Research Article Modeling and Optimization of the Drug ...downloads.hindawi.com/journals/sp/2016/3279423.pdf · of the oil-water separator. A mathematical model of the extraction

Research ArticleModeling and Optimization of the Drug ExtractionProduction Process

Dakuo He12 Zhengsong Wang1 Le Yang1 Tongshan Liu1 Yao Yao1 and Zhizhong Mao12

1College of Information Science and Engineering Northeastern University Shenyang Liaoning 110004 China2State Key Laboratory of Synthetical Automation for Process Industries Northeastern University Shenyang 110004 China

Correspondence should be addressed to Dakuo He hedakuoiseneueducn

Received 17 June 2016 Revised 31 August 2016 Accepted 14 September 2016

Academic Editor Chengyan Yue

Copyright copy 2016 Dakuo He 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

Optimized control of the drug extraction production process (DEPP) aims to reduce production costs and improve economicbenefit while meeting quality requirements However optimization of DEPP is hampered by model uncertainty Thus in thispaper a strategy that considers model uncertainty is proposed Mechanistic modeling of DEPP is first discussed in the contextof previous work The predictive model used for optimization is then developed by simplifying the mechanism Optimization fora single extraction process is first implemented but this is found to lead to serious wastage of herbs Hence the optimization of amultiextraction process is then conducted Tomanage the uncertainty in themodel a data-driven iterative learning control methodis introduced to improve the economic benefit by adjusting the operating variables Finally fuzzy parameter adjustment is adoptedto enhance the convergence rate of the algorithmThe effectiveness of the proposedmodeling and optimization strategy is validatedthrough a series of simulations

1 Introduction

Drug extraction or drug leaching is one of the mostsignificant operations in the pharmaceutical industry As thebasic and primary process of drug production it has beenwidely applied to many medicinal plants [1ndash7] In the drugextraction production process (DEPP) a solvent or chemicalreagent that offers high solubility for the effective constituent(EC) in the herbs and poor solubility for constituents thatneed not be extracted is applied to solid herbs The EC thendissolves out of the herb organization and into the solventor chemical reagent [8] The extracted EC is finally used invarious types of drugs such as granules tablets and capsulesin subsequent pharmaceutical processes

The disadvantages of this production process includelow extraction yield wastage of materials and high energyconsumptionModeling andprocess optimizationwhich aimto increase the extraction yield and minimize productioncosts while meeting specific quality requirements are there-fore particularly significant in both theoretical research andpractical applications

The optimization of drug extraction process has receivedincreasing attention For example Alam et al [9] studiedthe optimization of the extraction parameters of embelinfrom Embelia ribes through ultrasound-assisted extractionwith a BoxndashBehnken design Bochi et al [10] optimized theextraction conditions and anthocyanin yields in experimentswith high proportions of water Chen et al [11] applied anorthogonal experiment to optimize the extraction conditionsof polysaccharides from Ornithogalum caudatum Ait Chenet al [12] used the response surface methodology to optimizethe experimental conditions for ultrasonic-assisted extrac-tion of functional components from sugar beet molassesBae et al [13] successfully developed and validated a simplequalitative and quantitative method for the simultaneousdetermination of 15 phenolic compounds and caffeine fromteas and then optimized the extraction process using theresponse surface methodology based on a central compositedesign In addition to these innovations many other scholarshave made tremendous contributions to the theoretical andpractical optimization of DEPP [3 14ndash16] However many ofthese reports focus on optimizing the extraction conditions

Hindawi Publishing CorporationScientific ProgrammingVolume 2016 Article ID 3279423 15 pageshttpdxdoiorg10115520163279423

2 Scientific Programming

using experimental design or simulation techniques To thebest of the authorsrsquo knowledge the optimization of DEPP interms of improving the economic benefit of the whole pro-duction process has rarely been reported in the literatureThepresent work develops a mechanism model for DEPP basedon some previous efforts and then proposes an optimizationstrategy to resolve practical problems such as the productionefficiency and production costs

To implement this optimization a mechanism model ofDEPP should be developed Suchmechanisticmodeling playsseveral significant roles first the modeling process will ana-lyze the mechanism of the drug extraction process confirmits operating variables and quality indicators and analyze therelationship between them second an appropriatemodel canbe used to simulate the actual production process to generatethe required data and analyze the optimization results Asan actual simulator the mechanism model should be ableto link the extraction efficiency of the EC and volatile oilmdashthe quality indicatorsmdashwith the operating variables (steamflow at the bottom and side of the extraction tank and theextraction time)

The mechanistic modeling of DEPP mainly consists ofmodeling the following components extraction tank masstransfer process of EC volatile oil recycling and efficiencyof the oil-water separator A mathematical model of theextraction tank that describes the changes in temperatureand liquid level over time has been developed [17] As theprinciple and mechanism of the mass transfer process indrug extraction are very similar to those of metal leachingmechanistic models of metal leaching [3 18ndash22] can be usedas references in developing a mass transfer model for theEC Additionally Han et al derived a diffusion rate equationfor volatile oils allowing a mechanistic model of volatile oilrecovery to be developed [23] Finally the efficiency of theoil-water separator is introduced to describe the separationefficiency of oil droplets with a certain diameter [24] Theabove mechanistic models are combined to simulate thewhole DEPP and the rationality and validity of this approachare verified through a series of simulations The innovationand contribution of the DEPP model presented in this papercan be summarized as follows First we extend a modelingapproach for the leaching process to model the mass transferprocess of ECs Second we present a combined mechanisticmodeling framework for the overall DEPP by integrating fourdiscrete components described in previous studies

In addition to a mechanistic model a predictive modelis also necessary for such optimization In this work theestablished mechanism is simplified to serve as a predictivemodel The economic benefit per unit time is consideredas the optimization objective while the steam flow at thebottom and side of the extraction tank and the extractiontime are treated as decision variablesTheoptimizationmodelis then established under certain quality constraints Severalclassical optimization algorithms such as particle swarmoptimization (PSO) [25 26] differential evolution (DE) [27]and artificial bee colony (ABC) [28] are adopted to solvethis optimization problem Comparing these algorithms itis concluded that PSO achieves the best performance indetermining the optimal solution Thus a PSO algorithm

is used to solve this optimization problem and obtain theoptimal economic benefit and corresponding parametersincluding optimal quality indicators and operating variablesThe present work first considers the optimization of a singleextraction process However the extraction efficiency of theEC in this case is very low leading to serious wastage ofherb materials The optimization control for multiextractionis therefore investigated In the multiextraction process theextraction frequency is defined as the number of times thatthe herbs are subjected to the extraction process Howeverthe optimal extraction frequency in terms of economicbenefit is unknownThus the extraction frequency is treatedas one of the decision variables when establishing the opti-mization problem Note that the extraction frequency is aninteger in this problem

The optimal economic benefit of the multiextractionprocess is based on the predictive model whereas the actualoptimal economic benefit can be calculated by plugging thebest operating variables into themechanismmodelThere aresome discrepancies between the predicted and actual valuesof the optimal economic benefit In practice however it isunlikely that the actual production process can be modeledaccurately (or even approximately) with a process model[29 30] Process optimization is hampered by such modeluncertainty and so the ldquooptimalrdquo value given by the modelmay not necessarily mean ldquooptimal for the processrdquo [31]

Iterative learning control (ILC) is highly effective incontrolling systems with repetitive operations that preciselyfollow a desired target trajectory It has beenwidely applied inrepetitive industrial processes because of its perfect learningability from the repetitive tracking task [32ndash34] Recentlydata-driven ILC methods have been proposed to deal withcomplicated practical systems [35ndash37] The control scheme isdata-driven because there is no explicit model informationor training process and only the measured input and outputdata are used for the controller design analysis and imple-mentation [36] As one such method data-driven optimalterminal ILC (DDOTILC) works under the principle thatthe control law is only updated using the terminal outputtracking error [35] In this work DDOTILC is applied toimplement iterative optimization control for DEPP in orderto overcome themodel uncertainty via the online adjustmentof the operating variables The fuzzy adaptive adjustment ofparameters inDDOTILC is then implemented to enhance theconvergence rate Using this approach themodel uncertaintycan be reduced and the economic benefit improved byadjusting the operating variables

2 Principle and Production Technology of theDrug Extraction Process

21 Principle of the Drug Extraction Process

211 Mass Transfer Theory of Effective Constituent Drugextraction is one kind of solid-liquid extraction Thus themass transfer principle and computing method follow thesolid-liquid extraction system model shown in Figure 1 Itis assumed that the herb particles are composed of solute

Scientific Programming 3

Feed liquid

Liquid film Gas film

Herb residues

(1)

(2)

(3)

(4)

(5)

a rR C0

r0

core

C

Unextracted

Figure 1 Unextracted core shrinkingmodel of effective component

(EC) and inert carriers (herb residues) so the solid-liquidextraction system is composed of solute solvent and inertsolid Additionally there will be a gas-liquid film at theinterface between the solid particles and liquid phase It isgenerally acknowledged that this mass transfer process canbe divided into the five steps described in Figure 1 [3 8]

(1) The diffusion of solvent into the herb particle surface(2) The permeation of solvent from the herb surface to

the interior(3) The dissolution of the EC inside the herb particles(4) The diffusion of EC from inside the herb particles to

the surface (internal diffusion)(5) The diffusion of EC from the herb particle surface

to the solvent across the gas-liquid film (externaldiffusion)

212 Recycling Theory of Volatile Oil Volatile oil (VO) alsonamed essential oil is a generic term for the volatile and oilycomponents in plants VOs are insoluble in water and can bedistilled out alongwith thewater vaporDuring the extractionprocess the recycling of VO is divided into the followingthree steps (see Figure 2)

(1) Internal diffusion with increasing temperature VOsdiffuse into the outer surface of the solid herb particlefrom the interior

(2) External diffusion VOs diffuse into the water vaporfrom the surface of the solid particle by threading thegas-liquid film

(3) Gas-liquid transition VOs and water vapor enter thecondenser and are condensed into the liquid phaseafter which the VOs are separated from water thoughthe oil-water separator

22 Production Technology of the Drug Extraction ProcessGenerally DEPP includes the following three procedures

Gas filmLiquid film

(1)

(2)

R

r0

Water vapor

Heat

d1

Figure 2 Schematic diagram of volatile oil recycling

Volatile oilrecovery

ExtractingSteam flow Q2

Steam flow Q1

FilterFeed liquid

Volatile oilVolatile oilCondenser

Cooler

Backflow

Gas-liquidseparator

Oil-waterseparator

tank

Figure 3 Diagram of equipment used in the extraction procedure

(1) Preprocessing of HerbMaterials In this procedure the herbmaterials are smashed and soaked in water for some time toinflate the herb organization This preprocessing acceleratesthe dissolution and diffusion of EC during extraction

(2) Extraction As the most important process of DEPP thisprocedure involves various pieces of equipment includingthe extraction tank condenser gas-liquid separator oil-waterseparator and filter (see Figure 3) In this process the prepro-cessed herb materials are placed into the extraction tank andsteam is added through both the bottom and side of the tankAs the temperature increases the valuable components of theherb particles such as EC and VO will continually diffuseinto the extraction solution and water vapor respectively Fora batch of herb materials it is extremely difficult to achieveacceptable yields of EC and VO with a single extraction pro-cess Therefore multiple extractions are required to preventthe wastage of raw materials

(3) Separation In this procedure the feed liquid containingEC and VO are separated from the herb residues and steamrespectively using the filter and oil-water separator The feedliquid and VO are then sent to the next phase for furtherprocessing


The extraction efficiencies of EC and VO are the mainquality indicators of DEPP There are numerous factorsinfluencing these indicators such as the radius of the herbmaterial particles extraction temperature extraction timeconcentration difference and solid-liquid contact conditionFor the purpose of DEPP optimization the present studyexplores the impact on the extraction efficiency of the steamflow at both the bottom and side of the extraction tank andthe extraction time

3 Mechanistic Modeling of Drug ExtractionProduction Process

DEPP is a complex heat and mass transfer process andits mechanistic model mainly consists of the followingcomponents mathematical model of drug extraction tankmass transfer model of EC mechanistic modeling of VOrecycling and an efficiency model of the oil-water separatorThe mechanistic modeling work for DEPP is implementedbased on the following assumptions

