research article intelligent prediction of sieving...

Research ArticleIntelligent Prediction of Sieving Efficiency in Vibrating Screens

Bin Zhang12 Jinke Gong1 Wenhua Yuan2 Jun Fu2 and Yi Huang1

1The State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body Hunan University Changsha 410082 China2Department of Mechanical and Energy Engineering Shaoyang University Shaoyang 422004 China

Correspondence should be addressed to Jinke Gong gongjinke126com

Received 25 November 2015 Revised 22 February 2016 Accepted 15 March 2016

Academic Editor Longjun Dong

Copyright copy 2016 Bin Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In order to effectively predict the sieving efficiency of a vibrating screen experiments to investigate the sieving efficiency werecarried out Relation between sieving efficiency and other working parameters in a vibrating screen such as mesh aperture sizescreen length inclination angle vibration amplitude and vibration frequency was analyzed Based on the experiments leastsquare support vector machine (LS-SVM) was established to predict the sieving efficiency and adaptive genetic algorithm andcross-validation algorithm were used to optimize the parameters in LS-SVM By the examination of testing points the predictionperformance of least square support vector machine is better than that of the existing formula and neural network and its averagerelative error is only 42

1 Introduction

Sieving is one of the oldest physical size separation meth-ods and has been widely used both in industries and inlaboratories Vibrating screens which include a number oftypes are the main sieving tool for large-scale separationand classification of solid particles by size and they arewidely used in some practical engineering such as miningmetallurgy dry mortar artificial sand and agriculture pro-duction Probability screen is a special vibrating screen forthe separation and classification of fine particulate materialwhich exhibits problems of plugging holes and low sievingefficiency when the particle size is below 06mm Sievingefficiency is an essential evaluation indicator of sievingperformance and it is hard to be predicted based on theexisting sieving design parameters in the design process ofvibrating screens due to the comprehensive effect of complexparticle sieving process under multiple factors which willinfluence the selection or determination of these parametersTherefore an understanding of predicting sieving efficiencyhas a great practical significance

At present the research on the sieving efficiency ofvibrating screens has also made some progress There arelots of researchers studying the sieving process by DEMsimulations like Li et al [1] Dong et al [2] Liu [3] Delaney

et al [4] Jiao and Zhao [5] and Li et al [6] and qualitativerelation between sieving efficiency and sieving parametersin a vibrating screen such as amplitude vibration frequencyscreen mesh size particle size and vibration direction anglehas been analyzed which provides references for in-depthstudy But the results of DEM simulations need to be fur-ther explored and improved since particulate materials andboundary conditions of simulation are difficult to coincidewith the actual conditions Some scholars have studied thereal-time monitoring of sieving efficiency in the workingcourse of a vibrating screen by gathering its vibration signalsbut their research achievements only play the role of real-time monitoring and have little effect on the design of avibrating screen [7] In terms of sieving efficiency fittingGrozubinsky et al [8] and Chen and Tong [9] have respec-tively established formulas between the sieving efficiency andsieving parameters such as amplitude vibration frequencyvibration direction angle particle size and screen mesh sizebased on a probabilistic model and a discrete element modelbut these formulas only reflect the relationship between thesingle parameter and sieving efficiency Jiao et al [10] foundthe mathematical formula between sieving efficiency andparameters including screen deck angle and screen meshsize based on statistical analysis of experimental data whichprovides a theoretical basis for the design of vibrating screens

Hindawi Publishing CorporationShock and VibrationVolume 2016 Article ID 9175417 7 pageshttpdxdoiorg10115520169175417

2 Shock and Vibration

but ignores the impact of screen length Although somefitting function formulas of sieving efficiency have beenstudied there is still no widely accepted formula to predictsieving efficiency on the basis of sieving parameters Theintroduction of artificial intelligencemay provide a good pathto the solution of this problem [11]

Support vector machine (SVM) and neural network bothcan fit the nonlinear relations [12ndash14] whereas SVM ismore suitable when the sample size is relatively small andcan solve ldquocurse of dimensionalityrdquo problems The solutionof ldquocurse of dimensionalityrdquo can make the complexity ofalgorithm and the dimension of sample independent Atpresent SVM has been widely and effectively used in thepattern recognition intelligent fitting and prediction [15ndash18] However the application of SVM to predict the sievingefficiency has not been reported in the literatures yet

In this paper the experimental system and results werefirstly introduced and analyzed and then intelligent fittingmodel of least square support vector machine (LS-SVM) andadaptive genetic algorithmwere provided finally the contrastbetween the performance of the LS-SVMmodel the existingformula and the neural network was carried out

2 Sieving Experimental System

Sieving is a process in which a certain size range of materialsis separated into several products with different size throughone-deck or multideck screens that have sieving mesh withuniform apertures Theoretically the particles whose size islarger than the mesh aperture remain on the screen surfaceand leave the screen surface when they pass the end ofthe screen and these particles are called overflow particleshowever other smaller particles penetrate the sieving meshthrough the mesh aperture and are called undersize particlesSieving efficiency is the ratio between actual mass of under-size particles and the mass of the particles in raw materialswhose size is smaller than the mesh aperture Comparedwith the mesh aperture size the smaller the particles arethe easier the penetration is but the particles whose size isclose to the mesh aperture size penetrate the screen meshwith difficulty Probability screens have some advantages inall vibrating screens such as large sieving capacity and easypenetration because of their unique characteristics of thelarge mesh aperture and large inclination angle

