vibro-fluidizedbeddryingofpumpkinseeds:assessmentof

Research ArticleVibro-Fluidized Bed Drying of Pumpkin Seeds Assessment ofMathematical and Artificial Neural Network Models forDrying Kinetics

Priyanka Dhurve 1 Ayon Tarafdar 12 and Vinkel Kumar Arora 1

1Department of Food Engineering National Institute of Food Technology Entrepreneurship and Management KundliSonipat 131 028 Haryana India2Livestock Production and Management Section ICAR-Indian Veterinary Research Institute Izatnagar Bareilly 243 122Uttar Pradesh India

Correspondence should be addressed to Vinkel Kumar Arora vinkelarora17gmailcom

Received 19 September 2021 Accepted 21 October 2021 Published 8 November 2021

Academic Editor Igor Tomasevic

Copyright copy 2021 Priyanka Dhurve et al +is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Pumpkin seeds were dried in a vibro-fluidized bed dryer (VFBD) at different temperatures at optimized vibration intensity of 426and 4ms air velocity +e drying characteristics were mapped employing semiempirical models and Artificial Neural Network(ANN) Prediction of drying behavior of pumpkin seeds was done using semiempirical models of which one was preferred as itindicated the best statistical indicators Two-termmodel showed the best fit of data with R2 minus 0999 and lowest χ2 minus103times10minus4 andMSE 755times10minus5 A feedforward backpropagation ANNmodel was trained by the LevenbergndashMarquardt training algorithm usinga TANSIGMOID activation function with 2-10-2 topology Performance assessment of ANN showed better prediction of dryingbehavior with R2 09967 and MSE 521times 10minus5 for moisture content and R2 09963 and MSE 242times10minus5 for moisture ratiothan mathematical models In general the prediction of drying kinetics and other drying parameters was more precise in the ANNtechnique as compared to semiempirical models +e diffusion coefficient Biot number and hm increased from112times10minus9plusmn 362times10minus10 to 198times10minus9plusmn 461times 10minus10m2s 051plusmn 001 to 060plusmn 001 and 149times10minus7plusmn 489times10minus8 to310times10minus7plusmn 713times10minus8ms respectively as temperature elevated from 40 to 60degC Arrheniusrsquos equation was used to the obtain theactivation energy of 3271plusmn 105 kJmol

1 Introduction

Pumpkin belongs to the Cucurbitaceae family and is broadlygrown around the warmer regions across the world +eworldwide production of pumpkin squash and gourd was27 million tons (MT) in 2017 India is the second-largestproducer with about 20 (556MT) of the total worldwideproduction [1] Pumpkin contains flesh (72ndash76) by-product peel (26ndash16) and seeds (32ndash44) [2] +epumpkin processing industry separates useful parts of thefruit from by-products which constitute peel and seeds [3]Pumpkin seeds are a vital source of bioactive componentssuch as fats essential proteins vitamins phytosterolssqualene tocopherols and carotenoid pigments [4 5] It is

consumed as snack food in several countries and its oil isgenerally used in cooking and for pharmaceutical applica-tions +e pumpkin seeds have high moisture thereforethey are highly susceptible to microbial spoilage andchemical alteration [6]

+e demand for pumpkin seeds is increasing on accountof their high nutritional and functional properties +is islikely to encourage investigations on the effects of post-harvest processing and industrial by-product utilization toprevent degradation of quality Drying is the most appro-priate technique to stop microbial spoilage and to prolongthe storage of such seeds [7] Furthermore it also reducestransportation and storage costs However physical andnutritional changes can occur in food materials including

HindawiJournal of Food QualityVolume 2021 Article ID 7739732 12 pageshttpsdoiorg10115520217739732

some quality characteristics such as texture color andflavor [8] +us the selection of proper drying techniques isa particularly important step in food processing

A mechanical vibration-assisted fluidized bed is also apotential advanced drying technique to improve the fluid-ization of such particles [9] +e electrical energy consumedby blower and vibration motor in a vibro-fluidized bed dryer(VFBD) has been reported to be around 55 of the electricalenergy of the blower in FBD [10] Furthermore by inducingvibration to the fluidized bed homogeneous temperaturecirculation can be achieved [11] agglomeration of solidparticles can be prevented and the fluidization velocity andpressure drop can be reduced [12 13]

In drying heat and mass transfer take place at the sametime due to its complexity+erefore optimization of dryingprocess conditions is important and for this mathematicalmodeling is an exceptional tool [14] Moreover modeling isapplied to find out the drying time and general nature ofdrying To design and select dryers knowledge of dryingbehavior is very important +ere are several studies re-ported in the literature to predict or develop the mostsuitable mathematical model for drying kinetics Generallyto predict the drying behavior of agricultural commoditiesdifferent mathematical models namely empirical semi-empirical and theoretical are used In most of the dryingexperiments empirical models validate the exceptional fit-ting of data but overlook the basics of the drying processesWhile theoretical models justify diffusion mechanism orheat and mass transfer mechanism [15] there are severalinvestigations on mathematical modeling of pumpkin seedsdrying kinetics for natural and forced convection solar dryer[6] solar tunnel dryer [16] tray drying [17] fluidized beddrying [17ndash20] and infrared dryer [21] However no studywas found for pumpkin seed drying using a vibro-fluidizedbed dryer

+e drying of biological samples is a complex methodand on occasions may not be explained using traditionalmodels For that purpose a neural network approach wasalso attempted for this study considering the novel nature ofthe drying process Artificial neural networks (ANN) are amachine learning method applied to predict intricate cor-relations among input and output conditions of drying andnonlinear problems [22] Many researchers used ANN toexplain moisture content rate of drying moisture ratioeffective diffusivity and specific energy consumption fordifferent agriculture products [23ndash25] Alvarez et al [26]successfully used ANN to correlate the heat and masstransfer parameters and vibration parameters (amplitudefrequency and vertical motion) for poppy seeds dried in avibrated fluidized bed dryer Kumar et al [27] used afeedforward backpropagation ANN model to predict themoisture ratio by feeding drying temperature and time asinput parameters According to our intensive literaturesearch no work has been reported on themodeling of dryingkinetics of pumpkin seeds in a VFBD by ANN and itscomparison with semiempirical drying models to the best ofour knowledge Moreover information on the mass transferparameters for pumpkin seed drying using VFBD is notavailable Such parameters are useful in designing drying

equipment and optimizing industrial drying processes andhence were taken up in this investigation

+erefore the aim of the current work is to performpumpkin seeds drying in a VFBD at various drying pa-rameters along with the determination of drying and masstransfer parameters +e study also deals with the predictionand comparison of the drying behavior of pumpkin seedsusing semiempirical modeling and ANN

2 Materials and Methods

21 Sample Preparation Pumpkins (Cucurbita maxima)were procured from the market of Narela New Delhi Indiaduring the summer season +e pumpkins were cut in halffollowed bymanual removal of the seeds Undeveloped seedswere removed and the seeds exhibiting the same size werewashed with deionized water and pressed in a sieve toremove the stringy pulp +e washed seeds were stored inlow-density polyethylene (LDPE) airtight bags at minus10degC andwere subjected to drying treatment within 24 h of storageHot-air oven method was used to estimate initial moisturecontent at 105degC for 24 h [28] All readings were replicatedthrice for accuracy

22 Experimental Setup An electrical power-operatedvibro-fluidized bed dryer was fabricated at the Departmentof Food Engineering NIFTEM Haryana India as depictedin Figure 1 +e components and specifications of VFBD arepresented in Table 1

23 Vibration Intensity +e vibration intensity (Γ) wascalculated using the following equation [29]

Γ A(2πf)

2

g (1)

where A is the amplitude mm g is the acceleration due togravity mms2 and f is the frequency of vibration HzPakowski et al [30] recommended the optimum range of Γfor proper structure of bed and drying rate as 1ndash6

24 Drying Experiments +e experiments were conductedat different conditions as shown in Table 2 Air velocityselected for fluidization was 4ms as given by Kaveh et al[7] for squash seeds Before each experiment the threedryers were run for 30min in no-load condition to ac-complish the chosen operating parameters of the dryingchamber For drying pumpkin seeds of approximately200 g were placed on the perforated sieve of the VFBD +eweight of moisture was recorded at 5min intervals Dryingwas continued until 0007ndash0009 kg H2Okg dm moistureremained in the sample which is the safe storage moisturecontent for high-oil-content seeds +e dried samples werecooled in desiccators at an ambient temperature (27degC) for15min and then filled in LDPE bags for additionalinvestigations

