Research Article KPCA-ESN Soft-Sensor Model of ...downloads.hindawi.com/journals/mpe/2015/493248.pdf · sensor model for the VCM conversion rate and conversion velocityin thePVC productionprocess

Research ArticleKPCA-ESN Soft-Sensor Model of Polymerization ProcessOptimized by Biogeography-Based Optimization Algorithm

Wen-hua Cui12 Jie-sheng Wang12 and Shu-xia Li1

1School of Electronic and Information Engineering University of Science amp Technology Liaoning Anshan 114044 China2National Financial Security and System Equipment Engineering Research Center University of Science amp Technology LiaoningAnshan 114044 China

Correspondence should be addressed to Jie-sheng Wang wang jiesheng126com

Received 4 September 2014 Accepted 19 March 2015

Academic Editor Emilio Insfran

Copyright copy 2015 Wen-hua Cui 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

For solving the problem that the conversion rate of vinyl chloridemonomer (VCM) is hard for real-time onlinemeasurement in thepolyvinyl chloride (PVC) polymerization production process a soft-sensor modeling method based on echo state network (ESN)is put forward By analyzing PVC polymerization process ten secondary variables are selected as input variables of the soft-sensormodel and the kernel principal component analysis (KPCA) method is carried out on the data preprocessing of input variableswhich reduces the dimensions of the high-dimensional data The k-means clustering method is used to divide data samples intoseveral clusters as inputs of each submodelThen for each submodel the biogeography-based optimization algorithm (BBOA) is usedto optimize the structure parameters of the ESN to realize the nonlinear mapping between input and output variables of the soft-sensor model Finally the weighted summation of outputs of each submodel is selected as the final output The simulation resultsshow that the proposed soft-sensor model can significantly improve the prediction precision of conversion rate and conversionvelocity in the process of PVC polymerization and can satisfy the real-time control requirement of the PVC polymerization process

1 Introduction

Polyvinyl chloride (PVC) is one of the largest plastic productsin theworld Because PVChas characteristics of high strengthand good stability it has become a widely used syntheticmaterial in the world today According to different purposesby adding the different additives or plasticizers all kindsof PVC plastic products can be produced such as platesdoors andwindows profiles pipe fittings foammaterials andelectrical parts These products have widespread applicationsin industry agriculture health care and daily necessities andother fields As the embodiment of the superiority of PVCthe PVC production and improvement of the technology getmore and more attention of people

PVC is mainly produced by vinyl chloride monomer(VCM) so the quality of VCM directly affects the quality ofPVC resin production costs and economic benefits [1] Withthe large-scale development trend of polymerization kettleand the in-depth research of vinyl chloride polymerization

further improving the conversion rate of polymerizationkettle for productivity improvement and reducing the pro-duction cost have important significance The different VCMconversion has a certain impact on the molecular weight ofPVC resin thermal stability porosity the residues of VCMthe absorptivity of plasticizers and processing liquidity Asa result of the immature detection device the complexity ofthe suspension polymerization reaction and the strong non-linear and strong coupling in the actual production processvinyl chloride conversion rate and conversion velocity arehard to acquire real-time so it is difficult to achieve directclosed-loop control [2]

Echo state network (ESN) is a new type of recursionneural network [3 4] In terms of network structure andlearning mechanism it is different from the previous cyclenetworks ESN has better nonlinearity approximation capa-bility which makes it get good performance in the nonlinearprediction fields A kind of wavelet decomposition echostate network predictive model was proposed which adopts

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 493248 10 pageshttpdxdoiorg1011552015493248

2 Mathematical Problems in Engineering

the wavelet decomposition method to match different ESNmodels at each scale with different properties Then theleast square method realizes the optimal integration of thepredictive components through weight coefficients so as toreach accurate prediction of each scale and integration [5]ESNwas adopted to predict the conditions of flue gas turbineand the singular decompositionmethod was used to carry onthe modification of the linear regression training algorithmof ESN [6] The autocorrelation function method was usedto construct the input sequence of ESN for setting up thetime series forecast method [7] which is used in the fieldof the mobile communication traffic prediction The ESNprediction model based on the principal component analysismethod was established in order to reduce the training timeand improve the forecast speed [8] However the calculationof the ESN output weights based on the standard linearregression algorithm may easily lead to the pathologicalsolutions when dealing with the practical problems Onthe other hand the output weights are often with largeramplitudes In order to conquer the ill-conditioned matrixproblems of traditional echo state network model the evo-lutionary algorithms such as genetic algorithms (GAs) [910] particle swarm optimization (PSO) algorithm [11 12]memetic algorithm (MA) [13ndash15] and ant colony algorithm(ACA) [16 17] are applied to train the output weights of ESN

In this paper a kind of echo state network (ESN) soft-sensor model for the VCM conversion rate and conversionvelocity in the PVC production process based on the biogeo-graphic algorithm is put forward and the simulation resultsverify the effectiveness of the proposed method The paperis organized as follows In Section 2 the technique flowchartof the PVC polymerization process is introduced The datadimension reduction based on KPCA method is presentedin Section 3 In Section 4 the ESN soft-sensor model basedon BBO algorithm is introducedThe simulation experimentsand results analysis are introduced in detail in Section 5Finally the conclusion illustrates the last part

2 PVC Polymerization Process

In PVC polymerization process various raw materials andadditives are added to the reaction kettle which are full evenlydispersed under themixing actionThen the suitable amountsof the initiators are added to the kettle and start to react Thecooling water is constantly poured into the jacket and baffleof reaction kettle to remove the reaction heat The reactionwill be terminated and the final products are obtained whenthe conversion ratio of the vinyl chloride (VCM) reaches acertain value and a proper pressure drop appears Finallyafter the reaction completed and VCM contained in slurryseparated by the stripping technique the remaining slurryis fed into the drying process for dewatering and drying Atypical PVC polymerization kettle technological process isshown in Figure 1 [2]

According to characteristics of polymerization process10 process variables related to VCM conversion rate andconversion velocity are selected as secondary variables of soft-sensor modeling They respectively are kettle temperature

Table 1 Cumulative contribution ratio of different principal com-ponent number

Principalcomponentnumber

Percentage ofvariance ()

Cumulativepercentage ofvariance ()

1 5934 59342 1649 75833 835 84184 627 90455 491 95366 252 97887 101 98898 059 99489 052 1000010 0 10000

(TIC-P101) kettle pressure (PIC-P102) baffle water flow(FIC-P101) jacket water flow (FIC-P102) injection water flow(FIC-P104) seal water flow (FIC-P105) inlet temperature ofcooling water (for jacket water and baffles water sharing TI-P107) outlet temperature of jacket water (TI-P109) outlettemperature of baffle water (TI-P110) and inlet temperatureof injection water and seal water (namely the outlet temper-ature of the cold water tank TIC-WA01)

3 Data Dimension Reduction Based onKPCA Method

According to the above process characteristics 10 processvariables as auxiliary variables are determined But for neuralnetwork soft-sensor model too large dimensions of inputvector will cause dimension disaster which can lead to thefact that network topology becomes tedious and training iscomplicated In this paper the kernel principal componentanalysis (KPCA)method is adopted to reduce the dimensionsof the input vector KPCA introducing the concept of kernelfunction into principal component analysis (PCA) is a kindof nonlinear extension of PCA KPCA as a nonlinear formof PCA has the ability to deal with nonlinear problem betterthan PCA [18 19] Data sets composed by input variables ofthe model are given a kernel principal component analysisand the analysis results are shown in Table 1 The variancecontribution rate of the first five principal components hasreached more than 95 Original data primary variables dis-posed by KPCA are selected as inputs of the neural networkmodel which not only retains the characteristic informationof original variables but also simplifies the structure of neuralnetwork

