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.

     

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.     

Artificial intelligence-based estimation of flushing half-cone geometry

An accurate estimation of half-cone geometry (i.e., volume and length) created by pressure flushing operation in dam reservoirs is required for sediment management in the reservoir storage. In this study, two artificial intelligence techniques namely, Artificial Neural Network (ANN) and Adaptive Neuro-fuzzy Inference System (ANFIS) were utilized to estimate the volume and length of flushing half-cone based on influential variables, i.e., mean flow velocity through bottom outlet (u), water depth in reservoir (H_w), mean grain diameter of deposited sediments (d₅₀), thickness of deposited sediment (H_s) and bottom outlet diameter (D). Experimental data in both dimensional and non-dimensional forms were used to train and test ANN and ANFIS models. The results of the intelligence-based models were also compared with those of existing studies. The outcomes indicated that both ANN and ANFIS models predict the volume and length of flushing half-cone more accurately than existing studies. Also, it was found that the ANN model provides a better estimation of the geometry of flushing half-cone compared to the ANFIS model. Finally, sensitivity analysis was conducted to determine the most and the least influential variables affecting the flushing half-cone geometry. It was found that the sediment characteristics (H_s and d₅₀) and fluids properties (H_w and u) have respectively the most and the least effect on flushing half-cone volume and length.     

Hybrid ANFIS–PSO approach for predicting optimum parameters of a protective spur dike

In this study a new approach was proposed to determine optimum parameters of a protective spur dike to mitigate scouring depth amount around existing main spur dikes. The studied parameters were angle of the protective spur dike relative to the flume wall, its length, and its distance from the main spur dikes, flow intensity, and the diameters of the sediment particles that were explored to find the optimum amounts. In prediction phase, a novel hybrid approach was developed, combining adaptive-network-based fuzzy inference system and particle swarm optimization (ANFIS–PSO) to predict protective spur dike's parameters in order to control scouring around a series of spur dikes. The results indicated that the accuracy of the proposed method is increased significantly compared to other approaches. In addition, the effectiveness of the developed method was confirmed using the available data.     

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.

     

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.     

Evaluation and prediction of flyrock resulting from blasting operations using empirical and computational methods

Mines, quarries and construction sites face environmental impacts, such as flyrock, due to blasting operations. Flyrock may cause damage to structures and injury to human. Therefore, flyrock prediction is required to determine safe blasting zone. In this regard, 232 blasting operations were investigated in five granite quarries, Malaysia. Blasting parameters comprising maximum charge per delay and powder factor were prepared to predict flyrock using empirical and intelligent methods. An empirical graph was proposed to predict flyrock distance for different powder factor values. In addition, using the same datasets, two intelligent systems, namely artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS) were used to predict flyrock. Considering some model performance indices including coefficient of determination (R ²), value account for and root mean squared error and also using simple ranking procedure, the best flyrock prediction models were selected. It was found that the ANFIS model can predict flyrock with higher performance capacity compared to ANN predictive model. R ² values of testing datasets are 0.925 and 0.964 for ANN and ANFIS techniques, respectively, suggesting the superiority of the ANFIS technique in predicting flyrock.     

Prediction of penetration depth in a plunging water jet using soft computing approaches

The flow characteristics of the plunging water jets can be defined as volumetric air entrainment rate, bubble penetration depth, and oxygen transfer efficiency. In this study, the bubble penetration depth is evaluated based on four major parameters that describe air entrainment at the plunge point: the nozzle diameter (D _N), jet length (L _j), jet velocity (V _N), and jet impact angle (θ). This study presents artificial neural network (ANN) and genetic expression programming (GEP) model, which is an extension to genetic programming, as an alternative approach to modeling of the bubble penetration depth by plunging water jets. A new formulation for prediction of penetration depth in a plunging water jets is developed using GEP. The GEP-based formulation and ANN approach are compared with experimental results, multiple linear/nonlinear regressions, and other equations. The results have shown that the both ANN and GEP are found to be able to learn the relation between the bubble penetration depth and basic water jet properties. Additionally, sensitivity analysis is performed for ANN, and it is found that D _N is the most effective parameter on the bubble penetration depth.     

