research article modeling of energy demand in the...

Research ArticleModeling of Energy Demand in the Greenhouse Using PSO-GAHybrid Algorithms

Jiaoliao Chen12 Jiangwu Zhao1 Fang Xu1 Haigen Hu3 QingLin Ai1 and Jiangxin Yang2

1Key Laboratory of EampM Zhejiang University of Technology Ministry ofEducation amp Zhejiang Province Hangzhou 310014 China2Institute of Manufacturing Engineering Zhejiang University Hangzhou 310027 China3College of Computer Science and Technology Zhejiang University of Technology Hangzhou 310014 China

Correspondence should be addressed to Fang Xu fangxzjuteducn

Received 30 May 2014 Accepted 14 October 2014

Academic Editor Hiroyuki Mino

Copyright copy 2015 Jiaoliao Chen et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Modeling of energy demand in agricultural greenhouse is very important tomaintain optimum inside environment for plant growthand energy consumption decreasingThis paper deals with the identification parameters for physicalmodel of energy demand in thegreenhouse using hybrid particle swarm optimization and genetic algorithms technique (HPSO-GA) HPSO-GA is developed toestimate the indistinct internal parameters of greenhouse energymodel which is built based on thermal balance Experiments wereconducted to measure environment and energy parameters in a cooling greenhouse with surface water source heat pump systemwhich is located in mid-east China System identification experiments identify model parameters using HPSO-GA such as inertiasand heat transfer constantsThe performance of HPSO-GA on the parameter estimation is better than GA and PSOThis algorithmcan improve the classification accuracy while speeding up the convergence process and can avoid premature convergence Systemidentification results prove that HPSO-GA is reliable in solving parameter estimation problems for modeling the energy demandin the greenhouse

1 Introduction

Greenhouses are used to grow crops for better quality andto protect them against natural environmental effects such ashigh or low temperature The energy consumption is neces-sary tomaintain a suitable temperature for crop production inthe greenhouse Modeling of energy demand in agriculturalgreenhouse is very important to maintain optimum insideenvironment and decrease energy consumption [1]

Greenhouse is a complex systemwith nonlinear randomand strong coupling uncertain features [2] Mechanismmod-eling based on the physical processes uses unsteady heat andmass transfer to get the differential equations of greenhousedynamic process [3ndash5] But some physical parameters in themodel are difficult to measure or changing with the cropgrowth and outside weather Black-box modeling is obtainedfrom inputoutput measurements of a dynamical systemwithout knowledge of its inner physical and chemical lawsand it has been widely applied for various items [6] Neural

networks as the typical black-box have been applied tomodel the greenhouse microclimate [7ndash9] However in theblack-box model it is impossible to train all possible datawhich can result in overfitting

Systems identification is suitable in nonlinear systemsfor which a mathematical model is known and for whichinputoutput data is available in the experiments but forwhich actual values of parameters in the model are unknown[10] The evolutionary algorithms are model-based recog-nition methods and have been applied for uncertain opti-mization problems [11 12] Some researchers have appliedglobal optimization methods for calibration parameters ingreenhouse microclimate model such as genetic algorithm(GA) ant colony optimization (ACO) and particle swarmoptimization (PSO) [13ndash15] Hasni et al found that theperformance of a greenhouse climate model using PSO isbetter than GA in terms of calculation time and accuracy ofthe results [16]

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 871075 6 pageshttpdxdoiorg1011552015871075

2 Mathematical Problems in Engineering

Yet PSO is easy to prematurely converge and lead to theundesired local solution GA may require a large number ofredundant iterations and result in long computing times andlow problem-solving efficiency [17] Algorithmic operatorsand parameters typically interact with one another nonlin-early it is extremely hard to figure out the most optimalcombinatorial strategy [18] And the single algorithm defectmakes it not suitable for the mutative greenhouse model[19] HPSO-GA shows superiority compared with othersingle optimization methods such as GA and PSO and canovercome the disadvantages of particle swarm optimizationand genetic algorithm [20]

Therefore this paper proposes a novel method for energyconsumption prediction in the greenhouse based on theHPSO-GA The parameters for physical model of energydemand are calibrated using HPSO-GA for the profoundoptimization performance in the nonlinear greenhouse sys-tem with surface water source heat pumps system