(1) The herb particle has a spherical shape after crushing(2) The EC of herb materials in the solvent is distributed

uniformly under the condition of full stirring(3) The EC in the outer layer of the herb particles is first

spread to the solvent after which the EC in the innerlayer spreads to the outer layer and then to the solvent

31 Mathematical Modeling of Drug Extraction Tank Amechanistic model of the extraction tank has been developedaccording to the principles of mass and energy conservation[17] In this model the liquid level 119867 and feed liquidtemperature 119879 in the extraction tank can be calculated usingthe steam flow at the bottom and side of the tank 1198761 1198762and the extraction time 119905 The variation of liquid level andtemperature with extraction time 119905 can be expressed as

119889119867119889119905 = (1198761 minus 1198763) 1198751119860 (1)

119889119879119889119905 = 11198601198781119867 [(1198752 minus 11987811198791198751 + 11987821198791 minus 1198782119879)1198761+ 11987821198762 (1198791 minus 119879) + (11987811198791198751 minus 1198752) 1198763]

(2)

The mixture flow of VO and steam1198763 is assumed to havea nonlinear relationship with 119879

1198763 = 11987011198901198702119879 (3)

The symbols used in this model are as follows 1198761 1198762the steam flow at the bottom and side of the extractiontank respectively 1198763 mixture flow of VO and steam 1198791steam temperature before entering the extraction tank 1198781specific heat capacity of feed liquid 1198782 specific heat capacityof water 1198751 volume ratio of water (liquefied from steam)and steam 1198752 standard heat of liquefaction of vapor understandard atmospheric pressure 119860 cross-sectional area of theextraction tank

32 Mathematical Modeling of the Mass Transfer Processof Effective Constituent The mass transfer process for ECwas described in detail in Section 2 where it was notedthat the transfer could be divided into five steps In theusual extraction process the penetration of solvent anddissolution of solute are not the controlling factors and canthus be neglected The diffusion processes undoubtedly havea decisive effect on the speed ofmass transfer Hence externaldiffusion and internal diffusion are primarily considered inthe modeling of the mass transfer process

External diffusion also called liquid film diffusion isthe main resistance to mass transfer The gas film will nothamper the mass transfer process so it is neglected inthe modeling process as illustrated by the dashed line inFigure 1 Internal diffusion is the shrinking core process ofparticles containing EC as shown in Figure 1 In this studyusing the unreacted shrinking core theory from the metalore leaching process the drug extraction process can beapproximately regarded as the leaching of metallic mineralsalbeit under different reactions When the EC in the outerlayer has diffused into the extraction solvent the insolublecomponents are left on the surface of the solid particlesThusthe solid particles are surrounded by a grey layer composedof insoluble components as shown in Figure 1 The inner ECthen diffuses into the surface of the solid particles throughinternal diffusion after which this part of the EC in the solidparticle surface diffuses into the solvent once again Thisprocedure is repeated and the unextracted corewill graduallyshrink

The diffusion rate of the extraction process can beexpressed as [3 18ndash20]

119889119866119889119905 = 119869119878 (4)

where119866 is themass of EC extracted from solid herb particles119869 is the mass of EC diffused from solid herb particles tosolvent per unit time 119878 expresses the area of the interfacebetween the solid and liquid phase and 119905 is the extractiontime

It is assumed that internal diffusion and external diffusionoccur in series so the law of additive resistance can be appliedas follows [3 21 22]

119869 = 1198620 minus 11986211205731 + 11205732 =1198620 minus 119862(119877 minus 119903) 119863119904 + 1199030119863 (5)

where 1198620 is the solubility of EC in the liquid film on thesurface of solid particles119862 is the instantaneous concentrationof EC in extraction solvent 119863 and 119863119904 express the diffusioncoefficients of EC passing through the liquid film and theinside of solid particles respectively 119877 and 119903 denote theradius of the original solid particle and the solid particle asthe core gradually shrinks respectively and 1199030 expresses thethickness of the liquid film (see Figure 1) In addition1205731 is thecoefficient of internal diffusion (11205731 is the internal diffusionresistance) and 1205732 is the coefficient of external diffusion (11205732


is the external diffusion resistance)The parameters 1205731 and1205732are given by

1205731 = 119863119904119877 minus 119903 1205732 = 1198631199030

(6)

Combined with the model of the extraction tank it canbe concluded that119889119866119889119905 = 119889 (119881119862)119889119905 = 119889 (119860119867119862)119889119905 = 119860119867119889119862119889119905 + 119860119862119889119867119889119905 (7)

Based on (1) (4) (5) and (7) we have that

119889119862119889119905 = 1119860119867 [ (1198620 minus 119862) 119878(119877 minus 119903) 119863119904 + 1199030119863 minus 1198621198751 (1198761 minus 1198763)] (8)

The diffusion coefficients can then be determined asfollows

(1) For the solution with macromolecules of EC theexternal diffusion coefficient is obtained by

119863 = 119861119879 V119860119891119860 (9)

The resistance of EC sustained in solution 119891119860 can becalculated by Stokesrsquo equation

119891119860 = 6120587119877120583119861V119860 (10)

Combining (9) and (10) we obtain

119863 = 1198611198796120587119877120583119861 (11)

where 119861 is the Boltzmann constant V119860 is the kinematicvelocity of ECmolecules and120583119861 is the viscosity of the solvent

(2) For the dilute solutionwithmicromolecules of EC theexternal diffusion coefficient is generally expressed byWilkersquosequation [38]

119863 = 74 times 10minus12 (120595119872119861)05 11987912058311986111988106119860 (12)

where 120595 is the associating parameter of the solvent 119872119861 isthe molecular weight of the solvent and 119881119860 is the molecularvolume of EC In this work (12) is used to calculate thediffusion coefficient 119863

(3)The internal diffusion coefficient of EC inside the solidparticle 119863119904 is calculated by [39]

119863119904 = 120576119863120591 (13)

where 120576 and 120591 are the porosity and sinuosity of holes insidethe solid particles respectively

Another equation connects the radius of solid particlescontaining EC with the internal diffusion coefficient 119863119904the concentration of EC in the liquid film 1198620 and theinstantaneous concentration of EC in extraction solvent 119862[39]

119903 = 119877 minus (1198961198631199041198621199051198620 )12 (14)

33 Mechanistic Modeling of Volatile Oil Recycling The recy-cling principle of VO was described in Section 2 Becausethe internal diffusion occurs in the same phase it can beneglected However the external diffusion process in whichVO diffuses into the gas phase (water vapor) from the surfaceof the solid phase (solid particle) across the gas-liquid filmis interphase diffusion This external diffusion is the mainfactor controlling the diffusion velocity Because the VO isinsoluble in water its explicit diffusion in the liquid phasecan be ignored as denoted by the dashed line in Figure 2Consequently the resistance to external diffusion mainlyoccurs in the gas film [40]The diffusion velocity is expressedas [40]

119889119902119889119905 = 119870119866119878 (119862119897 minus 119862119894) (15)

where 119902 is the concentration of VO in the solid herbparticles 119870119866 is the gas phase mass transfer film coefficient119862119897 is the concentration of VO in the gas phase and 119862119894is the concentration of VO in the gas film The followingassumptions are made

(1) Because the VO in the gas phase will constantly enterthe condenser with water vapor 119862119897 asymp 0

(2) There is a linear counterbalance between the concen-trations of VO in the solid phase and gas film that is119862119894 = 119870119902[23] where119870 is a constant coefficient

Equation (15) can then be expressed as

119889119902119889119905 = minus119870119866119878119870119902 = minus11989011989601198631198781198701198891 119902 (16)

where

119870119866 = 11989011989601198631198891 (17)

in which 1198960 is a constant coefficient and 1198891 is the thickness ofthe gas film

As for the liquid density the density of VO will decreaseas the feed liquid temperature 119879 increases The VO densitycan be calculated as

1205880 = 1198601 + 1198602119879 + 11986031198792 + 11986041198793 + 11986051198794 (18)

where 1205880 is the density of VO and 1198601ndash1198605 are constantcoefficients

34 Mechanistic Modeling of the Efficiency of the Oil-WaterSeparator Under the effect of gravity the oil-water separatorachieves the separation of oil andwater in the static or flowingstate by taking advantage of the density difference between oiland water The kinetic state of a droplet in the disperse phasecan be described by Stokesrsquo law [24]

V119900119908 = (120588119908 minus 1205880) 11989211988922181205830 (19)

where V119900119908 is the lifting velocity of the oil droplet 120588119908 is thedensity of water 119892 is acceleration due to gravity 1198892 is thediameter of the oil droplet and 1205830 is the viscosity of water


The separation efficiency of oil droplets of a certain diam-eter can be determined according to shallow pool theory [41]as

1205780 = 1198780V1199001199081198760 = 11987801198921812058301198760 (120588119908 minus 1205880) 11988922 (20)

where 1205780 is the lifting efficiency of oil droplets of diameter 11988921198780 is the lifting area of the oil layer and 1198760 is the flow of theoil-water mixture

The separation efficiency 120578119904 is a key performance indica-tor in any oil-water separator and can be expressed as follows

120578119904 = 1 minus 119862119889119862119887 (21)

where 119862119889 and 119862119887 denote the oil content at the exit andentrance of the separator respectively

35 Processing the Mechanistic Model of the Drug ExtractionProduction Process For the convenience of calculationsdifferential equations in the models are discretized to givea set of algebraic equations Taking the model for the liquidlevel in the extraction tank we have

119867(119896 + 1) minus 119867 (119896)119879119878 = (1198761 (119896) minus 1198763 (119896)) 1198751119860 (22)

where 119879119878 is the sampling periodThus the liquid level at sampling time 119896 + 1 is

119867(119896 + 1) = (1198761 (119896) minus 1198763 (119896)) 1198751119860 119879119878 + 119867 (119896) (23)

where 1198763(119896) = 11987011198901198702119879(119896)Similarly the discretized model for the feed liquid tem-

perature is

119879 (119896 + 1)= 1198791198781198601198781119867(119896) [(1198752 minus 1198781119879 (119896) 1198751 + 11987821198791 minus 1198782119879 (119896))sdot 1198761 (119896) + 11987821198762 (119896) (1198791 minus 119879 (119896))+ (1198781119879 (119896) 1198751 minus 1198752) 1198763 (119896)] + 119879 (119896)

(24)

The discretized model for the concentration of EC is

119862 (119896 + 1) = 119879119878119860119867(119896) [ (1198620 minus 119862 (119896)) 119878(119877 minus 119903 (119896)) 119863119878 (119896) + 1199030119863 (119896)minus 119862 (119896) 1198751 (1198761 (119896) minus 1198763 (119896))] + 119862 (119896)

(25)

where

119863 (119896) = 74 times 10minus12 (Φ119872119861)05 119879 (119896)120583119861 (119896) 11988106119860 119863119878 (119896) = 120576119863 (119896)120591 119903 (119896) = 119877 minus (119896119863119878 (119896) 119862 (119896) 119905 (119896)1198620 )12

(26)

and the discretized model for the concentration of VO is

119902 (119896 + 1) = (1 minus 1198901198960119863(119896)1198781198701198791198781198891 )119902 (119896) (27)

It is assumed that the extraction time can be divided intosix equal intervals so the entire drug extraction process has 13input variables six steamflows at the bottomof the extractiontank (11987611 11987612 11987613 11987614 11987615 11987616) six steam flows at the sideof the extraction tank (11987621 11987622 11987623 11987624 11987625 11987626) and theextraction time 119905 The output variables are the extractionyields of EC and VO (1198651 1198652 resp) their extraction efficien-cies (1205781 1205782) and the total consumption of steam 1198653

The extraction yield of EC 1198651 and its extraction efficiency1205781 can be expressed as

1198651 = 1198911 (119896) = 119881 (119896) 119862 (119896) = 119860119867 (119896) 119862 (119896) 1205781 = 11986511198651 total

(28)

where 1198651 total is the total mass of EC in a batch of herbs whichwe consider to be 25 kg in this study

The decrement of VO in the extraction tank betweenadjacent sampling periods is

Δ119898 (119896) = 119898 (119896 minus 1) minus 119898 (119896)= (119902 (119896 minus 1) minus 119902 (119896)) 1198652 total (29)

