Critical flux and fouling in ultrafiltration of proteins

In this thesis different parameters influencing critical flux in protein ultrafiltration and membrane foul-ing were studied. Short reviews of proteins, cross-flow ultrafiltration, flux decline and criticalflux and the basic theory of Partial Least Square analysis (PLS) are given at the beginning. The experiments were mainly performed using dilute solutions of globular proteins, commercial polymeric membranes and laboratory scale apparatuses. Fouling was studied by flux, streaming potential and FTIR-ATR measurements. Critical flux was evaluated by different kinds of stepwise procedures and by both con-stant pressure and constant flux methods. The critical flux was affected by transmembrane pressure, flow velocity, protein concentration, mem-brane hydrophobicity and protein and membrane charges. Generally, the lowest critical fluxes were obtained at the isoelectric points of the protein and the highest in the presence of electrostatic repulsion between the membrane surface and the protein molecules. In the laminar flow regime the critical flux increased with flow velocity, but not any more above this region. An increase in concentration de-creased the critical flux. Hydrophobic membranes showed fouling in all charge conditionsand, furthermore, especially at the beginning of the experiment even at very low transmembrane pressures. Fouling of these membranes was thought to be due to protein adsorption by hydrophobic interactions. The hydrophilic membranes used suffered more from reversible fouling and concentration polarisation than from irreversible foul-ing. They became fouled at higher transmembrane pressures becauseof pore blocking. In this thesis some new aspects on critical flux are presented that are important for ultrafiltration and fractionation of proteins.

Reaction Kinetics and Viscosity Modelling in the Fusion Syntheses of Ca- and Ca/Mg-resinates

Rosin is a natural product from pine forests and it is used as a raw material in resinate syntheses. Resinates are polyvalent metal salts of rosin acids and especially Ca- and Ca/Mg- resinates find wide application in the printing ink industry. In this thesis, analytical methods were applied to increase general knowledge of resinate chemistry and the reaction kinetics was studied in order to model the non linear solution viscosity increase during resinate syntheses by the fusion method. Solution viscosity in toluene is an important quality factor for resinates to be used in printing inks. The concept of critical resinate concentration, c crit, was introduced to define an abrupt change in viscosity dependence on resinate concentration in the solution. The concept was then used to explain the non-inear solution viscosity increase during resinate syntheses. A semi empirical model with two estimated parameters was derived for the viscosity increase on the basis of apparent reaction kinetics. The model was used to control the viscosity and to predict the total reaction time of the resinate process. The kinetic data from the complex reaction media was obtained by acid value titration and by FTIR spectroscopic analyses using a conventional calibration method to measure the resinate concentration and the concentration of free rosin acids. A multivariate calibration method was successfully applied to make partial least square (PLS) models for monitoring acid value and solution viscosity in both mid-infrared (MIR) and near infrared (NIR) regions during the syntheses. The calibration models can be used for on line resinate process monitoring. In kinetic studies, two main reaction steps were observed during the syntheses. First a fast irreversible resination reaction occurs at 235 °C and then a slow thermal decarboxylation of rosin acids starts to take place at 265 °C. Rosin oil is formed during the decarboxylation reaction step causing significant mass loss as the rosin oil evaporates from the system while the viscosity increases to the target level. The mass balance of the syntheses was determined based on the resinate concentration increase during the decarboxylation reaction step. A mechanistic study of the decarboxylation reaction was based on the observation that resinate molecules are partly solvated by rosin acids during the syntheses. Different decarboxylation mechanisms were proposed for the free and solvating rosin acids. The deduced kinetic model supported the analytical data of the syntheses in a wide resinate concentration region, over a wide range of viscosity values and at different reaction temperatures. In addition, the application of the kinetic model to the modified resinate syntheses gave a good fit. A novel synthesis method with the addition of decarboxylated rosin (i.e. rosin oil) to the reaction mixture was introduced. The conversion of rosin acid to resinate was increased to the level necessary to obtain the target viscosity for the product at 235 °C. Due to a lower reaction temperature than in traditional fusion synthesis at 265 °C, thermal decarboxylation is avoided. As a consequence, the mass yield of the resinate syntheses can be increased from ca. 70% to almost 100% by recycling the added rosin oil.

