banana juice (fabt 2013)(1)

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Food and Bioprocess TechnologyAn International Journal ISSN 1935-5130 Food Bioprocess TechnolDOI 10.1007/s11947-013-1136-2

Optimization, Modeling, and OnlineMonitoring of the Enzymatic Extraction ofBanana Juice

Vrani Ibarra-Junquera, Pilar Escalante-Minakata, Arturo Moiss Chvez-Rodrguez, Isabel Alicia Comparan-Dueas, et al.

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ORIGINAL PAPER

Optimization, Modeling, and Online Monitoringof the Enzymatic Extraction of Banana Juice

Vrani Ibarra-Junquera & Pilar Escalante-Minakata & Arturo Moiss Chvez-Rodrguez &Isabel Alicia Comparan-Dueas & Juan Alberto Osuna-Castro & Jos de Jess Ornelas-Paz & Jaime David Prez-Martnez & Cristbal No Aguilar

Received: 25 May 2012 /Accepted: 20 May 2013# Springer Science+Business Media New York 2013

Abstract This article focuses on the optimization, model-ing, and online monitoring of banana juice productionthrough an enzymatic method. In order to perform thistask, a batch reactor was designed with automatic controlover the temperature and the agitation speed as well asonline monitoring of torque. The experiments were carriedout with the Musa AAA Cavendish banana variety (Enanogigante), the main variety planted in Mexico. Three differentripening stages were evaluated. Optimization of juice extrac-tion was evaluated as a function of the pulp/water relationshipand the concentration of the enzyme complex. The resultsshowed that the adding of water had no influence on theextraction of banana juice, and the optimal enzyme concen-tration per kilogram of banana pulp was found. Based on afuzzy logic approach, it was possible to relate the initial torque

with the ripeness stage. Furthermore, an observable dynamicalmodel based on ordinary differential equations and fuzzy logicis presented. With this model, the relationship between thetorque dynamic and the instant juice yield was found to dependon the amount of enzyme, the temperature, and the maturitystage of the banana used. In addition, a principal componentsanalysis was used to classify and to relate the final juicecharacteristics (e.g., L, a, and b colorimetric components) tothe processing conditions and the final appreciation of a groupof sensorial panelists. Additionally, a robust observer wasdesigned and implemented to filter the noise present in thetorque signal and to predict the instant juice yield.

Keywords Banana . Juice . Modeling . Observer .

Optimization . Processing

Introduction

Bananas are one of the worlds most important food crops,consumed by millions as part of a daily diet and for nutrientenrichment (Mohapatra et al. 2011) since they are an importantsource of polyphenols,minerals, and carbohydrates (Kiyoshi andWahachiro 2003; Wall 2006; Escalante-Minakata et al. 2013).Furthermore, the banana is widely appreciated for its flavor andaroma (Boudhrioua et al. 2003; Mohapatra et al. 2011). Thoughcommonly consumed as fresh fruit, bananas have an unfortu-nately short shelf-life due to softening and thus are often used inbanana juice processing as an alternative (Kyamuhangire et al.2002; Lee et al. 2006a, b; Lpez-Nicols et al. 2007; Mohapatraet al. 2011; Chvez-Rodrguez et al. 2013).

A relevant issue in banana juice extraction is the retentionof the juice in the pulp due to the great amount of polysac-charides, which prevent the release of intra-cell components,affecting the extraction yield and the clarification. The juicecan be extracted by a mechanical press and/or through the

V. Ibarra-Junquera (*) : P. Escalante-Minakata :A. M. Chvez-Rodrguez : I. A. Comparan-DueasBioengineering Laboratory, University of Colima, CarreteraColima-Coquimatln, Km 9,Coquimatln, Colima State, Mexicoe-mail: [email protected]

J. J. Ornelas-PazCentro de Investigacin en Alimentacin y Desarrollo A.C.(CIAD), Unidad Cuauhtmoc, Chihuahua State, Mexico

J. D. Prez-MartnezFaculty of Chemical Sciences, AutonomousUniversity of San Luis Potos,San Luis Potos, S.L.P. State, Mexico

J. A. Osuna-CastroFaculty of Biological and Agricultural Sciences,University of Colima, km 40 Autopista Colima-Manzanillo,28100, Tecomn, Colima, Mexico

C. N. AguilarDepartment of Food Science and Technology, School ofChemistry, Autonomous University of Coahuila, SaltilloCoahuila State, Mexico

Food Bioprocess TechnolDOI 10.1007/s11947-013-1136-2

Author's personal copy

action of pectinolytic enzymes, such as pectinase andpolygalactouronase (Casimir and Jayaraman 1971; Viquez etal. 1981; Kyamuhangire et al. 2002; Lee et al. 2006a). For thatreason, banana juice extraction can be considered a bioprocesswhen an enzymatic bioreactor is at its core. Such a processdemands high levels of quality and safety in food produc-tion, which calls for high standards in quality assurance andprocess control; satisfying this demand, in turn, requiresappropriate analytical tools for food analysis both duringand after production (Zhong 2010). Desirable features ofsuch tools include speed, ease of use, minimal or nosample preparation, and the avoidance of sample destruc-tion. It is also necessary to control and optimize the biore-actor environment via operating variables in order to favorthe desired functions and achieve cost-effective, large-scalemanufacture (Zhong 2010). Traditionally, a method toachieve this goal utilizes laboratory instruments to treatsamples taken from the processing plant and analyzed off-line (Ibarra-Junquera et al. 2010). This allows processinvestigation, checking of the specifications of raw mate-rials and final products, which aids in management anddecision making (Cozzolino et al. 2011). However, recentdevelopments in on-line measurements offer the possibilityof following process dynamics, achieving better and morerapid control, and eliminating questions about the statisticalsignificance of quality control based on sampling (Zhang2009; Ibarra-Junquera et al. 2010; Cozzolino et al. 2011).Several studies have described on-line instrumentation fordetermining the characteristics of particle systems in situ inthe processing plant and that describe how on-line mea-surements from such instruments lead to process improve-ments. In particular, better monitoring and control of bio-reactors requires reliable on-line estimation of process vari-ables and parameters that often cannot be measured directly(Zhang 2009; Ibarra-Junquera et al. 2010).