2 Journal of Food Quality

25 Drying Kinetics and Mathematical Modeling +emoisture ratio during drying was computed using thestandard equation (Babar et al 2020)

+e experimental data of drying of pumpkin seeds werefitted to six thin-layer drying models as shown in Table 3+e parameters of the models were estimated using a

12345

6 amp 789

10111213141516

Variable frequency drive (VFD)BlowerBall valveHeaterPID controllerThermocouplesSpringFrameDC motorEccentric connectorPlenum chamberDistributor plateDrying ChamberRe-circulation pipeDC motor controller

1

11

14

13

129

V A

1610

2

3

5

15

6

7

8

4

Temp

Figure 1 Schematic diagram of the vibro-fluidized bed dryer

Table 1 Design specifications of the vibro-fluidized bed dryer

Components Specifications

Drying chamberDimension 035mtimes 040m (diametertimes height)

Volume 00384m3

Capacity 10ndash15 kg per drying cyclePlenum chamber Dimension 035mtimes 025m (diametertimes height)Distributor plate Dimension 035m diameter and 00002m aperture diameter

Vibration motor (DC) with eccentric wheel blower1HP

2HP with 2800 rpm-3 phasesAir flow rate 650ndash670m3h

Variable frequency drive (delta VFD015S21D US) 15 kW-1 phaseFrequency 0ndash60Hz

Heating chamber 050times 050times 040mHeater 1 coil type 2 kW and 4 fins type 4 kWPID controller (Instron IN- 312 and KRITMAN GHC-100 India) 30degC to 600degCTemperature measurement PT-100 and k-type thermocouple

Hot-air anemometer (Mextech AM 4208 Mextech India)

Sensor 00072mAir velocity range 04ndash45msAir temperature range 0ndash50degC

Air flow 0ndash9999m3min

Table 2 Experimental parameters for VFBD

Operating parameters VFBDInitial moisture content (kg H2Okg dry matter) 1442plusmn 0082Air temperature (degC) 40 50 and 60Air velocity (ms) 4Vibration intensity 429 (A 10mm and f 103Hz)Bed height (cm) +in layerAmbient temperature (degC) 27ndash30Relative humidity () 45ndash50

Journal of Food Quality 3

nonlinear regression procedure For selecting the mostappropriate model to depict thin-layer drying determina-tion coefficient (R2) chi-square (χ2) and mean square error(MSE) were used +ese parameters were calculated usingstandard equations [18 31]

26 ANN Modeling ANN mimics the functionality of aneuron in the human brain It adapts to new knowledge andidentifies patterns in fuzzy and inaccurate data In thiswork the modeling of experimental data was also done by amultilayer FFBP neural network using the neural networktoolbox of MATLAB v2012a (MathWorks Inc USA) +eANN model was provided with different air temperatureand drying time data as input while MC and MR weregiven as output (supervised training) with one hidden layerto reduce the complexity of the model +e best ANNinfrastructure for accurate drying data prediction was doneon a trial-and-error basis +ere were numerous back-propagation training algorithms such as scaled conjugategradient (SCG) PolakndashRibiere conjugate gradient (CGP)BFGS quasi-Newton (BGF) LevenbergndashMarquardt (LM)resilient (Rprop) gradient descent (GDX) back-propagation etc [32] From these the Lev-enbergndashMarquardt training algorithm (TRAINLM) wasused because of its previously proven efficiency in dryingdata prediction [33]

For model development 70 was used for training and30 of the remaining data for testing and validation re-spectively +e TANSIGMOID activation function was ex-ercised to correlate the signal of input and output of eachlayer and to decrease the processing time As proposed byDorofki et al [34] as an approximation function thePURELIN transfer function was applied to the output layer+e number of iterations was limited to 1000 to reduce thevalidation time while ensuring proper model termination(attainment of error goals) As for performance indicators ofthe model MSE and correlation coefficient (R) wererecorded

+e signal received to the first HL from the input layerwas expressed as follows [22]

HLi 1113944n

j1111393610

i1Iiwij + bj (2)

+e output signal of neuron can be expressed using thefollowing equations respectively

H01 1

1 + eminus Hl1

+ b1 (3)

H01 e

Hl1 minus eminus Hl1

eHl1 + e

minusHl1+ b1 (4)

Output layer will receive 10 signals from 10 HL whichwas expressed using the following equation

Ol1 1113944

10

j1HojVj1 + b2 (5)

PURELIN function was employed to the receivingneurons of the output layer to obtain the outcome of theANN model as follows

Oo1 λOl1 sim Ol1 (6)

+e error between target and output of the selectedbackpropagation model was estimated and minimized to anacceptable level by adjusting the weights of the structure

27 Estimation of Effective Moisture Diffusivity (Deff) andActivation Energy (Ea) For the valuation of Deff slab ge-ometry was considered for pumpkin seeds owing to itssmall thickness as related to other dimensions [35] Anassumption was made that negligible shrinkage due todrying took place with uniform distribution of initial MCFickrsquos law was used to calculate Deff of pumpkin seeds [16]which was linearized as suggested by Golpour et al [36]Activation energy was determined using Arrhenius func-tion which expressed the relationship of Deff andtemperature

28 Mass Transfer Parameters +e parameters such as Biotnumber (Bi) and mass transfer coefficient (hm) were de-termined by the equation given by Dincer and Hussain [37]Bi a dimensionless number represents the correlation be-tween internal and external convective heat transfer [38] Italso specifies the resistance of moisture transfer inside aproduct and is affected by the drying medium and producttype Bi was calculated as

Bi 24848D

0375i

(7)

+e relationship between air velocity and heating andcooling coefficient is provided by the Dincer number (Di)Diwas expressed using

Di v

kH (8)

Additionally the convective mass transfer coefficientwas determined using the following equation

Bi hmH

Deff (9)

where v is the air velocity msH is the thickness of the seedm and k is the drying constant (taken from the best-fittedmodel)

Table 3 Most commonly used semiempirical models for illus-trating the drying kinetics of seeds

Models Model equationPage MR exp(minusk times tn)

Modified page MR exp (minusk times t)n

Newton MR exp(minusk times t)

Henderson and Pabis MR a times exp(minusk times t)

Two-term MR atimes exp (minusktimes t) + btimes exp (minusk0 times t)Logarithmic MR atimes exp (minusktimes tn) + b


3 Results and Discussion

31 Drying Characteristics +e initial moisture content ofpumpkin seeds was determined as 152plusmn 0013 kg H2Okgdry matter which reduced to 008plusmn 001 kg H2Okg drymatter +e drying curves of dried pumpkin seeds in VFBDat different temperatures are shown in Figure 2 +e re-duction of moisture content of pumpkin seeds with time wasobserved at all drying conditions as shown in Figure 2(a) Adecrease in moisture content showed that diffusion mech-anism was regulated by mass transfer within seeds (Ashtianiet al) [39] From Figure 2(b) it was observed that there wasno constant rate period this might be due to the thin-layerdrying of pumpkin seed which was unable to deliver aconstant supply of moisture while drying As drying pro-ceeds the free surface moisture evaporates and when surfacemoisture is insufficient moisture diffusion takes place fromthe core of the seeds to the surface which also explained thedecrease in MR as observed in Figure 2(c) +erefore areduction of drying rate was observed with time with theinitiation of falling rate Another possible reason for fastermoisture diffusion from pumpkin seeds could be its flatgeometry exhibiting large surface-to-volume ratio +emigration of water from larger surfaces to its surrounding ismuch faster than in smaller surface seeds

+e drying rate was found to increase from 00063 to00091 kg H2Okg dm min with the rise in temperature from40 to 60degC It showed that elevated temperature elevates heattransfer gradient between surrounding air and seeds whichstimulates a higher drying rate and subsequently reducesdrying time [40] Similar results of drying curves were foundin castor oil seeds (Ricinus communis) [31] watermelonseeds [41] pumpkin seeds [17] Jatropha curcas L seeds [42]and garlic clove [43 44] Stakic and Urosevic [45] driedpoppy seeds in VFBD and reported that with the rise oftemperature the drying rate improved and drying timereduced Lima et al [46] also concluded that propermoisture evaporation and homogeneity were obtained invibro-fluidized bed drying than conventional fluidized beddrying

