A cooperative expert based support vector regression (Co-ESVR) system to determine collar dimensions around bridge pier

Neurocomputing ∎ (∎∎∎∎) ∎∎∎–∎∎∎

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A cooperative expert based support vector regression (Co-ESVR) system to determine collar dimensions around bridge pier Afshin Jahangirzadeh a, Shahaboddin Shamshirband b,n, Saeed Aghabozorgi c, Shatirah Akib a, Hossein Basser a, Nor Badrul Anuar d, Miss Laiha Mat Kiah d a

Department of Civil Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia Department of Computer Science, Chalous Branch, Islamic Azad University (IAU), 46615-397 Chalous, Mazandaran, Iran c Department of Information Science, Faculty of Computer Science and Information Technology, University of Malaya, 50603 Kuala Lumpur, Malaysia d Department of Computer System and Technology, Faculty of Computer Science and Information Technology, University of Malaya, 50603 Kuala Lumpur, Malaysia b

art ic l e i nf o

a b s t r a c t

Article history: Received 5 August 2013 Received in revised form 17 January 2014 Accepted 15 March 2014 Communicated by T. Heskes

In this study, a new procedure to determine the optimum dimensions for a rectangular collar to minimize the temporal trend of scouring around a pier model is proposed. Unlike previous methods of predicting collar dimensions around a bridge pier, the proposed approach concerns the selection of different collar dimension sizes around a bridge scour in terms of the flume's upstream (Luc/D), downstream (Ldc/D) and width (Lw/D) of the flume. The projected determination method involves utilizing Expert Multi Agent System (E-MAS) based Support Vector Regression (SVR) agents with respect to cooperative-based expert SVR (Co-ESVR). The SVR agents (i.e. SVRLuc, SVRLdc and SVRLw) are set around a rectangular collar to predict the collar dimensions around a bridge pier. In the first layer, the Expert System (ES) is adopted to gather suitable data and send it to the next layer. The multi agent-based SVR adjusts its parameters to find the optimal cost prediction function in the collar dimensions around the bridge pier to reduce the collar around the bridge scour. The weighted sharing strategy was utilized to select the cost optimization function through the root mean square error (RMSE). The efficiency of the proposed optimization method (Co-ESVR) was explored by comparing its outcomes with experimental results. Numerical results indicate that the Co-ESVR achieves better accuracy in reducing the percentage of scour depth (re) with a smaller network size, compared to the non-cooperative approaches. & 2014 Elsevier B.V. All rights reserved.

Keywords: Scour Collar Cooperative Support vector regression Multi agent system Expert system

1. Introduction In many countries, bridges are built across canals and rivers as traffic volume increases due to economic development. Every year several bridges fail, not only for structural reasons, but owing to pier and abutment scouring [1]. Scouring is one of the most significant and destructive effects of floods on bridges. It occurs as a result of the erosive behavior of flowing water on the beds and banks of alluvial channels. Flow approaching a bridge pier or abutment is accompanied by enhanced sediment-carrying capacity. The scour phenomenon may cause catastrophic hazards accounting for reduction of pier support. A number of bridge failures ensuing from scouring have been reported over the past years. A Federal Highway Administration (FHWA) report states that 383 bridges collapsed due to catastrophic floods and scouring [2].

n

Corresponding author. Tel.: þ 98 60146266763. E-mail address: [email protected] (S. Shamshirband).

The complex vortex system in the vicinity of bridge piers is the key factor and main reason why scour holes develop. As flow affects the pier nose, a downward flow is formed in front of the pier. This impinges on the stream bed, causing scour-hole formation in front of the pier, and eventually a complex vortex system is formed. In addition, wake vortices are created due to downstream flow separation of the pier, which behave as small tornados instigating the bed material to lift and produce an independent scour hole downstream of the pier. Fig. 1a shows the scouring mechanism around a circular bridge pier and Fig. 1b depicts a bridge which experienced scour during a flood. Numerous researchers have studied the mechanism of scour phenomenon around bridge and other hydraulic structures like; Link et al., Heidarpour et al., Muzzammil et al., Dey and Raikar, Kirkil et al., Hendrickson et al., and Karami et al. [3–10]. Studying the mechanism of scour, researchers found out that scour phenomenon can be controlled and they proposed various countermeasure methods. The proposed methods are broadly grouped under two distinct categories: armoring and flow-altering countermeasures, which are also described as direct and indirect methods [11]. In the armoring

http://dx.doi.org/10.1016/j.neucom.2014.03.024 0925-2312/& 2014 Elsevier B.V. All rights reserved.

Please cite this article as: A. Jahangirzadeh, et al., A cooperative expert based support vector regression (Co-ESVR) system to determine collar dimensions around bridge pier, Neurocomputing (2014), http://dx.doi.org/10.1016/j.neucom.2014.03.024i

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Fig. 1. (a) scouring mechanism around a circular bridge pier (b) bridge scour happened during flood.