2 Materials and Methods

21 Experiment Setup A multispan glass greenhouse wasemployed in this experiment and it was located in JiangsuProvince China (longitude 120∘291015840 east latitude 31∘761015840north)This greenhouse is coveredwith a single layer of 4mmthickness glass 72m length in the north-south direction and75m height and consisted of 28 spans 4m wide each Theoutside air temperature wind speed and PARweremeasuredby a small weather station (GalCon Eldarshany Co Israel)The air temperatures at the height of 4m from the groundof four positions inside were measured by sensors (HMT100Vaisala Co Finland) Inside air temperature was the averageof 4 temperature sensors in the greenhouse Surface watersource heat pumps systemwas applied in the greenhouseTheenergy consumption ismeasured by energymeter (HCM1158Honeywell Co Germany) according to the water flow rateand the difference of supply and return water temperaturesThe data from the sensors were automatically recordedevery 5min by a data logger which we have developed Theexperiment was carried out from June 2 to June 7 2012

22 Greenhouse Environment Model Greenhouse environ-ment model in the physical and physiological methods thattake place inside greenhouses based on mass and energybalances including the biological behavior of plants Math-ematical models of greenhouse microclimate are influencedby several elements of the greenhouse (heat flow and conduc-tion vapor diffusion etc) and the outside boundaries (solarradiation air temperature etc) which is shown in Figure 1The thermal balance inside the greenhouse defines the rate ofchange of temperature which can be transferred to calculatethe energy supply requirements Consider

119902119904(119905) = 120588

119886119881119862119886

119889119879119894(119905)

119889119905+ 119902119897(119905) + 119902

119888(119905) + 119902

119908(119905)

+ 119902119890(119905) + 119902

119901(119905) minus 119902

119905(119905)

(1)

where 119902119904(119905) is the energy supply over time in W 120588

119886is the air

density in kgmminus3 119881 is the volume of the greenhouse in m3

ql

qw

qc qp qeqs

Crop

Top windows

Fan coil unit

qt

Figure 1 The thermal balance of greenhouse environment

119862119886is air specific heat in Jkgminus1Kminus1 119879

119894(119905) is air temperature

inside the greenhouse over time in K 119902119897(119905) is the energy flux

due to the long wave thermal radiation over time in W 119902119888(119905)

is the heat flux through the cover over time inW 119902119908(119905) is heat

flux from ventilation and infiltration over time in W 119902119890(119905) is

the heat flux due to crop transpiration over time in W 119902119901(119905)

is the heat flux due to the convection between greenhouseair with soil and crop leaves over time in W and 119902

119905(119905) is the

net solar radiation into greenhouse over time in W Sincethe top windows and side windows are all closed when thecooling system is working heat flux from ventilation 119902

119908can

be ignored and 119905 is time series variableThe net solar radiation into greenhouse 119902

119905(119905) can be

described as follows according to radiation law

119902119905(119905) = 119860

119904119868119886(119905) 120591119886 (2)

where 119860119904is the surface area of cover material in m2 119868

119886(119905) is

outdoor global radiation over time in Wmminus2 and 120591119886is cover

material absorption coefficientAccording to the nonlinear Stefan-Boltzmann law the

thermal long wave radiation exchange between interior andexterior can be written as follows

119902119897(119905) = 120576

12119860119904120590 (119879119894(119905)4

minus 119879sky (119905)4

) (3)

where 119860119904is the area of covering in m2 120590 is the Stefan-

Boltzmann constant of 567 times 10minus8Wmminus2Kminus4 119879sky(119905) issky temperature over time in K and 120576

12is the combined

emissivity between the cover and sky which is found fromthe individual emission coefficients 120576

1and 1205762

12057612= (1205761

minus1

+ 1205762

minus1

minus 1)minus1

(4)

According to Aubinet [21] sky temperature related totemperature outside the greenhouse is expressed as follows

119879sky (119905) = 94 + 126 ln (119890119900) minus 13119896 + 0341119879

119900(119905) (5)

where 119890119900is actual air water vapor pressure outside in Pa

119879119900(119905) is temperature outside the greenhouse over time in

K and 119896 is the sky clearness index which is 2233 Pa and39 respectively based on NASA Surface Meteorologicaland Solar Energy information [22]

The greenhouse air exchanges energy and water vapor(condensation) with the inner surface of the cover and

Mathematical Problems in Engineering 3

the cover exchanges energy with the outside air The heatexchanged by conduction and convection between the coverand the air resulted from driving force for the exchange dueto the temperature differenceThe heat exchanged by internalthermal curtain and infiltration is also dependent on theinside and outside air temperature Consider

119902119888(119905) = 119860

119904sdot 119870119892sdot 119870119888sdot (119879119894(119905) minus 119879

119900(119905)) (6)

where 119860119904is the area of greenhouse cover material in m2 119870

119892

is the heat transfer coefficient in Wmminus2Kminus1 and119870119888is correct

coefficient of internal thermal curtain and infiltrationThe transport of energy from the leaf is in general defined

in the same way as the heat transfer from other surfacesThe sensible heat flux 119902