Thus the recycle yield of VO 1198652 and its extractionefficiency 1205782 are computed by the following equations

1198652 = 1198912 (119896) = 1198912 (119896 minus 1) + Δ119898 (119896) 120578119904 (119896) 1205782 = 11986521198652 total

(30)

where 1198652 total is the total mass of VO in a batch of herbsassumed to be 36 kg and

120578119904 (119896) = 1 minus 119862119889 (119896)119862119887 (119896) = (11987911987811987511198763 (119896) minus Δ119898 (119896)) 1205780 (119896)11987911987811987511198763 (119896) minus Δ119898 (119896) 1205780 (119896) 1205780 (119896) = 11987801198921812058301198760 (119896) (120588119908 minus 1205880) 11988922

= 119878011989218120583011987511198763 (119896) (120588119908 minus 1205880) 11988922(31)

The total consumption of steam 1198653 is given by

1198653 = 6sum119894=1

(1198761119894 + 1198762119894) 1199056 (32)

In conclusion the input and output variables of themechanistic model for DEPP can be expressed as

119906 = (11987611 11987612 11987613 11987614 11987615 11987616 11987621 11987622 11987623 11987624 1198762511987626 119905)

119910 = (1198651 1198652 1198653 1205781 1205782) (33)


10

5

0

40

20

0

40

20

0

5454353252151050

5454353252151050

5454353252151050

Yiel

d of

EC

(kg)

Yiel

d of

VO

(kg)

Steam flows Q1 Q2 (m3h)



Con

sum

ptio

n of

steam

(m3)

Figure 4 Relationship between model outputs and steam flow inthe extraction process

To verify the rationality and effectiveness of the estab-lished mechanistic model a number of simulations wereconducted Figure 4 shows the effect of steam flows onthe model outputs In this simulation all the steam flowswere identical and the other operating or state conditionsremained unaltered For example 119905 = 3 h The parametersused in the mechanistic model are listed in Table 1

From Figure 4 it is clear that the extraction yields of ECand VO increase with the steam flow until reaching theirrespective equilibrium states and the consumption of steamexhibits a gradual linear rise First with other parametersfixed the increased steam flow causes the feed liquid tem-perature to rise and this rising temperature results in anincrement in the diffusion coefficients which will acceleratethe extraction of EC However when the temperature reachesa stable value owing to the characteristics of the feed liquidthe extraction of EC will gradually slow down and eventuallystop once the concentration of EC in the solvent is equal toits solubility at this temperature The recycling of VO has thesimilar tendency to that of EC but the reason for such anequilibrium state is that the VO has been fully extracted atthis temperature

The effect of the extraction time on the model outputs isplotted in Figure 5 In this simulation it was assumed thatall other operating or state conditions remained unalteredand the steam flows were set as 119876119894119895 = 25 119894 = 1 2 and119895 = 1 2 6 It can be seen that the extraction yields of ECand VO increase with the extraction time until they reach theequilibrium state As the extraction time increases the heatabsorbed by the feed liquid will continue to rise which leadsto the increment in the feed liquid temperature The analysisis then similar to that for the effect of the various steam flows

10

5

0

40

20

0

Yiel

d of

EC

(kg)

Yiel

d of

VO

(kg)

15

10

5

0

3252151050

Extraction time (h)

3252151050

Extraction time (h)

3252151050

Extraction time (h)C

onsu

mpt

ion

ofste

am (m

3)

Figure 5 Relationship between model outputs and extraction timein the extraction process

4 Optimization of the Drug ExtractionProduction Process

41 Identification of Predictive Model Parameters To carryout such optimization a predictive model of DEPP has beendeveloped This model links the operating variables (steamflow at both the bottom and side of the extraction tank andthe extraction time) with the extraction efficiencies of EC andVO In the present work the established mechanistic modelwas simplified to give a predictive model The followingsimplifications were made

(1) In modeling the extraction tank the nonlinear rela-tionship between the mixed steam flow 1198763 and temperature119879 was linearized that is 1198763 = 1198961119879 + 1198962 where 1198961 1198962 are theparameters to be identified

(2) As internal diffusion has less effect on the masstransfer than external diffusion the internal diffusion wasneglected to simplify the mechanistic model

Hence the differences between the predictive model 119891119898and mechanistic model 119891119901 can be described as

1198763 = 1198961119879 + 1198962 (34)

119889119862119889119905 = 1119860119867 [1198781198631199030 (1198620 minus 119862) minus 1198621198751 (1198761 minus 1198763)] (35)

and the other parts of the mechanistic model were retainedin the predictive model

To predict the extraction efficiencies under different oper-ating conditions the parameters 1198961 1198962 must be identifiedA best fit approach was adopted in which 1198961 1198962 in (34) arethe values that best predict the actual DEPP data [42] Theextraction efficiencies of EC and VO were used as criteria


Table 1 Parameters used in mechanistic model

Parameter Description Value119860 Cross-sectional area of extraction tank (m2) 31198791 Steam temperature before entering extraction tank (∘C) 1251198751 Volume ratio of water and steam 1801198752 Standard heat of liquefaction of vapor (kJmol) 40681198781 Specific heat capacity of feed liquid (kJ(kg times ∘C)) 41198782 Specific heat capacity of water (kJ(kg times ∘C)) 421198701 Coefficient in 1198763 441198702 Coefficient in 1198763 00011198780 Lifting area of oil layer (m2) 28120588119908 Density of water (gcm3) 11205880 Density of volatile oil (gcm3) 072119892 Acceleration of gravity (ms2) 981198892 Diameter of oil droplet (m) 03912119864 minus 51199020 Initial concentration of volatile oil in herbs 03119877 Radius of solid herb particle (m) 08202119864 minus 31199030 Thickness of liquid film (m) 0222119864 minus 31198891 Thickness of gas film (m) 06302119864 minus 3120591 Sinuosity of holes inside gray layer in solid particle 12120576 Porosity of gray layer in solid particle 0981198620 Solubility of EC in liquid film 085120595 Associating parameter of solvent 265119872119861 Molecular weight of solvent (D) 100119881119860 Molecular volume of EC (m3) 3062 lowast 10(minus8)119870 Linear equilibrium proportional constant 0151198670 Initial liquid level in extraction tank (m) 351198790 Initial temperature of feed liquid in extraction tank (∘C) 20119862in Initial concentration of EC in solvent 0119879119878 Sampling period (s) 005

for the parameter identificationThe identification algorithmused for the predictive model is as follows

Step 1 119899 sets of process data (119906119894 120578119894) are produced by mecha-nistic model 119891119901 in which 119906119894 denotes the vector of operatingvariables and 120578119894 is the vector of extraction efficiencies of ECand VO that is 120578119894 = (1205781119894 1205782119894) 119894 = 1 2 119899Step 2 Insert 119906119894 into predictive model 119891119898 to obtain thepredicted extraction efficiencies as follows

119894 = (1119894 2119894) = 119891119898 (119906119894) (36)

Step 3 Parameters 1198961 1198962 are determined by minimizing thefollowing objective function of the sum of square errors(SSE) of the extraction efficiencies through an optimizationalgorithm

min1198961 1198962

SSE = 119899sum119894=1

(1205781119894 minus 1119894)2 + 119899sum119894=1

(1205782119894 minus 2119894)2 (37)

Table 2 Parameter values and optimization results of each algo-rithm

119899 119908 Algorithm 1198961 1198962 SSE

30 10PSO 00044 44223 4646119864 minus 4DE 00049 43734 4971119864 minus 4ABC 00023 46205 6532119864 minus 4

We solved (37) using PSO DE and ABC and comparedthe performances of the algorithms with one another Thealgorithms were executed 119908 times and the results averagedThe optimization results are summarized in Table 2 fromwhich we can see that PSO achieved the best performance insolving the optimization problem

42 Optimization of Single Extraction The economic benefitper unit time is considered as the optimization objectiveand the operating variables are treated as decision variablesTaking economic income and production consumption intoconsideration (including the economic income of EC andVO


Table 3 Parameter values in optimization model

Parameters 119886 (USDKg) 119887 (USDKg) 119888 (USDm3) 119889 (USDKg) 1198654 (Kg)Value 1527 12217 0031 153 120

Table 4 Constraints in optimization model

Constrainedvariables

Quality indexes Operating variables1205781 1205782 119876119894119895 (m3h) 119905 (h)Range [08 1] [08 1] [0 5] [1 4]Table 5 Optimal economic benefits obtained by each algorithm

Algorithm PSO DE ABCEconomic benefit (USDh) 2293 2240 2252

and the consumption cost of herb materials and steam) thefollowing optimization model was established based on thepredictive model

max 119869 = 119886 times 1198651 + 119887 times 1198652 minus 119888 times 1198653 minus 119889 times 1198654119905st (1198651 1198652 1198653 1205781 1205782) = 119891 (119906)

1205781min le 1205781 le 1205781max1205782min le 1205782 le 1205782max119876min le 119876119894119895 le 119876max119905min le 119905 le 119905max119894 = 1 2119895 = 1 2 6

(38)

where 119886 119887 119888 and 119889 are the prices of EC VO steam and herbmaterials and1198654 is the weight of a batch of herbmaterialsTheparameters and constraints in this model are listed in Tables3 and 4 respectivelyThe PSO DE and ABC algorithms wereexecuted 10 times to determine the optimal solution to (38)and the results are presented in Table 5 The optimizationresults once again validate the superiority of PSO for theproblem considered in this study

The optimal values obtained by PSO for the operatingvariables are listed in Table 6 The optimal operating condi-tions were applied to the single extraction process and theoutput indexes are given inTable 7 Additionally the variationin the extraction yield of EC and VO and the consumption ofsteam are plotted in Figure 6

From this figure we can see that the mass of EC increaseswith extraction time in the initial stage of the single extrac-tion but the rate of increase gradually slows as we reach theequilibrium stateThe reason for this is that the concentrationof EC in the extracted solution reaches its saturated solubilityand so no more EC will be extracted from the herb materialseven if we continue the extraction process

There is also a comparatively small recycle yield of VO inthe initial 075 h because the temperature in the extraction

35

30

25

20

15

10

5

0

Yield of effective constituent (kg)Yield of volatile oil (kg)Total consumption of steam (m3)

252151050

Extraction time (h)

Figure 6 Variation trend of various output indexes in singleextraction

tank is too low to boil VO and little of it can be volatilizedand brought out together with vapor in the initial stages ofextraction When the temperature reaches the boiling pointof VO its recycle yield grows exponentially As the extractionprogresses there is less VO remaining in the herbs and theincreasing tendency of the recycle yield becomes slower untilall VO has been extracted

The actual results in Table 7 however suggest that theextraction efficiency of EC is only 3528 and so most ofthe EC has not been extracted Thus the quality constraintscannot be satisfied although there is a significant economicbenefit According to national production management reg-ulations such a huge wastage of herb materials is forbiddenand a multiextraction process is needed to avoid wasting rawmaterials

43 Optimization of Multiextraction As the extraction pro-cess progresses the extraction temperature does not alwaysrisewith an increase in the operating variablesThis is becauseof the self-regulating characteristics of the feed liquid Asdescribed above the concentration of EC in the feed liquidwill reach a maximum and only VO will be recycled alongwith the extraction This causes the low extraction efficiencyof EC in the single extraction case Therefore to avoid sucha situation the first extraction should be terminated and thefeed liquid containing EC should be separated from the solidherb via a filter After this a certain amount of new solventcan be added to the extraction tank and a second extractioncan be performed Depending on the total content of EC


Table 6 Best settings of operating variables produced by PSO

Steam flow Q1 (m3h) Steam flow Q2 (m3h) Extraction time (h)Q11 49554 Q21 49545 119905 23Q12 47633 Q22 43348Q13 45968 Q23 48391Q14 36422 Q24 43850 Optimal economic benefit (USDh)Q15 35999 Q25 23083 119869 2293Q16 31419 Q26 42665

Table 7 Actual optimal output indexes and economic benefit in single extraction

Single extraction F1 (Kg) F2 (Kg) F3 (m3) 1205781 1205782 119869 (USDh)Actual value 882 3224 1951 3528 8956 2218