technique, the structures are protected directly against scouring by covering the bridge pier area by riprap stones, reno-mattresses, cabled-tied blocks, gabions, tetrapods, dolos, concrete-filled mats or bags, and concrete aprons [12]. In flow-altering countermeasures, the flow pattern is modified by structures such as sacrificial piles and sills, collars, and slots to diminish scour [13]. A collar is a type of indirect countermeasure for controlling scour around piers by diverting the down-flow and acting as an obstacle in down-flow path to reduce the horseshoe vortex strength. Numerous researchers have examined the collar effect on reducing scour depth and its efficiency has been established in earlier studies [14–23]. Despite previous efforts, optimizing collar size in order to reach maximum collar efficiency for protecting pier has not yet been determined. In this paper, the main objective was to find the optimum dimensions of a rectangular collar and several experiments were performed using several sizes of collar in order to find the optimum sizes. But the experiments are too time consuming and expensive then developing a computer-based method is necessary and unavoidable. As mentioned before, due to expensive procedures of experimental and field work studies, numerical, mathematical and computer-based modeling methods have been considered recently in this scheme. Soft computing techniques, such as artificial neural networks are employed for predicting scour depth [24–27] and their performance was compared with various existing methods (i.e. fuzzy logic). The results of these studies suggest that the neural network approach performs better than empirical relations [28]. A neural network-based modeling algorithm requires setting up different learning parameters (e.g. learning rate and momentum), the optimal number of nodes in the hidden layer and the number of hidden layers. A large number of training iterations may force a neural network to over-train, which may affect the models’ predicting capabilities. The presence of local minima is a further problem when using a back-propagation neural network. Recent studies suggest the usefulness of neuro fuzzy in finding a neural network's optimal architecture for scour prediction. ANFIS was applied to estimate the current-induced scour depth around pile groups [29]. It has been reported [29] that a neuro fuzzy model was utilized to predict the scouring around an arch-shaped bed sill. Within the last decade, several studies reported the adoption of generalized regression neural networks and support vector machines in civil engineering [30–32], and it was found that they function adequately in comparison to a back-propagation neural network and the neuro fuzzy approach. The advantages of generalized regression neural networks and support vector machines are that both methods require few user-defined parameters and they do not face the problem of local minima.

In view of the enhanced performance by support vector machine based regression in civil engineering, in this study a cooperativebased prediction method is proposed, which applies support vector regression and a multi-agent system. The predicted value of scour depth reduction percentage (re) through SVR cooperative agents is implemented to select the optimal collar dimensions around a bridge pier. The expert-based decision maker agent around the bridge scour gathers suitable data to send to the next layer. The multi agent-based SVR in the second layer adjusts its parameters to find the optimal cost function for predicting collar dimensions around the bridge pier to reduce scour around the bridge pier. The weighted sharing strategy selects the optimized cost function through the root mean square error (RMSE). The proposed Co-ESVR compares its performance with two empirical relations, a Polynomial-based (SVR_Poly) and RBF-based SVR (SVR_rbf) in predictions of collar dimensions around bridge piers. In addition, the performance of the proposed Co-ESVR is compared with that of non-cooperative SVR agents.

2. Experimental setup and procedure The experiments were conducted in the hydraulic laboratory of the hydraulic engineering division at University of Malaya. The experimental flume in the laboratory is 12 m long, 30 cm wide and 45 cm high and has a slope of 0.0004. At the end of the flume there is a basin in which a triangular weir was placed to measure flow discharge with an accuracy of 0.1 l/s. Fig. 2 shows a schematic plan of the experimental flume in laboratory and all the items which are related to scouring process around a bridge pier. Water was circulated via two pumps. An adjustable tail gate was arranged downstream of the flume to measure the water depth. The water flow velocity was measured by a 3 Axis Electronic Current Velocity Meter and scour depth was measured and recorded by a Sand Surface Meter with an accuracy of 70.5 mm in depth. The flume floor was raised 15 cm with metal platforms. A movable bed was prepared by filling an area between the platforms with non-cohesive sediment to lengths of 2 m and 5 m from the beginning of the flume. In the experiment, the bridge pier model was set up in the middle of the 2 m area (the movable bed). The rectangular collars were constructed from rigid plastic with 0.8 mm thickness and were placed on the bed with two sides parallel to the flume walls. The experiments were repeated using various widths as well as upstream and downstream collar lengths to determine the optimum dimensions. Fig. 3 illustrates the plan of three variables in the experiments. Each series of experiments contained 10 distinct experiments. Having 10 experiments for each series, a total of 30 experiments were conducted.

Please cite this article as: A. Jahangirzadeh, et al., A cooperative expert based support vector regression (Co-ESVR) system to determine collar dimensions around bridge pier, Neurocomputing (2014), http://dx.doi.org/10.1016/j.neucom.2014.03.024i

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Fig. 2. Plan and profile of the experimental flume.

Fig. 3. The variables of collars in the experiments: (a) Luc (b) Ldc (c) Lw.

2.1. Input parameters As a data-driven model, the ability of the Cooperative Expertbased Support Vector Regression to make reasonable estimations is mostly dependent on input parameter selection. Adequate consideration of the factors controlling the system studied is therefore crucial to developing a reliable network. The scour geometry around a circular pier in a bend depends on channel geometry (channel width, channel radius and bed slope), pier characteristics (pier diameter and location in bend), collar characteristics (collar size, collar shape and location in bed), flow conditions (approach depth and discharge or velocity), sediment properties (specific gravity, grain size and friction angle), fluid parameters (density and viscosity) and time. Thus for equilibrium, depth of scour (dse) can be written in Eq. (1) dse ¼ f ðD; Luc ; Ldc ; Lw ; H; θ; Y; b; S0 ; V; V c ; g; d50 ; R; ρs ; φ; ρ; μÞ

ð1Þ

where D is pier diameter, Luc, Ldc and Lw are sizes of the collar, H is collar location in the bed, θ is pier location in the bend, Y is flow depth, b is channel width, S0 is bed slope, V is a flow velocity, Vc is critical velocity at the onset of bed material movement, g is gravitational acceleration, d50 is median grain size, R is bend radius, ρs is sediment density, φ is sediment friction angle, ρ is fluid density, μ is fluid viscosity, dse is the equilibrium scour depth. After neglecting the parameters with constant values (H, θ, b, S0, g, d50, R, ρs, φ, ρ, μ) and using dimensional analysis to have dimensionless variables, Eq. (2) was obtained. The parameters in Eq. (2) are the most influential parameters on the scour depth phenomenon around a collar
 dse Y V Luc Ldc Lw ; ¼f ; ; ð2Þ ; D Vc D D D D According to the experiments, the input parameters are collected in widths, and upstream and downstream collar lengths are to be defined as input for the learning techniques. In the experiments, 70%