Monitoring of crystallization processes by using infrared spectroscopy and multivariate methods

Väitöstutkimuksessa on tarkasteltuinfrapunaspektroskopian ja monimuuttujaisten aineistonkäsittelymenetelmien soveltamista kiteytysprosessin monitoroinnissa ja kidemäisen tuotteen analysoinnissa. Parhaillaan kiteytysprosessitutkimuksessa maailmanlaajuisesti tutkitaan intensiivisesti erilaisten mittausmenetelmien soveltamista kiteytysprosessin ilmiöidenjatkuvaan mittaamiseen niin nestefaasista kuin syntyvistä kiteistäkin. Lisäksi tuotteen karakterisointi on välttämätöntä tuotteen laadun varmistamiseksi. Erityisesti lääkeaineiden valmistuksessa kiinnostusta tämäntyyppiseen tutkimukseen edistää Yhdysvaltain elintarvike- ja lääkeaineviraston (FDA) prosessianalyyttisiintekniikoihin (PAT) liittyvä ohjeistus, jossa määritellään laajasti vaatimukset lääkeaineiden valmistuksessa ja tuotteen karakterisoinnissa tarvittaville mittauksille turvallisten valmistusprosessien takaamiseksi. Jäähdytyskiteytyson erityisesti lääketeollisuudessa paljon käytetty erotusmenetelmä kiinteän raakatuotteen puhdistuksessa. Menetelmässä puhdistettava kiinteä raaka-aine liuotetaan sopivaan liuottimeen suhteellisen korkeassa lämpötilassa. Puhdistettavan aineen liukoisuus käytettävään liuottimeen laskee lämpötilan laskiessa, joten systeemiä jäähdytettäessä liuenneen aineen konsentraatio prosessissa ylittää liukoisuuskonsentraation. Tällaiseen ylikylläiseen systeemiin pyrkii muodostumaan uusia kiteitä tai olemassa olevat kiteet kasvavat. Ylikylläisyys on yksi tärkeimmistä kidetuotteen laatuun vaikuttavista tekijöistä. Jäähdytyskiteytyksessä syntyvän tuotteen ominaisuuksiin voidaan vaikuttaa mm. liuottimen valinnalla, jäähdytyprofiililla ja sekoituksella. Lisäksi kiteytysprosessin käynnistymisvaihe eli ensimmäisten kiteiden muodostumishetki vaikuttaa tuotteen ominaisuuksiin. Kidemäisen tuotteen laatu määritellään kiteiden keskimääräisen koon, koko- ja muotojakaumansekä puhtauden perusteella. Lääketeollisuudessa on usein vaatimuksena, että tuote edustaa tiettyä polymorfimuotoa, mikä tarkoittaa molekyylien kykyä järjestäytyä kidehilassa usealla eri tavalla. Edellä mainitut ominaisuudet vaikuttavat tuotteen jatkokäsiteltävyyteen, kuten mm. suodattuvuuteen, jauhautuvuuteen ja tabletoitavuuteen. Lisäksi polymorfiamuodolla on vaikutusta moniin tuotteen käytettävyysominaisuuksiin, kuten esim. lääkeaineen liukenemisnopeuteen elimistössä. Väitöstyössä on tutkittu sulfatiatsolin jäähdytyskiteytystä käyttäen useita eri liuotinseoksia ja jäähdytysprofiileja sekä tarkasteltu näiden tekijöiden vaikutustatuotteen laatuominaisuuksiin. Infrapunaspektroskopia on laajalti kemian alan tutkimuksissa sovellettava menetelmä. Siinä mitataan tutkittavan näytteenmolekyylien värähtelyjen aiheuttamia spektrimuutoksia IR alueella. Tutkimuksessa prosessinaikaiset mittaukset