4.9 Anpassning av PLS till specifik m¨ atapplikation
4.9.2 Kalibrering och optimering
D˚a m¨atapparaturen f¨or¨andrades efter att datat som anv¨andes f¨or studien insamlats kan inte de framtagna resultaten anv¨andas f¨or att kalibrera eller optimera n˚agon modell. D¨aremot kan rutinerna ˚ateranv¨andas d˚a nytt data finns tillg¨angligt. Tro- ligtvis kommer uppst¨allningen p˚a processindustrin anv¨andas till aktiva akustiska m¨atningar och d˚a kommer ytterligare unders¨okningar kr¨avas f¨or att best¨amma prediktionsmodellernas utformning.
Kapitel 5
Diskussion
P˚a grund av of¨orutsedda omst¨andigheter kunde inte aktiv akustisk spektrosko- pi utv¨arderas inom detta examensarbete. Datamaterial fanns inte tillg¨angligt i tillr¨ackligt stor utstr¨ackning i god tid. Tillg˚angen till datamaterial har visat sig vara en mycket viktig faktor f¨or best¨amma vilka metoder som kan anv¨andas. De m¨atningar som referensmaterialet baseras p˚a ¨ar dyra och ¨ar begr¨ansande f¨or hur komplexa modeller som ¨ar l¨ampliga.
Ett artificiellt neuralt n¨atverk kan teoretiskt prediktera de s¨okta storheterna b¨attre ¨
an PLS d˚a det ¨aven tar h¨ansyn till icke-linj¨ara samband. Det kr¨avs dock ett myc- ket st¨orre datamaterial f¨or att tr¨ana ett n¨atverk med tillr¨acklig storlek d˚a det tenderar att modellera brus om inte det f¨orh˚allandevis stora antalet vikter och lo- adingmatrisen kan kalibreras tillr¨ackligt. Om stora m¨angder kalibreringsdata finns tillg¨angligt skulle neurala n¨atverk kunna anv¨andas men om data ¨ar l¨attillg¨angligt ¨
ar troligtvis nyttan med akustisk spektroskopi liten.
Resultatet fr˚an detta arbete kan endast appliceras p˚a de m¨atningar med passiv akustisk spektroskopi som unders¨okts. De kan vara v¨agledande d˚a de aktuella metoderna skall utv¨arderas inf¨or anv¨andandet av akustisk spektroskopi i liknan- de situationer med avseende p˚a m¨atsystemets utformning, m¨atapplikation och tillg˚ang p˚a referensdata.
Det ¨ar m¨ojligt att aktiv akustisk spektroskopi skulle kunna introducera fler icke- linj¨ara samband mellan akustiska signaler och s¨okta storheter som ett artificiellt neuralt n¨atverk skulle kunna prediktera b¨attre ¨an linj¨ar PLS. Vid aktiva m¨atningar kommer ytterligare ing˚aende variabler introduceras i form av det ing˚aende ljudet. Om detta ljud h˚alls konstant kommer dessa variabler att elimineras och antalet variabler vara lika stort som vid passiva m¨atningar. Problemet med antalet ka- libreringspunkter kvarst˚ar dock, eftersom komplexiteten hos systemet ¨okar med introduktionen av akustiska vibrationer till r¨or och fluid. Det ¨ar d¨arf¨or inte rim- ligt att antalet kalibreringspunkter som kr¨avs f¨or att uppn˚a samma kvalitet p˚a prediktionen minskar.
36 Diskussion M¨ojligheten f¨or att med god tillg˚ang till kalibreringsdata erh˚alla en b¨attre pre- diktion ¨okar med anv¨andandet av aktiv akustisk spektroskopi d˚a den frekvens- beroende absorptionen och liknande effekter torde f˚a st¨orre betydelse vid ana- lysen. Denna m¨ojlighet m˚aste dock st¨allas emot det eventuellt ¨okade behovet av kalibreringsdata f¨or att skapa en modell. En aktiv akustisk m¨atuppst¨allning med v¨aldigt god tillg˚ang till kalibreringsdata skulle kunna anv¨anda sig av olika feedback-konstruktioner som varierar det ing˚aende ljudet och analyserar frekvens- spektra, fasf¨or¨andringar och impulssvar dynamiskt. Komplexiteten p˚a ett s˚adant ¨
okar dock dramatiskt och de eventuella vinsterna i prediktionsf¨orm˚aga ¨ar os¨akra. Det vore d¨arf¨or intressant att utf¨ora m¨atningar p˚a ett v¨alk¨ant system d¨ar kalibre- ringsdata genereras kontinuerligt f¨or att unders¨oka s˚adana fr˚agor som behovet av kalibreringsdata n¨ar m¨atningarna utf¨ors med aktiv ist¨allet f¨or passiv akustisk spektroskopi.
