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Applied Soft Computing 30 (2015) 642–649

Contents lists available at ScienceDirect

Applied Soft Computing

j ourna l ho me page: www.elsev ier .com/ locate /asoc

ybrid ANFIS–PSO approach for predicting optimum parameters of arotective spur dike

ossein Bassera,∗, Hojat Karamib, Shahaboddin Shamshirbandc,∗, Shatirah Akiba,ohsen Amirmojahedia, Rodina Ahmadd, Afshin Jahangirzadeha, Hossein Javidniae

Department of Civil Engineering, University of Malaya, 50603 Kuala Lumpur, MalaysiaDepartment of Civil Engineering, Semnan University, Semnan, IranDepartment of Computer System and Information Technology, Faculty of Computer Science and Information Technology, University of Malaya, 50603uala Lumpur, MalaysiaDepartment of Software Engineering, Faculty of Computer Science and Information Technology, University of Malaya, 50603 Kuala Lumpur, MalaysiaElectrical and Electronic Engineering, Department of Engineering and Informatics, NUI, Galway, Ireland

r t i c l e i n f o

rticle history:eceived 16 February 2014eceived in revised form0 December 2014ccepted 2 February 2015

a b s t r a c t

In this study a new approach was proposed to determine optimum parameters of a protective spur diketo mitigate scouring depth amount around existing main spur dikes. The studied parameters were angleof the protective spur dike relative to the flume wall, its length, and its distance from the main spurdikes, flow intensity, and the diameters of the sediment particles that were explored to find the optimumamounts. In prediction phase, a novel hybrid approach was developed, combining adaptive-network-

vailable online 16 February 2015

eywords:courwarm optimizationrediction

based fuzzy inference system and particle swarm optimization (ANFIS–PSO) to predict protective spurdike’s parameters in order to control scouring around a series of spur dikes. The results indicated that theaccuracy 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.

© 2015 Elsevier B.V. All rights reserved.

euro-fuzzy

. Introduction

Spur dikes are hydraulic structures that are constructed for protecting canalsnd rivers against scour and erosion. Spur dikes are generally chosen to be built inroups and they may be constructed at a specified angle relative to the bank. Thesetructures lead to a considerable reduction of the flow velocity near banks, creatingn area in the water in which there is less motion, which influences deposition,esulting in a reduction in the width thereby creating a defined channel.

Constructing spur dikes against approaching flow stream, results in hydrostaticressure’s change upstream and downstream of the structure, and this causes aomplicated vortex area. These complicated vortex areas, which produce large vor-ices at the head of the spur dikes, provide the principle local scour mechanism. The

entioned local scour may jeopardize the safety of the structure and eventuallyead structural failure [1–3]. Fig. 1 illustrates a two dimensional view of the flowharacteristics and scour pattern around a spur dike.

For the reasons described above, the local scour around spur dikes has been onef the fundamental concerns of researchers for years. The scour hole around spurikes can be destructive at times, so developing a method to reduce the amount of

cour around the spur dikes has become an important and persistent challenge forcientists [2–10].

Generally, the techniques used by researchers to reduce scour depth around spurikes, are divided into two main groups, i.e., direct and indirect methods. In the direct

∗ Corresponding author. Tel.: +60 12 9247099.E-mail addresses: hosseinbasser@gmail.com (H. Basser),

hamshirband@um.edu.my (S. Shamshirband).

ttp://dx.doi.org/10.1016/j.asoc.2015.02.011568-4946/© 2015 Elsevier B.V. All rights reserved.

method, the structures are protected directly against flow attack by usually usingconstruction materials, i.e., revetments and riprap placed on spill slopes to resisterosion. In the indirect method, the flow pattern is modified by using a number ofspecial structures, such as a protective spur dike, a guide bank, or a collar, whichcause local scour to decrease [11].