toteutettiin in-situ reaktoriin sijoitettavalla uppoanturilla käyttäen vaimennettuun kokonaisheijastukseen (ATR) perustuvaa Fourier muunnettua infrapuna (FTIR) spektroskopiaa. Jauhemaiset näytteet mitattiin off-line diffuusioheijastukseen (DRIFT) perustuvalla FTIR spektroskopialla. Monimuuttujamenetelmillä (kemometria) voidaan useita satoja, jopa tuhansia muuttujia käsittävä spektridata jalostaa kvalitatiiviseksi (laadulliseksi) tai kvantitatiiviseksi (määrälliseksi) prosessia kuvaavaksi informaatioksi. Väitöstyössä tarkasteltiin laajasti erilaisten monimuuttujamenetelmien soveltamista mahdollisimman monipuolisen prosessia kuvaavan informaation saamiseksi mitatusta spektriaineistosta. Väitöstyön tuloksena on ehdotettu kalibrointirutiini liuenneen aineen konsentraation ja edelleen ylikylläisyystason mittaamiseksi kiteytysprosessin aikana. Kalibrointirutiinin kehittämiseen kuuluivat aineiston hyvyyden tarkastelumenetelmät, aineiston esikäsittelymenetelmät, varsinainen kalibrointimallinnus sekä mallin validointi. Näin saadaan reaaliaikaista informaatiota kiteytysprosessin ajavasta voimasta, mikä edelleen parantaa kyseisen prosessin tuntemusta ja hallittavuutta. Ylikylläisyystason vaikutuksia syntyvän kidetuotteen laatuun seurattiin usein kiteytyskokein. Työssä on esitetty myös monimuuttujaiseen tilastolliseen prosessinseurantaan perustuva menetelmä, jolla voidaan ennustaa spontaania primääristä ytimenmuodostumishetkeä mitatusta spektriaineistosta sekä mahdollisesti päätellä ydintymisessä syntyvä polymorfimuoto. Ehdotettua menetelmää hyödyntäen voidaan paitsi ennakoida kideytimien muodostumista myös havaita mahdolliset häiriötilanteet kiteytysprosessin alkuhetkillä. Syntyvää polymorfimuotoa ennustamalla voidaan havaita ei-toivotun polymorfin ydintyminen,ja mahdollisesti muuttaa kiteytyksen ohjausta halutun polymorfimuodon saavuttamiseksi. Monimuuttujamenetelmiä sovellettiin myös kiteytyspanosten välisen vaihtelun määrittämiseen mitatusta spektriaineistosta. Tämäntyyppisestä analyysistä saatua informaatiota voidaan hyödyntää kiteytysprosessien suunnittelussa ja optimoinnissa. Väitöstyössä testattiin IR spektroskopian ja erilaisten monimuuttujamenetelmien soveltuvuutta kidetuotteen polymorfikoostumuksen nopeaan määritykseen. Jauhemaisten näytteiden luokittelu eri polymorfeja sisältäviin näytteisiin voitiin tehdä käyttäen tarkoitukseen soveltuvia monimuuttujaisia luokittelumenetelmiä. Tämä tarjoaa nopean menetelmän jauhemaisen näytteen polymorfikoostumuksen karkeaan arviointiin, eli siihen mitä yksittäistä polymorfia kyseinen näyte pääasiassa sisältää. Varsinainen kvantitatiivinen analyysi, eli sen selvittäminen paljonko esim. painoprosentteina näyte sisältää eri polymorfeja, vaatii kaikki polymorfit kattavan fysikaalisen kalibrointisarjan, mikä voi olla puhtaiden polymorfien huonon saatavuuden takia hankalaa.