4 ESN Soft-Sensor Model Based onBBO Algorithm

41 Structure of Soft-Sensor Model Soft-sensor technology ismainly composed of four parts data acquisition and process-ing choice of auxiliary variables soft-sensor modeling and

Mathematical Problems in Engineering 3

P-12

FV-PX05

FV-PX03FV-PX01

FV-PX02

Vent

VSP-PX23VSP-PX37

VSP-PX03

VSP-PX04

VSP-PX13 VSP-PX14

VSP-PX19

VSP-PX15

VSP-PX33VSP-PX26

VSP-PX22

VSP-PX25

VSP-PX36 VSP-PX16

VSP-PX01

VSP-PX08

VSP-PX21

VSP-PX12

VSP-PX10

VSP-PX09

Cooling water

Air

TIP109

Sealing water

Feed of dispersingagent and initiating

agent TICWA01

FICP105

TIP107

Impact modifiers

Water feed

Terminate agent

TICP101

PICP102

TIP110

TICWA01

P-90

FICP102

FICP101

VCM feed

Flush water

TK-IE

SE-IF

Switched agents

High pressure flush water

Steam

Trench

PU-XE

Adding material water

Flush water

Steam

FICP104

P-96

P-98

P-101

Figure 1 Technique flowchart of polymerization kettle

Not directly measurable variables

Varia

ble d

imen

sion

Auxiliary variable

Dominant variable

Predicted value

Poly

mer

izat

ion

kettl

e sys

tem Kettle pressure

Baffle water flow

Jacket water flow

Outlet

of baffle water

of jacket water

Dat

a acq

uisit

ion

and

proc

essin

g

The c

hoic

e of a

uxili

ary

varia

bles

k-m

eans

clus

terin

g

Model 1

Model 2

Model k

etemperature

Outlettemperature

redu

ctio

n b

+

minusΣ

Figure 2 Structure of soft-sensor model

online correction The framework of the proposed multiplemodel soft-sensor modeling based on clustering is shown inFigure 2

The dimension of the process parameters space is reducedbased on KPCA method and the five input variables (kettlepressure 119909

1 baffle water flow 119909

2 jacket water flow 119909

3 outlet

temperature of baffle water 1199094 and outlet temperature of

jacket water 1199095) are selectedThe119870-means clusteringmethod

is adopted to divide the sample data into 119896 classes and eachclass will be as inputs of a sub-soft-sensor model Thus themultiple models soft-sensor modeling method based on 119870-means clustering method is established The conversion rateand velocity of VCM are the output variables The BBOalgorithm is used to optimize the ESN parameters to realizethe nonlinear relationship 119891sdot between them Thereforethe soft-sensor model of VCM conversion rate is set up


Experiment proves that this method can effectively improvethe prediction accuracy of models

42 119870-Means Clustering Method 119870-means clusteringmethod is a kind of widely used clustering algorithm Itsmainthought is that the data set is divided into different clustersthrough the iteration process making the criterion functionof evaluation clustering performance achieve optimiza-tion Objects within the cluster have a high similarity andthe objects between clusters have a low similarityThe generalsteps of the algorithm are described as follows

Step 1 For the sample data set 119883 = 119909119898| 119898 = 1 2

randomly select 119896 data samples 1198881 1198882 119888

119896 as the initial

cluster centers

Step 2 Calculate the distance 119889 of each residual sample andthe cluster center and assign it to the nearest cluster Thedistance between the samples expresses the similarity of thetwo samples The smaller the distance the more similarthe two samples and the smaller the difference degree Thedistance between the samples is calculated by Euclideandistance and its formula is shown as follows

119889 (119909119894 119909119895) = radic

119899

sum

119896=1

(119909119894119896minus 119909119895119896)

2

(1)

where 119909119894and 119909

119895are two samples and 119899 is the sample dimen-

sion

Step 3 Through Step 2 update and get the new clustersCalculate the square error criterion until the overall averageerror function is met Consider

119864 =

119896

sum

119894=1

sum

119901isin119883119894

1003817100381710038171003817119901 minus 119888119894

1003817100381710038171003817

2

(2)

where 119888119894is the clustering center and 119901 is sample data

Step 4 The average value of all objects of clusters is chosenas a new cluster center 119888

119894 Repeat Steps 2 and 3 and stop the

iteration until the center does not change

According to the chosen number of clusters and clustercenter the data objects are divided into 119896 different clustersFor different clustering data respectively establish submod-els shown in Figure 3 Through weighted summation ofpredicted value of each submodel the final output forecastvalue is got

43 Echo State Network In recent years neural network hasbeen widely applied in nonlinear systemsThemost commontypes of neural network are the feed-forward neural networkand recurrent neural network Most feed-forward neuralnetworks are static neural network without the ability ofdealing with information dynamically The recurrent neuralnetwork is joined by the dynamic mechanism of processinginformation on the basis of feed-forward neural network

Soft-sensor modelof echo state

network

Biogeography-basedoptimization algorithm

Dominant variable

Predicted value

Variable 1Variable 2

Variable m

+minus

Figure 3 Structure of submodel

Input layer Reservoir Output layer

u1

uK

W

x1x2

x3x4

x7

x6

x5

xN

y1

yL

Win Wout

Wfb

Figure 4 Structure of echo state neural network

whichmakes thewhole networkwith dynamic characteristicsand approximates the target value better Common recurrentneural networks are Elman network and Hopfield networkEcho state network (ESN) is a new type of recurrent neuralnetwork whose typical structure is shown in Figure 4

It can be seen from Figure 4 that the structure of ESN issimilar to that of most neural network which is composedof three parts input layer hidden layer and output layerUnlike other neural networks the hidden layer of the ESN is alarger dynamic reservoir (DR) and the number of neurons inthe ESN is much more than that of other neural networksThe dynamic reservoirs (DR) can unceasingly store a largenumber of teachers signals and have short-term memoryability Although there is no input signal after the trainingESN still can predict for a short period of time thus thisability can make the network reach the approximation effectfor learning system [20]

Suppose the input layer contains 119870 neurons DR con-tains 119873 neurons and the output layer contains 119871 neuronsInput sample of network is a 119870-dimensional vector 119906(119899) =[1199061(119899) 119906

119870(119899)]119879 the state vector of DR is 119873-dimensional

vector 119909(119899) = [1199091(119899) 119909

119873(119899)]119879 and the output sample is

119871-dimensional vector 119910(119899) = [1199101(119899) 119910

119871(119899)]119879 Between

the input neurons and DR a link weight matrix 119882in existswhose dimension is119873 times 119870119873 neurons of DR are connectedto a sparse network and the number of connections is1198732 (including the self-connection neurons) The matric 119882

expresses the link weight between DR neurons and it usually


keeps the sparse connection of 1sim5 so 119882 is the 119873 times 119873

sparse matrix and the element 119882119894119895of 119882 expresses the link

weight between the 119894-neuron and the 119895-neuron in the DRBetweenDR and output layer there is an outputweightmatrix119882

out whose dimension is (119870+119873+119871)times119871 In addition betweenthe output layer andDR there is a feedback connectionweight119882

fb and its dimension is119873 times 119871Suppose now we have 119872 samples (119906(119894) 119889(119894)) (119894 =

1 2 119872) where 119906(119894) 119889(119894) respectively are the 119894-input andoutput sample and its dimensions are respectively 119870 and 119871The basic equation of echo state network can be representedas follows

119909 (119899 + 1) = 119891 (119882in119906 (119899 + 1) + 119882119909 (119899) + 119882

fb119889 (119899)) (3)