Using a protective spur dike as an indirect method has been considered recently.Since spur dikes are commonly built consecutively, the spur dike that is the farthestupstream (henceforth called ‘the first spur dike’) should be built stronger becauseit will be subjected to the most destructive influence of flow [12]. Therefore, anyattempt to reduce local scour depth around the first spur dike is crucial. The useof a protective spur dike upstream from a set of parallel spur dikes changes thedirection of flow and lead to considerable reduction in scour depth around the mainspur dikes, especially the first spur dike, which is directly subjected to the flow as itapproaches.

Since the protective spur dike is often shorter than the main spur dikes, it is notexposed to significant scour. The main parameters of a protective spur dike that havesignificant effects on the scour pattern around the main spur dikes are its length,its distance from the protected spur dikes and its angle with respect to the bank[2,13].

Recently, new approaches working based on artificial intelligence have takenserious consideration of researchers. The effectiveness and accuracy of availablemethods related to artificial intelligence is challenging task which needs moredata collection and simulations. Going through the available literature proves that

improving forecasting accuracy and reducing the uncertainty rate requires novelmethods. This is not an exception for predicting the optimum parameters of a pro-tective spur dike using for scour mitigation around a series of spur dikes. In thisstudy, a new hybrid approach is proposed to predict the optimum parameters of aprotective spur dike.

H. Basser et al. / Applied Soft Computing 30 (2015) 642–649 643

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ig. 1. Schematic view of flow characteristics and scour pattern around a spur dike3].

In this approach, the particle swarm optimization (PSO) is combined withdaptive-network-based fuzzy inference system (ANFIS). In continue, the proposedethod is compared with other soft computing hybrid approaches like, ANFIS–ACO

ANFIS–ant colony computation), ANFIS–DE (ANFIS–differential evolutionary) andupport vector regression (SVR) [14–16] to describe its predicting accuracy, effec-iveness, and computation time.

Reviewing the literature surveys shows that other soft computing methods, e.g.,rtificial neural networks have been used to predict scouring depth [17–20]. Thesetudies’ explorations showed that using the neural network approach may result inetter outcomes than empirical relations [21].

Algorithms using neural network models always need applying learning param-ters such as learning rater, optimum number of nodes in the hidden layer, andumbers of hidden layers.

The neural network-based models and their capability of prediction may beffected by high numbers of training iterations and leads the model to over-train.

The presence of local minima is another problem when using a back-propagationeural network. Recent studies propose usefulness of neuro-fuzzy, in finding aeural network’s optimal architecture to maintain the maximal output power ofredicting optimum parameters in simulations [22]. Akib et al. [23] used adap-ive network-based fuzzy inference system (ANFIS) as a modeling tool to predictcouring depth in bridges. The results from ANFIS were compared with the classicalinear regression (LR). ANFIS’s results were highly accurate, precise, and satisfactory.lso Keshavarzi et al. [24], used a neuro-fuzzy model to predict scouring around anrch-shaped bed sill, and their results showed well reliability.

. Experiments and approaches

All experiments were conducted in the Porous Media Labo-atory, Amirkabir University of Technology in, Tehran, Iran. Theume section was rectangular with 14 m length, 1 m width, and

m depth. The bed and the sides of the flume were built usinglass material. A metal frame was used to support the glass flume.hree spur dikes made of Plexiglas were installed in the flume, andhey were, 25 cm long (Lf = 25 cm), impermeable, non-submerged,nd perpendicular to the flow alignment. The installation locationf the first spur dike was 6.16 m in distance with the entrance of theume. The spaces between the spur dikes were twice their length2Lf = 50 cm). These values were chosen according to the recom-

endations of Zhang [26] and Gissoni et al. [25]. In order to collectransported sediments, a small tank was installed at the down-tream end of the flume. The discharge of flow was regulated by annlet valve. A rectangular weir was placed in the flume to measurehe discharged water. The approach flow depth (Y) was adjusted as5 cm in all experiments. The flume bed was filled using uniform

ed sediments (�g < 1.4), with a thickness of 0.35 m, and specificravity (Ss) of 2.65, and geometric standard deviation (�g) of 1.38.n this study three different sizes of diameters were used to investi-ate the effect of changing the diameter. The discharge was changed

able 1haracteristics of the parameters used in experiments.