119890was expressed with respect to the

temperature difference between inside air and canopy

119902119901(119905) = 119860

119892120588119862119901LAI(

(119879V (119905) minus 119879119894 (119905))

119903119886

) (7)

Latent heat flux due to crop transpiration in greenhousecan be described in terms of the crop canopy available energyand from the inside air saturation deficit by means of thePenman-Monteith formula

119902119890(119905) = 119860

119892sdot 120582 sdot 119864 (119905) (8)

120582119864 (119905) =119868119886(119905) 120591119886Δ + 2LAI (120588119888

119886119903119904) (119890119904(119905) minus 119890

119886(119905))

Δ + 120574 (1 + 119903119888119903119886)

(9)

where 120582 is the latent heat of vaporization (245 kJkg) 119879V(119905)is the canopy temperature over time in K 119862

119901is the specific

heat of air at constant pressure LAI is theplant canopy leafarea index 119860

119892is the area of ground in m2 119864(119905) is canopy

transpiration rate over time in kgmminus2sminus1 119890119904(119905) is the saturated

vapor pressure of the air (assumed at the leaf temperature)over time in Pa 119890

119886(119905) is thewater vapor pressure of the air over

time in Pa 119903119888and 119903119886are the leaf aerodynamic and stomatal

resistances of the leaves of 150 sm and 290 sm respectively[23] 120574 is the psychometric constant of 00646 kPaKminus1 and Δ

is the slope of the water vapor saturation curve at119879119894in PaKminus1

Some parameters of the model are changing all the timeor are not easy to measure such as LAI 119870

119892 and 119870

119888 The

optimization method can be used to calibrate parametersaccording to root mean square error (Rmse) between theactual energy consumption and predicted values The objec-tive function of the algorithm estimation parameters is asfollows

Rmse = 1

Max 119905

Max 119905sum

119905=1

radic(119902119904(119905 120583) minus 119902real (119905))

2

(10)

where 119902real(119905) is real energy consumption Max t is the max-imum value in the time series and 120583 is estimated parametervector [LAI 119896

119892119896119888]

23 HPSO-GA Algorithm In the present study we proposethe HPSO-GA which could optimize the coefficients of

equations with better performance To better optimize theparameters of energy demand model in the greenhouse aneffective hybrid optimization algorithm is developed basedon PSO and GA which can fully combine the merits of thesetwo methods without their drawbacks

A 4N population is generated for an m-dimension opti-mization problem Randomly generated initial particleswarms 120578

1 1205782 1205783 120578

4119873calculate the fitness value according

to formula (9) To maintain the stability of the individualsthe better individuals are kept to speed up the convergenceThe 2N individuals with better fitness values are used in PSOevolution to create a new 2N population Further to avoidthe particle from getting stuck in the local minimum 2Nindividuals with worse fitness values are subjected to GAoperation to create a new 2N population Finally the new 2Npopulation by PSO is combined with the new 2N individualsby GA to form a new 4N population for the next generationoptimization When the algorithm reaches the maximumgeneration (max n) or Rmse is less than the setting value(min r) the best fitness value and best parameters are outputThe flowchart for the HPSO-GA is shown in Figure 2

The PSO evolution consists of a swarm of particles andeach particle represents a position in an 119899-dimensional spaceThe status of a particle in the search space is characterized bytwo factors such as the position and velocity Each particleis associated with a velocity and a memory of personal bestposition (119901119887119890119904119905) and a memory of the best position (119892119887119890119904119905)At each step by using the individual 119901119887119890119904119905 and 119892119887119890119904119905 a newvelocity for the particle is updated by

V119899+1119894

= 119908 sdot V119899119894

+ 1198881sdot 1199031sdot (119901119887119890119904119905

119899

119894

minus 120578119899

119894

) + 1198882sdot 1199032sdot (119892119887119890119904119905

119899

minus 120578119899

119894

)

(11)

Based on the updated velocity each particle changes itsposition as follows

120578119899+1

119894

= 120578119899

119894

+ V119899+1119894

(12)

where V119899119894

is the velocity of the particle 119894 in the 119899th iteration119908 is inertia weight 120578119899

119894

is current position vector 119901119887119890119904119905119899119894

is thebest previous position of this particle 119892119887119890119904119905119899 is global bestprevious position among all the particles in 119899th iteration 119903

1

and 1199032are two randomvariables with range [0 1] 119888

1and 1198882are

positive constant learning rates and the particle 119894 isin (1 4119873)In order to increase the particles diversity and inhibit

premature phenomenon GA operators crossover and muta-tion are utilized in the HPSO-GA m-dimension vector isconverted into binary according to resolution ratio 119903 Thecrossover andmutation operation are shown in Figures 3 and4 respectively