The repeated sieving tests are finished in an experimentalsystem which is illustrated in Figure 1 Sieving parameterssuch as inclination angle screen length mesh aperture sizeamplitude and vibration frequency are adjustable in thisvibration sieving test bench which is a circular experimentalsystem and includes themultideck probability screen storagebin of raw materials vibrating feeder and automatic feedingsystem Samples used for measuring the sieving efficiencyby Hancockrsquos total efficiency formula are gotten when thescreen is in steady working condition The ldquosteady work-ing conditionrdquo means that the screen works steadily afterstarting the screen on the sieving test bench meanwhileraw materials cover the whole screen mesh surface and thefeed rate of raw materials from vibrating feeder reaches

Raw materials

Storage bin of rawmaterials

Vibrating feeder

Belt conveyer

Bucket elevator Probability screen

Figure 1 Schematic diagram of the vibration sieving test bench

Raw materials

Undersize particles

Overflow particles

(Q 120583)

(C 120575)

(D 120582)

Screen surface (L)Mesh aperture (a)

Inclination angle (120579)

Figure 2 Schematic diagram of total efficiency calculation

a stable state Total efficiency is the difference betweenthe penetration probability of the particles whose size issmaller than separation size and the penetration probabilityof the particles whose size is larger than separation size Theschematic diagram of total efficiency calculation is shown inFigure 2

In Figure 2 119876 is the total mass of raw materials into thescreen 119862 is the mass of overflow particles 119863 is the massof undersize particles 120583 is the percentage of the particleswhose size is smaller than separation size in raw materials120575 is the percentage of the particles whose size is smaller thanseparation size in overflow particles 120582 is the percentage ofthe particles whose size is smaller than separation size inundersize particles119886 ismesh aperture size of the screenmesh

Shock and Vibration 3

Table 1 Sand properties and operating conditions

Parameters Actual valuesSand sizemm 0ndash475Moisture ratio 03Fineness modulus 268Sieving capacity(th) 50

0

20

40

60

80

100

Perc

enta

ge o

f cum

ulat

ive s

ievi

ng re

sidue

()

0 2 3 4 51

Particle size (mm)

Upper limitLower limit

Sand sample

Figure 3 Grading curves of sands

119871 is screen length and 120579 is inclination angle of the screensurface Total efficiency is calculated as follows [10]

120578total =(120583 minus 120575) (120582 minus 120583)

120583 (120582 minus 120575) (100 minus 120583)times 100 (1)

In test process the screen mesh with rectangular aper-tures which is woven by steel wire is selected and the com-mon II area sands in construction industry whose particlediameter is between thick sands and fine sands are selectedas raw materials Sand properties and operating conditionsare shown in Table 1 and grading curves of sands are shownin Figure 3

As is shown in Figure 3 the particle diameter correspond-ing to the 6 data points is 015mm 03mm 06mm 118mm236mm and 475mm the grading curve of the sand sampleis almost in the middle position between the upper and lowerlimits of the common sand Since the raw sands are shiftedwith this multideck probability screen whose separation sizeis 236mm 118mm and 06mm respectively from top tobottom and generally the 06mm layer of this probabilityscreen has a smallest sieving efficiency which sieves finestmaterials with the particle diameter below 06mm the siev-ing efficiency of the 06mm layer is viewed as the probabilityscreenrsquos one

3 Experimental Results

According to experimental results the sievingefficiency 120578 first increases with the increase of vibration

50

55

60

65

70

75

80

120578(

)

1410 16 18 2012

ad

120579 = 20∘

120579 = 25∘120579 = 30∘

120579 = 35∘

Figure 4 Effect of mesh aperture size on the sieving efficiency

amplitude 119860119898and screen length 119871 and then decreases with

the increase of vibration frequency 120596 mesh aperture size119886 and inclination angle 120579 This paper focuses on detailedanalysis of 119886 119871 and 120579 and the effect of 119860

119898and 120596 on the

sieving efficiency is detailed in literature [7]

31 Effect of Mesh Aperture Size on the Sieving Efficiency Themesh aperture size can also be characterized by the ratiobetween mesh aperture size 119886 and separation size 119889 119886119889is greater than 1 in probability screens Figure 4 shows theeffect of mesh aperture size 119886 on the sieving efficiency when119860119898

is equal to 35mm 120596 is equal to 960 rmin and 119871 isequal to 24m 120578 first increases and then decreases with theincrease of 119886 When the mesh aperture size is small thesieving efficiency is low due to the approximate size between119886 and 119889 and the lower penetration probability of the fineparticles and a greater proportion of fine particles remainedin overflow particles When the mesh aperture size is largerthe sieving efficiency is higher due to the larger penetrationprobability of the fine particles When the mesh aperturesize is too large the sieving efficiency becomes lower due tothe higher penetration probability of the particles whose sizeis larger than separation size and undersize particles mixedwith a greater proportion of larger particles The optimummesh aperture size is between 08mm and 11mm and themaximum efficiency can reach above 80 when 120579 is 25∘

32 Effect of Screen Length on the Sieving Efficiency Figure 5shows the effect of screen length 119871 on the sieving efficiencywhen 119860

119898is equal to 3mm 120596 is equal to 960 rmin and 120579 is

equal to 25∘ 120578 increases significantly with the increase of 119871and the increase of 120578 becomes slow after 119871 reaches a certainvalue However 120578 decreases with the further increase of 119871under the condition of larger value of 119886119889 due to the highpenetration probability of the particles whose size is largerthan separation size and undersize particles mixed with anincreasing number of impurities If 119886119889 is larger the optimum