119910 (119899 + 1) = 119882out[119909 (119899 + 1) 119906 (119899 + 1)] (4)

where 119891(sdot) is the activation function of reservoir neurongenerally taking sigmoid function tanh() It can be seen from(3) 119909(119899 + 1) is associated with 119906(119899 + 1) 119909(119899) and 119889(119899) When119899 = 0 there is no definition for 119889(0) so use 119889(0) = 0 asthe output sample In the training process119882in119882fb and119882always remain the same and119882out is not involved in networktraining process so the value119882out is calculated at the end ofthe network trainingThe error of the network forecast output119910(119899) and actual output of test samples 119889(119899) is smaller theprediction performance of the network is better

44 BBO Algorithm In recent years due to the naturersquosinspiration many scholars have proposed some optimizationalgorithms based on swarm intelligence to solve complexoptimization problems such as genetic algorithm simulatedannealing algorithm and artificial fish swarm algorithmAlthough these intelligent algorithms have appeared for ashort time their good ability to solve complex optimiza-tion problems makes them extensively applied into manyactual production processes Biogeography-based optimiza-tion algorithm was put forward by an American scholarSimon inspired by the biogeography [21]

Biogeography is a kind of natural science that researchesspecies distribution migration and extinction and so forthIn nature the distribution of biology population is differentThe place where population lives is named as the ldquohabitatrdquoAnd every habitat living environment is not the same suchas rainfall temperature humidity and geology (appropriateindex variables SIV) The habitat suitability index (HSI) isadopted to describe whether the habitat living environmentis good or bad The HSI is higher in which the environmentis suitable for the survival of species on the contrary it isnot suitable for the survival of species The correspondingrelation between biogeography mathematical model andBBO algorithm variables is listed in Table 2

Every habitat space is limited and the number of accom-modated species is also limited When the high HSI habitataccommodates more than the largest number of speciesand the habitat resources are not enough for allocationcompetition between species becomes anabatic making HSIlow At this time some species will choose to leave the habitatand migrate to a place whose resources are relatively rich

Table 2 Corresponding relation between biogeography mathemat-ical model and BBO algorithm variables

Biogeography mathematicalmodel

Biogeography-basedoptimization (BBO) algorithm

Habitat IndividualHabitat suitability index (HSI) Fitness of the individualSuitability index variables (SIVs) Individual variablesHigh HSI habitats Excellent individual

Rate

Number of species

I

E

120583

120582

S0 Smax

Figure 5 Migration ratio of single island species

thus improving the HSI lower habitat So due to species ofthe space with high HSI which is multifarious and relativelystable it has a low immigration rate and high emigration rateThat is to say low HSI habitats have higher immigration rateand low emigration rate

441MigrationOperation BBOalgorithmadopts themigra-tion operation to share information between habitatsmakingthe achievement of the global optimal objective faster In thehighHSI habitats because of the diversity of species and largenumber of species the emigration rate is higher Due to itshigh emigration rate the characteristics information of betterhabitat is shared to lower HSI habitats This does not meanthat the HSI of better habitat reduces but its features arecopied to the habitats with lower HSI A species migrationmodel of a single island is shown in Figure 5 In order toillustrate the basic principle of biogeography this model isadopted to describe BBO algorithm

In Figure 5 119878max is the largest number of species Suppose119878max = 119899 for the 119896th island the immigration rate is 120582

119896 the

emigration rate is 120583119896 119868 is the biggest immigration rate and 119864

is the biggest emigration rate When the number of species ofan island is zero (119878 = 0) 120582

119896= 119868 As the number of species

in the island increases the number of species in the habitatgradually tends to saturation value therefor the immigrationrate 120582

119896decreases linearly When the species number reaches

maximum 119878max 120582119896 = 0 that is to say no species move in


For the emigration rate 120583119896 when 119878 = 0 no species move out

namely 120583119896= 0 With the increase of species number in order

to find more suitable survival habitats the emigration rateincreases When the species number reaches maximum 120583

119896=

119864 When 120582119896= 120583119896 the species number of the habitat reaches

an equilibrium state According to Figure 5 the immigrationrate and emigration rate can be calculated as follows

120582119896= 119868 times (1 minus

119896

119899

)

120583119896= 119864 times

119896

119899

(5)

442 Mutation Operation As species migrate between habi-tats the number of species in each island is constantly chang-ing Suppose the probability of habitats including speciesnumber 119878 is 119875

119904 the change value formula of the probability

119875119904at time 119905 to 119905 + Δ119905 [21] is described as follows

119901119904(119905 + Δ119905) = (1 minus 120582

119904minus 120583119904) 119875119904Δ119905 + 120582

119904minus1119875119904minus1Δ119905

+ 120583119904+1119875119904+1Δ119905

(6)

where 120582119904and120583119904express immigration rate and emigration rate

when the habitat contains species 119878Assuming that Δ119905 is small enough the calculation of

probability 119875119904is shown as the following formula

119875119904

=

minus (120582119904+ 120583119904) 119875119904+ 120583119904+1119875119904+1 119878 = 0

minus (120582119904+ 120583119904) 119875119904+ 120582119904minus1119875119904minus1

+ 120583119904+1119875119904+1 1 le 119878 lt 119878max minus 1

minus (120582119904+ 120583119904) 119875119904+ 120582119904minus1119875119904minus1 119878 = 119878max

(7)

The above formula can be abbreviated to 119875 = 119860119875 Whenthe largest species number of the habitat is equal to 119878max theprobability 119875

119904function corresponding to different habitats is

a symmetric function about equilibrium point Individualswith larger species number and less species number all havelow stable probability that is to say the probability is smallthe number of species near the equilibrium point is relativelystable and the existence probability is higher On this basisthe variation rate119898

119894is designed as the following equation

119860

=

[

[

[

[

[

[

[

[

[

minus (1205820+ 1205830) 120583

1

1205820

minus (1205821+ 1205831) 1205832

1205821

sdot sdot sdot sdot sdot sdot

sdot sdot sdot minus (120582119899minus1

+ 120583119899minus1) 120583

119899minus1

120582119899minus1

minus (120582119899+ 120583119899)

]

]

]

]

]

]

]

]

]

119898119894= 119898max (

1 minus 119875 (119878119894)

119875max)

(8)

where 119898max is the biggest mutation rate and 119875119904is the

probability of habitat accommodating species 119878For the mutation operation whether the habitat needs to

mutate first should be determined If the random number is

less than the mutation probability 119898119894 it means the habitat

needs to mutateThen a group of randomly generated vectorsare used to replace the original vector In nature incidents(such as volcanic eruptions tsunamis and disease) areoften unavoidable the occurrence of these events will affectthe number of species makes the ecological environmentunstable and reduces the habitat suitability index If islandsof low suitability index are given a variation the chance ofgetting a better solution will increase if islands of highersuitability index are given a variation it may not get a bettersolution so retain islands with high suitability index andmake a mutation for islands with low suitability index

45 Algorithm Procedure First main parameters of ESNare the input matrix 119882in the reservoir weight matrix 119882the output feedback weight matrix 119882

fb and the outputweight matrix 119882out So optimizing the ESN is equivalentto optimizing the four matrixes In the network learningprocess119882in119882fb and119882 always remain the same and119882out

is not involved in the network training process and its valueis calculated after the end of the network training So in thispaper the habitat of biogeographic optimization algorithm isin correspondence with the output connection weight of theESN Through biogeography-based optimization algorithmthe weight of ESN is optimized to realize the ideal predictedvalues The algorithm flowchart of ESN prediction modeloptimized by BBO algorithm is shown in Figure 6