Therefore, this study has three main goals. The first goalis to optimize the enzymatic method for banana juice ex-traction by finding the minimum amount of water andenzymatic complex needed to obtain the maximum juiceyield in a given span of time. Second, this study aims todevelop a minimalist model to describe, in general terms,banana juice extraction dynamics, allowing its usage for on-line monitoring and automatic control. Thus, such a modelshould include on-line measurable variables and the juiceyield as one of its states, and then construct a model-basedobserver algorithm to infer in real time the juice yield fromthe on-line measurable output. Under the hypothesis that thetorque evolution can be associated with the juice yielddynamic, a batch reactor was designed with automatic con-trol over the temperature and the agitation speed and withon-line monitoring of torque. The studys third goal is torelate the visual characteristics of the final banana juice tothe processing conditions.

Methodology

Bioreactor

The enzymatic juice extractions were performed in a 4-Lstainless steel batch-jacketed reactor (i.d. 12.5 cm),equipped with automatic control over the temperature, basedon a cooling thermostat with a precision of 0.02 C (RE630S; Lauda Eco Silver, Germany). The bioreactor agitationspeed control is composed of the Compact cRio-9074 dataacquisition system (DAS) (National Instruments, TX, USA),a PC for the control of the DAS, a stepper motor (NEMA 23Stepper Motor; National Instruments) connected to aMicrostepping Drive (National Instruments), and two inde-pendent power supplies. The stepper motor movement isdirected by using an application developed within theLabview platform (National Instruments). An open-paddleimpeller (width 9.6 cm, height 12.3 cm) is connected to themotor through a drill chuck. The torque was monitoredonline using a rotary torque sensor with a maximum capac-ity of 2 Nm (FSH01979; FUTEK, CA, USA) connected to aPC through a data acquisition system from National Instru-ments (Cryo-9074) and Labview-based interface.

Biological Material

Bananas of the cultivar Enano gigante (Musa AAA, sub-group Cavendish) were acquired in the local market whenthey were green (Fig. 1) with a minimum length of 13 cm.The banana bunches were ripened in laboratory conditionsat 20 C without atmospheric control for different storagetimes. The color of the peel was monitored by comparisonwith a scale ranging from 1 to 3, with values representingthe following stages of ripeness: Green (1), ranging frommore yellow than green to yellow with green endings;Yellow (2), ranging from completely yellow to yellow withslight brown specks; and Brown (3), which included yellowwith many brown specks. Additionally, the parts of individ-ual samples were weighed in an analytical balance to deter-mine the pulp-to-peel ratio. The results were expressed asthe percent weight of pulp relative to peel.

Fig. 1 Peel color changes in different stages of banana ripeness, thenumbers 1, 2, and 3 corresponds to green, yellow, and brown,respectively

Food Bioprocess Technol


Juice Extraction Procedure

The banana fruits were washed in 0.2 % (v/v) sodiumhypochlorite aqueous solutions for 5 min, peeled, and cutinto pieces. In order to homogenize the banana pulp, appro-priate volumes of water were added to achieve a bananapulp/water ratio of 0.8, 0.9, and 1.0. Then, the mixture washomogenized to puree in an electrical blender. The enzy-matic extractions were performed using a commercial mix-ture of three plant-cell-wall-degrading enzymespectinase,cellulase, and hemicellulase (Macerex PM, ENMEX, S.A.de C.V. (2003)), which hydrolyze the polysaccharide sub-strates from banana cell wallranging from 100 to 600 Lof enzyme mixture per kilogram of puree. The enzymaticextractions took place in a batch reactor (filled with 3 kg ofbanana puree) and continuously agitated (100 rpm) at roomtemperature (25 C) for 2 h. Subsequently, the juice wascentrifuged at 12,000g using a centrifuge (RC6+; Sorvall,Newtown, CT, USA) in an SLA-3000 rotor for 15 min, andthe supernatant was collected and filtered. Finally, the totalsoluble solids content was determined for each banana juiceobtained, using a digital refractometer (RP-101; Atago, To-kyo, Japan) with a scale ranging between 0 and 45 degreesBrix (Bx). The soluble solids content were reported asdegrees Brix.

Juice Yield

The banana juice yield was calculated based on the weightof the resulting juice, the added water, and the banana pulp,according to the following equation:

Juice yield % jw g ww g bw g 100 1

where jw is the amount of juice recovered, ww is the weightof the added water, and bw is the weight of the total bananapuree used. All weight measurements were expressed ingrams (g). The juice was recovered by centrifugation atthe same conditions mentioned in the juice extraction meth-odology. The samples weights were obtained through ananalytical balance (OHAUS; Explorer Pro, Pine Brook,NJ, USA; accuracy 0.1 mg).

