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使用RBF神经网络进行优化冷藏库的控制施正荣,成国栋,王琦鸿,徐燕和薛国信213023年常州江苏机构PetrochemicaITechnology,代为办理1999年11月26日(收到)文摘:近年来,先进控制技术最优控制冷藏但仍有许多缺陷的一种重要问题是,老式措施不能实目前线预测最优控制制冷系统的简朴而有效的算法一种RBF神经网络有很强日勺非线性映射能力,一种好的插值性能,价值和更高的训练速度因此本文提出了一种两级RBF神经网络将测量值与预测值,两级RBF神经网络用于在线预测最优控制的冷藏温度新措施时应用效果显示一种巨大的成功关键词:RBF神经网络、冷藏、在线预测最优控制简介冷库温度的预测最优控制找到了广泛应用在农业工程,尤其是冷藏的水果和蔬菜保鲜日勺所有欧I currently-used温度控制单元面临怎样选择最适温度为控制对象的问题,怎样进行冷藏库温度的变化,和怎样实现最优控制大量的工作研究了前面的措施是基于泰勒级数理论和PID控制算法[1,5]后来,毛皮商的转换措施,切比雪夫的理论和某些基础知识日勺系统我们得到了并且使用了更好的J结论(
2、3)近年来,英国石油企业将神经网络用于冷库温度日勺最优控制BP神经fresh bycold storage.All of the currently-used temperaturecontrolunits facethe problemson how to choose the optimumtemperature asthecontrolled object,how to predict the temperature variationof therefrigerating storehouseandhowtorealize the optimum control.A lot of studyefforts have been made.The earliermethodswere based on theTaylor9s series theory and the PID controlalgorithm[1,5].Later,Furriers transformationmethod,Chebyshev5stheoryandknowledge-based systemwere usedand betterresults weregot[2,3].In recentyears,BPneural networkshave beenused for the optimum control of the cold storage temperature.ABP neural network has a good performance ofnonlinear mapping,but ithas toomany localminimumpoints,and usuallyits training speed istoo slow[2,5].Hence itcouldnt beusedfor on-line controlcalculation conveniently.This paperproposes atwo-stage RBF neuralnetwork torealize theon-line optimum control of the cold storage temperature.The firststage is used to determinethe currentoptimum refrigeratingtemperature of the system,andthe second is used to predict the temperaturevalues in the comingtime points.Furthermore,an optimumproblem issolved,whose solutionis used to direct the actionof therefrigeratingsystem..
2.A TWO-STAGE RBFNEURAL NETWORKAtwo-stage RBF neural network is adopted.The firststageis used to determine theoptimumvalue of the cold storage temperature,and thesecondis used topredict thetemperature.Generally,suppose that there aren input variables X[and moutput variables”.Let1Using RBFNeural Networkfor Optimumcontrol of a ColdStorage wherex denotesapoint in the n-dimensional inputspace,whiledenotes apoint in the mdimensional outputspaceH,Suppose thatthe numberof the hidden unitsisH.Every hiddenunit usestwo parameters,one isscalar quantity°,the otherisvector”.Suppose thatthe set of thetraining samplesis{K Generally,nK should be satisfied.RBF neural networks arebased ontheinterpolating valueperformance of radius-based functions.To improvethisperformance,the followingequation isused tocalculate theJ-the outputof anRBF neuralnetwork.a exp一h=\Here,the numerator is atraditional RBFinterpolating algorithmexpression,and thedenominatoris theinterpolating expressionof constantl.With thisdenominator,theattenuation of exponent functionsin thenumeratoriscanceled outgreatly bythat of thedenominator.In thisway,the improvedRBF neural network hasa betterperformance.