Step 1 (initialization parameters) Initialize the followingalgorithm parameters the largest species number of island119878max the number of island 119873 the emigration rate 120582

119896and

immigration rate 120583119896 the maximum variation rate 119898max and

the number of iterations 119894119905119890119903max Initialize a group of islandseach island namely each habitat all represents an individualwhich is the solution of the problem

Step 2 (calculate the fitness value) Use suitability index HSIof the island as the fitness value Calculate the fitness value ofeach island 119891119894119905119899119890119904119904 function Judge whether the terminationcondition is met or not If satisfied output the optimalsolution otherwise continue Step 3

Step 3 According to the fitness values the individuals arearranged in a descending order and the highest HSI indi-vidual is stored Calculate species number 119878 correspondedby each island the emigration rate 120582

119896 the immigration rate

120583119896 and the mutation probability 119898max Then the optimal

individual is noted as 119901

Step 4 (migration operation) According to the emigrationrate120582

119896and the immigration rate120583

119896 judgewhether the islands

119896 need to perform the migration operation or not If neededperform the migration operations generate new individualsand recalculate the fitness value of island 119896 Compare it withthe optimal individual 119901 and retain the best individual notedas 1199011015840

Step 5 (mutation operation) Make a mutation operation forislands with lower HSI and recalculate the fitness value of


Start

Set the initial parameters

Generate initial population and define initial parameters of biogeography

Convert individual expression form to

Read the data and calculate the outputof neural network

Calculate error of sum squareand convert to individualrsquos fitness

Find out the contemporary

Judge termination conditionsare met

Output the final result

Over

Calculate species numberemigration rate and

immigration rate of habitat

Calculate the mutation rate of habitat

Choose better individuals of population as the parent

individuals of next generation to iterate

Migration operation

Mutation operation

No

Yes

optimal individual and record

ESN neural network weight Wout

Figure 6 Algorithm flowchart of ESN prediction model optimized by BBO algorithm

each island Record the best individual now Compare withthe optimal individual 1199011015840 and keep the optimal individualnoted as 11990110158401015840

Step 6 Check the same individual and use random vectorsinstead of the same individuals Reorder all individuals andmaintain the individual corresponded by the highest HSIRecord the best individual at this time If the terminatingcondition is satisfied exit iteration Otherwise repeat fromStep 3

Step 7 (End) Return the vector corresponding to the highestHSI individual

5 Simulation Results

In this paper the polymerization industrial process of achemical factory with 40000 tonsyear polyvinyl chloride(PVC) production device is taken as background whosetechnology is introduced by America BsdotFsdotG company takingvinyl chloride monomer (VCM) as raw material and usingsuspension polymerization technology to produce polyvinylchloride (PVC) resin A soft-sensor model of the VCMconversion rate and velocity in the polyvinyl chloride (PVC)production process based on BBOA-ESN algorithm is put

forward After reducing ESN dimensions the number ofinput variables is 5 and the output dimension is 2 In additionsuppose the reservoir size is 100 the sparse connection rateof reservoir weight matrix is 5 the activation function ofreservoir is tanh() and the output unit adopts linear activa-tion function Suppose the initial values of ESN parameters119882

in= 03119882 = 02 and119882in

= 003The initialized parameters of adopted BBO algorithm are

described as follows the habitat size 119873 = 100 the largestspecies number 119878max = 100 the largest immigration rate119868 = 1 the largest emigration rate 119864 = 1 the largest mutationprobability 119898max = 0005 and the maximum iterationsnumber is 200

Before setting up the soft-sensor model of VCM conver-sion rate and velocity in the PVC polymerization processin order to measure the performances of prediction modelsseveral performance indicators are defined in Table 3 where119910(119905) is predicted value and 119910

119889(119905) is actual value

The production historical data of PVC polymerizationprocess are collected and 2 kettles including 1600 sets his-torical data with the uniformity and representativeness arechosenThen after data preprocessing the data is divided intotwo parts in which the front 1350 data are the training dataand the rest 250 data are used to validate the performanceof soft-sensor models The simulation results are shown in


Table 3 Definition of model performance index

Mean absolutepercentage error MAPE = 100

119879

119879

sum

119905=1

1003816100381610038161003816119910 (119905) minus 119910

119889(119905)1003816100381610038161003816

119910119889(119905)

Mean-square error MSE = 1

119879

119879

sum

119905=1

(119910 (119905) minus 119910119889(119905))2

Root mean squareerror RMSE = [ 1

119879

119899

sum

119905=1

(119910119889(119905) minus 119910 (119905))

2

]

12

Normalized rootmean square error NRMSE = radic 1

1198791003817100381710038171003817119910119889

1003817100381710038171003817

2

119879

sum

119905=1

(119910 (119905) minus 119910119889(119905))2

Sum of squarederror

SSE =119899

sum

119905=1

(119910119889(119905) minus 119910(119905))

2

0 50 100 150 200 25004

06

08

1

12

14

16

18

2

Sequence

Rate

of c

onve

rsio

n

The actual output

The predicted

The predicted output

The predicted outputoutput of ESN of BBO-MESN

of BBO-ESN

Figure 7 Predicted output curves of VCM conversion velocity

Figures 7ndash10 Figure 7 shows the output comparison curves ofconversion velocity of VCM respectively predicted by ESNsoft-sensor model BBO-ESN soft-sensor model and BBO-MESN soft-sensor model Figure 8 shows the predicted errorcurves of VCM conversion velocity Figure 9 shows the out-put comparison curves of VCM conversion rate respectivelypredicted by ESN soft-sensor model BBO-ESN soft-sensormodel and BBO-MESN soft-sensor model Figure 10 showsthe predicted error curves of VCM conversion rate

Themodel performances comparison is shown in Table 4From the simulation results the prediction accuracy ofBBO-MESN soft-sensor model proposed in this paper ishigher than that of ESN and BBO-ESN soft-sensor modelIts application of predicting the VCM conversion rate andvelocity in PVCpolymerization process has great significancein improving the capacity of equipment and reducing theproduction cost

0 50 100 150 200 250

0

01

02

03

04

Sequence

The p

redi

ctio

n er

ror o

f con

vers

ion

rate

The prediction error of ESNThe prediction error of BBO-ESNThe prediction error of BBO-MESN

minus04

minus03

minus02

minus01


0 50 100 150 200 250

0

10

20

30

40

50

60

70

80

Sequence

The actual output

The predicted



of BBO-ESN

Con

vers

ion

ratio

()

minus10

Figure 9 Predicted output curves of VCM conversion ratio

Table 4 Performances comparison of different soft-sensor models

MAPE MSE RMSE NMSE SSEESN 53509 00078 00880 00201 19381BBO-ESN 50907 00073 00856 00044 18322BBO-MESN 41694 00051 00713 00036 12692

6 Conclusions

Based on that ESN has good capability of nonlinear approx-imation and biogeography-based optimization algorithm



0 50 100 150 200 250

0

10

20

30

40

Sequence

The p

redi

cted

erro

r of c

onve

rsio

n ra

tio

minus10

minus20

minus30

Figure 10 Predicted error curves of VCM conversion ratio

(BBOA) is simple and easy-to-implement which can obtainthe global extreme and avoid falling into local extremea BBO-MESN soft-sensor model is proposed to predictVCM conversion rate and conversion velocity BBOA is usedto optimize the output weights of the ESN network Thesimulation results show that the neural network soft-sensormodel based on BBO-MESN has higher prediction accuracy

Conflict of Interests

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

Acknowledgments

This work is partially supported by the Program for ChinaPostdoctoral Science Foundation (Grant no 20110491510)the Program for Liaoning Excellent Talents in University(Grant no LR2014008) the Project by Liaoning ProvincialNatural Science Foundation of China (Grant no 2014020177)and the Program for Research Special Foundation of Uni-versity of Science and Technology of Liaoning (Grant no2011ZX10)