Protein Quantification

The protein concentration of the enzymatic complex wasdetermined by the Bradford method (1976) as modified byBioRad (using bovine serum albumin protein as standard).The samples were diluted to a ratio of 1:20 by addingdistilled water. The absorbance of the samples was deter-mined at 595 nm using a lambda 25 UVVis spectropho-tometer (Perkin-Elmer Instrument, USA).

Colorimetric Analysis

Analysis of color variation was performed with a totalvolume of 20 mL from each banana juice sample anddispensed into separate Petri dishes. The color values ofeach sample were obtained with a LABSCAN XE chromameter (Hunterlab, VA, USA) at room temperature. Equip-ment was set up for illuminant D65 and 10 observer angle.CIE-Lab values of L (lightness), a (redness), and b(yellowness) were determined to describe the precise loca-tion of a color inside a three-dimensional visible colorspace.

Statistical Analysis

All statistical analyses were carried out using MatLab soft-ware (MathWorks Inc., USA). The analysis of variances(ANOVA) was applied to compare the mean values ofsamples according to the different factors. In addition, prin-cipal component analysis (PCA) was used as a data multi-variate technique. The purpose of this method is to decom-pose the data matrix and concentrate the source of variabil-ity in the data into the first few principal components. Here,PCA was applied to two different groups of values: thematrix of maturity mean attribute ratings across bananasamples (initial torque and the peel-to-pulp ratio) and thematrix of mean color measurements (L, a, and b). The twocases were also analyzed by cluster analysis (average link-age method) in an attempt to classify the samples in terms oftheir maturity and processing method.

Visual Evaluation

The juice data, coming from the colorimetric analysis, wereevaluated using PCA and cluster analysis. As an additionalreference, the resulting groups were classified in terms ofvisual acceptance by a five-judge panel belonging to thefaculty of Chemical Sciences and research scholars of theBioengineering Laboratory (both of the University Colimain Mexico). This general appearance of the juice was mea-sured subjectively on a three-point hedonic scale: poor(dislike), good (like), and excellent (like very much).

Optimization Procedure

The optimization methodology used in this work is based ona three-step process: (1) generating a mesh of experimentaldata within the design space, (2) modeling the data setsthrough nonlinear fitting, and (3) using the fitted modeland ANOVA analysis to obtain the optimal condition.

The dependent variables selected for these studies wereX, enzyme concentration (L/kg), taking values in the set{0, 25, 50, 100, 150, 300, 600 L/kg}; Y, ratio of



water/banana pulp taking values in the set {1, 0.9, 0.8}; andZ, response variable. Given are a total of 63 experiments, tobe performed in triplicate. The juice yield, as evaluated inEq. 1, was the response variable. Based on the preliminarydata, the following generalized MichaelisMenten responsesurface (Hirst et al. 1996) is used to model the data behav-ior:

Z X ; Y bXYc dYZ 2

Exclusively for the optimization process, the previouslymentioned banana juice extraction methodology was slight-ly modified since all experiments were carried out at 50 Cfor 30 min, and the yield was calculated at the end of theprocess.

Fuzzy Logic Approach

The complexity of biological processes often renders im-practical the development of detailed, structured phenome-nological models. Fuzzy modeling is based on sets of fuzzyifthen rules derived from expert domain knowledge tohandle uncertainty. The concept of fuzzy logic provides anatural way of dealing with problems where the absence ofwell-defined criteria could be a source of imprecision. Sincefuzzy systems can simultaneously handle numerical dataand linguistic knowledge, they provide opportunities formodeling of conditions that are inherently imprecisely de-fined, like fruit ripeness.

The quality of banana juice is defined by its phys-ical appearance and taste, both of which are directlyrelated to its stage of ripeness. Thus, the ripenessstage directly influences the quality of the final juice.Therefore, the purpose of the fuzzy modeling is torelate the banana maturity as perceived by human eyesbased on color and general physical characteristics(e.g., appearance of spots) to standard measurementsthat can allow the modeling and monitoring of thejuice extraction process.

Triangular membership functions have been used forsimilar problems (Sinija and Mishra 2011). For example,triangle a1b1c1 represents the membership function forripeness stage 1, triangle a2b2c2 represents the distribu-tion function for ripeness stage 2, etc. Figure 2 representsthe triplets associated with three ripeness stages. The secondnumber of the triplet denotes the coordinate of the abscissaat which the value of the membership function is 1. The firstand third numbers of the triplet designate the distance to theleft and right, respectively, of the second number where themembership function is 0.

Enzymatic Juice Extraction Model

The main goal of this paper is to develop a minimalist modelto describe, in general terms, banana juice extraction dy-namics to be used for monitoring and control. This unstruc-tured and nonsegregated model is given by Eqs. 3 and 4.

dx1dt

m T ; x2;0

xmax T ; x2;0

x1 3

dx2dt

m T ; x2;0

y T ; x2;0 xmax T ; x2;0 x1 4

where the state variables are as follows: x1 stands for juiceyield and x2 stand for torque. The parameters are as follows:T stands for temperature (C) and M for the maturity stage,i.e., M (1,2,3). The rest of the functions are given inTable 1. The mathematical expressions given in Eqs. 3 and4 were selected since the preliminary data showed an expo-nential growth of the juice yield and an exponential decay ofthe torque signal as well as a temperature and maturity stagedependence of the kinetic rate, m, the maximum juice yield,xmax, and the torque initial condition x2,0. The functiony(T,x2,0) allows to relate the juice yield x1(t) with the torque

Table 1 Functions and units used in dynamical model given by Eqs. 3and 4

Variable Dependence Units

xmax(T,x2,0) f1(T,M)

y(T,x2,0) f2(T,M) 1/N m

m(T,x2,0) maxS kmS

kmBe M X 2;0

L/kg

maxAe

1T

( M(X2,0))2+w M(X2,0)+ C

A e Y M X 2;0

Fig. 2 Memberships function with triangular membership distribution



measurements x2(t). Thus, this methodology can be consid-ered as a data-driven approach to the modeling of theenzymatic extraction of banana juice in which its structureand the parameter identification is based on off-line and on-line time series obtained from a rigorous experimental set.