U/Ucr D50 � (deg)

0.65, 0.75, 0.85, 0.95 0.5, 0.91, 2.0 45, 90, 13

Fig. 2. Schematic diagram of the geometric parameters used in the experiments.

to change the flow velocity (U) in order to achieve different amountsof flow intensity (U/Ucr).

Protective spur dike with different lengths, angles and distanceswith the first spur dike also were installing upstream of the mainspur dikes. Fig. 2 shows the parameters of the protective spur dikes.

Table 1 provides the value of the variables in the experiments.Bed profile variations around the spur dikes for all tests were

scanned using a laser bed profiler (LBP). The accuracy of the LBP was±1 mm in channel’s width and ±0.1 mm in its depth. The experi-mental phase included two levels with 84 experiments. In the firstphase, the experiments were conducted with no protective spurdike, and, in the second phase, the experiments were conductedusing a protective spur dike to evaluate the extent of the protec-tion against scouring it provided for the main spur dikes. Fig. 3illustrates plan view of the flume, protective spur dike, and mainspur dikes in the laboratory. In this figure, a 90◦ protective spurdike is displayed.

2.1. Input parameters

Since in some spur dikes, the first spur dike is mostly exposedto failure [3], in this study the protective effect of the experimentalprotective spur dike on reducing scour around the first spur dike isinvestigated. The efficiency of a protective spur dike and its effect onthe amount of scour reduction at the first spur dike mostly dependson channel geometry (width, and bed slop), the first spur dike’sproperties (length, shape, angle, space between them), character-istics of the bed sediment (size of the sediment particles, thresholdmovement of the particles), flow conditions (density, water level,and velocity), and the protective spur dike properties (length, angle,and its distance with the first spur dike). Therefore, the most impor-tant parameters of scour reduction around the first spur dike canbe written as follows:

RSD1 = f (B, S0, Ssh, Lf, D50, Ucr, �, Y, U, Lp, Xp, g) (1)

where B stands for width of channel, S0 is the bed slope, Lf is thelength of first spur dike, Lp is the protective spur dike length, SSh isthe symbol of shape of first spur dike, � is the angle between protec-tive spur dike and flow direction, Xp is the space between the firstand protective spur dike, Y is the water flow depth, U is the velocity

of approaching flow, Ucr is the critical velocity for incipient motionfor bed sediment movement, D50 is the median grain size, � is thedensity of fluid, � is the viscosity of fluid and g is the gravitationalacceleration.

Lp/Lf (mm) X/Lf (mm)

5 50, 100, 150, 200 250, 375, 500, 625

644 H. Basser et al. / Applied Soft Computing 30 (2015) 642–649

erime

Ssi

R

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wcsTd

2

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ig

2

Epmab

mr

TS

Fig. 3. Schematic view of exp

After neglecting the constant parameters in experiments (B, S0,sh, Y, �, g) and dimensional analysis, Eq. (2) was achieved. Eq. (2)hows the most influential parameters of the protective spur diken terms of reducing scour depth around the first spur dike:

SD1(%) = f(

Lp

Lf,

Xp

Lf, �,

U

Ucr, Fd

)(2)

here RSD1(%) = reduction percentage of scour at the first spur dike;p = actual length of the protective spur dike; Lf = actual length of theain spur dikes; Xp = distance between the protective spur dike and

he first spur dike; � = angle between protective spur dike and flowirection; U/Ucr = flow intensity; Fd = densimetric Froude numberFd = U/

√�gD50).

According to the experiments, the above mentioned parametersere assigned as input parameters for the learning process. In the

omputations, 70% of the experimental data was used to train theamples and the other 30% utilized to verify the samples’ accuracy.able 2 provides the statistical properties of the protective spurikes’ parameters.