of the data was used to train samples and the subsequent 30% served to test the samples. A summary of the statistical properties of the scour database in the pier for upstream, downstream and width is provided in Table 1. 2.2. Supervised machine learning Support vector machine (SVM) are a type of supervised machine learning technique belonging to a family of generalized linear classifier. The formulation embodies the structural risk minimization (SRM) concept, as opposed to the empirical risk minimization (ERM) approach commonly employed within statistical learning methods. SRM minimizes an upper bound on the generalization error rather than ERM which minimizes training data error. It is this difference that equips SVMs with a greater potential to generalize. Moreover, the solutions offered by traditional neural network models may tend to fall into a local optimal solution, whereas a global optimum solution is guaranteed for SVM. SVMs can be applied to both classification and regression problems [33]. 2.2.1. Feature space and kernel functions The basic working principle of SVMs is to map the data in some other dot product space (called the feature space) via non-linear mapping and perform the linear algorithm in the feature space. As the evaluation of a dot product is involved, the feature space is highly dimensional and thus requires great computational resources and time. In some cases, however, a simple kernel can be formulated and its efficiency evaluated. Real-world intricate problems require a more expressive hypothesis space than linear functions, as the available linear learning machines are limited by their computational powers. In other words, the target data cannot be expressed as a simple linear combination of the given attributes. One important property of linear learning machines is that they can be expressed in a dual representation. This means that the hypothesis can be conveyed as a linear

Please cite this article as: A. Jahangirzadeh, et al., A cooperative expert based support vector regression (Co-ESVR) system to determine collar dimensions around bridge pier, Neurocomputing (2014), http://dx.doi.org/10.1016/j.neucom.2014.03.024i

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Minimum value (xmin)

12.66 0.16 0.21 26.25 2

Maximum value (xmax)

14.08 0.2 0.21 32.35 20

4

combination of the training points, so that the decision rule may be evaluated using only the inner products between the test points and training points. If a way of computing the inner product in the feature space directly as a function of the original input points is available, it becomes possible to build a non-linear learning machine known as a direct computation method of a kernel function, denoted by K. Essentially, a kernel function can be defined as a function k, such that for all x,zAX, ð3Þ

There are two basic characteristics of a kernel function, and in Eq. (3) the function must be symmetric, i.e. 0.38 0.08 0 1.93 5.19

Standard derivation (r)

Kðx; zÞ ¼ 〈∅ðxÞ  ∅ðzÞ〉

Kðx; zÞ ¼ 〈∅ðxÞ  ∅ðzÞ〉 ¼ 〈∅ðzÞ  ∅ðxÞ〉 ¼ Kðz; xÞ

ð4Þ

13.44 0.19 0.21 28.98 10.91 Y (cm) V (ms  1) Vc (ms  1) dse (mm) Luc (mm) 12.69 0.16 0.21 18.5 4 13.9 0.2 0.21 25.35 48 13.42 0.19 0.21 9.55 33.24 Y (cm) V (ms  1) Vc (ms  1) dse (mm) Lw (mm)

0.32 0.08 0 9.18 8.71

12.73 0.16 0.21 0 18

Y (cm) V (ms  1) Vc (ms  1) dse (mm) Ldc (mm)

13.43 0.19 0.21 22.27 13.87

0.32 0.08 0 2.86 5.81

13.9 0.2 0.21 28.56 24

Input parameters Minimum value (xmin) Maximum value (xmax) Average value x~ Input parameters Maximum value (xmax) Standard derivation (r) Average value x~ Input parameters

Pier width

Table 1 Statistical properties of scour database in three dimensions.

Minimum value (xmin)

Pier downstream

Standard derivation (r)

Pier upstream

Average value x~

and Eq. (4) must satisfy the Cauchy–Schwartz inequality [34]. Kðx; zÞ2 ¼ 〈∅ðxÞ  ∅ðzÞ〉2 r jj∅ðxÞjj2 jj∅ðzÞjj2

ð5Þ

Although the above equations are necessary, they are not adequate to promise a feature space as defined by the kernel function. Nevertheless, once characterized, kernel representations offer an alternative solution by projecting the data into a high-dimensional feature space to increase the computational power of the linear learning machines. Out of the various kernel functions available for model development, non-linear kernel functions tend to be more efficient in analyzing complex relations between real-world issues and are therefore used in the present work. This study makes use of least squares support vector machine (LS-SVM), a kind of SVM learning approach which consists of the radial basis function (RBF) kernel, to develop a model for determining the optimum dimensions of a rectangular collar. 2.2.2. Radial basis function as kernel The flexibility of SVM is a result of using kernel functions that implicitly map the data to a higher dimensional feature space. A linear solution in the higher dimensional feature space corresponds to a non-linear solution in the original, decreased dimensional input space. This makes SVM a feasible choice for solving a variety of problems in hydrology, which are non-linear in nature. There are methods accessible that use non-linear kernels inside their strategy towards regression problems while applying SVMs. One particular method known as LS-SVM requires using the radial basis function (RBF). The main advantage of LS-SVM is that it is computationally more efficient than the standard SVM method, since the training of (least squares SVM) LS-SVM necessitates only the solution of a set of linear equations instead of the long and computationally demanding quadratic programming problem involved in the standard SVM [35]. In comparison to various other probable kernel features, the RBF is a more compact, supported kernel and in a position to limit the computational training process and enhance the generalization efficiency of LS-SVM, a feature of great value in designing a model. Behzad et al. [36] applied different kernels in SVR to rainfall–runoff modeling and demonstrated that the RBF outperforms other kernel functions. Lin et al. [37] indicated that the centralized feature of the RBF enables it to effectively model the regression process. Also, several works on SVR application in hydrological modeling and forecasting have demonstrated the favorable efficiency of RBF [38–40]. Therefore, RBF with a parameter s, is adopted in this study. 2.2.3. Support vector regression (SVR) ε-Support vector regression (SVR) was introduced as an alternative ε-insensitive loss function [41]. The objective of SVR is to find the function with the most ε deviations from the actual destination vector for all received training information and it must be as flat as possible. The kernel function is identified for the non-linear support vector regression concept. SVR requires fewer established user-defined parameters for setting up kernel-specific parameters [42]. Furthermore, the optimal values of the legalization argument C and size errors in