Several non-linear models in estimating air-overpressure resulting from mine blasting

This research presents several non-linear models including empirical, artificial neural network (ANN), fuzzy system and adaptive neuro-fuzzy inference system (ANFIS) to estimate air-overpressure (AOp) resulting from mine blasting. For this purpose, Miduk copper mine, Iran was investigated and results of 77 blasting works were recorded to be utilized for AOp prediction. In the modeling procedure of this study, results of distance from the blast-face and maximum charge per delay were considered as predictors. After constructing the non-linear models, several performance prediction indices, i.e. root mean squared error (RMSE), variance account for (VAF), and coefficient of determination (R ²) and total ranking method are examined to choose the best predictive models and evaluation of the obtained results. It is obtained that the ANFIS model is superior to other utilized techniques in terms of R ², RMSE, VAF and ranking herein. As an example, RMSE values of 5.628, 3.937, 3.619 and 2.329 were obtained for testing datasets of empirical, ANN, fuzzy and ANFIS models, respectively, which indicate higher performance capacity of the ANFIS technique to estimate AOp compared to other implemented methods.     

Multiple regression,ANN and ANFIS models for prediction of backbreak in the open pit blasting

Backbreak is one of the undesirable effects of blasting operations causing instability in mine walls, falling down the machinery, improper fragmentation and reduction in efficiency of drilling. Backbreak can be affected by various parameters such as the rock mass properties, blasting geometry and explosive properties. In this study, the application of the artificial neural network (ANN), an adaptive neuro-fuzzy inference system (ANFIS) for prediction of backbreak, was described and compared with the traditional statistical model of multiple regression. The performance of these models was assessed through the root mean square error, correlation coefficient (R ²) and mean absolute percentage error. As a result, it was found that the constructed ANFIS exhibited a higher performance than the ANN and multiple regression for backbreak prediction.     

Artificial neural network approaches for prediction of backwater through arched bridge constrictions

This paper presents the findings of laboratory model testing of arched bridge constrictions in a rectangular open channel flume whose bed slope was fixed at zero. Four different types of arched bridge models, namely single opening semi-circular arch (SOSC), multiple opening semi-circular arch (MOSC), single opening elliptic arch (SOE), and multiple opening elliptic arch (MOE), were used in the testing program. The normal crossing (ϕ = 0), and five different skew angles (ϕ = 10°, 20°, 30°, 40°, and 50°) were tested for each type of arched bridge model. The main aim of this study is to develop a suitable model for estimating backwater through arched bridge constrictions with normal and skewed crossings. Therefore, different artificial neural network approaches, namely multi-layer perceptron (MLP), radial basis neural network (RBNN), generalized regression neural network (GRNN), and multi-linear and multi-nonlinear regression models, MLR and MNLR, respectively were used. Results of these experimental studies were compared with those obtained by the MLP, RBNN, GRNN, MLR, and MNLR approaches. The MLP produced more accurate predictions than those of the others.     

A comparative study of artificial neural network and adaptive neurofuzzy inference system for prediction of compressional wave velocity

In this study, two solutions for prediction of compressional wave velocity (p wave) are presented and compared: artificial neural network (ANN) and adaptive neurofuzzy inference system (ANFIS). Series of analyses were performed to determine the optimum architecture of utilized methods using the trial and error process. Several ANNs and ANFISs are constructed, trained and validated to predict p wave in the investigated carbonate reservoir. A comparative study on prediction of p wave by ANN and ANFIS is addressed, and the quality of the target prediction was quantified in terms of the mean-squared errors (MSEs), correlation coefficient (R ²) and prediction efficiency error. ANFIS with MSE of 0.0552 and R ² of 0.9647, and ANN with MSE of 0.042 and R ² of 0.976, showed better performance in comparison with MLR methods. ANN and ANFIS systems have performed comparably well and accurate for prediction of p wave.     

Estimation of soil dispersivity using soft computing approaches

The accurate estimation of soil dispersivity (α) is required for characterizing the transport of contaminants in soil. The in situ measurement of α is costly and time-consuming. Hence, in this study, three soft computing methods, namely adaptive neuro-fuzzy inference system (ANFIS), artificial neural network (ANN), and gene expression programming (GEP), are used to estimate α from more readily measurable physical soil variables, including travel distance from source of pollutant (L), mean grain size (D ₅₀), soil bulk density (ρ _b), and contaminant velocity (V _c). Based on three statistical metrics [i.e., mean absolute error, root-mean-square error (RMSE), and coefficient of determination (R ²)], it is found that all approaches (ANN, ANFIS, and GEP) can accurately estimate α. Results also show that the ANN model (with RMSE = 0.00050 m and R ² = 0.977) performs better than the ANFIS model (with RMSE = 0.00062 m and R ² = 0.956), and the estimates from GEP are almost as accurate as those from ANFIS. The performance of ANN, ANFIS, and GEP models is also compared with the traditional multiple linear regression (MLR) method. The comparison indicates that all of the soft computing methods outperform the MLR model. Finally, the sensitivity analysis shows that the travel distance from source of pollution (L) and bulk density (ρ _b) have, respectively, the most and the least effect on the soil dispersivity.