35

40

45

50

55

60

65

70

75

80

85

120578(

)

12 1816 2410 2214 20 2826

L (m)

ad = 1

ad = 12

ad = 15

ad = 18

Figure 5 Effect of screen length on the sieving efficiency

4035

120579 (∘)302520

45

50

55

60

65

70

75

80

85

120578(

)

L = 18mL = 20m

L = 22mL = 24m

Figure 6 Effect of inclination angle on the sieving efficiency

119871 is shorter due to the high penetration probability of theparticles whose size is smaller than separation size duringthe beginning time of sieving The optimum range of screenlength is between 20m and 26m

33 Effect of Inclination Angle on the Sieving EfficiencyInclination angle 120579 mainly affects the horizontal projectionsize ofmesh aperture and themoving speed of particles on thescreen surface Figure 6 shows the effect of inclination angle120579 on the sieving efficiency when 119860

119898is equal to 35mm 120596 is

equal to 960 rmin and 119886 is equal to 09mm 120578 first increasesand then decreases with the increase of 120579 and 120578 reachesthe maximum value with a certain inclination angle Whenthe inclination angle increases the horizontal projection sizeof mesh aperture decreases and penetration probability of

10 15 20 25 30 35

Am (mm)

50

55

60

65

70

75

80

85

120578(

)

120596 = 850 rmin120596 = 900 rmin

120596 = 960 rmin120596 = 1000 rmin

Figure 7 Effect of vibration amplitude on the sieving efficiency

particles in the vertical direction decreases which resultsin a lower penetration amount of the particles whose sizeis larger than separation size Meanwhile penetration andstratification capacity of the particles whose size is smallerthan separation size is enhanced with increasing movingspeed of particles on the screen surfaceWhen the inclinationangle increases further the sieving efficiency becomes lowdue to sharp decrease of the horizontal projection sizeof mesh aperture sharp increase of the moving speed ofparticles on the screen surface and shorter stay time ofparticles on the screen surface The optimum inclinationangle is about 25∘ and the maximum efficiency can reachabove 82 when 119871 is equal to 24m

34 Effect of Vibration Amplitude on the Sieving EfficiencyFigure 7 shows the effect of vibration amplitude 119860

119898on the

sieving efficiency when 119886 is equal to 09mm 119871 is equal to24m and 120579 is equal to 25∘ 120578 increases with the increase of119860119898 and 120578 first increases and then decreases with the increase

of120596 When119860119898and120596 increase the penetration probability of

particles whose size is smaller than separation size becomeslarger so the sieving efficiency increases However when 120596

increases to 1000 rmin 120578 decreases because larger vibrationfrequency can lead to larger penetration probability of par-ticles whose size is larger than separation size Optimumvibration amplitude and vibration frequency are 35mm and960 rmin respectively

4 Establishment of the IntelligentModel Based on LS-SVM

It is supposed that there are lots of training points 119867 =

119909119894 119910119894 (119894 = 1 2 119899) (119909

119894is the input value 119910

119894is the output

value and 119899 is the total number of training points) to be fitted


according to the basic theory of SVM these problems can beconverted to the solution of the following equations

max 119886119895 119886lowast

119895

= minus1

2

119899

sum

119894=1

119899

sum

119895=1

(119886119894minus 119886lowast

119894) (119886119895minus 119886lowast

119895) 119896 (119909

119894 119909119895)

minus 120576

119899

sum

119894=1

(119886119894+ 119886lowast

119894) +

119899

sum

119894=1

119910119894(119886119894minus 119886lowast

119894)

st119899

sum

119894=1

(119886119894minus 119886lowast

119894) = 0

119886119894 119886lowast

119894isin [0 119888]

(2)

119891 (119909) =

119899

sum

119894=1

(119886119894minus 119886lowast

119894) 119896 (119909 119909

119894) + 119887 (3)

where 119896(sdot) is kernel function 119886119894 119886lowast119894 and 119887 are the parameters

which could be obtained by the solution of the optimizationproblem (such problem is described in the form of (2)) and119888 is the penalty factor

SVM algorithm is sensitive to noise and its calculationspeed does not depend on the dimensions of input vectorsbut on the sample size The large sample size will result incomplex quadratic programming problem based on SVMslow operational speed and the long time that the calculationwill spend Therefore LS-SVM is introduced on the basis ofthe traditional theory of SVM

According to the theory of LS-SVM (2) can be convertedto the following linear equation

[0 A

ℎ

I Ω + Cminus1ℎ][

ba] = [

0

y] (4)

where y = [1199101 1199102 119910

ℎ]T Aℎ

= [1 1 1] a =

[1198861 1198862 119886

ℎ]T I is the unit matrix and Ω

119894119895= 120593(119909

119894)120593(119909119895) =

119896(119909119894 119909119895) Here Gauss function is selected as Kernel function

119896(sdot) and it meets the following equation

K (119909119896 119909ℎ) = Φ (119909

119896)TΦ (119909ℎ) (5)

Accordingly (3) can be converted into the followingequation

119891 (119909) =

119899

sum

119894=1

119886119894119896 (119909 119909

119894) + 119887 (6)

When LS-SVM is applied into the intelligent fitting ofsieving efficiency 120578 the five-dimensional input vector isa L 120579A

119898120596 and the one-dimensional output vector is 120578

The 82 training samples come from the experimental resultsdiscussed above and the prediction value of the LS-SVMmodel can be acquired finally by solving the value of 120572