ECtotal

VOtotal

u1

EC1

u2

VO1

VOleft1

ECleft1

extraction extraction

EC2

ECleft2

VO2

VOleft2

uk

ECleftkminus1

leftkminus1VOextraction

ECleftk

leftkVO

VOextract

ECextractECk

VOk

middot middot middot

middot middot middot2nd kth1st

Figure 7 Schematic diagram of multiextraction

in the herb and its solubility in the solvent at least threeextractions are needed to remove all of the EC A schematicdiagram of the multiextraction process is shown in Figure 7where each extraction represents a single extraction Basedon the principle of multiextraction any surplus in the qualityindexes after the (119894minus1)th extraction such as the total residualmass of VO and radius of unextracted core of EC is regardedas the initial input conditions of the 119894th extraction where119894 = 2 3 119896 According to this principle a predictive modelfor the multiextraction process can be developed

In developing a predictive model for the multiextractionscenario the extraction frequency 119896 is treated as one of theoperating variables (119896 = 3 4 5) In this study predictivemod-els were established for three four and five extractions Wenow describe the three-time extraction model the modelingapproach for four and five extractions is similar The three-extraction case is composed of three single extractions eachof which has the 13 input variables described previouslyThusthere are 39 input variables in the three-extraction predictivemodel

119880 = (1199061 1199062 1199063) (39)

where 119906119894 is the vector of operating variables in the 119894th singleextraction and

119906119894 = (11987611119894 11987612119894 11987613119894 11987614119894 11987615119894 11987616119894 11987621119894 11987622119894 1198762311989411987624119894 11987625119894 11987626119894 119905119894) 119894 = 1 2 3 (40)

The predictive outputs for the three extractions includingthe total extraction yield of EC and VO consumption ofsteam and extraction efficiencies can be calculated as

1198651 = 3sum119894=1

11986511198941198652 = 3sum119894=1

1198652119894

1198653 = 3sum119894=1

( 6sum119895=1

((1198761119895119894 + 1198762119895119894) 1199051198946 )) 1205781 = 11986511198651 total 1205782 = 11986521198652 total

(41)

Therefore the predictive model of three-time extractioncan be summarized as

(1198651 1198652 1198653 1205781 1205782) = 1198651198983 (119880) (42)

After developing predictive models for 119896 = 3 4 and5 the optimization model for multiextraction was derived


by treating the extraction frequency as one of the decisionvariables

max 119869 = 119886 times 1198651 + 119887 times 1198652 minus 119888 times 1198653 minus 119889 times 1198654sum119896119894=1 119905119894st (1198651 1198652 1198653 1205781 1205782) = 119865119898119896 (119880)

1205781min le 1205781 le 1205781max1205782min le 1205782 le 1205782max119876min le 1198761119895119896 le 119876max119876min le 1198762119895119896 le 119876max119905min le 119905119894 le 119905max119896 = 3 4 5119895 = 1 2 6

(43)

In this optimization model the extraction frequency 119896is treated as one of the decision variables (119896 = 3 4 5) Thedecision variables must be carefully handled in solving thisoptimization problem For example when 119896 = 3 the decisionvariable vector 119880119889 can be expressed as

119880119889 = (119896 1199061 1199062 1199063 1199064 1199065) (44)

where 1199064 = 1199065 = 0 Similarly 1199065 = 0 when 119896 = 4The advantages of PSO in solving such optimization

problems have been verified many times and are not coveredhereTheparameters used in the PSOalgorithmare presentedin Table 8 and the optimal multiextraction solution obtainedby the PSO method with 10 runs is given in Table 9

From Table 9 it is clear that the optimal extractionfrequency is 3 so the operating variables in the fourthand fifth extractions are all zero These optimal operatingvariables were used in the mechanistic model of the multi-extraction process to calculate the actual output indexes andeconomic benefit The results together with their predictedvalues are given in Table 10 However owing to the inherenterrors of predictive models it is difficult to achieve theoptimized economic benefit in an actual process The resultsin Table 10 indicate that a discrepancy of 64 exists betweenthe predicted and actual economic benefit which means thatldquooptimal in the modelrdquo may not translate to ldquooptimal forthe processrdquo as mentioned before This model uncertaintyhampers the optimization of the multiextraction processHence as discussed in Section 5 the ILCmethodwas adoptedto overcome the problem of model uncertainty

5 Use of Iterative Learning Control toOvercome Model Uncertainty

To eliminate the impact of themodel uncertainty the iterativenature of numerical optimization and certain repetitive prop-erties can be utilizedThe idea of ILC is introduced to improve

Table 8 Parameter settings of PSO

Swarm size Iterations Inertiaweight

Learningfactor

100 100Linear

decrease09sim02

1198881 25sim101198882 10sim25

the economic benefit In this study we used DDOTILC withthe control law (see [35] for details)

119896 = 119896minus1 + 120585 (Δ119910119896minus1 (119873) minus 119896minus1Δ119906119896minus1) Δ119906119879119896minus1120583 + 1003817100381710038171003817Δ119906119896minus110038171003817100381710038172119906119896 = 119906119896minus1 + 120588119879119896120582 + 100381710038171003817100381711989610038171003817100381710038172 119890119896minus1 (119873)

(45)

where 120588 120582 120585 and 120583 are positive constants 119896 is the iterationnumber of the batch process and119873 is their terminalmoment119896 is the estimated pseudo-partial-derivative of the 119896th batchprocess and 119890119896minus1(119873) is the terminal tracking error of theoutput

In the application of this approach the economic benefitis treated as the terminal output and the operating variablesare adjusted online to improve the economic benefit Thedesired economic benefit 119869119889 is set as the predicted valueobtained by solving (43) The parameters used in (45) arelisted in Table 11 The blue curves in Figure 8 describe theevolution of the economic benefit under DDOTILC Theresults indicate that the actual economic benefit achieves anincrement of 15 after six batches which partly improves theeconomic benefit although this is still short of the desiredeconomic benefit In addition the extraction efficienciesdecrease with the increase in economic benefit as shown inFigure 8 When the extraction efficiencies reach a thresholdthe economic benefit will be inversely proportional to theextraction yields of EC and VO because the costs of extract-ing the remaining EC and VO will be much greater thanthe additional income Thus the optimal economic benefitmay not correspond to adjusting the operating variables tomaximize the extraction of EC and VO

The parameter settings will affect the convergence rate ofILC and the best parameter settings should have the abilityto change adaptively with the tracking error and variationsin system output In this study the parameter 120588 in (45)was varied though fuzzy adaptive adjustment over the range[0 120572] The convergence rate of economic benefit can bechanged by adjusting 120588 When the absolute values of thetracking error of economic benefit and its variation are highthe value of 120588 should also be high Moreover the value of 120588should decrease as the absolute values of tracking error andits variation decrease According to this principle the fuzzyadjustment rule was formulated as shown in Table 12 where119864119869 andΔ119864119869 represent the absolute values of the tracking errorof economic benefit and its variation respectively The mem-bership functions of119864119869 Δ119864119869 and 120588 are shown in Figure 9Thefirst red curve in Figure 8 shows the trajectory of economicbenefit based on the fuzzy adjustment of parameter 120588


Table 9 Best settings of operating variables

1st extraction 2nd extraction 3rd extraction 4th extraction 5th extraction

Steam flow 1198761 (m3h)Q11 45538 36784 42887 00000 00000Q12 46789 27554 09895 00000 00000Q13 44342 32861 41627 00000 00000Q14 15664 49991 22495 00000 00000Q15 37135 49160 09995 00000 00000Q16 00477 16587 42214 00000 00000


Extraction time (h) 119905 16628 10992 30475 00000 00000

Table 10 Output indexes and economic benefit in multiextraction

Multiextraction F1 (Kg) F2 (Kg) F3 (m3) 1205781 1205782 J (USDh)Predicted value 2439 3446 3759 9757 9573 1333Actual value 2109 3440 3759 8436 9550 12473

Table 11 Parameters of DDOTILC

Parameter 120588 120583 120585 120582Value 0003 1 01 001

Table 12 Fuzzy adjustment rule

120588 Δ119864119869119864119869 NB NM NS Z PS PM PBNB Z Z Z PS PS PM PMNM Z Z Z PS PM PM PMNS Z PS PS PM PM PM PMZ Z PS PM PM PM PM PMPS PS PS PM PM PM PM PMPM PS PM PM PM PM PM PMPB PM PM PM PM PM PM PM

with which the advantage of the fuzzy-adjusted DDOTILCmethod is validated In this simulation 120572 = 00056 Conclusion

This paper proposed a mechanistic modeling and optimiza-tion control strategy for DEPP First a mechanistic modelof the drug extraction process was developed based onprevious efforts to simulate the actual production process andproduce process data A simulation was conducted to verifythe rationality and effectiveness of this mechanistic modelA predictive model was then developed by simplifying someof the processes in the mechanistic model Simulation results

1265

1260

1255

1250

1245

0846

0844

0842

084

0838

097

096

095

094

10987654321

10987654321

10987654321

1

2

Iterations

Iterations

Iterations

DDOTILCDDOTILC with fuzzy adjustment

Econ

omic

ben

efit

(USD

h)

Figure 8 Comparison of economic benefit between originalDDOTILC and DDOTILC with fuzzy adjustment

demonstrated the effectiveness of this predictive model Pro-cess optimization was first implemented for single extractionand the results indicated an extremely low extraction yieldof EC which indicates serious wastage of herbs although


1

08

06

04

02

0

1

08

06

04

02

0

1

08

06

04

02

0

times10minus3151050 6420 543210

Deg

ree o

f mem

bers

hip

Deg

ree o

f mem

bers

hip

Deg

ree o

f mem

bers

hip

PBPMPSZNSNMNB PBPMPSZNSNMNB PMPSZNSNM

EJ (USDh) ΔEJ (USDh)

Figure 9 Membership functions of 119864119869 Δ119864119869 and 120588

this gave a preferable economic benefit Such wastage of rawmaterials is forbidden according to national productionman-agement regulations A multiextraction DEPP is thereforenecessary and so process optimization for multiextractionwas investigated However such optimization is hamperedby model uncertainty Therefore the DDOTILC methodwas applied to partly overcome this model uncertainty Thesimulation results indicate that the economic benefit canbe improved by 15 Finally the idea of fuzzy adjust-ment was introduced to adaptively adjust the parameter120588 in DDOTILC which increases the convergence rate ofeconomic benefit The simulation results indicate that theproposed modeling and optimization control method caneffectively solve the practical problems encountered in DEPP

The proposed modeling and optimization control strat-egy is easy to implement in practical applications because itrequires lesser accuracy of predictive models The researchin this paper is based on a mechanistic model developedto simulate actual DEPP and produce process data How-ever there is no empirical research from pharmaceuticalenterprises to test the validity of the model and methodAll parameters used for the mechanistic modeling suchas the device parameters for the extraction tank and stateparameters of DEPP correspond to the actual productionsituation so the model proposed in this work has the abilityto simulate the actual DEPP and it is reasonable to test thevalidity of the proposed method through simulations Thesecond limitation of this study is that the fuzzy rules shouldbe based on the actual situation For example the initial rangeof 120588must be set according to the actual DEPP scenario whenapplying DDOTILC

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The authors would like to thank National Natural ScienceFoundation of China under Grant nos 61374147 61004083and 61203103 and Fundamental Research Funds for theCentral Universities under Grant nos N150402001 andN120404014 for supporting this research work

References

[1] B E Richter B A Jones J L Ezzell N L Porter N Avdalovicand C Pohl ldquoAccelerated solvent extraction a technique forsample preparationrdquo Analytical Chemistry vol 68 no 6 pp1033ndash1039 1996

[2] B Benthin H Danz and M Hamburger ldquoPressurized liquidextraction of medicinal plantsrdquo Journal of Chromatography Avol 837 no 1-2 pp 211ndash219 1999

[3] K F Hou Q Zheng Y Li J Shen and S Hu ldquoModelingand optimization of herb leaching processesrdquo Computers ampChemical Engineering vol 24 no 2ndash7 pp 1343ndash1348 2000

[4] R M Smith ldquoExtractions with superheated waterrdquo Journal ofChromatography A vol 975 no 1 pp 31ndash46 2002

[5] P Li S P Li C M Fu et al ldquoPressurized solvent extractionin quality control of Chinese herbrdquo China Journal of ChineseMateria Medica vol 29 no 8 pp 723ndash726 2004