     

Performance evaluation of hybrid FFA-ANFIS and GA-ANFIS models to predict particle size distribution of a muck-pile after blasting

Accurately predicting the particle size distribution of a muck-pile after blasting is always an important subject for mining industry. Adaptive neuro-fuzzy inference system (ANFIS) has emerged as a synergic intelligent system. The main contribution of this paper is to optimize the premise and consequent parameters of ANFIS by firefly algorithm (FFA) and genetic algorithm (GA). To the best of our knowledge, no research has been published that assesses FFA and GA with ANFIS for fragmentation prediction and no research has tested the efficiency of these models to predict the fragmentation in different time scales as of yet. To show the effectiveness of the proposed ANFIS-FFA and ANFIS-GA models, their modelling accuracy has been compared with ANFIS, support vector regression (SVR) and artificial neural network (ANN). Intelligence predictions of fragmentation by ANFIS-FFA, ANFIS-GA, ANFIS, SVR and ANN are compared with observed values of fragmentation available in 88 blasting event of two quarry mines, Iran. According to the results, both ANFIS-FFA and ANFIS-GA prediction models performed satisfactorily; however, the lowest root mean square error (RMSE) and the highest correlation of determination (R²) values were obtained from ANFIS-GA model. The values of R² and RMSE obtained from ANFIS-GA, ANFIS-FFA, ANFIS, SVR and ANN models were equal to (0.989, 0.974), (0.981, 1.249), (0.956, 1.591), (0.924, 2.016) and (0.948, 2.554), respectively. Consequently, the proposed ANFIS-GA model has the potential to be used for predicting aims on other fields.

     

Performance evaluation of hybrid Wavelet-ANN and Wavelet-ANFIS models for estimating evapotranspiration in arid regions of India

This paper evaluates the ability of wavelet transform in improving the accuracy of artificial neural network (ANN) and adaptive neuro-fuzzy interface systems (ANFIS) models. In this study, the performance of hybrid Wavelet-ANN and Wavelet-ANFIS models for estimating daily evapotranspiration in arid regions was evaluated. Prior to the development of models, gamma test was used to identify the best input combinations that could be used under limited data scenario. Performance of the proposed hybrid models was compared to ANN, ANFIS, and conventionally used Hargreaves equation. The results revealed that use of wavelet transform as data preprocessing technique enhanced the efficiency of ANN and ANFIS models. Wavelet-ANN and Wavelet-ANFIS performed reasonably better than other models. Better handling of wavelet-decomposed input variables enabled Wavelet-ANN models to perform slightly better than the Wavelet-ANFIS models. W-ANN2 (RMSE = 0.632 mm/day and R = 0.96) was found to be the best model for estimating daily evapotranspiration in arid regions. The proposed W-ANN2 model used second-level db3 wavelet-decomposed subseries of temperature and previous day evapotranspiration values as inputs. The study concludes that hybrid Wavelet-ANN and Wavelet-ANFIS models can be effectively used for modeling evapotranspiration.

     

Research on axial bearing capacity of rectangular concrete-filled steel tubular columns based on artificial neural networks

Design of rectangular concrete-filled steel tubular (CFT) columns has been a big concern owing to their complex constraint mechanism. Generally, most existing methods are based on simplified mechanical model with limited experimental data, which is not reliable under many conditions, e.g., columns using high strength materials. Artificial neural network (ANN) models have shown the effectiveness to solve complex problems in many areas of civil engineering in recent years. In this paper, ANN models were employed to predict the axial bearing capacity of rectangular CFT columns based on the experimental data. 305 experimental data from articles were collected, and 275 experimental samples were chosen to train the ANN models while 30 experimental samples were used for testing. Based on the comparison among different models, artificial neural network model1 (ANN1) and artificial neural network model2 (ANN2) with a 20-neuron hidden layer were chosen as the fit prediction models. ANN1 has five inputs: the length (D) and width (B) of cross section, the thickness of steel (t), the yield strength of steel (f _y), the cylinder strength of concrete (f′_c). ANN2 has ten inputs: D, B, t, f _y, f′_c, the length to width ratio (D/B), the length to thickness ratio (D/t), the width to thickness ratio (B/t), restraint coefficient (ξ), the steel ratio (α). The axial bearing capacity is the output data for both models.The outputs from ANN1 and ANN2 were verified and compared with those from EC4, ACI, GJB4142 and AISC360-10. The results show that the implemented models have good prediction and generalization capacity. Parametric study was conducted using ANN1 and ANN2 which indicates that effect law of basic parameters of columns on the axial bearing capacity of rectangular CFT columns differs from design codes.The results also provide convincing design reference to rectangular CFT columns.     

