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•

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APPLICATION OF ARTIFICIAL NEURAL NETWORK ~(ODELING IN

THERJ.\lAL PROCESS CALCULATIONS OF CANNED FOOnS

by

~lAHTAB KHODAVERDI AFAGID

Depamnent of Food Science and Agricultural Chemisrry

~[acdonald Campus of McGil1 University

~[ontreal. Canada

February,2000

A Thesis submined to me Faculty of Graduate Studies and Research in partial fuifillment

of the requirements of the degree of ~[asters of Science

©l\Ilahtab Afaghi, 2000

NationalLJbraryofC8nada

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~12-64381-6

Canadl

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Suggested short title:

.-\1~ modeling of thermal process calcuJaüon methods

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ABSTRACT

The feasibility of using Artificial Neural Network (ANN) models for application in

thermal process calculations was studied. As a preliminary srudy, A1'IN models were

developed based on tabulated data for BalI and Stumbo methods of process calculations.

The ANN rnodels for BalI method related g-value, a measure of process time. and fJlU. a

measure of process lethaliry. Optimizing training data set size, number of hidden layers

and PEs in each hidden layer as weil as leaming parameters is important in obtaining an

efficient k'J1'I model. Development of Al'fN model for Stumbo method followed the same

procedures as the BalI's method. except that jee value (cooling lag factor) was included as

an additional input. The developed ANN models for BalI and Stumbo methods were

validated using a set of processing conditions, resulting in a new set of g and liIU values.

A range of reton temperatures (Rn. initiai temperatures lm. heating rate indexes (fit) ..

heating lag factors Ul:h) and cooling lag factors U,·c) were used ta calculate the related

process rime and process lethality. The developed AJ.'IN models were recalled with the

new set of parameters. The relative prediction errors of the ANN modcls were 1% and 3%

for BalI and Stumbo method .;\l'iN models. respectively. The higher error of A.\IN models

of Sfumbo method could be possibly due to the smaller number of training data and wider

range of parameters in tables of this method than the [ables in Bali rnethod. [n general. the

AJ~N morlels were able [0 simulate the BalI and Stumbo methods of process calculations

reasonably weil.

For a berter understanding of the effect of process parameters on the evaluation of

thermal process. the accuracy of several formula methods (Steele & Board. Bali. Stumbo

and Pham) were studied over a wide range of commercial conditions. A computer

simulation based on flnite difference method of numerical solutions of heat transfer ta

packaged foods in cylindricaI containers was applied ta obtain the time-temperamre data

for designed conditions (retort and initiai temperatures. thennal diffusivity. package sizes

and processing time). ~[oreover't the process time and process lethality from this

simulation were used as the reference values for the purpose of comparison. The accuracy

of rnethods was evaIuated based on the variation of each parameter aver the range of

conditions employed in the study. Retort temperature had the most significant effect on

•

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calculated process deviations. and Stumbo and Pham methods had the best performance.

In a more specifie evaluation~ the comparison of the methods was carried out based on the

can dimensions and g-vaLue. Higher g-values resulted in higher errors and HID near unity

had the highest relative error.

As the final goal of the studYt a multi-Iayer Al.~ model was developed

as an alternative ta thermal process calculations. In developing this model,

the time-temperature data from the finite difference simulation was used ta

compute the process lethality, process time as weIl as heat penetration

parameters: /:, i~fa' f.: and ier' which were needed for training and testing of the

models. The Ai~ preclicted process time or process lethality was compared ta

respective values from finite difference model. The performance of ANN

models \vas aIso compared ta the different formula methods (BalI, Stumbo and

Pham)...o\J.~~ model was able ta predict the process times with a mean average

error of 2 minutes, which was comparable to Pham method. The mean

prediction error of process lethality was 2.74%, which was comparable to

Stumbo method.

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RÉs~1É

L"applicabilité des réseaux d'intelligence artificielle (RIA) aux calculs impliqués

dans les traitements thermiques a été étudiée. Les travaux préliminaires consistaient à

développer des modèles RIA basés sur les données des méthodes de calcul du traitement de

BaIl et Stumbo. Le RIA basé sur la méthode de BalI tentait d~établir la relation entre la

t,'aleur-g• mesurant le temps de traitement.. et filU. mesurant le point d'asepsie du

traitement. L'optimisation de la taille des données d~entraînement du réseau" le nombre de

couches cachées, les noeuds dans chaques ces couches ainsi que les paramètres

d'apprentissage était cruciale pour l'obtention d'un modèle efficace. Pour le RIA basé sur

la méthode de Stumbo. le cheminement était similaire à celui utilisant la méthode de BaIL

mais celle-ci intégrait aussi la facteur de retardement du refroidissement.. jn:' Les modèles

RIA développés pour les méthodes Bali et Stumbo ont été validés en utilisant une série de

valeurs de g et f,/U obtenue en variant la température du milieu (TM)~ la température

initiale ITn. l'index de vitesse d'échauffement (/h). et les facteurs de retardement de

réchauffement (jch) et du refroidissement (jcc). L'erreur relative de prédiction était de 1%

pour la méthode basée sur 1" approche de Bail et 3% pour celle de Stumbo. La valeur

relativement élevée de 1'erreur pour la méthode RIA de Stumbo peut être attribuée au

nombre restreint de données d'tentrainement par rapport au nombre de paramètre. En

général.. les modèles RIA ont simulé de façon acceptable les méthodes de BalI et Stumbo

pour le calcul du traitement.

Pour mieux comprendre reffet des paramètres de traitement sur l'évaluation du

processus thennique't rexactitude de plusieurs formules (Steele & Board. BalI. Stumbo and

Pham) a été étudiée pour une variété de conditions industriellement utilisées. Une

simulation basée sur la méthode de différence finie à solution numérique du transfert de

chaleur dans un produit emballé dans un contenant cylindrique a été appliquée pour obtenir

les données de temps et de température reliées aux conditions d'étude sélectionnées (la

température du milieu. la température initiale.. diffusion thermique" taille de r emballage, et

longueur du traitement). De plus, la longueur de traitement et le point d~asepsie du

traitement ainsi prédits ont fait l'objet de comparaison pour évaluer ['effet de chaque

paramètre. La. température du milieu affectait de façon significative ['erreur sur la

iü

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prédiction. Les méthodes de Stumbo et Pham ont produit les meilleurs résultats. Une étude

plus poussée démontre qu·une augmentation de la valeur-g entraîne une erreur plus élevée..

alors qu'un rapprochement du paramètre H/D.. relié à la dimension de remballage. à runité

se traduit par une erreur relative supérieure.

Pour but final de cette étude.. un modèle RIA rnulti--couches a été développé. Cette

alternative aux calculs du processus thennique. utilise les données de temps et de

températures obtenues par la simulation basée sur la méthode de différence tïoie pour

prédire I~ point d"asepsie du traitement, la longueur de traitement ainsi que les

paramètres de pénétrations de chaleurs: {,., j ..h1 t: and j~. Ces valeurs sont

nécessaires pour entraîner et tester les modèles. Les valeurs prédites par les

RIA ont été comparées aux valeurs obtenues par les calculs basés sur la

différence finie ainsi qutun nombre de formules acceptées (BalI, Stumbo and

Pham). Les modèles RIA développés ont pu prédire le temps de traitement

avec une erreur moyenne de 2 mins, une valeur comparable à celle obtenue

avec la méthode de Pham. L'erreur moyenne de prédiction pour le point d"asepsie

du traitement était de 2.74%, valeur comparable à l'approche Stumbo.

iv

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ACKNO~DG&~NTS

l wouId like to extend my sincere appreciation and thanks to my thesis supervisor~

Dr. Hosahalli Ramaswamy for his guidance, valuable advice, encouragemenc keen interest

and support throughout the course of the study.

Also l aIse thank Dr. L Alli~ Chairman of the Departrnent of Food Science and

Agricultural Chernistrv and Dr. F.R.van de Voort for their mat advice at the stan of the..... ...study. ~lany thanks are also extended to Dr. S.O. Prasher. research committee member. for

his helpful suggestions on sorne aspects of the projece

r rhank Dr. S. Sreekanth for his very vaiuable help and advice in starting the projece

Dr...~Iain LeBail's rechnical assistance for modification of the flnite difference program of

Dr. S. Sablani (Ph.D. Thesis. 1995) for adoption to this work is gratefully acknowledged.

Nlany thanks to Dr. Farhad Salehi for his precious insight and guidance throughout the

study. .-\Iso. [ would Iike to thank ~ls. Aline Dimitri for the French translation of the

abstrJ,ct.

~ly sincere thanks to ail my colleagues in the Food Science Department. especially

the Food Processing group: Dr. Tatiana Koutchma. Dr. Reza Zareifard. Dr. Nlichelle

~[arcotte. Dr. Dina ~[ussa. Dr. Sasithorn Tajchakavit.. Nls. Sarmista Basale. ~Ir. PrJmod

Pandey. ~[s. Farideh Nourian. Mr. Harish Krishnamurthy. Mr. Curien Chen. ~Is. Lawrende

Chiu. ~lr. Olivier Turpin and ~Is. Nada Houjaij.

Above ail. 1 thank my wonderful parents. my dearest brothers. Keyhan and Soheyl

for their encouragement. love and suppon•

v

• a

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XY

Yo

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.:l

•

NOMENCLATURE

Significant dimension. the radius of cylinder (m)

Decimai reduction time (min)

Cooling rate index (min)

Heating rate index (min)

Process lethality (min)

Temperature difference between product and heating medium (reton) at end ofheating (IlC)

Vertical position in cylinder (m)

Fluid heut transfer coefficient (W/m!.K)

lnitial Temperature (oC)

Cooling lag factor

Heating lag factor

Bessel function of arder zero

Cylinder thermal diffusivity (W/m.K)

Lethal rate: Thickness or half thickness of a slab depending on il being heated orcooled from one side or bath sides. respectively

~umber of records

Radial position in cylinder (m)

Reton Temperarure (Ile)

Temperature (oC)

Time (min)

Cooling time (min)

Cooling water temperature (C)

Hearing rime (min)

Product temperarure at the end of heating (oC)

Reference temperature (oC)

Dimensionless temperature ratio =<.T-RT)/(IT-TR)

The equivalent of all lethal heut received by sorne designed point in the containerduring process at the reton temperature (min)

Distance from the coldest plane of a slab

.~'"N predicted valueDesired value

Temperature sensitivity indicator (CO)

Step size (used with space or time)

vi

• Subscripts

1.2 Refer to two levels with respect to temperature

Initial condition. space index

IT Initial condition of product

J Spaceindexref Reference

RT (Retort) heating medium

Greek symbols

a Thermal diffusivity (m~/s)

~ Roct of the characteristic equation (4.3)

.., Roct of characteristic equation (4.4)

Dimension Jess numbers

Bi Biot number

Fa Fourier number

AbbreviatioDs

•

Ai'INCERFI1R

LOS~[AE

~[ll\t[O

~lL\fN

~lRE

~

~~

OCR

PCA

PERMS

Artitïcial neural network

Carbon dioxide evolution rate

Fourier transform infrared

Linear discriminate analysis~[ean absolute error

~[ultiple input and multiple output~lulùple layer neural networkMean relative error

Near infra red

Nitrogen utilization rate

Oxygen consumption ratePrinciple component analysisProcessing element

Root mean square

vii

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TABLE OF CONTENTS

ABSTRACT

RÉsc~lÉ iii

AC~'IOWLEDGMENTS v

NOME1\lCLATURE vi

LIST OF TABLES x

LIST OF FIGURES xii

CONNECTIN'G STAThvŒ1'ITS xiv

CONTRIBUTION OF AUTHORS xv

CHAPTER 1 L.'ITRODUCTION 1

CHAPTER 2 LITERATURE REVIEW 5

Principles of thermal processing 5

Kinetics of microbial destruction 6

Thermal process calculations 9

Thermal process calculation methocis [0

General method [0

Improved General method 11

Formula methods 12

Barrs method 12

Stumbo·s method 17

Hayakawa's method 17

Steele and Board's method 18

Pham's method 18

Evaluation of Formula methods 19

:'Iumericai models of thermal process calculations 21

Anitïcial neural networks 24

Development of an Al'lN modeI 26

Applications of ANN in Food Science and l\griculture 29

CHAPTER 3 ANN SIMlJLAnON OF HALL AND STUMBO FO~IULA

;\,IETHODS OF THERMAL PROCESS CALCULATIONS 3S

vii

ABSTRAeT 35• INTRODUCTION 36

Anificial neural network models 37

~[ATERIAL AND METHOOS 39

ANN modeling of BalI and Stumbo methods 39

Development of AJ.'JN models 39

BalI model 39

Stumbo model 41

Validating the ANN models 42

RESLLTS Al~1) DISCUSSION 43

ANN based BalI model 43

Nlodel development and oprimization 4-3

~[odel verification 4-9

AJ.~~ based Stumbo model 49

CONCLUSIONS 54

CHAPTER 4 COl\IPARISON OF FODIlTLA ~lETHODS OF THERl\-lAL

PROCESS CALCULATIONS FOR PACKAGED FOOOS IN

CYLINDRICAL CONTAINERS 55

ABSTR;\CT 55

INTRODUCTION 56

Brier review of formula methods 57Ball·s method 57Srumbo.5 method 58

Steele and Board's method 58

Pham's method 58~tATERIAL AND ~ŒTHODS 59

Finite difference program 59The basis of finite difference models 59

Overall accuracy evaluation of the fonnula methods 64-

Evaluation of fonnula methods under specifie conditions 65

RESULTS Al'ID DISCUSSIONS 65

Optimization of fmite difference model 65

OveraiI evaluation of formula methods 67

• Specifie evaluation of fonnula methods 73

viü

• CONCLUSIONS 79

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CH..\PTER 5 ARTIFICIAL NEURAL NETWORK ~IODELS AS ALTERNATIVES

TO THE~IALPROCESS CALCULATION ~ŒTHODS 80

ABSTRACT 80

~TRODUCTION 81

~[ATER.L\L Al'fD ~ŒTHODS 82

Data generation 82

Al"~ model development 84

Optimization of Al'IN models 86

Comparison of ANN models with fonnula methods 87

RESCLTS AND DISCUSSION 87

~'IN models optimization 87

Performance of the Al'IN models 89

Comparison of A1~N models 92

CONCLUSIONS 99

CHAPTER 6 GENER.-\L CONCLUSIONS 100

REFERENCES 102

ix

• UST OF TABLES

Table 3.1 Combinations of training and testing data for network optimization 41

Table 3.! Range of network architecture and learning parameters used in thestudy 41

Table 3.3 Range of parameters for validating k\fN based BalI and Stumbomodels 43

Table 3A Effeet of PEs and hidden layer(s) on the performance of .-\1'fNbased BalI models 46

Table 3.5 Effeet of epoch size on prediction ability: AJ.'lN based BalI models 46

Table 3.6 Effect of momentum on prediction ability of AJ.'m based BaliModels 47

Table 3.7 Optimallevels of architectural parameters for .-\l~~ based Bali andStumbo models 47

Table 3.8 Error parameters for AZ~"N based BalI and Stumbo models 49

Table 4.1 Errors in process rime calculation influenced by processingconditions and thennal diffusivity of product 69

Table 4.2 Errors in process lethality calculation intluenced by processingconditions and thennal diffusivity of product 69

Table -t3 ~Ieans and Standard Deviations (SD) of relative errors in processtime caIculations for selected process calculation methods 71

Table -l.A ~leans and Standard Deviations (SD) of relative crrors in process[ethality calculations for selected process calculation methods 72

Table 4.5 Maximum. Nlinimum. ~[ean and Standard Deviations of errors fordifferen t methods 72

Table 5.1 Range of parameters used in finite difference program 83

Table 5.2 Combinations of training and testing data for network optimization 86

Table 5.3 Range of network architecture and Iearning parameters used in thestudy 87

• Table 5A Effect of momentum. and epoch size on the perfonnance of ModelAandB 89

Table 5.5 Error parameters for perfonnance and verification of Al~'N models• AandB 92

Table 5.6 ~[eans and Standard Deviations (SO) of relative errors in processtime calculations for selected process calculation methods 95

Table 5.7 ~[eans and Standard Deviations (SD) of relative errors in processlethality calculations for selected process calculation methods 96

Table 5.8 Range. mean and standard deviation of errors for aIl thecombination of parameters 96

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• UST OF FIGURES

Figure 2.1 Typical semi logarithmie heating and cooling curves 13

Figure 2.1 Grid format for temperature calculation using a numerieal method 23

Figure :!.3 Basic structure of a biologicaJ neuran 25

Figure lA Typieal diagram of Al'lN model 25

Figure .!.5 Diagram of a processing element and related calculations 27

Figure 3.1 Learning curve for ANN model A (prediction log g) .f5

Figure 3.1 Learning curve for ANN model B (prediction f,/U) 45

Figure 3.3 Comparison of .-\l'IN predicted vaIues and Bali table parametersrespect ta input variable 4-8

Figure 3A Validation of ...u'IN models of BalI method 50

Figure 3.5 Comparison of A.N'N predicted values and Stumbo table parametersrespect to input variable 52

Figure 3.6 Validation of AN~ models of Srumbo's method 53

Figure .f.l Optimization of tïnite difference model for al number of nodes ineach a:<is and b) time step 66

Figure ·tl Validation of tïnite difference model against the analvtical solution 68~ -

Figure .f.3 Errors in process time caIculations for different g-vaIues (a: g=O.05C. b: 2=1 CO: c: g=5 Co: d: 2:=10 CO: e: 2=15 CO) 74- . ~ ~

Figure .fA Errors in process lethality calculations for different g-values (a:g=O.OS CO. b: g=l CO; c: g=5 C: d: g=IO CO: e: g=IS c; 75

Figure -t-.5 Errors for process IethaIity calculations with respect to different g-values (a: Steele & Board's methocL b: Ball's method; c: Stumbo'smethod) 77

Figure ..t6 Errors for process time calcuIations with respect to different g-values (a: Steele & Boarcrs metho<L b: Bairs method: c: Smmbo'smethod: d: Pham's method) 78

• Figure 5.1 Arrangement and procedure of developing AJ.'lN models 85

xii

Figure 5.2 Learning curve for ANN model A 88• Figure 5.3 Learning curve for Al'fN modeI B 88

Figure 5A- Effect of PEs and hidden layers on the performance of model AandB 90

Figure 5.5 Performance of AJ.'lN models A and B with respect to predictedoutput 91

Figure 5.6 Performance of A1';~ models A and B in process time and processlethality prediction 93

Figure 5.7 Performance of Ai'1N model in process time calculation incomparison with the other selected Formula methods 97

Figure 5.S Performance of A:.'lN model in process lethality calculation incomparison with the other selected Formula methods 98

•XÏü

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CONNECTING STATEl\'1EJ.'ITS

This thesis research is divided into three parts. The first pan is a feasibility study

demonstrating the potential of ANN modeling in simulating two simple (and most popular)

process ca1culation methods (BalI and Stumbo methods). In this pan.. input for the Al'IN

models were obtained from tables developed by Bail and Stumbo. which large1y simplifies

the situation for generating input data. The development of such simplified AJ.\fN models is

described in Chapter 3. and tS part of the manuscript number 4 listed on next page.

The accuracy of existing fonnula methods against the data predicted by a fioite difference

computer model under a range of commercial operating conditions were evaluated in the

next chapter as a prelude ta developing a more general Al'IN model. which is the final

objective of the study. This aspect is detailed in Chapter -+ demonstrating the discrepancy

of sorne process calculation methods in predicting accurate values under certain

circumstances. This forros the basis for another publication (number St

The tinal Chapter 5 i5 the principal fceus of this srudy. However. the basis for the

developed final ~~'N models came from Chapter 3 (for optimizing the fu~N performance)

and Chapter -+ (. for generating the input data using the finite difference mode[). The

different methods are ultimarely compared in Chapter 5. demonstrating the utility of A1\fN

models. This aspect fonns the basis of the final manuscript (number 6). The details of the

manuscripts/presentations arising From the thesis are highlighted in the next section with an

explanation to the raIe of co-authors.

xiv

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CONTRIBUTION OF AL'THORS

The following papers have been prepared for different presentations and/or publications:

1. Afaghi. ~1. and Ramaswarny. R.S. 1997. A neural network approach for thermalprocess ca1cularions. Presented at rhe CIFST AnnuaI Conference. Radisson Hotel.~[ontreal. QC. September 22-25.

2. Afaghi. ~[ and Ramaswamy. R.S. 1999. Artiticial neural network models asalternatives to formula methods of thennal process calculations. Presenred at theCIFST AnnuaI Conference. Grand Okanagan Horel. Kelowna. BC. June 6-9.

3. Afaghi. NI. and Ramaswamy. H.S. 1999. Comparison of formula methods of thermalprocess calculations for foocis in cylindrical containers. Presented at the Annual~{eeting of the [nstirute of Food Technologists (IFT). ~[CCormick Place South.Chicago. IL USA. July 24-28.

-1.. Afaghi. yI. and Ramaswamy. H.S. 1999. A1\fN simulation of Bail and Srumbo formulamethods of thermal process calculations. (Submitted. Food Research International).