.2. Proposed approach

In this study, an approach benefitting from combination ofdaptive-network-based fuzzy inference system (ANFIS) and parti-le swarm optimization (PSO) is proposed to predict the optimumarameters of a protective spur dike [27,28]. In this approach, theSO is applied to enhance the performance of ANFIS by tuning theembership functions and subsequently minimize the error.The ANFIS forecasts permits reconstructing of the future behav-

or of the flexure strengths of the bricks and therefore to predictround stability.

.2.1. Particle swarm optimization (PSO)PSO, as an initiated method, was proposed by Kennedy and

berhart [29]. This method is considered as an evolutionary com-utational method optimizing continues and discontinues decisionaking functions. Furthermore, PSO algorithm may be considered

s biological and sociological behavior of animals. e.g., flocks of

irds looking for their food [30].

Additionally, PSO is considered as a population-based searchethod where each potential solution, known as a swarm, rep-

esents a particle of a population. In this approach, the particle’s

able 2tatistical properties of the parameters of the protective spur dike.

Inputs Average x Standardderivation (�)

Maximum (xmax) Minimum (xmin)

Fd 2.578 0.416 2.856 1.037U/Ucr 0.864 0.113 0.950 0.650Lp/Lf 0.500 0.205 0.800 0.200� (rad) 1.570 0.645 2.355 0.785Xp/Lf 1.857 0.443 2.500 1.000

ntal flume in the laboratory.

position is changed continuously zir in a multidimensional searchspace, until reaching the optimal response and/or computationallimitations.

Previous empirical studies have shown the effectiveness andusefulness of this approach for optimization purposes [31]. PSOapproach has been used in several optimization studies to exploreits efficiency [32].

For an optimization issue with D variables, a swarm of N par-ticles is instated so that every particle is dispensed an arbitraryposition in the hyperspace with D measurements. For this situa-tion, each particle’s position is related to a hopeful answer for theoptimization issue. x and v are considered as a particle’s position(direction) and the particle’s flight speed over an solution space,separately. Every individual x in the swarm is scored by a scoringcapacity which attains a wellness worth demonstrating that howfar it is competent to take care of the issues

Pbest is the best previous position of a particle. Also, Gbest rep-resents the index of the best particle among all particles in theswarm. Every particle has the capability to record its own per-sonal best position (Pbest) and find the most suitable positionsrecognized by all particles in the swarm (Gbest). Afterwards all par-ticles which fly over the D-dimensional solution space are subjectedto updated rules for new positions, till the time that the globaloptimum position is achieved. The following stochastic and deter-ministic update rules indicate how the velocity and position of aparticle are updated (Eq. (3)):

vi(t) = ωvi(t − 1) + �1(XPbesti− xi(t)) + �2(XGbesti

− xi(t)) (1)

xi(t) = xi(t − 1) + vi(t)(3)

where x is an inertia weight, q1 and q2 are random variables.The random variables are defined as q1 = r1c1 and q2 = r2c2, with

r1, r2, U(0, 1), and C1 and C2 are positive acceleration constants. Theweights of the stochastic increasing speed terms which push a par-ticle to Pbest and Gbest are spoken to by the speeding up constantsof C1 and C2, individually. When the qualities are little, a particlehas the capacity wander a long way from the target locales. Thenagain, huge qualities bring about the sudden development of par-ticles to target locales. In this study, as per the average practice in[33] both constants C1 and C2 are viewed as equivalent to 2.0. Thebest possible amendment of dormancy x in Eq. (3) offers a harmonybetween the worldwide and nearby investigations which bringsabout diminishing the quantity of emphases needed to discover anenough ideal arrangement. In this exploration work, a latency rec-tification capacity named “idleness weight approach (IWA)” is used[33,34]. Amid the IWA, the latency weight x is altered based uponthe accompanying relationship:

ω = ωmax − ωmax − ωmin Itr (4)

Itrmax

In Eq. (4), ωmax and ωmin represent the initial and final iner-tia weights, respectively. Also, Itrmax is the maximum number ofiteration while Itr is the current number of iteration.