References

[1] S Zhou G Ji Z Yang and W Chen ldquoHybrid intelligentcontrol scheme of a polymerization kettle for ACR productionrdquoKnowledge-Based Systems vol 24 no 7 pp 1037ndash1047 2011

[2] S-Z Gao J-S Wang and N Zhao ldquoFault diagnosis methodof polymerization kettle equipment based on rough sets andBP neural networkrdquoMathematical Problems in Engineering vol2013 Article ID 768018 12 pages 2013

[3] H J Jaeger ldquoAdaptive nonlinear system identification with echostate networksrdquo in Advances in Neural Information ProcessingSystems S Thrun and K Obermayer Eds vol 15 pp 593ndash600MIT Press Cambridge Mass USA 2002

[4] H J Jaeger ldquoTutorial on training recurrent neural coveringBPTT RTRL EKF and the lsquoecho state networkrsquo approachrdquo GHDReport 159 German National Research Center for InformationTechnology 2002

[5] ZQWang andZG Sun ldquoMethod for prediction ofmulti-scaletime series with WDESNrdquo Journal of Electronic Measurementand Instrument vol 24 no 10 pp 947ndash952 2010

[6] S H Wang T Chen X L Xu et al ldquoCondition trendprediction based on improved echo state network for flue gasturbinerdquo Journal of Beijing Information Science and TechnologyUniversity vol 4 pp 18ndash20 2010

[7] Y Peng J-MWang andX-Y Peng ldquoResearches on times seriesprediction with echo state networksrdquo Acta Electronica Sinicavol 38 no 2 pp 148ndash154 2010

[8] Y Guo J Sun L Fu and Z Zhai ldquoA new and better predictionmodel for chaotic time series based on ESN and PCArdquo Journalof Northwestern Polytechnical University vol 28 no 6 pp 946ndash951 2010

[9] D M Xu J Lan and J C Principe ldquoDirect adaptive controlan echo state network and genetic algorithm approachrdquo inProceedings of the IEEE International Joint Conference on NeuralNetworks vol 3 pp 1483ndash1486 August 2005

[10] G Acampora V Loia S Salerno and A Vitiello ldquoA hybridevolutionary approach for solving the ontology alignmentproblemrdquo International Journal of Intelligent Systems vol 27 no3 pp 189ndash216 2012

[11] Q Ge and C J Wei ldquoApproach for optimizing echo statenetwork training based on PSOrdquo Computer Engineering andDesign vol 8 pp 1947ndash1949 2009

[12] Q Song and Z Feng ldquoStable trajectory generatormdashecho statenetwork trained by particle swarm optimizationrdquo in Proceed-ings of the IEEE International Symposium on ComputationalIntelligence in Robotics and Automation (CIRA rsquo09) pp 21ndash26December 2009

[13] G Acampora J M Cadenas V Loia and E M BallesterldquoAchieving memetic adaptability by means of agent-basedmachine learningrdquo IEEE Transactions on Industrial Informaticsvol 7 no 4 pp 557ndash569 2011

[14] G Acampora J M Cadenas V Loia and E Munoz BallesterldquoA multi-agent memetic system for human-based knowledgeselectionrdquo IEEE Transactions on Systems Man and CyberneticsPart ASystems and Humans vol 41 no 5 pp 946ndash960 2011

[15] Z Zhou Y S Ong M H Lim and B S Lee ldquoMemetic algo-rithm using multi-surrogates for computationally expensiveoptimization problemsrdquo Soft Computing vol 11 no 10 pp 957ndash971 2007

[16] K K Lim Y-S Ong M H Lim X Chen and A AgarwalldquoHybrid ant colony algorithms for path planning in sparsegraphsrdquo Soft Computing vol 12 no 10 pp 981ndash994 2008

[17] Y-S Ong M-H Lim F Neri and H Ishibuchi ldquoSpecial issueon emerging trends in soft computing memetic algorithmsrdquoSoft Computing vol 13 no 8-9 pp 739ndash740 2009

[18] L J Cao K S Chua W K Chong H P Lee and Q M GuldquoA comparison of PCA KPCA and ICA for dimensionalityreduction in support vector machinerdquo Neurocomputing vol 55no 1-2 pp 321ndash336 2003

[19] J-M Lee C Yoo S W Choi P A Vanrolleghem and I-B Lee ldquoNonlinear process monitoring using kernel principalcomponent analysisrdquo Chemical Engineering Science vol 59 no1 pp 223ndash234 2004


[20] X Lin Z Yang and Y Song ldquoShort-term stock price predictionbased on echo state networksrdquo Expert Systemswith Applicationsvol 36 no 3 pp 7313ndash7317 2009

[21] C Gallicchio and A Micheli ldquoArchitectural and Markovianfactors of echo state networksrdquo Neural Networks vol 24 no 5pp 440ndash456 2011

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


the wavelet decomposition method to match different ESNmodels at each scale with different properties Then theleast square method realizes the optimal integration of thepredictive components through weight coefficients so as toreach accurate prediction of each scale and integration [5]ESNwas adopted to predict the conditions of flue gas turbineand the singular decompositionmethod was used to carry onthe modification of the linear regression training algorithmof ESN [6] The autocorrelation function method was usedto construct the input sequence of ESN for setting up thetime series forecast method [7] which is used in the fieldof the mobile communication traffic prediction The ESNprediction model based on the principal component analysismethod was established in order to reduce the training timeand improve the forecast speed [8] However the calculationof the ESN output weights based on the standard linearregression algorithm may easily lead to the pathologicalsolutions when dealing with the practical problems Onthe other hand the output weights are often with largeramplitudes In order to conquer the ill-conditioned matrixproblems of traditional echo state network model the evo-lutionary algorithms such as genetic algorithms (GAs) [910] particle swarm optimization (PSO) algorithm [11 12]memetic algorithm (MA) [13ndash15] and ant colony algorithm(ACA) [16 17] are applied to train the output weights of ESN

In this paper a kind of echo state network (ESN) soft-sensor model for the VCM conversion rate and conversionvelocity in the PVC production process based on the biogeo-graphic algorithm is put forward and the simulation resultsverify the effectiveness of the proposed method The paperis organized as follows In Section 2 the technique flowchartof the PVC polymerization process is introduced The datadimension reduction based on KPCA method is presentedin Section 3 In Section 4 the ESN soft-sensor model basedon BBO algorithm is introducedThe simulation experimentsand results analysis are introduced in detail in Section 5Finally the conclusion illustrates the last part

2 PVC Polymerization Process

In PVC polymerization process various raw materials andadditives are added to the reaction kettle which are full evenlydispersed under themixing actionThen the suitable amountsof the initiators are added to the kettle and start to react Thecooling water is constantly poured into the jacket and baffleof reaction kettle to remove the reaction heat The reactionwill be terminated and the final products are obtained whenthe conversion ratio of the vinyl chloride (VCM) reaches acertain value and a proper pressure drop appears Finallyafter the reaction completed and VCM contained in slurryseparated by the stripping technique the remaining slurryis fed into the drying process for dewatering and drying Atypical PVC polymerization kettle technological process isshown in Figure 1 [2]

According to characteristics of polymerization process10 process variables related to VCM conversion rate andconversion velocity are selected as secondary variables of soft-sensor modeling They respectively are kettle temperature

Table 1 Cumulative contribution ratio of different principal com-ponent number

Principalcomponentnumber

Percentage ofvariance ()

Cumulativepercentage ofvariance ()