32 Mathematical Modeling +e results of experimentaldata were fitted to semiempirical models and the modelcoefficients were determined and are presented in Table 4+e best-fittedmodel was selected based on themaximum R2

and lowest value of MSE and χ2 +e range of R2 MSE andχ2 for all experiments were 09923 to 09990 755times10minus5 to777times10minus4 and 848times10minus5 to 648times10minus4 respectively +eexperimental data was fitted well in all the models with R2

greater than 099 But the two-term model was fitted ex-ceptionally well with the highest R2 minus 0999 and lowestχ2 minus103times10minus4 and MSE 755times10minus5 at a temperature of60degC+e validation of the best-fit model (ie two-term) wasalso conducted using MATLAB curve fitting tool +egoodness of validation as predicted parameters are SSE000113 and RMSE 000870 It was observed that drying rateconstant (k) was significantly (plt 005) improved with therise of temperature +e residual plots for moisture ratio are

presented in Figure 3(b) Heteroscedasticity of residual plotwas observed for best-fitted model which showed that themodel prediction is good and the data quality is highGenerally heteroscedasticity of residual is expected fornonlinear regression models

33 ANN Performance ANN model was successfullytrained by TRAINLM algorithm with 10 neurons in the HL+e correlation coefficients (R) of ANN model for trainingtesting and validation were 09999 09997 and 09999respectively with a mean square error of 212 times 10minus4 asshown in Figure 4 +e weights and bias of the final ANNtopography for pumpkin seed drying in VFBD are shown inTable 5

+e predicted moisture content (R2 09967MSE 529times10minus5) and moisture ratio (R2 09963MSE 242 times 410minus5) of optimum network structure (2-10-2topology) was projected by TANSIGMOID as shown inFigure 5 Kaveh [35] found that the ANN model-FFBPprovided the best extrapolation of moisture ratio(R2 09944) of squash seeds dried in an FBD Jafari et al[23] determined that FFBP network with TRAINLMTANSIGMOID activation function and 2-5-1 topologyshowed R2 of 09996 and minimum MSE of 394times10minus5 forpredicting the moisture ratio of onion dried in fluidized beddryer +e reported work was similar to our findings forpumpkin seeds

34 Comparative Assessment of Semiempirical and ArtificialNeural NetworkModel Two-term model was found to mostadequately fit the experimental data with maximum R2 andminimum MSE Subsequently the two-term model wasselected for comparison with the ANN model +e com-parative statistical indicators are presented in Table 6 ANNprovided a relatively reasonable fit at all drying conditionswhich was in the range of the maximum R2 and minimumMSE values of the semiempirical model +is illustrates thatANN is more capable of correlating all external and internalvariables and is more likely to provide accurate predictionsat other unseen processing conditions [22 23]

35 Moisture Diffusivity and Activation Energy +e Deff wasestimated from the slope obtained from the graph presentedin Figure 6(a) for VFBD +e values for the same are dis-played in Table 7+e outcomes illustrated thatDeff values ofpumpkin seeds changed from 112 va10minus9plusmn 362 610minus10 to228 to10minus9plusmn 143 410minus10m2s in the temperature range of 40to 60degC in VFBD respectively +e values attained in thisanalysis were within the range of food materials which isusually in the range of 10minus11 to 10minus9m2s [47]

It was observed that the moisture diffusivity significantly(plt 005) improved with rise in temperature As explainedbefore the increased temperature reduces external resis-tance of the boundary layer which accelerates heat transferbetween the surface and center part of the seeds Due to hightemperature vapor pressure within the seeds increaseswhich causes faster moisture migration to the surface


Moi

sture

Con

tent

(kg

H2O

kg

dm)

20 40 60 80 100 1200Drying time (min)

40degC50degC60degC

002040608

1121416

(a)

Dry

ing

rate

(kg

H2O

kg

dmm

in)

20 40 60 80 100 1200Drying time (min)

40degC50degC60degC

00000001000200030004000500060007000800090010

(b)

0010203040506070809

1

Moi

sture

ratio

20 40 60 80 100 1200Drying time (min)

40degC50degC60degC

(c)

Figure 2 Drying characteristics of pumpkin seed in VFBD change in (a) moisture content (b) drying rate and (c) moisture with dryingtime

Table 4 Statistical parameters and the coefficients of pumpkin seeds dried in VFBD

Model Temperature degC Empirical constants R2 MSE χ2

Two-term

40 k 00397plusmn 00049 a 04842plusmn 00048 09967 266times10minus4 272times10minus4b 04842plusmn 00049 k0 00396plusmn 00013



Newton40 k 00410plusmn 663times10minus4 09956 300times10minus4 314times10minus4

50 k 00611plusmn 00015 09939 489times10minus4 518times10minus4


Logarithmic

40 k 00416plusmn 00012 a 09637plusmn 00011 09972 236times10minus4 217times10minus4b 00136plusmn 00059

50 k 00592plusmn 00027 a 1010plusmn 00215 09943 451times 10minus4 541times 10minus4b minus00109plusmn 00101

60 k 006430plusmn 00025 a 09746plusmn 0015 09971 225times10minus4 281times 10minus4b 00012plusmn 00088

Modified page40 k 00252plusmn 338times10minus4 n 1plusmn 0 09956 301times 10minus4 328times10minus4

50 k 00306plusmn 796times10minus4 n 1plusmn 0 09939 488times10minus4 550times10minus4

60 k 00329plusmn 681times 10minus4 n 1plusmn 0 09964 279times10minus4 323times10minus4


resulting in increased Deff +e diffusivity of different ma-terials depends on their structure temperature and mois-ture content [48]

+e graphical representation of logarithmic moisture ratioln Deff versus Tminus1 for drying of pumpkin seed at the differenttemperatures is shown in Figure 6(b) for VFBD Ea of pumpkinseeds was determined as 3271plusmn 105 kJmol in VFBDAccording to Bezerra et al [49] if Ea is greater the evaporationof moisture from the surface of the sample is slower due tostrongly bonded moisture with other compounds+e value of

Ea found in this report was within the range of Ea obtained forfood products and low as compared to values reported inprevious studies [18 19]

36 Mass Transfer Parameters Bi represents the rate ofmoisture diffusion during the process of drying +e Bi andhm values are summarized in Table 7 As expected the Binumber and hm were significantly (plt 005) increased from051plusmn 001 to 060 plusmn 001 and 242 010minus7plusmn 924 210minus8 to

Table 4 Continued


Page40 k 00578plusmn 00025 n 09000plusmn 0012 09989 777times10minus5 848times10minus5

50 k 00503plusmn 0007 n 1064plusmn 0044 09947 424times10minus4 477times10minus4


Henderson and Pabis40 k 00397plusmn 749times10minus4 a 09683plusmn 0011 09967 225times10minus4 248times10minus4

50 k 00615plusmn 00019 a 10046plusmn 00197 09939 526times10minus4 549times10minus4


Model

Reduced Chi-SqrR-Square (COD)

a

b

kk0

twoterm (User)010137 plusmn 003734044054 plusmn 038012005939 plusmn 000197089868 plusmn 003602

103283E-4099904

8020 7010 300 40 50 60Drying time (min)

00

02

04

06

08

10

Moi

sture

ratio

Experimental MRTwo-term model (Predicted MR)

(a)

8020 7010 300 40 50 60Drying time (min)

-002

-001

000

001

Resid

ual o

f MR

(b)

-002 -001 001000Residual of MR

0

2

4

6

Cou

nts

(c)

Resid

ual o

f pre

dict

ed M

R

0400 080602 1210Predicted MR

-002

-001

000

001

(d)

Figure 3 (a) Two-term model fitting plot (b) Variation of residuals with time (c) Normal probability plot of residuals (d) Hetero-scedasticity plot


745 to 10minus7plusmn 552 510minus8ms respectively with the in-crease of temperature from 40degC to 60degC Bi can be classifiedas follows Bi lt 01 01lt Bi lt 100 and Bi gt 100 If Bi lt 01

then there is less internal resistance and more exteriorresistance to moisture diffusion through fluid boundarylayer within a product If 01lt Bi lt 100 it specifies that

