Although there has been progress in the area of Multivariate Statistical Process Control (MSPC), there are numerous limitations as well as unanswered questions with the current techniques. MSPC charts plotting Hotelling's T2 require the normality assumption for the joint distribution among the process variables, which is not feasible in many industrial settings, hence the motivation to investigate nonparametric techniques for multivariate data in quality control. In this research, the goal will be to create a systematic distribution-free approach by extending current developments and focusing on the dimensionality reduction using Principal Component Analysis. The proposed technique is different from current approaches given that it creates a nonparametric control chart using robust simplicial depth ranks of the first and last set of principal components to improve signal detection in multivariate quality control with no distributional assumptions. The proposed technique has the advantages of ease of use and robustness in MSPC for monitoring variability and correlation shifts. By making the approach simple to use in an industrial setting, the probability of adoption is enhanced. Improved MSPC can result in a cost savings and improved quality.

The broader research area investigated during this programme was conceived from a goal to contribute towards solving the challenge of food security in the 21st century through the reduction of crop loss and minimisation of fungicide use. This is aimed to be achieved through the introduction of an empirical approach to agricultural disease monitoring. In line with this, the SYIELD project, initiated by a consortium involving University of Manchester and Syngenta, among others, proposed a novel biosensor design that can electrochemically detect viable airborne pathogens by exploiting the biology of plant-pathogen interaction. This approach offers improvement on the inefficient and largely experimental methods currently used. Within this context, this PhD focused on the adoption of multidisciplinary methods to address three key objectives that are central to the success of the SYIELD project: local spore ingress near canopies, the evaluation of a suitable model that can describe spore transport, and multivariate analysis of the potential monitoring network built from these biosensors. The local transport of spores was first investigated by carrying out a field trial experiment at Rothamsted Research UK in order to investigate spore ingress in OSR canopies, generate reliable data for testing the prototype biosensor, and evaluate a trajectory model. During the experiment, spores were air-sampled and quantified using established manual detection methods. Results showed that the manual methods, such as colourimetric detection are more sensitive than the proposed biosensor, suggesting the proxy measurement mechanism used by the biosensor may not be reliable in live deployments where spores are likely to be contaminated by impurities and other inhibitors of oxalic acid production. Spores quantified using the more reliable quantitative Polymerase Chain Reaction proved informative and provided novel of data of high experimental value. The dispersal of this data was found to fit a power decay law, a finding that is consistent with experiments in other crops. In the second area investigated, a 3D backward Lagrangian Stochastic model was parameterised and evaluated with the field trial data. The bLS model, parameterised with Monin-Obukhov Similarity Theory (MOST) variables showed good agreement with experimental data and compared favourably in terms of performance statistics with a recent application of an LS model in a maize canopy. Results obtained from the model were found to be more accurate above the canopy than below it. This was attributed to a higher error during initialisation of release velocities below the canopy. Overall, the bLS model performed well and demonstrated suitability for adoption in estimating above-canopy spore concentration profiles which can further be used for designing efficient deployment strategies. The final area of focus was the monitoring of a potential biosensor network. A novel framework based on Multivariate Statistical Process Control concepts was proposed and applied to data from a pollution-monitoring network. The main limitation of traditional MSPC in spatial data applications was identified as a lack of spatial awareness by the PCA model when considering correlation breakdowns caused by an incoming erroneous observation. This resulted in misclassification of healthy measurements as erroneous. The proposed Kriging-augmented MSPC approach was able to incorporate this capability and significantly reduce the number of false alarms.