[6] Y Chen J K Tian and Y Y Cheng ldquoA novel techniqueof extracting essential oil from Chinese herb and medicinendashsubcritical water extractionrdquo Chemical Engineering vol 34 no8 pp 59ndash62 2006

[7] Y T Lau K M Ng D T W Lau and C Wibowo ldquoQualityassurance of Chinese herbal medicines procedure for single-herb extractionrdquo AIChE Journal vol 59 no 11 pp 4241ndash42542013

[8] G C Rodrıguez-Jimenes A Vargas-Garcia D J Espinoza-Perez M A Salgado-Cervantes V J Robles-Olvera and M AGarcıa-Alvarado ldquoMass transfer during vanilla pods solid liquid


extraction effect of extraction methodrdquo Food and BioprocessTechnology vol 6 no 10 pp 2640ndash2650 2013

[9] M S Alam Z A Damanhouri1 A Ahmad et al ldquoDevelopmentof response surface methodology for optimization of extractionparameters and quantitative estimation of embelin from Embe-lia ribes Burm by high performance liquid chromatographyrdquoPharmacognosy Magazine vol 11 supplement 1 pp S166ndashS1722015

[10] V C Bochi M T Barcia D Rodrigues C S Speroni M MGiusti and H T Godoy ldquoPolyphenol extraction optimisationfrom Ceylon gooseberry (Dovyalis hebecarpa) pulprdquo FoodChemistry vol 164 pp 347ndash354 2014

[11] R Z Chen Y Li H Dong et al ldquoOptimization of ultrasonicextraction process of polysaccharides from Ornithogalum Cau-datumAit and evaluation of its biological activitiesrdquoUltrasonicsSonochemistry vol 19 no 6 pp 1160ndash1168 2012

[12] M Chen Y Zhao and S Yu ldquoOptimisation of ultrasonic-assisted extraction of phenolic compounds antioxidants andanthocyanins from sugar beet molassesrdquo Food Chemistry vol172 pp 543ndash550 2015

[13] I K Bae H M Ham M H Jeong D H Kim and H JKim ldquoSimultaneous determination of 15 phenolic compoundsand caffeine in teas and mate using RP-HPLCUV detectionmethod development and optimization of extraction processrdquoFood Chemistry vol 172 pp 469ndash475 2015

[14] M Bravi R Bubbico F Manna and N Verdone ldquoProcessoptimisation in sunflower oil extraction by supercritical CO2rdquoChemical Engineering Science vol 57 no 14 pp 2753ndash27642002

[15] Y-J Choi T-I Kwon and Y-K Yeo ldquoOptimization of thesulfolane extraction plant based on modeling and simulationrdquoKorean Journal of Chemical Engineering vol 17 no 6 pp 712ndash718 2000

[16] X C Gong Y Zhang J Y Pan H B Qu and Q ZhangldquoOptimization of the ethanol recycling reflux extraction processfor saponins using a design space approachrdquo PLoS ONE vol 9no 12 Article ID e114300 2014

[17] ZXHuangAStudy on Strategy ofOptimalControl in Procedureof Chinese TraditionalMedicine Central SouthUniversity PressChangsha China 2006

[18] G H Hu Z Z Mao D K He and F Yang ldquoHybrid modelingfor the prediction of leaching rate in leaching process basedon negative correlation learning bagging ensemble algorithmrdquoComputers and Chemical Engineering vol 35 no 12 pp 2611ndash2617 2011

[19] Z Tong ldquoLeaching kinetics of calcium aluminate slagrdquo TheChinese Journal of Process Engineering vol 5 no 4 pp 399ndash4022005

[20] S Zhan ldquoStudy on leaching kinetics of pyrite cinderrdquo ChemicalEngineering vol 34 no 11 pp 36ndash39 2006

[21] JMDelValle and J CDe La Fuente ldquoSupercritical CO2 extrac-tion of oilseeds review of kinetic and equilibrium modelsrdquoCritical Reviews in Food Science and Nutrition vol 46 no 2pp 131ndash160 2006

[22] M Perrut J Y Clavier M Poletto and E Reverchon ldquoMathe-matical modeling of sunflower seed extraction by supercriticalCO2rdquo Industrial and Engineering Chemistry Research vol 36no 2 pp 430ndash435 1997

[23] Y P Han Y C Xiang S B Wang et al ldquoRelationship betweenthe yield and extraction time of volatile oilrdquo Chinese TraditionalPatent Medicine vol 23 no 1 pp 11ndash13 2001

[24] L C Wang The Indoor Experiment Study of Crown-Type Oil-Water Separator Northeast PetroleumUniversity PressDaqingChina 2011

[25] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoIEEE International Conference on Neural Networks vol 4 no8 pp 1942ndash1948 1995

[26] T C Carneiro S P Melo P C M Carvalho and A P DS Braga ldquoParticle swarm optimization method for estimationof weibull parameters a case study for the Brazilian northeastregionrdquo Renewable Energy vol 86 pp 751ndash759 2016

[27] K Rajesh A Bhuvanesh S Kannan and C Thangaraj ldquoLeastcost generation expansion planning with solar power plantusing Differential Evolution algorithmrdquo Renewable Energy vol85 pp 677ndash686 2016

[28] W F Gao L L Huang S Y Liu and C Dai ldquoArtificialbee colony algorithm based on information learningrdquo IEEETransactions on Cybernetics vol 45 no 12 pp 2827ndash2839 2015

[29] H Fei X Jinwu L Min and Y Jianhong ldquoProduct qualitymodelling and prediction based on wavelet relevance vectormachinesrdquo Chemometrics and Intelligent Laboratory Systemsvol 121 pp 33ndash41 2013

[30] K Kim J-M Lee and I-B Lee ldquoA novelmultivariate regressionapproach based on kernel partial least squares with orthogonalsignal correctionrdquo Chemometrics and Intelligent LaboratorySystems vol 79 no 1-2 pp 22ndash30 2005

[31] Z H Xiong and J Zhang ldquoA batch-to-batch iterative optimalcontrol strategy based on recurrent neural network modelsrdquoJournal of Process Control vol 15 no 1 pp 11ndash21 2005

[32] N Sanzida and Z K Nagy ldquoIterative learning control for thesystematic design of supersaturation controlled batch coolingcrystallisation processesrdquoComputers andChemical Engineeringvol 59 pp 111ndash121 2013

[33] X Jin and J-X Xu ldquoIterative learning control for output-constrained systems with both parametric and nonparametricuncertaintiesrdquo Automatica vol 49 no 8 pp 2508ndash2516 2013

[34] X H Bu F H Yu Z S Hou and F Z Wang ldquoIterative learningcontrol for a class of nonlinear systems with random packetlossesrdquo Nonlinear Analysis Real World Applications vol 14 no1 pp 567ndash580 2013

[35] R H Chi D W Wang Z S Hou and S T Jin ldquoData-drivenoptimal terminal iterative learning controlrdquo Journal of ProcessControl vol 22 no 10 pp 2026ndash2037 2012

[36] R H Chi Z S Hou and S T Jin ldquoA data-driven adaptiveILC for a class of nonlinear discrete-time systems with randominitial states and iteration-varying target trajectoryrdquo Journal ofthe Franklin Institute vol 352 no 6 pp 2407ndash2424 2015

[37] S-T Jin Z-S Hou R-H Chi and X-B Liu ldquoData-drivenmodel-free adaptive iterative learning control for a class ofdiscrete-time nonlinear systemsrdquo Control Theory and Applica-tions vol 29 no 8 pp 1001ndash1009 2012

[38] C R Wilke and P Chang ldquoCorrelation of diffusion coefficientsin dilute solutionsrdquo AIChE Journal vol 1 no 2 pp 264ndash2701955

[39] E L Cussler Diffusion Mass Transfer in Fluid Systems Cam-bridge University Press New York NY USA 2002

[40] M Y Wu J H Zhao H Liang H Kang and S Xu ldquoKineticmodel for extraction process of volatile oil from traditional Chi-nese medicinerdquo Journal of Chemical Industry and Engineeringvol 59 no 12 pp 2990ndash2995 2008

[41] Y B Xu S X Wang and X W Yang ldquoApplying shallowpool theory and coalescence technology to improve oily water


treatment system in oilfieldrdquo Technology of Water Treatmentvol 36 no 10 pp 115ndash118 2010

[42] H Liu and M Li ldquoPopulation balance modelling and multi-stage optimal control of a pulsed spray fluidized bed granula-tionrdquo International Journal of Pharmaceutics vol 468 no 1-2pp 223ndash233 2014

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Distributed Sensor Networks


Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014


ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014


Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications


Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia


Biomedical Imaging


ArtificialNeural Systems

Advances in


RoboticsJournal of



Computational Intelligence and Neuroscience

Industrial EngineeringJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in



using experimental design or simulation techniques To thebest of the authorsrsquo knowledge the optimization of DEPP interms of improving the economic benefit of the whole pro-duction process has rarely been reported in the literatureThepresent work develops a mechanism model for DEPP basedon some previous efforts and then proposes an optimizationstrategy to resolve practical problems such as the productionefficiency and production costs

To implement this optimization a mechanism model ofDEPP should be developed Suchmechanisticmodeling playsseveral significant roles first the modeling process will ana-lyze the mechanism of the drug extraction process confirmits operating variables and quality indicators and analyze therelationship between them second an appropriatemodel canbe used to simulate the actual production process to generatethe required data and analyze the optimization results Asan actual simulator the mechanism model should be ableto link the extraction efficiency of the EC and volatile oilmdashthe quality indicatorsmdashwith the operating variables (steamflow at the bottom and side of the extraction tank and theextraction time)

The mechanistic modeling of DEPP mainly consists ofmodeling the following components extraction tank masstransfer process of EC volatile oil recycling and efficiencyof the oil-water separator A mathematical model of theextraction tank that describes the changes in temperatureand liquid level over time has been developed [17] As theprinciple and mechanism of the mass transfer process indrug extraction are very similar to those of metal leachingmechanistic models of metal leaching [3 18ndash22] can be usedas references in developing a mass transfer model for theEC Additionally Han et al derived a diffusion rate equationfor volatile oils allowing a mechanistic model of volatile oilrecovery to be developed [23] Finally the efficiency of theoil-water separator is introduced to describe the separationefficiency of oil droplets with a certain diameter [24] Theabove mechanistic models are combined to simulate thewhole DEPP and the rationality and validity of this approachare verified through a series of simulations The innovationand contribution of the DEPP model presented in this papercan be summarized as follows First we extend a modelingapproach for the leaching process to model the mass transferprocess of ECs Second we present a combined mechanisticmodeling framework for the overall DEPP by integrating fourdiscrete components described in previous studies

In addition to a mechanistic model a predictive modelis also necessary for such optimization In this work theestablished mechanism is simplified to serve as a predictivemodel The economic benefit per unit time is consideredas the optimization objective while the steam flow at thebottom and side of the extraction tank and the extractiontime are treated as decision variablesTheoptimizationmodelis then established under certain quality constraints Severalclassical optimization algorithms such as particle swarmoptimization (PSO) [25 26] differential evolution (DE) [27]and artificial bee colony (ABC) [28] are adopted to solvethis optimization problem Comparing these algorithms itis concluded that PSO achieves the best performance indetermining the optimal solution Thus a PSO algorithm

is used to solve this optimization problem and obtain theoptimal economic benefit and corresponding parametersincluding optimal quality indicators and operating variablesThe present work first considers the optimization of a singleextraction process However the extraction efficiency of theEC in this case is very low leading to serious wastage ofherb materials The optimization control for multiextractionis therefore investigated In the multiextraction process theextraction frequency is defined as the number of times thatthe herbs are subjected to the extraction process Howeverthe optimal extraction frequency in terms of economicbenefit is unknownThus the extraction frequency is treatedas one of the decision variables when establishing the opti-mization problem Note that the extraction frequency is aninteger in this problem

The optimal economic benefit of the multiextractionprocess is based on the predictive model whereas the actualoptimal economic benefit can be calculated by plugging thebest operating variables into themechanismmodelThere aresome discrepancies between the predicted and actual valuesof the optimal economic benefit In practice however it isunlikely that the actual production process can be modeledaccurately (or even approximately) with a process model[29 30] Process optimization is hampered by such modeluncertainty and so the ldquooptimalrdquo value given by the modelmay not necessarily mean ldquooptimal for the processrdquo [31]