5. Afaghi. ~l. and Ramaswamy. H.S. 1999. Comparison of formula methods of thermalprocess calculations for cylindrical packaged foods. 1To be submittedt

6. Afaghi. yI. Ramaswamy. H.S. 1999. Artificial neural network models as alternative ofthermal process calculation methods. <To be submitted)

[n the above papers. ail the experimental (modeling) work. analysis of results and

preparation of manuscripts were done by the candidate (~1. Afaghi). under the supervision

of Dr. H.S. Ramaswamy.

xv

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CHAPTERI

LNTRODUCTION

Thermal processing is one of the most imponant methods of food preservation of

the twenrierh century. Since the innovation of this method by Nicholos Appert in i810.

thennal processing of packaged fooels has been improved extensively in ail related aspects

of the process. Design of an effective process requires a sound knowledge of the

destruction kinetics of the concemed microorganism and temperarure history of the

product. Process calculation rnethods are commonly designed to compute the required

processing time for a target sterilization value or to ~valuate the sterilization value for a

given process. Accurate process caIculation methods are required with respect to bath

safety and quaIity consideration of product.

Bigelow et al. (1920) established the first graphical procedure of thermal process

determination. referred as General method. Bali (1923) introduced a mathematical method.

known as the tïrst Formula method. Bail's method has broadly served the food industry

despite sorne of its sweeping assumptions. which results in sorne inaccuracies. BalI' s

fonnula method is based on the equation for the straight-line portion of tlie semi­

logarithmic hearing curve at the cao center. Ta calculate the process time for defined

process lethality or to calculate the lethality of a given process. Bali developed sorne tables

and graphs. Srumbo' s method ( 1966). developed as the revised version of Bali' s method.

result~ in more accurate process calculations (Smith and Tung. 198:2). However. the

procedures of process calculation in these two methods are quite sirnilar and the accuracy

of each rnethod depends on the accuracy of the evaluated parameters and addition of

correct cooling lethality to process calculation through the tables and graphs. The

application of these tables and graphs can be time consuming and may become a source of

error in process calculations. In addition ta these [wo methods.. several other methods e:dst

in literarure as alternatives to the existing process calculation methods developed through

modifying procedures (Hayakawa. 1970: Pham. 1987. 1990: Vinters. 1975: Steele and

Board. 19ï9a.b).

•

•

Smith and Tung (982) evaluated the accuracy of sorne fonnula methods as

compared to a numericaI method for a range of processing conditions and can sizes. and

poinœd out differences in their performances. Studies have been aIsa carried out [0 check

the accuracy of fannula methods in relation to a computer simulation of thermal processing

using finite difference numericaI solutions for thin profile packaged foods tGhazala el aL.

(990). Stoforos el aL (1997) reviewed in detail the basis of different methods of process

calculations and the accuracy of these methods as compared to a tinite difference

simulation of heut transfer for one set of processing conditions and can size.

Advent of computers and ease of programming has provided the potentia!

application of mathematical roodels in process design.. validation. controL and optimization

(Hayakawa. 1970. 1978: ~lanson et al.. 1970: Stumbo. 1973: Teixeira et aL. 1969a. b:

Teixeira.. 1978). These models are mainly used in temperature protile prediction of product

undergoing thermal processes. as they provide a more versatile alternative to rime

consummg and expensive heat penetration tests. [n addition to time-temperarure

prediction. with these roodels the retort temperarure need not be held constant and cao be

vmed in any prescribed manner throughout the process. The rapid evaluation of an

unscheduled process deviation is another important application of these models tHeldman

and Lund. (992).

The application of anitïcial neural network t.fu~') methods has been growing in

the several :ueas of food technology and agriculture. fu'IN is a powerfUl technique for

correlating data using a number of processing elements. Lsing the .-\.'fN technique. the

computer leams to make intelligent decisions using known input-output data and adjusting

sorne internal parameters of the network through repetitive introduction of known

examples. The strength of ANNs is in their ability to handle complex nonlinear

relationships with ease and without any prior knowledge of their relationships. The Al'IN

has polentia! advantages of adaptation and learning ability. fault tolerance of noisy or

incomplete data. and high computationaI speed. Eerikainen et al. (1993) introduced the

early application of neural networks in food related subjects. .~'lN has shown a promising

application in extrusion process control (Eerikainen et al.. 1994), As an alternative ta

statistical models in data analysis of FfIR. GS-MS and sensory evaluation. AJ.'\iN models

had a higher performance (Bochereau et al.~ 1992: Tomlins and Gay. 1994: Vallejo-

2

•

•

Cordoba et al.. 1995). Sablani et al. (1995) investigated the potentiai of A1'lN models for

prediction of optimal sterilization temperatures.

One typical type of Ai.'lN structure in known as back-propagation networks. which

has shown promising results in prediction modeling and classification (Sreekanth el aL.,

1998~ Lacroix. et al.. 1997: Bochereau et al., 1992: Freeman. 1993). A back-propagation

network consists of a sequence of layers with full connection between the layers. Three

required layers in these networks are input layer.. hidden layer(s) and output layer. Input

layer transfers the input information to the network to be processed by hidden layer(s). The

processed information is passed to an external source through the output layer. During

training. the internai parameters are adjusted to produce the possible c10sest k\fN output ta

the desired output. The adequacy of a trained network depends on the nature and size of

the training data set as well as selecting the optimal internaI parameters. In other words.

the performance of the ANN model greatly depends on the training data with respect ta

bath quantity and quality (Swingler. 1996). Once trained. the AJ.\fN model presents rapid

answers to any input variable in the domain of training data sel. If the conditions change in

such a way that deprives perfonnance of the network. the Al.'IN model can be trained

further under the new conditions ta correct its performance (Baughman and Liu. (995).

Considering th~se abilities. AJ.'iN models render themselves as a possible alternative ta

mathematicaI models and regression techniques (Ni and Gunasekaran. 1998~ Tomilins and

Gay. 1994),

During the sterilization process. there are severa! parameters. which affect the

accuracy and efficiency of heating process evaIuation. The most relevant factors in

evaluation of a heat treatrnent are type and heat resistance of microorganisms. pH of food

product. heating conditions. thenno-physical properties of food and package size and type

1Valenras et al.. (991). An accurate thennaI process caIculation model takes into account

the signitïcance of producing a high quality product while ensuring the minimum required

qualiry.

The following were the objectives of this research:

3

• 1.

1

3.

Development of A1'\lN models based on input data from Bali and Stumbo's tables as

J. preliminary study to evaluate the feasibility of ANN models in thermal process

calculations~

Evaluating the accuracy of different formula methods over a wide range of

processing condiùons and can sizes against a reference computer simulaüon model

based on numerical solution of partial differential equations related to heur

conduction equa[ion involving finite cylinders.

Development of an M'lN model using the data obtained from the finite difference

simulation under a wide range of conditions and comparison of the performance of

A.\j~ model with traditional fonnula methods.

•

Successful thermal processing encompasses the assurance of safety and high quality

ùf the food products. Several methods developed to establish thermal processes have been

improved with respect to innovation and application of computers in food technology. [n

this study. ~rtitïcial neural network technique is being evaluated [0 develop a possible more

versatile thermal process calculation method. Due ta the fact that A~'N technique has the

ability in modeling non-linear systems. it is hoped that ~'IN based thermal process

calculation model will he capable of pursuing me objectives of an nccurate thermal process

caiculatÎon model.

4

•

•

CHAPTER2

LITERATURE REVIEW

Principles of thermal processing

Thermal pracessing of packaged foocis basically involves heating of food products

for a selected rime at a selected temperature ta destroy pachagenic microorganisms

endangering public health as weil as thase microorganisms and enzymes that deteriarate

the food during storage. For the first time. Nicolas Appen. in 1810. introduced the concept

of in-container thennal processes. Extensive emphasis has been given ta improvements in

thermal processing. as this is one of the mosr important methods of food preservation.

Although the heur labile nature of microorganisms is the basis of thennally preservation of

food products. yet the same but undesirable effect can destroy part of nutrients and quality

factors. Therefore. an efficient thermal processing requires to be accurarely designed to

ensure bath the safery and quality of food products.

An effective thermal processing is defined based on the detïnition of commercial

sterilization. Commercial sterilization of food producr inhibits the growth of both

microorganisms and their spores under normaI storage conditions in the container. A

commerciaJly sterile food product may contain viable spores. such as thennophilic spores.

which will not develop under normal storage conditions. The US Food and Drug

Administr.ltion in 1977 defined the concept of ftminimal thermal process" as "the

application of heat to food. either before or after sealing in a hermetically seaIed container.

for a period of rime and at a temperature.. scientifically detennined to be adequate ro ensure

the destruction of microorganisms of public health concem."

Severa! important factors determine the extent of thermal processing. such as:

1) Type and heat resistance of the target microorganism.. spore or enzyme

2) pH of food product

3) Heating conditions

-1-) ThermophysicaI properties of food product and container shape and size

5) Storage conditions following the process

5

•

•

The primary step in thennal process establishment. which is defining and selecting

the target microorganism or enzyme~ is directly related to food product conditions.

Temperature and oxygen are important factors in optimum growth of microorganisms.

Based on appropriate remperature for growth, microorganisms are c1assitied into

psychrophiles with rapid growth between 0-5°C, mesophiles with optimum growth between

5~OL.lC and thermophiles with optimum growth at temperatures higher than 40LlC (Rose,

1965). With respect to oxygen requirement for growth. microorganisms are classified as

obligate aerobes'O facultative anaerobes and obligate anaerabes. Packaged foods under

vacuum in sealed containers provide low levels of oxygen. therefore. these conditions do

not support the growth of obligate aerobes.. and further the spores of obligate aerabes are

(~ss hear resistant to heat as compared to the spores of facultative and obligate anaerobes.

The growth and activity of anaerobic microorganisms are highly pH dependent. From a

thermal processing standpoint'O foods are divided into three graups based on pH:

1) High acid foods (pH<3.7)

2) Acid or medium acid foods (3.7<pH<4.5)

3) Low acid foocis (pH>4.5)

[n thennaI processing a special attention is devoted ta CLostridùlIn botulinum which

is a highly heat-resistant.. spore-forming.. anaerobic pathogen that produces botulism toxin.

Clostridill1ll botulinum does not generaIly grow and produce toxin at pH below 4.6.

Therefore.. in thennaI processing. a. pH of 4.5 is considered as dividing line between the

acid and low acid food products. Molds. yeasts and bacteria. which tolerate high acidic

conditions are targeted in thermal processing of high-acid food praducts. Bacillus

coagulase and Saccharomyces cerevisiae are important in high-acid foods.

~licroorganisms such as Bacillus Stearothermphilus'O Bacillus thermoacidurans and

Clostridium thermodaccolyticum are more heat resistant than C. bontlinum. but they are

mostly thennophilic in nature and in case of storage of cans at temperatures below 30°C..

they are not of much concem.

Kinetics of microbial destruction

EvaIuating the thermal resistance of target microorganisms is required in thermal

processing design. Thermal destruction of microorganisrns generally fol1ows a first-order

6

• reaction indicating a logarithmic order of death. Therefore. if the Iogarithm of number of

microorganisms surviving a given heat treatment at a partÏCular temperature is plotted

a!!ainst heating tirne. it will result in a straieht line. called the survivor curve. The'-' .... .....

microbiai destruction rate is generally detïned in terms of a decimal reduction time (D-

value), which is heating time that results in 90% destruction of the existing microbial

population. This is concept is represenred rnathematically as:

where:

D[logtl) -log(b)]

a: number of survivors at time [t

b: number of survivors at rime t1

[:-[1: heating rime

(2.1 )

Detïn~d as such.. the D-value represents the negative reciprocal slope of the survivor curve.

Thennal death time (TDn is another approach reflecting the relative resistance of bacteria

to different remperatures. These data are obtained by subjecting a micrabial population to

a series of hear treatment at a given temperature and testing for survivors. TDT is the

measurement with respect to an initial microbial laad and it simply represents a certain

multiple of D-vaLues. The temperature sensitivity of D-value is detïned by the term :­

ralue. which is temperature range resulting in ten-fold change in D-value:

where:

... -[log(Dt ) -log(Dz)J

D,: D-value at temperature T,

D~: D-value at temperature Tz

(2.2)

•AIso the z-value cao be obrained from IDTcurve using TDT[ and TDTz instead of Dl and

Dl-values. Thus. z represents the negative reciprocaI sIope of D value or TDTcurve.

7

• In order to compare the relative sterilization capacities of thermal processes~ the

terro lethality (F-value) is introduced. The F-value is detïned as the nurnber of minutes

required at a specifie temperature to destroy a specitied number of microorganisms with a

specifie :-vaLue. For convenience a unit of Iethality is detined as equivalent hearing of one

minute at a reference temperature of 121oC (250~ for the steriliza[Îon process. Thus. the

F-vallie represents a certain multiple or fraction of D-value depending on the type of

microorganism. ~Iathematicai equivalent of this definition is:

where:

'T,-Tl

F=nD=F.lO ="

T" Reference temperature

E,: Lethality at Tt)

(1.3)

Lethal rate is defined for comparing different processes in terms of achieved lethality and it

is considered to be the heating time at the reference temperature relative to an equivalent

heating of one minute at the given temperature:

T-Trr;

L=LO : (2.4)

[n a real process in which the food product undergoes a time-ternperamre protïle. the lethal

rate is integrated over the processing rime to result in an ovenul process lethality (also

defined by F,.):

t

Fil =fL.dtrj

(2.5)

•[u terms of food product safeey. assurance of a minimum lethality at the thermal center of

food product is required. However it is desirable ta minimize the overall destruction of

quality factors.

8

• Thermal process calculations

The purpose of thermal process calculations is to determine an appropriate process

time under specified heating conditions required ta achieve a given process lethality or

~stirnating the lethality for a given process. Thermal process deterrnination through a

physical-mathematical approach requires the basic information of thermal destruction

kinetics of microorganisms and quality factors conjoined with time-temperature data of

product to integrate the lethal effects of thermal processing.

Therefore. an efficient process design requires sound information on the heat

penetration data and their characteristics. Heat penetration data. are function of severa!

factors and different combinations of factors can result in same process lethality. These

factors can he summarized as follows:

1) ~[ethod of heating process (eg. still process vs. agitated process)

2) Type of heating medium (steam. water)

3) Heating conditions (reton ternperature. initial temperature of productl

4) Product type (solid. liquid. particu[ate)

5) Container type. shape and size

Obtaining accurate data regarding the heating and/or cooling of a food product in

container is important for accurate detennination of time and temperature with respect to

sterilization of a given product. However.. it is impractical to obtain hear penetration

protïles for the whole range of conditions. Accordingly.. thermal process calculation

procedures are developed with ability of time-temperature prediction with respect to sorne

experimentally deterrnined parameters. Obviously. the applicability and restrictions of each

method are defined by the assumptions taken inta account to obtain temperature prediction

mode1.

Following each heating phase of thermal processing operation is a cooling phase to

control and terminate the lethal effect of thermal processing. In order to account the

cooling effect. the lethality equation (2.5) can he rearranged as folIow:

•, :

F = J- 10 •T - T~ I!:: dt"

o

t.

+ J10 1T - T~ 1::: deo

(2.6)

9

•

•

where:

tg: total heating time

dt: small time interval

le: total cooling time

The duration of cooling process longer than bringing the product temperature to a

level enough to stop the lethality is not important. However. the achieved lethality during

the initial cooling phase is accounted in process calculation methods. For a known time­

temperature profile the solution of equation (2.6) will result in a relationship between Fr,

(process lethality) and Cr: (process time).

Thermal process calculatioD methods

The methods of process calculations are divided into two broad groups: General

methods and Formula methods. General methods apply the real time-temperamre data

l'rom test containers to integrate graphically or numerically their lethal effects over the

process. Therefore. this group of methods IS the most accurate rnethod for given

experimented conditions. Conversely. Formula methods apply the time-temperature data in

the forro of parameters. with use of mathematical procedures. to integrate the lethaI effects.

Process calculation methods have been extensively reviewed and evaluated (Hayakawa.

1977. 1978: ~[erson et al.. 1978: Stumbo and Langley.. 1966: Smith and Tung. 1982:

Ghazala et al.. 1990: Larkin and Berry. 1991: Stoforos. (997).

GeneraI ~(ethod

For the first time. Bigelow et al. (1920) introduced the Original General method.

which is the fundamental of ail other process calculation methods. General method is the

most accurate method of process evaluation as it relies on discrete. experimentaI or

numerical time-temperature data to determine the sterilization value of the process. Once

the [Îrne-temperature is known. the sterilization value is derermined by graphical or

numerical integrating of equation (2.5). OveralI.. Generai method has the advantage of

versatility in applicabiliry for any kind of heat transfer. However. the application Îs

resrricted to the condition under which the time-temperature data is obtained. and any

10

• change in either processing conditions (retort temperature. initial temperature)~ product or

package size requires a related temperature profile.

The original General method is based on lethal rate as the reciprocal of TDT value.

The area under the lethal rate curve vs. heating time will result in a sterilization value of the

thermal process. In arder to detennine the process sterilization value (Fil) \Vith General

rnethod. different works has been carried out, both in graphical and numerical Integration

to make chis method less [aborious. Schultz and Oison (1940) developed lethaI rate papers

and dimensionless temperature differences in faons of TRrTffRrTrr to account for

variation in reton temperature and initial temperature of product independent of

experimenrally obtained data. E;(tended works have been carried out for different z-values

and procc:ssing temperatures (Cass.. 1947: Hayakawa. [973: Leonhardt. 1978). Simpson's

mie. [rapezoidal mie and Gaussian Integration are improved techniques for numerical

imegration. Patashink l L953) used a trapezoidal mie by considering sorne assumptions in

this tt:chnique. Hayakawa (1968) developed a method using Gaussian Integration fonnula.

involving a remplace, which couId be used with the graphical method.

The limitation of General method is in determining the process lime for rarger

process lethality. For this purpose a trial and error method is proposed. Also it is tedious

ta consider a leth'al rate curve during cooling which depends on the heating rime. Often a

singlt: shape of cooling curve is imposed irrespective of the heating curve. Obviously. this

cannat be right for aIl situations as the lethal rate is related to temperarure difference of the

product and heating medium at the end of heating (g-va[lle) and this assumption applies to

onl y to cases with g-value close ta zero.

Improved General ~(ethod

BaIl (1913) introduced improved General method with a graphical approach for

sterilization value determination. A hypothetical thermal destruction curve was

constructed parallel ta thennal death time curve. resulting in F-value equal to 1 min at

1:!1.1 ·Je (250~. This modification permined the comparison of different processes in

terms of target lethality. According to this method the Iethal rate could he determined as

follow:

•L =lO,r-l!l.ll/:

(2.7)

il

•

•

The area under the curve. resulting from ploning L vs. heating time. represents the

equivalent minutes at 121.I lle. The urea under the curve can be determined by counting

the number of squares. using a planimeter or by approximating to standard shapes. AIso

for this method. process time determination for target process lethality requires a trial and

error technique.

Formula ~Iethods

The procedure that Bali (1923) applied in thermal process calculation was the basis

for a new set of methods termed ··Formula. methods·... Process determination using Fonnula

methods is considerably faster due to applying heat penetration data in form of heating and

cooling rate indexes (fil andJ~) and lag factors (jc:h andjtr). Formula method determines the

process rime for a pre-selected process lethality or alternatively. process lethality of a given

process. H~nce using the parametric fonn of heut penetration data with appropriate

mathematical procedures. the effect of processing conditions (Jeton temperature and initial

temper~ture of the product> as weil as the effect of different package sizes. Following is a

brief review of sorne of the most applied Formula methods.

Ball's method: As mentioned previously. Balrs method (1923) is considered to be

the tïrsl developed Formula method and it has a great contribution to the value of

mathematics in food processing (Merson et al.. 1978). BalI developed equations for

predicting the temperature al the critical point inside a cano This equation was applied in

general equation of (2.5) to determine the process lethality. The temperature prediction

equations were based on the experimental observations that a semilogarithmic plot of the

difference between medium and product temperatures vs. rime. after sorne initialtime lag.

was usually a straight line. The same approach is applied for cooling portion. 5uch typical

heating and cooling curves are shown in Figure 2.1. They basically comprise of a

hyperbolic heating lag portion. a logarithmic straight-line heatingy a hyperbolic cooling lag

and a logarithmic straight Hne cooling. BalI ignored the effect heating lag portion. as in

usual conditions the product temperature in below the Iethal temperature and the

accumulated achieved lethality is negligibie. However. the effect of heating lag can he

included for processes with high fI,. large :-value. or processes with low heating required

12

80

•

Heating Curve

100 _. 1

--...._---,_.

~ ~'

: IO:~='~-~==:=='='=-='~-,~~ __'8 ~:=:__.._.. ~~~§~L;~~~~tt :=---~=::_;.....---..-..---.- ..----

- ...--- --..-..-,------t~ ------- ------_._-----

T '--__........LI ....I ...lI~__._I

Q 20 olO 60

Tme (rnn)

Cooling Curve

'000

cr~

ê'S- taO ~jeu~ -...CI ,.S; -~

~.........

tO ' .......

g i---

'8 -_.~

ttt 1 1 1 1 1

a 20 .lO 60 80 TaO t20

Trre (rm)

•

Figure 1.1 Typical semi-Iogarithmic heating and cooling curves

[3

•lethality. Foh• Therefore. only the equation for the straight-line portion was considered for

the heating portion. This equation with respect of heating rate index (fi.) and heating lag

factor (jh) was described as follows:

where:

T =T - J' (T - T )lO-r,,:' l"RT <:h RT IT

TRT: retort temperature (oq

T rr: initial temperature of the product (oC)

th: hearing rime (min)

fh: heating rate index (min)

jl.:h: heating lag factor

(2.8)

For the cooling curve. the effect of cooling lag \Vas considered in calculation of

sterilization vaIue. After start of cooling. the crilicaI center of the package is still al lethai

temperatures and the effect of this lag should be considered in addition ta the logarithmic

straight portion of the cooling. In order to account for cooling. BalI used two separate

equations to predict the temperature during cooling.