The parts of 1205781and 120578

2between crossover site 1 and

crossover site 2 are exchangedThe crossover site is generatedrandomly and 119901

119888is the crossover probability 119901

119898is the

mutation probability in GA and the bits mutate randomlydepending on 119901

119898 The 2N particle 120578

1015840

119894

is reborn by theGA operators The velocity is assigned randomly and bestprevious position 119901119887119890119904119905

119894is set as 12057810158401015840

119894

for PSO evolution of thenext generation


Sort the particles according to fitness value

Update velocity of

Update position of

particle

Evaluate the fitness values respectively

Output the best Rmse andparameters

PSOGA

No

Yes

Update pbest gbest

Best 2N Worst 2N

Old population

New population

Initializeparameters N pc

pm and n

n + 1

1205781 1205782middot middot middot 1205782N+1 1205784Nmiddot middot middot


particle 120578998400i

Crossover operator get 120578998400i

Mutation operator get 120578998400998400i

Set v randomly and pbesti = 120578998400998400i

n gt max nor Rmse lt min r

Figure 2 The flowchart for HPSO-GA

3 Results and Discussion

According to formulas (1)ndash(8) the physical energy model inthe experimental greenhouse is built in the MatlabSimulinkThe optimization algorithm is programmed in a Matlab M-file which is used to calibrate estimated parameters vector120583 in the Simulink simulation rapidly and efficiently Theascertained parameters in the model and the HPSO-GAparameters are shown in Table 1

A computer with 235GHz Core Duo processor and 2GBRAM memory was used to run each optimization algorithm10 times independentlyThe simulation data in Table 2 showsthe average of optimization results with three optimizationalgorithms According to the best parameters the predictioncurve for energy consumption can be achieved in Figure 5

When the objective fitness value Min r was set as 24 times105 HPSO-GA decreases the exit generation Computationaltime by HPSO-GA is 156 seconds which is automaticallyrecorded by the optimization software Compared with PSOandGA HPSO-GA saves time of 33 seconds and 521 secondsrespectively In Figure 5 it can be observed that there is adeviation between the simulation value and actual energyconsumption particularly during the night However thethree optimization algorithms results were all fitted to actualenergy consumption which implies that three optimizationalgorithms are successful in estimating greenhouse modelparameters

As seen in Table 2 the HPSO-GA with better efficiencyat estimating the parameters saves computational time of21 and 77 compared with PSO and GA respectively


Parent 1205781

Crossover site 1 Crossover site 2

Crossover

Parent 1205782

l11 l12

l11 l12

l11 l12

l11 l12

middot middot middot middot middot middot

middot middot middot






l1r

l1r

l1r

l1r

l21

l21

l21

l21

l22

l22

l22

l22

lmr

lmr

lmr

lmr

Offspring 1205789984001

Offspring 1205789984002

Figure 3 Crossover operation on the individuals

Mutationparticle

New

l11 l1r

l1r

l12 l21 l22

l22l21l12

l13 middot middot middot



middot middot middotl13998400l11998400

lmrminus1 lmr

lmrminus1 lmr

Particle 120578998400i

120578998400998400i

Figure 4 Mutation operation on the individuals

Table 1 The parameters in the greenhouse model and the HPSO-GA

Parameters Symbol ValueVolume 119881m3 99584Glass transmissivity 120591 086Sky emissivity 120576

1

090Glass emissivity 120576

2

090Air density 120588

119886

kgmminus3 12Specific heat 119862

119886

Jkgminus1Kminus1 1008The size of the populations 4119873 20Dimension of the vector 119898 3Positive constant learning rates 119888

1

and 1198882

14995Crossover probability 119901

119888

01Mutation probability 119901

119898

001Resolution ratio 119903 10Evolution generation max 119899 200Setting minimum value Rmse Min 119903 240000

When the max n is set to be less than 80 the HPSO-GAgives a better estimation of energy consumption with a 15significant level than PSO and with an 85 significant levelthan GA When the max n is more than 115 the objectivefitness value optimized by HPSO-GA is similar to PSO andGA The HPSO-GA can quickly obtain the optimal solutionin the early evolution since it speeds up the convergenceprocess During the optimization process of ten times thelocal optimumhas been resulted fromPSO formore than twotimes while it does not occur by HPSO-GA Overcoming theundesired local solution the reliability and stability ofHPSO-GA are successfully approved in the parameters estimationapplications of greenhouse model