119894and

119887In the theory of LS-SVM the parameters needed to be

optimized are the penalty factor 119888 and the kernel parameter

119903 and the fitting performance of LS-SVM depends on theselection of 119888 and 119903

Nowadays there are many kinds of intelligent algorithmthat can be used to optimize 119888 and 119903 such as particle swarmoptimization algorithm genetic algorithm grid search andchaos optimization algorithm [19 20] In these methodsgenetic algorithm has been considered with increasing inter-est in a wide variety of applications and it is widely usedto solve linear and nonlinear problems by exploring allregions of state space and exploiting potential areas throughmutation crossover and selection operations applied toindividuals in the population In this paper adaptive geneticalgorithm is applied to determine the value of 119888 and 119903

5 Intelligent Prediction ofSieving Efficiency Based on LS-SVM

51 Optimization of Parameters by Adaptive Genetic Algo-rithm The key of adaptive genetic algorithm [21] is todetermine the fitness functionHere it is described as follows

119865 (119888 119903) =1

sum119899

119894=1[119910119894minus 119891 (119909

119894)]2

+ 119890 (7)

where 119910119894is the expected output 119891(119909

119894) is the actual output

and 119890 is a small real number which is to prevent the situationof zero denominator here 119890 = 10

minus3The initial crossover probability and the initial mutation

probability are determined by

119875l119888=

09 minus 031198911015840

minus 119891avg

119891max minus 119891avg 119891 ge 119891avg

09 119891 lt 119891avg

119875l119898=

01 minus 0099119891max minus 119891


01 119891 lt 119891avg

(8)

where 1198911015840 is the larger fitness function value of the cross twobodies119891 is the fitness function value of individual119891avg is theaverage fitness function value in the samples and 119891max is themaximum fitness function value of individual in the samples

Crossover probability and mutation probability changewith the evolutional generation and their changing rules areas follows

119875119905

119888=

09radic1 minus (119905

119905max)

2

119875119905

119888lt 06

06 119875119905

119888ge 06

119875119905

119898=

01119890(minus120582119905119905max) 119875

119905

119898lt 0001

0001 119875119905

119898ge 0001

(9)

where 119905 is the genetic algebra 119905max is the terminated geneticalgebra and 120582 is a constant here 120582 = 10


The basic steps of ldquoadaptive genetic algorithmrdquo are listedas follows

Step 1 Generate initial population 119875(0) algebra is set to 0and the number of individuals is119872

Step 2 Run selection operator crossover operator andmuta-tion operator in proper order and calculate the fitness ofindividuals

Step 3 Sort individuals by fitness value and run the intelligentfitting model of LS-SVM once for the individual which hashighest fitness value

Step 4 Get a new generation of population 119875(119905 + 1) andalgebra increases by 1

Step 5 Judge whether it meets the optimization criterion Ifit meets the criteria the optimization process is over elsereturn to Step 2

There are two factors that may lead to the failure of LS-SVM (1) ldquooverfittingrdquo issue (the objective function can reduceto a very low value during the training phase but the testingerror is relatively large) (2) ldquounderfittingrdquo issue (the objectivefunction cannot reduce to a low value during the trainingphase) For solving these issues ldquocross-validationrdquo method isintroduced [22 23]

The basic steps of ldquocross-validationrdquo are listed as follows

Step 1 Divide the training samples into 119899 subsamples and set119894 = 1

Step 2 Regard the 119894th subsamples as the testing samples andthe others as the training samples

Step 3 Optimize the parameters (119888119894 119903119894) in LS-SVM based on

the new training samples by adaptive genetic algorithm

Step 4 119894 = 119894 + 1 and repeat Steps 1ndash3 till 119894 = 119899 and 119888 = sum 119888119894119899

119903 = sum 119903119894119899

In this paper the population size is 40 the dimension ofparameters to be optimized is 2 themaximumgenetic algebrais 400 and the binary digit of each variable is 20 And afterthe optimization process 119888 asymp 55 and 119903 asymp 12 Error functionis defined as follows

119891119864=

1

119899

119899

sum

119894=1

1003816100381610038161003816119891 (119909119894) minus 119910119894

1003816100381610038161003816

119910119894

(10)

where119891(119909119894) is the actual output and 119910

119894is the expected output

52 Comparison of the LS-SVM Model the Existing Formulaand Neural Network An existing fitting formula of sievingefficiency from literature [10] is shown as follows

120578 = 8076 + 251119886 minus 332120573 (11)

where 119886 is screen mesh size 120573 is screen deck angle and 120578 issieving efficiency

0

5

10

15

20

25

30

Erro

r (

)

2 14 180 10 1264 168

Sample number

BP neural networkRBF neural network

Literature [10]LS-SVM

Figure 8 Fitting error comparison of the LS-SVMmodel literature[10] and neural network

Neural network is also a usual intelligent model to fitthe numerical relation besides LS-SVM the training pointsin LS-SVM are still selected as training samples to optimizethe parameters in neural network The training methods ofneural network have detailed descriptions in literature [24]The prediction error between LS-SVM BP neural networkRBF neural network and the existing fitting formula inliterature [10] is shown in Figure 8

Figure 8 shows that the prediction error of selected 16testing samples is analyzed the average relative error of BPneural network is 73 the average relative error of RBFneural network is 64 the average relative error of literature[10] is 162 and the average relative error of LS-SVMmodelis 42 So the prediction performance of LS-SVM modelis better than that of neural network and the existing fittingformula in literature [10]

