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ID:33189733
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时间:2019-02-21
《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
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