Please cite this article as: A. Jahangirzadeh, et al., A cooperative expert based support vector regression (Co-ESVR) system to determine collar dimensions around bridge pier, Neurocomputing (2014), http://dx.doi.org/10.1016/j.neucom.2014.03.024i

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sensitive area ε need to be determined. The selection of these settings controls the prediction complexity. One of the biggest advantages of SVR is the algorithm that includes resolution of quadratic programming function, leading to a unique, optimum and comprehensive solution. In this paper, an attempt is made to solve the setback of predicting collar dimensions around a bridge scour using SVR. To do so, we employed multi agent system-based [43] computational intelligence [15] to each dimension. The proposed agents, namely SVR_Luc, SVR_Ldc and SVR_Lw, are responsible for collecting data, utilizing SVR for prediction, and collaborating with master agents to attain high accuracy detection and prediction. The agents are meant to share their knowledge (i.e. predicted data using SVR) through a negotiating mechanism to improve the accuracy of prediction and false alarm rate. p In SVR, fxi ; yi gN i ¼ 1 is considered a training set where xi A K represents a ρ-dimensional input vector and yi A K is a scalar measured output that signifies the system output. The goal is to construct a function y ¼ f ðxÞ which corresponds to the dependence of output yi on input xi . The form of this function is shown in Eq. (6). y ¼ wT φðxÞ þ b

ð6Þ

where w is the weight vector and b is the bias. This regression model can be constructed using a nonlinear mapping function, ϕð UÞ. By mapping the original input data onto a high-dimensional space, the non-linear separable problem becomes linearly separable in space. The function ϕð U Þ ¼ Kp -Kh is a mostly non-linear function that maps the data into a higher, possibly infinite, dimensional feature space. The major difference from the standard SVM is that LS-SVM involves equality constraints in place of inequality constraints, and works with a least squares cost function. The optimization problem and equality constraints are defined by Eq. (7) 1 1 N min Jðw; eÞ ¼ wT w þ γ ∑ e2i 2 2i¼1

ð7Þ

Subject to Eq. (8). yi ¼ wT ∅ðxi Þ þ b þ ei ;

i ¼ 1; …; N

ð8Þ þ

where ei is the random error and y A K is a regularization parameter in optimizing the trade-off between minimizing the training errors as well as the model's complexity. The objective is now to find the optimal parameters that minimize the prediction error of the regression model. The optimal model will be chosen by minimizing the cost function where the errors ei are minimized. This formulation corresponds to the regression in the feature space, and since the dimension of the feature space is high, possibly infinite, this problem is difficult to solve. Therefore, to solve this optimization problem, the following Lagrange function is given (Eq. (9)) N

Lðw; b; e; αÞ ¼ Jðw; eÞ  ∑ αi fwT ∅ðxi Þ þ b þei  yi g

ð9Þ

i¼1

The solution to Eq. (9) can be obtained by partially differentiating with respect to w; b; e; α; (i.e. Eqs. (10)–(13)). N ∂L ¼ 0-w ¼ ∑ αi ∅ðxi Þ ∂w i¼1

ð10Þ

N ∂L ¼ 0-b ¼ ∑ αi ¼ 0 ∂b i¼1

ð11Þ

∂L ¼ 0-αi ¼ γei ; ∂ei

ð12Þ

i ¼ 1; …; N

∂L ¼ 0-wT ∅ðxi Þ þ b þ ei  yi ¼ 0; ∂xi

i ¼ 1; …; N

ð13Þ

5 ^

Finally, the estimated values of b and α1, i.e. b and α^i , can be obtained by solving the linear system and the resulting LS-SVM model can be expressed as Eq. (14). N

^

y ¼ f ðxÞ ¼ ∑ α^i Kðx; xi Þ þ b

ð14Þ

i¼1

where K(x,xi) is a kernel function. Here, the non-linear RBF kernel is defined in Eq. (15).   
 1  ð15Þ Kðx; xi Þ ¼ exp  2 x  xi j2

s

where s is the kernel function parameter of the RBF kernel. The regularization parameter γ is also necessary in the LS-SVM model and it determines the trade-off between the fitting error minimization and smoothness of the estimated function. It is not known beforehand which γ and s are the best for a particular application problem to achieve maximum performance with LS-SVM models. Thus, the regularization parameter γ and the value of s from the kernel function must be tuned during model calibration. In this work, a grid-search technique is used for tuning these two parameters, by applying cross-validation on the training set to identify the optimal parameter values. The LS-SVM model thus obtained serves to estimate the desired output that is finally employed to predict the optimum dimensions for a rectangular collar in order to minimize the temporal trend of scouring around a pier model. 2.3. Multi agent-based computational intelligence (MCI) The intelligent agent technique has found use in domains ranging from itinerary arrangement to information retrieval. Its application can reduce work load and allow the user to assign a specific task to the agent or collaborate with the agent to reach a common objective [44]. The multi-agent system corresponds with the cooperative agents to negotiate during communication. multi agent system-based computational intelligence [15], or MCI techniques, enhance detection and response performance [45]. The principal objective of MCI consists of distributing agents to each cluster to provide a computational intelligence (CI) mechanism that makes individual and cooperative decisions [46]. Multi agent system has been employed in the domain of bridge disaster prevention [47]. The non-cooperative multi agent system (MAS) adapts to monitor bridge disaster prevention to improve detection accuracy, but the complexity of detection causes a lack of such integration and delays alert notification from being disseminated to relevant administrative agencies in a timely manner, thus stalling necessary decision making and magnifying the disaster. To overcome the detection complexity, the cognitive sensors in terms of anomaly detection agents are proposed in two phases: which local agents support vector machines in the training mode and which use mobile agents in the decision mode to classify suspicious behavior [48]. Some methods suggest a multi-agent system where each local agent collects data through a mobile agent [49]. The local agent then examines the integrity of the system with an SVM classifier at the corresponding time an attacker enters the system. Also, in communication mode the mobile agent verifies the activity; if there is no suspicious activity, the message is forwarded to a neighboring node. The decision-making component of detection is based on the Bayes theory, whereby if the probability of normal activity is smaller than the assumed abnormality threshold, the current activity is categorized as abnormal [50]. To determine optimal fault detection, Shamshirband et al. [51] proposed cooperative-based computational intelligence. A data exchange platform serves to integrate and exchange data between distributed systems using software agent techniques designed to exchange data automatically. Agents become active at the onset of a disaster event and compile data from various resources to report on the current state of bridges. Also, action recommendations