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.     

Application of several non-linear prediction tools for estimating uniaxial compressive strength of granitic rocks and comparison of their performances

Uniaxial compressive strength (UCS) of rock is crucial for any type of projects constructed in/on rock mass. The test that is conducted to measure the UCS of rock is expensive, time consuming and having sample restriction. For this reason, the UCS of rock may be estimated using simple rock tests such as point load index (I _s(50)), Schmidt hammer (R _n) and p-wave velocity (V _p) tests. To estimate the UCS of granitic rock as a function of relevant rock properties like R _n, p-wave and I _s(50), the rock cores were collected from the face of the Pahang–Selangor fresh water tunnel in Malaysia. Afterwards, 124 samples are prepared and tested in accordance with relevant standards and the dataset is obtained. Further an established dataset is used for estimating the UCS of rock via three-nonlinear prediction tools, namely non-linear multiple regression (NLMR), artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS). After conducting the mentioned models, considering several performance indices including coefficient of determination (R ²), variance account for and root mean squared error and also using simple ranking procedure, the models were examined and the best prediction model was selected. It is concluded that the R ² equal to 0.951 for testing dataset suggests the superiority of the ANFIS model, while these values are 0.651 and 0.886 for NLMR and ANN techniques, respectively. The results pointed out that the ANFIS model can be used for predicting UCS of rocks with higher capacity in comparison with others. However, the developed model may be useful at a preliminary stage of design; it should be used with caution and only for the specified rock types.     

Neural computing models for prediction of permeability coefficient of coarse-grained soils

Correlations are very significant from the earliest days; in some cases, it is essential as it is difficult to measure the amount directly, and in other cases it is desirable to ascertain the results with other tests through correlations. Soft computing techniques are now being used as alternate statistical tool, and new techniques such as artificial neural networks, fuzzy inference systems, genetic algorithms, and their hybrids were employed for developing the predictive models to estimate the needed parameters, in the recent years. Determination of permeability coefficient (k) of soils is very important for the definition of hydraulic conductivity and is difficult, expensive, time-consuming, and involves destructive tests. In this paper, use of some soft computing techniques such as ANNs (MLP, RBF, etc.) and ANFIS (adaptive neuro-fuzzy inference system) for prediction of permeability of coarse-grained soils was described and compared. As a result of this paper, it was obtained that the all constructed soft computing models exhibited high performance for predicting k. In order to predict the permeability coefficient, ANN models having three inputs, one output were applied successfully and exhibited reliable predictions. However, all four different algorithms of ANN have almost the same prediction capability, and accuracy of MLP was relatively higher than RBF models. The ANFIS model for prediction of permeability coefficient revealed the most reliable prediction when compared with the ANN models, and the use of soft computing techniques will provide new approaches and methodologies in prediction of some parameters in soil mechanics.     

Adaptive neuro-fuzzy inference system–based model for elevation–surface area–storage interrelationships

In the developing of an optimal operation schedule for dams and reservoirs, reservoir simulation is one of the critical steps that must be taken into consideration. For reservoirs to have more reliable and flexible optimization models, their simulations must be very accurate. However, a major problem with this simulation is the phenomenon of nonlinearity relationships that exist between some parameters of the reservoir. Some of the conventional methods use a linear approach in solving such problems thereby obtaining not very accurate simulation most especially at extreme values, and this greatly influences the efficiency of the model. One method that has been identified as a possible replacement for ANN and other common regression models currently in use for most analysis involving nonlinear cases in hydrology and water resources–related problems is the adaptive neuro-fuzzy inference system (ANFIS). The use of this method and two other different approaches of the ANN method, namely feedforward back-propagation neural network and radial basis function neural network, were adopted in the current study for the simulation of the relationships that exist between elevation, surface area and storage capacity at Langat reservoir system, Malaysia. Also, another model, auto regression (AR), was developed to compare the analysis of the proposed ANFIS and ANN models. The major revelation from this study is that the use of the proposed ANFIS model would ensure a more accurate simulation than the ANN and the classical AR models. The results obtained showed that the simulations obtained through ANFIS were actually more accurate than those of ANN and AR; it is thus concluded that the use of ANFIS method for simulation of reservoir behavior will give better predictions than the use of any new or existing regression models.