0 05 1 15Target

0 05 1 15Target

15

1

05

0

Out

put~

= 1

Targ

et +

00

005

15

1

05

0

Out

put~

= 1

Targ

et +

-00

011

Training R=09999 Validation R=099992

DataFitY = T

0 05 1 15Target

0 05 1 15Target

15

1

05

0

Out

put~

= 1

Targ

et +

-00

029

15

1

05

0

Out

put~

= 1

Targ

et +

00

0024

Test R=099973 All R=099985

DataFitY = T

DataFitY = T

DataFitY = T

0 50 100 150155 Epochs

10-1

10-7

10-6

10-5

10-4

10-3

10-2

Best Validation Performance is 000021259 at epoch 43

TrainValidationTestBestGoal

Mea

n Sq

uare

d Er

ror (

mse

)

Figure 4 Training performance of the generated neural network with 2 inputs (temperature and drying time) 10 hidden layer neurons and2 outputs (moisture content and moisture ratio)


there is presence of both internal and exterior resistanceand if Bigt 100 it suggests maximum internal and very lessexternal resistance to the moisture diffusion with theproduct due to drying [50] +e values of Bi in the present

investigation lies in the second category which reveals theexistence of both internal and external resistance tomoisture removal +e rise in accessible thermal energy infood material due to elevated temperature stimulates thewater molecules which causes a high rate of mass transfer[51] Similar trends were observed in cocoyam dried in aconvective dryer [52] in apples (cv Golden Delicious)dried in a vacuum drying with the temperature escalatedfrom 50degC to 70degC [53] and moringa leaves vacuum-driedin the range of 40degC to 60degC [22]

Table 5 Weights and biases for the obtained neural network

j kWeights Bias

w1j w2j wj1 wj2 bj bk1 34253 minus26199 03718 03905 minus4959 217452 33791 50788 08209 08345 minus50407 222523 minus54467 61391 minus061 minus06045 37684 mdash4 44125 minus22221 minus06507 minus06479 minus17083 mdash5 05999 33198 minus00667 minus00666 minus1105 mdash6 minus53801 minus33426 02788 02695 minus08644 mdash7 minus40007 minus17235 minus02726 minus02522 minus08594 mdash8 01321 40858 minus35083 minus35636 47189 mdash9 36053 21813 minus04538 minus04614 47392 mdash10 17939 47844 20048 20376 72173 mdash

w weight b bias i input layer node j hidden layer node and k output layer node

MCpred= 09815MCexp + 00061R2= 09967

MRpred = 09829MRexp + 00032R2= 09963

00

02

04

06

08

10

00 02 04 06 08 10

Pred

ucte

d m

oistu

re co

nten

t (g

H2O

g d

m)

Experimental moisture content (g H2O)g dm)

0 20 40 60

Erro

r in

MC

pred

ictio

n

Experimental data points

00 02 04 06 08 10

Pred

icte

d m

oistu

re ra

tio

Experimental moisture ratio

0 20 40 60

Erro

r in

MR

pred

ictio

n


-0015

-0010

-0005

0000

0005

0010

0015

0020

0025

0030

00

02

04

06

08

10

-0010

-0005

0000

0005

0010

0015

0020

Figure 5 Simulated performance of the generated neural network along with error variation graph showing ANN learning (random errorindicates proper training)

Table 6 Comparative analysis of semiempirical and ANN model

Model R2 MSETwo-term 09949ndash09990 103times10minus4ndash627times10minus4

ANN 09963 242times10minus5


4 Conclusions

Pumpkin seeds were dried in a VFBD at 40 50 and 60degC at aconstant air velocity of 4ms with 426 (A 10mm andf 103Hz) vibration intensity It was noted that air temper-ature significantly influenced the drying characteristics ofpumpkin seeds Among all six semiempirical models the two-term model fitted more precisely to investigational data withmaximum R2minus 0999 and lowest χ2minus103times10minus4 and MSE755times10minus5 A comparative assessment between the predictedtwo-term model and ANN was performed ANN gave a betteroverall prediction for the drying characteristics in terms ofstatistical indicators +e value of Deff Bi and hm of pumpkinseeds increased with the increase in drying temperature Ac-tivation energy calculated from the Arrhenius equation showsthat a moderate amount of energy that is 3271plusmn105 kJmol isessential to start the dryingDrying of pumpkin seeds at 60degC for115h inVFBD is suggested at 4ms air velocity with a vibrationintensity of 426

Data Availability

All data pertaining to this work are available within themanuscript

Conflicts of Interest

+e authors declare that there are no conflicts of interest

Acknowledgments

+e authors are thankful to members of the Department ofFood Engineering NIFTEM (Sonipat) for their facilities

support and encouragement +e first author thanks theMinistry of Tribal Affairs Government of India for pro-viding fellowship vide Grant no 201718-NFST-MAH-02452

References

[1] FAO ldquoFAOSTATrdquo FAO Rome Italy 2018 httpwwwfaoorghomeen

[2] X Rico B Gullon J Luis Alonso and R Yantildeez ldquoRecovery ofhigh value-added compounds from pineapple melon wa-termelon and pumpkin processing by-products an overviewrdquoFood Research International vol 132 pp 1ndash21 2020

[3] J F Ayala-Zavala V Vega-Vega C Rosas-Domınguez et alldquoAgro-industrial potential of exotic fruit byproducts as asource of food additivesrdquo Food Research International vol 44no 7 pp 1866ndash1874 2011

[4] R P Cuco L Cardozo-Filho and C d Silva ldquoSimultaneousextraction of seed oil and active compounds from peel ofpumpkin (cucurbita maxima) using pressurized carbon di-oxide as solventrdquo e Journal of Supercritical Fluids vol 143pp 8ndash15 2019

[5] P G Peiretti G Meineri F Gai E Longato andR Amarowicz ldquoAntioxidative activities and phenolic com-pounds of pumpkin (cucurbita pepo) seeds and amaranth(amaranthus caudatus) grain extractsrdquo Natural Product Re-search vol 31 no 18 pp 2178ndash2182 2017

[6] A Can ldquoAn analytical method for determining the tem-perature dependent moisture diffusivities of pumpkin seedsduring drying processrdquo Applied ermal Engineering vol 27no 2-3 pp 682ndash687 2007

[7] M Kaveh V Rasooli and R Amiri ldquoANFIS and ANNsmodelfor prediction of moisture diffusivity and specific energyconsumption potato garlic and cantaloupe drying under

ln M

R

-7

-6

-5

-4

-3

-2

-1

00 20 40 60 80 100 120

Drying time (min)

40degC50degC60degC

(a)

ln D

eff

-207

-206

-205

-204

-203

-202

-201

-2000029 0003 00031 00032 00033

1T (K-1)

(b)

Figure 6 (a) Experimental ln MR with time at different temperatures (b) Plot for determination of activation energy

Table 7 Deff Ea and mass transfer constraints of pumpkin seeds at different drying temperatures

Temperature (degC) Deff (m2s) Ea (kJmol) k Bi hm (ms)40 112plusmn 362times10minus10

3271plusmn 105004plusmn 000 051plusmn 001 149plusmn 489times10minus8

50 155plusmn 67times10minus11 0064plusmn 000 060plusmn 001 242plusmn 924times10minus8



convective hot air dryerrdquo Information Processing in Agri-culture vol 5 no 3 pp 372ndash387 2018

[8] N D Mrad N Boudhrioua N Kechaou F Courtois andC Bonazzi ldquoInfluence of air drying temperature on kineticsphysicochemical properties total phenolic content andascorbic acid of pearsrdquo Food and Bioproducts Processingvol 90 no 3 pp 433ndash441 2012

[9] A S Mujumdar ldquoResearch and development in drying recenttrends and future prospectsrdquo Drying Technology vol 22no 1ndash2 pp 1ndash26 2004

[10] S Soponronnarit S Wetchacama S Trutassanawin andW Jariyatontivait ldquoDesign testing and optimization ofvibro-fluidized bed paddy dryerrdquo Drying Technology vol 19no 8 pp 1891ndash1908 2001

[11] D Jia O Cathary J Peng et al ldquoFluidization and drying ofbiomass particles in a vibrating fluidized bed with pulsed gasflowrdquo Fuel Processing Technology vol 138 pp 471ndash482 2015