Please cite this article as: A. Jahangirzadeh, et al., A cooperative expert based support vector regression (Co-ESVR) system to determine collar dimensions around bridge pier, Neurocomputing (2014), http://dx.doi.org/10.1016/j.neucom.2014.03.024i

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delivered by the system can assist bridge managers make appropriate decisions. The cooperative multi agent based computational intelligence method proposed [51] has motivated us to utilize the support vector regression-based learning to determine the optimal collar dimensions around a bridge pier.

3. System model: Cooperative expert-based support vector regression (Co-ESVR) The designed architecture is called Cooperative Expert-based Support Vector Regression system (Co-ESVR), and it predicts the collar dimensions around a bridge scour. In the first layer of the proposed Co-ESVR architecture, Expert System (ES) agents proceed to audit bridge scour records. In the ES scheme, data collector agents included for each rectangular collar subsystem collect the values of features, after which a normal profile is created with the defined rules and the desired scenario is produced in the expert system. The gain of the first phase is normal labeled data, which then sends the new dataset to the next layer. In the second phase, the support vector regression begins

to process data with the test and train the data. To do this, each SVR agent (i.e. SVRLuc, SVRLdc and SVRLw) creates the prediction model to audit data, resulting in collar dimensions and detection precision. The gain of phase two can be stored in the dataset for final decision making by multi-agent systems. Finally, E-SVR uses a cooperative algorithm to provide a negotiation mechanism for improving the accuracy of collar dimension precision and decreasing the learning processing time of prediction. Fig. 4 depicts the architecture of Cooperative Expert Support Vector Regression (Co-ESVR). In the paradigm of Cooperative Expert-based Support Vector Regression (Co-EVSR) prediction systems, we employed multi-agents for different collars (i.e. upper stream agent, downstream agent, and width agent) to predict the collar dimensions around a bridge scour. Every dimension in the rectangular collar system has agents installed in it. By having an agent platform installed in each dimension, installation and running of local agents in every dimension of the rectangular collar system are feasible.

 Expert system (ES) policy uses an expert-based decision tree to decrease the redundant bridge dataset samples for processing.

Phase 1: Data collection & preprocessing-Fuzzy Expert System Expert System

Bridge database Collection information

Preprocessing Data

Normal labeled Data

Decision Support

Phase 2: Data Prediction – Support Vector Regression (Local integration)

Gaining collar dimensions by SVM detection model

Creating SVM prediction model

Feature extraction

Data acquisition

Gaining detection precision

Creating testing samples

SVR-Upstream agent

SVR-Downstream SVR-Downstream agent agent

Creating Training Samples

SVR-with SVR-with agent agent

Phase 3: Data Prediction –Cooperative Support Vector regression (Global integration) Evaluate expertness

RMSE

Evaluate Cost Function Weight Strategy Optimization

Fig. 4. Architecture of cooperative expert-based support vector machine (Co-ESVR).

Please cite this article as: A. Jahangirzadeh, et al., A cooperative expert based support vector regression (Co-ESVR) system to determine collar dimensions around bridge pier, Neurocomputing (2014), http://dx.doi.org/10.1016/j.neucom.2014.03.024i

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The output of this phase is to create normalized labeled bridge data. Support vector regression (SVR) policy creates a prediction model for auditing data, resulting in collar dimension and detection precision. To do this, SVR agents (i.e. SVRLuc, SVRLdc and SVRLw) are installed in each collar dimension. Cooperative-ESVR (Co-ESVR) policy aims to synchronize the negotiation policy in communication sensors by utilizing the measurement in multiple expert based support vector regressions (ESVRs). In this scheme, agents apply an appropriate cooperative mechanism to improve precision accuracy and the best cost function.

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Consequently, some type of model parameter calibration should be produced. To solve the problem of choosing parameters in SVM, the RBF and poly based support vector regression adjust their kernel specific parameters, optimum values of the regularization parameter C and the size of the error-insensitive zone e. A default value of e¼0.1 seemed to work well. In our scheme, three agents that make use of SVR in three different collar dimensions were applied. These types of agents consist of an SVR agent installed upstream (SVRLuc), an SVR agent installed downstream (SVRLdc), and an SVR agent installed at the width (SVRLw). The task details of each agent are described as:

 Data acquisition is responsible for processing the normal 3.1. Expert system for data collection and preprocessing An expert-based decision tree was applied to the collector agent and preprocessing agent components. Fig. 5 shows the component details of the proposed multi agent-based expert detection system architecture.

 Data collector agent gathers bridge records and prepares the  

base information for the preprocessing agents. Data preprocessing agent automatically filters content collected by the data collection agent and selects desired content based on certain rules. The inference engine and knowledge base: The knowledge base stores the rules used by the inference engine to obtain new facts. The gain of the proposed ES is to classify the dataset in three dimensions: upstream, downstream and width.