3.THE ON-LINE CALCULATIONOF THE COLD STORAGETEMPERATURETochoosethetarget value of the coldstorage temperature,it isneeded totake overallconsiderationsabout allfactors.In orderto useenergy reasonably,the refrigerationprocessshould havea highperformance coefficiente°which is the ratioof therefrigerationquantum°to theneeded energyP satisfying4Research resultsshow thate°increases asthe evaporation temperature increasesor thecondensationtemperature decreases[4,6],and a higher evaporation temperature and alower condensationtemperature arebeneficial tokeep fruits and vegetablefresh.Thus therefrigerationsystem shouldrun undera higherevaporationtemperatureand alowercondensation temperature.However theevaporationtemperatureis apparentlylimited bythe temperature of the objectunder refrigeration.For aspecial kindof fruit or vegetablejust entering the coldstorage,its optimumstorage temperature can be gotwith theorthogonal experimentalmethod.The optimumstorage temperature decreaseswith theincreasing of the storage time.The lossof perunit厂仇of fitor vegetable isru尸以)+甲5L□⑴£2whereis producedby frostbiting,while1by deteriorating.When£1£2temperature increases,/decreases andz increases.Both of them arerelated譬⑴[力-力,一^=力⑵⑶,-力6to the storagetime1,thus力⑴where decreasesand increasesrespectively whenthe temperatureT°_z ttincreases,123456denotes thetime ofenteringthestorage,while7denotes thestoragetime,then we haveSr-二°8Let thegravity of1流fruit or vegetable be,its storageloss g,,then thetotalstorage lossin aunit timeinterval is乎=@g,⑴3-力+八力}62[711t㈢9Let/denote theoptimum storage temperature ingeneral.It should satisfy—,,_0持T10that is,一£/力+工⑵力一°,{}2g T--°iiThe calculation of Tin aboveformulae withtraditional methodsis timez*consuming.Hence weuse anRBF neural network toaccomplish thesolution ofT.zThis RBF neural networkis thefirst partof the two-stage RBFneural networkproposed in询the paper.It hasonly oneoutput,.,「and2〃inputs,that isgiJ nand一%,1几.=〃hidden unitsare usedhere.Equationll is4=6⑴UA力+/⑵0A力}力7邛For1-m fruitor vegetable,its optimumstoragetemperaturez should satisfy thefollowingequation工叫力?力⑵[[*/力7;1usedtoproduce enoughtraining samples.
4、THE ON-LINE PREDICTIONOF THECOLD STORAGETEMPERATUREOne of thekey problemsof theoptimum control over thestoragetemperatureis howtopredictthe temperature accurately.Because of their robustness,the predictionmethodsbased onneural networkshave attractedmore andmore attentions.BP neural networkis akind ofearlier usedneural networkfor thispurpose.But itstraining timeis usuallytoo long,and ithas manylocal minimumpoints.Thus theRBFneuralnetwork hasattracted moreandmore attentionthanks toits highertraining speed.This paperemploys atwo-stage RBFneuralnetworktopredictthestoragetemperature..Inthe predictionprocess,the couplingrelation betweenthe temperatureand thehumidityshould betaken intoaccount.The paperselects theoutput variablesin away thatthe set ofthe variablesinclude thetemperature variablesand thehumidity variablesatthesame time.The choosingof theinput variablesshould betaken intoaccount nomatter whetherthecontrol isperformed ornot,with the following twodifferent casesinvolved:Case1Automatic controlsystem isoffSuppose thatthere areR operatingvariables of thecoldstorage…and Sstatevariables VpV
5.Consider atime windowcomposed of20time points,Q-Q-—t-~t-—tQ+l=,+D...,2Q=Z+QD12u utUse rand5to denote the values ofrand5at timepoint qrespectively°2L ey=产…俨…产,..收714Where n=R+SQ,m=QS.The taskof the prediction isto determiney of14according tothe vectorx of
13.For the current timef,all ofthe measuredresults canbeusedtoconstruct theinputs ofthe predictionnetwork.Suppose thatall ofthe operatingvariablesand statevariables canbe gotby measuring,and theirvalues inthe futureare玲unknown.To constructa predictionsample,the relatedtime tshouldsatisfytQCt.Otherwise,unknown valueswould becontained inthe samplewhich wouldbeunreasonable.Suppose thatenough samples攵=1,2,・・・,K havebeen got.First,calculate theparameters ofthehiddenunits,then calculate thepredictionvalue ofthestorage temperature.Case2Automatic controlsystem isonAt thistime,the setoftheinputvariablesonly containsthe environmentaltemperature,humidity andquantum ofthe storedfruits and vegetables,etc.Any oftheinput variablesdoesnt appearinthe control algorithm,while theprediction variablesarethe stable values ofthe statevariables.The nonlinear mapping functionoftheRBF neuralnetworkisusedto designthe stablemodels.When thestablevaluesofthestate variableshavebeen obtained,the control algorithm isusedtocalculatethetemperature ofthestorehouse,thus the setofthe predicted variables wouldntcontainany variable to becontrolled.Thats whythesetofthe predictedvariablesand thesetofthecontrolled variablesunder Case2are differentfrom thoseunder Casel.