Short-term forecasting of power demand in the Nord Pool market

Sähkönkulutuksen lyhyen aikavälin ennustamista on tutkittu jo pitkään. Pohjoismaisien sähkömarkkinoiden vapautuminen on vaikuttanut sähkönkulutuksen ennustamiseen. Aluksi työssä perehdyttiin aiheeseen liittyvään kirjallisuuteen. Sähkönkulutuksen käyttäytymistä tutkittiin eri aikoina. Lämpötila tilastojen käyttökelpoisuutta arvioitiin sähkönkulutusennustetta ajatellen. Kulutus ennusteet tehtiin tunneittain ja ennustejaksona käytettiin yhtä viikkoa. Työssä tutkittiin sähkönkulutuksen- ja lämpötiladatan saatavuutta ja laatua Nord Poolin markkina-alueelta. Syötettävien tietojen ominaisuudet vaikuttavat tunnittaiseen sähkönkulutuksen ennustamiseen. Sähkönkulutuksen ennustamista varten mallinnettiin kaksi lähestymistapaa. Testattavina malleina käytettiin regressiomallia ja autoregressiivistä mallia (autoregressive model, ARX). Mallien parametrit estimoitiin pienimmän neliösumman menetelmällä. Tulokset osoittavat että kulutus- ja lämpötiladata on tarkastettava jälkikäteen koska reaaliaikaisen syötetietojen laatu on huonoa. Lämpötila vaikuttaa kulutukseen talvella, mutta se voidaan jättää huomiotta kesäkaudella. Regressiomalli on vakaampi kuin ARX malli. Regressiomallin virhetermi voidaan mallintaa aikasarjamallia hyväksikäyttäen.

Advanced chemometric methods: Applicability on industrial data

Recent years have produced great advances in the instrumentation technology. The amount of available data has been increasing due to the simplicity, speed and accuracy of current spectroscopic instruments. Most of these data are, however, meaningless without a proper analysis. This has been one of the reasons for the overgrowing success of multivariate handling of such data. Industrial data is commonly not designed data; in other words, there is no exact experimental design, but rather the data have been collected as a routine procedure during an industrial process. This makes certain demands on the multivariate modeling, as the selection of samples and variables can have an enormous effect. Common approaches in the modeling of industrial data are PCA (principal component analysis) and PLS (projection to latent structures or partial least squares) but there are also other methods that should be considered. The more advanced methods include multi block modeling and nonlinear modeling. In this thesis it is shown that the results of data analysis vary according to the modeling approach used, thus making the selection of the modeling approach dependent on the purpose of the model. If the model is intended to provide accurate predictions, the approach should be different than in the case where the purpose of modeling is mostly to obtain information about the variables and the process. For industrial applicability it is essential that the methods are robust and sufficiently simple to apply. In this way the methods and the results can be compared and an approach selected that is suitable for the intended purpose. Differences in data analysis methods are compared with data from different fields of industry in this thesis. In the first two papers, the multi block method is considered for data originating from the oil and fertilizer industries. The results are compared to those from PLS and priority PLS. The third paper considers applicability of multivariate models to process control for a reactive crystallization process. In the fourth paper, nonlinear modeling is examined with a data set from the oil industry. The response has a nonlinear relation to the descriptor matrix, and the results are compared between linear modeling, polynomial PLS and nonlinear modeling using nonlinear score vectors.

The influence of crystallization conditions on the filtration characteristics of sulphathiazole suspensions