[12] R V Daleffe M C Ferreira and J T Freire ldquoDrying of pastesin vibro-fluidized beds effects of the amplitude and frequencyof vibrationrdquo Drying Technology vol 23 no 9ndash11pp 1765ndash1781 2005

[13] L Meili F B Freire M do Carmo Ferreira and J T FreireldquoFluid dynamics of vibrofluidized beds during the transientperiod of water evaporation and drying of solutionsrdquoChemical Engineering amp Technology vol 35 no 10pp 1803ndash1809 2012

[14] O A Babar A Tarafdar S Malakar K Arora andP K Nema ldquoDesign and performance evaluation of a passiveflat plate collector solar dryer for agricultural productsrdquoJournal of Food Process Engineering vol 43 no 10 Article IDe13484 2020

[15] A Sander ldquo+in-layer drying of porous materials selection ofthe appropriate mathematical model and relationships be-tween thin-layer models parametersrdquo Chemical Engineeringand Processing Process Intensification vol 46 no 12pp 1324ndash1331 2007

[16] K Sacilik ldquoEffect of drying methods on thin-layer dryingcharacteristics of hull-less seed pumpkin (cucurbita pepo L)rdquoJournal of Food Engineering vol 79 no 1 pp 23ndash30 2007

[17] Z Uddin P Suppakul and W Boonsupthip ldquoEffect of airtemperature and velocity on moisture diffusivity in relation tophysical and sensory quality of dried pumpkin seedsrdquo DryingTechnology vol 34 no 12 pp 1423ndash1433 2016

[18] R A Chayjan K Salari Q Abedi and A A SabziparvarldquoModeling moisture diffusivity activation energy and specificenergy consumption of squash seeds in a semi fluidized andfluidized bed dryingrdquo Journal of Food Science amp Technologyvol 50 no 4 pp 667ndash677 2013

[19] W Jittanit ldquoKinetics and temperature dependent moisturediffusivities of pumpkin seeds during dryingrdquo KasetsartJournalmdashNatural Science vol 45 no 1 pp 147ndash158 2011

[20] SMujaffar and S Ramsumair ldquoFluidized bed drying of pumpkin(cucurbita sp) seedsrdquo Foods vol 8 no 147 pp 1ndash13 2019

[21] I Doymaz ldquoExperimental study on drying characteristics ofpumpkin seeds in an infrared dryerrdquo Latin American AppliedResearch vol 46 pp 169ndash174 2016

[22] A Tarafdar N Jothi and B P Kaur ldquoMathematical andartificial neural network modeling for vacuum drying kineticsof moringa olifera leaves followed by determination of energyconsumption and mass transfer parametersrdquo Journal of Ap-plied Research on Medicinal and Aromatic Plants vol 24Article ID 100306 2021

[23] M G Jafari D Dehnad and V Ghanbari ldquoMathematicalfuzzy logic and artificial neural network modeling techniques

to predict drying kinetics of onionrdquo Journal of Food Processingand Preservation vol 40 no 2 pp 329ndash339 2016

[24] M Kaveh R A Chayjan I Golpour S Poncet F Seirafi andB Khezri ldquoEvaluation of exergy performance and oniondrying properties in a multi-stage semi-industrial continuousdryer artificial neural networks (ANNs) and ANFIS modelsrdquoFood and Bioproducts Processing vol 127 pp 58ndash76 2021

[25] E Taghinezhad M Kaveh E Khalife and G Chen ldquoDryingof organic blackberry in combined hot air-infrared dryer withultrasound pretreatmentrdquo Drying Technology vol 39 no 14pp 1ndash17 2020

[26] P I Alvarez R Blasco J Gomez and F A Cubillos ldquoA firstprinciplesndashneural networks approach to model a vibratedfluidized bed dryer simulations and experimental resultsrdquoDrying Technology vol 23 no 1-2 pp 187ndash203 2005

[27] D Kumar A Tarafdar Y Kumar and P C Badgujar ldquoIn-telligent modeling and detailed analysis of drying hydrationthermal and spectral characteristics for convective drying ofchicken breast slicesrdquo Journal of Food Process Engineeringvol 42 no 5 pp 1ndash14 2019

[28] AOAC AOAC Official Methods of Analysis Association ofOfficial Analytical Chemists Arlington TX USA 15th edi-tion 1990

[29] H Perazzini F Bentes Freire and J Teixeira Freire ldquo+einfluence of vibrational acceleration on drying kinetics invibro-fluidized bedrdquo Chemical Engineering and ProcessingProcess Intensification vol 118 no 4 pp 124ndash130 2017

[30] Z Pakowski A S Mujumdar and C Strumillo ldquo+eory andapplication of vibrated beds and vibrated fluid beds for dryingprocessesrdquo Advances in Drying vol 3 pp 245ndash306 1984

[31] M J Perea-Flores V Garibay-Febles J J Chanona-Perezet al ldquoMathematical modelling of castor oil seeds (ricinuscommunis) drying kinetics in fluidized bed at high temper-aturesrdquo Industrial Crops and Products vol 38 no 1pp 64ndash71 2012

[32] D Zare H Naderi and M Ranjbaran ldquoEnergy and qualityattributes of combined hot-airinfrared drying of paddyrdquoDrying Technology vol 33 no 5 pp 570ndash582 2015

[33] A Tarafdar N Chandra Shahi and A Singh ldquoFreeze-dryingbehaviour prediction of button mushrooms using artificialneural network and comparison with semi-empirical modelsrdquoNeural Computing amp Applications vol 31 no 11 pp 7257ndash7268 2018

[34] M Dorofki A H Elshafie O Jaafar O A Karim andS Mastura ldquoComparison of artificial neural network transferfunctions abilities to simulate extreme runoff datardquo in Pro-ceedings of the 2012 International Conference on EnvironmentEnergy and Biotechnology pp 39ndash44 Kuala LumpurMalaysia May 2012

[35] M Kaveh ldquoModeling drying properties of pistachio nutssquash and cantaloupe seeds under fixed and fluidized bedusing data-driven models and artificial neural networksrdquoDEGRUYTER International Journal of Food Engineeringvol 24 no 1 pp 1ndash19 2018

[36] I Golpour M Z Nejad R A Chayjan and A M NikbakhtR P F Guine and M Dowlati Investigating shrinkage andmoisture diffusivity of melon seed in a microwave assistedthin layer fluidized bed dryerrdquo Journal of Food Measurementand Characterization vol 11 no 1 pp 1ndash11 2017

[37] I Dincer and M M Hussain ldquoDevelopment of a new bindashdicorrelation for solids dryingrdquo International Journal of Heatand Mass Transfer vol 45 no 15 pp 3065ndash3069 2002

[38] S Sevik M Aktas E Can E Arslan and A Dogus ldquoPer-formance analysis of solar and solar-infrared dryer of mint


and apple slices using energy-exergy methodologyrdquo SolarEnergy vol 180 pp 537ndash549 2019

[39] M Ashtiani S Hassan A Salarikia and M R GolzarianldquoAnalyzing drying characteristics and modeling of thin layersof peppermint leaves under hot-air and infrared treatmentsrdquoInformation Processing in Agriculture vol 4 no 2 pp 128ndash139 2017

[40] J Mitra S L Shrivastava and P Srinivasa Rao ldquoVacuumdehydration kinetics of onion slicesrdquo Food and BioproductsProcessing vol 89 no 1 pp 1ndash9 2011

[41] I Doymaz ldquoExperimental study and mathematical modelingof thin-layer infrared drying of watermelon seedsrdquo Journal ofFood Processing and Preservation vol 38 no 3 pp 1377ndash1384 2014

[42] Y G Keneni A K Trine Hvoslef-Eide and J M MarchettildquoMathematical modelling of the drying kinetics of Jatrophacurcas L seedsrdquo Industrial Crops and Products vol 132pp 12ndash20 2019

[43] S Malakar and V K Arora ldquoMathematical modeling ofdrying kinetics of garlic clove in forced convection evacuatedtube solar dryerrdquo Lecture Notes In Mechanical EngineeringSpringer Berlin Germany pp 813ndash820 2021

[44] S Malakar V K Arora and P K Nema ldquoDesign and per-formance evaluation of an evacuated tube solar dryer for dryinggarlic cloverdquo Renewable Energy vol 168 pp 568ndash580 2021