5.THE ON-LINE OPTIMUMCONTROL OFTHECOLDSTORAGETEMPERATUREThe commonPIDcontrolalgorithm of a variableunit takesthe following formuk=Kc{ek+^^ei+Zl[e6-ek-1]}+/15E i=o TsWhereu anduk are the initialvalue and thecurrentvalue ofthe controlledvariablesrespectively.e⑺is thedifference betweenthe assignedvalue and the real value ofthecontrol object,that is-v016where vzandtaretherealvalueat i-th timepoint andthe assignedvalue ofthecontrol objectrespectively.Write equation15intheincremental form,then wehave=uk-uk-l=K[ek-ek-1]+K ek+KJek-2ek-I+ek-c i172]Where isthe integraicoefficient,isthedifferentialcoefficient.Write theabove equationsin anotherform,then wehaveD«Z=!%+K ek+KRek18iUnder thecase ofhaving gotthe predictedvalueofthe controlledvariable,equations17and18shouldbechanged.Let tdenotethecurrent time,andksuppose thatthe predicted values atthe instantst andtofvariable vwithk+[k+2RBFneuralnetwork arevk+1and vk+2respectively,Letek+1-t-vZ+l ek+2-t-vk+219Combine thehistoric values with thepredictedvaluesofthevariabletocalculatethe rightside ofequation
18.LetuDe左-e左-l]+Z[eZ+l-ek]+g[ek+2-ek+l]20uek-a ek+b ek+1+g ek+222221uI^ek=a.[ek-2ek-l+ek-2]+b[ek+l322-2ek+ek-l]+g[^+2-2e女+1+eQ]3In thisway,equation18is changedinto thefollowingform但D«Z=KDeW+Kj eQ+K”E ek23The valuesof a^b^g\x\above equationsshouldsatisfya+b+g=1a+b+g=132223331物],4,g]1,0#a,b,g1,I0#a,b,g142223332Hence thereare only6independent coefficientsto bedetermined.Choose themas外,匕匕3the conditiontodeterminethem isthat theyshould letthe2,2,2,〃3,2mathematical expectationofek get its minimum,that is,wehavethe followingequationminE[e2k]25with thefollowing constraintcondition0a-b[#l;0a,b;l-a-b#l;0-Z x222231All ofthe initialvaluesof也乃也canbechosen as
6.APPLICATIONThe methods proposed inthe paperhavebeenused fortheoptimum controloverthetemperature ofa coldstorage forfruits andvegetables.Table1lists thedaily storinglossesof thefruits andvegetables beforeand afterthe methodsproposed inthe paperare used.For aspecial kindof fruitor vegetable,its daily loss rateis definedasEQ#i NWhereN isthe numberofthekinds offruitsandvegetables,L andE arethe lossandi ithe market priceof dailyentry volumeof i-th specialkind fruitorvegetablerespectively,1#i MTheloss doesnot onlyinclude thediscarded partcaused bydeteriorating,but alsotheprice decreasecaused bythe decreasingofthefreshness.Suppose thatthemarketvalue ofi-th fruitorvegetablebasedonitsN storingvolume is叱,define叱=叱唱W.J六1The totaldailyloss rate canbe calculatedaccording tothefollowingequationN/=wL i=lFrom Table1,we cansee thatby usingthecontrolmethodsproposed inthe paper,thefresh-keeping resulthas beenimproved greatlyandthesystem runsmore stablyTable1The comparisonoftheloss rateof vegetableswith thestandard temperaturevariationBias ofthetemperaturefrom theassignedLoss rate%value℃DateTraditional methodsNew methodsTraditional methodsNew methods
17.
55.
51.
220.
3828.
54.
21.
020.
3239.
23.
10.
950.
4147.
33.
50.
830.
3356.
64.
61.
340.
2369.
74.
31.
530.
2478.
15.
01.
120.