Cooling crystallization is one of the most important purification and separation techniques in the chemical and pharmaceutical industry. The product of the cooling crystallization process is always a suspension that contains both the mother liquor and the product crystals, and therefore the first process step following crystallization is usually solid-liquid separation. The properties of the produced crystals, such as their size and shape, can be affected by modifying the conditions during the crystallization process. The filtration characteristics of solid/liquid suspensions, on the other hand, are strongly influenced by the particle properties, as well as the properties of the liquid phase. It is thus obvious that the effect of the changes made to the crystallization parameters can also be seen in the course of the filtration process. Although the relationship between crystallization and filtration is widely recognized, the number of publications where these unit operations have been considered in the same context seems to be surprisingly small. This thesis explores the influence of different crystallization parameters in an unseeded batch cooling crystallization process on the external appearance of the product crystals and on the pressure filtration characteristics of the obtained product suspensions. Crystallization experiments are performed by crystallizing sulphathiazole (C9H9N3O2S2), which is a wellknown antibiotic agent, from different mixtures of water and n-propanol in an unseeded batch crystallizer. The different crystallization parameters that are studied are the composition of the solvent, the cooling rate during the crystallization experiments carried out by using a constant cooling rate throughout the whole batch, the cooling profile, as well as the mixing intensity during the batch. The obtained crystals are characterized by using an automated image analyzer and the crystals are separated from the solvent through constant pressure batch filtration experiments. Separation characteristics of the suspensions are described by means of average specific cake resistance and average filter cake porosity, and the compressibilities of the cakes are also determined. The results show that fairly large differences can be observed between the size and shape of the crystals, and it is also shown experimentally that the changes in the crystal size and shape have a direct impact on the pressure filtration characteristics of the crystal suspensions. The experimental results are utilized to create a procedure that can be used for estimating the filtration characteristics of solid-liquid suspensions according to the particle size and shape data obtained by image analysis. Multilinear partial least squares regression (N-PLS) models are created between the filtration parameters and the particle size and shape data, and the results presented in this thesis show that relatively obvious correlations can be detected with the obtained models.

Motivational Influences on Transfer: Dimensions and Boundary Conditions

The focus of this dissertation is the motivational influences on transfer in higher education and professional training contexts. To estimate these motivational influences, the dissertation includes seven individual studies that are structured in two parts. Part I, Dimensions, aims at identifying the dimensionality of motivation to transfer and its structural relations with training-related antecedents and outcomes. Part II, Boundary Conditions, aims at testing the predictive validity of motivation theories used in contemporary training research under different study conditions. Data in this dissertation was gathered from multi-item questionnaires, which were analyzed differently in Part I and Part II. Studies in Part I employed exploratory and confirmatory factor analysis, structural equation modeling, partial least squares (PLS) path modeling, and mediation analysis. Studies in Part II used artifact distribution meta-analysis, (nested) subgroup analysis, and weighted least squares (WLS) multiple regression. Results demonstrate that motivation to transfer can be conceptualized as a three-dimensional construct, including autonomous motivation to transfer, controlled motivation to transfer, and intention to transfer, given a theoretical framework informed by expectancy theory, self-determination theory, and the theory of planned behavior. Results also demonstrate that a range of boundary conditions moderates motivational influences on transfer. To test the predictive validity of expectancy theory, social cognitive theory, and the theory of goal orientations under different study settings, a total of 17 boundary conditions were meta-analyzed, including age; assessment criterion; assessment source; attendance policy; collaboration among trainees; computer support; instruction; instrument used to measure motivation; level of education; publication type; social training context; SS/SMC bias; study setting; survey modality; type of knowledge being trained; use of a control group; and work context. Together, the findings cumulated in this thesis support the basic premise that motivation is centrally important for transfer, but that motivational influences need to be understood from a more differentiated perspective than commonly found in the literature, in order to account for several dimensions and boundary conditions. The results of this dissertation across the seven individual studies are reflected in terms of their implications for theory development and their significance for training evaluation and the design of training environments. Limitations and directions to take in future research are discussed.

Novel Regression Methods For Spectral Data

Singular Value Decomposition (SVD), Principal Component Analysis (PCA) and Multiple Linear Regression (MLR) are some of the mathematical pre- liminaries that are discussed prior to explaining PLS and PCR models. Both PLS and PCR are applied to real spectral data and their di erences and similarities are discussed in this thesis. The challenge lies in establishing the optimum number of components to be included in either of the models but this has been overcome by using various diagnostic tools suggested in this thesis. Correspondence analysis (CA) and PLS were applied to ecological data. The idea of CA was to correlate the macrophytes species and lakes. The di erences between PLS model for ecological data and PLS for spectral data are noted and explained in this thesis. i