Software Sensor Design

Taking into account the fact that rarely can one have asensor on every state variable, and some form of reconstruc-tion from the available measured output data is needed,software can be constructed using the mathematical modelof the process to obtain an estimate of the true state x. Eversince the original work by Luenberger (1971), the use ofstate observers has proven useful in process monitoring andfor many other tasks. In the sense of control theory, analgorithm capable of giving a reasonable estimation of theunmeasured variables of a process will be called anobserver.

Numerous attempts have been made to develop observerdesign methods for bioprocess applications (Escalante-Minakata et al. 2009; Zhang 2009; Fernndez-Fernndezand Prez-Correa 2010). The first systematic approach forthe development of a theory of observers was proposedsome time ago by Krener and Isidori (1983). Nevertheless,it is well known that classical proportional observers tend toamplify the noise of on-line measurements, which can leadto the degradation of the observer performance. In order toavoid this drawback, in this paper, the observer algorithm isbased on the work of Ibarra-Junquera et al. (2005) becausethe proposed integral observer provides robustness againstnoisy measurements and uncertainties.

In this section, the design of the software sensor ispresented in which xj, for j(1n), is the naturally mea-sured state (i.e., the variable easiest to measure). Therefore,it seems logical to take xj as the output of the system, y=h(x)=xj. Now, considering that the output function h(x) is con-taminated with a Gaussian noise, the model given by theaforementioned Eqs. 3 and 4 acquires the form:

X f X y cX

where f(X) is a matrix containing the left-hand side of Eqs. 3and 4, y represents the noisy on-line measurable output, isthe additive bounded measurement noise, X=[x1,x2] is thevector of states, and the vector cX=[0,1]T[x1,x2] defines theon-line measurable output, x2 in this particular case. Then,the task of designing an observer for the system Eqs. 3 and 4is to estimate the vector of states X, despite the noise butconsidering that y is measured on-line and that the system isobservable.

Results and Discussion

Optimization Procedure

Many recent works show that the use of polysaccharidasesfacilitates the release of juice and increases the extractionyield (Kyamuhangire et al. 2002; Sreenath et al. 1994;Cheirsilp and Umsakul 2008; Buenrostro-Figueroa et al.2010; Bahramian et al. 2011). In addition, in the case ofbanana and mango juice extraction, many protocols includedilution of pulp in water, ranging from undiluted extractionprocesses (Khalil et al. 1989; Reddy and Reddy 2005;Buenrostro-Figueroa et al. 2010) to water/pulp ratios of1:1 (Cheirsilp and Umsakul 2008; Kyamuhangire andPehrson 1999; Onwuka and Awam 2001), 1:2 (Lee et al.2006a, b; Lee et al. 2007), 1:4 (Falade and Babalola 2004),and 1:5 (Akubor 1996). However, none of these workspresent a justification for the selected dilution ratio. Whilethere is clear evidence that the application of enzyme com-plexes in the extraction of banana juice is efficient, no studyhas reported on the variables of ripeness stage andwater/pulp ratio.

The results of the Bradford assay show that the commer-cial enzymatic complex contains 12.06 1.20 mgprotein/mL. The juice yield was affected by the enzymaticcomplex concentration and water/pulp ratio within the stud-ied conditions (P

develop a simplified model that relates on-line measurablevariables with off-line ones. In addition, the resulting modelshould allow the construction of an observer scheme to re-build, in real time, the non-measurable on-line variables.

It has been previously reported that the use ofpolysaccharidases improves the juice yield and modifiesthe physicochemical and rheological properties of the mix-ture during the process (Aguilar et al. 2008; Bahramian et al.2011). Formerly, off-line viscosity measurements of pectinsolut ion were used to determine the activity ofpolysaccharidases because a decrement of this parameter isrelated to this endohydrolase activity (Combo et al. 2012).Since torque is the measurement of the force that rotates anobject around its axis (e.g., an open-paddle impeller), thisforce represents the resistance that a fluid offers to rotationalmotion. Based on that fact, Virgen-Ortz et al. (2012) mea-sured the pectinolytic activity throughout the slope of the

decrement of the on-line torque in a pectin solution whenthe pectinase was added. Although this procedure involvesthe on-line measure of the torque, it is in fact an off-lineprocedure since the analysis is performed after the enzymaticprocess has ended. Thus, the relation between juice yield andthe torque on-line monitoring is investigated here.