For the tÏrst portion or when 0 ~ t..- ~ 1.. log( j, 10.657 ):

The temperature in the criticai point of the package was predicted with Equation

•

r J: \: l

T = T~ ~ 0.31 T. - T ) x [- 1~ [ t :. ..... _ 0.5275 loge l 10.657 ) f) J

where:

~: cooling rime

jl:: cooling Iag factor

f~: cooling rate index

Tg: product temperature at the end of heating

(:2.9)

14

•T~: cooling medium temperature

For the straight-line portion of the cooling curve when the equaùon was same as

heating ponion with reIated coaling f c: log( j L- 10 .657 ) ~ t.:

T = T + J. (T - T )10 - t. { 1.cw c: ~ cw (1.10)

•

After defining the temperature prediction equations. BaIl substituted (hem in the

equation (2.5). The resulting equation cauld nat he integrated analytically and concluded

in a direct relation between Fil and tg lprocess ùme). Hence Bail solved the equation

graphically by evaluating the resulting integraIs. The results of integrals were presented in

table and graph fonnats. These tables and graphs related g-value. as a measure of process

time. to Ji/LI ratio. as a measure of sterilization value. BalI applied parameter U as the F

value of the process at the reton temperature. These tables and graphs could be applied for

uny:-vafue.

During development of the tables and graphs. BalI assumed a constant cooling lag

factor (j. 1). equal to 1A 1. Aiso the heating rate (/h) was applied for the cooling portion. or

in other words t... was equal to th. Further. in the development of the methad (Bali and

Oison. [95ï). with respect to two dimensionless parameters of Ph and P,: for determining

the sterilization value. they accounted for variation offh andi. Obviously the conditions of

aH processes do not comply with these assumptions and result in eITors in process

calculations. ~Ierson et aL (1978) and Hayakawa l(978) evaluated this method and

reported the inaccuracies of the method. BalI method overestimates the process lime.

which provides a safety factor (Merson et aL. 1978) for process calculations.

The time duration until retort reaches the processing cemperature is termed come-up

rime 1CCT) and a ponion of this cime can hold lethality effect. BalI assurned 42% of chis

time should be added ta process time. which hoIds the product at retart temperature uotil

the steam off. He implemented chis time duratioo in his method by shifting the zero of the

heating time axis by 0.58 of eUT. It should be mentioned that this percentage is not

aIways same and severa! researchers have caken into accoUDt to carefully evaluate the

effect of CeT (Hayakawa and Bail. 1971: Ramaswamy~ (993).

15

•

•

Further there are sorne food products that do not follow a constant mode of hear

transfer. and due to modification of the nature of the food product during the heating, the

mode of heat transfer will change. This condition of heatine is known as broken heating~ - -

and is more common of those kinds of food products initially heat by convection: then. due

to the activity of sorne thickening agents as starch gelatinization, the mode of heat transfer

changes to conduction. Bali and Oison (1957) accounted for this effect by considering two

straight-line segment of the heating curve with different slopes instead of one straight line

(broken heating) in semi-logarithmic hearing graph.

Hicks (1958) round severa! marhematical errors related [0 the lethality of heating

phases. F"h' in BalI and Olson's parametric values. He prepared a numerica.! table of

recalculated parametric values. Gillespy (1951) defined a method for estimating the F­

\"ldut! for the whole can by using Balrs asymptotic approximation for heating and

developed an approximate method for cooling. Hemdon et al. (1968) prepared compurer­

denved tables based on Ball"s method. Griffin el al. (1969: (971) improved these tables for

broken-heating curves and for cooling curves. Pflug (1968) compiled abridged tables from

BalI and Olsoo's tables and aIso from Hick's table in parametric values and considerably

simplitïed [he caIculation required for process evaluations.

Spinak and Wiley ( (982) reviewed BaII"s method and considered the accuracy of

method in comparison with a General method. [n this work they compared the process

rimes for processing selected food products in retart pouch with respect to Bail"s method

assumptions and reaI vaIues from the process. The result shawed the process time

detennined by BalI"s fonnula method requires the effect of reton come-up time lethality

and the actual cooling lag factor UnJ. However. actual j~. value showed no significant

effect in at:curacy of Bali's fonnula method.

In a funher review of Ball's method (Steele and Board. 1979a). the inaccuracy of

BaIl"s method was considered to he in a safe region for underestimating the process

sterilization ratio. Therefore. it was concluded in this work that related inaccuracy

introduces a safety factor to sorne calculated processes and of course me producüon of safe

products is one of the prirnary criteria of thermal processing.

16

•

•

Vinters et al. (1975) parameterized the data from the tables in Balrs formula

method. replaced tables and graphs in this method by algebraic. regression equations.

Therefore. this method could be used in a programmable calculator.

Stumbo's method: While attempting to revise the tables developed by Bail.

Stumbo and Langley t1966) developed a new set tables ta account for the variability of jo:

values. The values of these tables were abtained by graphicai measurement of hand drawn

temperurure profiles plaued on the lechal rate papers and subsequent interpolation of these

tables. As the authors implied. these tables were applicable for cases in which the

difference between fh and (were less than 20% of the respectivefh values.

Larer. the revised form of these tables were published (Stumbo. 1973t The revised

tables were based on computer integration of temperature protïles generated from heat

tr~nsfer equarions.. using tïnite difference simulations. However. it should be noted that

these tables are applicable aoly whenJirJ~· (Hayakawa.. (978). A correction for Jh~i· can be

made as long as the value for the heating lethality cao be obtained through a different

method 1Stoforos.. 1997). The rest of procedures for process calculation were same as

Bail"s method. Computer irnplementatÎon of Srumbo's method was introduced first by

~[anson and Zahradnik ( 1967). using Stumbo and Longley's tables and after by Tung and

Garland 11978 t using Stumbo's revised table values.

Hayakawa's method: For the tïrst time Hayakawa (1970) applied a set of

empirical formulas. each of them eoncerned to a specifie range of j values. The curvilinear

parts of the heating and cooling eurve were represented by exponential cotangent and

cosine functions. The minimum and ma:<imum j values that are related to these tables are

0.045 and 3.0. respectively. He also prepared a table of new parametric values by using his

empiricaI formulas .. and developed a procedure for the evaluation of heat processes. These

tables were applicable ta aImost any :-value.. resulted in eliminating the required

interpolation for the =-\'alue. Therefore.. the process calculation was significantly

simplitïed.

li

•

•

Steele and Board's metbod: Steele and Board (l979b) and Steele et al. (1979)

reviewed Ball's method and improved this method by introducing sterilization ratios to he

used instead of temperature differences. This ratio was defined as the temperature

difference between the heating (or cooling) medium and product by the slope of the

thermal death time curve for the concerned microorganism. C'sing these dimensionless

ratios \Vas advantageous in four main aspects. Firstly. the method could be applied for any

tempertlture scale whilst the same scale was used in determining the sterilization ratios.

Secondly. the number of associated tables were less compare to Bail·s method as z-value

was incorporated in the sterilization ratio. Thirdly. the tables could be approxirnated more

readily for a programmable calculator. as one variable was eliminated and tïnally. the

limits of integration were selected in such a way that errors in tabulated values were

negligible.

Pham's method: In an attempt ta revise and improve the Stumbo's method. Pham

( 1987) introduced two serious of algebraic equations for thermal process calculation. The

method relied on the conduction heat transfer equation of a tïnite cylinder. Heat transfer

coefticient at the container walls was intinite and the initial temperature distribution was

uniform. Two ranges of sterilization values were considered: high sterilization value or in

cases when the product temperature is very close ta heating medium temperature at the end

of heating t UIf> 1) and low sterilization value (U/f< 1). For high sterilization value range an

analytical solution \Vas applied for the temperature prediction equation. the resulting

solution of equations where simple aIgebraic equations. relating g-value to li directly

within 39é error (Pham. 1987). For the low sterilization value range a numericai solution

was applied and regression equations were generated. However. the result of these

solutions was introduced in tabulated format. in fonn of dimensionless parameters. Pham

considered the variability of Trr and Tcw in these tables and equations. It should be noted

that none of the previous mentioned methods took into account the variability of these

parameters. .-\Iso. Pham ( 1990) incorporated the variability of fh and f;.- in the development

studies of a. new method. As the author implies. the applied method for considering this

variability can be used in many other methods. In addition. Pham (1990) compared msmethod (with and without equality of fh and fc) with other methods using Smith and Tung

[8

•

•

(1982) methodology. In case of/1Ft: the method was as accurate as the Stumbo~s method.

and in cases of!h./c. 1% error was reponed for a 20% difference between these parameters.

This method has the advantage of being applied in on-line computer control and

optimization of the thermal process. for being introduced in form of algebraic equations

relating U and g directly together.

Evaluation of Formula methods

The accuracy evaluation of formula methods is essential for an efficient and

successful thennal processing determination. Smith and Tung (l982) necessitared such a

study for the importance of an accurate thermal process resulting in the minimum

nutritional 1055 and improving quaIity of the product. Five major fonnula methods: Balrs

table method. BaIl"s equation method. Stumbo's method. Steele & Board~s method and

Hayakaw's method were examined in this study. The reference model was based on a

numerical general method to caIculate the accumulated achieved lethality of the process for

conduction heating food products in cylindrical packaging. A set of processing condition.

product thermal diffusivity and can dimensions were used as the initial inputs of the model

ta obtain achieved process lethality. rn an initial srudy. unachieved temperarure difference

at the end of heating 19-value) and can dimensions 1H/D) were assigned as the most

signitïcant factors in deviations in caJculation. A general increase in deviation for HID

near to unity was observed and the magnitude of g-value had a direct effect on deviations.

Stumbo method had the highest accuracy in process lethality calculations. AlI the methods

underestimated the process lethality. which represented an extra safety Iimit.

Pham (1990) used the same methodology as Smith and Tung (1982) after

developing a fonnula method accommodating the variability off,. andt·. Pham·s formula

method 1 198ï) had about the same accuracy as the method of Stumbo and had the better

accuracy than BalI. Sreele & Board and Hayakawa's methods. The sarne accuracy of Pham

and Stumbo·s method is for similarity in their derivation. however the major difference is

the algebraic expressions used in Pham method.

GhazaIa et al. (1990) examined the accuracy of five formula rnethods in

comparison with a finite difference model based on conduction heat transfer of thin profile

packaged food products. The comparison was performed based on a set of processing

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•

conditions.. food properties and a range of packaging size. A tïxed value of process

lethality was assurned to arrive at different process times with respect to selected

conditions. Although Pham and Stumbo had the smaller errors compare to Steele & Board

methods (equation and table) and BalI method.. within the r-ange of experimental conditions

the overall differenee between the methods were small. It was believed that finite

difference models based on a chin profile paekaging result in a better estimation of process

parameters (especiaIly j("C..). whieh formula methods are based on.

Larkin and Berry (1991) had a more specifie estimation of different formula

methoci..lii based on cooling lethality. A range of eooling rates (resulted from the variation in

thermal diffusivity of product or ean size).. cooling lag factors (by changing the relative

position along the radius within the can). ean dimensions and temperature differences

between tinaI heating and cooling temperatures were considered for this study. AIl the

selected formula methods rclther than Pham·s and Bail"s rnethod with a constant jn' of 1.4 [.

underestimated the cooling lethality of the process for a complete range of seleeted can

dimensions. However with an increase injt:c value. Pham's method began to underestimate

tht: cooling lethality also. The temperarure difference at the beginning of cooling and

cooling medium temperature affected the cooling lethality but the differences between the

lethalities predicted by different formula methods did "not change. Retort temperature had

onlv effect on Pham's method in cooline [ethalitv calculation and the other formula. - ~

methods were independent of this variable. Aiso this study showed that lower jcc values

than 1..+1 results in more overestimation of eooling lethality. Nevertheless. smaller J:cvalut:s showed lower contributions of cooling lethality to total process lethality.

Stoforos et al. (1997) carried out a broad and comprehensive study on thermal

process calculation rnethods. The performance of sorne of the methods was compared

against temperature prediction using a tinite difference model for conduction hear transfer

t:quations. Bail method has inability of temperature prediction at the beginning of the

he~lting. showed as a cornparison with Hayakawa's method and tïnite difference mode!.

However. this initial lag in temperature prediction is negIigible as the product temperature

is below the lethal temperature and the achieved lethality in the initial portion of heating tS

insignificant. Besides. the accuracy of each mode1 at the beginning of the heating

determines which particular model can be used in handling time-varying medium

20

• temperatures. Numerical solutions of heat conduction equations, which are capable of

accommodating the medium temperature variability, are amang the most preferred methods

for handling time-varying medium temperarures.

Numerical models of thermal process calculations

~umerical methods are based on simulating the conduction hear transfer in

packaged foods. Numerical solutians ta Fourier's partial differential equatian of

conduction hear transfer results in a temperature protïle of product during the thermal

processes. For a regular shaped container such as a cylinder or a rectangular slab. which

are more common in food industry'O a finite difference solution based on a regular gridwork

of the nodes i5 applied. Hawever'O for irregular shapes.. a more camplex technique of finite

element method is required.

The equation'O which expresses transient temperature at the center of a finite

cylinder. is as follows in cylindrical coordinates:

(2.11 )

where:

T: temperarure

t: rime

ct: thermal diffusivity

r: radial position in cylinder

h: vertical position in cylinder

This equation is the partial differential equation for two-dimensional unsteady state

conduction heat transfer in a finite cylinder. This equation can be written in finite

differences to he solved with a numerical solution:

•(2.12)

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Finite differences are discrete Increments of time and space defined as small

fractions of process time and container space (.dt• .1h and Lir. respectively). For

convenience in calculations and based on symmetry, usually half or a quarter of the

container Is considered in calculations. The temperature nodes are assigned for mis

selected volume as shown in Figure 2.2. Appropriate boundary and initial conditions are

required to calculate the new temperature at each node. after a small time interval. At the

beginning of the process. the inrerior nodes are set equal to initial temperature of the

product and nodes in surface are set equal ta retart temperuture (when the associated

surface heat transfer coefficient is large). Afrer each time intervaI the new temperature at

each oode is calculated. which replaces the previous remperarure. This procedure is

continued until the end of heating when the boundary conditions change from heating to

cooling and computation continues usually with a finite heat tronsfer coefficient associated

at the container surface. In this way. the temperature at the center of can is caIculated after

each rime inœrva1. which results in a temperature profile from which the process

sterilization value can he computed.

~umerical models can be used instead of heut penetration test to obtain the

temperarure protïle of the product. when the thermal properties of the product are known.

AIso the retort temperarure need not be held constant and cao vary during the·process.

Therefore these models can he used in continuous processes. when the caus pass from one

chamber ta another. and the heating medium temperature changes during heating process.

This advantage has provided the patenciaI of these models in on-Hoe control of thennal

processing. Teixeira et al. 1.(969) applied such numerical models in optimizing the nutrient

retention in conduction-heated foods. The main importance of these models was providing

the tempermure at any position inside the can. The application of these models in on-Hne

control has been extensively studied (Datta et al.. 1986: Teixeira and Manson. 1982:

Tucker. 1991: Teixeira and Tucker. 1997).

22

•

R

i,j-l--0--0--0--

i- Lj 1.J i+ Lj---Of-----...-

1 h11111

.. l 11.J+ i

--- ---------------------------------;-

·1Figure 2.2 Gnd format for temperature ca1cularion using a numerical method

•23

•

•

Artificial Neural Networks

Artificial neural networks (AJ.'INs) are computing systems built up of

interconnected processing elements.. which are able [0 map information between a set of

input variables to related output variables. A very fundamental component of brain or

nerve ceUs. neurons. is also the basis of the Al'IN computing.

Regard to this similarity.. there are three main sections of biological neurons, which

are important in understanding the structure of ANNs. A biological neuron consists of

three main components (Figure 2.3), Dendrites (input paths) receive the infonnation as

signaIs from other neurons. Signais are chemicais in nature. but they have electricaI side

effects. which can he measured. The soma or cell body SUffiS the incoming signais and

after receiving sufficient inputs. it will fire signal through its a.'(ons (output paths). The

a.'(on of a neuron splits up and connects to dendrites of other neurons through a junction

referred ta as a synapse. The strength or synaptic efficiency depends on released chemicals

From axon and the amount thar is received by dendrites. The synaptic ~fficiency is what is

moditïed when the brain learos.

[n simulating the brain neural network. a processing element (PE) with its

connections is the Al'IN equivaIent of a neuron. The PE acts as the cell body. There are

input connections to the PE. like dendrites.. which transfers the signais to the PE. Output

connections from PE.. like the axon. transfer the signais to the other PEso The

interconnections possess pararneters known as weights.. which will be modified through the

leaming procedure (as the change in synaptic strength). The information transformation i5

performed through the interconnections between aIl the PEso In a typicaI ..-u'fN structure.

processing elements are arranged through layers l,Figure 2.4.).

Usually an A1'lN consists of one input layer. at least one hidden layer and one

output layer. Input layer receives the information from an external source and sends them

to the network. Hidden layers process the information from input layer and transfer them

to the output layer. Output layer receives Ûle processed informalion and sends them to an

external source. When the PEs in input layer send the information in the form of signals to

the network.. the strengths of interconnections are altered based on the amplitude of the

signais. These changes are distributed ail over the network through connections and. at the

24

•

s ./);ac DedileofAnadIIrNaD

Figure 2.3 Basic stnlcture of a biological neuron

Processing elements

1-----.Ir • ~A~~'~

Input

lHidden layer

2Hidden layer

Output

0,

•Figure 2.4 Typicai diagram of AJ.\fN model

25

•end. manifest themselves in the forro of outputs. One important characteristic of ANN is

that it processes information numerically rather than symbolically. The network retains irs

information through the magnitude of the signais passing through the network and

interconnections between processing elements.

Figure 2.5 shows the basic structure of a proeessing element and its connections.

The inputs into /h layer are basieally the outputs of the previous layer processing elements

as an input vector. a. with components ai (i=l to n). The output of proeessing element (hj )

is the result of a transfer funetion (j) over a summation of inputs multiplied by weight

parameters and addition of a bias value (1j). Transfer function can be varied depending on

the nature of the data. The most common transfer functions in solving non-lïnear problems

are sigmoid funetion and hyperbolic tangent. A sigmoid (S-shaped) function is depieted

mathemmicully as fol1ows:

1j(:c) =--­

1+ e- l(2.13)

This funetion varies between 0 (aLtr=-oc:) and 1 (at x,=+OC). Sigmoid functions. due to their

limiting values. are known as threshold functions. At very low input values. the threshold­

function output is zero. At very high input values. the output value is one.

Hyperbolic tangent functions aIso typieally produce well-behaved networks. This

function also has two limiting boundaries of +l and -1 :

t -le -e[(x) =tanh( x) =---

et +e-\(2.14)

•

As the response of this funetion includes bath positive and negative region. their

application are recommended for data set with negative and positive output range

1Swingler. 1996).

Development of an artiticial neural network model

An imponant factor. wrnch distinguishes different neural networks. is the method of

setting the values of the weights or training the network. In training~ AL'1Ns generally cao

26

•

Input variables

Output = f(L"<j.Wi) +8..

•

Figure 2.5 Diagram of a processing element and related calculations

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either be supervised or unsupervised. In supervised training~ there i5 an associated output

aIong with any input vector in training data set. Therefore. the weights are adjusted

according to the target output. The most common application of this method is in

classitication.. prediction.. and pattern association problems. On Lqe other hand. in an

unsupervi5ed learning, a sequence of input vector is provided but no target outputs are

specitïed. The network will act in a self-organizing manDer to modify the weights 50 that

mos[ similar input vectors are assigned [0 the same output (or cluster) unit. As the

detinition reveals. unsupervised learning i5 mostly applicable in data clu5tering problems.

Besides the mentioned classification. in each group. there are severa! algorithms of

training. Backpropagation is one of the most applicable algorithm5 in problems involving

mapping of a given set of inputs ta a specified set of turget outputs (Fausett. (994).

Backpropagarion ulgorithm is simply a gradient descent method ta minimize the total

squared error between the output computed by the network and target output. There are

three main stages in backpropagation algorithm: a feedforwurd of the input training pattern.

calculation and backpropagation of associated error and adju5tment of weights with respect

to calculated error. Althou~h the trainine of AL'lN model i5 rime consumin~. a trainedy ~ ~

network will only apply a feedforward phase to compute the associated output and renders

chis phase very rapidly.

The major task in training a network is to bring the network to a balance between

memorization and generaIization. ~lemorization i5 the ability of the network in correctly

responding to input vectors used in training. Generalization is the ability of network ta

respond ta input vectors in the domain of training vectors but not identical to input vectors.

A proposed procedure for achieving this goal applies two disjoint sets of data known as

training and testing data sets. Training data set is used to updating of weights: however~ at

intervals during training. the network is tested with testing data. As long as the network

errer for testing data is decreasing~ the training continues. When this errer begins to

increase the network stans to memorize the features in input pattern too specitïcally and

loses its generalization ability therefore at this point the training is terrninated.