[EN] This thesis is aimed to study the implications of the statistical modeling approaches proposed for the bilinear modeling of batch processes, develop new techniques to overcome some of the problems that have not been yet solved and apply them to data of biochemical processes. The study, discussion and development of the new methods revolve around the four steps of the modeling cycle, from the alignment, preprocessing and calibration of batch data to the monitoring of batches trajectories. Special attention is given to the problem of the batch synchronization, and its effect on the modeling from different angles. The manuscript has been divided into four blocks. First, a state-of- the-art of the latent structures based-models in continuous and batch processes and traditional univariate and multivariate statistical process control systems is carried out. The second block of the thesis is devoted to the preprocessing of batch data, in particular, to the equalization and synchronization of batch trajectories. The first section addresses the problem of the lack of equalization in the variable trajectories. The different types of unequalization scenarios that practitioners might finnd in batch processes are discussed and the solutions to equalize batch data are introduced. In the second section, a theoretical study of the nature of batch processes and of the synchronization of batch trajectories as a prior step to bilinear modeling is carried out. The topics under discussion are i) whether the same synchronization approach must be applied to batch data in presence of different types of asynchronisms, and ii) whether synchronization is always required even though the length of the variable trajectories are constant across batches. To answer these questions, a thorough study of the most common types of asynchronisms that may be found in batch data is done. Furthermore, two new synchronization techniques are proposed to solve the current problems in post-batch and real-time synchronization. To improve fault detection and classification, new unsupervised control charts and supervised fault classifiers based on the information generated by the batch synchronization are also proposed. In the third block of the manuscript, a research work is performed on the parameter stability associated with the most used synchronization methods and principal component analysis (PCA)-based Batch Multivariate Statistical Process Control methods. The results of this study have revealed that accuracy in batch synchronization has a profound impact on the PCA model parameters stability. Also, the parameter stability is closely related to the type of preprocessing performed in batch data, and the type of model and unfolding used to transform the three-way data structure to two-way. The setting of the parameter stability, the source of variability remaining after preprocessing and the process dynamics should be balanced in such a way that multivariate statistical models are accurate in fault detection and diagnosis and/or in online prediction. Finally, the fourth block introduces a graphical user-friendly interface developed in Matlab code for batch process understanding and monitoring. To perform multivariate analysis, the last developments in process chemometrics, including the methods proposed in this thesis, are implemented. / [ES] La presente tesis doctoral tiene como objetivo estudiar las implicaciones de los métodos estadísticos propuestos para la modelización bilineal de procesos por lotes, el desarrollo de nuevas técnicas para solucionar algunos de los problemas más complejos aún por resolver en esta línea de investigación y aplicar los nuevos métodos a datos provenientes de procesos bioquímicos para su evaluación estadística. El estudio, la discusión y el desarrollo de los nuevos métodos giran en torno a las cuatro fases del ciclo de modelización: desde la sincronización, ecualización, preprocesamiento y calibración de los datos, a la monitorización de las trayectorias de las variables del proceso. Se presta especial atención al problema de la sincronización y su efecto en la modelización estadística desde distintas perspectivas. El manuscrito se ha dividido en cuatro grandes bloques. En primer lugar, se realiza una revisión bibliográfica de las técnicas de proyección sobre estructuras latentes para su aplicación en procesos continuos y por lotes, y del diseño de sistemas de control basados en modelos estadísticos multivariantes. El segundo bloque del documento versa sobre el preprocesamiento de los datos, en concreto, sobre la ecualización y la sincronización. La primera parte aborda el problema de la falta de ecualización en las trayectorias de las variables. Se discuten las diferentes políticas de muestreo que se pueden encontrar en procesos por lotes y las soluciones para ecualizar las variables. En la segunda parte de esta sección, se realiza un estudio teórico sobre la naturaleza de los procesos por lotes y de la sincronización de las trayectorias como paso previo a la modelización bilineal. Los temas bajo discusión son: i) si se debe utilizar el mismo enfoque de sincronización en lotes afectados por diferentes tipos de