Store experiences and their influence on store performance and brand strength: Case Samsung Experience Store

Experiential marketing is increasingly seen as a new magical key to consumers’ hearts. Brands are turning brick-and-mortar stores into state of the art retail spaces where memorable experiences and strong brand relationships are hoped to be born. Around the globe, several brands have opened up a special format of stores – the experience store. Although many speculations on the positive effects of experiences have been presented, few studies have provided empirical, quantified evidence for the link between store experiences and brand success. In consequence, research was needed to find out whether experience stores truly are so special. The purpose of this thesis was to investigate whether store experiences are capable of building brands and influencing store performance. For this purpose, empirical research was conducted in the Samsung Experience Store Helsinki. As main constructs of the study, store experience, brand equity, store performance, and product class involvement were measured, along with relevant background variables. Data was collected with an electronic survey from actual customers of the store, resulting in a sample of 131 respondents. Partial least squares structural equations modeling (PLS) was used for the analysis of the research model. Also, regression analysis was conducted to account for mediation and moderation effects. The results showed that store experiences do positively influence first, store performance, and second, separate dimensions of brand equity (that is, brand awareness, brand personality, and brand loyalty). Also, the effect of store experiences on store performance was found to be mediated by brand equity. Interestingly, customers’ product class involvement was detected to moderate the effect of store experience on store performance. That is, those who were highly involved with electronics had greater store experiences, and also displayed a stronger linkage between store experience and store performance. The results encourage marketers to continue with efforts to create great experiences for their customers. Experience stores can – and should be seen – as both powerful brand building tools and profitable sales channels. The creation of exceptional experiences can act as an important function of physical stores in the face of severe online competition.

Modelling the simultaneous effects of intellectual capital and knowledge management on the organisational performance of Finnish companies

The aim of this study was to contribute to the current knowledge-based theory by focusing on a research gap that exists in the empirically proven determination of the simultaneous but differentiable effects of intellectual capital (IC) assets and knowledge management (KM) practices on organisational performance (OP). The analysis was built on the past research and theoreticised interactions between the latent constructs specified using the survey-based items that were measured from a sample of Finnish companies for IC and KM and the dependent construct for OP determined using information available from financial databases. Two widely used and commonly recommended measures in the literature on management science, i.e. the return on total assets (ROA) and the return on equity (ROE), were calculated for OP. Thus the investigation of the relationship between IC and KM impacting OP in relation to the hypotheses founded was possible to conduct using objectively derived performance indicators. Using financial OP measures also strengthened the dynamic features of data needed in analysing simultaneous and causal dependences between the modelled constructs specified using structural path models. The estimates were obtained for the parameters of structural path models using a partial least squares-based regression estimator. Results showed that the path dependencies between IC and OP or KM and OP were always insignificant when analysed separate to any other interactions or indirect effects caused by simultaneous modelling and regardless of the OP measure used that was either ROA or ROE. The dependency between the constructs for KM and IC appeared to be very strong and was always significant when modelled simultaneously with other possible interactions between the constructs and using either ROA or ROE to define OP. This study, however, did not find statistically unambiguous evidence for proving the hypothesised causal mediation effects suggesting, for instance, that the effects of KM practices on OP are mediated by the IC assets. Due to the fact that some indication about the fluctuations of causal effects was assessed, it was concluded that further studies are needed for verifying the fundamental and likely hidden causal effects between the constructs of interest. Therefore, it was also recommended that complementary modelling and data processing measures be conducted for elucidating whether the mediation effects occur between IC, KM and OP, the verification of which requires further investigations of measured items and can be build on the findings of this study.