To develop an optirnized networ~ the number of hidden layers and processing

dements in each layer should he selected carefully. In addition to structure of network.

relared pararneters to irnprove the leaming task should he optimized. Two of these

28

•

•

important factors are momentum and learning rate.. wnich control how effectively

backpropagation trains the network (Baughman and Liu.. (995). The learning rate is a

positive constant and controls the rate at which the new weight factors are adjusted based

on the calculated gradient descent correction terro. The momentum coefficient is an extra

weight added onto the weight factors that accelerates the rate at which the weight factors

are adjusted. helping the network to avoid the local minimas. A well-optimized network

has the ability of extracring the relationship between the training data set and adapting its

internaI structure based on related information.

Applications of ANN in Food Science and Agriculture

~[any problems encountered in food.. agricultural and biological industries lend

themselves to a neural network solution. The application of A.NN in different problems is

introduced.

One of the tïrst applications of neuro-eomputing in food technology was introduced

by Thai and Shewfelt (1991). The combination of neuro-computing and statistical

techniques was used to determine the most relevant factors in relating sensory judgment by

human and physical measurements of extemal color of tomato and peach. In this study'.. the

application of neural networks was faster compared to statistical techniques for having

fewer sœps in analysis step: however. statistical techniques were slightly more

advantageous for higher accuracy. Consequently.. neuro-computing technique were applied

to get [he basic features of [he relation: and stutistÏCal techniques were used to improve the

numerical accuracy of resulting mathematical functions. With respect to this study and

above mentioned procedure. the relationship bet\veen sensory evaluations and physical

measurements of tomato and peuch were identified as particu[arly linear.

Bochereau et al. ( (992) applied neural network technique as a parr of procedure for

prediction of apple qualiry using Near Infra-Red (NlR) spectra data. In order to reduce the

nurnber of input parameters and excluding uncorrelated inputs to the neural networlc modeL

principal component analysis (PCA) was appliecl A multiple regression analysis was then

carried out to derive the best linear estîmator and finally the neural network model was

developed to exrract the non-tinear function input and output components. The final result

29

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was a model for predicting the apple quality From NIR spectra. ANN modeling resulted in

5 % increase in accuracy of the linear model with R2 equal ta 0.82

Linko and Zhu (1992) studied the potentiaI of ANN techniques to construct an

appropriate real-rime state estimation and prediction model applicable ta process control in

glucoamylase fermentation. In comparison with conventional modeling, ANN had the

abiliry of handling uncertainties~ complexity. noise and unavailability of data. which are the

common cases in the biochemical reaction analyses. The most related on-Hne data as

oxygen consumption rate (OCR). carbon dioxide evollltion rate (CER) and the nitrogen

utilization rate (Nù"R) along with other inputs were applied to estimate the enzyme activity

and biomass in on-line control. The ANN models had the advantages of ease of use

wirhout a prior knowledge on the complex mechanism of microbial physiology or on the

interrelationships of the variables. Once trained on a typical example data. it .~~~ model

could suppress the noisy dara. The developed A1~~ model performed very satisfactory and

compared weil with real values from off-Hne analyses.

A~'t')i models were applied as a quality prediction model for black teu and resin

samples based on data From chromatography and sensory information (Tomlins and Gay.

1994). Although multiple regression techniques were more aCCllrate compared ta Ai'IN

modeling. the results of A.NN model were improved by reducing the training variables

assigned by srepwise multiple regression. In addition. A4'ms for cases in which the

accuracy is not important (for example in quality control) provides more advantageous

application in predicting severa! parameters simultaneously. The combination of statisticaI

procedures and A1'IN were suggested as useful tools in pattern recognition and regression

of chromatographie (GC and HPLO and sensory data.

Park et al. (1994) applied an Al'fN model for predicting and classifying beef

characteristics using ultrasonic spectral feautures as the input data for training the models.

A.'N models provided becter results compared to statistical regression models for

predicting the sensory attributes of beef as juiciness. muscle fiber tenderness. connective

tissue. overall tenderness and tlavor intensity. The relationships between physical

attributes and sensory properties were mostly linear as an Ai'fN model developed without

hidden layers performed best. The accuracy of ANN mode1 for classification were a

function of learning schedules. number of processing elements in hidden layer and number

30

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of input variables. Increasing the ultrasonic spectral fearnres as input variables increased

the accuracy of classification.

Sayeed et al. (1995') investigated the possibility of an ANN model development for

sank quality evaluation. For this purpose a machine vision technique was applied to

quantify the quality features of typical snack products in the forro of texture (reflecting the

internai structure) aIong with size and shaPe fearnres. The relationship between the

mentioned variables and sensory attributes were not adequarely linear as examined by

linear regression. merefore the input variables were applied to train a backpropagation

Al'IN model to leuro the non-linearity between input and output variables. The developed

ANi\' model was validated with a set of untrained data and the prediction results were

compared to those from a taste paneL The developed methodology had a potential

application in snack production industry as a non-destructive method of quality evaluation.

The potential A1~N models for milk shelf-life prediction was evaIuated by Vallejo­

Cordoba et al. (1995). Dynamic headspace gas chromatographie data collected during the

storage of pasteurized milk were applied as input to he reluted to tlavor-based shdf-life of

milk in days as dependent variable. A~'fN and Principle Component Regression (PCR)

techniques were used and compared for their predietability. A.l\fN. with 2-day standard

error in shelf-life prediction. performed better that the 4-day error PCR technique. and

indicated a higher predictability for chis concept.

Sablani et al. (1995) investigated the potential of .'-\l'IN models for prediction of

optimal sterilization temperarures. A finite difference model generated the data for a set of

assigned conditions (can size. thermal diffusivity and kinetic parameters of quality factor)

ta obtain the associated sterilization temperarures. Afterwards the optimum conditions and

relared quality factors were applied as inputs to train the AJ."~ mode!. The trained madel

was able ta predict the optimal sterilization temperarnres with less chan 5% error. In

artempt to predict the overaIl heut transfer coefficient and fluid ta particle hear trafisfer

coefficient using Al'lN modeling technique. Sablani et al. (1997) obtained significantly

superior results compared to dimensionless correlation techniques. Beside the higher

aecuracy of prediction. ~'iN models were more versatile man dimensionless number

models.

31

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Rauan et al. (1997) compared the predietability of ANN models for rheoligical

properties of a coolde dough. The raw input data were obtained from mixing power

consumption curves. The investigated rheologieal properties were farinograph peak.

extensibility and ma'<imum resistance. Two speetrum analysis techniques. Fast Fourier

Tr~nsform (FIT) and power spectral densiry (PSD) were used for data preproeessing as a

part of .-\l~ model development. Using these techniques the raw data (time domain data)

were converted into frequency domain data. The above-mentioned techniques improved

the training abilitv of Al.'IN models for reducing the noise and size of the initial raw data... - ...and \Vere recognized as successful techniques of data preprocessing in this study.

Ghazanfari et al. (1996) studied the suitability of multi-structure neural networks

(~ISl\rN) over a single multi-Iayer neural network (NrL~) for classification of pistachio

nuts. The yIS~~ classitier was constructed from four single Ai'IN models. which were

[rain~d separately with one output variable from each network representing one variety

(class) of pistachio nuts. The input data for these madels were physicaI attributes of nuts

derived from their images. The c1assitication accuracy of developed NIS!'4N was compared

with y[L~N modeI. The MSNN technique significantly increased the classitïcation

performance. In addition. ~ISNN had the advantage of smaller network architecture.

which is more preferable for hardware and software implemenration.

.-\ngerosa el al. (1996) developed an Al'1i madel as alternative ta sensory

evaluation performed by a taste panel for virgin olive oil by panel test. A wide range of

samples tcovering different variery. quality. ripeness. sanitary and geographicaJ ongin) was

subjected to a sensory evaluation by a taste panel. The results of quantification of volatile

fractions using headspace gas chromatographie technique were used as input data to predict

the panel test scores (output variables). The ANN mode1 was able to generalize the

relationship between these two sets of data successfully with a high degree of aceuracy.

5uggesting the substitution of developed A.L\lN model with panel test.

Briandet et al. (1996) applied ANN technique as one of alternative statistical

approaches for correlating data from Fourier transform infrared (FrIR) for detection of

adulterated freeze dried instant caffee. This FI1R technique was applied as a rapid

alternative to wet chemistry methods~ however~ data analysis of this technique were more

complicated. AL"'N models were compared to principle component regression and partial

.....,-'-

•

•

least square regression.. and the superior perfonnance and generalization potential of Ai'JN

model was demonstrated with an independent set of data with 100% correct classifications

ability.

Pamer ec aL. (l997) developed an AJ.'IN mode1 [0 evaluate the factors involved in

the contamination process and aIse the significant factors in the magnitude of aflatoxin

contamination of in preharvest peanuts. Alternative to ANN model. a stepwise traditional

regression model was developed for this purpose. The input variables (soil temperature..

drought duration. crop age and accumulated heat units) were related to at1atoxin levels.

This study showed the ability of A1'lN models for this purpose in addition ta better

performance than Hnear regression technique.

Kim and Cho (1997) applied three developed Al'lN models as a part of a fuzzy

controller in bread baking process. For this purpose three main parameter in bread baking

process namely volume. browning and temperature were measured in 3 seconds and :!

minutes intervals. resulting in training data for 3 AJ.\fN model development. The neural

networks showed a good performance for predicting temperature. volume and browning.

The knowledge from developed models and an experienced operator \vere used ta detïne

[1 mies for fuzzy controller. Using a fuzzy contro[[er instead of a human operator can

reduce the cast of heating of the oven.. withont the loss of bread quality.

•o.\1\j~ models as an alternative in data-processing technique to partial least squares

(PLS) and principle component analysis (peA) showed better prediction ability (Horimoto

el al.. 199ït In order to classify the tlavor quality of milk as a part of qualîty control.

dynamic hcadspace gas chromatographie was used to quantify the off-flavor components.

UHT milk \Vas inoculated with various bacteria! species and storage rimes. The content of

training and testing data as weil as optimized parameters.. which were related to Al'lN

model development (learning rate. momenturn factor and hidden PEs). intluenced the

predictive ability model.

During ~sobaric-isothermal inactivation of ex-amylase enzyme. pressure and

temperature had a complex effect (Geeraerd et al.. 1998). A model based on Arrhenius Iaw

presented a non-lïnear description of the system. Due to lack of data. an A1~ model was

applied with respect to its ability in prediction of complex systems. The ANN model was

able to predict the complex effect of pressure and temperature on the inactivation rate

33

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constant using a limited set of experimental data. The effect of transfer funerion of eaeh

neuron was believed to be imponant in a low complex Al'IN model development.

Gebri et al. (1998) applied Ai'lN modeling in predieting the origin of white vinegar.

Among different chemico-physieal and sensory analysis. seleeted parameters such as

polyalcohols. pH. tartane acid and proline had the Most reliable rule in discrimination of

the product. A broad data set covering products from a variety of raw materials and from

various countries subjected ta multivariate statistical analysis were used ta develop the

.~'N model. The Ai~~ model was able to predict the botanical origin of the product and

also was able to re-elassify products with unknown origin.

The above review indicates the status of available methods of process calculations

1with sufficient scope for developing new method. which can reduce process calculation

errors 1. as \vell as the poœntial of Al'lN models for use in process calculations. The present

thesis aims at developing an ANN based process calculation model. which would be more

versatile and accurate chan the existing methods.

•

•

CHAPTER3

Al'N S~IlJLAnON OF BALL Al~DSTmmo FORMULA ~IETHODSOF THEIUtIAL

PROCESS CALCULATIONS

ABSTRACT

Application of Al'lN models to simulate BalI and Stumbo methods of thennal process

caIculaùons i5 presented in this srudy..ANN models were developed based on relating Bali and

Srumbo table parameters to facilirate process calculations. The A~\lN models related g value (as

a measure of process [Îmel [0 fiIU (as a measure of process lethality). Tables developed by

Stumbo accommodate the jd: (cooling lag factor) while relating g and JilU. therefore. for

devdoping :\~N models of Srumbo metbod, jn: was also considered as an additionai input

variable. The developed fu~'N models for BalI and Srumbo methods were validated using a new

set of processing conditions. involving a range of retort temperatures. initial temperarures.

heating roltes and heating lag factors [and additionaIly. for Stumbo method. cooling lag factors

lj,,)}. The prediction eftïciency of .~'lN models were a function of the size of training data set.

number of hidden Iayers and PEs in each hidden layer as weIl as other leaming pararneters.

.--\."~ based Bali models had an average error of 1% for the validation data set while the AJ.~~

based Stumbo models had a slightly higher 3% average error for process time and process

lethaIity calculations. The smaller size of data set and a wider range of parameters associated

with Stumbo tables were considered to be the reason for the associated higher errors with the

.-\1'"N based Stumbo models. In generaI. the Al\lN models were considered ta simulate BalI and

Stumbo methods of process calculations weil providing a basis for further exploration of the

concept.

35

•INTRODUCTION

Thennal processing of packaged foocis is one of the most widely used methods of

preservation in twentieth century (TeL'<eira and Tucker. (997). Nicholas Appert introduced this

method for the first time in 1810. The concept of thermal processing is based on heating of

packaged foods for a certain length of rime to obtain a safe product complying with public health

standards. Thermal processing is based on established time-temperature protïles. Associated

with thermal processing is aIways sorne degradation of heat-sensitive quality factors that is

undesirable. Since much demand is on safe and shelf-stable food products aIong with a high

quality attributes. processing schedules are designed to keep the process rime to the required

mInImum.

The main objective of thermal process calculations is to detennine the process rime for

Jchieving a pre-selected process lethaIity or evaluating the lethality of a given process. For the

tïrsr üme. Bigelow et al. t 1920) introduced a graphicai procedure of evaluating the eftîciency of

heat treatment process for packaged foods. Bail (1923) retined the concept and develaped a

mathematical model (referred ta as BalI method) for calculating the required process rime of

canned food~. Besides sorne limitations in this method. the BalI methad is considered a

milestone in canning industry and still is a widely used method in industry. This method is

positioned a.'i a classical tribute ta the value of mathematics in food processing.

BalI method is based on the observation that a semi-logarithmic graph of temperature

difference between product and medium vs. rime is a straight line after an initial curved portion

(lag rime). Bali t 1923) caIculated the process time based on the equation of this straight line and

integrating the effect of process time over the kinetic data of microbial destruction. LTsuaIly the

effect of curved portion of heating is not considered. as the lethal effect of this panion is

negligible compared ta the total achieved lethality. However.. under conditions of high initial

remperature. large :-values or processing for low required Iethality. the efficiency of this portion

of heating should be taken into consideration.

The estimation of proper heat processes is essentially based on the calculation of process

lethality. F. .. camputed as fallows:

•c Trpf-T

F =JI0--;- .dttJ

o(l)

36

where:

• T~t: reference temperarure

T: ~enter point temperarure

z: temperature sensitivity indicator of F value.

For law acid food products. 250~ (l21.1')C) is widely used as a reference temperature. BalI

deveIoped tables and graphs (0 relate process rime and process lethaIity. These tables and graphs

\Vere based on relating two parameters: g (temperature difference between product and heating

medium at the end of heating) as a measure of process rime (0 Jill} (ratio of heating rate to

srerilization value) as the measure of process lethaIity. Sorne restrictive assumptions were made

Juring the development of these tables and graphs. One of the most important parameters. which

~~m somerimes cause crrors in calculations.. was a constant cooting lag factor. jn value.. equal to

1A1. Therefore. BaIl method overestimates process lethality when ix< lAI and underestimates

when jll> 1Al (Bail and Oison.. 1957: Hayakawa. (978). Also.. BalI (1923) assumed an equal

heating and cooling rate tJir=ll. In practice.. the values of these two parameters differ from each

tlther. It has becn found that for steam heating and water cooling j;.-1.3Jir (Pham.. 1990) and

L)bviously disregarding this inequity interferes with the accuî~cy of process calculations. BalI

method has been wide[y reviewed and evaluated by several researchers (~[erson et al.. 1978:

Rambert et d/. .. 1977: Steele and Board.. 19;9: Spinak and WiIey. 1982: Stoforos. 1991).

Stumbo and Langley <.1966) reviewed and revised tables developed by Bali 11923). The

variability of il- value was considered in these tables for more reliable and accurate thermal

processes calculations (Stumbo. (973). These tables are obtained from hand drawn heat­

penetration curves and relate JiIU and g values with respect to variability of i:c- Also the

variability of 1;, and l· was considered in developing these tables. but it applies only to cases

where the difference ofth and f~ is not more than 20% of respective.th value 1Hayakawa. 1978..

Stoforos el al.. (997).

ArtificiaI Seural ~etwork~Iodels

Artitïciai Neural Setwork (Ai'lN) rnodels are computationai models made up of several

processing dements l PEs).. which are connected through weighted links.. Development of model

•37

is basically based on adjusting the weights through presenting adequate number of examples

• consisting of input and output variable pairs.

GenerJ1ly Ai\iN models are constructed from an input layer. an output layer and one or

more hidden layerts). Input layer tr'ansfers the information ta the network for proeessing.

Output layer receives the processed information and sends it to extemal receptor. Hidden layers

process the received information from input layer. extraets the existing features in input variables

and predict an output. Among different networks. back-propagation network has the mose

applicability in prediction and classification problems. Baekpropagation network is a feed­

forward network. which propagales back a portion of error between desired and ANN predieted

output ta correct the weight pararneters.

Recently. ANNs have shown a potential for applications in food science and technology

areas. Eerikainen el al. (1993) presented a series of examples of potential application of AJ.'lN

modds in food-related applications. Parmer er al. (1997) applied neural network modeling for

~stimation of atlatoxin contamination in peanuts which performed better than trnditional linear

regression techniques. ~i and Gunasekaran ( 1998) simulated the complex task of food quality

prediction using .·\NN models. Boucherau el al. (1992) developed a neural-network-based

method for prediction of apple juice quality using near infrared spectra. Neural networks were

used to detennine the significant variables in harvesting and processing effects on Surimi quality

by Peters t!C ul. ( (996). Kim and Cho (1997) developed an .o-\i~~ model for the bread baking

process. using three quality factors of volume. browning and temperature. In thermal processing.

Sablani et al. t (995) applied neural network models to predict optimum thennal processing

~onditions. As an application in drying. Sreekanth el al. (1998) developed an A..'iN mode1 for

prediction of psychometrie parameters.

The global objective of this study was ta evaluate the potential of A.L'IN models as an

alternative [0 conventional process ealeulation methods. As a first step in this direction. data

from two dassical methods: BalI and Stumbo methods. were used to develop the .o.\i~ models

and assess rheir perfonnanee. Renee. the specific objective of this paper is fu\fN simulation of

Bail and Stumbo formula methods of process calculations.

•38

•

•

~IATERIAL AND ~IETHODS

ANN modeling of Bali and Stumbo methods

Bail and Stumbo methods relate process time and pracess lethality by employing t\va

parameters. g andfJlU. in the form of tables or graphs. In tables developed by Stumbo. the effect

of jn on this relation is aise considered. For a known process time aIong with the other

processing conditions. g-value will he known; altematively for a given process lethality.f,/U will

be known. For developing A1~~ based process calculation models. Bail and Srumbo methods

were simulated based on relating the parameters of these tables. Data (jilU vs. g or g vs. f,;u) for

both training and verification were obtained from tables published in Lapez (1987) for BaIl

method and Stumbo ([973) for Stumbo method. Detailed tables were available in Lapez (1987)

and hence 1050 data pairs were used in Bali model for training. For Stumbo method. only 44­

data sets relatingjilU vs. g (and vice versa). were available al 9 different values of jl..l. A :-value

ùf IOC was used for both models. For each method. two modeis were developed one for

predicting.tilU ba."ied on g. and vice versa.

Development of .-\~N models

Bail model

~eural\Vorks Professionai WPlus.. version 5.23 (~euraIWare me.. Pittsburgh. PA) was

~mployed for :\J.~~ modeling. .~ standard back-propagatian algarithm with tangent hyperbolic

transfer functian and narmalized cumulative delta learning rule was applied as the basic

architecture of nt=twork. As the input and output variables had a broad range. for a better

presentation of input and outputs ta the network and a more uniform data set. a mathematical

transfonn function \Vas applied. Therefore. log g was predicted From [og(j'/u). and liIU in the

fonn of arctangent([og /,./U) \Vas predicted From log g. For a more convenient recalling of

models. from now prediction of log g will he denoted. as Madel A and prediction of f,;rJ will he

denoted as ~[odel B.

It has been recognized that the network predictability and performance should be

optimized wîth respect to the size of the training data set. structure of the network. number of

hidden Iayers. number of processing elements in the hidden layer. type of learning rule and

trmsfer function. Severa! other variables aIso affect the ANN model development and

39

perfOl1nance. Among them momentum and epoch size have the most significant effect on the

• network performance. The momentum represents a fractional value from the previous weight

change added to the present weight correction. Its value can change between 0 and 1. however.

higher momentum values speed up the leaming process and prevent the model from being

trapped in a local minimum. At the same rime. large values of momentum will cause large error

oscillations 1NerualWare. 1996: Baughman and Liu. 1995). Epoch is the number of training

presentations between weight updates. This method of updating weights which increases the

convergence speed is known as cumulative delta mie leaming. However. using cumulative

deita-rule learning for updating weights will require more calculation and. if the epoch is too

large. the advanrage of using overall error function can be lost Therefore. depending on the

problem. the epoch size should be optimized.