[45] M Stakic and T Urosevic ldquoExperimental study and simu-lation of vibrated fluidized bed dryingrdquo Chemical Engineeringand Processing Process Intensification vol 50 no 4pp 428ndash437 2011

[46] R A B Lima A S Andrade and M F G FernandesJ T Freire and M C Ferreira +in-layer and vibrofluidizeddrying of basil leaves (ocimum basilicum L) analysis ofdrying homogeneity and influence of drying conditions on thecomposition of essential oil and leaf colourrdquo Journal of Ap-plied Research on Medicinal and Aromatic Plants vol 7pp 54ndash63 2017

[47] H Li L Xie M Yue M Zhang Y Zhao and X Zhao ldquoEffectsof drying methods on drying characteristics physicochemicalproperties and antioxidant capacity of okrardquo LWT-FoodScience and Technology vol 101 no 11 pp 630ndash638 2019

[48] Z Erbay and F Icier ldquoA review of thin layer drying of foodstheory modeling and experimental resultsrdquo Critical Reviewsin Food Science and Nutrition vol 50 no 5 pp 441ndash464 2010

[49] C V Bezerra L H Meller da Silva D F CorreaA M C Rodrigues M Antonio and C Rodrigues ldquoAmodeling study for moisture diffusivities and moisturetransfer coefficients in drying of passion fruit peelrdquo Inter-national Journal of Heat and Mass Transfer vol 85pp 750ndash755 2015

[50] I Dincer ldquoMoisture transfer analysis during drying of slabwoodsrdquo Heat and Mass Transfer vol 34 no 4 pp 317ndash3201998

[51] H Darvishi Z Farhudi and N Behroozi-Khazaei ldquoMasstransfer parameters and modeling of hot air drying kinetics ofdill leavesrdquo Chemical Product and Process Modeling vol 12no 2 pp 1ndash12 2017

[52] M C Ndukwu C Dirioha F I Abam and V E IhediwaldquoHeat and mass transfer parameters in the drying of cocoyamslicerdquo Case Studies in ermal Engineering vol 9 pp 62ndash712017

[53] F Nadi and D Tzempelikos ldquoVacuum drying of apples (cvgolden delicious) drying characteristics thermodynamicproperties and mass transfer parametersrdquo Heat and MassTransfer vol 54 no 7 pp 1853ndash1866 2018


some quality characteristics such as texture color andflavor [8] +us the selection of proper drying techniques isa particularly important step in food processing

A mechanical vibration-assisted fluidized bed is also apotential advanced drying technique to improve the fluid-ization of such particles [9] +e electrical energy consumedby blower and vibration motor in a vibro-fluidized bed dryer(VFBD) has been reported to be around 55 of the electricalenergy of the blower in FBD [10] Furthermore by inducingvibration to the fluidized bed homogeneous temperaturecirculation can be achieved [11] agglomeration of solidparticles can be prevented and the fluidization velocity andpressure drop can be reduced [12 13]

In drying heat and mass transfer take place at the sametime due to its complexity+erefore optimization of dryingprocess conditions is important and for this mathematicalmodeling is an exceptional tool [14] Moreover modeling isapplied to find out the drying time and general nature ofdrying To design and select dryers knowledge of dryingbehavior is very important +ere are several studies re-ported in the literature to predict or develop the mostsuitable mathematical model for drying kinetics Generallyto predict the drying behavior of agricultural commoditiesdifferent mathematical models namely empirical semi-empirical and theoretical are used In most of the dryingexperiments empirical models validate the exceptional fit-ting of data but overlook the basics of the drying processesWhile theoretical models justify diffusion mechanism orheat and mass transfer mechanism [15] there are severalinvestigations on mathematical modeling of pumpkin seedsdrying kinetics for natural and forced convection solar dryer[6] solar tunnel dryer [16] tray drying [17] fluidized beddrying [17ndash20] and infrared dryer [21] However no studywas found for pumpkin seed drying using a vibro-fluidizedbed dryer

+e drying of biological samples is a complex methodand on occasions may not be explained using traditionalmodels For that purpose a neural network approach wasalso attempted for this study considering the novel nature ofthe drying process Artificial neural networks (ANN) are amachine learning method applied to predict intricate cor-relations among input and output conditions of drying andnonlinear problems [22] Many researchers used ANN toexplain moisture content rate of drying moisture ratioeffective diffusivity and specific energy consumption fordifferent agriculture products [23ndash25] Alvarez et al [26]successfully used ANN to correlate the heat and masstransfer parameters and vibration parameters (amplitudefrequency and vertical motion) for poppy seeds dried in avibrated fluidized bed dryer Kumar et al [27] used afeedforward backpropagation ANN model to predict themoisture ratio by feeding drying temperature and time asinput parameters According to our intensive literaturesearch no work has been reported on themodeling of dryingkinetics of pumpkin seeds in a VFBD by ANN and itscomparison with semiempirical drying models to the best ofour knowledge Moreover information on the mass transferparameters for pumpkin seed drying using VFBD is notavailable Such parameters are useful in designing drying

equipment and optimizing industrial drying processes andhence were taken up in this investigation

+erefore the aim of the current work is to performpumpkin seeds drying in a VFBD at various drying pa-rameters along with the determination of drying and masstransfer parameters +e study also deals with the predictionand comparison of the drying behavior of pumpkin seedsusing semiempirical modeling and ANN

2 Materials and Methods

21 Sample Preparation Pumpkins (Cucurbita maxima)were procured from the market of Narela New Delhi Indiaduring the summer season +e pumpkins were cut in halffollowed bymanual removal of the seeds Undeveloped seedswere removed and the seeds exhibiting the same size werewashed with deionized water and pressed in a sieve toremove the stringy pulp +e washed seeds were stored inlow-density polyethylene (LDPE) airtight bags at minus10degC andwere subjected to drying treatment within 24 h of storageHot-air oven method was used to estimate initial moisturecontent at 105degC for 24 h [28] All readings were replicatedthrice for accuracy

22 Experimental Setup An electrical power-operatedvibro-fluidized bed dryer was fabricated at the Departmentof Food Engineering NIFTEM Haryana India as depictedin Figure 1 +e components and specifications of VFBD arepresented in Table 1

23 Vibration Intensity +e vibration intensity (Γ) wascalculated using the following equation [29]

Γ A(2πf)

2

g (1)

where A is the amplitude mm g is the acceleration due togravity mms2 and f is the frequency of vibration HzPakowski et al [30] recommended the optimum range of Γfor proper structure of bed and drying rate as 1ndash6

24 Drying Experiments +e experiments were conductedat different conditions as shown in Table 2 Air velocityselected for fluidization was 4ms as given by Kaveh et al[7] for squash seeds Before each experiment the threedryers were run for 30min in no-load condition to ac-complish the chosen operating parameters of the dryingchamber For drying pumpkin seeds of approximately200 g were placed on the perforated sieve of the VFBD +eweight of moisture was recorded at 5min intervals Dryingwas continued until 0007ndash0009 kg H2Okg dm moistureremained in the sample which is the safe storage moisturecontent for high-oil-content seeds +e dried samples werecooled in desiccators at an ambient temperature (27degC) for15min and then filled in LDPE bags for additionalinvestigations




12345

6 amp 789

10111213141516


1

11

14

13

129

V A

1610

2

3

5

15

6

7

8

4

Temp





Volume 00384m3
















HLi 1113944n

j1111393610

i1Iiwij + bj (2)


H01 1

1 + eminus Hl1

+ b1 (3)

H01 e


eHl1 + e

minusHl1+ b1 (4)


Ol1 1113944

10

j1HojVj1 + b2 (5)






Bi 24848D

0375i

(7)


Di v

kH (8)


Bi hmH

Deff (9)






















Moi

sture

Con

tent

(kg

H2O

kg

dm)

20 40 60 80 100 1200Drying time (min)

40degC50degC60degC

002040608

1121416

(a)

Dry

ing

rate

(kg

H2O

kg

dmm

in)

20 40 60 80 100 1200Drying time (min)

40degC50degC60degC

00000001000200030004000500060007000800090010

(b)

0010203040506070809

1

Moi

sture

ratio

20 40 60 80 100 1200Drying time (min)