1 5934 59342 1649 75833 835 84184 627 90455 491 95366 252 97887 101 98898 059 99489 052 1000010 0 10000

(TIC-P101) kettle pressure (PIC-P102) baffle water flow(FIC-P101) jacket water flow (FIC-P102) injection water flow(FIC-P104) seal water flow (FIC-P105) inlet temperature ofcooling water (for jacket water and baffles water sharing TI-P107) outlet temperature of jacket water (TI-P109) outlettemperature of baffle water (TI-P110) and inlet temperatureof injection water and seal water (namely the outlet temper-ature of the cold water tank TIC-WA01)

3 Data Dimension Reduction Based onKPCA Method

According to the above process characteristics 10 processvariables as auxiliary variables are determined But for neuralnetwork soft-sensor model too large dimensions of inputvector will cause dimension disaster which can lead to thefact that network topology becomes tedious and training iscomplicated In this paper the kernel principal componentanalysis (KPCA)method is adopted to reduce the dimensionsof the input vector KPCA introducing the concept of kernelfunction into principal component analysis (PCA) is a kindof nonlinear extension of PCA KPCA as a nonlinear formof PCA has the ability to deal with nonlinear problem betterthan PCA [18 19] Data sets composed by input variables ofthe model are given a kernel principal component analysisand the analysis results are shown in Table 1 The variancecontribution rate of the first five principal components hasreached more than 95 Original data primary variables dis-posed by KPCA are selected as inputs of the neural networkmodel which not only retains the characteristic informationof original variables but also simplifies the structure of neuralnetwork

4 ESN Soft-Sensor Model Based onBBO Algorithm

41 Structure of Soft-Sensor Model Soft-sensor technology ismainly composed of four parts data acquisition and process-ing choice of auxiliary variables soft-sensor modeling and


P-12

FV-PX05

FV-PX03FV-PX01

FV-PX02

Vent

VSP-PX23VSP-PX37

VSP-PX03

VSP-PX04

VSP-PX13 VSP-PX14

VSP-PX19

VSP-PX15

VSP-PX33VSP-PX26

VSP-PX22

VSP-PX25

VSP-PX36 VSP-PX16

VSP-PX01

VSP-PX08

VSP-PX21

VSP-PX12

VSP-PX10

VSP-PX09

Cooling water

Air

TIP109

Sealing water


agent TICWA01

FICP105

TIP107

Impact modifiers

Water feed

Terminate agent

TICP101

PICP102

TIP110

TICWA01

P-90

FICP102

FICP101

VCM feed

Flush water

TK-IE

SE-IF

Switched agents


Steam

Trench

PU-XE


Flush water

Steam

FICP104

P-96

P-98

P-101



Varia

ble d

imen

sion

Auxiliary variable

Dominant variable

Predicted value

Poly

mer

izat

ion

kettl

e sys

tem Kettle pressure

Baffle water flow

Jacket water flow

Outlet

of baffle water

of jacket water

Dat

a acq

uisit

ion

and

proc

essin

g

The c

hoic

e of a

uxili

ary

varia

bles

k-m

eans

clus

terin

g

Model 1

Model 2

Model k

etemperature

Outlettemperature

redu

ctio

n b

+

minusΣ






3 outlet










cluster centers


119889 (119909119894 119909119895) = radic

119899

sum

119896=1

(119909119894119896minus 119909119895119896)

2

(1)

where 119909119894and 119909


sion


119864 =

119896

sum

119894=1

sum

119901isin119883119894

1003817100381710038171003817119901 minus 119888119894

1003817100381710038171003817

2

(2)








network


Dominant variable

Predicted value


Variable m

+minus



u1

uK

W

x1x2

x3x4

x7

x6

x5

xN

y1

yL

Win Wout

Wfb






vector 119909(119899) = [1199091(119899) 119909



119871(119899)]119879 Between










119909 (119899 + 1) = 119891 (119882in119906 (119899 + 1) + 119882119909 (119899) + 119882

fb119889 (119899)) (3)

119910 (119899 + 1) = 119882out[119909 (119899 + 1) 119906 (119899 + 1)] (4)









Rate

Number of species

I

E

120583

120582

S0 Smax





119896 the











119896=



120582119896= 119868 times (1 minus

119896

119899

)

120583119896= 119864 times

119896

119899

(5)




119901119904(119905 + Δ119905) = (1 minus 120582

119904minus 120583119904) 119875119904Δ119905 + 120582

119904minus1119875119904minus1Δ119905

+ 120583119904+1119875119904+1Δ119905

(6)




119875119904

=

minus (120582119904+ 120583119904) 119875119904+ 120583119904+1119875119904+1 119878 = 0


+ 120583119904+1119875119904+1 1 le 119878 lt 119878max minus 1


(7)





119860

=

[

[

[

[

[

[

[

[

[

minus (1205820+ 1205830) 120583

1

1205820

minus (1205821+ 1205831) 1205832

1205821



+ 120583119899minus1) 120583

119899minus1

120582119899minus1

minus (120582119899+ 120583119899)

]

]

]

]

]

]

]

]

]

119898119894= 119898max (

1 minus 119875 (119878119894)

119875max)

(8)










119896and














Start









Over






Migration operation

Mutation operation

No

Yes










in= 03119882 = 02 and119882in









119879

119879

sum

119905=1

1003816100381610038161003816119910 (119905) minus 119910

119889(119905)1003816100381610038161003816

119910119889(119905)


119879

119879

sum

119905=1

(119910 (119905) minus 119910119889(119905))2


119879

119899

sum

119905=1

(119910119889(119905) minus 119910 (119905))

2

]

12


1198791003817100381710038171003817119910119889

1003817100381710038171003817

2

119879

sum

119905=1

(119910 (119905) minus 119910119889(119905))2

Sum of squarederror

SSE =119899

sum

119905=1

(119910119889(119905) minus 119910(119905))

2

0 50 100 150 200 25004

06

08

1

12

14

16

18

2

Sequence

Rate

of c

onve

rsio

n

The actual output

The predicted



of BBO-ESN




0 50 100 150 200 250

0

01

02

03

04

Sequence

The p

redi

ctio

n er

ror o

f con

vers

ion

rate


minus04

minus03

minus02

minus01


0 50 100 150 200 250

0

10

20

30

40

50

60

70

80

Sequence

The actual output

The predicted



of BBO-ESN

Con

vers

ion

ratio

()

minus10




6 Conclusions




0 50 100 150 200 250

0

10

20

30

40

Sequence

The p

redi

cted

erro

r of c

onve

rsio

n ra

tio

minus10

minus20

minus30





Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










P-12

FV-PX05

FV-PX03FV-PX01

FV-PX02

Vent

VSP-PX23VSP-PX37

VSP-PX03

VSP-PX04

VSP-PX13 VSP-PX14

VSP-PX19

VSP-PX15

VSP-PX33VSP-PX26

VSP-PX22

VSP-PX25

VSP-PX36 VSP-PX16

VSP-PX01

VSP-PX08

VSP-PX21

VSP-PX12

VSP-PX10

VSP-PX09

Cooling water

Air

TIP109

Sealing water


agent TICWA01

FICP105

TIP107

Impact modifiers

Water feed

Terminate agent

TICP101

PICP102

TIP110

TICWA01

P-90

FICP102

FICP101

VCM feed

Flush water

TK-IE

SE-IF

Switched agents


Steam

Trench

PU-XE


Flush water

Steam

FICP104

P-96

P-98

P-101



Varia

ble d

imen

sion

Auxiliary variable

Dominant variable

Predicted value

Poly

mer

izat

ion

kettl

e sys

tem Kettle pressure

Baffle water flow

Jacket water flow

Outlet

of baffle water

of jacket water

Dat

a acq

uisit

ion

and

proc

essin

g

The c

hoic

e of a

uxili

ary

varia

bles

k-m

eans

clus

terin

g

Model 1

Model 2

Model k

etemperature

Outlettemperature

redu

ctio

n b

+

minusΣ






3 outlet










cluster centers


119889 (119909119894 119909119895) = radic

119899

sum

119896=1

(119909119894119896minus 119909119895119896)