Uppdelningen av datamaterialet kan ha p˚averkat resultaten i viss utstr¨ackning. Duplexmetoden ger en uppdelning som ger goda matematiska f¨oruts¨attningar f¨or att skapa valideringsset. F¨orhoppningen var att den eventuella tidskorrelationens inverkan skulle minskas. N¨ar tekniken skall implementeras kommer inga liknande uppdelningar g¨oras, all tillg¨anglig information kommer att anv¨andas till att skapa en modell. Eventuellt kan korsvalidering anv¨andas f¨or att best¨amma antalet laten- ta variabler som skall anv¨andas. Scenariot kommer att likna en blockuppdelning d¨ar tidskorrelationen inte kommer att kunna bortses fr˚an. Att en blockuppdel- ning inte anv¨andes i detta arbete grundas i att m˚alet med arbetet var att j¨amf¨ora metoder i allm¨anhet inte deras stabilitet gentemot ”nya” data. Resultatet fr˚an j¨amf¨orelse med blockuppdelning skulle emellertid vara intressant utifr˚an en imple- mentationssynvinkel f¨or att unders¨oka uppdelningens inverkan p˚a prediktionsfel och residualer.
¨
Aven anv¨andningen av RMSEP och uppdelningen i kalibrerings- och valideringsset kan diskuteras d˚a det inte kommer att anv¨andas f¨or att utforma modeller inf¨or slutlig implementering. ˚Aterigen beror valet av arbetss¨att p˚a att m˚alet avser en utv¨ardering av metoderna generellt och inte specifikt f¨or en s¨arskild till¨ampning. Det ¨ar m¨ojligt att artificiella neurala n¨atverk eller hybridmodellen har l¨agre predik- tionsfel ¨an PLS f¨or just den storlek p˚a dataset och den m˚alvariabel som anv¨andes. Detta kan inte uteslutas utan st¨orre dataunderlag. Det som unders¨okningarna visar ¨ar endast att storleken p˚a kalibreringssetet inte ¨ar tillr¨ackligt stort f¨or att tr¨ana ett neuralt n¨atverk till b¨attre prediktiv f¨orm˚aga ¨an en PLS-modell baserad p˚a samma antal observationer. Gr¨ansen f¨or n¨ar artificiella neurala n¨at ger b¨attre prediktioner skulle kunna ligga mellan antalet kalibreringspunkter och det tota- la antalet observationer i datasetet. Allts˚a skulle fler observationer beh¨ovas f¨or att utr¨ona om gr¨ansen verkligen g˚ar d¨ar. Detta resonemang leder dock till ett stegvis ¨okat behov av data ¨anda tills datamaterialet ¨ar tillr¨ackligt omfattande f¨or att visa att n¨atverket ¨ar b¨attre ¨an PLS, om det ens n˚agon g˚ang intr¨affar. De un- ders¨okningar som gjordes med temperatur som m˚alvariabel antogs vara tillr¨ackligt lika de f¨or de andra m˚alvariablerna s˚a att slutsatserna fr˚an temperatur-modellerna kan appliceras ¨aven p˚a de andra. Om detta antagande ¨ar sant s˚a kan gr¨ansen f¨or antalet n¨odv¨andiga observationer vid anv¨andandet av artificiella neurala n¨at
37 h¨ojas avsev¨art j¨amf¨ort med storleken p˚a kalibreringsseten. I likhet med andra fr˚agest¨allningar skulle fr˚agan om likheten mellan prediktion av temperatur och andra m˚alvariabler kunna utredas n¨armre med st¨orre tillg˚ang till datamaterial. Om framtiden p˚avisar en m¨ojlighet att anv¨anda artificiella neurala n¨atverk i och med nya m¨atapplikationer finns en grund f¨or att snabbt kunna utv¨ardera om det ¨
ar l¨ampligt eller ej. Vidare kan framtagna strukturer och funktioner anv¨andas f¨or att med relativt liten arbetsinsats j¨amf¨ora alternativa metoder f¨or multivariat analys av akustisk spektroskopidata.