Iterative learning control (ILC) is highly effective incontrolling systems with repetitive operations that preciselyfollow a desired target trajectory It has beenwidely applied inrepetitive industrial processes because of its perfect learningability from the repetitive tracking task [32ndash34] Recentlydata-driven ILC methods have been proposed to deal withcomplicated practical systems [35ndash37] The control scheme isdata-driven because there is no explicit model informationor training process and only the measured input and outputdata are used for the controller design analysis and imple-mentation [36] As one such method data-driven optimalterminal ILC (DDOTILC) works under the principle thatthe control law is only updated using the terminal outputtracking error [35] In this work DDOTILC is applied toimplement iterative optimization control for DEPP in orderto overcome themodel uncertainty via the online adjustmentof the operating variables The fuzzy adaptive adjustment ofparameters inDDOTILC is then implemented to enhance theconvergence rate Using this approach themodel uncertaintycan be reduced and the economic benefit improved byadjusting the operating variables

2 Principle and Production Technology of theDrug Extraction Process

21 Principle of the Drug Extraction Process

211 Mass Transfer Theory of Effective Constituent Drugextraction is one kind of solid-liquid extraction Thus themass transfer principle and computing method follow thesolid-liquid extraction system model shown in Figure 1 Itis assumed that the herb particles are composed of solute


Feed liquid


Herb residues

(1)

(2)

(3)

(4)

(5)

a rR C0

r0

core

C

Unextracted












Gas filmLiquid film

(1)

(2)

R

r0

Water vapor

Heat

d1




Steam flow Q1

FilterFeed liquid


Cooler

Backflow

Gas-liquidseparator

Oil-waterseparator

tank













119889119867119889119905 = (1198761 minus 1198763) 1198751119860 (1)


(2)


1198763 = 11987011198901198702119879 (3)





119889119866119889119905 = 119869119878 (4)







1205731 = 119863119904119877 minus 119903 1205732 = 1198631199030

(6)






119863 = 119861119879 V119860119891119860 (9)


119891119860 = 6120587119877120583119861V119860 (10)


119863 = 1198611198796120587119877120583119861 (11)



119863 = 74 times 10minus12 (120595119872119861)05 11987912058311986111988106119860 (12)



119863119904 = 120576119863120591 (13)



119903 = 119877 minus (1198961198631199041198621199051198620 )12 (14)


119889119902119889119905 = 119870119866119878 (119862119897 minus 119862119894) (15)





119889119902119889119905 = minus119870119866119878119870119902 = minus11989011989601198631198781198701198891 119902 (16)

where

119870119866 = 11989011989601198631198891 (17)



1205880 = 1198601 + 1198602119879 + 11986031198792 + 11986041198793 + 11986051198794 (18)



V119900119908 = (120588119908 minus 1205880) 11989211988922181205830 (19)




1205780 = 1198780V1199001199081198760 = 11987801198921812058301198760 (120588119908 minus 1205880) 11988922 (20)



120578119904 = 1 minus 119862119889119862119887 (21)



119867(119896 + 1) minus 119867 (119896)119879119878 = (1198761 (119896) minus 1198763 (119896)) 1198751119860 (22)


119867(119896 + 1) = (1198761 (119896) minus 1198763 (119896)) 1198751119860 119879119878 + 119867 (119896) (23)


perature is


(24)



(25)

where


(26)


119902 (119896 + 1) = (1 minus 1198901198960119863(119896)1198781198701198791198781198891 )119902 (119896) (27)



1198651 = 1198911 (119896) = 119881 (119896) 119862 (119896) = 119860119867 (119896) 119862 (119896) 1205781 = 11986511198651 total

(28)





1198652 = 1198912 (119896) = 1198912 (119896 minus 1) + Δ119898 (119896) 120578119904 (119896) 1205782 = 11986521198652 total

(30)



= 119878011989218120583011987511198763 (119896) (120588119908 minus 1205880) 11988922(31)


1198653 = 6sum119894=1

(1198761119894 + 1198762119894) 1199056 (32)


119906 = (11987611 11987612 11987613 11987614 11987615 11987616 11987621 11987622 11987623 11987624 1198762511987626 119905)

119910 = (1198651 1198652 1198653 1205781 1205782) (33)


10

5

0

40

20

0

40

20

0

5454353252151050

5454353252151050

5454353252151050

Yiel

d of

EC

(kg)

Yiel

d of

VO

(kg)




Con

sum

ptio

n of

steam

(m3)





10

5

0

40

20

0

Yiel

d of

EC

(kg)

Yiel

d of

VO

(kg)

15

10

5

0

3252151050

Extraction time (h)

3252151050

Extraction time (h)

3252151050


onsu

mpt

ion

ofste

am (m

3)







1198763 = 1198961119879 + 1198962 (34)









119894 = (1119894 2119894) = 119891119898 (119906119894) (36)


min1198961 1198962

SSE = 119899sum119894=1

(1205781119894 minus 1119894)2 + 119899sum119894=1

(1205782119894 minus 2119894)2 (37)


119899 119908 Algorithm 1198961 1198962 SSE














(38)





35

30

25

20

15

10

5

0


252151050

Extraction time (h)










ECtotal

VOtotal

u1

EC1

u2

VO1

VOleft1

ECleft1


EC2

ECleft2

VO2

VOleft2

uk

ECleftkminus1


ECleftk

leftkVO

VOextract

ECextractECk

VOk






119880 = (1199061 1199062 1199063) (39)


119906119894 = (11987611119894 11987612119894 11987613119894 11987614119894 11987615119894 11987616119894 11987621119894 11987622119894 1198762311989411987624119894 11987625119894 11987626119894 119905119894) 119894 = 1 2 3 (40)


1198651 = 3sum119894=1

11986511198941198652 = 3sum119894=1

1198652119894

1198653 = 3sum119894=1

( 6sum119895=1

((1198761119895119894 + 1198762119895119894) 1199051198946 )) 1205781 = 11986511198651 total 1205782 = 11986521198652 total

(41)


(1198651 1198652 1198653 1205781 1205782) = 1198651198983 (119880) (42)






(43)


119880119889 = (119896 1199061 1199062 1199063 1199064 1199065) (44)








Learningfactor

100 100Linear

decrease09sim02

1198881 25sim101198882 10sim25



(45)













Parameter 120588 120583 120585 120582Value 0003 1 01 001





1265

1260

1255

1250

1245

0846

0844

0842

084

0838

097

096

095

094

10987654321

10987654321

10987654321

1

2

Iterations

Iterations

Iterations


Econ

omic

ben

efit

(USD

h)




1

08

06

04

02

0

1

08

06

04

02

0

1

08

06

04

02

0

times10minus3151050 6420 543210

Deg

ree o

f mem

bers

hip

Deg

ree o

f mem

bers

hip

Deg

ree o

f mem

bers

hip






Competing Interests


Acknowledgments


References






















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




Feed liquid


Herb residues

(1)

(2)

(3)

(4)

(5)

a rR C0

r0

core

C

Unextracted












Gas filmLiquid film

(1)

(2)

R

r0

Water vapor

Heat

d1




Steam flow Q1

FilterFeed liquid


Cooler

Backflow

Gas-liquidseparator

Oil-waterseparator

tank













119889119867119889119905 = (1198761 minus 1198763) 1198751119860 (1)


(2)


1198763 = 11987011198901198702119879 (3)





119889119866119889119905 = 119869119878 (4)







1205731 = 119863119904119877 minus 119903 1205732 = 1198631199030

(6)






119863 = 119861119879 V119860119891119860 (9)


119891119860 = 6120587119877120583119861V119860 (10)


119863 = 1198611198796120587119877120583119861 (11)



119863 = 74 times 10minus12 (120595119872119861)05 11987912058311986111988106119860 (12)



119863119904 = 120576119863120591 (13)



119903 = 119877 minus (1198961198631199041198621199051198620 )12 (14)


119889119902119889119905 = 119870119866119878 (119862119897 minus 119862119894) (15)





119889119902119889119905 = minus119870119866119878119870119902 = minus11989011989601198631198781198701198891 119902 (16)

where

119870119866 = 11989011989601198631198891 (17)



1205880 = 1198601 + 1198602119879 + 11986031198792 + 11986041198793 + 11986051198794 (18)



V119900119908 = (120588119908 minus 1205880) 11989211988922181205830 (19)




1205780 = 1198780V1199001199081198760 = 11987801198921812058301198760 (120588119908 minus 1205880) 11988922 (20)



120578119904 = 1 minus 119862119889119862119887 (21)



119867(119896 + 1) minus 119867 (119896)119879119878 = (1198761 (119896) minus 1198763 (119896)) 1198751119860 (22)


119867(119896 + 1) = (1198761 (119896) minus 1198763 (119896)) 1198751119860 119879119878 + 119867 (119896) (23)


perature is


(24)



(25)

where


(26)


119902 (119896 + 1) = (1 minus 1198901198960119863(119896)1198781198701198791198781198891 )119902 (119896) (27)



1198651 = 1198911 (119896) = 119881 (119896) 119862 (119896) = 119860119867 (119896) 119862 (119896) 1205781 = 11986511198651 total

(28)





1198652 = 1198912 (119896) = 1198912 (119896 minus 1) + Δ119898 (119896) 120578119904 (119896) 1205782 = 11986521198652 total

(30)



= 119878011989218120583011987511198763 (119896) (120588119908 minus 1205880) 11988922(31)


1198653 = 6sum119894=1

(1198761119894 + 1198762119894) 1199056 (32)


119906 = (11987611 11987612 11987613 11987614 11987615 11987616 11987621 11987622 11987623 11987624 1198762511987626 119905)

119910 = (1198651 1198652 1198653 1205781 1205782) (33)


10

5

0

40

20

0

40

20

0

5454353252151050

5454353252151050

5454353252151050

Yiel

d of

EC

(kg)

Yiel

d of

VO

(kg)




Con

sum

ptio

n of

steam

(m3)





10

5

0

40

20

0

Yiel

d of

EC

(kg)

Yiel

d of

VO

(kg)

15

10

5

0

3252151050

Extraction time (h)

3252151050

Extraction time (h)

3252151050


onsu

mpt

ion

ofste

am (m

3)







1198763 = 1198961119879 + 1198962 (34)









119894 = (1119894 2119894) = 119891119898 (119906119894) (36)


min1198961 1198962

SSE = 119899sum119894=1

(1205781119894 minus 1119894)2 + 119899sum119894=1

(1205782119894 minus 2119894)2 (37)


119899 119908 Algorithm 1198961 1198962 SSE














(38)





35

30

25

20

15

10

5

0


252151050

Extraction time (h)










ECtotal

VOtotal

u1

EC1

u2

VO1

VOleft1

ECleft1


EC2

ECleft2

VO2

VOleft2

uk

ECleftkminus1


ECleftk

leftkVO

VOextract

ECextractECk

VOk






119880 = (1199061 1199062 1199063) (39)


119906119894 = (11987611119894 11987612119894 11987613119894 11987614119894 11987615119894 11987616119894 11987621119894 11987622119894 1198762311989411987624119894 11987625119894 11987626119894 119905119894) 119894 = 1 2 3 (40)


1198651 = 3sum119894=1

11986511198941198652 = 3sum119894=1

1198652119894

1198653 = 3sum119894=1

( 6sum119895=1

((1198761119895119894 + 1198762119895119894) 1199051198946 )) 1205781 = 11986511198651 total 1205782 = 11986521198652 total

(41)


(1198651 1198652 1198653 1205781 1205782) = 1198651198983 (119880) (42)






(43)


119880119889 = (119896 1199061 1199062 1199063 1199064 1199065) (44)








Learningfactor

100 100Linear

decrease09sim02

1198881 25sim101198882 10sim25



(45)













Parameter 120588 120583 120585 120582Value 0003 1 01 001





1265

1260

1255

1250

1245

0846

0844

0842

084

0838

097

096

095

094

10987654321

10987654321

10987654321

1

2

Iterations

Iterations

Iterations


Econ

omic

ben

efit

(USD

h)