   

labeled data received from the first phase and converting the resulting samples into numeric values that can be manipulated by an SVR. Feature extraction has the task of extracting features based on the target model in the training and testing modules. In other words, the training and testing data is formed in this component. Creating an SVR prediction model is responsible for creating the target model by adjusting SVR parameters. Prediction of collar dimensions predicts the different collar dimensions based on the SVR agents. Detection precision evaluates the prediction accuracy in each collar dimension based on the SVR agents.

The prediction process by a multi agent-based SVM is shown in Fig. 6.

3.3. Cooperative-ESVR (Co-ESVR) policy 3.2. Multi agent-based support vector regression for prediction A kernel function can be utilized to form a qualified function used by SVM. Guo et al. [52] pointed out that SVM demonstrates high performance in prediction accuracy for stream flow. As such, SVM has the advantage that it can handle classes with complex nonlinear decision boundaries. Furthermore, researchers have demonstrated how SVR helps predict hydrological modeling and they pointed out the positive RBF (radial basis function) performance [53,54]. Asefa et al. [55] proposed different kernels in SVR for rainfall–runoff modeling and confirmed that the radial basis function (RBF) outperforms other kernel functions. Hence, the RBF is applied as the kernel function for predicting discharge in this research study. Three parameters associated with RBF kernels are C, e and r. SVM model accuracy largely depends on model parameter selection. However, structured parameter selection methods are still lacking.

Studies on the impacts of Multi-Criteria Expertness (MCE) based cooperative Q-learning have been presented [51] to improve the cooperative learning process in a detection procedure. This shared information conducts episodes (state, action, and reward), sensation (state), and policies. The aim of this segment is to contribute the following question: “How can an Expert Support Vector Regression (ESVR) agent benefit from exchanging information during the learning process, in order to improve the correct rate of the prediction system?” In the current research work, the cooperative policy evaluates the proficiency of an agent in optimizing the cost function based on weight strategy sharing incorporating the expertness and weight assignment mechanisms for real-time collar dimension prediction. These two mechanisms result as modules employed in Co-ESVR architecture and system implementation to accelerate the learning process.

Expert System Query User Interface

Inference Engine

System Output: The features in three dimensions Preprocessing agent

Knowledge Base

(Rules)

Collector agent

Luc Ldc Lw Bridge Dataset Fig. 5. The architecture of the proposed expert system.

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iterations. Basically, the criterion of agent expertness is calculated for collar dimension prediction. The objective is to evaluate the agent's proficiency measures during collar dimension prediction. The expertness value for each agent in terms of (RMSE per 10 iterations) can be used in the weight assignment mechanism. The RMSE will be applied to the sharing strategy using a weight assignment mechanism.

3.3.1. Expertness criteria The agent's expertness (ei) is evaluated based on the average of Root Mean Square Error (RMSE) received per iteration (Eq. (16)). ∑jRMSEj N

ð16Þ

where the average RMSE value is divided by the number of total

Agent 2

Agent 3

SVR_Ldc

SVR_Lw

Data acquisition

Data acquisition

Data acquisition

Feature extraction

Feature extraction

Feature extraction

Creating Sample

Creating Sample

Creating sample

Agent 1 SVR_Luc

Detection Precision

Creating SVR upstream model

Training

Creating SVR downstream model

Gain

Gain

Predict Upstream Collar dimensions

Testing

Detection Precision

Testing

Training

Testing

Creating SVR width model

Gain

Gain

Gain

Gain

Predict Width Collar dimensions

Predict Downstream Collar dimensions

Report the results from SVR Upstream Agent

Training

Detection Precision

ðexpertnessÞ ¼ ei ¼

Report the results from SVR Width Agent

Report the results from SVR Downstream Agent

Fig. 6. The process of prediction by non-cooperative SVM agents.

D Pier Collar

Y

ei

w id th

downstream

upstream U

s

Water surface

ej

Agent E-SVR Upstream

ek

Agent E-SVR Upstream

Agent E-SVR Downstream

dse

Wij Wjk Wik Fig. 7. The weight assignment for homogeneous agents around a circular pier with a rectangular collar.

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3.3.2. Weight assignment mechanism This mechanism utilizes the RMSE received from each E-SVR agent to assign a suitable weight to corresponding agents (Eq. (17)). 8 > > > <

1  αi; ej  ei Wij ¼ αi∑n ðej  eiÞ ; > j¼1 > > : 0;

ei ¼ ej ej 4 ei

9

The procedure of negotiating between agents reiterates until the weighted strategy is finished, upon which the agent looks up table values or the agent's knowledge is modified as in Eq. (18) to update their knowledge to predict the reduction of scour depth percentage. Cost function ðQ new Þ ¼ ð1  αiÞ  Q new þ αi i i

ð17Þ

otherwise

where 0 o αi o 1 is the impressibility factor that depicts how an E-SVR agent depends on others’ knowledge. For instance, when the proficiency measure of agent i is less than that of agent j, its weight is relative to the amount of expertness difference between agent j and agent i divided by the sum of the other experts’ differences [56]. Fig. 7 depicts the weight assignment strategy for the ESVR agents. In this case, ESVRi evaluates the expertness of ESVRj and then assigns a weight based on Eq. (17).