H. Basser et al. / Applied Soft Computing 30 (2015) 642–649 645

FIS s

2

fr

it

tt

O

w

a

f

bpc

claa

w

m

summing up the inputs released by the fourth layer. It is also usedto transform the fuzzy classification results into a crisp (binary). In

Fig. 4. AN

.2.2. ANFISIn this study, three bell-shaped membership functions are taken

or each input with maximum and minimum amount of 1 and 0espectively. Fig. 4 shows the ANFIS structure with four inputs.

To perform the predictions the first-order Sugeno model includ-ng four inputs, fuzzy IF–THEN rules of Takagi, as well as Sugeno’sype was used as follows:

if i is A and j is C and k is E and l is G then

f1 = p1i + q1j + r1k + s1k + t (5)

The first layer includes the input variables membership func-ions (MFs). The first layer provides the next layer’s input values. Inhe first layer, each node is an adaptive node with a node function

= �(1),

here �(i)i are MFs.Eq. (6) provides the bell-shaped MFs (2) for which the highest

nd lowest amounts are 1 and 0, respectively.

(x; a, b, c) = 1

1 + ((x − c)/a)ab(6)

Based on Eq. (6), the function depends on three parameters of a, and c. Fig. 5 shows a bell-shaped membership function in whicharameter c is located in the center of the curve. Furthermore, it isommon that parameter b is a positive value.

The weight of MFs is deliberated in the second layer which isalled membership layer as well. The input values for the secondayer are obtained from the first layer. The nodes in the second layerre non-adaptive. The incoming signals in this layer are multiplied,nd the layer sends out the product as follows,

i = �(i)i · �(i)i+1 (7)

Each node output denotes the firing strength of a rule or weight.The third layer is the rule layer. In this layer, the pre-condition

atching of the fuzzy rules is performed by each node, i.e. they

tructure.

compute the activation level of each rule, and it calculates the nor-malized weights. This layer is also non-adaptive, and each nodecalculates the ratio of the rule’s firing strength to the sum of allrules’ firing strengths as follows

w∗i = wi

w1 + w2(8)

i = 1, 2.The third layer’s outputs are named normalized firing strenghts

or normalized weights.The fourth layer (defuzzification layer), which all of its nodes are

adaptive nodes with node function. This layer preapares the outputvalues resulted from the inference of rules.

O4i = w∗

i · f = w∗i p1i + q1j + r1k + s1k + t (9)

where {pi, qi, ri, si, t} is consequent parameters set in this layer.In continue, the fifth layer is the output layer that is used for

Fig. 5. Bell-shaped membership function (a = 2, b = 4, c = 6).

646 H. Basser et al. / Applied Soft Computing 30 (2015) 642–649

Fig. 6. Flow chart of sequential combination of ANFIS and PSO [35].

Table 3Characteristics of the parameters used in experiments.

Populationsize

Maximumnumber ofiterations

Inertiaweight

Inertiaweightdampingratio

Personallearningcoefficient

Globallearningcoefficient

member of the neighborhood is tracked in pi. For a global ver-

sion of PSO, the most suitable position in the total population is

represented by �pgi.

F(

ig. 7. Scour hole in laboratory when using; (a) no protective spur dike; (b) a protective sd) a protective spur dike with an angle of � = 135.

40 1000 1 0.99 1 2

this layer, the single node is not adaptive. This node computes theoverall output as the summation of all incoming signals as follows,

O5i

∑i

w∗i · f =

∑iwi · f∑

iwi(10)

In this paper, the PSO method is used to assist ANFIS for adjustingthe parameters of the membership functions [34]. The PSO tech-nique’s main advantage is its friendly manner for computationsin a given size network topology. In this study, the membershipfunctions are triangular-shaped.