The perfonnance of an ANN model is intluenced greatly by the quantity and quality of

dam llsed as the training set (Linko and Zhu. 1992). The training data should have suftïcient

information to describe relation between input and output variables. A correct format of input

~nd output variables could increase the leaming ability of AJ.'INs by detecting and extracting the

relation between input and output variables (NeuralWare. (996). This stage of Al'IN models

deve(opment is thus regarded as data preprocessing~which could be petformed in different ways

to improve the model efficiency llaeroix er al.. 1997).

Keeping the above constraints in mind. to select the required number of examples in

tr~ining set. a leaming curve was developed. The original data l 1050 dataI were sorted from the

lowest [0 highest value. To have six equal groups of data. every seventh data row was selected

and removed from the original set. These fonned the tïrst <Group Al data set of 175 data points.

The same procedure was repeated with the remaining data until six homogenous groups (A ta F)

of data each with [75 data points were obtained from the original data. Each of the group thus

covered the entire range of data in original set. Different combinations of these groups were

used ta achieve different sizes of training and testing data sets. These arrangements are shown

in Table 3.1. The data sets that were not used for trainini! were used for testing durin~... --development of model. The developed models were tested also with ail the available data from

the original data set ta evaluate the consistency of performance. This procedure was followed

for both models lA and B).

•40

Various network architectures and network learning parameters (momentum and epoch

• size) were examined. as summarized in Table 3.2. To avoid over-training of models. the original

data were separated into two groups as training and testing data sets. Testing data were applied

to cross-val idate the model during the training stage. For this purpose. the NeuralWare software

provides an option called ··save besf·. Function of this option is to stop the training stage mer a

certain number of cycles. testing with testing data and saving the results of the network in a file.

Each rime. the result of most recent and better network replaces the last saved network. This

procedure is continued until a pre-selected error of network is reached or after number of

Iterations without any improvement in leaming of network. Finally. the "save besc" network is

retained. and the model is ready for veritïcation.

Table 3.1 Combinations of training and testing data for network optimization

Grouplsl in TfOlining GroupfsJ in Testing Sumber or data pairs Number or dataset set in Training set pairs in Testing set

.-\ B.C.O.E.F liS 875

A.F B. C. D. E 350 700

A.C.F B.D. E 5~ 5~

A. B. C. F D.E 700 300

A.B.C.D.F E 875 175

Table 3.2 Range of network architecture and learning parameters used in the study

Sumber or Pes~(omentum Epoch

1 hidden layer 2 bidden layers

2 2&1 0.2 ~

5 2&5 0.3 8

10 5&5 0..1 16

15 10&5 0.6 10

- - 0.8 32

" Bold numbers .,,-[(Ir rmderscore are default values provided in software.

Stumbo model

The number of data pairs avaiIable for chis modeI was 396 (44t,.;rJ vs. g combinations for

• 9 j( f' values) and covered a Iarger range of[JIU and g as compared to BalI table. Input variables

41

• in developing A~~ model for Stumbo method were fiIU and jc.'C: for predicting g value or

altematively g andjcc to predictf,;lJ. Thejc:c variability was considered as the second input. As

in Bali modeIs. notations of ~Iodel A and Madel B were used for prediction of log g and f,/U

values, respectively. A part of original data was used for testing. The selection of the Al'lN

structure and related learning parameters \Vere followed as defined for the BaIl mode!.

Validating the ANN models

After developing A1~~ models for BalI and Stumbo methods. a new set of data covering

a specitïed range of processing conditions. as shown in Table 3.3. was applied. A Lotus® based

spreadsheet program for process calculations by fonnula methods, developed by Ramaswamy

1 1991). was applied to caIculate the corresponding process time or process lethaIity. The

~alculared g (or ji/V) from the processing conditions and process time/process lethality were

used ta recall the ..\J.\IN models and obtain the corresponding A.l.~~ value. After. these recalled

.-\1\fN values were applied ta calculate the .-\l'IN based process time or process lethality. the

accuracy of .-\..'i~ predicted values were compared with the respective values from each method.

The following criteria were used for evaluating Al'fN models performance:

I~(r:)-y):'Root y[ean Square (RJ.v[S) of error= V~ n'

~[ean Absolule Error (NIAE) =Mean of 1Yt , - YI

y[ean Relative Error ~~'1RE. %) = ~Iean of

where:

y,): Desired value

Y: .~'i~ predicted value

n: number of records

Ir _yi

l} 1 *100Yo

•For vaIidating ..~'IN models of Stumbo method. the variability of j,x was aIso considered

between the processing conditions. Table 3.3 shows the range of conditions used to caIculate

Stumbo process rime and process lethality.

42

Table 3.3 Range of parameters for validaring A1'lN based BalI and Stumbo models

• Parameters BaU Stumbo

RT (oC) 115-125 110-130rr (oC) 65 70-90

fh (minI 10-20 23-[85

Jch 1.2-2.0 1.80-2.04

Jec lAI 1.70-2.00

Process letha1ity (min) 5-64 5-15

Process rime (min) 13.7-147 25-400

RESULTS AND DISCUSSION

A~N based Bail ~[odel

•

:\Iodel development and optimization

Ir has been recognized that the network predictability and performance is dependent on

the nature and size of training data set. strucmre of the network and sorne relevant pararneters

during training. Training data set should ideally cover the desired range of problem and consist

of ~nough records to let the network leam the features. Al'1N models learo trend From the data in

training data set. This capacity is based on the number of processing elements (PE) or more

specifically number of connections. [f the number of PEs are more than what is needed with

respect to training of the model. the network may lose the generaIization ability and begin to

memorize the data which is mostly undesirable (NeruaIWare. 1996).

A well-trained network is optimized between generalization ability and Iearning the

trends in training data set. To prevent the memorizing problem~ a separate data set from training

data should normally be selected randomly and this data set will be applied during training stage.

After certain number of cycles. the training is stopped and the testing data set is used to calculate

the error. After the network has converged to or reached a minimum global error. the training

can be stopped.

For developing the Ai'1N-based Bail mode!. the first objective was to choose the correct

size of the training set. which ensured the Iearning and generalization ability of network

43

simultaneously. Figures 3.1 and 3.2 illustrate the effect of number of examples in training data

• set based on recalling training data set (as a measure of network ability to learn the data). as weil

as testing the network with testing data which were not used in training data set (as a measure of

generalization ability of network). Also. each network model was tested with the entire original

data set and the combined results are shown in these graphs. For both models. the errors

associated with training and testing data sets were very close for each training set size.

demonstrating the potentiaJ ability the of network for generalization. The results also confirm

that the !!eneralization abilitv of network was not affected bv trainin~ data set. However. the size......, . .....

of the training set had a signitïcant impact on the prediction ability of network. At the lowest

level tried. the CITors were quite high. For the Ai'IN based Ball-method. a training data set of size

containing as many as 175 data points could be accommodated because of the availabiIity over

1000 data points in the original set. And even at this size. the associated errors were high and

converged to lower values only after the size was increased. The network had minimum errors

with a size of 525 data points which was se[ected for both models (A and B). the remaining

being used exclusively for testing.

Th~ error parameters for selecting the required number of hidden layers and PEs in each

hidden layer are shown in Table 3.4. Changing the number of PEs in networks. with one hidden

layer. generally resulted only in a smaii improvement in performance. However. the addition of

a second layer. markedly improved the prediction ability. which was more significant for ~lodel

B than for NIodel A. Increasing the number of hidden layers ta 3 did not result in uny advantage

l)Ver the model with 2 hidden layers. but increased the computation rime. H~nce. ~lodel A was

selected with 1 hidden layers and 2 PEs in each layer. and a 2-hidden layer network with 5

processing elements in each layer was assigned for Madel B. It has been generally recognized

that assigning the appropriate number of PEs and hidden layer(s) is mostly a trial and error

m~thod. however. two hidden layers for most of problems is sufficient (NeuraIware. 1996).

•

•0.012

0.01

0.008

~

-< 0.006~

0.004

0.002

0175 350 525 700 875

Number of examples in training set

.Training OTesting .Testing W/I050

Figure 3.1 Learning curve for ANN model A (prediction log g)

0.006

0.005

0.004

;:;< 0.003~

0.002

0.001

0175 350 525 700 875

• Figure 3.2

Number of ~xamples in training set

.Training DTesting • Testing W/I050

Learning curve for Ai'lN model B (prediction/JIU)

45

0.361

0.903

1.09J

3.106

0.032

0.051

0.057

0.073

Effect of PEs and hidden layer(s) on the performance of ANN based BalI models

la~ers

Table 3.4

1 Model A (predicting log g) ~[odd B (predictingf,.lu)~umberor

Number of PEs!

hiddenin layers

i layers Rl.\lS error ~[AE ~[S error MAE

2 0.068 0.037 3.584 1.041 1

On~ hidd~n 5 0.067 0.038 5.792 1.709

1

layer 10 0.067 0.039 2.418 0.715

15 0.076 0.051 2.722 0.7981

2&2 0.043 0.024 6.332 ! 1.~81!i 1

1 hiddcn 2&5 0.0421

0.023 1.903 0.589. , - - 1 ....

•

S~veral other parameters have a role in a successful training and increasing the

performance of the network: momentum and epoch size. and leaming role. The epoch size was

systemarically varied between the limits and its effect on the R.MS was evaluated (Table 3.5).

Epoch size did not affect prediction ability of Madel A: however. it affecled the prediction

abililY of ANN model B. After selecting the correct epoch size. this parameter was tïxed and the

variability of momentum was considered. Table 3.6 shows the impact of momentum on learning

of network. Increasing this parameter decreased the error paramelers. but increasing il beyond

sorne values increased the error. The increase of momentum value can speed up the leaming rate

and prevent the network from trapping in ta local minima: however this increase C3.1l increase the

error oscillation and consequently affecting the performance of model.

Table 3.5 Effect of epoch size on prediction ability: ANN based Bali models

Epochsize~[odel A lpredicting log g) t ~Iodel B (predictingf,.ll;1

R.\[S ~(AE 1 R1\IS ~[AE

0.020 0.015 1 0.712 0.811

8 0.021 0.016 1 0.542 0.836

16 0.021 0.016 1.093 0.936

•20

32

0.021

0.022

0.016

0.011

1.481

2505

1.031

1.448

46

Table 3.6 Effect of momentum on prediction ability of Ai'lN based BalI rvlodels

• ~lomeDtum~Iodel A (predicting log g) ~Iodel B (predicting/tlll)

ValueRMS MAE R.'\1S ~LU:

0.2 0.047 0.024- 1.756 1.112

0.3 0.039 0.018 1.426 1.0lO

OA 0.043 0.024 1.093 0.936

0.6 0.045 0.028 1.610 1.057

0.8 0.080 0.050 1.7:!1 1.071

Based on [his initial e:<ercise. the optimal configuration of the network for [he two ANN

b~lSed BalI models were determined and are shown in Table 3.7. The prediction performance of

the AJ.\fN models with ail learning parameters selected as detailed in Table 3.7 is illustrated in

Figure 3.3 as plots of AJ.\IN predicted vaIues vs. BalI table values. The predicted values were

very close [0 the BalI table values and were evenly distributed throughout the entire range.

CaIculated error parameters and R~ are given in Table 3.8 which show thar .o\1'fN models were

able to accurately predict Bail table parameter.

Table 3.1 Optimal levels of architecrural parameters for ANN based Ball and Stumbo

models

•

ParameterANN ~Iodel A ANN ~lodel8 ANN ~(odeIA &~ ~Iodel B

Ballmethod BaUmethod Stumbo met/rad Stumb(J melhod

~umber of hldden laycrs 2 2 2 2

~umber llf PEs in hidden layers 2&2 5&5 2&2 1&2

Epoch size ..f. g 4- g

~[omentum 0.3 OA OA 0.2

47

2

• ~ .. .. , ..

1

~0

Q

1-1

~2o Table data

+A~ prIIIctedGraphA

-3 1

0 50 100 150 200 250

thIU

2CO ,..----------....,..----_..--.,

150 ~

i 100 ~-

o Table data

+ ANN predicted

•

Figure 3.3

50-

Grpeh B ~0 ".

-3 -2 -1 a 1 2Dg;

Comparison of fu~~ predicted values and BalI table parameters respect to inputvariable

48

ANN BaU ~Iodel A ANN Bail Model BError parameters

Logg Process time /IIU Process lethality

lU.tlS 0.04 0.607 2.48 0.165

~IAE 0.02 0.458 0.66 0.084

~IRE 4.98 1.025 1.14 1.321R- 0.99 0.99 0.99 0.99

ANN Stumbo ~[odel A ANN Stumbo ~[odel BError parameters

Logg Process lime /,.IU Process lethality

R..',.IS 0.08 6.43 3.15 0.33

y[AE 0.06 5.06 1.35 0.241

~[RE 6.13 3.04 2.78 3.03 :

R- 0.99 0.99 0.99 0.99 i

•Table 3.8 Error parameters for ANN based Bail and Stumbo models

•

~Iodel verification

Figure 3A illustrates the results of validation of the developed models with a new set of

data which involved a wide range of operating parameters normally encountered in commercial

thennal processing operations (Table 3.3). The predict.ion error parameters are aiso summarized

in Table 3.8. For bath models (process time prediction. Madel A and process lethaIity

prediction. ~Iodel 8) the R: was close to unity. which showed excellent correlation between the

ANN model and Bali method. The associated mean relative errors for both process rime and

process lethality predictions were 1.0 and 1.3%. respectively. The mean relative error is more

meaningfui with respect to process lethality. while for process time. the mean absolute error (0.5

min) which indicates the error in user units (min) is more easily reconcilable. Over the range of

process time encountered (Up to 150 min). this represents a mean range ~rror of about 0.3%

which was considered smalI.

A~N based Stumbo ~Iodel

The various pre-processing constraints were aIso evaluated with respect to the Stumbo

model aIthough sorne could not he accommodated because of the smaIler size of the available

data. For example. since ooly 44 data pairs were avaiIable at eachj(:c value. the size optimization

49

• 200 r------------------.,

•1 100

lliCD 50ZZ< oANN.lue

20050 100 150

Bail pme•• Ume (min)

OL.----........-----""-----------o

o ANN \fÛue

~ 40 8C ~

Bali pme•• letharlty (min)

'ê"80...------------------...,l~!m1•18 40a-i3!2Q1i<O...~----L-----'-----"--------o

Figure 3.4 Validation of Ai'ffl models of BalI method

• 50

•

•

couId not be done. The required number of processing elements and the number hidden

layerswere optimized based on the RMS of eITors and MAE. Since the quality of data between

these [WO tables (BalI and Stumbo) were similar, optimal conditions with respect ta momentum,

transfer function. and learning mIe were expected ta he somewhat similar ta those achieved in

the .~'lN based BalI model. Aguin. 2-hidden-layer network performed considerably better than

I-hidden-Iayer networks. The optimal conditions for number of PEs were 2 PEs in each layer.

white for one of the Bali models. the best model had 5 PEs in each hidden layer. The appropriate

architecture of networks was also used to select the proper values for epoch and momenrurn. and

these were also slightly different. The differences in the architectural configurations were

considered [0 be the result of smaller size of data set available for Stumbo model. The optimal

conditions are summarized in Table 3.7.

The performance of the A~ based Stumbo models as a plot of ANN predicted value vs.

desired output vaiue is shown in Figure 3.5. The computed errors and the associated R~ values

are included in Table 3.8. The tïgure demonstrates an excellent agreement between predicted

and expected values with a high R1 value. The mean errors \Vere.. however. somewhat higher

than those observed with A1\4~ based Bail models. For Nlodel A. for example. the ~[RE was

6. 1~ for the Stumbo model as compared ta 5% for Bali model for log g prediction and 2.8% and

LI ct. respective[y for ft/U predictions. The differences were considered to be primarily the

resuIt of differences in the size of available data over a wider range of/ilU and the addition of jn:

as a second input. Accommodating these changes probably requires a larger training set. but the

number of data in Stumbo tables were far less chan that in Ball table. It was shawn earlier with

:\.'IX based Bali model that the perfonnance errors were quite high even with the availabiliry of

175 data points. It may thus be logicai ta assume a higher performance error with Stumbo

models.

The results for validating ..:\.L'lN models in the fonn of predicted vs. expected process time

and process lethality is shawn in Figure 3.6. With respect ta process lethality and pracess

lethality predictions. the associated errors (MRE) for Al'IN based Stumbo models. were again

3% while they were about 1% with Al'lN based BalI models. The associated R! were aguin very

high and the quaiity of predictions was excellent. The slightly higher errors with predictions by

the .-\i~ based Srumbo madels were again ascribed ta non-availability of adequate number of

data sets ta properly train and develap the Al'1N models. The associated errors were. however.

51

ModelA• 4

2 •••••••• • ,.• •0

ca

1-2

olegg .ANNlogg

~

0 200 600 800 1000 1200l1IU

Model B

1200

1000 o1hlU .ANN thlU -8QO

::)600~

400

200

0..e ·2 0 2 4

Iogg

•

Figure 3.5 Comparison of A..'fN predicted values and Stumbo table parameters respect toinput variable

52

500 ......------------------.••1300l1200Ü=;l5. 100ZZC e ANNWllue

100 200 300 400

Stumbo proc_ lime (nin)

O~----L..---...I..---......I.---""""'--_--'

a

21

eANN

1 10 11 20Stumbo process JethaIity (nin)

o L.....__--L ..L- .......__........ ""'"

a

21-------------------,

Figure 3.6 Validation of .Au'fN models of Stumbo·s method

• 53

considered low enough and demonstrate the utility of the Al~~ concept for simulating BalI and

• Stumbo process calculation techniques.

CONCLUSIONS

The feasibility of A.i~~ modelling for process calculations was evaluated in this srudy

based on their ability to simulate BalI and Stumbo methods. The Ai'lN roodels were able to

correlare the parameters of Ball and Stumbo tables with good accuracy (mean relative errors of

1-3%). [t \Vas found essential to optimize the network contiguration with an approprïare size of

training data set. and severa! learning parameters. The developed AJ.'lN models were validated

with a new set of data for process time and process lethality calculations covering a wide range

of commercial processing conditions. ANN roodels predicted the process time and process

lethality with mean relative errcr of 1% for BalI models and 3% for Stumbo models. The slightly

higher errors associated with .~'m based Stumbo modeIs were considered to be due to a wider

range of parameters and smaller size of available training data set as compared to Bali model.

However. the associated low errors and high R.! value with the A!\lN based models in simulating

BaIl and Stumbo data demonstrate a good potential for the development of A..:.'rN models for

process calculations.

•54

•

•

CHAPTER4

CO~lPARISONOF FODllJLA ~IETHOnSOF TllEDIAL PROCESS

C.-\LCULATIONS FOR PACKAGED FOOnS 1J.'l CYLINDRICAL CONTAINERS

ABSTRACT

Evaluating the accuracy of fonnula methods provides a basis for their use and a

better understanding of the effect of process parameters on the required minimum process

and hence on nutritional and sensory qualities of processed food. Selected fonnula

methods were tested for accuracy against a fioite difference model accommodating

different processing conditions (retort and initial temperarures. thermal diffusivity. process

rime 1 and package sizes within the range used in commercial applications. For selected

range of process conditions and container sizes. temperature profiles \Vere abtained using

an optimized tinite difference mode1 for conduction heat transfer involving cylindrical

shapes. Time-temperature data gathered were used for computing hcating and cooling

parameters If and j). l!sing these parameters and appropriate process conditions. process

lethalitytprocess lime was computed using selected fonnula methods (BalI. Steele & Board.

Stumbo and Pham). Prediction errors were computed based on deviations in process

tîme/lethality From the tïnite difference model. In addition [0 comparing them aver the

broad range of testing conditions. the sensitivity of the methods to selected process

parameters were evaluated. The parameters included retort temperature (11 Q-130IlC),

product initial temperature t70-90oa. thennal diffusivity of food product ( 1.0* 10-7-2* 10.7

m:/sL cans dimension (HID) and the unaccomplished temperature difference (g-valuel.

Retort temperature was the mast significant parameter affecting the associated errors for

the selected methods. Steele & Board~s method had the highest error of process rime

calcuIation with a ma."<imum 34 min over-processing for a l-hr process. Srumbo's method

had the highest accuracy. however in sorne cases. under-estimation of process time up ta 8

min for a l-hr process was observed. Higher g-values increased the caIculation errors and

can dimensions with HID near to unity had higher errors.

55

•

•

INTRODUCTION

Methods of process calculations are grouped into two main categories: General and

Formula methods. Using graphicai or numericai procedures. the General methods integrate

the experimentaIly gathered time-temperature data for lethal effects and therefore. this

group of methods is considered the most accurate one for test situations. However. for any

change in processing conditions. product formulation or container size~ a new temperature

protïle is required. For this reason their application has been restricted ta producr. package

and process specifie conditions. under which test data were gathered. Conversely. Formula

method~ are developed with less restrictive assurnptions on food product. package size and

type and heat processes. and within a certain range. they have the tlexibility for adaptation

to variation in test conditions. Therefore. these methods have become more popular in

food industry. The approach that Bail (1923) followed in establishing a method of process

calculation is known as the tïrst Fonnula method. After this work. extensive analysis has

been accomplished in enhancement of this type of methods. Formula methods have been

revi~wed by several researchers (Hayakawa. 1977. 1978: ~Ierson et al.. 1978: Stumbo and

Langley. 1966: Smith and Tung. 1982: Stoforos. 1997).