∑

ðWij  Q old Þ i

ð18Þ

j A ExpertðiÞ

where Q old is the previous knowledge of each agent to maintain its i RMSE, and 0 r αir 1 is the impressibility factor that shows to what extent agent i relies on the others’ knowledge. The cost function value corresponds to the accuracy of precision in reducing the scour depth percentage. The main advantage of the proposed method is that the Cooperative based SVR not only mitigates high computational complexity such as time consumption and updating knowledge, but also enhances detection and prediction performance. 3.4. Performance metrics

Table 2 Performance criteria. Criteria Root mean squared error (RMSE) Correlation coefficient (R) Accuracy (A)

Calculation sffiffiffiffiffiffi 1 Nt ∑ ðd  yi Þ2 (19) NT i ¼ 1 i   ∑di yi  ∑di yi =N R ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ð∑di  ð∑di Þ2 =NÞ=ð∑y2i  ð∑yi Þ2 =NÞ (20)
 jva  vp j 1 n  100% Accuracy ¼ ∑ 1 (21) ni¼1 va RMSE ¼

where n is the total number of test data, di is the experimental value and yi is the forecast value. 2/3 of the dataset was used for training and 1/3 for proposed model validation.

To evaluate the performance of the Co-ESVM model several measures were employed. The root mean squared error (RMSE) served to evaluate the differences between the expected and actual values. Meanwhile, the predictive accuracy (A) was calculated to determine the correctness of the forecast models and coefficient of (R). The parameters were calculated based on Eqs. (19)–(21), as indicated in Table 2.

4. Results and discussion In the experiments, rectangular collars were employed in order to estimate the most effective upstream collar length (Luc), downstream

Fig. 8. (a) Bridge pier model and fitted collar in hydraulics laboratory, (b) scouring around experimental bridge pier and (c) controlling scour due to collar installation on the pier.

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Table 3 User-defined parameters for agent-based SVR. Support Vector regression Agent SVR_Luc

Agent SVR_Ldc

SVR_rbf

SVR_poly

Agent SVR_Lw

SVR_rbf

SVR_poly

SVR_rbf

SVR_poly

C

γ

e

C

d

e

C

γ

e

C

d

e

C

γ

e

C

d

e

1

0.5

0.1

0.25

2

0.1

1

0.5

0.1

0.25

2

0.1

1

0.5

0.1

0.25

2

0.1

Fig. 9. Plot of observed and predicted equilibrium scour depth with the original data set using SVR_rbf and SVR_poly model during training and testing. (a) Performance of SVR-rbf and SVR_poly on the upstream collar case in training phase, (b) Performance of SVR-rbf and SVR_poly on the downstream collar case in training phase, (c) Performance of SVR-rbf and SVR_poly on the width collar case in training phase, (d) Performance of SVR-rbf and SVR_poly on the upstream collar case in testing phase, (e) Performance of SVR-rbf and SVR_poly on the downstream collar case in testing phase and (f) Performance of SVR-rbf and SVR_poly on the width collar case in testing phase.

collar length (Ldc), and width collar length (Lw) (Fig. 8a). In this empirical study, three series of experiments to optimize three mentioned dimensions ðLuc ; Ldc and Lw Þ were conducted. In each experiment series 10 experiments were done. Fig. 8b shows the scouring around bridge pier in laboratory. Fig. 8c shows one of the installed collars in flume which could control scour around bridge pier. The results obtained from 30 tests indicate that the upstream (Luc/D) and downstream (Ldc/D) optimum proportions were estimated at 0.86 and 1.42, respectively. Moreover, the optimum collar width was estimated to be 2.8 times of the pier's diameter. In the computational phase, RBF was applied as the kernel function for discharge prediction in this study. The three parameters associated with RBF kernels are C, e and r. SVM model accuracy is principally dependent on model parameter selection. In our scheme, a default value of e¼0.1 seemed to perform well. To select user-defined parameters (i.e. C, d and g), a large number of trials were carried out with different combinations of C and d for polynomial kernels and C

Table 4 Performance indices of various approaches. Dimension

Upstream

Method

Training

Testing

Error Coefficient of (RMSE) determination (R2)

Error Coefficient of (RMSE) determination (R2)

SVR_rbf 3.580 SVR_poly 2.892 Downstream SVR_rbf 3.012 SVR_poly 2.907 Width SVR_rbf 12.945 SVR_poly 6.498

0.422 0.750 0.696 0.687 0.982 0.802

5.254 2.912 3.203 3.021 13.587 7.254

0.441 0.758 0.721 0.698 0.91 0.836

and g for radial basis function kernels. Table 3 provides the optimal values of user-defined parameters for this dataset with polynomial and RBF kernel-based SVR. For reasonable appraisal of outcomes with

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set of 200. Fig. 10 compares equilibrium scour depth values estimated using the Co-ESVR model and the non-cooperative SVR_poly method. The proposed method enhances scour depth prediction. For the best existing method (Cooperative SVR adopted in Ldc) RMSE¼0.805 compared to RMSE¼ 1.168 for the non-cooperative SVR agent adopted in the Ldc model. 5. Conclusions

Fig. 10. Convergence of cooperative and non-cooperative SVR_poly in terms of RMSE.

both RBF and polynomial kernels, a similar parameter e value was applied with SVR. 4.1. Equilibrium scour depth prediction using the non-cooperative SVR The initial, original data helped establish the polynomial and RBF kernel-based SVR. The data was essentially predicted using SVR agent-based RBF and polynomial, in three collar dimensions separately. The results of R2 and RMSE of the SVR_Luc, SVR_Ldc and SVR_Lw models are presented in Fig. 8 in terms of training and testing. The SVR_rbf and SVR_poly models in the upstream collar dimension had very small RMSE (ranging from 6.821 to 6.868) during validation and the value was slightly higher (between 8.821 and 12.626 m). The models showed consistently good correlation throughout training and testing. To evaluate SVR model performance, observed equilibrium scour depth values were plotted against the predicted ones. Due to the small sample size, the dataset was split into training and testing (80/20 as a fair split). Fig. 8a–c illustrate the results with the performance indices between predicted and observed data in the training phase, while Fig. 8d–f indicate the results for the testing phase, respectively. Although the performance of SVR_rbf and SVR_poly on the width collar case in the testing phase is not on a par with other sides, due to the small number of samples (training data), the optimal kernel function type of SVR is poly in the width collar case dataset. Generally speaking, as seen from Fig. 9, SVR poly performed well in predicting equilibrium scour depth. Comparing SVR_poly results with SVR_rbf reveals that SVR_poly outperforms the RBF model in terms of prediction accuracy. 4.2. Performance analysis To evaluate the performance of the proposed Co-ESVR method, experiments were conducted to determine the relative significance of each independent parameter (input SVR) on the scour depth (output). The root mean squared error (RMSE) and correlation coefficient (R) served to evaluate the differences between the expected and actual values for single SVR and cooperative SVR. Table 4 compares the single SVR_rbf, SVR_poly models with the cooperative SVR. The results in Table 4 indicate that the SVR_poly has the most significant effect on equilibrium scour depth for various collar dimensions. For instance, RMSE¼2.892 in the training phase for SVR_poly upstream is less than RMSE¼3.580 for SVR_rbf. To assess the accuracy of Co-ESVR models in predicting scour depth, a comparison between the proposed Co-ESVR models and non-cooperative SVR was undertaken using the same observed data

