ch544multivariatedataanalysis：ch544多元数据分析

《ch544multivariatedataanalysis：ch544多元数据分析》由会员上传分享，免费在线阅读，更多相关内容在应用文档-天天文库。

1、CH544:MULTIVARIATEDATAANALYSISASSIGNMENT41.TwentysixsamplesofdifferentconcentrationsofamixtureofCo,Cr,andNiionsindilutenitricacidwerepreparedinalaboratoryandtheirspectrarecordedovertherange300-650nmusingaHP8452UVdiodearrayspectrophotometer.Themeasurementswe

2、remadeat2nmintervalsgivingrisetoanabsorbancematrixofsize26x176(storedinMATLABvariableabsorbance).Theconcentrationsofthe26samples,whichisa26x3matrixisstoredinMATLABvariableconc.(Thefiledata1.matcanbeloadedinMATLABusingloadfunctiontoaccessthesevariables).(a)U

3、singthesedatadevelopacalibrationmodelbetweenconcentrationsandabsorbancespectrawhichcanbeusedtopredicttheunknownconcentrationofamixture(containingthesamethreespecies)givenitsabsorbancespectra.Fordevelopingthecalibrationmodel,assumethattheabsorbancemeasuremen

4、tscontainerrors,buttheconcentrationmeasurementsareperfect.(b)Inordertoassessthequalityofthecalibrationmodel,wecanperform‘leaveonescoreoutvalidation’.Inthisapproach,thecalibration(regression)modelbetweenconcentrationandabsorbancescoresisdevelopedbyleavingthe

5、scoresandcorrespondingconcentrationofoneofthesamples.Theconcentrationofthesamplewhichhasbeenleftoutispredictedusingtheregressionmodelandcomparedwiththemeasuredconcentration.Thesumsquaredifferencebetweenmeasuredandpredictedvaluesforeachspeciesarecomputed.Thi

6、sprocedureisrepeatedleavingeachsampleoutinturnandthetotalsumsquaredpredictionerrorsarecomputedforeachspecies.Applythisprocedureandreporttheresultsfortheabovedata.2.Provethattheoptimumobjectivefunctionvalueforalineardatareconciliationproblem,isequaltowhere,a

7、nd.Aistheconstraintmatrix,arethemeasurements,andisthemeasurementerrorcovariancematrix.Assumeforsimplicity,thattherearenounmeasuredvariables.3.UsingMATLABsolvethefollowingreconciliationproblemsa.ExamplefromRipps(Chem.Eng.Prog.Symp.Ser61,8-13,1965).Reconcilet

8、hedataforaprocessgivenbelowandcomputetheerrorsinreconciledestimatesa.ExamplefromthebookbyRomagnoliandSanchez(AcademicPress,2000).Figure1showsaflowprocessconsistingof7unitsand15streams.Theflowsofstreams