6 Conclusions

The effects of different factors on sieving efficiency wereinvestigated based on the vibration sieving test benchAccording to experimental results the sieving efficiency 120578

increases with the increase of vibration amplitude 119860119898and

screen length 119871 and it first increases and then decreases withthe increase of vibration frequency 120596 mesh aperture size 119886and inclination angle 120579

The intelligent model to predict the sieving efficiencywas established based on the experimental results LS-SVMtheory and the adaptive genetic algorithm The averageprediction error of the LS-SVM model examined by testingpoints can be reduced to 42 which is much less than thatof neural network and the existing fitting formula So the LS-SVM model has a better prediction performance on sievingefficiency which provides a theoretical basis for the optimaldesign and parameters selection of sieving screens


Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors thank the National Science Foundation of China(nos 51276056 and 51305045) for financial support

References

[1] J Li C Webb S S Pandiella and G M Campbell ldquoDiscreteparticle motion on sievesmdasha numerical study using the DEMsimulationrdquo Powder Technology vol 133 no 1ndash3 pp 190ndash2022003

[2] K J Dong A B Yu and I Brake ldquoDEM simulation of particleflow on a multi-deck banana screenrdquoMinerals Engineering vol22 no 11 pp 910ndash920 2009

[3] K S Liu ldquoSome factors affecting sieving performance andefficiencyrdquo Powder Technology vol 193 no 2 pp 208ndash213 2009

[4] G W Delaney P W Cleary M Hilden and R D MorrisonldquoTesting the validity of the spherical DEMmodel in simulatingreal granular screening processesrdquo Chemical Engineering Sci-ence vol 68 no 1 pp 215ndash226 2012

[5] H G Jiao and Y M Zhao ldquoScreen simuliation using a particlediscrete element methodrdquo Journal of China University of Miningand Technology vol 36 no 2 pp 232ndash236 2007

[6] H C Li Y M Li and Z Tang ldquoNumerical simulation andanalysis of vibration screening based on EDEMrdquo Transactionsof the Chinese Society of Agriculture Engineering vol 27 no 5pp 117ndash121 2011

[7] Z Z Shi and Y J Huang ldquoResearch on screening efficiencybased on AR model of high-order cumulant LS-SVMrdquo ChinaMechanical Engineering vol 22 no 16 pp 1965ndash1969 2011

[8] V Grozubinsky E Sultanovitch and I J Lin ldquoEfficiency ofsolid particle screening as a function of screen slot size particlesize and duration of screeningrdquo International Journal ofMineralProcessing vol 52 no 4 pp 261ndash272 1998

[9] Y H Chen and X Tong ldquoModeling screening efficiency withvibrational parameters based on DEM 3D simulationrdquo MiningScience and Technology vol 20 no 4 pp 615ndash620 2010

[10] H G Jiao J R Li and Y M Zhao ldquoTest and research onoptimum configuration of diameter of screen aperture andincline of screen deckrdquoCoal Preparation Technology vol 35 no2 pp 1ndash4 2007

[11] E Jia-Qiang Intelligent Fault Diagnosis and Its ApplicationHunan University Press Changsha China 2006

[12] S Umehara T Yamazaki and Y Sugai ldquoA precipitation esti-mation system based on support vector machine and neuralnetworkrdquo Electronics and Communications in Japan vol 89 no3 pp 38ndash47 2006

[13] A Kuh and P De Wilde ldquoComments on pruning errorminimization in least squares support vector machinesrdquo IEEETransactions on Neural Networks vol 18 no 2 pp 606ndash6092007

[14] K Lamorski Y Pachepsky C Sławinski and R T WalczakldquoUsing support vector machines to develop pedotransfer func-tions for water retention of soils in Polandrdquo Soil Science Societyof America Journal vol 72 no 5 pp 1243ndash1247 2008

[15] C H Wang Z P Zhong R Li and E Jia-Qiang ldquoPredictionof jet penetration depth based on least square support vectormachinerdquo Powder Technology vol 203 no 2 pp 404ndash411 2010

[16] C H Wang Z P Zhong R Li and J Q E ldquoIntelligent fittingof minimum spout-fluidised velocity in spout-fluidised bedrdquoCanadian Journal of Chemical Engineering vol 89 no 1 pp 101ndash107 2011

[17] J E C Qian T Liu and G Liu ldquoResearch on the vibrationcharacteristics of the new type of passive super static vibratoryplatform based on the multiobjective parameter optimizationrdquoAdvances in Mechanical Engineering vol 2014 Article ID569289 pp 1ndash8 2014

[18] L J Dong X B Li M Xu and Q Li ldquoComparisons of randomforest and support vector machine for predicting blastingvibration characteristic parametersrdquo Procedia Engineering vol26 pp 1772ndash1781 2011

[19] E Jiaqiang C Qian H Liu and G-L Liu ldquoDesign of the 119867infin

robust control for the piezoelectric actuator based on chaosoptimization algorithmrdquoAerospace Science and Technology vol47 pp 238ndash246 2015

[20] E Jiaqiang C Qian T Liu and G Liu ldquoChaos analysis onthe acceleration control signals of the piezoelectric actuators inthe stewart platformrdquo Shock and Vibration vol 2016 Article ID8087176 9 pages 2016

[21] K P Ferentinos and T A Tsiligiridis ldquoAdaptive design opti-mization of wireless sensor networks using genetic algorithmsrdquoComputer Networks vol 51 no 4 pp 1031ndash1051 2007