asincronismos, y ii) si la sincronización es siempre necesaria aún y cuando las trayectorias de las variables tienen la misma duración en todos los lotes. Para responder a estas preguntas, se lleva a cabo un estudio exhaustivo de los tipos más comunes de asincronismos que se pueden encontrar en este tipo de datos. Además, se proponen dos nuevas técnicas de sincronización para resolver los problemas existentes en aplicaciones post-morten y en tiempo real. Para mejorar la detección de fallos y la clasificación, también se proponen nuevos gráficos de control no supervisados y clasificadores de fallos supervisados en base a la información generada por la sincronización de los lotes. En el tercer bloque del manuscrito se realiza un estudio de la estabilidad de los parámetros asociados a los métodos de sincronización y a los métodos estadístico multivariante basados en el Análisis de Componentes Principales (PCA) más utilizados para el control de procesos. Los resultados de este estudio revelan que la precisión de la sincronización de las trayectorias tiene un impacto significativo en la estabilidad de los parámetros de los modelos PCA. Además, la estabilidad paramétrica está estrechamente relacionada con el tipo de preprocesamiento realizado en los datos de los lotes, el tipo de modelo a justado y el despliegue utilizado para transformar la estructura de datos de tres a dos dimensiones. El ajuste de la estabilidad de los parámetros, la fuente de variabilidad que queda después del preprocesamiento de los datos y la captura de las dinámicas del proceso deben ser a justados de forma equilibrada de tal manera que los modelos estadísticos multivariantes sean precisos en la detección y diagnóstico de fallos y/o en la predicción en tiempo real. Por último, el cuarto bloque del documento describe una interfaz gráfica de usuario que se ha desarrollado en código Matlab para la comprensión y la supervisión de procesos por lotes. Para llevar a cabo los análisis multivariantes, se han implementado los últimos desarrollos en la quimiometría de proc / [CA] Aquesta tesi doctoral te com a objectiu estudiar les implicacions dels mètodes de modelització estadística proposats per a la modelització bilineal de processos per lots, el desenvolupament de noves tècniques per resoldre els problemes encara no resolts en aquesta línia de recerca i aplicar els nous mètodes a les dades dels processos bioquímics. L'estudi, la discussió i el desenvolupament dels nous mètodes giren entorn a les quatre fases del cicle de modelització, des de l'alineació, preprocessament i el calibratge de les dades provinents de lots, a la monitorització de les trajectòries. Es presta especial atenció al problema de la sincronització per lots, i el seu efecte sobre el modelatge des de diferents angles. El manuscrit s'ha dividit en quatre grans blocs. En primer lloc, es realitza una revisió bibliogràfica dels principals mètodes basats en tècniques de projecció sobre estructures latents en processos continus i per lots, així com dels sistemes de control estadístics multivariats. El segon bloc del document es dedica a la preprocessament de les dades provinents de lots, en particular, l' equalització i la sincronització. La primera part aborda el problema de la manca d'equalització en les trajectòries de les variables. Es discuteixen els diferents tipus d'escenaris en que les variables estan mesurades a distints intervals i les solucions per equalitzar-les en processos per lots. A la segona part d'aquesta secció es porta a terme un estudi teòric de la naturalesa dels processos per lots i de la sincronització de les trajectòries de lots com a pas previ al modelatge bilineal. Els temes en discussió són: i) si el mateix enfocament de sincronització ha de ser aplicat a les dades del lot en presència de diferents tipus de asincronismes, i ii) si la sincronització sempre es requereix tot i que la longitud de les trajectòries de les variables són constants en tots el lots. Per respondre a aquestes preguntes, es du a terme un estudi exhaustiu dels tipus més comuns de asincronismes que es poden trobar en les dades provinents de lots. A més, es proposen dues noves tècniques de sincronització per resoldre els problemes existents la sincronització post-morten i en temps real. Per millorar la detecció i la classificació de anomalies, també es proposen nous gràfics de control no supervisats i classificadors de falla supervisats dissenyats en base a la informació generada per la sincronització de lots. En el tercer bloc del manuscrit es realitza un treball de recerca sobre l'estabilitat dels paràmetres associats als mètodes de sincronització i als mètodes estadístics multivariats basats en l'Anàlisi de Components Principals (PCA) més utilitzats per al control de processos. Els resultats d'aquest estudi revelen que la precisió en la sincronització per lots te un profund impacte en l'estabilitat dels paràmetres dels models PCA. A més, l'estabilitat paramètrica està estretament relacionat amb el tipus de preprocessament realitzat en les dades provinents de lots, el tipus de model i el desplegament utilitzat per transformar l'estructura de dades de tres a dos dimensions. L'ajust de l'estabilitat