The accuracy of these methods has been the core of attention of many studies ta

assure the safety and economic aspects of the thermal processing. While the destructive

effect of thermal processes on microbiai population is desirable. their deleteriou5 effect on

the nutnents and quality attributes of the food product is undesirable. In addition avoiding

over-processing is a signitïcant step in energy conservation and economic aspects of

thennal processes. With respect ta growing application of computers in retort control. an

extensive knowledge in application of different methods of calculation becomes necessary.

This concept necessitates evaluation of the accuracy of these methods with different

process parameters. packaging size and type and product characteristics. Accuracy of these

methods should ideally be tested against data from real time-temperature profiles.

However. since such experiments are often expensive and mostly impractical over the

broad range of conditions encountered in food industry.. alternate methods of data gathering

has been sought.

56

•

•

In this regard. computer generation of data based on numerical soLution of finite

difference models has largely replaced the need to perform extensive heat penetration tests.

The study by Texieria et al. (1969) perhaps~ provided the first successful application of

computer assisted finite difference technique in thermal processing research. Since then

Mumerous srudies have made use of these technique (Teixeira and Ntanson. 1982: Datta et

al.. 1986: Tucker. 1991: Teixeira and Tucker. 1997). Today ir is taken for granted that

these techniques are as accurace as experimental tests when the appropriate processing

conditions. thermo-physical properties and boundary condition are incorporated into the

mode!. Since the performance of these models depends on the accuracy of input data for

the above variables. their accuracy should nevertheless be checked to make sure they are

compatible with the test situation.

The objective of these study was to evaluate the accuracy of sorne selected Formula

methods againsl a finite difference rnodel based on conduction heat transfer in canned food

product~. under a wide range of processing conditions as employed in commercial

applications.

Brief review of Formula methods

A few of the existing methods selected for eva1uation is brietly discussed in this

part. They have been detailed elsewhere (Chapter 2).

Ball's method

Intfoduced in 1923. Ball's formula method is the most widely used method by the

food industry. The temperature prediction equations are based on the observation that the

semi-Iogarithmic plot of temperature difference between product and heating medium

temperature tS a straight line mer an initial lag time. Achieved process lethality and

process time are computed from each other. using processing conditions (retort temperature

and initial temperature) and table or graphs of related parameters (jJIU and g).

Development of these tables and graphs was carried out with respect to sorne limiting

assumptions. which resulted in sorne inaccuracies in the method. The most significant

assumptions were a constant cooling lag factor (jee) equal to 1.41. and equal heating and

57

•

•

cooling rate indexes ifh=tl Obviously~ for processes deviating from these assumptions,

Ball's method will inaccurately compute the process lime or process lethality.

Stumbo's method

While revising BalI's method ta increase irs aceuracy, Stumbo and Longley (1966)

published a new set of tables with respect to the variability of jcc in real processes. The

procedure for process time and process Iethality calcuIation in this method is quite similar

to BaIl' s method. These tables were originally based on data from hand drown hem

penetration curves. On subsequent works, the parameters of table were reealculated

(Srumbo. 1973) using a finite difference solution to prediet the time-temperature data of

product. The equation applied in mis model was similar to what was used by Gillespy

11953) and identieal assumptions were used for solving them.

Steele and Board's method

This method was developed following recognition of inaccuracies in BalI's formula

method for thermal processes (Steele and Board. 1979). Based on the method developed

by Steele and Board. the tables to be applied in thermal process calculations were based on

~rerilization ratios rather than temperàture differences. These tables were obtained using

Simpson"s rule to solve the lethality equation. This sterilization value was defined as the

temperature difference between the coId point of me can and the heating or cooling

medium over the slope of the thermal death time curve for the rnicroorganism of concem.

Vinters et aL (1975) and Steele et al. (1979) introduced sorne polynomials to be used

instead of developed tables in programmable calculations and on-line computers.

Pbam's method

This method is a modified version of Stumbo's method (Pham. 1987 and 1990). and

is based on two ranges of sterilization values. For high sterilization values (in cases that

product temperature \Vas close to retart temperature) an analyrical solution was applied for

conduction heat transfer in a finite cylinder with infinite heat rransfer coefficients at the

container walls and unifonn initial ternperature. For low sterilization values a numerical

solution was used to solve these equations. Variability of jcc value aise was considered in

58

•

•

this method by calculating temperatures at different positions in the can. The variability of

th and 1~ was also considered in this Methode This method was tested against a finite

difference model simulating the center temperature in can (Pham. 1990) and the method

was reported to be at Ieast as accurate as Stumbo's method. The one table required for the

use of this method substituted the 57 tables in Stumbo's method using dimensionless

parameters.

~IATERIAL A1~ ~IETHODS

Finite difference program

A tinire difference program was wrirren in FORTRAi'i language and developed

primarily by Sablani (1995). This program was modified for conduction heat transfer

equation for cylindrical cano The measured process time and process lethality were the

reference values against which the selected Formula methods were cornpared. The finite

difference model was applied to generate temperarure profiles based on achieving a

selected heating lethality from which the actual process time (during which medium

temperature is set to heating temperature) and delivered process lethality (total lethality

calculated at the end of cooling) were computed.

The basis of tinite ditTerence models

The finite difference models were based on numerical solution of unsteady stare

heat conduction for an object of known geometric shape. providing transient temperature

distribution throughout the container. At the beginning of the process time. all the incerior

points of the cylinder were set to the initial temperature of the product. while the

temperarure at the surface was set at the reton temperature. With a known set of initial

conditions. these equations were solved at each time interval. The new temperature

distribution at the end of each time inrerval was used to set the initial conditions for the

following time interval. This procedure was continued for a predetennined process time.

during which the temperature profile of product was computed. The same procedure was

applied for cooling of the product by changing the ambient temperature to cooling water

temperarure and continuing the calculation process.

59

•The goveming partial differential equation for transient heut transfer into a finite

cylinder is as follows:

The initial and boundary conditions are:

(4.1)

T(r,h.O)=Tr

art o./z.n =0dr

aT( r.O.n =0dr

dTk..~=h~.(I: -T,)

or

at t=O

at DO and O<h<L

at DO and O<r<a

at r=a: O<h<.L and t>O

ark . ah =fz 'l' .lI: - T,} at h=L : O<r<a and DO

where:

T: center temperature (oC)

t: cime (5)

r: radial distance (m)

h: vertical distance (m)

a: r.ldius of cylinder (m)

L: half length of cylinder (m)

hf: t1uid heut transfer coefficient (W/m!.K)

~: cylinder thermal diffusivity (W/m.K)

CL: thennal diffusivity (m2/s)

Fiuite difference method is one of the techniques used to solve these types of

equations in which the partial derivatives are traDsferred ta discrete differences under

appropriate boundary and initial conditions. Carslaw and l aeger ( (986) indicated in detaiI

• the analyticaI solution of this equation. Two major criteria in soIving these equations using

60

•numerical methods are stability and convergence of the solutions. Convergence issue is the

convergence of the solutions of the difference equation to the solutions of the partial

differential equations as the time and space steps are made smaller. However. stability is

the question of whether numerical errors and round-off errors decrease or increase as the

computation rime increases. Although decreasing time step increases the convergence of

the solutions. it can affect the stability of the method. Since in numerical differences are

very small. and the subtracted value is divided by anorher very small value. the round-off

error becornes predominant when the step size is reduced beyond an optimum limita Bath

mentioned criteria depend on the form of initial and boundary conditions. The Crank­

Nicholson scheme was used for first and second arder spatial derivatives appeared in the

hem tlow equations and backward difference scherne for the first arder derivative in

boundary equations. An implicit method was used for time derivatives. Sinee transfonned

~quations contain temperarure values of next rime steps. it was necessary to employ

iterative technique in the solution procedure.

T0 evaluate the accuracy of finite difference solution of heat conduction and in

arder ta optimize the required rime step and space steps sizes. the time-temperatures

predicted from this model were verified against the data obtained from the analyticaI

solution of heat conduction in afinite cylinder. Ta evaluate the unsteady temperature in a

tinire cylinder. the solution of temperature ratios (Cf) under transient temperature for

infinite slab and intinite cylinder is applied as a tïnite cylinder is considered as intersection

of an Întinite slab with an infinite cylinder (Ramaswamy ee al.. 1982).

The equations for intïnite slab and infinite cylinder obtained by Carslaw and Jaeger

11959L For an infinite slab the equaüon is as follows:

•

- 2sin fJ ..U =L ,_ Il.. .cos(f3rtxl L).exp(-p:F,)

rr-I 13ft ~ SIn {3" cos Pif

And for an infinite cylinder:

where:

(4.3)

(4.4)

61

•l;: dimensionless temperature ratio =(T-Rn/(IT-TR)

RT: reton temperature (oC)

IT: initial temperature (oC)

T: temperature (oC)

Bi: Biot number

Fo: Fourier number

~: root of the characteristic equation (4.3)

y. root of characteristic equation (4.4)

x: distance from the coldest plane of a slab

L: thickness or half thickness of a slab depending on it being heated or cooled from

one side or both sides. respectively (m)

r: radius of a cylinder (m)

a: significant dimension. the radius of cylinder

ln: Bessel function of arder zero

\Vhen the heating rimes are sufficiently long (Fo>O.2t the series expansion of

equations -1..3 and -1..4 converges rapidly. and U can be estimated accurately by the tïrst

terro of the series. Therefore. the above mentioned equarion of 4.3 and 4.4 for the center

temperature in center of an infinite slab will be simpHfied as follows:

(4.5)

And of intïnite cylinder:

Rp• R. Sr and Sc are the characteristic functions of Biot number and their value is constant

for heating condition with infinite heat transfer coefficient (R,r1.273. Sp=2.467. R~-L602

and Sc=5.783t Therefore. the unsteady temperature at the center of a finite cylinder (UtJ;c)

can be obtained From soluùon for an infinite slab and an infmite cylinder:

• U"fi: =Uup .uue

(4.6)

(4.7)

62

The general equation to describe the temperature CT) as a function of rime Ct) during

• heating or cooling periods with known initial temperature (m and ambient temperature

(Rn is as follows known as the BalI equation:

log<IT - RTl) =-t1f + loge j(11T - RTl) (4.8)

Paramerers of f and j are known as the heating or cooling rate index and lag factor.

respectively. These parameters can be obtained from following equations:

j=R,,,.R,

(4.9)

(4.10)

The center temperature in a tinite cylinder was calculated through equation 4.8 to 4.10

(anal ytical solutions) and the temperature profiles from the finite difference models were

compared against the analytical solution of BalI equation. Along with the computation

time of the model.. the R.\IS of the error between the tinite difference model and analytical

solution. caIculated as below. were used as two criteria of model optimization:

where:

RiWS of

1 rt

~L{~1lOd!i. - T.uw,..ncui"

errors= ...;.,1"=...;.,1 _

n

(4.11 )

T;maiyn...~: temeprature predicted by analytical solution (oC)

Tmode= temperature predicted by finite difference model (oC)

i: each time step (Sec)

n: number of points

Five different time steps of L 5. 10 and 20 seconds and four grid sets in both of

horizontal and vertical a:ds (5&5. [0&10. 15&[5 and 20&20) were examined.

•63

•Overall accuraey evaluation of the formula metbod

A wide range of processing conditions and commercial can sizes (15 can sizes)

were emplayed as testing conditions for the finite difference program ta obrain the required

time-temperature data The finite difference model was programmed ta change the

medium temperature from heating to cooling based on a selected heating period lethality

(Ffi) in the range of 5-15 minutes. Each run of the program would provide the proeess

rime. process lethality and the temperature profile of the product at the cold point of the

cano

From each temperature profile. heating and coaling curves were separated in the

forro of logarithmic temperarure difference of the product and medium vs. proeessing time.

Determination of j and f values for heating and cooling were based on repetitive regression

to [oeaee the straight portion af heating or cooling. These values along with process time or

process lethality obtained from finite difference program were compiled in a Lotus based

program. Process lime and process lethality for selected Formula methods were calculated

using a computer program developed for this purpose (Ramaswamy. 1991). Deviations

from tinite difference model values (reference vaIues) were determined as follows:

F -F .E"or = '" 'Il' ) ,Il mllth"c;'. 1 xl00F"t,r:r J

(4.5)

•

The same method was applied to evaluate the deviations in process time

calculations. A negative percentage deviation in process Iethality demonstrates an

underes[Îmation of the lethality with the respective Formula method (and hence

undesirablet where a positive error shows inaecuraey on the conservative side. For

process time computations. on the other hand. positive errors show underestimation of

process time (and hence undesirable). while negative errors show overestimation of

methods. but on the safe side.

The accuracy evaluation of the methods was performed from two perspectives.

First.. the accuraey of methods was compared as a fonction of one parameter. while the rest

parameters had a constant value. In the second approach. the accuracy of eaeh method was

evaluated for each variable parameter over the eotire set of data.

64

•

•

Evaluation of formula methods onder specifie conditions

Accuracy evaluation of the methods was based on the g-vallie and cao sizes in fonn

of height over diameter (HID) as these were reponed eaclier as conditions under which the

methods deviate from reality (Smith and Tung. 1982). A reton temperarure of 12DoC and

initial temperarure of S013C were considered. As the tables in BalI and Stumbo methods

were based on the assumption tbat cooling water was 1OO~C below reron temperarure. the

cooling warer temperature was flXed to 20°C. The instantaneous come-up time to retort

temperature and instantaneous drop in medium temperature to the cooling water

temperature was assumed. Heat transfer coefficient of 5000 W/m~C was assumed for

steam as the heating medium and 500 W/mlC for water as the cooling medium. Thermal

conductivity of the product was constant (0.6 W/rnC) within the simulation. In order to

evaluàte the effect of g-\.'alue. the finite difference model was programmed to change the

medium tcmperature from heating to cooling based on reaching different g-values in the

range 01'0.05-15 cù•

RESTJLTS .<\l'ID DISCUSSION

Optimization of tinite difference model

The optimization results of the modeI are shown in Figure 4.1 based on the number

of nodes. both in venical and horizontal axes. as weil as time step size. Increasing the

number of nodes in each a.'(is increased the computational time due to additionaI

caicuIations ta be perfonned for center temperature prediction. Smaller increments in the

axes increase the accuracy of model in temperature prediction. aIthough as shawn in the

Figure ·t l. after an initial sharp drop from 5 nodes to la nodes. increasing the number of

nodes further had less effect. With this respect. a 10 by 10 grid size was selected as the

optimum number of nodes in both a'(es. Same trend was applied to select optimum number

of rime steps used in computation. As computation time was increasing intensely for time

step sizes less than 5 and Rl\tlS of error was not changing significantly for variation of time

steps below 5 seconds. a 5 second time step size was assigned as the optimum vaIue for this

pa.rameter in modeI.

65

• 8 2.5

7 •ta 1

-2';6 :

E 11

i= 5 .. 11 ~

- 1.5 eëa 1

1~

! • CDc 4 1.2 / 0-; i ~ 1 Cf)

"5 3 ~ /' ~c.. CI:E 2 ~a ,// - 0.5U /1 .,",•a 0

a 5 10 15 20 25

Number of grids in each axis

-- Computational time -.- RMS of error

~.5 0.79;a

~ O.ïS4 -~ 0.77

3.5 - .- - 0.76CI)~- 3 - 0

Cl) - 0.75 ~

:§~

2.5 1

- 0.74'Q)

0(ij 2 il - 0.73c "; CIJ.2

1 5 - 0.72 ~êti - cr:'S - 0.71~

, -~ 0.7E '.

0 0.5 -~ 7 0 .69

0 • •0 0.68a 5 la 15 20 25

Time Step

•

Figure 4.1

_____ Com putational tim e --.- RM S of error

Optimization of finite difference model for a) number of nodes in each a..us

and b) time step

66

•

•

Mter optimization of the modeL the predicted temperature profiles based on finite

difference model and analytical equation were compared with each other to validate the

accuracy of the finite difference model. The result of validation is depicted in Figure 4.2 in

the farm of center temperarure profiles. The discrepancy at the beginning of the heating is

for the situation when fo<O.2 under which the two procedures were not expected to match.

However. the predicted temperatures ufter this initial deviation coincide with each other.

This should be expected as the main basis of heating equations used by each method is in

agreement \Vith the experimental data. A perfect overlapping of these two methods in this

section of time-temperarure curve demonstrate an excellent accuracy of the finÎte

difference model.

Overall evaluation of formula methods

Overall evaIuarion of selected formula methods was carried out in two directions.

First ail the considered parameters were maintained at a base condition (RT=I:!O°C.

lT=80ù C. a=1.5*IO·7m!/s and can size=303 x 509) and one pararneter at a rime was vaIied

over a selected range. Errors in process rime and process Iethality calculation were

calcuIated as relative errors (percentage deviation from reference values). Subsequently.

each parameter was'varied over the entire range with respect to ail other conditions and the

associated errors were calculated. Tables 4.1 and -t2 summarize the results of errors

associared with different models for each parameter at the base condition as weil as the

overall. [n process tinle caIculations (Table 4.1). retort temperature was the most

intluencing factor compared to product initial temperature and thermal diffusivity for a can

size 303 x. 509. Associated erroTS varied From a high -7 to -21 % for Steele & Board

method to -0.7 to -1.5% for Stumbo's method. Balrs method was close ta Steele & Board

moditïcation. while the method of Pham had errors varying from -1.5 to -8.3%. The

higher errer in process rime using the Pham method was the result of using processing

conditions and can size which resulted in high sterilization values (U(fh<O.04). below the

range of studied by Pham. Sïnce the developed process calculation equations (Pham. 1987)

were for a defined range of sterilization ratios (U/fh: 0.04-1.5). processing conditions.

which do not satisfy this range. cao result in high errors in process calculations. With

reference to initiai temperature and methods of Bail and Steele & Board

61

•140 "T""l----------------

l/ AnaJyti:aJ solution

li

40 i/

120 ~11

-1ooJo .;.-'-----t~",~ 1

~ 80 ~~ ,

- !ca~

~ 60 1EQ)

f-i,,:

20 .f

605020 30 40

TIme (min)

10

1o ~I _L... ~-----

o

Figure ·tl Validation of finite difference model against the analyticaI solution

•68

•had errors between -5 and -10%. With process lethality calculations (Table 4.2)y retort

temperature was the major factor: howevery thermal diffusivity and initial temperarure were

aIso factors influencing the accuracy of methods. An increase in thermal diffusivity

improved the accuracy of method~ while an increase in retort temperature increased the

associared errors.

Table·t 1 Errors in process time calculation intluenced by processing conditions and

thennal diffusivity of product

f u a*107 IT RT Cao Proc:ess time ~leaD Relative Enor (%)

tmint tm!/sl tOC) (oC) Sïze Steele Bali Stumbo Pham

5 1 70 110 303 x 509 -7 -6.8 -I.S -1.55 1 70 120 303 x 509 -15.5 -Il.S -0.8 -2.25 1 70 130 303 x 509 -21 -17.5 -0.7 -8.35 1 70 110 303 x 509 -8 -6.8 -1.5 -1.6

5 1 80 110 303 x S09 -9 -7.5 -0.9 -0.85 1 90 110 303 x S09 -10 -8.7 -1.5 -0.-+5 1 70 110 303 x 509 -8 -6.8 -1.5 -1.65 1.5 70 110 303 x 509 -6.7 -S.5 -0.3 -0.75 2~O 70 110 303 x S09 -6 -S.5 -O.S -0.5

Table +.2 Errors in process lethality caIculation intluenced by processing conditionsand thermal diffusivity of product

Fil a*107 IT RT Cao F0 Relative error (% )

(minI tmz/s) (OC) (oC) Size Steele Bail Stumbo

5 1 70 110 303:< 509 20.3 17.0 3.8

S 1 70 120 303 x 509 56.6 -1-7.6 4.35 l 70 130 303 x 509 80.0 73.0 -+.25 1 70 LLO 303 x 509 20.3 16.0 3.85 1 80 llO 303 x 509 20.7 17.0 2.85 1 90 liO 303 x 509 21.5 18.0 3.3

5 1 iD lIa 303:< 509 20.3 17.0 3.85 1.5 70 lIO 303:< 509 13.2 il.5 0.55 2.0 70 110 303 x 509 10.[ 10.0 l.1

•69

•

•

Compared to the process rime. the mean relative errors associated with process

lethalities were much higher because of prediction of fixed low process Iethality of 5.0

minutes (while the process rime varied from 25 to 400 minutes). Bail and Steele & Board

methods over estimated the process lethality by 17 to 80% with respect to the reton

temperature. while the error range with respect ta initial temperature and thermal

diffusivity remained at 10-20%. Stumbo·s method was fairlyaccurate with error ranges up

to ~%. Initial temperature and thermal diffusivity have been reponed ta only have

minimum effect on calculation accurney (Ghazala et aL.. 1990: Smith and Tung. 1982). In

general the relative arder with decreasing accuraey was Stumbo. Pham. BalI and Steele &

Board. [t is interesting ta note that ail mean relative eITors were negative for process time

and positive for process lethality. indicating errors generally on the eonservative side for ail

the methods.

In arder ta study the overall effeet of each parameter on process caleulation over a

broader range of processing conditions. mean and standard deviation of eITors for cach

specitïc parameter was calculated and summarized in Tables 4.3 and 4.4 for process time

and process lethality calculations. respeetively.