40degC50degC60degC

(c)




Two-term







Logarithmic












Table 4 Continued








Model


a

b

kk0


103283E-4099904

8020 7010 300 40 50 60Drying time (min)

00

02

04

06

08

10

Moi

sture

ratio


(a)

8020 7010 300 40 50 60Drying time (min)

-002

-001

000

001

Resid

ual o

f MR

(b)


0

2

4

6

Cou

nts

(c)

Resid

ual o

f pre

dict

ed M

R

0400 080602 1210Predicted MR

-002

-001

000

001

(d)





0 05 1 15Target

0 05 1 15Target

15

1

05

0

Out

put~

= 1

Targ

et +

00

005

15

1

05

0

Out

put~

= 1

Targ

et +

-00

011


DataFitY = T

0 05 1 15Target

0 05 1 15Target

15

1

05

0

Out

put~

= 1

Targ

et +

-00

029

15

1

05

0

Out

put~

= 1

Targ

et +

00

0024

Test R=099973 All R=099985

DataFitY = T

DataFitY = T

DataFitY = T

0 50 100 150155 Epochs

10-1

10-7

10-6

10-5

10-4

10-3

10-2



Mea

n Sq

uare

d Er

ror (

mse

)






j kWeights Bias



MCpred= 09815MCexp + 00061R2= 09967

MRpred = 09829MRexp + 00032R2= 09963

00

02

04

06

08

10

00 02 04 06 08 10

Pred

ucte

d m

oistu

re co

nten

t (g

H2O

g d

m)


0 20 40 60

Erro

r in

MC

pred

ictio

n


00 02 04 06 08 10

Pred

icte

d m

oistu

re ra

tio


0 20 40 60

Erro

r in

MR

pred

ictio

n


-0015

-0010

-0005

0000

0005

0010

0015

0020

0025

0030

00

02

04

06

08

10

-0010

-0005

0000

0005

0010

0015

0020






4 Conclusions


Data Availability




Acknowledgments



References








ln M

R

-7

-6

-5

-4

-3

-2

-1

00 20 40 60 80 100 120

Drying time (min)

40degC50degC60degC

(a)

ln D

eff

-207

-206

-205

-204

-203

-202

-201

-2000029 0003 00031 00032 00033

1T (K-1)

(b)





























































12345

6 amp 789

10111213141516


1

11

14

13

129

V A

1610

2

3

5

15

6

7

8

4

Temp





Volume 00384m3
















HLi 1113944n

j1111393610

i1Iiwij + bj (2)


H01 1

1 + eminus Hl1

+ b1 (3)

H01 e


eHl1 + e

minusHl1+ b1 (4)


Ol1 1113944

10

j1HojVj1 + b2 (5)






Bi 24848D

0375i

(7)


Di v

kH (8)


Bi hmH

Deff (9)






















Moi

sture

Con

tent

(kg

H2O

kg

dm)

20 40 60 80 100 1200Drying time (min)

40degC50degC60degC

002040608

1121416

(a)

Dry

ing

rate

(kg

H2O

kg

dmm

in)

20 40 60 80 100 1200Drying time (min)

40degC50degC60degC

00000001000200030004000500060007000800090010

(b)

0010203040506070809

1

Moi

sture

ratio

20 40 60 80 100 1200Drying time (min)

40degC50degC60degC

(c)




Two-term







Logarithmic












Table 4 Continued








Model


a

b

kk0


103283E-4099904

8020 7010 300 40 50 60Drying time (min)

00

02

04

06

08

10

Moi

sture

ratio


(a)

8020 7010 300 40 50 60Drying time (min)

-002

-001

000

001

Resid

ual o

f MR

(b)


0

2

4

6

Cou

nts

(c)

Resid

ual o

f pre

dict

ed M

R

0400 080602 1210Predicted MR

-002

-001

000

001

(d)





0 05 1 15Target

0 05 1 15Target

15

1

05

0

Out

put~

= 1

Targ

et +

00

005

15

1

05

0

Out

put~

= 1

Targ

et +

-00

011


DataFitY = T

0 05 1 15Target

0 05 1 15Target

15

1

05

0

Out

put~

= 1

Targ

et +

-00

029

15

1

05

0

Out

put~

= 1

Targ

et +

00

0024

Test R=099973 All R=099985

DataFitY = T

DataFitY = T

DataFitY = T

0 50 100 150155 Epochs

10-1

10-7

10-6

10-5

10-4

10-3

10-2



Mea

n Sq

uare

d Er

ror (

mse

)






j kWeights Bias



MCpred= 09815MCexp + 00061R2= 09967

MRpred = 09829MRexp + 00032R2= 09963

00

02

04

06

08

10

00 02 04 06 08 10

Pred

ucte

d m

oistu

re co

nten

t (g

H2O

g d

m)


0 20 40 60

Erro

r in

MC

pred

ictio

n


00 02 04 06 08 10

Pred

icte

d m

oistu

re ra

tio


0 20 40 60

Erro

r in

MR

pred

ictio

n


-0015

-0010

-0005

0000

0005

0010

0015

0020

0025

0030

00

02

04

06

08

10

-0010

-0005

0000

0005

0010

0015

0020






4 Conclusions


Data Availability




Acknowledgments



References








ln M

R

-7

-6

-5

-4

-3

-2

-1

00 20 40 60 80 100 120

Drying time (min)

40degC50degC60degC

(a)

ln D

eff

-207

-206

-205

-204

-203

-202

-201

-2000029 0003 00031 00032 00033

1T (K-1)

(b)































































HLi 1113944n

j1111393610

i1Iiwij + bj (2)


H01 1

1 + eminus Hl1

+ b1 (3)

H01 e


eHl1 + e

minusHl1+ b1 (4)


Ol1 1113944

10

j1HojVj1 + b2 (5)






Bi 24848D

0375i

(7)


Di v

kH (8)


Bi hmH

Deff (9)






















Moi

sture

Con

tent

(kg

H2O

kg

dm)

20 40 60 80 100 1200Drying time (min)

40degC50degC60degC

002040608

1121416

(a)

Dry

ing

rate

(kg

H2O

kg

dmm

in)

20 40 60 80 100 1200Drying time (min)

40degC50degC60degC

00000001000200030004000500060007000800090010

(b)

0010203040506070809

1

Moi

sture

ratio

20 40 60 80 100 1200Drying time (min)

40degC50degC60degC

(c)




Two-term







Logarithmic












Table 4 Continued








Model


a

b

kk0


103283E-4099904

8020 7010 300 40 50 60Drying time (min)

00

02

04

06

08

10

Moi

sture

ratio


(a)

8020 7010 300 40 50 60Drying time (min)

-002

-001

000

001

Resid

ual o

f MR

(b)


0

2

4

6

Cou

nts

(c)

Resid

ual o

f pre

dict

ed M

R

0400 080602 1210Predicted MR

-002

-001

000

001

(d)





0 05 1 15Target

0 05 1 15Target

15

1

05

0

Out

put~

= 1

Targ

et +

00

005

15

1

05

0

Out

put~

= 1

Targ

et +

-00

011


DataFitY = T

0 05 1 15Target

0 05 1 15Target

15

1

05

0

Out

put~

= 1

Targ

et +

-00

029

15

1

05

0

Out

put~

= 1

Targ

et +

00

0024

Test R=099973 All R=099985

DataFitY = T

DataFitY = T

DataFitY = T

0 50 100 150155 Epochs

10-1

10-7

10-6

10-5

10-4

10-3

10-2



Mea

n Sq

uare

d Er

ror (

mse

)






j kWeights Bias



MCpred= 09815MCexp + 00061R2= 09967

MRpred = 09829MRexp + 00032R2= 09963

00

02

04

06

08

10

00 02 04 06 08 10

Pred

ucte

d m

oistu

re co

nten

t (g

H2O

g d

m)


0 20 40 60

Erro

r in

MC

pred

ictio

n


00 02 04 06 08 10

Pred

icte

d m

oistu

re ra

tio


0 20 40 60

Erro

r in

MR

pred

ictio

n


-0015

-0010

-0005

0000

0005

0010

0015

0020

0025

0030

00

02

04

06

08

10

-0010

-0005

0000

0005

0010

0015

0020






4 Conclusions


Data Availability




Acknowledgments



References








ln M

R

-7

-6

-5

-4

-3

-2

-1

00 20 40 60 80 100 120

Drying time (min)