dels paràmetres, la font de variabilitat que queda després del preprocessament i la captura de la dinàmica de procés ha de ser equilibrada de tal manera que els models estadístics multivariats són precisos en la detecció i diagnòstic de fallades i/o en la predicció en línia. Finalment, el quart bloc del document introdueix una interfície gràfica d'usuari que s'ha dissenyat e implementat en Matlab per a la comprensió i la supervisió de processos per lots. Per dur a terme aquestes anàlisis multivariats, s'han implementat els últims desenvolupaments en la quimiometria de processos, incloent-hi els mètodes proposats en aquesta tesi. / González Martínez, JM. (2015). ADVANCES ON BILINEAR MODELING OF BIOCHEMICAL BATCH PROCESSES [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/55684 / TESIS / Premios Extraordinarios de tesis doctorales

This Master's thesis focuses on improving the understanding and monitoring of the Hot Isostatic Pressing (HIP) sintering process used by Seco Tools AB to manufacture cemented carbides for cutting tools. While essential for producing cutting tools with superior hardness and toughness the HIP sintering process introduces a complex relationship between the selected process parameters and the achieved materials properties. With the goal of establishing batch process monitoring capabilities, this master thesis employs Multivariate Statistical Process Control (MSPC) strategies through the creation of Batch Evolution Models (BEMs) and Batch Level Models (BLMs) to monitor, predict end-product quality, and analyze the batch production HIP sintering process.  The developed models effectively account for significant variation in the HIP sintering process and demonstrate potential in identifying deviant batches. Enhancements to the models' performance are achieved through the incorporation of preprocessing, phase-specific variable selection, and specialized model training. These proposed enhancements yield discernible improvements, as evidenced by enhanced model fit and other statistical metrics.  Challenges arise when the models are tested with real-time data due to progressive changes in some tracked process variables. Block-scaling is applied to restore the real-time monitoring capabilities, but also introduces additional complexity to the models. In addition, this master thesis highlights the need for continuous and regular maintenance of these models to ensure real-time monitoring and anomaly detection capabilities. The models demonstrate varied effectiveness in predicting final product quality. For instance, they exhibit some potential in predicting Magnetic Saturation (MS), but their ability to predict Magnetic Coercivity (HC) seems nonexistent. Despite attempts to improve the predictive abilities the models are still not able to confidently predict these metrics. The master’s thesis highlights variability in powder contents and access to data of known quality nonconformities as potential areas for improving the predictive models.

The initial portion of this research focuses on appropriate parameter estimators within a general context of multivariate quality control. The goal of Phase I analysis of multivariate quality control data is to identify multivariate outliers and step changes so that the estimated control limits are sufficiently accurate for Phase II monitoring. High breakdown estimation methods based on the minimum volume ellipsoid (MVE) or the minimum covariance determinant (MCD) are well suited to detecting multivariate outliers in data. Because of the inherent difficulties in computation many algorithms have been proposed to obtain them. We consider the subsampling algorithm to obtain the MVE estimators and the FAST-MCD algorithm to obtain the MCD estimators. Previous studies have not clearly determined which of these two estimation methods is best for control chart applications. The comprehensive simulation study here gives guidance for when to use which estimator. Control limits are provided. High breakdown estimation methods such as MCD and MVE can be applied to a wide variety of multivariate quality control data. The final, lengthier portion of this research considers profile monitoring. Profile monitoring is a relatively new technique in quality control used when the product or process quality is best represented by a profile (or a curve) at each time period. The essential idea is often to model the profile via some parametric method and then monitor the estimated parameters over time to determine if there have been changes in the profiles. Because the estimated parameters may be correlated, it is convenient to monitor them using a multivariate control method such as the T-squared statistic. Previous modeling methods have not incorporated the correlation structure within the profiles. We propose the use of mixed models (both linear and nonlinear) to monitor linear and nonlinear profiles in order to account for the correlation structure within a profile. We consider various data scenarios and show using simulation when the mixed model approach is preferable to an approach that ignores the correlation structure. Our focus is on Phase I control chart applications. / Ph. D.