267.CONCLUSIONThe paperproposes atwo-stage RBFneuralnetworkforthecalculationoftheoptimum coldstoragetemperatureandtheprediction ofthetemperature.Based onit,amodified PIDcontrolalgorithmis proposed.In thisway theon-line optimum control ofthetemperature isrealized,and satisfactoryresults aregot.The two-stage RBFneural networkhasa strongability ofnonlinear mappingand a goodperformanceof interpolating value.Italso hasahighertrainingspeed.The methodsproposedinthepapermay beused inothercontrol problemsin agricultural engineering witha greatprospect.REFERENCES[l]Foster WR,Collopy F,Ungar LH.Neural NetworkForecasting ofShort NoisyTimeSeries.Computers Chern.Engin.,1992,164:293-
297.
[2]Ruan RR,Aimer S,Zhang J.Predietion ofDough TheologicalProperties UsingNeural Networks.Cereal Chemistry,1995,723:7-
13.
[3]Kernen M,Lee LL,Perez-Blaneo H.A Studyof SolutionProperties to网络具有良好的J非线性映射的性能,但它有太多日勺地方并不是那么理想,一般是其训练速度太慢了(
2、5)因此它不能以便地用于在线控制计算后来也提出了一种两阶段RBF神经网络实目前线o最优控制的冷藏温度在第一阶段时使用过程中确定目前最佳制冷系统的温度,和第二个阶段是用于在未来时间点进行确定温度时值止匕外,他的处理方案是用于制冷系统的I直接行动,一种最难的问题是处理了采用RBF神经网络分为两个阶段第一阶段是用来确定最佳值的冷藏温度,而第二个是用来预测温度一般来说,假设n个输入变量当和m个输出变量,,…,y”.则%二(%1,...,尤“)7
(1)y=(%••・,/”)⑵使用RBF神经网络最优控制冷藏,X代表一种点日勺n维输入空间R,而y代表一种点的m维输出空间胪,假设隐藏欧I单位欧J数量是Ho每个隐单元使用了两个参数,一种是标井一量,另一种是矢量假设的训练样本集是{(%叫严))}k K般来说,应当满足〃#HKRBF神经网络是基于插值radius-based功能的性能为了改善性能,使用下列方程计算出RBF神经网络的输出joa vmexp(「)匕=---------------舁——,1m
(3)支,(、)2()a exp-----2-卜h=l$在这里,分子是一种老式日勺RBF插值算法体现式,而分母不变的插值体现式Optimize AbsorptionCycle Cop.International Journalof Refrigeration,1995,181:42-
50.
[4]Rubes DJ,Bullard CW.Factors Contributingto RefrigeratorCycling Losses.International Journalof Refrigeration,1995,183:168-
176.
[5]Zhang DavidD.Neural NetworksSystem DesignMethodology.TsinghuaUniversity Press,1996:1-
7.
[6]Davey LM,Pham QJ.Predicting theDynamic ProductHeat Loadand WeightLossDuring BeefChilling Usinga Muiti-Region FiniteDifference Approach.International Journalof Refrigeration,1997,207:470-
482.Shi Guodongwas bornin Changzhouin
1956.He iscurrently aprofessor ofDepartment of Computer Science and Engineering at Jiangsu Institute of PetrochemicalTechnology.His researchinterests arein neuralnetwork andcontrol,electricaltechnology.Wang Qihongwas bornin Beijingin
1956.She graduatedfrom DepartmentofAutomation ofTianjin University in