Reconstruction of 3D Planar Objects with Partial Occlusion

Kolmiulotteisten kappaleiden rekonstruktio on yksi konenäön haastavimmista ongelmista, koska kappaleiden kolmiulotteisia etäisyyksiä ei voida selvittää yhdestä kaksiulotteisesta kuvasta. Ongelma voidaan ratkaista stereonäön avulla, jossa näkymän kolmiulotteinen rakenne päätellään usean kuvan perusteella. Tämä lähestymistapa mahdollistaa kuitenkin vain rekonstruktion niille kappaleiden osille, jotka näkyvät vähintään kahdessa kuvassa. Piilossa olevien osien rekonstruktio ei ole mahdollista pelkästään stereonäön avulla. Tässä työssä on kehitetty uusi menetelmä osittain piilossa olevien kolmiulotteisten tasomaisten kappaleiden rekonstruktioon. Menetelmän avulla voidaan selvittää hyvällä tarkkuudella tasomaisista pinnoista koostuvan kappaleen muoto ja paikka käyttäen kahta kuvaa kappaleesta. Menetelmä perustuu epipolaarigeometriaan, jonka avulla selvitetään molemmissa kuvissa näkyvät kappaleiden osat. Osittain piilossa olevien piirteiden rekonstruointi suoritetaan käyttämäen stereonäköä sekä tietoa kappaleen rakenteesta. Esitettyä ratkaisua voitaisiin käyttää esimerkiksi kolmiulotteisten kappaleiden visualisointiin, robotin navigointiin tai esineentunnistukseen.

Boundary identification in the domain of a parabolic partial differential equation

Bakgrunden och inspirationen till föreliggande studie är tidigare forskning i tillämpningar på randidentifiering i metallindustrin. Effektiv randidentifiering möjliggör mindre säkerhetsmarginaler och längre serviceintervall för apparaturen i industriella högtemperaturprocesser, utan ökad risk för materielhaverier. I idealfallet vore en metod för randidentifiering baserad på uppföljning av någon indirekt variabel som kan mätas rutinmässigt eller till en ringa kostnad. En dylik variabel för smältugnar är temperaturen i olika positioner i väggen. Denna kan utnyttjas som insignal till en randidentifieringsmetod för att övervaka ugnens väggtjocklek. Vi ger en bakgrund och motivering till valet av den geometriskt endimensionella dynamiska modellen för randidentifiering, som diskuteras i arbetets senare del, framom en flerdimensionell geometrisk beskrivning. I de aktuella industriella tillämpningarna är dynamiken samt fördelarna med en enkel modellstruktur viktigare än exakt geometrisk beskrivning. Lösningsmetoder för den s.k. sidledes värmeledningsekvationen har många saker gemensamt med randidentifiering. Därför studerar vi egenskaper hos lösningarna till denna ekvation, inverkan av mätfel och något som brukar kallas förorening av mätbrus, regularisering och allmännare följder av icke-välställdheten hos sidledes värmeledningsekvationen. Vi studerar en uppsättning av tre olika metoder för randidentifiering, av vilka de två första är utvecklade från en strikt matematisk och den tredje från en mera tillämpad utgångspunkt. Metoderna har olika egenskaper med specifika fördelar och nackdelar. De rent matematiskt baserade metoderna karakteriseras av god noggrannhet och låg numerisk kostnad, dock till priset av låg flexibilitet i formuleringen av den modellbeskrivande partiella differentialekvationen. Den tredje, mera tillämpade, metoden kännetecknas av en sämre noggrannhet förorsakad av en högre grad av icke-välställdhet hos den mera flexibla modellen. För denna gjordes även en ansats till feluppskattning, som senare kunde observeras överensstämma med praktiska beräkningar med metoden. Studien kan anses vara en god startpunkt och matematisk bas för utveckling av industriella tillämpningar av randidentifiering, speciellt mot hantering av olinjära och diskontinuerliga materialegenskaper och plötsliga förändringar orsakade av “nedfallande” väggmaterial. Med de behandlade metoderna förefaller det möjligt att uppnå en robust, snabb och tillräckligt noggrann metod av begränsad komplexitet för randidentifiering.

Nutrient and light availability to white spruce seedlings in partial and clearcut harvested aspen stands

Abstract