P˚a basis av de resultat som framkommit verkar PLS och liknande metoder vara b¨ast l¨ampade f¨or anv¨andning vid applikationer liknande de unders¨okta. Exempel- vis skulle ”Partial M-Regression”, PRM[29] eller ”Wavelet Transform-Multi Re- solution Spectra”, WT-MRS[6] unders¨okas med liknande metoder som anv¨ants i detta arbete. Valet av analysmodell kan bara till en viss del p˚averka hela m¨atuppst¨allningens prestanda. D¨arf¨or ¨ar det viktigt att instrumentet som hel- het utv¨arderas och f¨orb¨attras utifr˚an vilka f¨or¨andringar som ger st¨orst ¨okningar i prestanda och att inte fokusera alltf¨or mycket p˚a den multivariata statistiska analysen.
Kapitel 6
Slutsatser
PLS visade sig vara b¨attre l¨ampat f¨or prediktering av s¨okta egenskaper utifr˚an akustisk spektroskopidata ¨an alla andra metoder som unders¨oktes. Bayesiska n¨atverk visade sig inte vara l¨ampliga f¨or ¨andam˚alet och unders¨oktes d¨arf¨or in- te n¨armare. Vid en vidareutveckling av tekniken f¨oresl˚as d¨arf¨or att PLS eller liknande metoder s˚asom PRM[29] eller WT-MRS anv¨ands[6].
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Bilaga A
¨
Oversikt ¨over funktioner
MLR.m
% ---
% function: DATA=MLR(DATA,exponents) % ---
% Aim:
% Perform a MLR based on DATA.X to predict DATA.Y % ---
% Input:
% DATA, information container as decribed in % initializeDATA.m
% expontents, exponents for x exponents=[0 1 2] means [1 x % x^2] PCR.m % --- % function: DATA=PCR(DATA,h,exponents) % --- % Aim:
% Perform a Principal Component Regression based on DATA.X % to predict DATA.Y
% --- % Input:
% DATA, information container as decribed in % initializeDATA.m
% h, number of principal components
% expontents, exponents for x exponents=[0 1 2] means [1 x 45
46 Oversikt ¨¨ over funktioner x^2] PLS.m % --- % function: % DATA=PLS(DATA,manualCrossvalidation,maxNumberOfPCs) % --- % Aim:
% Perform a PLS based on DATA.X to predict DATA.Y % ---
% Input:
% DATA, information container as decribed in % initializeDATA.m
% manualCrossvalidation, perform a manual crossvalidation % (select a number latent variables manually)
% maxNumberOfPCs, maximum number of latent variables to use % in crossvalidation addNoise.m % --- % Function: X=addNoise(X,percentage) % --- % Aim:
% Add normally distributed random numbers with
% std=(percentage of (max-min)) and mean=0 for each variable % ---
% Input:
% X, data matrix
% percentage, percentage of (max-min) to use as std for noise % Output: % X, data matrix autoscale.m % --- % Function: DATA=autoscale(DATA) % --- % Aim:
% Autoscales (mean=0, std=1) predictors and predictand % ---
47
% Input:
% DATA, information container as decribed in initializeDATA.m
% --- % Output:
% DATA, information container as decribed in % initializeDATA.m createMonitoring.m % --- % Function: DATA=createMonitoring(DATA) % --- % Aim:
% use a fourth of the calibration observations for % monitoring of training
% --- % Input:
% DATA, information container as decribed in % initializeDATA.m
% --- % Output:
% DATA, information container as decribed in % initializeDATA.m divideDATA.m % % --- % Function: % DATA=divideDATA(DATA,fractionToValidation,setMonitoring) % --- % Aim:
% Divide the data into calibration-, prediction- and % optionally a
% monitoring set % --- % Input:
% DATA, information container as decribed in % initializeDATA.m
% fractionToValidation, fraction of the material use for % validation
48 Oversikt ¨¨ over funktioner
% --- % Output:
% DATA, information container as decribed in % initializeDATA.m
hybrid.m
% ---
% function: [DATA NN]=hybrid(DATA,latentVariables,numberOfPCs,sizeOfNN) % ---
% Aim:
% Prediction of DATA.Y from DATA.X based on a combination % of PLS and ANN
% --- % Input:
% DATA, as described in initializeDATA.m
% latentVariables, number of latent variables to be used % numberOfPCs, number of principal components to be used % sizeOfNN, number of nodes in hidden layer of ANN % ---
% Output:
% DATA, as described in initializeDATA.m
% NN, Neural net settings including MATLAB neural net % object NN.net initializeDATA.m % --- % Function: NN=initializeNN(DATA,sizeOfNN) % --- % Aim:
% This function initializes/resets information-container % DATA to default
% values
% --- % Output:
% DATA, information container as described in % % initializeDATA.m
49
% ---
% Function: NN=initializeNN(DATA,sizeOfNN) % ---
% Aim:
% Initializes/resets neural net % ---
% Input:
% DATA, information container as decribed in % % initializeDATA.m
% sizeOfNN, size of hidden layer % ---
% Output:
% NN, information container for neural network
nnPCA.m
% Perform a neural network prediction based on PCA
optimizeHybrid.m % ---
% Function: [DATA,NN]=optimizeNN(DATA,NNsize,nPC) % ---
% Aim:
% Optimize structure of hybrid model % ---
% Input:
% DATA, information container as decribed in % % initializeDATA.m
% NNsize, initial guess for size of hiddel layer
% nPC, initial guess for number of principal components % lv, initial guess for number of latent variables % ---
% Output:
% DATA, information container as decribed in % initializeDATA.m
% NN, information container for neural network as described % in initializeNN
50 Oversikt ¨¨ over funktioner % --- % Function: [DATA,NN]=optimizeNN(DATA,NNsize,nPC) % --- % Aim: % Optimize structure of NN % --- % Input:
% DATA, information container as decribed in % initializeDATA.m
% NNsize, initial guess for size of hiddel layer
% nPC, initial guess for number of principal components % ---
% Output:
% DATA, information container as decribed in % initializeDATA.m
% NN, information container for neural network as described % in initializeNN optimizePCR.m % --- % Function: DATA=optimizePCR(DATA,exponents) % --- % Aim:
% Optimize structure of hybrid model % ---
% Input:
% DATA, information container as decribed in % initializeDATA.m
% expontents, exponents for x exponents=[0 1 2] means [1 x x^2] % ---
% Output:
% DATA, information container as decribed in % initializeDATA.m
optimizePLS.m % ---
% Function: [DATA ERRORR]=optimizePLS(DATA) % ---
% Aim:
51
% --- % Input:
% DATA, information container as decribed in % initializeDATA.m
% --- % Output:
% DATA, information container as decribed in % initializeDATA.m
% ERRORR, vector containing RMSEP-values for all tested % number of lv:s optimizePRM.m performPCA.m % --- % function: DATA=performPCA(DATA) % --- % Aim:
% Perform a PCA on the X-matrix % ---
% Input:
% DATA, information container as decribed in % initializeDATA.m plotIteration.m % --- % function: plotIteration(newCoord,oldCoord) % --- % Aim:
% Visualize the latest optimization iteration through a plot % ---
% Input:
% newCoord, the new coordinate to plot % oldCoord, the old coordinate to plot
52 Oversikt ¨¨ over funktioner plotYhatY.m % --- % function: plotYhatY(DATA,NN,hybrid) % --- % Aim:
% Plot predicted y versus observed y for the different % models
% --- % Input:
% DATA, information container as decribed in % initializeDATA.m
% NN, information container for neural network as described % in initializeNN
% hybrid, boolean for determining if to plot hybrid model % or not plotYhatYPCR.m % --- % function: plotYhatYPCR(DATA,NN,hybrid) % --- % Aim:
% Plot predicted y versus observed y for PCR model % ---
% Input:
% DATA, information container as decribed in % initializeDATA.m projectOntoPCs.m % --- % Function: DATA=projectOntoPCs(DATA) % --- % Aim:
% Projects the X-data onto principal components % for PCA model
% --- % Input:
% DATA, information container as decribed in initializeDATA.m % ---
% Output:
53 projectOntoPCsHybrid.m % --- % Function: DATA=projectOntoPCsHybrid(DATA) % --- % Aim:
% Projects the X-data onto principal components % for hybrid model
% --- % Input:
% DATA, information container as decribed in initializeDATA.m % ---
% Output:
% DATA, information container as decribed in initializeDATA.m
projectOntoPCsPCR.m % ---
% Function: DATA=projectOntoPCsPCR(DATA) % ---
% Aim:
% Projects the X-data onto principal components % for PCR model
% --- % Input:
% DATA, information container as decribed in initializeDATA.m % ---
% Output:
% DATA, information container as decribed in initializeDATA.m
setDATA.m
% ---
% function: DATA=setDATA(source,factor,whichOne,noise) % ---
% Aim:
% Load data from file according to inputs % ---
% Input:
% source, either ’anders’ or ’EKA’ depending on which data to load
% factor, if specified every factor:th observation is used. % if not specified for EKA, manual measurements are used
54 Oversikt ¨¨ over funktioner
% whichOne, specifies lower boundary of particle-size % interval to read
% noise, if true, noise will be added to X-matrix, see % addNoise.m
% --- % Output:
% DATA, information is stored in the container DATA, see % initializeDATA.m
% for details