1986.She iscurrently aassociate professorofDepartmentofComputerScienceandEngineeringat JiangsuInstituteofPetrochemicalTechnologyXue Guoxinwas bornin Changzhouin
1962.He receivedthe M.S.degree fromBeijingUniversityin
1986.Currently heisaassociate ProfessoratJiangsuInstitute ofPetrochemical Technology.1通过这种分母,衰减指数函数的分子是取消了极大的I分母通过这种方式,改善日勺RBF神经网络具有更好日勺性能
3、在线计算的冷藏温度选择的目的价值冷藏温度,需要综合考虑所有的原因为了合理地使用能源,制冷过程中应当有一种高性能系数%,而分和制冷量子与所需的能源P欧I关系应当满足公式%*4研究成果表明,/随蒸发温度和冷凝温度的下降而增长,并且一种更高的蒸发温度和冷凝温度较低有助于保持新鲜的水果和蔬菜因此,制冷系统应当运行在更高的蒸发温度和冷凝温度较低的环境中然而,蒸发温度显然是在冷藏条件下的温度对象日勺限制为一种特殊的水果或蔬菜就进入冷藏,它的最佳储存温度可以得到正交试验措施最佳储存温度伴随储存时间的增长而减小单位水果或者蔬菜的损失满足公式H+甲5式中是由水果或蔬菜被冻伤导致的,而以是由于时间关系而日益恶化导致的当环境温度升高了,减少不过£2会升高这两个数据都和存储时间/有关因此,名⑴力,上二斤2[乙Y]6在这个式子中,力⑴会伴随温度7日勺升高而减少,不过力⑵会升高表达进入存储的时间,入则表达表达存储时间,然后我们有4=6⑴[力-力+力⑵[TA力}山对于水果或者蔬菜来说,其最佳储存温度,应当满足如下方程/□*/力J/⑵口1力抖T T设水果或蔬菜的重力是©,其存储损失为则在单位时间间隔内总存储/-力+厂[「—]}911ti=l损失为设〃表达最佳储存温度它应当满足『拌TSi.10〃9力”1力J.力⑵力o f•}二dia就是/{-用上面老式的措施计算乙是比较费时间的,因此我们使用RBF神经网络实现时处理乙方案这种RBF神经网络的第一部分提出两级RBF神经网络这种网络只有一种输出,i.e.,T\,并且有2n个输入,即g.,1#i n和n二〃在这里作为隐臧欧I单位使用,方程11用于产生足够的训练样本o
4、冷库温度口勺在线预测最优控制的关键问题之一的存储温度是怎样精确预测温度由于他们日勺鲁棒性,基于神经网络的预测措施吸引了越来越多的关注BP神经网络是一种初期的神经网络用于这一目的但它的训练时间一般是太长,和它有诸多局部最小值点因此,RBF神经网络由于其较高的I训练速度吸引了越来越多的关注本文采用两级RBF神经网络预测存储温度在预测过程中,温度和湿度之间的耦合关系应当考虑本文选择输出变量,在同一时间内设置包括温度变量和湿度变量输入变量的选择考虑与否有执行控制,波及如下两种不一样的状况案例1:自动控制系统假设有R个冷藏欧I操作变量/,…即和S个状态变量匕,..%考虑一种时间窗口构成日勺2Q个时间点,4=%-(Q-右=,--2)D,…—t12^Q+\=t+H,...t Q=t+QDt2分别用和4)表达乙和人在q时的值,令(⑴..
(1)V(D V(D〃()(Q)V(G)v(Q)[T13•/V11/1/|,•••,1/1/R,V|,•••,V S,•••,H j,•••,1/1/R r|)=(产),…,产),…叫…,啜了y M式中〃=(R+S),根=QS,这些预测的J作用是根据
(13)式中曰勺向量%确定
(14)式中的y,在目前时间%,所有的测量成果可以用来构造预测网络日勺输入假设所有的操作变量和状态变量可以被测量,不过在后来他们时值都是未知的I为了构建一种预测样本,有关的时间应当满足公式0D否则,未知值将包括在示例将是不合理H勺()ttt假设已经得到了足够多H勺样品(x出,y⑹)次=1,2,…,K,首先,计算隐藏单位H勺参数,然后计算存储温度的预测价值例自动控制系统2:此时,输入变量日勺设置只包括环境温度、湿度和量子存储的水果和蔬菜,等等任何输入变量不出目前控制算法,而预测变量是稳定状态变量的值神经网络日勺非线性映射函数RBF是用来设计稳定模型当状态变量的稳定值,控制算法用于计算仓库的温度,因此预测变量日勺集合不包括任何变量控制这就是为何预例中设置预测变量和控制变量与例时不一样之处
21、在线最优控制的冷藏温度5一般控制算法的一种变量单位需要如下公式PIDuk=K{ek+—a ei+—[ek-ek-l]}+w15c v小=o Tsu和分别是初始值和控制变量的目前值是分派值和控制对象的实际价值口勺区别,es即=t-vz16和,分别是妨时间点处的实际值和分派的控制对象时值,写出方程的增量形式,yi115然后我们可以得到D/Z=〃%-uk-l=K[ek-ek-1]+KM+17K[e{ky2eZ-l+ek-2]d式子中是积分系数,是微分系数用另一种形式写上面日勺1TK“=Kc”s方程,我们可以得到由式EhZ=!Z+K^k+K1k18在得到控制变量的预测值日勺状况下,式和就会发生变化表达目前时间,1718并且设在%I和*2时刻变量u的预测时值分别是贝左+1和贝左+2,令ek+l=t-vZ+l ek+2-t-vk+219结合历史值和变量日勺预测值计算方程日勺右边令18uDek=a[ek-ek-l]+b[ek+l-ek]+g[ek+2-ek+l]u[ek=a ek+b e{k+X+g ek+2u22221,^ek=a[ek-2ek l+ek-2]+b[ek+133-2ek+ek-l]+g[^+2-2ek+l+ek]322用这个措施,方程18可以变成一下格式脩D/Q=K,Dek+Kj eZ+K»ek上式中的,々出也送送的值应当满足1,〃22,3,3323a\+b\+g\a+b+g=1a+b+g=1222333i0#a,b g1,i物2也,且21,1物3也遭3124i[9i因此系统中只有6独立系数待定选择这些系数即如出,/,作为条件3/3来保证他们可以让的数学期望最小,也就是说,我们有如下方程min£[/%]25与下面日勺约束条件0a-h,#1;02也;1一生一九#1;0%也;1一%-九?1]1111乙乙乙乙.