In this paper, the application of two multi agent-based support vector regression types, namely Polynomial-based (SVR_Poly) and RBFbased SVR (SVR_rbf), in the estimation of equilibrium and time-dependent scour depth around piers has been outlined. The study includes the manipulation of collected laboratory data to train and validate the networks. It was shown that the agent-based SVR_poly approaches predict scour depth much more accurately than the agent-based SVR_rbf methods in different dimensions. The multi agent-based SVR prediction model adjusts its parameters to find the optimal cost function in predicting the collar dimension around the bridge scour to reduce the collar. The efficacy of the proposed optimization method (Co-ESVM) was compared with a conventional approach using data generated from the hydraulic laboratory at University of Malaya. Numerical results indicate that the Co-ESVR achieves better accuracy in terms of scour depth (re) percentage reduction with a smaller network size, compared to the non-cooperative approaches. Hence, in contrast to the non-cooperative approach, the Co-ESVR is the recommended model for the scouring phenomenon around a rectangular collar installed on a bridge pier. To broaden the results, further works remain to be done on different scales and under different hydraulic conditions to generalize the application results.

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Afshin Jahangirzadeh obtained his M.Sc. in civil engineering-Hydraulic from faculty of Civil and Environmental Engineering of Amirkabir University of Technology, Iran. He started his career as a civil Engineer at Mahab Ghodss consulting company from 2005 to 2007. He also has work as a University lecturer in Azad University of Tonakabon, Iran form 2007 to 2011. Currently, he is his PhD Candidate and research assistant on civil engineeringhydraulic structure in University of Malaya, Malaysia. His main research covers hydraulic structure, Hydraulic, Bridge engineering, River Engineering and Scour Phenomenon.

Shahaboddin Shamshirband received his M.Sc. degree in Computer Science from Islamic Azad University of Mashhad (IAUM), Iran in 2006. He joined the Faculty of Computer Science, Islamic Azad University, Iran for seven years. Currently, he is pursuing his PhD in University of Malaya, Malaysia. His main research covers networking, security, computational intelligence, and cloud computing.

Saeed Aghabozorgi received his B.Sc. in Computer Engineering and Software Discipline from University of Isfahan, Iran, in 2002. He received his M.Sc. from Islamic Azad University, Iran, in 2005, and his Ph.D. from University of Malaya in 2013. Currently, he is a lecturer at the Department of Information System, Faculty of Computer Science and Information Technology, University of Malaya, Kuala Lumpur, Malaysia. His current research area is data mining.

Shatirah M Akib received her M.Sc. in Civil Engineering from University of Wales, Cardiff, United Kingdom, in 2003 and her Ph.D. in Hydraulic Structure Engineering from University of Malaya, Malaysia in 2009. Currently, she is a Senior lecturer at the Department of Civil Engineering, Faculty of Engineering, University of Malaya, Kuala Lumpur, Malaysia. Her current research areas are Hydrology and Hydraulic Engineering, Water Resources and Coastal and Offshore Engineering.

Hossein Basser received his B.Sc. in Civil Engineering from University of Tabriz, Iran, in 2008. He received his M.Sc. from Amirkabir University of Technology, Iran, in 2011. Currently, he is pursuing his Ph.D. in University of Malaya, Malaysia. His main research covers Sediment transport, Scour countermeasures, Computational Fluid Dynamics, Flow pattern and Scour and Flow Monitoring.

Please cite this article as: A. Jahangirzadeh, et al., A cooperative expert based support vector regression (Co-ESVR) system to determine collar dimensions around bridge pier, Neurocomputing (2014), http://dx.doi.org/10.1016/j.neucom.2014.03.024i

A. Jahangirzadeh et al. / Neurocomputing ∎ (∎∎∎∎) ∎∎∎–∎∎∎ Nor Badrul Anuar obtained his Ph.D. in Information Security from Centre for Security, Communications and Network Research (CSCAN), Plymouth University, UK in 2012 and Master of Computer Science from University of Malaya, Malaysia in 2003. He is a senior lecturer at the Faculty of Computer Science and Information Technology in University of Malaya, Kuala Lumpur. He has published a number of conference and journal papers locally and internationally. His research interests include information security (i.e. intrusion detection systems), artificial intelligence and library information systems.

13 M.L. Mat Kiah received her M.Sc. in 1998 and PhD in 2007 from Royal Holloway, University of London, UK. She joined the Faculty of Computer Science & Information Technology, UM as a tutor in 1997. Her current research interests include key management, secure group communication and wireless mobile security. She is also interested in routing protocols and mobile Ad-Hoc networks. She has published 30 papers and authored books.

Please cite this article as: A. Jahangirzadeh, et al., A cooperative expert based support vector regression (Co-ESVR) system to determine collar dimensions around bridge pier, Neurocomputing (2014), http://dx.doi.org/10.1016/j.neucom.2014.03.024i