2

(1)

where 119909119894and 119909


sion


119864 =

119896

sum

119894=1

sum

119901isin119883119894

1003817100381710038171003817119901 minus 119888119894

1003817100381710038171003817

2

(2)








network


Dominant variable

Predicted value


Variable m

+minus



u1

uK

W

x1x2

x3x4

x7

x6

x5

xN

y1

yL

Win Wout

Wfb






vector 119909(119899) = [1199091(119899) 119909



119871(119899)]119879 Between










119909 (119899 + 1) = 119891 (119882in119906 (119899 + 1) + 119882119909 (119899) + 119882

fb119889 (119899)) (3)

119910 (119899 + 1) = 119882out[119909 (119899 + 1) 119906 (119899 + 1)] (4)









Rate

Number of species

I

E

120583

120582

S0 Smax





119896 the











119896=



120582119896= 119868 times (1 minus

119896

119899

)

120583119896= 119864 times

119896

119899

(5)




119901119904(119905 + Δ119905) = (1 minus 120582

119904minus 120583119904) 119875119904Δ119905 + 120582

119904minus1119875119904minus1Δ119905

+ 120583119904+1119875119904+1Δ119905

(6)




119875119904

=

minus (120582119904+ 120583119904) 119875119904+ 120583119904+1119875119904+1 119878 = 0


+ 120583119904+1119875119904+1 1 le 119878 lt 119878max minus 1


(7)





119860

=

[

[

[

[

[

[

[

[

[

minus (1205820+ 1205830) 120583

1

1205820

minus (1205821+ 1205831) 1205832

1205821



+ 120583119899minus1) 120583

119899minus1

120582119899minus1

minus (120582119899+ 120583119899)

]

]

]

]

]

]

]

]

]

119898119894= 119898max (

1 minus 119875 (119878119894)

119875max)

(8)










119896and














Start









Over






Migration operation

Mutation operation

No

Yes










in= 03119882 = 02 and119882in









119879

119879

sum

119905=1

1003816100381610038161003816119910 (119905) minus 119910

119889(119905)1003816100381610038161003816

119910119889(119905)


119879

119879

sum

119905=1

(119910 (119905) minus 119910119889(119905))2


119879

119899

sum

119905=1

(119910119889(119905) minus 119910 (119905))

2

]

12


1198791003817100381710038171003817119910119889

1003817100381710038171003817

2

119879

sum

119905=1

(119910 (119905) minus 119910119889(119905))2

Sum of squarederror

SSE =119899

sum

119905=1

(119910119889(119905) minus 119910(119905))

2

0 50 100 150 200 25004

06

08

1

12

14

16

18

2

Sequence

Rate

of c

onve

rsio

n

The actual output

The predicted



of BBO-ESN




0 50 100 150 200 250

0

01

02

03

04

Sequence

The p

redi

ctio

n er

ror o

f con

vers

ion

rate


minus04

minus03

minus02

minus01


0 50 100 150 200 250

0

10

20

30

40

50

60

70

80

Sequence

The actual output

The predicted



of BBO-ESN

Con

vers

ion

ratio

()

minus10




6 Conclusions




0 50 100 150 200 250

0

10

20

30

40

Sequence

The p

redi

cted

erro

r of c

onve

rsio

n ra

tio

minus10

minus20

minus30





Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra















cluster centers


119889 (119909119894 119909119895) = radic

119899

sum

119896=1

(119909119894119896minus 119909119895119896)

2

(1)

where 119909119894and 119909


sion


119864 =

119896

sum

119894=1

sum

119901isin119883119894

1003817100381710038171003817119901 minus 119888119894

1003817100381710038171003817

2

(2)








network


Dominant variable

Predicted value


Variable m

+minus



u1

uK

W

x1x2

x3x4

x7

x6

x5

xN

y1

yL

Win Wout

Wfb






vector 119909(119899) = [1199091(119899) 119909



119871(119899)]119879 Between










119909 (119899 + 1) = 119891 (119882in119906 (119899 + 1) + 119882119909 (119899) + 119882

fb119889 (119899)) (3)

119910 (119899 + 1) = 119882out[119909 (119899 + 1) 119906 (119899 + 1)] (4)









Rate

Number of species

I

E

120583

120582

S0 Smax





119896 the











119896=



120582119896= 119868 times (1 minus

119896

119899

)

120583119896= 119864 times

119896

119899

(5)




119901119904(119905 + Δ119905) = (1 minus 120582

119904minus 120583119904) 119875119904Δ119905 + 120582

119904minus1119875119904minus1Δ119905

+ 120583119904+1119875119904+1Δ119905

(6)




119875119904

=

minus (120582119904+ 120583119904) 119875119904+ 120583119904+1119875119904+1 119878 = 0


+ 120583119904+1119875119904+1 1 le 119878 lt 119878max minus 1


(7)





119860

=

[

[

[

[

[

[

[

[

[

minus (1205820+ 1205830) 120583

1

1205820

minus (1205821+ 1205831) 1205832

1205821



+ 120583119899minus1) 120583

119899minus1

120582119899minus1

minus (120582119899+ 120583119899)

]

]

]

]

]

]

]

]

]

119898119894= 119898max (

1 minus 119875 (119878119894)

119875max)

(8)










119896and














Start









Over






Migration operation

Mutation operation

No

Yes










in= 03119882 = 02 and119882in









119879

119879

sum

119905=1

1003816100381610038161003816119910 (119905) minus 119910

119889(119905)1003816100381610038161003816

119910119889(119905)


119879

119879

sum

119905=1

(119910 (119905) minus 119910119889(119905))2


119879

119899

sum

119905=1

(119910119889(119905) minus 119910 (119905))

2

]

12


1198791003817100381710038171003817119910119889

1003817100381710038171003817

2

119879

sum

119905=1

(119910 (119905) minus 119910119889(119905))2

Sum of squarederror

SSE =119899

sum

119905=1

(119910119889(119905) minus 119910(119905))

2

0 50 100 150 200 25004

06

08

1

12

14

16

18

2

Sequence

Rate

of c

onve

rsio

n

The actual output

The predicted



of BBO-ESN




0 50 100 150 200 250

0

01

02

03

04

Sequence

The p

redi

ctio

n er

ror o

f con

vers

ion

rate


minus04

minus03

minus02

minus01


0 50 100 150 200 250

0

10

20

30

40

50

60

70

80

Sequence

The actual output

The predicted



of BBO-ESN

Con

vers

ion

ratio

()

minus10




6 Conclusions




0 50 100 150 200 250

0

10

20

30

40

Sequence

The p

redi

cted

erro

r of c

onve

rsio

n ra

tio

minus10

minus20

minus30





Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















119909 (119899 + 1) = 119891 (119882in119906 (119899 + 1) + 119882119909 (119899) + 119882

fb119889 (119899)) (3)

119910 (119899 + 1) = 119882out[119909 (119899 + 1) 119906 (119899 + 1)] (4)









Rate

Number of species

I

E

120583

120582

S0 Smax





119896 the











119896=



120582119896= 119868 times (1 minus

119896

119899

)

120583119896= 119864 times

119896

119899

(5)