[22] L J Dong X B Li andGN Xie ldquoNonlinearmethodologies foridentifying seismic event and nuclear explosion using randomforest support vector machine and naive bayes classificationrdquoAbstract and Applied Analysis vol 2014 Article ID 459137 8pages 2014

[23] L J Dong and X B Li ldquoComprehensive models for evaluatingrockmass stability based on statistical comparisons of multipleclassifiersrdquo Mathematical Problems in Engineering vol 2013Article ID 395096 9 pages 2013

[24] J Q E H Y Zuo and Z Q Luo Fuzzy Inference Neural NetworkIntelligent Information Fusion and Its Engineering ApplicationChina Water Power Press Beijing China 2012

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but ignores the impact of screen length Although somefitting function formulas of sieving efficiency have beenstudied there is still no widely accepted formula to predictsieving efficiency on the basis of sieving parameters Theintroduction of artificial intelligencemay provide a good pathto the solution of this problem [11]

Support vector machine (SVM) and neural network bothcan fit the nonlinear relations [12ndash14] whereas SVM ismore suitable when the sample size is relatively small andcan solve ldquocurse of dimensionalityrdquo problems The solutionof ldquocurse of dimensionalityrdquo can make the complexity ofalgorithm and the dimension of sample independent Atpresent SVM has been widely and effectively used in thepattern recognition intelligent fitting and prediction [15ndash18] However the application of SVM to predict the sievingefficiency has not been reported in the literatures yet

In this paper the experimental system and results werefirstly introduced and analyzed and then intelligent fittingmodel of least square support vector machine (LS-SVM) andadaptive genetic algorithmwere provided finally the contrastbetween the performance of the LS-SVMmodel the existingformula and the neural network was carried out

2 Sieving Experimental System

Sieving is a process in which a certain size range of materialsis separated into several products with different size throughone-deck or multideck screens that have sieving mesh withuniform apertures Theoretically the particles whose size islarger than the mesh aperture remain on the screen surfaceand leave the screen surface when they pass the end ofthe screen and these particles are called overflow particleshowever other smaller particles penetrate the sieving meshthrough the mesh aperture and are called undersize particlesSieving efficiency is the ratio between actual mass of under-size particles and the mass of the particles in raw materialswhose size is smaller than the mesh aperture Comparedwith the mesh aperture size the smaller the particles arethe easier the penetration is but the particles whose size isclose to the mesh aperture size penetrate the screen meshwith difficulty Probability screens have some advantages inall vibrating screens such as large sieving capacity and easypenetration because of their unique characteristics of thelarge mesh aperture and large inclination angle

The repeated sieving tests are finished in an experimentalsystem which is illustrated in Figure 1 Sieving parameterssuch as inclination angle screen length mesh aperture sizeamplitude and vibration frequency are adjustable in thisvibration sieving test bench which is a circular experimentalsystem and includes themultideck probability screen storagebin of raw materials vibrating feeder and automatic feedingsystem Samples used for measuring the sieving efficiencyby Hancockrsquos total efficiency formula are gotten when thescreen is in steady working condition The ldquosteady work-ing conditionrdquo means that the screen works steadily afterstarting the screen on the sieving test bench meanwhileraw materials cover the whole screen mesh surface and thefeed rate of raw materials from vibrating feeder reaches

Raw materials

Storage bin of rawmaterials

Vibrating feeder

Belt conveyer

Bucket elevator Probability screen

Figure 1 Schematic diagram of the vibration sieving test bench

Raw materials

Undersize particles

Overflow particles

(Q 120583)

(C 120575)

(D 120582)

Screen surface (L)Mesh aperture (a)

Inclination angle (120579)

Figure 2 Schematic diagram of total efficiency calculation

a stable state Total efficiency is the difference betweenthe penetration probability of the particles whose size issmaller than separation size and the penetration probabilityof the particles whose size is larger than separation size Theschematic diagram of total efficiency calculation is shown inFigure 2

In Figure 2 119876 is the total mass of raw materials into thescreen 119862 is the mass of overflow particles 119863 is the massof undersize particles 120583 is the percentage of the particleswhose size is smaller than separation size in raw materials120575 is the percentage of the particles whose size is smaller thanseparation size in overflow particles 120582 is the percentage ofthe particles whose size is smaller than separation size inundersize particles119886 ismesh aperture size of the screenmesh




0

20

40

60

80

100

Perc

enta

ge o

f cum

ulat

ive s

ievi

ng re

sidue

()

0 2 3 4 51

Particle size (mm)


Sand sample









50

55

60

65

70

75

80

120578(

)

1410 16 18 2012

ad

120579 = 20∘

120579 = 25∘120579 = 30∘

120579 = 35∘




119898and 120596 on the








35

40

45

50

55

60

65

70

75

80

85

120578(

)

12 1816 2410 2214 20 2826

L (m)

ad = 1

ad = 12

ad = 15

ad = 18


4035

120579 (∘)302520

45

50

55

60

65

70

75

80

85

120578(

)

L = 18mL = 20m

L = 22mL = 24m






10 15 20 25 30 35

Am (mm)

50

55

60

65

70

75

80

85

120578(

)

