moving vehicle. Besides, some dynamic response laws are obtained. Considering an irregular road profile, the effects of the moving vehicle velocity, the moving vehicle mass, the crack location and the crack depth on dynamic response of a beam-like bridge are analysed by a numerical example, combining a vehicle–bridge coupled vibration MATLAB program with ANSYS. In addition, the neural network is used to identify the damage of the structure. Numerical results of the numerical model predictions, compared with those obtained from the continuous elements beam, support the accuracy of the discrete elements beam model in both cases of undamaged beam and damaged one. The evidence for condition assessment and damage identification of bridge is obtained from this simulation as obtaining the vibrational characteristics of the damaged beam structure subjected to a moving vehicle. And the inversion results show that the neural network method can identify the injury location and injury size of the structure accurately.