2.2.3. ANFIS–PSO algorithmThe flow chart of the sequential combination of ANFIS and PSO

is shown in Fig. 6 [35]. The swarm in PSO is initialized with a pop-ulation of random solutions. Every potential solution is named aparticle. The particle’s position is presented by �Si. Also, a swarmof particles moves through the problem space which the particle’svelocity is expressed by �vi. At each time step, a function f is assessedbased upon the �Si as an input. Each particle keeps track of its ownbest position associated with the best fitness that it has obtainedso far, in a vector �pi. The most suitable position recognized by any

�g

pur dike with an angle of � = 45; (c) a protective spur dike with an angle of � = 90◦;

H. Basser et al. / Applied Soft Computing 30 (2015) 642–649 647

SVR-Radial: y = 0.9894x + 0.0035

SVR-Polynomal: y = 0.4841x + 0.2135

ANFIS-PSO: y = 0.949x + 0.0201

ANFIS- ACO : y = 0. 612 8x + 0. 152 6

ANFIS-D E: y = 0.60 42x + 0.15 590

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Pred

icte

d va

lues

Actual values

(a) (b)

Training

SVR-Radial

SVR-Polynomial

ANFIS-PSO

ANFIS-ACO

ANFIS-DE

SVR-Radial: y = 0.3351x + 0.1737ANFIS- ACO : y = 0. 192 3x + 0.31 79ANFIS-PSO : y = 0. 447 4x + 0. 179 9

SVR-Polynomial: y = 0.1387x + 0.3528ANFIS-DE: y = 0.1893x + 0.3193

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.2 0.4 0.6 0.8 1 1.2

Pred

icte

d va

lues

Actual values

Tes�ng

SVR-Radial

SVR-Polynomial

ANFIS-PSO

ANFIS-ACO

ANFIS-DE

F hase

s

c

S

o[

wuv

a

titt

basp

eop

TP

ig. 8. Performance of ANFIS–PSO, ANFIS–ACO, ANFIS–DE and SVR in (a) training ppur dike.

Depending upon the velocities, the position of each particle ishanged based upon the following relation [35]:

�i(t + 1) = �Si(t) + �vi(t + 1) (11)

The utilization of the PSO to design an FS or in other words theptimization of all free parameters in an FS, is defined as follows35],

Ri : if x1(k) is Ai1 And. . .And xn(k) is Ain, Then

u(k) is ai (12)

here k is the time step, x1(k), . . ., xn(k) are the input variables,(k) is the system output variable, Aij is a fuzzy set, and ai is a crispalue.

After the rule generation and initialization process, the initialntecedent part parameters can be identified.

PSO searches the optimal antecedent part parameters. Popula-ion size in the PSO is equal to Ps. The performance of each particles assessed based upon the FS it represents. The evaluation func-ion f is defined as the error index E(t) described above. Accordingo f, the individual best position �pi of each particle and the global

est particle �pgi

in the whole population can be found. The speednd position of every particle are overhauled by Eqs. (10) and (11),eparately. The entire learning procedure is done once a predefinedaradigm is met [35].

The main PSO parameters are given in Table 3. These param-ters represent population size of the domain, maximum numberf iterations, inertia weight, and inertia weight damping ratio,ersonal learning coefficient and global learning coefficient. These

able 4erformance analysis of different approaches for estimation of the optimum parameters

Method Training

Error (RMSE) Coefficient ofdetermination

ANFIS–PSO 0.033248 0.9511

ANFIS–ACO 0.094495 0.6049

ANFIS–DE 0.094563 0.6042

SVR-polynomial 0.098417 0.5975

SVR-radial 0.022270 0.9782

and in (b) testing phase for estimation of the optimum parameters of a protective

parameters are determined by trial and error procedure andpresents optimum values for this case study.

2.2.4. Model performance evaluationTo evaluate the accuracy of the ANFIS–PSO approach different

criterions are used:

(1) Root-mean-square error (RMSE)

RMSE =√∑n

i=1(Oi − Pi)2

n, (13)

(2) Coefficient of determination (R2)

R2 =[∑n

i=1(Oi − Oi) · (Pi − Pi)]2

∑ni=1(Oi − Oi) ·

∑ni=1(Pi − Pi)

(14)

where Oi = predicted values of protective spur dike,Pi = measurement values of protective spur dike, and n = thetotal number of test data.