120596 = 850 rmin120596 = 900 rmin

120596 = 960 rmin120596 = 1000 rmin




119898on the







119909119894 119910119894 (119894 = 1 2 119899) (119909


119894is the output




max 119886119895 119886lowast

119895

= minus1

2

119899

sum

119894=1

119899

sum

119895=1

(119886119894minus 119886lowast

119894) (119886119895minus 119886lowast

119895) 119896 (119909

119894 119909119895)

minus 120576

119899

sum

119894=1

(119886119894+ 119886lowast

119894) +

119899

sum

119894=1

119910119894(119886119894minus 119886lowast

119894)

st119899

sum

119894=1

(119886119894minus 119886lowast

119894) = 0

119886119894 119886lowast

119894isin [0 119888]

(2)

119891 (119909) =

119899

sum

119894=1

(119886119894minus 119886lowast

119894) 119896 (119909 119909

119894) + 119887 (3)





[0 A

ℎ

I Ω + Cminus1ℎ][

ba] = [

0

y] (4)

where y = [1199101 1199102 119910

ℎ]T Aℎ

= [1 1 1] a =

[1198861 1198862 119886


119894119895= 120593(119909

119894)120593(119909119895) =



K (119909119896 119909ℎ) = Φ (119909

119896)TΦ (119909ℎ) (5)


119891 (119909) =

119899

sum

119894=1

119886119894119896 (119909 119909

119894) + 119887 (6)




119894and







119865 (119888 119903) =1

sum119899

119894=1[119910119894minus 119891 (119909

119894)]2

+ 119890 (7)






119875l119888=

09 minus 031198911015840

minus 119891avg


09 119891 lt 119891avg

119875l119898=

01 minus 0099119891max minus 119891


01 119891 lt 119891avg

(8)



119875119905

119888=


119905max)

2

119875119905

119888lt 06

06 119875119905

119888ge 06

119875119905

119898=

01119890(minus120582119905119905max) 119875

119905

119898lt 0001

0001 119875119905

119898ge 0001

(9)
















119903 = sum 119903119894119899


119891119864=

1

119899

119899

sum

119894=1

1003816100381610038161003816119891 (119909119894) minus 119910119894

1003816100381610038161003816

119910119894

(10)




120578 = 8076 + 251119886 minus 332120573 (11)


0

5

10

15

20

25

30

Erro

r (

)

2 14 180 10 1264 168

Sample number






6 Conclusions






Competing Interests


Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












0

20

40

60

80

100

Perc

enta

ge o

f cum

ulat

ive s

ievi

ng re

sidue

()

0 2 3 4 51

Particle size (mm)


Sand sample









50

55

60

65

70

75

80

120578(

)

1410 16 18 2012

ad

120579 = 20∘

120579 = 25∘120579 = 30∘

120579 = 35∘




119898and 120596 on the








35

40

45

50

55

60

65

70

75

80

85

120578(

)

12 1816 2410 2214 20 2826

L (m)

ad = 1

ad = 12

ad = 15

ad = 18


4035

120579 (∘)302520

45

50

55

60

65

70

75

80

85

120578(

)

L = 18mL = 20m

L = 22mL = 24m






10 15 20 25 30 35

Am (mm)

50

55

60

65

70

75

80

85

120578(

)

120596 = 850 rmin120596 = 900 rmin

120596 = 960 rmin120596 = 1000 rmin




119898on the







119909119894 119910119894 (119894 = 1 2 119899) (119909


119894is the output




max 119886119895 119886lowast

119895

= minus1

2

119899

sum

119894=1

119899

sum

119895=1

(119886119894minus 119886lowast

119894) (119886119895minus 119886lowast

119895) 119896 (119909

119894 119909119895)

minus 120576

119899

sum

119894=1

(119886119894+ 119886lowast

119894) +

119899

sum

119894=1

119910119894(119886119894minus 119886lowast

119894)

st119899

sum

119894=1

(119886119894minus 119886lowast

119894) = 0

119886119894 119886lowast

119894isin [0 119888]

(2)

119891 (119909) =

119899

sum

119894=1

(119886119894minus 119886lowast

119894) 119896 (119909 119909

119894) + 119887 (3)





[0 A

ℎ

I Ω + Cminus1ℎ][

ba] = [

0

y] (4)

where y = [1199101 1199102 119910

ℎ]T Aℎ

= [1 1 1] a =

[1198861 1198862 119886


119894119895= 120593(119909

119894)120593(119909119895) =



K (119909119896 119909ℎ) = Φ (119909

119896)TΦ (119909ℎ) (5)


119891 (119909) =

119899

sum

119894=1

119886119894119896 (119909 119909

119894) + 119887 (6)




119894and







119865 (119888 119903) =1

sum119899

119894=1[119910119894minus 119891 (119909

119894)]2

+ 119890 (7)






119875l119888=

09 minus 031198911015840

minus 119891avg


09 119891 lt 119891avg

119875l119898=

01 minus 0099119891max minus 119891


01 119891 lt 119891avg

(8)



119875119905

119888=


119905max)

2

119875119905

119888lt 06

06 119875119905

119888ge 06

119875119905

119898=

01119890(minus120582119905119905max) 119875

119905

119898lt 0001

0001 119875119905

119898ge 0001

(9)
















119903 = sum 119903119894119899


119891119864=

1

119899

119899

sum

119894=1

1003816100381610038161003816119891 (119909119894) minus 119910119894

1003816100381610038161003816

119910119894

(10)




120578 = 8076 + 251119886 minus 332120573 (11)


0

5

10

15

20

25

30

Erro

r (

)

2 14 180 10 1264 168

Sample number






6 Conclusions






Competing Interests


Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










35

40

45

50

55

60

65

70

75

80

85

120578(

)