A presente tese apresenta proposições para o uso da seleção de variáveis no aprimoramento do controle estatístico de processos multivariados (MSPC) em bateladas, a fim de contribuir com a melhoria da qualidade de processos industriais. Dessa forma, os objetivos desta tese são: (i) identificar as limitações encontradas pelos métodos MSPC no monitoramento de processos industriais; (ii) entender como métodos de seleção de variáveis são integrados para promover a melhoria do monitoramento de processos de elevada dimensionalidade; (iii) discutir sobre métodos para alinhamento e sincronização de bateladas aplicados a processos com diferentes durações; (iv) definir o método de alinhamento e sincronização mais adequado para o tratamento de dados de bateladas, visando aprimorar a construção do modelo de monitoramento na Fase I do controle estatístico de processo; (v) propor a seleção de variáveis, com propósito de classificação, prévia à construção das cartas de controle multivariadas (CCM) baseadas na análise de componentes principais (PCA) para monitorar um processo em bateladas; e (vi) validar o desempenho de detecção de falhas da carta de controle multivariada proposta em comparação às cartas tradicionais e baseadas em PCA. O desempenho do método proposto foi avaliado mediante aplicação em um estudo de caso com dados reais de um processo industrial alimentício. Os resultados obtidos demonstraram que a realização de uma seleção de variáveis prévia à construção das CCM contribuiu para reduzir eficientemente o número de variáveis a serem analisadas e superar as limitações encontradas na detecção de falhas quando bancos de elevada dimensionalidade são monitorados. Conclui-se que, ao possibilitar que CCM, amplamente utilizadas no meio industrial, sejam adequadas para banco de dados reais de elevada dimensionalidade, o método proposto agrega inovação à área de monitoramento de processos em bateladas e contribui para a geração de produtos de elevado padrão de qualidade. / This dissertation presents propositions for the use of variable selection in the improvement of multivariate statistical process control (MSPC) of batch processes, in order to contribute to the enhacement of industrial processes’ quality. There are six objectives: (i) identify MSPC limitations in industrial processes monitoring; (ii) understand how methods of variable selection are used to improve high dimensional processes monitoring; (iii) discuss about methods for alignment and synchronization of batches with different durations; (iv) define the most adequate alignment and synchronization method for batch data treatment, aiming to improve Phase I of process monitoring; (v) propose variable selection for classification prior to establishing multivariate control charts (MCC) based on principal component analysis (PCA) to monitor a batch process; and (vi) validate fault detection performance of the proposed MCC in comparison with traditional PCA-based and charts. The performance of the proposed method was evaluated in a case study using real data from an industrial food process. Results showed that performing variable selection prior to establishing MCC contributed to efficiently reduce the number of variables and overcome limitations found in fault detection when high dimensional datasets are monitored. We conclude that by improving control charts widely used in industry to accomodate high dimensional datasets the proposed method adds innovation to the area of batch process monitoring and contributes to the generation of high quality standard products.