40degC50degC60degC

(a)

ln D

eff

-207

-206

-205

-204

-203

-202

-201

-2000029 0003 00031 00032 00033

1T (K-1)

(b)








































































Moi

sture

Con

tent

(kg

H2O

kg

dm)

20 40 60 80 100 1200Drying time (min)

40degC50degC60degC

002040608

1121416

(a)

Dry

ing

rate

(kg

H2O

kg

dmm

in)

20 40 60 80 100 1200Drying time (min)

40degC50degC60degC

00000001000200030004000500060007000800090010

(b)

0010203040506070809

1

Moi

sture

ratio

20 40 60 80 100 1200Drying time (min)

40degC50degC60degC

(c)




Two-term







Logarithmic












Table 4 Continued








Model


a

b

kk0


103283E-4099904

8020 7010 300 40 50 60Drying time (min)

00

02

04

06

08

10

Moi

sture

ratio


(a)

8020 7010 300 40 50 60Drying time (min)

-002

-001

000

001

Resid

ual o

f MR

(b)


0

2

4

6

Cou

nts

(c)

Resid

ual o

f pre

dict

ed M

R

0400 080602 1210Predicted MR

-002

-001

000

001

(d)





0 05 1 15Target

0 05 1 15Target

15

1

05

0

Out

put~

= 1

Targ

et +

00

005

15

1

05

0

Out

put~

= 1

Targ

et +

-00

011


DataFitY = T

0 05 1 15Target

0 05 1 15Target

15

1

05

0

Out

put~

= 1

Targ

et +

-00

029

15

1

05

0

Out

put~

= 1

Targ

et +

00

0024

Test R=099973 All R=099985

DataFitY = T

DataFitY = T

DataFitY = T

0 50 100 150155 Epochs

10-1

10-7

10-6

10-5

10-4

10-3

10-2



Mea

n Sq

uare

d Er

ror (

mse

)






j kWeights Bias



MCpred= 09815MCexp + 00061R2= 09967

MRpred = 09829MRexp + 00032R2= 09963

00

02

04

06

08

10

00 02 04 06 08 10

Pred

ucte

d m

oistu

re co

nten

t (g

H2O

g d

m)


0 20 40 60

Erro

r in

MC

pred

ictio

n


00 02 04 06 08 10

Pred

icte

d m

oistu

re ra

tio


0 20 40 60

Erro

r in

MR

pred

ictio

n


-0015

-0010

-0005

0000

0005

0010

0015

0020

0025

0030

00

02

04

06

08

10

-0010

-0005

0000

0005

0010

0015

0020






4 Conclusions


Data Availability




Acknowledgments



References








ln M

R

-7

-6

-5

-4

-3

-2

-1

00 20 40 60 80 100 120

Drying time (min)

40degC50degC60degC

(a)

ln D

eff

-207

-206

-205

-204

-203

-202

-201

-2000029 0003 00031 00032 00033

1T (K-1)

(b)































































Table 4 Continued








Model


a

b

kk0


103283E-4099904

8020 7010 300 40 50 60Drying time (min)

00

02

04

06

08

10

Moi

sture

ratio


(a)

8020 7010 300 40 50 60Drying time (min)

-002

-001

000

001

Resid

ual o

f MR

(b)


0

2

4

6

Cou

nts

(c)

Resid

ual o

f pre

dict

ed M

R

0400 080602 1210Predicted MR

-002

-001

000

001

(d)





0 05 1 15Target

0 05 1 15Target

15

1

05

0

Out

put~

= 1

Targ

et +

00

005

15

1

05

0

Out

put~

= 1

Targ

et +

-00

011


DataFitY = T

0 05 1 15Target

0 05 1 15Target

15

1

05

0

Out

put~

= 1

Targ

et +

-00

029

15

1

05

0

Out

put~

= 1

Targ

et +

00

0024

Test R=099973 All R=099985

DataFitY = T

DataFitY = T

DataFitY = T

0 50 100 150155 Epochs

10-1

10-7

10-6

10-5

10-4

10-3

10-2



Mea

n Sq

uare

d Er

ror (

mse

)






j kWeights Bias



MCpred= 09815MCexp + 00061R2= 09967

MRpred = 09829MRexp + 00032R2= 09963

00

02

04

06

08

10

00 02 04 06 08 10

Pred

ucte

d m

oistu

re co

nten

t (g

H2O

g d

m)


0 20 40 60

Erro

r in

MC

pred

ictio

n


00 02 04 06 08 10

Pred

icte

d m

oistu

re ra

tio


0 20 40 60

Erro

r in

MR

pred

ictio

n


-0015

-0010

-0005

0000

0005

0010

0015

0020

0025

0030

00

02

04

06

08

10

-0010

-0005

0000

0005

0010

0015

0020






4 Conclusions


Data Availability




Acknowledgments



References








ln M

R

-7

-6

-5

-4

-3

-2

-1

00 20 40 60 80 100 120

Drying time (min)

40degC50degC60degC

(a)

ln D

eff

-207

-206

-205

-204

-203

-202

-201

-2000029 0003 00031 00032 00033

1T (K-1)

(b)





























































0 05 1 15Target

0 05 1 15Target

15

1

05

0

Out

put~

= 1

Targ

et +

00

005

15

1

05

0

Out

put~

= 1

Targ

et +

-00

011


DataFitY = T

0 05 1 15Target

0 05 1 15Target

15

1

05

0

Out

put~

= 1

Targ

et +

-00

029

15

1

05

0

Out

put~

= 1

Targ

et +

00

0024

Test R=099973 All R=099985

DataFitY = T

DataFitY = T

DataFitY = T

0 50 100 150155 Epochs

10-1

10-7

10-6

10-5

10-4

10-3

10-2



Mea

n Sq

uare

d Er

ror (

mse

)






j kWeights Bias



MCpred= 09815MCexp + 00061R2= 09967

MRpred = 09829MRexp + 00032R2= 09963

00

02

04

06

08

10

00 02 04 06 08 10

Pred

ucte

d m

oistu

re co

nten

t (g

H2O

g d

m)


0 20 40 60

Erro

r in

MC

pred

ictio

n


00 02 04 06 08 10

Pred

icte

d m

oistu

re ra

tio


0 20 40 60

Erro

r in

MR

pred

ictio

n


-0015

-0010

-0005

0000

0005

0010

0015

0020

0025

0030

00

02

04

06

08

10

-0010

-0005

0000

0005

0010

0015

0020






4 Conclusions


Data Availability




Acknowledgments



References








ln M

R

-7

-6

-5

-4

-3

-2

-1

00 20 40 60 80 100 120

Drying time (min)

40degC50degC60degC

(a)

ln D

eff

-207

-206

-205

-204

-203

-202

-201

-2000029 0003 00031 00032 00033

1T (K-1)

(b)






























































j kWeights Bias



MCpred= 09815MCexp + 00061R2= 09967

MRpred = 09829MRexp + 00032R2= 09963

00

02

04

06

08

10

00 02 04 06 08 10

Pred

ucte

d m

oistu

re co

nten

t (g

H2O

g d

m)


0 20 40 60

Erro

r in

MC

pred

ictio

n


00 02 04 06 08 10

Pred

icte

d m

oistu

re ra

tio


0 20 40 60

Erro

r in

MR

pred

ictio

n


-0015

-0010

-0005

0000

0005

0010

0015

0020

0025

0030

00

02

04

06

08

10

-0010

-0005

0000

0005

0010

0015

0020






4 Conclusions


Data Availability




Acknowledgments



References








ln M

R

-7

-6

-5

-4

-3

-2

-1

00 20 40 60 80 100 120

Drying time (min)

40degC50degC60degC

(a)

ln D

eff

-207

-206

-205

-204

-203

-202

-201

-2000029 0003 00031 00032 00033

1T (K-1)

(b)



























































4 Conclusions


Data Availability




Acknowledgments



References








ln M

R

-7

-6

-5

-4

-3

-2

-1

00 20 40 60 80 100 120

Drying time (min)

40degC50degC60degC

(a)

ln D

eff

-207

-206

-205

-204

-203

-202

-201

-2000029 0003 00031 00032 00033

1T (K-1)

(b)



























































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