0 12 24 36 48 60 72 84 96 108 1200

2

4

6

8

10

12

14

16

Hours

Ener

gy d

eman

d (W

)

Energy costPSO

HPSO-GAGA

times105

Figure 5 Simulated energy demand with three optimization algo-rithms and actual energy consumption

Table 2 Optimization results with three optimization algorithms

Parameters PSO GA HPSO-GA119870119892

661 669 618119870119888

065 078 075LAI 408 516 525Time spent (seconds) 189 677 156Exit generation 86 115 73Rmse 238525 239228 238914

4 Conclusions

In this study HPSO-GA is developed to estimate the indis-tinct internal parameters of greenhouse energy model whichis built based on thermal balance Experiments were con-ducted to measure environment and energy parameters in acooling greenhouse with surface water source heat pump sys-tem Simulated energy consumption by the identified modelusing HPSO-GA is in agreement with the actual energyconsumption which proves that HPSO-GA can be used topredict the energy demand in the greenhouse Comparedwith GA and PSO HPSO-GA saves the optimization timeof more than 21 when the maximum generation is lessthan 80 The HPSO-GA shows excellent ability in solvingparameter estimation problems in the greenhouse systemincluding the optimized speed and accuracy

Conflict of Interests

The authors declare no conflict of interests regarding thepublication of this paper


Acknowledgments

The authors would like to thank the staffs of Shentai Hi-TechDemonstration Garden of Agriculture for their experimentalassistance This work was supported by the National NaturalScience Foundation of China (nos 61374094 and 51275470)the Program for Zhejiang Leading Team of SampT Innovation(no 2011R50011-02) and the Open Foundation of Key Labo-ratory of EampM (ZhejiangUniversity of Technology)Ministryof Education amp Zhejiang Province (no EM2013061802)

References

[1] A Marucci M Carlini S Castellucci and A CappuccinildquoEnergy efficiency of a greenhouse for the conservation of for-estry biodiversityrdquo Mathematical Problems in Engineering vol2013 Article ID 768658 7 pages 2013

[2] J L Tovany R Ross-Leon J Ruiz-Leon A Ramırez-Trevinoand O Begovich ldquoGreenhouse modeling using continuoustimed Petri netsrdquo Mathematical Problems in Engineering vol2013 Article ID 639306 9 pages 2013

[3] G P A Bot ldquoPhysical modelling of greenhouse climaterdquo inProceedings of the IFACISHS Workshop pp 7ndash12 1991

[4] I Impron S Hemming and G P A Bot ldquoSimple greenhouseclimate model as a design tool for greenhouses in tropicallowlandrdquo Biosystems Engineering vol 98 no 1 pp 79ndash89 2007

[5] K S Kumar M K Jha K N Tiwari and A Singh ldquoModelingand evaluation of greenhouse for floriculture in subtropicsrdquoEnergy and Buildings vol 42 no 7 pp 1075ndash1083 2010

[6] D-P Tan P-Y Li Y-X Ji D-H Wen and C Li ldquoSA-ANN-based slag carry-over detection method and the embeddedWME platformrdquo IEEE Transactions on Industrial Electronicsvol 60 no 10 pp 4702ndash4713 2013

[7] I Seginer ldquoSome artificial neural network applications to green-house environmental controlrdquo Computers and Electronics inAgriculture vol 18 no 2-3 pp 167ndash186 1997

[8] P M Ferreira E A Faria and A E Ruano ldquoNeural networkmodels in greenhouse air temperature predictionrdquo Neurocom-puting vol 43 no 1ndash4 pp 51ndash75 2002

[9] M Trejo-Perea G Herrera-Ruiz J Rios-Moreno R CMiranda and E Rivas-Araiza ldquoGreenhouse energy consump-tion prediction using neural networks modelsrdquo InternationalJournal of Agriculture and Biology vol 11 no 1 pp 1ndash6 2009

[10] D P Tan and L B Zhang ldquoA WP-based nonlinear vibrationsensing method for invisible liquid steel slag detectionrdquo Sensorsand Actuators B Chemical vol 202 pp 1257ndash1269 2014

[11] T Ganesan I Elamvazuthi K Z K Shaari and P Vas-ant ldquoSwarm intelligence and gravitational search algorithmfor multi-objective optimization of synthesis gas productionrdquoApplied Energy vol 103 pp 368ndash374 2013

[12] T Ganesan P Vasant and I Elamvazuthi ldquoOptimization ofnonlinear geological structure mapping using hybrid neuro-genetic techniquesrdquoMathematical andComputerModelling vol54 no 11-12 pp 2913ndash2922 2011