Thesis (MScEng (Process Engineering))--University of Stellenbosch, 2010. / Thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Engineering (Extractive Metallurgy) In the Department of Process Engineering at the University of Stellenbosch / ENGLISH ABSTRACT: Multivariate statistical process control (MSPC) approaches are now widely used for performance monitoring, fault detection and diagnosis in chemical processes. Conventional MSPC approaches are based on latent variable projection methods such as principal component analysis and partial least squares. These methods are suitable for handling linearly correlated data sets, with minimal autocorrelation in the variables. Industrial plant data invariably violate these conditions, and several extensions to conventional MSPC methodologies have been proposed to account for these limitations. In practical situations process data usually contain contributions at multiple scales because of different events occurring at different localizations in time and frequency. To account for such multiscale nature, monitoring techniques that decompose observed data at different scales are necessary. Hence the use of standard MSPC methodologies may lead to unreliable results due to false alarms and significant loss of information. In this thesis a multiscale methodology based on the use of singular spectrum analysis is proposed. Singular spectrum analysis (SSA) is a linear method that extracts information from the short and noisy time series by decomposing the data into deterministic and stochastic components without prior knowledge of the dynamics affecting the time series. These components can be classified as independent additive time series of slowly varying trend, periodic series and aperiodic noise. SSA does this decomposition by projecting the original time series onto a data-adaptive vector basis obtained from the series itself based on principal component analysis (PCA). The proposed method in this study treats each process variable as time series and the autocorrelation between the variables are explicitly accounted for. The data-adaptive nature of SSA makes the proposed method more flexible than other spectral techniques using fixed basis functions. Application of the proposed technique is demonstrated using simulated, industrial data and the Tennessee Eastman Challenge process. Also, a comparative analysis is given using the simulated and Tennessee Eastman process. It is found that in most cases the proposed method is superior in detecting process changes and faults of different magnitude accurately compared to classical statistical process control (SPC) based on latent variable methods as well as the wavelet-based multiscale SPC. / AFRIKAANSE OPSOMMING: Meerveranderlike statistiese prosesbeheerbenaderings (MSPB) word tans wydverspreid benut vir werkverrigtingkontrolering, foutopsporing en .diagnose in chemiese prosesse. Gebruiklike MSPB word op latente veranderlike projeksiemetodes soos hoofkomponentontleding en parsiele kleinste-kwadrate gebaseer. Hierdie metodes is geskik om lineer gekorreleerde datastelle, met minimale outokorrelasie, te hanteer. Nywerheidsaanlegdata oortree altyd hierdie voorwaardes, en verskeie MSPB is voorgestel om verantwoording te doen vir hierdie beperkings. Prosesdata afkomstig van praktiese toestande bevat gewoonlik bydraes by veelvuldige skale, as gevolg van verskillende gebeurtenisse wat by verskillende lokaliserings in tyd en frekwensie voorkom. Kontroleringsmetodes wat waargenome data ontbind by verskillende skale is nodig om verantwoording te doen vir sodanige multiskaalgedrag. Derhalwe kan die gebruik van standaard-MSPB weens vals alarms en beduidende verlies van inligting tot onbetroubare resultate lei. In hierdie tesis word . multiskaalmetodologie gebaseer op die gebruik van singuliere spektrumontleding (SSO) voorgestel. SSO is . lineere metode wat inligting uit die kort en ruiserige tydreeks ontrek deur die data in deterministiese en stochastiese komponente te ontbind, sonder enige voorkennis van die dinamika wat die tydreeks affekteer. Hierdie komponente kan as onafhanklike, additiewe tydreekse geklassifiseer word: stadigveranderende tendense, periodiese reekse en aperiodiese geruis. SSO vermag hierdie ontbinding deur die oorspronklike tydreeks na . data-aanpassende vektorbasis te projekteer, waar hierdie vektorbasis verkry is vanaf die tydreeks self, gebaseer op hoofkomponentontleding. Die voorgestelde metode in hierdie studie hanteer elke prosesveranderlike as . tydreeks, en die outokorrelasie tussen veranderlikes word eksplisiet in berekening gebring. Aangesien die SSO metode aanpas tot data, is die voorgestelde metode meer buigsaam as ander spektraalmetodes wat gebruik maak van vaste basisfunksies. Toepassing van die voorgestelde tegniek word getoon met gesimuleerde prosesdata en die Tennessee Eastman-proses. . Vergelykende ontleding word ook gedoen met die gesimuleerde prosesdata en die Tennessee Eastman-proses. In die meeste gevalle is dit gevind dat die voorgestelde metode beter vaar om prosesveranderings en .foute met verskillende groottes op te spoor, in vergeleke met klassieke statistiese prosesbeheer (SP) gebaseer op latente veranderlikes, asook golfie-gebaseerde multiskaal SP.