119901119904(119905 + Δ119905) = (1 minus 120582

119904minus 120583119904) 119875119904Δ119905 + 120582

119904minus1119875119904minus1Δ119905

+ 120583119904+1119875119904+1Δ119905

(6)




119875119904

=

minus (120582119904+ 120583119904) 119875119904+ 120583119904+1119875119904+1 119878 = 0


+ 120583119904+1119875119904+1 1 le 119878 lt 119878max minus 1


(7)





119860

=

[

[

[

[

[

[

[

[

[

minus (1205820+ 1205830) 120583

1

1205820

minus (1205821+ 1205831) 1205832

1205821



+ 120583119899minus1) 120583

119899minus1

120582119899minus1

minus (120582119899+ 120583119899)

]

]

]

]

]

]

]

]

]

119898119894= 119898max (

1 minus 119875 (119878119894)

119875max)

(8)










119896and














Start









Over






Migration operation

Mutation operation

No

Yes










in= 03119882 = 02 and119882in









119879

119879

sum

119905=1

1003816100381610038161003816119910 (119905) minus 119910

119889(119905)1003816100381610038161003816

119910119889(119905)


119879

119879

sum

119905=1

(119910 (119905) minus 119910119889(119905))2


119879

119899

sum

119905=1

(119910119889(119905) minus 119910 (119905))

2

]

12


1198791003817100381710038171003817119910119889

1003817100381710038171003817

2

119879

sum

119905=1

(119910 (119905) minus 119910119889(119905))2

Sum of squarederror

SSE =119899

sum

119905=1

(119910119889(119905) minus 119910(119905))

2

0 50 100 150 200 25004

06

08

1

12

14

16

18

2

Sequence

Rate

of c

onve

rsio

n

The actual output

The predicted



of BBO-ESN




0 50 100 150 200 250

0

01

02

03

04

Sequence

The p

redi

ctio

n er

ror o

f con

vers

ion

rate


minus04

minus03

minus02

minus01


0 50 100 150 200 250

0

10

20

30

40

50

60

70

80

Sequence

The actual output

The predicted



of BBO-ESN

Con

vers

ion

ratio

()

minus10




6 Conclusions




0 50 100 150 200 250

0

10

20

30

40

Sequence

The p

redi

cted

erro

r of c

onve

rsio

n ra

tio

minus10

minus20

minus30





Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra













119896=



120582119896= 119868 times (1 minus

119896

119899

)

120583119896= 119864 times

119896

119899

(5)




119901119904(119905 + Δ119905) = (1 minus 120582

119904minus 120583119904) 119875119904Δ119905 + 120582

119904minus1119875119904minus1Δ119905

+ 120583119904+1119875119904+1Δ119905

(6)




119875119904

=

minus (120582119904+ 120583119904) 119875119904+ 120583119904+1119875119904+1 119878 = 0


+ 120583119904+1119875119904+1 1 le 119878 lt 119878max minus 1


(7)





119860

=

[

[

[

[

[

[

[

[

[

minus (1205820+ 1205830) 120583

1

1205820

minus (1205821+ 1205831) 1205832

1205821



+ 120583119899minus1) 120583

119899minus1

120582119899minus1

minus (120582119899+ 120583119899)

]

]

]

]

]

]

]

]

]

119898119894= 119898max (

1 minus 119875 (119878119894)

119875max)

(8)










119896and














Start









Over






Migration operation

Mutation operation

No

Yes










in= 03119882 = 02 and119882in









119879

119879

sum

119905=1

1003816100381610038161003816119910 (119905) minus 119910

119889(119905)1003816100381610038161003816

119910119889(119905)


119879

119879

sum

119905=1

(119910 (119905) minus 119910119889(119905))2


119879

119899

sum

119905=1

(119910119889(119905) minus 119910 (119905))

2

]

12


1198791003817100381710038171003817119910119889

1003817100381710038171003817

2

119879

sum

119905=1

(119910 (119905) minus 119910119889(119905))2

Sum of squarederror

SSE =119899

sum

119905=1

(119910119889(119905) minus 119910(119905))

2

0 50 100 150 200 25004

06

08

1

12

14

16

18

2

Sequence

Rate

of c

onve

rsio

n

The actual output

The predicted



of BBO-ESN




0 50 100 150 200 250

0

01

02

03

04

Sequence

The p

redi

ctio

n er

ror o

f con

vers

ion

rate


minus04

minus03

minus02

minus01


0 50 100 150 200 250

0

10

20

30

40

50

60

70

80

Sequence

The actual output

The predicted



of BBO-ESN

Con

vers

ion

ratio

()

minus10




6 Conclusions




0 50 100 150 200 250

0

10

20

30

40

Sequence

The p

redi

cted

erro

r of c

onve

rsio

n ra

tio

minus10

minus20

minus30





Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Start









Over






Migration operation

Mutation operation

No

Yes










in= 03119882 = 02 and119882in









119879

119879

sum

119905=1

1003816100381610038161003816119910 (119905) minus 119910

119889(119905)1003816100381610038161003816

119910119889(119905)


119879

119879

sum

119905=1

(119910 (119905) minus 119910119889(119905))2


119879

119899

sum

119905=1

(119910119889(119905) minus 119910 (119905))

2

]

12


1198791003817100381710038171003817119910119889

1003817100381710038171003817

2

119879

sum

119905=1

(119910 (119905) minus 119910119889(119905))2

Sum of squarederror

SSE =119899

sum

119905=1

(119910119889(119905) minus 119910(119905))

2

0 50 100 150 200 25004

06

08

1

12

14

16

18

2

Sequence

Rate

of c

onve

rsio

n

The actual output

The predicted



of BBO-ESN




0 50 100 150 200 250

0

01

02

03

04

Sequence

The p

redi

ctio

n er

ror o

f con

vers

ion

rate


minus04

minus03

minus02

minus01


0 50 100 150 200 250

0

10

20

30

40

50

60

70

80

Sequence

The actual output

The predicted



of BBO-ESN

Con

vers

ion

ratio

()

minus10




6 Conclusions




0 50 100 150 200 250

0

10

20

30

40

Sequence

The p

redi

cted

erro

r of c

onve

rsio

n ra

tio

minus10

minus20

minus30





Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra












119879

119879

sum

119905=1

1003816100381610038161003816119910 (119905) minus 119910

119889(119905)1003816100381610038161003816

119910119889(119905)


119879

119879

sum

119905=1

(119910 (119905) minus 119910119889(119905))2


119879

119899

sum

119905=1

(119910119889(119905) minus 119910 (119905))

2

]

12


1198791003817100381710038171003817119910119889

1003817100381710038171003817

2

119879

sum

119905=1

(119910 (119905) minus 119910119889(119905))2

Sum of squarederror

SSE =119899

sum

119905=1

(119910119889(119905) minus 119910(119905))

2

0 50 100 150 200 25004

06

08

1

12

14

16

18

2

Sequence

Rate

of c

onve

rsio

n

The actual output

The predicted



of BBO-ESN




0 50 100 150 200 250

0

01

02

03

04

Sequence

The p

redi

ctio

n er

ror o

f con

vers

ion

rate


minus04

minus03

minus02

minus01


0 50 100 150 200 250

0

10

20

30

40

50

60

70

80

Sequence

The actual output

The predicted



of BBO-ESN

Con

vers

ion

ratio

()

minus10




6 Conclusions




0 50 100 150 200 250

0

10

20

30

40

Sequence

The p

redi

cted

erro

r of c

onve

rsio

n ra

tio

minus10

minus20

minus30





Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











0 50 100 150 200 250

0

10

20

30

40

Sequence

The p

redi

cted

erro

r of c

onve

rsio

n ra

tio

minus10

minus20

minus30





Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra



















Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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