[13] J P Coelho P B D M Oliveira and J B Cunha ldquoGreenhouseair temperature predictive control using the particle swarmoptimisation algorithmrdquo Computers and Electronics in Agricul-ture vol 49 no 3 pp 330ndash344 2005

[14] J M Herrero X Blasco MMartınez C Ramos and J SanchisldquoNon-linear robust identification of a greenhouse model using

multi-objective evolutionary algorithmsrdquo Biosystems Engineer-ing vol 98 no 3 pp 335ndash346 2007

[15] R Guzman-Cruz R Castaneda-Miranda J J Garcıa-EscalanteI L Lopez-Cruz A Lara-Herrera and J I de la Rosa ldquoCali-bration of a greenhouse climate model using evolutionary algo-rithmsrdquo Biosystems Engineering vol 104 no 1 pp 135ndash1422009

[16] A Hasni R Taibi B Draoui and T Boulard ldquoOptimization ofgreenhouse climate model parameters using particle swarmoptimization and genetic algorithmsrdquo Energy Procedia vol 6pp 371ndash380 2011

[17] R Brits A P Engelbrecht and F van den Bergh ldquoLocatingmultiple optima using particle swarm optimizationrdquo AppliedMathematics and Computation vol 189 no 2 pp 1859ndash18832007

[18] S Panda BMohanty and P K Hota ldquoHybrid BFOA-PSO algo-rithm for automatic generation control of linear and nonlinearinterconnected power systemsrdquoApplied SoftComputing Journalvol 13 no 12 pp 4718ndash4730 2013

[19] Z Zhang Y Jiang S Zhang SGengHWang andG Sang ldquoAnadaptive particle swarm optimization algorithm for reservoiroperation optimizationrdquo Applied Soft Computing Journal vol18 pp 167ndash177 2014

[20] S Yu K Zhu and X Zhang ldquoEnergy demand projection ofChina using a path-coefficient analysis and PSO-GA approachrdquoEnergy Conversion and Management vol 53 no 1 pp 142ndash1532012

[21] M Aubinet ldquoLongwave sky radiation parametrizationsrdquo SolarEnergy vol 53 no 2 pp 147ndash154 1994

[22] PW Stackhouse andCHWhitlock ldquoSurfaceMeteorology andSolar Energy (SSE) rel 60rdquo NASA May 2014 httpeosweblarcnasagovsse

[23] T Boulard and S Wang ldquoGreenhouse crop transpiration simu-lation from external climate conditionsrdquoAgricultural and ForestMeteorology vol 100 no 1 pp 25ndash34 2000

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


Yet PSO is easy to prematurely converge and lead to theundesired local solution GA may require a large number ofredundant iterations and result in long computing times andlow problem-solving efficiency [17] Algorithmic operatorsand parameters typically interact with one another nonlin-early it is extremely hard to figure out the most optimalcombinatorial strategy [18] And the single algorithm defectmakes it not suitable for the mutative greenhouse model[19] HPSO-GA shows superiority compared with othersingle optimization methods such as GA and PSO and canovercome the disadvantages of particle swarm optimizationand genetic algorithm [20]

Therefore this paper proposes a novel method for energyconsumption prediction in the greenhouse based on theHPSO-GA The parameters for physical model of energydemand are calibrated using HPSO-GA for the profoundoptimization performance in the nonlinear greenhouse sys-tem with surface water source heat pumps system

2 Materials and Methods

21 Experiment Setup A multispan glass greenhouse wasemployed in this experiment and it was located in JiangsuProvince China (longitude 120∘291015840 east latitude 31∘761015840north)This greenhouse is coveredwith a single layer of 4mmthickness glass 72m length in the north-south direction and75m height and consisted of 28 spans 4m wide each Theoutside air temperature wind speed and PARweremeasuredby a small weather station (GalCon Eldarshany Co Israel)The air temperatures at the height of 4m from the groundof four positions inside were measured by sensors (HMT100Vaisala Co Finland) Inside air temperature was the averageof 4 temperature sensors in the greenhouse Surface watersource heat pumps systemwas applied in the greenhouseTheenergy consumption ismeasured by energymeter (HCM1158Honeywell Co Germany) according to the water flow rateand the difference of supply and return water temperaturesThe data from the sensors were automatically recordedevery 5min by a data logger which we have developed Theexperiment was carried out from June 2 to June 7 2012

22 Greenhouse Environment Model Greenhouse environ-ment model in the physical and physiological methods thattake place inside greenhouses based on mass and energybalances including the biological behavior of plants Math-ematical models of greenhouse microclimate are influencedby several elements of the greenhouse (heat flow and conduc-tion vapor diffusion etc) and the outside boundaries (solarradiation air temperature etc) which is shown in Figure 1The thermal balance inside the greenhouse defines the rate ofchange of temperature which can be transferred to calculatethe energy supply requirements Consider