12 1816 2410 2214 20 2826

L (m)

ad = 1

ad = 12

ad = 15

ad = 18


4035

120579 (∘)302520

45

50

55

60

65

70

75

80

85

120578(

)

L = 18mL = 20m

L = 22mL = 24m






10 15 20 25 30 35

Am (mm)

50

55

60

65

70

75

80

85

120578(

)

120596 = 850 rmin120596 = 900 rmin

120596 = 960 rmin120596 = 1000 rmin




119898on the







119909119894 119910119894 (119894 = 1 2 119899) (119909


119894is the output




max 119886119895 119886lowast

119895

= minus1

2

119899

sum

119894=1

119899

sum

119895=1

(119886119894minus 119886lowast

119894) (119886119895minus 119886lowast

119895) 119896 (119909

119894 119909119895)

minus 120576

119899

sum

119894=1

(119886119894+ 119886lowast

119894) +

119899

sum

119894=1

119910119894(119886119894minus 119886lowast

119894)

st119899

sum

119894=1

(119886119894minus 119886lowast

119894) = 0

119886119894 119886lowast

119894isin [0 119888]

(2)

119891 (119909) =

119899

sum

119894=1

(119886119894minus 119886lowast

119894) 119896 (119909 119909

119894) + 119887 (3)





[0 A

ℎ

I Ω + Cminus1ℎ][

ba] = [

0

y] (4)

where y = [1199101 1199102 119910

ℎ]T Aℎ

= [1 1 1] a =

[1198861 1198862 119886


119894119895= 120593(119909

119894)120593(119909119895) =



K (119909119896 119909ℎ) = Φ (119909

119896)TΦ (119909ℎ) (5)


119891 (119909) =

119899

sum

119894=1

119886119894119896 (119909 119909

119894) + 119887 (6)




119894and







119865 (119888 119903) =1

sum119899

119894=1[119910119894minus 119891 (119909

119894)]2

+ 119890 (7)






119875l119888=

09 minus 031198911015840

minus 119891avg


09 119891 lt 119891avg

119875l119898=

01 minus 0099119891max minus 119891


01 119891 lt 119891avg

(8)



119875119905

119888=


119905max)

2

119875119905

119888lt 06

06 119875119905

119888ge 06

119875119905

119898=

01119890(minus120582119905119905max) 119875

119905

119898lt 0001

0001 119875119905

119898ge 0001

(9)
















119903 = sum 119903119894119899


119891119864=

1

119899

119899

sum

119894=1

1003816100381610038161003816119891 (119909119894) minus 119910119894

1003816100381610038161003816

119910119894

(10)




120578 = 8076 + 251119886 minus 332120573 (11)


0

5

10

15

20

25

30

Erro

r (

)

2 14 180 10 1264 168

Sample number






6 Conclusions






Competing Interests


Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











max 119886119895 119886lowast

119895

= minus1

2

119899

sum

119894=1

119899

sum

119895=1

(119886119894minus 119886lowast

119894) (119886119895minus 119886lowast

119895) 119896 (119909

119894 119909119895)

minus 120576

119899

sum

119894=1

(119886119894+ 119886lowast

119894) +

119899

sum

119894=1

119910119894(119886119894minus 119886lowast

119894)

st119899

sum

119894=1

(119886119894minus 119886lowast

119894) = 0

119886119894 119886lowast

119894isin [0 119888]

(2)

119891 (119909) =

119899

sum

119894=1

(119886119894minus 119886lowast

119894) 119896 (119909 119909

119894) + 119887 (3)





[0 A

ℎ

I Ω + Cminus1ℎ][

ba] = [

0

y] (4)

where y = [1199101 1199102 119910

ℎ]T Aℎ

= [1 1 1] a =

[1198861 1198862 119886


119894119895= 120593(119909

119894)120593(119909119895) =



K (119909119896 119909ℎ) = Φ (119909

119896)TΦ (119909ℎ) (5)


119891 (119909) =

119899

sum

119894=1

119886119894119896 (119909 119909

119894) + 119887 (6)




119894and







119865 (119888 119903) =1

sum119899

119894=1[119910119894minus 119891 (119909

119894)]2

+ 119890 (7)






119875l119888=

09 minus 031198911015840

minus 119891avg


09 119891 lt 119891avg

119875l119898=

01 minus 0099119891max minus 119891


01 119891 lt 119891avg

(8)



119875119905

119888=


119905max)

2

119875119905

119888lt 06

06 119875119905

119888ge 06

119875119905

119898=

01119890(minus120582119905119905max) 119875

119905

119898lt 0001

0001 119875119905

119898ge 0001

(9)
















119903 = sum 119903119894119899


119891119864=

1

119899

119899

sum

119894=1

1003816100381610038161003816119891 (119909119894) minus 119910119894

1003816100381610038161003816

119910119894

(10)




120578 = 8076 + 251119886 minus 332120573 (11)


0

5

10

15

20

25

30

Erro

r (

)

2 14 180 10 1264 168

Sample number






6 Conclusions






Competing Interests


Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation























119903 = sum 119903119894119899


119891119864=

1

119899

119899

sum

119894=1

1003816100381610038161003816119891 (119909119894) minus 119910119894

1003816100381610038161003816

119910119894

(10)




120578 = 8076 + 251119886 minus 332120573 (11)


0

5

10

15

20

25

30

Erro

r (

)

2 14 180 10 1264 168

Sample number






6 Conclusions






Competing Interests


Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Competing Interests


Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article intelligent prediction of sieving...

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