3. Results and discussion

3.1. Experimental results

The experimental results indicated that, using a protective spurdike having � = 90◦; Xp/Lf = 2.5; and Lp/Lf = 0.8 provided the great-

est percentage reduction in scour depth (74.7%) around the firstspur dike. According to the results, the protective spur dike withthe following similar characteristics provided more reductions andare proposed to be used; � = 90◦ and 45◦ (i.e., they are better than

of a protective spur dike.

Testing

(R2)Error (RMSE) Coefficient of

determination (R2)

0.17218 0.36580.18256 0.17580.18294 0.17240.18208 0.13130.21693 0.3728

648 H. Basser et al. / Applied Soft Computing 30 (2015) 642–649

00.10.20.30.40.50.60.70.80.9

0 10 20 30 40 50

(a) (b)

RSD1

Data samples

ANFIS-PSO predic�on of training data

RSD1

ANFIS-PSO

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25

RSD1

ANFIS-PSO pred ic�on of tes�ng d ata

RSD1

ANFIS-PSO

Fig. 9. Prediction of the optimum parameters of a protective sp

Table 5Performance analysis of various approaches for estimation of the optimum param-eters of a protective spur dike.

ANFIS–ACO ANFIS–DE ANFIS–PSO SVR-polynomial SVR-radial

Train dataMSE 0.0089293 0.0089421 0.0011055 0.0096860 0.000496StD 0.09564 0.095709 0.033651 0.095285779 0.152190366

Test dataMSE 0.033329 0.033469 0.029647 0.03315502 0.0470596

S

�bdarvsa

3

mTddy

3

aweTAtp

4

owo

t

a

[

[

[

[

[

[

[

[

[

[

[

StD 0.15349 0.15381 0.13643 0.064672783 0.092687106

tD: error standard deviation.

= 135◦); Lp/Lf = 0.8 or 0.6 (i.e., the greatest actual lengths haveetter results); mostly, Xp/Lf = 2 or 2.5 (i.e., the largest allowableistances had better results). Also, the results showed that thepplication of a protective spur dike can be more effective in theeduction of the scour depth around the first spur dike for lowerelocity ratios and lower size of the sediments. Fig. 7 shows thecour depths before and after using a protective spur dikes for anngle of; 45◦, 90◦ and 135◦.

.2. Simulation results

The initial data helped to establish the hybrid soft computingethods. The data was essentially predicted using the five methods.

he estimation of the optimum parameters of a protective spurike is presented using scatterplot in Fig. 8. After developing theiagram, the fit line was developed and the obtained equation was

= aox + a1.

.3. Performance analysis

The performance of the methods was assessed using thevailable experimental data and significance of the parametersas determined. The RMSE and R2 were used to compare the

xpected and actual values for the all soft computing techniques.ables 4 and 5 provide the comparison between the ANFIS–PSO,NFIS–ACO, ANFIS–DE and SVR. Finally in Fig. 9 the prediction of

he optimum parameters of a protective spur dike by ANFIS–PSO isresented for training and testing data.

. Conclusions

In this study a new hybrid method was proposed for predictingf the optimum parameters of a protective spur dike. This approachorks based on the combination of ANFIS and PSO. The application

f the proposed approach is both novel and effective.

The results showed that the ANFIS–PSO accuracy is well enough

o predict the optimum parameters of a protective spur dike.The ANFIS–PSO as a soft computing method showed accept-

ble learning and prediction capabilities. Furthermore, the results

[

Data sa mples

ur dike by ANFIS–PSO for (a) training and (b) testing data.

showed the method’s capability to overcome the main shortcomingof the artificial neural network without defining network structureand trapping in the local optimum.

The performance of the ANFIS–PSO approach against the resultsprovided by ANFIS–ACO, ANFIS–DE and SVR confirms acceptableimprovements in prediction methods.

Acknowledgments

The financial support of the high impact research grants fromthe University of Malaya (UM.C/625/1/HIR/61, account number:H-16001-00-D000061) is gratefully acknowledged. Also authorswould like to thank the porous media laboratory of Amirkabir Uni-versity of Technology for the experimental facilities.

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