[n process time calculation. retort temperature and length of processing time were

more obvious parameters affecting the accuracy of methods. An increase in retort

temper.lture. increased the error terms for ail the methods. except for Stumbo·s methed.

which had the lowest error without any specifie trend in mean values. AlI methods

overestimated the process rime. as shawn by the negative sign for mean errers except for

Stumbo's method. whieh underestimated process time under sorne conditions. Sorne

~arlier researchers have observed similar results. However. it should aIso he noted that

Stumbo's method was in faet most accurate amongst the different methods. The mean

errors were less than 1% for ail situations. On an average. this accounts for a 2 minutes

error over a 100 minutes process time. obviously smalI. In comparison. BalI and Steele &

Board methods had up to 15 and 20% over estimation~ respectively. Pham's method was

close to Stumbo·s method.. with mean errors mostly in the conservative side. However. as

indicared by the aceompanying standard deviations of me mean errors (up to 2%). it is

logical to assume situations did erist for over estimation of process time. As discussed

70

•earlier. larger errars of high retort temperatures using Pham method is due ta resulted

steriliza[ion values. which were not defined by Pham (Pham.. 1987. 1990)

Table 4.3 Means and Standard Deviations (SD) of relative errors in process time

calculation for selected process calculation methods

Steele BaIl StumboParameter Range

~Iean sn }Iean sn Mean snPham

~Iean sn

-15.64 3.46

Retort

temperature

llO(ÙQ

120 (iJC)

130 (oC)

2.44

-12.93 3.66

-19AO ·"-~3

-6.20

-9.91

3.06

2.71

0.71

-0.55

lA3

0.64

1.19

-0.25

-0.35

-3.36

0.51

0.90

2.62

Initial

temperature

70 (llC)

sn (oC)

90 (üC)

-1l.3 5.25

·12A5 6.00

-14.63 7.62

-9.55 3.92

-10.57 ~.48

-12.48 5.66

OA8

0.32

-0.16

1.56

1.5S

1.85

-1.76

-1.5 1

-0.69

2.20

2.18

2.01

Thermal

diffusivity1.5*10'- tm=/sl ·11.58 6.34

!* Hr~ 1m=/st -1l.34 5.97

-11.51 5.20

-10.93 ~.97

-10.08 .t.3t

-0.21

0.24

0.61

1.34

1.65

1.93

-1.83

-1.25

-0.87

2.75

1.95

1.56

Small -11.21 5.85

Mc:diurn -[OA3 6.60Can Sïze

Urge -13 fi.51

-l.OII ~.39

-9.65 5.16

-10.38 .t.74

O...B

0.81

0.21

2.08

2.12

1.19

-1.05

-O.S7

-1.12

1.58

1.76

2.·H

-15.78 5.05 -12.71 .1.28Processing

time

Lûw

~{edium

Long

-Ll.8

-8.83

5.57

5.06

-9.34

-7.87

3.67

3.76

-0.03

0.51

0.58

1.14

1.31

2.06

-1.80

-0.79

-0..11

2.L0

2.10

l.I7

•

Based on tiU weieht: small: (<0.5 kg). ~ledium: (0.5-1 kg). Lan!e: (>1 kg): Processine..... -..... ...... """ -....,;

rime: Low: I<LOO min). Average: (100-200 min). Lang: (>200 min>

Trends observed with process lethaIity were similar (Table 4At Conditions which..

under estimated process rime. obviously over estimated the process lethality and vice versa.

With process lethality_BalI and Steele & Board methads had up ta 70% over estimation.

~lethods of Stumbo and Pham perfonned better with mean errors less than 7%.

Table 4.5 summarizes the parametric range.. mean and standard deviation of errors

for combination of parameters. The maximum error in process time caIcuIation belanged

to the method of Steele & Board with about 37% mean relative error. while methad of

Stumbo had only 5% ma'<imum mean relative error. However~ as it tS been reported

71

(Smith and Tung. 1982~ Ghazala et al.. 1990) there were sorne cases that Stumbo·s method

• under estimates the process tirne as shown in Table 4.3 with a positive sign.

Table ~A Means and Standard Deviations (SO) of relative errors in process lethality

calculations for selected process calculation methods

Steele Bali Stumbo PhamParameter Range

~Iean 50 ~Iean sn ~(ean SO Mean sn110 ("C) Il.36 7.20 ILL:! 5.70 ·0.81 3.95 ·0.23 ~.~o

Retort120 (ûC) ~O.7i Il.66 33.03 10.70 1.88 ., .... 7.07 ~.18_ • .).J

temperature130 (oC) 70.9 8.15 57 6.66 ·3.2 6.86 29.85 LO.12

70 (oC) ~O.3Î 25.66 31 ..22 19.06 -2.06 5.31 -0.25 0.35

Initial80 ("C) ~0.85 25.85 31.62 19.19 ·l.09 J.SI -0.22 0030

temperature90 ("C) ~tA3 26.34 31.73 lq.~5 0.95 5.06 ·0.15 0.25

,(-[O' (m-/si J5.68 26.13 31.85 19.36 0.36 5.20 ·0.23 0.29

ThermalL5:k IO'~ 1m:/sl ~O.~9 25.37 31.35 19.16 -0.75 -f..91 -0.25 0.38

diffusivity -2-10' Imïs) 36.87 25.21 31.51 19.16 -1.~5 5.32 -0.19 O.2-f.

Small 36.J6 25.21 31.85 19.61 -0.69 5...f.4 -0.29 0.39

Cao Sïze ~Iedium ~1.5~ 25.82 30.58 19A3 -0.66 ~.81 '/).16 0.23

L1rge 50.76 .;s.31 32.71 17.65 -0.94 5.37 -0.17 0.22

Law 55..33 18.86 ~2.26 16.30 ·0.63 5.81 18,46 13.77Processing

y[edium 36.83 ~.j8 25.62 16 -0.6:! J.83 ·n.33 O.~~time

Long 16.63 17.58 15.62 13.69 -(.09 J.l:! -0.19 0.24

Based on till weight: smaII: (<0.5 kg). Medium: (1-0.5 kg). Large: l> 1 kg): Processingtime: Low: t<lOO min). Average: (100-200 min). Long: l>200 min)

Table 4-.5 Ma'<imuffi. minimum. mean and standard deviation of errors for different

methods

%Error in process time caladatioDS %Error in process lethality caJculatioDS}[ethods

}[jn ~Ia.~ }Iean sn Min Ma~ ~Iean snSteele l.75 37.60 18.44 -+.21 2.02 89.09 41.01 25.99

BalI l.63 26.31 15.61 3.29 0.75 68.02 31.57 19.22

Stumbo 0.01 5.18 1.03 0.69 0.06 19.05 2.60 3.50

• Pham 0.00 8.64 2.71 2.18 0.04 6.05 0.60 0.60

72

•

•

Specifie evaluation of formola methods

Errors basecf on the can shape or HID ratio had a consistent pattern for different

Formula methads. The results are presented in [WO different fannars for comparative

purposes. First the different methods are compared at a given g-value. Then each method

is compared at different g-val[les~ In both situations HID raüo was used as the basis~

The comparison of different Formula methads at a given g-value is shawn in

Figures -1..3 and 4.4 for the process time and process lethality calculations~ respectively.

The maximum error for almost all the methods was observed for HID near to unity. Smith

and Tung (1989) and Pham (1990) observed the same trend in error patterns. Steele &

Board's method had the largest errors (-2 ta -20%) arnong evaluated methods and

Stumbo's and Pham's methods were the most accurate methods. Stumbo's method

predicted process time wirh accuracy of 1% for g-value of O.05°C and 9% for g-value of

1SoC and Pham's method had similar accuracy in process time calculation. They appeared

to deviate from each other more at g=15t)C.

Trends were similar with respect to prediction of process lethality except that the

errors were on the opposite side. Steele & Board method had the highest positive error

120-ïOce) while Stumbo's method had the least (<20% L Pham's method as suggested is

ûnly for ~stimation of process rime.. and for process lethaIity~ the method hàd to be solved

using a trail and error approach. While this approach was employed for sorne test

situations. it was not possible to extend this approach for aIl the test situations because of

the time consuming iteration process. Since methods of Pham and Stumbo were reported

be similar in most cases.. similar trends could he probably assumed for predicting the

process lethality.

With respect to sterilization values.. Lenz and Lund (1977) also considered

processes with large g-\:alues uncertain. The larger errors for processes at large g-values

are due ta accomplishment of a large part of sterilization during cooling section. In these

processing conditions. cooling time and also the product properties during cooling can be

the reason for the high errors in total sterilization value of the process~ However. for

processes with smaIler g-values~ which is more common~ the error values are small ranging

from 10% for Steele and Board~s method to 1% for Stumbo and Pham methods.

73

• a Il 0• -0.5 SIIrio

~ ·1_ ·1-. FhIm1·1.5""'= ·2

·2 1-3a: .2.5

\sz:::::.a:~

~:::wi~ t~~

~ ~ ·7~.5 ...

0 2 3 .- a 1 2 3 .-~rItiD HDratiD

c 0- ·2 Phan~

Î ~~Ia: -8t -la~~e~ ·12

·140 1 2 3 4

HOratb

42 3

HO ratio

e 0 ----........--~- .....

# ·5'ii ·10~1 ·15

;! ·20

·25 .......--------.....o4123

HO'"

·20 ---------....o

d 0 ~-------.....,

~ ·5

Îa: ·tO

t -15~

Figure 4.3 Errors in process time calculations for different g-values (a: g=O.OS C, b:g:I C: c: ~=5 CO: d: g=lO CO: e: !l=15 CO).... ... ,... ....

•74

• • 10 b 259~..8 2D ;;:.-.....-~ 7 lr 6 j'---..W l 15

5 'j'--i..f &f

f4

1103

~ 2 51

.. .A. A..su.t.o SUrDo

O. A ....... .. ~0 -0 1 2 3 4

0 1HD~ 3 4

HDr6

e ~

C~...#"35

""':30~~125

.f20f 15~ 10

SIuntlo5

.........MIJr •••00 2 3 ..

HO,.

d 70 e 1)

60~.. 70 •

lso ~fJ) ::~::::::-ÎC ~~ -19)0 ~4J ..ÂM6• .....~U.30

f20 1\... SbmIo I!J~ .... ~3J

10 10a 0

0 1 2 3 .. 0 1 2 3 4HDrd:I HO'*'

•Figure 4.4 Errors in process [ethality caIculations for different g-vaIues (a: g=O.05 CO"

b: g=L CO; c: g=5 CO; d: g=LO CO; e: g=15 CO)

15

•

•

The effect of g-value on deviations in calculation i5 a1so due to temperature

difference at the end of heating between heating medium and the product. For smaller g­

vallies. when the product temperature and retort temperature at the end of heating are close

ta each other. the effect of temperature gradient i5 insignificant. However. for Iarger g­

values. when this difference is Iarger. this effect can cause errors in calculation. In this

case. while the reton temperature IS changed from heating ta cooling water. there would be

a longer lag for center of the can ta receive the effect of cooling water temperature. and

even after cooling was began. the center temperature will continue increase for a short

while. ~one of the Formula methods correctly account for this effect and deviate from

reality at larger g-vaLues.

Figures 4.5 and -k6 show the performance of each formula method for at different

g-vlliues. The effect of g-vallie on each method cao be seen more clearly in this

presentation. With an increase in g-value. the associated errors for each method increased.

showing a systematic increase in crrors for methods of Bail and Steele & Board. With

respect to Stumbo and Pham methods. the errors were smalI up to a g-value of 5ù C. but

then the inaccuracy begins ta increase markedly. Again Srumba and Pham had the highest

accuracy. The deviations in process lethality and pracess rime prediction increased for HID

close to unity and for Iarger HID values the eITors decreàsed.

ï6

• • la70 ........... ...... 1.1'

l 60

Î '0 1-10

l 40~66,*

130 ..... r'

20 ............ -- _riCI:

la .' ....... • • • r O•O'a

0 1 2 3 4

HID ratio

b 70

80 ga15

l 50~g.tal 40

0

~..'*"- 3D gaS

1 ....20

~ w''' ••• •• • "a110 .' ...... • • • ,aO.05

00 2 3 .-

HJD ratio

C 40

3' v:--- .... ri'

- 30~

Î 2'

0 20 A.UNII.

115• If te 1-10

CI:10

5 r'rI

01-0•05

0 1 2 3 4

HJD ratla

•Figure 4.5 Errors for process lethaIity calculations with respect ta different g-values (a:

Steele & Board's method. b: Baies method: c: Stumbo~s methad)

n

• • 0 b 0

::;:: Il MI • ••• ro·O! ·2:::::::: • ••• ,.0.05

l.,

••• r l - -4'# ~

•• .-rl••• - ~rSÎ ·10 ~,., Î ..&: &: -10

~rloI-U riO 1'12-14

cr .10 ~r15 c .16 ~ru-II

-1$ -200 1 2 3 .. 0 1 1 3 ..

IfDrIIb HOrIID

c 0rl

d 0

-1 ·1 rI·1

..,l ·3 l-Z

Î ... riO Î -]5: ·S o -4

~

i -6 ,-'-1•cr .. «~

-9rU -1

-10 ..0 2 ] .. 0 2 3 ..

HDrIdD HDrIIIID

•

Figure 4.6 Errors for process rime calculations with respect ta different g-vaIues (a:Steele & Board9 s method!' b: BaIl's method: c: Stumbo's method: d: Pham9 smethod)

78

•

•

CONCLUSIONS

The accuracy of selected formula methods was determined with respect to data

generated from a tïnite difference model. Finite difference models have the potentiaI for

accornmodating variations in processing conditions and cao size. and provide data for a

wide range of processing conditions. The optimization of the fioire difference mode1

against an analyrical solution of hear transfer equation with lOx 10 grid size predicted

accurare cemperature profiles. Process caIculation eITors were evaluated based on the

variation of each paramerer. Retort temperature was one of the most major parameters

intluencing the accuracy of the selected process calculation methods. NIost methods

overestimated the process rime with the exception of Stumbo's method for sorne cases of

underestimation. Based on the cao shapes. errors had an increase for HID values near [0

unity. Errors increased at larger g-values. where a substantial amount of process

sterilization is accomplished during the early cooling stage. This trend in errors was

observed for aIl the methods. Stumbo·s methad was considered the mast accurate method.

following it was Pham's method.

79

•

•

CHAPTER5

ARTIFICIAL NEURAL NETWORK MODELS AS ALTERNATIVES TO

THERi'lAL PROCESS CALCULATION ~IETHODS

ABSTRACT

Artificial Neural Network (ANN) is a computing system capable of

processing information by its dynamic state response to extemaIinputs.Al.JNs

learn from examples through iteration by adjusting the internaI structure ta

match the pattern between input and output. In this study, finite difference

simulations, which are widely recognized as' practical alternatives to

experimental methods, were used ta generate temperature profiles for a wide

range of can sizes under variaus pracessing conditions. The time-temperature

data were used ta compute the process lethality, process time as weIl as heat

penetration parameters: 1:, ilt, t: and jer:. These data were used for developing

the Al\fN models (bath training and testing). The accuracy and ability of ANN

models were compared with selected Formula methods, bath with respect ta

process time and process Iethality computations. Process calculation results

from ..~\fN model were comparable to Pham's and Stumbo·s methods, which

\vere previously evaluated as the most accurate amongst the process

calculation methods.

80

•

•

INTRODUCTION

Artitïcial Neural Networks (ANNs) have been the focus of interest in many diverse

tields of science and technology. Neural networks are basically computer models. which

simulate very simple abilities of our brain. Rather than being programmed for use in a

particular application, neural network models generate their own mIes by leaming from

provided examples. Al.'IN has the ability of approximating arbitrary continuous functions

based on a set of given observations. As they obtain this ability through the stage of

learning. they are known as truly adaptive systems, which do not need any prior knowledge

of the nature of relationships between the set of parameters. A.1'lN models are thought to be

robust to noise and inconsistencies in data. rendering them more advantageous compared to

empirical models. Also. AJ.'1N models can be multiple-input and multiple-out (~IThIO)

systems fBaughman and Liu, 1995). Therefore, variability of multiple parameters in the

development of an AJ.\fN model is possible. NeuralWare (1995) provides a wide overview

of potential applications of neural network as classitïcation. prediction. data association

and optimization. Most food related work involves estimation. prediction and control

(Eerikainen et al.. (993).

\Vîrh respect to ANN characteristics and their abilities in modeling. their

application has been considered in the development of a general model in thermal process

caIculations. Accurate detennination of thermal processes is required \Vith respect ta

assurance of safety. as weil as retention of quality attributes and nutritional values of food

products. For this purpose. different methods have been developed for facilitating thermal

process calculations. AIl these different methods are aimed at determining the lethality

(F,,) for a given process or calculating the process time for achieving a given process

lethality. [n arder ta establish thermal processes.. time..temperarure data of the product

undergoing the thermal processes is required. ~[ore versatile. less expensive and less rime

consuming alternative of experimental procedures are mathematical models.

Finite difference models of heat transfer inco packaged food have been successfully

applied in optimization and control (Teixeira et al. a. b~ 1969: Dana et aL, 1986: Teixeira

and Manson. 1982: Tucker. 1991: Teixeira and Tucker. (997). The main feature of these

models is the prediction of temperature profùe based on the goveming heat rransfer

81

•

•

equations of packaged food products. Fmite difference rnodels require sorne specification

of the food product and system such as thermal diffusivity of the food product.. heat transfer

coefficient of the heating or cooling medium and thermal conductivity of package. When

these conditions are known.. the time-temperature data can he obtained at any specitic point

of the packaged food product for any processing condition and package sizes. The ease of

use of tinite difference model can he considered in providing an expanded data set.

including a wide range of parameters.

In Chapter 3. the patentia! of Al'IN to simulate two of the rnost widely used process

calculation rnethods was demonstrated. In Chapter 4. the prediction errors associated with

the available process caIculation methods were evaluated using those computed from a

tïnite difference numerical model as reference. Ir was shawn that the prediction errors vary

depending on the processing conditions. and hy far Stumbo and Pharn·s method are the

most aCCUïJ.te. In Chapter 4. a basis was aIso established for generating parametric vaIues

~uch asJh.j~.jc-L· andi:h for various operating conditions involving different retort and initial

product temperature. thermal diffusivity of the product and can size as well as the

associated process time and lethality. This provides a wide range of input-output

parameters for establishing and/or verifying useful process calculation modeIs such as chey

are airned in the present research-an A1'J~ based process calculation mode!.

Hence. the specitïc objective of mis chapter was to develop an AJ.'lN model as an

alternative to existing thermal process calculation methods using the wide range of data set

obtained from the appropriate finite difference models and initial conditions.

~lATERIAL A1~ ~IETHODS

Data generation

ln arder to obtain the training data set for Al'lN models development. a wide range

of processing conditions. product characteristics and packaging sizes were considered as

detailed in Chapter 4 and summarized in Table 5.1. The defined range of each parameter

covered the cornmon range of processing conditions. and different cao sizes were selected

from those used in industry. A fmite difference program wrinen in Fortran language

82

•(Sablani. 1995) was applied ta obtain the related time-temperature profile ta each set to

conditions. This model was based on the conduction heut transfer for cylindrical packaged

food products. The heat transfer coefficient of heating medium (steam) and cooling

medium (wacer) were assumed ta be 5000 (W/m2C) and 500 (W/m2C).. respectively. Each

combination of detïned values was applied as the initial inputs of finite difference model to

obtain the respective temperature profiles.

Each time-temperarure profile was divided into two semi-Iogarithmic curves of

heating and cooling. In order ta locate the beginning of straight Hne in each curve an

Iterative regression technique was applied andfh,!ctjn: andjch were obtained for each set of

condition. Hence a data set was obtained which.. consisted of processing condition (initial

remperature. reton temperature). can size (height and diameter). product characteristic

(thermal diffusivity). process time. process lethaliry and respective heating and cooling

parameters. This data set with 1215 data records was considered as the basis for A1'iN

models training.

Table 5.l Range of parameters used in finire difference program

Retort Temp.. l Initial Temp. Thermal diffusivity Heatiog lethaHty(oC) (oC) *I01(m2/S1 (min)110 70 1.0 5.0120 80 1.5 10.0130 90 2.0 15.0

Cao size no. 1

Cao size , Approximate fill wt. (kg) Radius*Hieghtl2(cm)

'6z 0.170 2.70:< ~.50, : 8 z taIl 0.240 3A·l :<~.13.... ; ~o.l picnic 0.300 3..1.1 :< 5.08~

~ : No.211 cylinder 0.370 3.41 :<6.195 ' No. 300 0.410 3.81 :< 5.046 No.l taH 0.454 3.89 :< 5.957 ' ~o.303 0.454 4.05 :< 5.56S ~o.303 cylinder 0.595 4.05 x 7.079 ~o.l vacuum 0.340 4.]6 x 4.2910 : No.l 0.568 4.36 x 5.80II ~o.2 cylinder 0.738 4.36:< 7.3012 No.2 ~/2 0.822 5.16 :< 5.9513 No.] cylinder 1.420 5.40:< 8.891~ No.5 1.645 6.51 x 7.1515 No. 10 3.000 7.86:< 8.89

•83

•

•

A.J.~N model development

A precise ANN model training requires selection of independent input variables

(Baughman and Liu. 1995). If a prior relation between input variables in not available. one

of the proposed methods to select the independent variables between input variables. is to

discard one variable and train the Ai'lN mode1 based on the remained set of data.