In order to effectively model the juice extraction process,96 experiments were carried out (only for dynamical model-ing purposes), at various enzymatic complex concentrations,fruit ripeness stages, and the process temperatures but withno additional water, since the optimization has shown thatthis is not necessary. From these experiments, the maximumjuice yield was identified as a function of ripeness stage andtemperature. Then, for each temperature, ripeness stage, andenzymatic complex concentration, the right-hand side ofEq. 3 can be integrated as follows: ln(x1max x1)=mt. Then,the juice yield rate m was determined by plotting the naturallogarithm of maximum juice yield minus the instant juiceyield (obtained from the off-line monitoring of the process)versus time. The slope of the line is the kinetic rate m. Thus,a specific value of m was obtained for each temperature,enzymatic complex concentration, and ripeness stage.

Next, the equation m E maxE kmE was used to model therelation between the value of m and the enzymatic complexconcentration (E) at each temperature and ripeness stage. Thenonlinear fitting was performed in MatLab (R 2010b). Theobserved deviations when plotting the predictedm values versusthe experimental data are graphically presented in Fig. 4, where itis possible to appreciate the good accuracy of the prediction.

It is important to note that the kinetic rate m decreases at50 C in all of the enzymatic complex concentrations andripeness stages studied. Thus, the data obtained at 50 Cwere not taken into account for the temperature dependencestudies (although this phenomenon is briefly studied at theend of this subsection).

The calculated values of km reveal no change as a functionof the temperature, while the dependence of max on the

0200

400600

0.8

0.85

0.9

0.95

145

50

55

60

65

70

75

enzyme concentration (L/kg)

water/pulp ratio

juic

e yi

eld

(%)

Fig. 3 Graphic shows the nonlinear fitting of the experimental data(blue circles) and the model given by Eq. (2). The model estimatedparameters are a=49.5, b=225.4, c=100, and d=10, with R2=0.9808

0 2 40

1

2

3

4 x 10-3

m

Concentration (L/kg)0 2 4

0

1

2

3

4 x 10-3

m

Concentration (L/kg)0 2 4

0

1

2

3

4 x 10-3

m

Concentration (L/kg)x 102 x 102 x 102

a) b) c)

Fig. 4 Plots show the nonlinear regression plots for kinetic of juiceyield by the enzymatic complex, the lines (. . .), (__), (-+-+), and (- - -)stand for the model prediction at 20, 30, 40, and 50 C, respectively.

The symbols (), (*), (), and () stand for experimental data at 20, 30,40, and 50 C, respectively. Plots (a), (b), and (c) correspond toripeness stages 1, 2, and 3, respectively



temperature was modeled using the following equation

Ae 1T . To perform the identification ofA and , a linear fitting

using the natural logarithm of max versus the inverse oftemperature was performed for each of the three ripenessstages. Figure 5 graphically demonstrates the accuracy of theaforementioned procedure.

Then, the dependence of km, A, and values with respectto the ripeness stages were calculated. To perform the iden-tification of these parameters, a linear fitting using thenatural logarithm of A and versus the inverse of theripeness stages (expressed as 1, 2, and 3) was performed,while a nonlinear correlation was needed for the case of the and ripeness stage relation. Figure 5 graphically demon-strates the accuracy of these results.

Data presented in Table 2 summarizes the identifiedmodel parameters values and their units. It is worth men-tioning that the mathematical model has been formulated insuch a way as to allow the description of the juice produc-tion rate and its relation with the torque over the work rangeof ripeness stages and temperatures.

At this point, twomore correlations were needed in order tofully model the processthe relation xmax(T,M) and y(T,M). Inboth cases, the relations given in Fig. 6 were found.

Since bananas are a climacteric fruit, when harvested at thepreclimacteric matured green stage, the fruit undergoesvarious physicochemical changes in terms of composition,color, texture, aroma, and taste, pertaining to changes inmetabolic rates and biochemical reactions like respiration,ripening, and senescence in the climacteric phase (Mohapatraet al. 2011). In fact, such changes in the physicochemicalproperties are the manifestation of various complex biochem-ical reactions (Zolfaghari et al. 2010). Thus, bananas can havedifferent uses in function of its maturity stage.

In order to correlate the fruits physicochemical charac-teristics (pulp-to-peel ratio, average of the data correspond-ing to the first 10 min of torque values and the Brix degree

measured in the obtained juice) with the visual bananaripeness stage (Fig. 1), a PCA analysis was performed.The scatter plot for the first two principal components ispresented in the Fig. 7, where it is possible to appreciate anoverlap between the groups corresponding to the fruit ripe-ness stages visually classified according to Fig. 1. Similarly,the ANOVA analysis indicates that there are no significantdifferences between the nearest neighbors corresponding tothe mean values of first 10 min of the torque signal of eachripeness stages and processing temperature, except in theripeness extremes; however, it is possible to appreciate aclear gradient of change in the torque signal as the ripenessstages advance.

Thus, to correlate the initial torque measurements withthe ripeness stages, a fuzzy logic approach is proposed thatmakes it possible to correlate the visual criteria used toclassify the bananas with the initial online torque measure-ments. The fuzzy logic algorithm is based on the knowledgeacquired with the previous results. To infer the maturitystage from on-line torque measurements M(X2,0), it is firstnecessary to create the membership functions for the torquemeasurements (input of the fuzzy logic model) and the

Ln

max

Ln

max

Ln

max

1/T 1/T0.03 0.04 0.05 0.03 0.04 0.05 0.03 0.04 0.05

1/T

1 2 3

Ln K

m

Ripeness stage1 2 3

-7

-6.5

-6

-5.5

-6

-5.5

-5

Ln A

Ripeness stage1 2 3

-7

-6.5

-6

-5.5

-30

-20

-10

Ripeness stage

a) b) c)

d) e) f)