119902119904(119905) = 120588

119886119881119862119886

119889119879119894(119905)

119889119905+ 119902119897(119905) + 119902

119888(119905) + 119902

119908(119905)

+ 119902119890(119905) + 119902

119901(119905) minus 119902

119905(119905)

(1)

where 119902119904(119905) is the energy supply over time in W 120588

119886is the air

density in kgmminus3 119881 is the volume of the greenhouse in m3

ql

qw

qc qp qeqs

Crop

Top windows

Fan coil unit

qt

Figure 1 The thermal balance of greenhouse environment

119862119886is air specific heat in Jkgminus1Kminus1 119879

119894(119905) is air temperature

inside the greenhouse over time in K 119902119897(119905) is the energy flux

due to the long wave thermal radiation over time in W 119902119888(119905)

is the heat flux through the cover over time inW 119902119908(119905) is heat

flux from ventilation and infiltration over time in W 119902119890(119905) is

the heat flux due to crop transpiration over time in W 119902119901(119905)

is the heat flux due to the convection between greenhouseair with soil and crop leaves over time in W and 119902

119905(119905) is the

net solar radiation into greenhouse over time in W Sincethe top windows and side windows are all closed when thecooling system is working heat flux from ventilation 119902

119908can

be ignored and 119905 is time series variableThe net solar radiation into greenhouse 119902

119905(119905) can be

described as follows according to radiation law

119902119905(119905) = 119860

119904119868119886(119905) 120591119886 (2)

where 119860119904is the surface area of cover material in m2 119868

119886(119905) is

outdoor global radiation over time in Wmminus2 and 120591119886is cover

material absorption coefficientAccording to the nonlinear Stefan-Boltzmann law the

thermal long wave radiation exchange between interior andexterior can be written as follows

119902119897(119905) = 120576

12119860119904120590 (119879119894(119905)4

minus 119879sky (119905)4

) (3)

where 119860119904is the area of covering in m2 120590 is the Stefan-

Boltzmann constant of 567 times 10minus8Wmminus2Kminus4 119879sky(119905) issky temperature over time in K and 120576

12is the combined

emissivity between the cover and sky which is found fromthe individual emission coefficients 120576

1and 1205762

12057612= (1205761

minus1

+ 1205762

minus1

minus 1)minus1

(4)

According to Aubinet [21] sky temperature related totemperature outside the greenhouse is expressed as follows

119879sky (119905) = 94 + 126 ln (119890119900) minus 13119896 + 0341119879

119900(119905) (5)

where 119890119900is actual air water vapor pressure outside in Pa

119879119900(119905) is temperature outside the greenhouse over time in

K and 119896 is the sky clearness index which is 2233 Pa and39 respectively based on NASA Surface Meteorologicaland Solar Energy information [22]

The greenhouse air exchanges energy and water vapor(condensation) with the inner surface of the cover and



119902119888(119905) = 119860


119900(119905)) (6)


119892






119902119901(119905) = 119860

119892120588119862119901LAI(

(119879V (119905) minus 119879119894 (119905))

119903119886

) (7)


119902119890(119905) = 119860

119892sdot 120582 sdot 119864 (119905) (8)

120582119864 (119905) =119868119886(119905) 120591119886Δ + 2LAI (120588119888

119886119903119904) (119890119904(119905) minus 119890

119886(119905))

Δ + 120574 (1 + 119903119888119903119886)

(9)












119892 and 119870

119888 The


Rmse = 1

Max 119905

Max 119905sum

119905=1

radic(119902119904(119905 120583) minus 119902real (119905))

2

(10)


119892119896119888]




1 1205782 1205783 120578




V119899+1119894

= 119908 sdot V119899119894

+ 1198881sdot 1199031sdot (119901119887119890119904119905

119899

119894

minus 120578119899

119894

) + 1198882sdot 1199032sdot (119892119887119890119904119905

119899

minus 120578119899

119894

)

(11)


120578119899+1

119894

= 120578119899

119894

+ V119899+1119894

(12)

where V119899119894


119894



1


1and 1198882are







119898is the



1015840

119894


119894is set as 12057810158401015840

119894




Update velocity of

Update position of

particle



PSOGA

No

Yes

Update pbest gbest

Best 2N Worst 2N

Old population

New population


pm and n

n + 1















Parent 1205781


Crossover

Parent 1205782

l11 l12

l11 l12

l11 l12

l11 l12








l1r

l1r

l1r

l1r

l21

l21

l21

l21

l22

l22

l22

l22

lmr

lmr

lmr

lmr

Offspring 1205789984001

Offspring 1205789984002


Mutationparticle

New

l11 l1r

l1r

l12 l21 l22

l22l21l12





lmrminus1 lmr

lmrminus1 lmr


120578998400998400i




1


2


119886


119886


1

and 1198882


119888


119898



0 12 24 36 48 60 72 84 96 108 1200

2

4

6

8

10

12

14

16

Hours

Ener

gy d

eman

d (W

)