Obviously. discarding variables. which are function of the other. will not affect the

training. However. when a science of relation between variables is provided. this

information should be applied to reduce the number of input variables and increase the

accuracy of A.l~~ modeI. Based on the infonnation obrained. while developing Al\iN

model for methods of BaIl and Stumbo. the key variables for relating process time (g­

value) and process lethality (f,/U) were considered as the major inputs. As the variation of

j({' values is oot integrated. therefore jn: was considered as another independenr input for

each model.

Input variables (g-l/alue or f,/U) were calculated based on the procedure applied in

the Bail method (Figure 5.1). Accordingly. the combination of these variables is used in

forro of log g or fi/V. alang with variability of jl"C related the process time [0 process

lethality or vise versa. The procedures of .~\i'N model development were followed much

closely [0 the A.l\l'N model development of Stumbo's method. The data set was divided [0

training subset and testing subset to be used during the training procedure.

NeuralWorks Professional IIIPlus. version 5.23 (NeuralWare Inc.. Pittsburgh. PA)

was employed for ~\fN modeling. A standard backpropagation algorithm with Tangent

hyperbolic transfer function and normalized cumulative delta leaming mie were seIected

for .-\..\rN models training. Same fonnats of input and output variables as detailed in the

Stumbo .-\l\i"N model were applied. For predicting the process time.JiIU were used as well

as jn [0 predict g-value and subsequently. for predicting the process lethality. g-value and

j,x were used to predictlj/U. The predicted parameters from ANN models were applied to

calculated the respective process rime and process lethality. For convenience !vIodel A and

Madel B were used to name each model for process rime and process lethality prediction.

respective1y.

84

•

RT fh/U100' crIT or ee

fh 100' cr or+OR ee

fhlli(

J~h

Figure 5.1 Arrangement and procedure of developing .-\l'IN models

•85

• Optimization of ANN models

The ANN models were optimized for the number of data records in training set.

number of processing elements~ momentum vaIue and epoch size. The assigned values for

each of these parameters are summarized in Tables 5.1 and 5.3. The first step was to select

the optimum number of data in training set with respect ta default values of network

architecture. The selected training set sizes were applied to choose the optimum topology

of the networks. Afterwards. two learning pararneters. momentum and epoch. were tested.

The following criteria were used for evaluating Ai'IN models performance:

~ (Yo -Y):Roat ~lean Square (R1\1S) of error= L n

~Iean Absolute Error (~IAE) =~[ean of 1Y" - YI

Ir -yiylean Relative Error (YIRE. %) =Nlean of . Il *100

Ya

where:YI): Desired value

Y: fu~'N predicted value

n: number of records

Table 5.2 Combinations of training and testing data for network optimization

•

Group(s) inTraining set

.-\

.-\.f

.\. C. F

.-\. B. C. F

.-\.B.C.O.F

Group(s) inTesting set

B.C.D.E.FB.C.D.E

B.D.. EO.E

E

Number of datapairs in Training

set

202

.J04

606

808

1010

~umber of datapairs in Testing

set

1010

404

606

808

202

86

•Table 5.3 Range of network architecture and leaming parameters used in the study

Number of Pes~(omentum Epoch

1 hidden layer ! 2 hidden layers1.,i 2&2 0.2 4

5 1 2&5 l 0.3 81

10 5&51

0.4 16

L5 10&51

0.6 20

!1 0.8 321

• 80ld numbers wirh underscore are default values provided in software.

Comparison of ANN models

The predicted k'iN values of process time and process Iethality were compared

with respective values of the selected fonnula methods. The same methodology as the one

used in comparison of formula methods was applied to compare the performance of the

developed .-\l'IN models. Ail the predicted values from either ANN mode1 or formula

methods were compared against the reference modeL which \Vas the data from tinite

difference modeL Relative error computed as follows. was applied as the error parameter:

F -FError = .Ilrrr 1 o/tnétNIJ.JJ .rlOO

F.'I~! l

(5. L)

•

This error panlmeter was calculated based on lethality and rherefore a positive error

of Iethality calculation demonstrates an underestimation. while a negative sign shows an

overestimation of process rime. The error signs for under and overestimation are reversed.

while predicting the process rime.

RESULTS A1~ DISCUSSIONS

A1~ models optimization

Figures 5.2 and 5.3 shows the required number of data for ~Iodel ..~ and Model B~

respectively. In Model A. the performance of the network was not a function of training

set size. and a training set with 808 data (50%) was selected. However. Madel B was more

Si

• O.t

0.09

0.08

O.Oï

0.06

<'( 0.05:;;

0.04

0.03

I).O~

0.01

l)

~O~ .w4 606 SOS 1010

:"lumber or ~xarnples ID tr.umng sel

.Tr.ùrnng DTesllng .Tesung W!1050

Figure 5.2 Leaming curve for .-\!~N model A.

I}.O"

I}O~5

no~

Il 0:5

-( Il.0!~

Il III ~

IlOI

tlO05

n::0:: J04- 606 SOS IOIO

~umber of examples ln tralDlng set

.Tr:uning Cl Tc:stmg .T~stingW/I050

•

Figure 5.3 Leaming curve for .o\1\i~ model B

88

•

•

dependent on the training set size, and a data set with LOlO dat~ which had the lowest errer

of prediction was used. Although the source of data for both models was same. the nature

of variables affected the performance of the network and the question how weB network

can lcarn depended on the input variable.

Figure 5.4 depicts the effect of PEs and number of hidden layers for ~Iodel A and

B. In bath models. 2 hidden layer networks had a significanùy higher performance

(Baughman and Liu. 1995: Swingler. 1996). A network with 2 and 5 PEs in each hidden

layer had the highest performance for Madel A and 2 PEs in each hidden layer for ~lodel

B. which \vere selected as the optimum topology. Table 5.4 shows the result of learning

paramerers variations for bath models. The effects of momentum and epoch were not

signitïcant for ~lodel A and increasing momentum increased the error. A momentum value

of 0.4 and epoch size of 4 was selected for ~todel A. The effect of rhese parameters was

even Iess significant for ~lodel B. Therefore. the default value of momentum and epoch of

4 were selected.

Table 5A Effect of momentum and epoch size on the pelformance of ~lodel A and B

~IRE MRE~Iomentum . Epoch

Jfodel.-\ .\lfodeL B .'IIodeL.-\ .Hodel B

0.2 0.039 0.029 4 0.035 0.028

0.3 0.039 0.029 8 0.037 0.028

OA 0.041 0.029 16 0.041 0.029

0.6 0.049 0.019 20 0.043 0.029

0.8 0.116 0.030 .. .., 0.053 0.030~-

Performance of the ANN models

The performance of ANN models A and 8 are ShO\\l1 in Figure 5.5 as plots of Al'lN

predicted values vs. reference values from the finite difference simulation. The predicted

values for bath models were very close to desired vaIues and were evenly distributed

throughout the entire range. The associated error parameters are summarized in Table 5.5.

High R: values shows the excellent perfonnance of bath Al.'lN models in predicùng the

output variables.

89

• ModelA

0.12

0..1 0---0.08 \w •i 0..06 " ~

0..04 "'.-/0.02

0

0 S 10 lS 20

Total number of PEs

-.-1 hidden layer -.-2 hidden layers

Model B

0.06--------~-----

0.05

0.04

20

•

15

•

105

..- .wi 0.03

0.02

0.01

O+---~--~--......,.....--~

oTotal numberof PEs

-'-1 hidden layer -e-2 hidden [ayers

Figure 5A Effect of PEs and hidden layers on the performance of modeL A and B

•90

• 2ModelA

-8 -6 -4 2

0)

0.QZ •• -3 ~z

~.<{

/ -4-/

1

~'-5 ..1

-6J...7

logg

1.5 ,

~..::Cl)

.2c::ca(;

ZZ -1oC(

•

Figure 5.5

atan log fh/U

Perfonnance of ANN models A and B with respect to predicted output

91

•The performance of Al\fN models is shown in Figure 5.6 in forrn of process time

and process lethality calculated from ANN predicted g-value or f,/U vs. me process time

and process lethality obtained from the finite difference model. Both ANN rnodels showed

a good perfonnance for predicting process rime and process lethality. The error parameters

of Al~N models prediction are 5ummarized in Table 5.5. Both models had a high R2 close

ta unity showing excellent correlation between A1~ predicted values and reference values.

R~[S of crrors for proce5s time prediction was higher than process lethality since process

time had higher values compare ta process lethality. however close mean relative crrors of

bath models shows close performance of models. Hawever. with respect to process

lethality mean relative error i5 more imponant error parameter and provides better

evaluation. [n process time calculation. mean average error of 2.7 minutes indicated high

accuracy of ANN model in process time prediction applied range of this pararneter

1between -1-0-450 minutes)

Table 5.5 Errar parameters for performance and veritïcation of AJ.'IN models A and B

•

ANN~[odel A :\NN ~Iodel 8Error parameters

logg Process lime Alan log/ilL" Process lethality

R1\(S 0.05 .+.17 0.02 nA!

MAE 0.03 l.70 0.01 0.27

MRE ~.93 2.1.+ .+.~ l.7"R; 0.998 0.997 0.997 0.999

Comparison of Al'iN models with existing fonnula methods

The performance of Al~~ models were compared for range of processing

conditions. thermal diffusivity of product. can size and processing lime with the

performance of three selected Formula methods of Bail. Stumbo and Pham. The

performance of each method is showed based on the mean of relative errors and standard

deviation of error for both process rime and proces5 lethality (Tables 5.6 and 5.7).

Althaugh no particular trend was observed in mean and SO of errors based on Al'IN

models. the performance of A1'IN models was fairly in range of methods of Stumbo and

Pham.. if not better. It shauld he mentioned these two methods have the highest accuracy of

92

• 500 j

l ModelA

400 1 /l~ 1

; 300 i

~ 200 j<{ :

1

!100 11

1

1

1

Q'

a 100 200 300 400 500

lime (min)

35-----------------~-

35302515 20

lethality (min)

105

5 11

a .....1------------------o

. Madel B

30 ~

ê 25 ~

'Ë :;: 20 t

=: 1tU !~ 1

j 15 ~zz<{ 10 ~

1

Figure 5.6 Performance of A1\lN models ..1\ and B in process tirne and process lethality

prediction

•93

•

•

calculations compared ta other formula methods (Smith and Tung. 1982: Pham. 1990~

Stoforos. et al.. 1997).

The general performance of the selected formula methods and the Al'IN models are

compared in Figures 5.7 and 5.8. BalI method. for considering the restrictive assumptions.

had the most deviation while other methods have a close perfonnance (R~.99). The

same trend was applied while comparing the performance of other methods and ANN

models with respect to process Iethality calcuIations. As the tinite difference program was

run based on a. pre-assigned heating lethality. the process lethality is clustered around three

tïxed lethality values (one of the reasons for higher errors).

Table 5.8 shows the range of errors for process time and process lethality for

formula methods and A1\fN models. The range of errors as weil as the mean and SD of

A~\jN model for process lime prediction was in range of Pham's method. Also. in process

Iethalitv prediction the range of errors varied between Stumbo's method and Pham"s

method. The range of errors in process lethality calculations was very close to Pham·s

method and the same trend in range of errors applied for process time calculations.

94

Table 5.6 Means and Standard Deviations (SD) of relative errors in process time

• calculations for selected process calculation methods

Parameter RangeBaU Stumbo Pham A1"~~Iean SD ~Iean SD Mean 5D ~[eaD SO

1[Q ('JC) -6.2 3.06 0.71 2A3 -0.25 0.51 -0.05 2.18Retort 120 (oC) -9.91 2.72 -0.55 0.64 -0.35 0.9 -2A7 1.88temperature

[30 (oC) 0.48-15.64 3.46 1.19 -3.36 2.62 2.48 3.36

70 (oC) -9.55 3.92 OA8 1.56 -1.76 ' ., 0.18 3.00Initial 80 (oC) -10.57 ~.4S 0.32 1.58 -1.51 2.18 0.07 3.21temperature

90 (oC) -12.48 5.66 -0.16 1.85 -0.69 2.01 -0.31 3.53

1'1110.7(mZ/s) -11.51 5.2 -0.21 1.34- -1.83 2.75 0.32 3.87

Thermal 1.5* [Q-~ (m:/s) -10.93 ~.97 0.24 1.65 -1.5 1.95 -0.15 3.02diffusivity

2*1O'-lmz/S) -lO.08 4.31 0.61 1.93 -0.87 1.56 -0.22 2.76

SmalL -1.011 4.39 0.43 2.08 -L.05 1.58 -0.29 2.52

Can Size ~(edium -9.65 5.16 0.82 2.12 ·oJn l.76 0.65 2.9~

Large -10.38 ....74 0.21 1.19 -1.12 2Al n.S4 3.64

Law -12.71 J..28 ·0.03 1.1... -1.80 2.10 0.20 3.03Processing

~Iedium -9.34 3.67 0.51 1.31 -0.79 2.10 1.20 3.66rime

Long -7.87 3.76 058 2.06 -OAI l.17 0.11 3.3~

Based on till weight: small: «0.5 kg). ~ledium: (0.5-1 kg). Large: (>1 kg): Processingrime: Low: 1<100 min). Average: (100-200 min). Long: (>200 min)

•95

Table 5.7 l\'[eans and Standard Deviations (SO) of relative errors in process lethality

• calculations for selected process calculation methods

Parameter Range Ball Stumbo Pham A1~

~Iean SD Mean sn ~Iean sn ~leaD SO110 (oC) 11.12 5.70 -0.81 3.95 -0.23 0.32 -0.23 4.40

Retort120 (oC) 33.03 10.70 1.88 2.33 1.74 3.14

temperature130 (oC) 57 6.66 -3.2 6.86 -0.23 4AO

70 (ùC) 31.12 19.06 -2.06 5.32 -0.25 0.35 -1.91 5.20Initial 80 (oC) 31.62 19.19 -1.09 4.81 -O.~ 0.30 -1.25 4.89temperature

90 (')e) 31.73 19A5 0.95 5.06 -0.15 0.25 0.36 4.71

l''IO·~ (m:/s) 31.85 19.36 0.36 5.20 -0.23 0.29 ·OA3 5.33

Thermal l.5*10·-:- (m:/sl 31.35 19.16 -0.75 4.91 -0.25 0.38 -0.72 4.37diffusivity

2* 10'-:- (m:'s 1 31.51 19.16 -1.85 5.32 -0.19 0.24 -1.59 5.36

Small 31.85 19.61 -0.69 5.44 -O.~9 0.39 -1.25 5.12

Cao Size Medium 30.58 19.43 -0.66 4.81 -0.16 (l.23 -0.31 3.79

Large 32.71 17.65 ·0.94 5.37 -0.17 0.22 -1.14 6.50

Low 42.26 16.30 ·0.63 5.82 -1.78 4.78

Processiog Medium 25.62 16 -0.62 -1..83 -0.33 OA2 ·0.07 4.Y}lime

Long 15.62 13.69 -1.09 4.22 -0.19 0.24 ·0.14 5.49

Based on tïll weight: smaJI: «0.5 kg). ~[edium: (0.5-1 kg). Large: (> 1 kg): Processingtime: Law: «100 min). Average: (100-200 min). Long: f>200 min)

•

Table 5.8 Range. mean and standard deviation of errors for aIl the combination of

parameters

1

Error in process time caIculations i Error in process lethality calculations~[ethods

, ~lin ~[a.'~ ~(ean SD ! ~lin ~[a.~ ~Iean snl

Bali : 1.63 16.31 15.61 3.29 : 0.75 68.02 31.57 19.12

Stumbo 0.01 5.18 1.03 0.691

0.06 19.05 2.60 3.50

Pham 0.00 8.64- 3.25 1.96 6.05 0.60 0.601 0.00

i 0.01 8.92 2.71 2.18 1

6.63 1.60 3.10A.L\fN : 0.06

96

• 500500

450 0 450 • 0

400 400·

ê 350 "2 350 .

"Ë 300 ~ §. 300 •- ' a:: 250 ;â: 25Q ~

Z 200 ~ ~ 200·Z ~

< 150 ~ a.. 150 ~:

100 • 100 •

~: 0.998!

R2: 0.99950 . 5010 0

0 200 400 600 0 200 400 600

Ref. Pt (min) Ret. Pt (min)

o

400 600200

100 .

600 ~,-----------

500 ~;1

'2 400 \

lâ: 300·

aiCD 200 ~

400 600200

500 ------------

-150 .

~OO ~

:s 350 .E- 300 .

â: 250.o"ê 200·

.2 150­CI)

100 .

50 .

0-----------o

Ref. Pt (min) Ref. Pt (min)

Figure 5.7 Performance of A1\fN model in process time calculation in comparison with

the other selected Formula methods

•97

• 1a 18

16~

16 ,14 / 14

;

C ;

c 12 / §. 12E 10 • 0 10 ~

,0 U- ,

U- a ,-~ B -

Z c: ;

Z m 6 j -'

6 = .'« 9 CL4 ~ ~

2 R2: 0.999 2 ~ R2: 0.999

a 0

a 5 la 15 20 0 5 TO 15 20

Ref. F0 (min) Ret. F0 (min)

~8 ~-- 18 1~6 ;

~T6 1

/i14 . T4ê' ./

/g 12 ~ / ê 12 /1 • §.u: 10 ~ / 10 /-10

0 8 ; U- a~

/ (ij6 : • CD 6

éii 4 1 •..1 •, 12 '* R2: 0.998 21 ~: 0.994a o '

a 5 TO 15 20 a 5 10 T5 20

Ret. Fa (min) Ref. Fa (min)

•

Figure 5.8 Performance of Ai'IN model in process Iethality calculation in comparison

with the other selected Formula methocis

98

•

•

CONCLUSIONS

With respect to preliminary results from ANN modeling of BalI and Stumbo's

method. the possibility of Al'fN model deveIopment as an alternative to existent methods of

thermal process caIcuIations was studied. A finite difference modeI was applied to obtain a

wide range of data covering the applicable range of processing conditions and can sizes.

Considering the accuracy of Al\JN based Sturnbo's modeI. the same procedure of A.:.~

model development was applied. ANN Madel A with 50% data from the total data set. had

the best training error. while the M'IN ~[odel B required higher number of examples in

training 11010 data). Both models had 2 hidden layers. ~[odel A with 2 and 5 PEs in each

layer and ~(odel B with 2 PEs in each hidden layer. The initial data was transfonned to

comply with Stumbo's table and relating of process time and process lethality was

perfonned through g (or fil'}) andi:t: to fr/Cf (or g). Using Al.'lN predicted values. process

rime or process lerhality was calculated. Al'IN Model A with 2.70 minutes ~IAE was

comparable with Pham method in process time prediction. AIso. the ANN ~[odel B

predicted the process lethaIity with 2.74% of relative error. which was very close ta

Stumbo's method. As the methods of Pham and Srumbo were assigned as the most

accurate methods of process calculations. the Al'lN models had the· patential of application

in process calculation methods.

99

•

•

l.

,

CHAPTER6

GEl~ERALCONCLUSIONS

The first phase of the research was development of ANN based on Bali and Stumbo

methods~ which are the [WO major and most widely used methods of thermal

process calculations. This work was carried out ta evaluate the potentiaI for the

application of A.:.\TN technique for process calculations. A well-trained network

required appropriare number of training data set. optimized number of processing

c:lements and hidden layers and internai parameters of the network. For validating

rhese A.'IN models for each method. a new set of processing conditions were used..

and the ANN predicted values were compared to correspondent values from

method. A~~N models had 1% error in both process time and process lethality

prediction based on Bali table data and 3% error for Stumbo table data. The higher

error of Stumbo method could be possibly because of the limited number of data

and extended range of variables in A1~'N model development. However. a close ta

unüy value for R: showed good patential of .'-\l'lN technique in thermal process

l:alculario.ns.

The accuracy of selected formula methods (Steele and Board. BaIl. Stumbo and

Pham) were evaJuated for a wide range of processing conditions~ product thermal

diffusivity and cao sizes. A finite difference simulation was used to provide the

reference values of process rime and process calculations as weil as the heat

penetration parameters (fh ! jetb t~ and jcc). The performance of the finite difference

model was optimized and verified against the analytical solution of conduction heat

transfer equarion. Retorr temperature was the mast significant parameter on the

performance of methods. Methods of Stumbo and Pham had the higher accuracy as

compare to the IWO other methods. AIso in a more specifie evaluation. the methods

were compared based on the cao shapes and g-values. For dimension of HID close

[0 unity the errors were highest and they farmer increased with g-vailles.

[00

•

•

As the final goal of this study? Ai'lN models were developed as the alternatives to

present process calculation methods. The dara from the Hnite difference simulation

was applied to develop A1'lN models. Training set size was selected based on a

developed a learning curve. Using [wo hidden layers for networks significandy

increased the perfonnance of the A1'iN models: however. learning parameters were

less meaningful during development of models. A1\fN models had ex.cellent abiliry

in process rime and process lethality prediction with 2.7 minutes of mean relative

errors for process time prediction and 0.27 minutes of mean average error for

process (ethality prediction. The accuracy of Al'iN model was compared to

perfonnance of existing fonnula methods and mey closely performed to methods of

Stumbo and Pham.

101

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•

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