-7

-6.5

-6

-5.5

-1.5

-1

-0.5

Fig. 5 The plots (a), (b), and(c) graphically show thecorrelation between the naturallogarithm of the experimentalvalues and inverse oftemperature (C) for eachripeness stage. From left toright, the results for ripenessstages 1, 2, and 3 are shown.Plots (d) and (e) correspond tothe correlation between thenatural logarithm of theexperimental and values and theripeness stage, while the plot (f)corresponds to the second-orderpolynomial used to model therelation between and theripeness stage

Table 2 Identified model parameters and functions

Parameter Value Units

xmax(T,x2,0) 0.14T+1.5M(X2,0)+62.63

y(T,x2,0) 46T1,400M(X2,0)373.33 1/N m

0.008325768

0.3308

B 0.234898 L/kg

0.25541

9.1405 C

10.4698 C

38.422 C



membership functions for the maturity stage (output of thefuzzy logic model) and name them. Each membership func-tion is described in the form of a triplet (a, b, and c) asrepresented in Fig. 2. The triplets corresponding to the inputand output sets as well as the group names are shown inTable 3.

The fuzzy rules were set according to the understandingof the behavior of the system. Since the relation betweentorque and ripeness stage is a single-input single-outputrelation, the following rules were used: If (input is Brown)then (output is 3); If (input is Yellow) then (output is 2); If(input is Green) then (output is 1).

In order to infer the juice yield initial condition fromonline torque and temperature measurements, the member-ship functions for the error (input of the fuzzy logic control-ler) and the gains (output of the fuzzy logic controller) areneeded. The group names are shown in Table 3 and anillustration of the functions is shown in Fig. 2.

Since the relation between torque and ripeness stage is amultiple-input single-output relation, the following ruleswere used: If (input is Brown), then (output is 3); If (inputis Yellow), then (output is 2); If (input is Green), then(output is 1). The rules were stated as follows: If (Torqueis Brown) and (Temperature is 20 C), then (Output is 60); If(Torque is Brown) and (Temperature is 30 C), then (Outputis 60); If (Torque is Brown) and (Temperature is 40 C),

then (Output is 65); If (Torque is Brown) and (Temperatureis 50 C), then (Output is 65); If (Torque is Yellow) and(Temperature is 20 C), then (Output is 50); If (Torque isYellow) and (Temperature is 30 C), then (Output is 55); If(Torque is Yellow) and (Temperature is 40 C), then (Outputis 60); If (Torque is Yellow) and (Temperature is 50 C),then (Output is 60); If (Torque is Green) and (Temperature is20 C), then (Output is 40); If (Torque is Green) and (Tem-perature is 30 C), then (Output is 40); If (Torque is Green)and (Temperature is 40 C), then (Output is 45); If (Torqueis Green) and (Temperature is 50 C), then (Output is 45).

Remarks on Enzyme Activity and Temperature

As shown Fig. 8, the reaction rate decreases at 50 C in allthree stages of maturity. This apparently contradicts theenzymatic complex data sheet, regarding the optimal tem-perature. Therefore, we sought to measure the protein con-centration by Bradford both as banana juice in distilledwater at the same pH 5 (pH featuring banana juice) andpH 3.5, which is recommended as optimal in the technicalsheet. The one-way ANOVA results of the Bradfordperformed to the protein solutions have shown a significantdecrement in the concentration when the solution has thesame pH as the juice and 50 C. This can be due to a lack ofsolubility, and this can explain decrement in the enzyme

2030

4050

12

3

65

70

75

Ripeness stageTemperature (C)

Xm

ax (

T,M

)

2030

4050

12

3

-10000

-5000

0

Ripeness stage

y (T

,M)

Temperature (C)

Fig. 6 From left to right, theplots correspond to the linearcorrelation between theexperimental values obtained atdifferent temperatures andripeness stages

-3 -2 -1 0 1 2 3-2

-1

0

1

2

First Principal Component (71.1%)Sec

ond

Prin

cipa

l Com

pone

nt (

18.2

%)Fig. 7 The plot corresponds to

the scatter plot for the first twoprincipal components of thefruit physicochemicalcharacteristics matrix; green,blue, and brown stand forripeness stages 1, 2, and 3,respectively. The percentage ofthe total variance explained byeach principal component isindicated in brackets



activity. It is known that the tridimensional structure of proteinsis sensitive to minor changes in factors in the environment,including pH, temperature, and medium composition, and suchstructure changes could alter the catalysis activity of the pro-teins (Srivatsa 1996).

Colorimetric Analysis

The color of a product is one of the most importantproperties that influence the consumers response to it.Therefore, one of the objectives of this study was todetermine how the characteristic of the raw material andthe process conditions influence the final color attributesof the banana juice. In order to allow the interpretationthe color results from the L.a.b. analysis, a PCA tech-nique plus a clustering analysis were performed. Theresults appear in Fig. 9.

Cluster analysis groups data objects with similar charac-teristics that were also made then different from objects ofother group. Therefore, the three clusters formed in Fig. 9correspond to the banana juice with similar colorimetric com-ponents. The sensorial panelists were asked to categorize thesamples corresponding to each attribute of all samples. Fromthe PCA score, the cluster analysis, and opinions of thepanelists, it can be concluded that the clusters of green di-amonds obtained in Fig. 9 are the ones with the best visualattributes. This group corresponds to ripeness stage 1 (green)and with no influence of the temperature or the enzymeconcentration; however, it is important to mention that theclosest neighbors were samples of the blue star group corre-sponding to ripeness stage 2 (yellow) and produced at tem-peratures of 40 and 50 C.