1

08

06

04

02

0

1

08

06

04

02

0

1

08

06

04

02

0

times10minus3151050 6420 543210

Deg

ree o

f mem

bers

hip

Deg

ree o

f mem

bers

hip

Deg

ree o

f mem

bers

hip






Competing Interests


Acknowledgments


References






















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in











119889119867119889119905 = (1198761 minus 1198763) 1198751119860 (1)


(2)


1198763 = 11987011198901198702119879 (3)





119889119866119889119905 = 119869119878 (4)







1205731 = 119863119904119877 minus 119903 1205732 = 1198631199030

(6)






119863 = 119861119879 V119860119891119860 (9)


119891119860 = 6120587119877120583119861V119860 (10)


119863 = 1198611198796120587119877120583119861 (11)



119863 = 74 times 10minus12 (120595119872119861)05 11987912058311986111988106119860 (12)



119863119904 = 120576119863120591 (13)



119903 = 119877 minus (1198961198631199041198621199051198620 )12 (14)


119889119902119889119905 = 119870119866119878 (119862119897 minus 119862119894) (15)





119889119902119889119905 = minus119870119866119878119870119902 = minus11989011989601198631198781198701198891 119902 (16)

where

119870119866 = 11989011989601198631198891 (17)



1205880 = 1198601 + 1198602119879 + 11986031198792 + 11986041198793 + 11986051198794 (18)



V119900119908 = (120588119908 minus 1205880) 11989211988922181205830 (19)




1205780 = 1198780V1199001199081198760 = 11987801198921812058301198760 (120588119908 minus 1205880) 11988922 (20)



120578119904 = 1 minus 119862119889119862119887 (21)



119867(119896 + 1) minus 119867 (119896)119879119878 = (1198761 (119896) minus 1198763 (119896)) 1198751119860 (22)


119867(119896 + 1) = (1198761 (119896) minus 1198763 (119896)) 1198751119860 119879119878 + 119867 (119896) (23)


perature is


(24)



(25)

where


(26)


119902 (119896 + 1) = (1 minus 1198901198960119863(119896)1198781198701198791198781198891 )119902 (119896) (27)



1198651 = 1198911 (119896) = 119881 (119896) 119862 (119896) = 119860119867 (119896) 119862 (119896) 1205781 = 11986511198651 total

(28)





1198652 = 1198912 (119896) = 1198912 (119896 minus 1) + Δ119898 (119896) 120578119904 (119896) 1205782 = 11986521198652 total

(30)



= 119878011989218120583011987511198763 (119896) (120588119908 minus 1205880) 11988922(31)


1198653 = 6sum119894=1

(1198761119894 + 1198762119894) 1199056 (32)


119906 = (11987611 11987612 11987613 11987614 11987615 11987616 11987621 11987622 11987623 11987624 1198762511987626 119905)

119910 = (1198651 1198652 1198653 1205781 1205782) (33)


10

5

0

40

20

0

40

20

0

5454353252151050

5454353252151050

5454353252151050

Yiel

d of

EC

(kg)

Yiel

d of

VO

(kg)




Con

sum

ptio

n of

steam

(m3)





10

5

0

40

20

0

Yiel

d of

EC

(kg)

Yiel

d of

VO

(kg)

15

10

5

0

3252151050

Extraction time (h)

3252151050

Extraction time (h)

3252151050


onsu

mpt

ion

ofste

am (m

3)







1198763 = 1198961119879 + 1198962 (34)









119894 = (1119894 2119894) = 119891119898 (119906119894) (36)


min1198961 1198962

SSE = 119899sum119894=1

(1205781119894 minus 1119894)2 + 119899sum119894=1

(1205782119894 minus 2119894)2 (37)


119899 119908 Algorithm 1198961 1198962 SSE














(38)





35

30

25

20

15

10

5

0


252151050

Extraction time (h)










ECtotal

VOtotal

u1

EC1

u2

VO1

VOleft1

ECleft1


EC2

ECleft2

VO2

VOleft2

uk

ECleftkminus1


ECleftk

leftkVO

VOextract

ECextractECk

VOk






119880 = (1199061 1199062 1199063) (39)


119906119894 = (11987611119894 11987612119894 11987613119894 11987614119894 11987615119894 11987616119894 11987621119894 11987622119894 1198762311989411987624119894 11987625119894 11987626119894 119905119894) 119894 = 1 2 3 (40)


1198651 = 3sum119894=1

11986511198941198652 = 3sum119894=1

1198652119894

1198653 = 3sum119894=1

( 6sum119895=1

((1198761119895119894 + 1198762119895119894) 1199051198946 )) 1205781 = 11986511198651 total 1205782 = 11986521198652 total

(41)


(1198651 1198652 1198653 1205781 1205782) = 1198651198983 (119880) (42)






(43)


119880119889 = (119896 1199061 1199062 1199063 1199064 1199065) (44)








Learningfactor

100 100Linear

decrease09sim02

1198881 25sim101198882 10sim25



(45)













Parameter 120588 120583 120585 120582Value 0003 1 01 001





1265

1260

1255

1250

1245

0846

0844

0842

084

0838

097

096

095

094

10987654321

10987654321

10987654321

1

2

Iterations

Iterations

Iterations


Econ

omic

ben

efit

(USD

h)




1

08

06

04

02

0

1

08

06

04

02

0

1

08

06

04

02

0

times10minus3151050 6420 543210

Deg

ree o

f mem

bers

hip

Deg

ree o

f mem

bers

hip

Deg

ree o

f mem

bers

hip






Competing Interests


Acknowledgments


References






















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





1205731 = 119863119904119877 minus 119903 1205732 = 1198631199030

(6)






119863 = 119861119879 V119860119891119860 (9)


119891119860 = 6120587119877120583119861V119860 (10)


119863 = 1198611198796120587119877120583119861 (11)



119863 = 74 times 10minus12 (120595119872119861)05 11987912058311986111988106119860 (12)



119863119904 = 120576119863120591 (13)



119903 = 119877 minus (1198961198631199041198621199051198620 )12 (14)


119889119902119889119905 = 119870119866119878 (119862119897 minus 119862119894) (15)





119889119902119889119905 = minus119870119866119878119870119902 = minus11989011989601198631198781198701198891 119902 (16)

where

119870119866 = 11989011989601198631198891 (17)



1205880 = 1198601 + 1198602119879 + 11986031198792 + 11986041198793 + 11986051198794 (18)



V119900119908 = (120588119908 minus 1205880) 11989211988922181205830 (19)




1205780 = 1198780V1199001199081198760 = 11987801198921812058301198760 (120588119908 minus 1205880) 11988922 (20)



120578119904 = 1 minus 119862119889119862119887 (21)



119867(119896 + 1) minus 119867 (119896)119879119878 = (1198761 (119896) minus 1198763 (119896)) 1198751119860 (22)


119867(119896 + 1) = (1198761 (119896) minus 1198763 (119896)) 1198751119860 119879119878 + 119867 (119896) (23)


perature is


(24)



(25)

where


(26)


119902 (119896 + 1) = (1 minus 1198901198960119863(119896)1198781198701198791198781198891 )119902 (119896) (27)



1198651 = 1198911 (119896) = 119881 (119896) 119862 (119896) = 119860119867 (119896) 119862 (119896) 1205781 = 11986511198651 total

(28)





1198652 = 1198912 (119896) = 1198912 (119896 minus 1) + Δ119898 (119896) 120578119904 (119896) 1205782 = 11986521198652 total

(30)



= 119878011989218120583011987511198763 (119896) (120588119908 minus 1205880) 11988922(31)


1198653 = 6sum119894=1

(1198761119894 + 1198762119894) 1199056 (32)


119906 = (11987611 11987612 11987613 11987614 11987615 11987616 11987621 11987622 11987623 11987624 1198762511987626 119905)

119910 = (1198651 1198652 1198653 1205781 1205782) (33)


10

5

0

40

20

0

40

20

0

5454353252151050

5454353252151050

5454353252151050

Yiel

d of

EC

(kg)

Yiel

d of

VO

(kg)




Con

sum

ptio

n of

steam

(m3)





10

5

0

40

20

0

Yiel

d of

EC

(kg)

Yiel

d of

VO

(kg)

15

10

5

0

3252151050

Extraction time (h)

3252151050

Extraction time (h)

3252151050


onsu

mpt

ion

ofste

am (m

3)







1198763 = 1198961119879 + 1198962 (34)









119894 = (1119894 2119894) = 119891119898 (119906119894) (36)


min1198961 1198962

SSE = 119899sum119894=1

(1205781119894 minus 1119894)2 + 119899sum119894=1

(1205782119894 minus 2119894)2 (37)


119899 119908 Algorithm 1198961 1198962 SSE














(38)





35

30

25

20

15

10

5

0


252151050

Extraction time (h)










ECtotal

VOtotal

u1

EC1

u2

VO1

VOleft1

ECleft1


EC2

ECleft2

VO2

VOleft2

uk

ECleftkminus1


ECleftk

leftkVO

VOextract

ECextractECk

VOk






119880 = (1199061 1199062 1199063) (39)


119906119894 = (11987611119894 11987612119894 11987613119894 11987614119894 11987615119894 11987616119894 11987621119894 11987622119894 1198762311989411987624119894 11987625119894 11987626119894 119905119894) 119894 = 1 2 3 (40)


1198651 = 3sum119894=1

11986511198941198652 = 3sum119894=1

1198652119894

1198653 = 3sum119894=1

( 6sum119895=1

((1198761119895119894 + 1198762119895119894) 1199051198946 )) 1205781 = 11986511198651 total 1205782 = 11986521198652 total

(41)


(1198651 1198652 1198653 1205781 1205782) = 1198651198983 (119880) (42)






(43)


119880119889 = (119896 1199061 1199062 1199063 1199064 1199065) (44)








Learningfactor

100 100Linear

decrease09sim02

1198881 25sim101198882 10sim25



(45)













Parameter 120588 120583 120585 120582Value 0003 1 01 001





1265

1260

1255

1250

1245

0846

0844

0842

084

0838

097

096

095

094

10987654321

10987654321

10987654321

1

2

Iterations

Iterations

Iterations


Econ

omic

ben

efit

(USD

h)




1

08

06

04

02

0

1

08

06

04

02

0

1

08

06

04

02

0

times10minus3151050 6420 543210

Deg

ree o

f mem

bers

hip

Deg

ree o

f mem

bers

hip

Deg

ree o

f mem

bers

hip






Competing Interests


Acknowledgments


References






















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





1205780 = 1198780V1199001199081198760 = 11987801198921812058301198760 (120588119908 minus 1205880) 11988922 (20)



120578119904 = 1 minus 119862119889119862119887 (21)



119867(119896 + 1) minus 119867 (119896)119879119878 = (1198761 (119896) minus 1198763 (119896)) 1198751119860 (22)


119867(119896 + 1) = (1198761 (119896) minus 1198763 (119896)) 1198751119860 119879119878 + 119867 (119896) (23)


perature is


(24)



(25)

where


(26)


119902 (119896 + 1) = (1 minus 1198901198960119863(119896)1198781198701198791198781198891 )119902 (119896) (27)



1198651 = 1198911 (119896) = 119881 (119896) 119862 (119896) = 119860119867 (119896) 119862 (119896) 1205781 = 11986511198651 total

(28)





1198652 = 1198912 (119896) = 1198912 (119896 minus 1) + Δ119898 (119896) 120578119904 (119896) 1205782 = 11986521198652 total

(30)



= 119878011989218120583011987511198763 (119896) (120588119908 minus 1205880) 11988922(31)


1198653 = 6sum119894=1

(1198761119894 + 1198762119894) 1199056 (32)


119906 = (11987611 11987612 11987613 11987614 11987615 11987616 11987621 11987622 11987623 11987624 1198762511987626 119905)

119910 = (1198651 1198652 1198653 1205781 1205782) (33)


10

5

0

40

20

0

40

20

0

5454353252151050

5454353252151050

5454353252151050

Yiel

d of

EC

(kg)

Yiel

d of

VO

(kg)




Con

sum

ptio

n of

steam

(m3)





10

5

0

40

20

0

Yiel

d of

EC

(kg)

Yiel

d of

VO

(kg)

15

10

5

0

3252151050

Extraction time (h)

3252151050

Extraction time (h)

3252151050


onsu

mpt

ion

ofste

am (m

3)







1198763 = 1198961119879 + 1198962 (34)