7.7J所有的〃冷田也,%也的初始值可以被选为:
6、应用程序本文提出的措施已被用于最优控制温度冷藏日勺水果和蔬菜表1列出了水果和蔬菜的平常存储损失之前和之后使用本文提出的措施对于一种特殊勺水果或蔬菜来说,H其平常损失率是指/月/用N=4式中N表达水果和蔬菜的种类的数量,L,.和耳分别表达每天入口的济特殊水果或蔬菜的损失和市场价格,1抗N只是损失不包括水果或蔬菜腐烂而被丢弃的部分,并且也存在越来越不新鲜了而导致欧I价格减少,假设水果N或蔬菜日勺市场价值是基于其存储容量叫,叱=叱值吗每天总损失率可以根据六1N如下公式计算/=茬皿/=1从表,我们可以看到,通过使用本文提出的控制措施,保鲜效果已经大大提高,系统运行更稳定Table1The comparisonofthelossrateof vegetableswith thestandard temperaturevariationBias ofthetemperaturefrom theassigned valueLossrate%℃DateTraditional methodsNew methodsTraditional methodsNew methods
17.
55.
51.
220.
3828.
54.
21.
020.
3239.
23.
10.
950.
4147.
33.
50.
830.
3356.
64.
61.
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2369.
74.
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2478.
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267.结论本文提出了一种两级RBF神经网络计算的最佳冷藏温度和温度的预测在此基础上,修改后的PID控制算法以这种方式实现温度时在线优化控制,并得到了满意的成果两级RBF神经网络具有强大H勺非线性映射能力和插值的一种很好的性能值,它也有一种更高的训练速度本文提出的措施可用于其他控制问题在农业工程与一种伟大的前景Using RBFNeuralNetworkfor OptimumControlofaCold StorageShiGuodong,Wang Qihong,Xu YanXue GuoxinJiangsuInstitution ofPetrochemicalTechnology,ChangzhouReceived November26,1999Abstract:In recentyears,advanced controltechnologies havebeen forthe optimumcontrolofacoldstorage.But thereare stilla lotof shortcomings.Oneofthe mainproblemsis thatthe traditionalmethods cantrealize theon-line predictiveoptimumcontrolof arefrigeratingsystem withsimple andvalid algorithms.An RBFneuralnetworkhasastrongability innonlinearmapping,agoodinterpolatingvalueperformance,andahigher trainingspeed.Thus atwo-stage RBFneuralnetworkis proposedin thispaper.Combining themeasuredvalueswiththepredictedvalues,thetwo-stage RBFneuralnetworkisusedforthe on-line predictiveoptimumcontrolofthecoldstoragetemperature.The applicationresultsofthenew methodsshow agreat success.Keywords:RBFneuralnetwork,Cold storage,On-line prediction,optimumcontrol.
1.INTRODUCTIONThe predictiveoptimumcontrolof coldstoragetemperaturehas founda wideapplicationin aagriculturalengineering,especially forkeeping fruitsandvegetables。