Energy costPSO

HPSO-GAGA

times105




661 669 618119870119888


4 Conclusions





Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119902119888(119905) = 119860


119900(119905)) (6)


119892






119902119901(119905) = 119860

119892120588119862119901LAI(

(119879V (119905) minus 119879119894 (119905))

119903119886

) (7)


119902119890(119905) = 119860

119892sdot 120582 sdot 119864 (119905) (8)

120582119864 (119905) =119868119886(119905) 120591119886Δ + 2LAI (120588119888

119886119903119904) (119890119904(119905) minus 119890

119886(119905))

Δ + 120574 (1 + 119903119888119903119886)

(9)












119892 and 119870

119888 The


Rmse = 1

Max 119905

Max 119905sum

119905=1

radic(119902119904(119905 120583) minus 119902real (119905))

2

(10)


119892119896119888]




1 1205782 1205783 120578




V119899+1119894

= 119908 sdot V119899119894

+ 1198881sdot 1199031sdot (119901119887119890119904119905

119899

119894

minus 120578119899

119894

) + 1198882sdot 1199032sdot (119892119887119890119904119905

119899

minus 120578119899

119894

)

(11)


120578119899+1

119894

= 120578119899

119894

+ V119899+1119894

(12)

where V119899119894


119894



1


1and 1198882are







119898is the



1015840

119894


119894is set as 12057810158401015840

119894




Update velocity of

Update position of

particle



PSOGA

No

Yes

Update pbest gbest

Best 2N Worst 2N

Old population

New population


pm and n

n + 1















Parent 1205781


Crossover

Parent 1205782

l11 l12

l11 l12

l11 l12

l11 l12








l1r

l1r

l1r

l1r

l21

l21

l21

l21

l22

l22

l22

l22

lmr

lmr

lmr

lmr

Offspring 1205789984001

Offspring 1205789984002


Mutationparticle

New

l11 l1r

l1r

l12 l21 l22

l22l21l12





lmrminus1 lmr

lmrminus1 lmr


120578998400998400i




1


2


119886


119886


1

and 1198882


119888


119898



0 12 24 36 48 60 72 84 96 108 1200

2

4

6

8

10

12

14

16

Hours

Ener

gy d

eman

d (W

)

Energy costPSO

HPSO-GAGA

times105




661 669 618119870119888


4 Conclusions





Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Update velocity of

Update position of

particle



PSOGA

No

Yes

Update pbest gbest

Best 2N Worst 2N

Old population

New population


pm and n

n + 1















Parent 1205781


Crossover

Parent 1205782

l11 l12

l11 l12

l11 l12

l11 l12








l1r

l1r

l1r

l1r

l21

l21

l21

l21

l22

l22

l22

l22

lmr

lmr

lmr

lmr

Offspring 1205789984001

Offspring 1205789984002


Mutationparticle

New

l11 l1r

l1r

l12 l21 l22

l22l21l12





lmrminus1 lmr

lmrminus1 lmr


120578998400998400i




1


2


119886


119886


1

and 1198882


119888


119898



0 12 24 36 48 60 72 84 96 108 1200

2

4

6

8

10

12

14

16

Hours

Ener

gy d

eman

d (W

)

Energy costPSO

HPSO-GAGA

times105




661 669 618119870119888


4 Conclusions





Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Parent 1205781


Crossover

Parent 1205782

l11 l12

l11 l12

l11 l12

l11 l12








l1r

l1r

l1r

l1r

l21

l21

l21

l21

l22

l22

l22

l22

lmr

lmr

lmr

lmr

Offspring 1205789984001

Offspring 1205789984002


Mutationparticle

New

l11 l1r

l1r

l12 l21 l22

l22l21l12





lmrminus1 lmr

lmrminus1 lmr


120578998400998400i




1


2


119886


119886


1

and 1198882


119888


119898



0 12 24 36 48 60 72 84 96 108 1200

2

4

6

8

10

12

14

16

Hours

Ener

gy d

eman

d (W

)

Energy costPSO

HPSO-GAGA

times105




661 669 618119870119888


4 Conclusions





Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article modeling of energy demand in the...

Documents