The Software Sensor

On-line availability of the juice yield measurement is veryimportant for the control and particularly for the process ofsupervision and fault detection; however, there exists nodevice that provides an on-line juice yield measurement.One way to overcome this problem is to use softwaresensors to estimate missing state variables on-line. As itis described in the Methodology section, a robust observerwas constructed. In order to provide the observer withrobust properties, the following representation of the system(Eqs. 3 and 4) is proposed:

x0 x2 5

x1 m xmaxx1 6

x2 m

Yxmaxx1 7

y0 x0 8where x0 is the dynamical extension that allows us tointegrate the noisy signal in order to recover a filtered

Fig. 8 The plot corresponds to the correlation between the kinetic rateand temperature in the banana juice extraction process. Green squares,blue triangles, and red circles correspond to ripeness stages 1, 2, and 3,with and R2 of 0.885, 0.998, and 0.992, respectively

Table 3 Values of the different membership functions used in thefuzzy logic algorithm that relates the on-line torque measurements tobanana ripeness stage, i.e., M(X2,0), as well as the values of thedifferent membership functions used in the fuzzy logic algorithm thatinfer the initial juice yield condition [x1,0 = x1(0)] from the on-linemeasurements of temperature and torque

Set name a b c Set type

Torque

Brown (0.008,0) (0.0113,1) (0.0145,0) Input

Yellow (0.0135,0) (0.0149,1) (0.0205,0) Input

Green (0.0195,0) (0.024,1) (0.0285,0) Input

Ripeness stage

1 (0.5,0) (1,1) (1.5,0) Output

2 (1.4,0) (2,1) (2.45,0) Output

3 (2.4,0) (3,1) (3.6,0) Output

Temperature

20 C (14,0) (20,1) (26,0) Input

30 C (24,0) (30,1) (36,0) Input

40 C (34,0) (40,1) (46,0) Input

50 C (44,0) (50,1) (56,0) Input

Initial yield

40 (36,0) (40,1) (44,0) Output

45 (41,0) (45,1) (49,0) Output

50 (46,0) (50,1) (54,0) Output

55 (51,0) (55,1) (59,0) Output

60 (56,0) (60,1) (64,0) Output

65 (61,0) (65,1) (69,0) Output

Set type refers to the nature of the set that is an input and/or output tothe fuzzy logic algorithm



signal. Thus, the task becomes the estimation of thisnew state bX i (a standard task for an observer).X AX By CX Where

A 000

0mm=Y

100

24 35; B mm

xmaxxmax=Y

24 35and C 1 0 0 :An asymptotic-type observer of the system is given as

follows:

cX 0 bX 2 k1 y0bX 0 9bX 1 m xmaxbX 1 k2 y0bX 0 10bX 2 mY XmaxbX 1 k3 y0bX 0 11where the gain vector of the observer is given by:

K S1 CT

Si; j Si; ji j1

Each entry of the matrix S is given by the aboveequation, where S is an n n matrix (i and j run from1 to n) and St,j are entries of a symmetric positive

definite matrix that do not depend on . Thus, St,j aresuch that S is a positive solution of the algebraicRiccati equation,

S A 2 I

A 2I

S CTC:

In particular, for our case, the resulting vector K is givenby:

K k1k2k3

24 35 32mm 2 2m Ym2m3 m

" #

It is worth mentioning that we can think of this observeras a slave system that follows the master system, whichis precisely the real experimental system. In addition, S, asfunctional components of the gain vector, guarantee theaccurate estimation of the observer through the convergenceto zero of the error dynamics, i.e., the dynamics of thedifference between the measured state and its correspondingestimated state. One can see that generates an extra degreeof freedom that can be tuned by the user such that theperformance of the software sensor becomes satisfactoryfor him (here, we use = 0.01).

The reason for the filtering effect is that the dynamicextension acts at the level of the observer as an inte-gration of the output of the original system (see the firstequation of the system given by Eqs. 58 and the errorpart in the equations of system given by Eqs. 911).The integration has averaging effects upon the noisymeasured states. More exactly, the difference betweenthe integral of the output of the slave part of systemand the integral of the output of the original system

-3 -2 -1 0 1 2 3-2

-1

0

1

2

First Principal Component (74.2%)Sec

ond

Prin

cipa

l Com

pone

nt (

21.4

%)

G-30-100L

G-50-100L G-50-300L

G-40-100L

G-30-500L

G-40-300L

G-30-300L

G-50-500L

G-20-300L

Y-50-500L

Y-40-500L

Y-40-100L

B-50-100L

Y-50-100L

B-50-300LB-50-500L

B-40-300L

B-40-500LB-30-100L

Y-40-300L

Y-30-100L

B-40-100L

Y-50-300LY-30-300L

Y-30-500L

B-20-500LY-20-500L

Y-20-500LB-20-300L

B-20-100LY-20-300L

B-30-500LY-20-100L

B-30-300L

Fig. 9 Scatter plot for the first two principal components with coloredclusters corresponding to the matrix of juice color (L, a, and b) atdifferent process conditions: temperatures, enzymatic complex concen-tration, and ripening stages (the three generated clusters are marked asred triangles, blue five-pointed stars, and green diamonds). The letters

B, Y, and G stand for brown, yellow, and green, corresponding toripeness stages 1, 2, and 3, respectively. The percentage of the totalvariance explained by each principal component is indicated inbrackets



gives the error, and the observer is planned in such away that the error dynamics go asymptotically to zero,which results in the recovering of both the filtered stateand the unmeasured states.