119894 = (1119894 2119894) = 119891119898 (119906119894) (36)


min1198961 1198962

SSE = 119899sum119894=1

(1205781119894 minus 1119894)2 + 119899sum119894=1

(1205782119894 minus 2119894)2 (37)


119899 119908 Algorithm 1198961 1198962 SSE














(38)





35

30

25

20

15

10

5

0


252151050

Extraction time (h)










ECtotal

VOtotal

u1

EC1

u2

VO1

VOleft1

ECleft1


EC2

ECleft2

VO2

VOleft2

uk

ECleftkminus1


ECleftk

leftkVO

VOextract

ECextractECk

VOk






119880 = (1199061 1199062 1199063) (39)


119906119894 = (11987611119894 11987612119894 11987613119894 11987614119894 11987615119894 11987616119894 11987621119894 11987622119894 1198762311989411987624119894 11987625119894 11987626119894 119905119894) 119894 = 1 2 3 (40)


1198651 = 3sum119894=1

11986511198941198652 = 3sum119894=1

1198652119894

1198653 = 3sum119894=1

( 6sum119895=1

((1198761119895119894 + 1198762119895119894) 1199051198946 )) 1205781 = 11986511198651 total 1205782 = 11986521198652 total

(41)


(1198651 1198652 1198653 1205781 1205782) = 1198651198983 (119880) (42)






(43)


119880119889 = (119896 1199061 1199062 1199063 1199064 1199065) (44)








Learningfactor

100 100Linear

decrease09sim02

1198881 25sim101198882 10sim25



(45)













Parameter 120588 120583 120585 120582Value 0003 1 01 001





1265

1260

1255

1250

1245

0846

0844

0842

084

0838

097

096

095

094

10987654321

10987654321

10987654321

1

2

Iterations

Iterations

Iterations


Econ

omic

ben

efit

(USD

h)




1

08

06

04

02

0

1

08

06

04

02

0

1

08

06

04

02

0

times10minus3151050 6420 543210

Deg

ree o

f mem

bers

hip

Deg

ree o

f mem

bers

hip

Deg

ree o

f mem

bers

hip






Competing Interests


Acknowledgments


References






















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




10

5

0

40

20

0

40

20

0

5454353252151050

5454353252151050

5454353252151050

Yiel

d of

EC

(kg)

Yiel

d of

VO

(kg)




Con

sum

ptio

n of

steam

(m3)





10

5

0

40

20

0

Yiel

d of

EC

(kg)

Yiel

d of

VO

(kg)

15

10

5

0

3252151050

Extraction time (h)

3252151050

Extraction time (h)

3252151050


onsu

mpt

ion

ofste

am (m

3)







1198763 = 1198961119879 + 1198962 (34)









119894 = (1119894 2119894) = 119891119898 (119906119894) (36)


min1198961 1198962

SSE = 119899sum119894=1

(1205781119894 minus 1119894)2 + 119899sum119894=1

(1205782119894 minus 2119894)2 (37)


119899 119908 Algorithm 1198961 1198962 SSE














(38)





35

30

25

20

15

10

5

0


252151050

Extraction time (h)










ECtotal

VOtotal

u1

EC1

u2

VO1

VOleft1

ECleft1


EC2

ECleft2

VO2

VOleft2

uk

ECleftkminus1


ECleftk

leftkVO

VOextract

ECextractECk

VOk






119880 = (1199061 1199062 1199063) (39)


119906119894 = (11987611119894 11987612119894 11987613119894 11987614119894 11987615119894 11987616119894 11987621119894 11987622119894 1198762311989411987624119894 11987625119894 11987626119894 119905119894) 119894 = 1 2 3 (40)


1198651 = 3sum119894=1

11986511198941198652 = 3sum119894=1

1198652119894

1198653 = 3sum119894=1

( 6sum119895=1

((1198761119895119894 + 1198762119895119894) 1199051198946 )) 1205781 = 11986511198651 total 1205782 = 11986521198652 total

(41)


(1198651 1198652 1198653 1205781 1205782) = 1198651198983 (119880) (42)






(43)


119880119889 = (119896 1199061 1199062 1199063 1199064 1199065) (44)








Learningfactor

100 100Linear

decrease09sim02

1198881 25sim101198882 10sim25



(45)













Parameter 120588 120583 120585 120582Value 0003 1 01 001





1265

1260

1255

1250

1245

0846

0844

0842

084

0838

097

096

095

094

10987654321

10987654321

10987654321

1

2

Iterations

Iterations

Iterations


Econ

omic

ben

efit

(USD

h)




1

08

06

04

02

0

1

08

06

04

02

0

1

08

06

04

02

0

times10minus3151050 6420 543210

Deg

ree o

f mem

bers

hip

Deg

ree o

f mem

bers

hip

Deg

ree o

f mem

bers

hip






Competing Interests


Acknowledgments


References






















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in








119894 = (1119894 2119894) = 119891119898 (119906119894) (36)


min1198961 1198962

SSE = 119899sum119894=1

(1205781119894 minus 1119894)2 + 119899sum119894=1

(1205782119894 minus 2119894)2 (37)


119899 119908 Algorithm 1198961 1198962 SSE














(38)





35

30

25

20

15

10

5

0


252151050

Extraction time (h)










ECtotal

VOtotal

u1

EC1

u2

VO1

VOleft1

ECleft1


EC2

ECleft2

VO2

VOleft2

uk

ECleftkminus1


ECleftk

leftkVO

VOextract

ECextractECk

VOk






119880 = (1199061 1199062 1199063) (39)


119906119894 = (11987611119894 11987612119894 11987613119894 11987614119894 11987615119894 11987616119894 11987621119894 11987622119894 1198762311989411987624119894 11987625119894 11987626119894 119905119894) 119894 = 1 2 3 (40)


1198651 = 3sum119894=1

11986511198941198652 = 3sum119894=1

1198652119894

1198653 = 3sum119894=1

( 6sum119895=1

((1198761119895119894 + 1198762119895119894) 1199051198946 )) 1205781 = 11986511198651 total 1205782 = 11986521198652 total

(41)


(1198651 1198652 1198653 1205781 1205782) = 1198651198983 (119880) (42)






(43)


119880119889 = (119896 1199061 1199062 1199063 1199064 1199065) (44)








Learningfactor

100 100Linear

decrease09sim02

1198881 25sim101198882 10sim25



(45)













Parameter 120588 120583 120585 120582Value 0003 1 01 001





1265

1260

1255

1250

1245

0846

0844

0842

084

0838

097

096

095

094

10987654321

10987654321

10987654321

1

2

Iterations

Iterations

Iterations


Econ

omic

ben

efit

(USD

h)




1

08

06

04

02

0

1

08

06

04

02

0

1

08

06

04

02

0

times10minus3151050 6420 543210

Deg

ree o

f mem

bers

hip

Deg

ree o

f mem

bers

hip

Deg

ree o

f mem

bers

hip






Competing Interests


Acknowledgments


References






















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in













(38)





35

30

25

20

15

10

5

0


252151050

Extraction time (h)










ECtotal

VOtotal

u1

EC1

u2

VO1

VOleft1

ECleft1


EC2

ECleft2

VO2

VOleft2

uk

ECleftkminus1


ECleftk

leftkVO

VOextract

ECextractECk

VOk






119880 = (1199061 1199062 1199063) (39)


119906119894 = (11987611119894 11987612119894 11987613119894 11987614119894 11987615119894 11987616119894 11987621119894 11987622119894 1198762311989411987624119894 11987625119894 11987626119894 119905119894) 119894 = 1 2 3 (40)


1198651 = 3sum119894=1

11986511198941198652 = 3sum119894=1

1198652119894

1198653 = 3sum119894=1

( 6sum119895=1

((1198761119895119894 + 1198762119895119894) 1199051198946 )) 1205781 = 11986511198651 total 1205782 = 11986521198652 total

(41)


(1198651 1198652 1198653 1205781 1205782) = 1198651198983 (119880) (42)






(43)


119880119889 = (119896 1199061 1199062 1199063 1199064 1199065) (44)








Learningfactor

100 100Linear

decrease09sim02

1198881 25sim101198882 10sim25



(45)













Parameter 120588 120583 120585 120582Value 0003 1 01 001





1265

1260

1255

1250

1245

0846

0844

0842

084

0838

097

096

095

094

10987654321

10987654321

10987654321

1

2

Iterations

Iterations

Iterations


Econ

omic

ben

efit

(USD

h)




1

08

06

04

02

0

1

08

06

04

02

0

1

08

06

04

02

0

times10minus3151050 6420 543210

Deg

ree o

f mem

bers

hip

Deg

ree o

f mem

bers

hip

Deg

ree o

f mem

bers

hip






Competing Interests


Acknowledgments


References






















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in








ECtotal

VOtotal

u1

EC1

u2

VO1

VOleft1

ECleft1


EC2

ECleft2

VO2

VOleft2

uk

ECleftkminus1


ECleftk

leftkVO

VOextract

ECextractECk

VOk






119880 = (1199061 1199062 1199063) (39)


119906119894 = (11987611119894 11987612119894 11987613119894 11987614119894 11987615119894 11987616119894 11987621119894 11987622119894 1198762311989411987624119894 11987625119894 11987626119894 119905119894) 119894 = 1 2 3 (40)


1198651 = 3sum119894=1

11986511198941198652 = 3sum119894=1

1198652119894

1198653 = 3sum119894=1

( 6sum119895=1

((1198761119895119894 + 1198762119895119894) 1199051198946 )) 1205781 = 11986511198651 total 1205782 = 11986521198652 total

(41)


(1198651 1198652 1198653 1205781 1205782) = 1198651198983 (119880) (42)






(43)


119880119889 = (119896 1199061 1199062 1199063 1199064 1199065) (44)








Learningfactor

100 100Linear

decrease09sim02

1198881 25sim101198882 10sim25



(45)













Parameter 120588 120583 120585 120582Value 0003 1 01 001





1265

1260

1255

1250

1245

0846

0844

0842

084

0838

097

096

095

094

10987654321

10987654321

10987654321

1

2

Iterations

Iterations

Iterations


Econ

omic

ben

efit

(USD

h)




1

08

06

04

02

0

1

08

06

04

02

0

1

08

06

04

02

0

times10minus3151050 6420 543210

Deg

ree o

f mem

bers

hip

Deg

ree o

f mem

bers

hip

Deg

ree o

f mem

bers

hip






Competing Interests


Acknowledgments


References






















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in







(43)


119880119889 = (119896 1199061 1199062 1199063 1199064 1199065) (44)








Learningfactor

100 100Linear

decrease09sim02

1198881 25sim101198882 10sim25



(45)













Parameter 120588 120583 120585 120582Value 0003 1 01 001





1265

1260

1255

1250

1245

0846

0844

0842

084

0838

097

096

095

094

10987654321

10987654321

10987654321

1

2

Iterations

Iterations

Iterations


Econ

omic

ben

efit

(USD

h)




1

08

06

04

02

0

1

08

06

04

02

0

1

08

06

04

02

0

times10minus3151050 6420 543210

Deg

ree o

f mem

bers

hip

Deg

ree o

f mem

bers

hip

Deg

ree o

f mem

bers

hip






Competing Interests


Acknowledgments


References






















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in












Parameter 120588 120583 120585 120582Value 0003 1 01 001





1265

1260

1255

1250

1245

0846

0844

0842

084

0838

097

096

095

094

10987654321

10987654321

10987654321

1

2

Iterations

Iterations

Iterations


Econ

omic

ben

efit

(USD

h)




1

08

06

04

02

0

1

08

06

04

02

0

1

08

06

04

02

0

times10minus3151050 6420 543210

Deg

ree o

f mem

bers

hip

Deg

ree o

f mem

bers

hip

Deg

ree o

f mem

bers

hip






Competing Interests


Acknowledgments


References






















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




1

08

06

04

02

0

1

08

06

04

02

0

1

08

06

04

02

0

times10minus3151050 6420 543210

Deg

ree o

f mem

bers

hip

Deg

ree o

f mem

bers

hip

Deg

ree o

f mem

bers

hip






Competing Interests


Acknowledgments


References






















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in













Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in










Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



Documents

Research Article Modeling and Optimization of the Drug ...downloads.hindawi.com/journals/sp/2016/3279423.pdf · of the oil-water separator. A mathematical model of the extraction