From Fig. 10, it is possible to appreciate that thealgorithm developed here is able to infer very accuratelythe instant juice yield only based on the online mea-sures of torque and temperature. Since the algorithmdoes not need to be fed with the ripeness stage, it canbe also used to confirm the adequate selection of ba-nana ripeness. Additionally, from Fig. 10, it is possibleto see that the torque measurements by themselves arenot enough to detect with precision the end of theprocess, while the prediction of juice yield could bethe criterion to stop the enzymatic process and continuethe next downstream step. Thus, the software sensordeveloped here effectively rebuilds the unmeasured on-line juice yield and also is able to filter the noisy torquesignal under different experimental situations.

Conclusions

The optimization of the banana juice extraction processshows that the addition of water did not significantly affectthe juice yield, while the enzymatic complex concentrationexhibits a positive impact on the juice yield. As such, theoptimal conditions for juice extraction (i.e., more sustain-able) were 150 L/kg enzyme complex concentration with-out water addition. Moreover, from this study, it can beconcluded that the model here developed could be a valu-able instrument for monitoring and controlling enzymaticbanana juice extraction. Furthermore, enzyme reactors canoperate fed-batch-wise or continuously, and the model is ahelpful tool for optimization. Moreover, the software sensordeveloped here effectively rebuilds the unmeasured on-linejuice yield and also is able to filter the noisy torque signal.In addition, the computational scheme provides a very ap-propriate tool for fast and reliable quality control and can beused to ensure the homogeneity of the final product. The

0 500 1000 1500 2000 2500 3000 3500 4000 45000.01

0.015

0.02

0.025

Time(s)

Tor

que

(Nm

)

0 500 1000 1500 2000 2500 3000 3500 4000 450020

40

60

80

Time(s)

Juic

e Y

ield

(%

)

0 500 1000 1500 2000 2500 3000 3500 4000 45000.01

0.015

0.02

0.025

Time(s)

Torq

ue (

Nm

)

0 500 1000 1500 2000 2500 3000 3500 4000 450020

40

60

80

Time(s)

Juic

e Y

ield

(%

)

0 500 1000 1500 2000 2500 3000 3500 4000 45000.01

0.015

0.02

Time (s)

Tor

que

(Nm

)

0 500 1000 1500 2000 2500 3000 3500 4000 4500

40

60

80

Time (s)

Juic

e Y

ield

(%

)

0 500 1000 1500 2000 2500 3000 3500 4000 45000.01

0.015

0.02

Time (s)

Tor

que

(Nm

)

0 500 1000 1500 2000 2500 3000 3500 4000 450040

60

80

Time (s)

Juic

e Y

ield

(%

)

0 500 1000 1500 2000 2500 3000 3500 4000 45000.01

0.0120.0140.016

Time (s)

Tor

que

(Nm

)

0 500 1000 1500 2000 2500 3000 3500 4000 4500

40

60

80

Time (s)

Juic

e Y

ield

(%

)

0 500 1000 1500 2000 2500 3000 3500 4000 45000.01

0.012

0.014

0.016

Time (s)

Tor

que

(Nm

)

0 500 1000 1500 2000 2500 3000 3500 4000 450040

60

80

Time (s)

Juic

e Y

ield

(%

)

a) b)

c) d)

e) f)

Fig. 10 The plots show the application of the software sensor todifferent experimental situations: in all cases, red solid lines representthe filtered states and juice yield prediction, while blue lines representthe noisy measured torque signal, and blue points represent offlinejuice yield quantification. In all cases, the enzymatic complex was

added to the 1,320 s (22 min). Ripeness stage 1 at 20 C (a) and at30 C (b) both with 100 L of enzyme complex. Ripeness stage 2 at30 C (c) with 500 L of enzyme complex and at 50 C (d) with300 L of enzyme complex. Ripeness stage 3 at 30 C (e) with 300 lof enzyme complex and at 20 C (f) with 300 l of enzyme complex



methodology presented in this paper is general and can beused also in automatic control applications. This supervisionscheme provides instantaneous access to batch records, andprovides audit tracking and traceability. This tool presentsvaluable characteristics like real-time usage, ease of use, noneed for sample preparation, and no sample destruction. Inaddition, PCA proves to be a valuable tool to relate the bestvisual attributes of the banana juice with the maturity fruitripeness stage selection and the operation conditions, show-ing that the juice processing temperature presents positiveeffects on juice color attributes.

Acknowledgments This work was supported by the CONACyT,Mxico (No. 169048) and to PROMEP-SEP by funding the project.The authors would like to thank the anonymous reviewers for theirvaluable comments and suggestions to improve the document.

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Optimization, Modeling, and Online Monitoring of the Enzymatic Extraction of Banana JuiceAbstractIntroductionMethodologyBioreactorBiological MaterialJuice Extraction ProcedureJuice YieldProtein QuantificationColorimetric AnalysisStatistical AnalysisVisual EvaluationOptimization ProcedureFuzzy Logic ApproachEnzymatic Juice Extraction ModelSoftware Sensor Design

Results and DiscussionOptimization ProcedureModeling the Enzymatic Juice ExtractionRemarks on Enzyme Activity and TemperatureColorimetric AnalysisThe Software Sensor

ConclusionsReferences

banana juice (fabt 2013)(1)

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