We consider a principal components based decomposition of the expected value of the multivariate quadratic loss function, i.e., MQL. The principal components are formed by scaling the original data by the contents of the loss constant matrix, which defines the economic penalty associated with specific variables being off their desired target values. We demonstrate the extent to which a subset of these ``loss-scaled principal components", i.e., LSPC, accounts for the two components of expected MQL, namely the trace-covariance term and the off-target vector product. We employ the LSPC to solve a robust design problem of full and reduced dimensionality with deterministic models that approximate the true solution and demonstrate comparable results in less computational time. We also employ the LSPC to construct a test statistic called loss-scaled T^2 for multivariate statistical process control. We show for one case how the proposed test statistic has faster detection than Hotelling's T^2 of shifts in location for variables with high weighting in the MQL. In addition we introduce a principal component based decomposition of Hotelling's T^2 to diagnose the variables responsible for driving the location and/or dispersion of a subgroup of multivariate observations out of statistical control. We demonstrate the accuracy of this diagnostic technique on a data set from the literature and show its potential for diagnosing the loss-scaled T^2 statistic as well.

Multivariate statistical process control (MSPC) techniques play an important role in industrial batch process monitoring and control. This research illustrates the capabilities and limitations of existing MSPC technologies, with a particular focus on partial least squares (PLS).In modern industry, batch processes often operate over relatively large spaces, with many chemical and physical systems displaying nonlinear performance. However, the linear PLS model cannot predict nonlinear systems, and hence non-linear extensions to PLS may be required. The nonlinear PLS model can be divided into Type I and Type II nonlinear PLS models. In the Type I Nonlinear PLS method, the observed variables are appended with nonlinear transformations. In contrast to the Type I nonlinear PLS method, the Type II nonlinear PLS method assumes a nonlinear relationship within the latent variable structure of the model. Type I and Type II nonlinear multi-way PLS (MPLS) models were applied to predict the endpoint value of the product in a benchmark simulation of a penicillin batch fermentation process. By analysing and comparing linear MPLS, and Type I and Type II nonlinear MPLS models, the advantages and limitations of these methods were identified and summarized. Due to the limitations of Type I and II nonlinear PLS models, in this study, Neural Network PLS (NNPLS) was proposed and applied to predict the final product quality in the batch process. The application of the NNPLS method is presented with comparison to the linear PLS method, and to the Type I and Type II nonlinear PLS methods. Multi-way NNPLS was found to produce the most accurate results, having the added advantage that no a-priori information regarding the order of the dynamics was required. The NNPLS model was also able to identify nonlinear system dynamics in the batch process. Finally, NNPLS was applied to build the controller and the NNPLS method was combined with the endpoint control algorithm. The proposed controller was able to be used to keep the endpoint value of penicillin and biomass concentration at a set-point.

Diese Dissertation konzentriert sich auf das hochdimensionale Financial Engineering, insbesondere in der Dependenzmodellierung und der sequentiellen Überwachung. Im Bereich der Dependenzmodellierung wird eine Einführung hochdimensionaler Kopula vorgestellt, die sich auf den Stand der Forschung in Kopula konzentriert. Eine komplexere Anwendung im Financial Engineering, bei der eine hochdimensionale Kopula verwendet wird, konzentriert sich auf die Bepreisung von Portfolio-ähnlichen Kreditderivaten, d. h. CDX-Tranchen (Credit Default Swap Index). In diesem Teil wird die konvexe Kombination von Kopulas in der CDX-Tranche mit Komponenten aus der elliptischen Kopula-Familie (Gaussian und Student-t), archimedischer Kopula-Familie (Frank, Gumbel, Clayton und Joe) und hierarchischer archimedischer Kopula-Familie vorgeschlagen. Im Abschnitt über finanzielle Überwachung konzentriert sich das Kapitel auf die Überwachung von hochdimensionalen Portfolios (in den Dimensionen 5, 29 und 90) durch die Entwicklung eines nichtparametrischen multivariaten statistischen Prozesssteuerungsdiagramms, d.h. eines Energietest-basierten Kontrolldiagramms (ETCC). Um die weitere Forschung und Praxis der nichtparametrischen multivariaten statistischen Prozesskontrolle zu unterstützen, die in dieser Dissertation entwickelt wurde, wird ein R-Paket "EnergyOnlineCPM" entwickelt. Dieses Paket wurde im Moment akzeptiert und veröffentlicht im Comprehensive R Archive Network (CRAN), welches das erste Paket ist, das die Verschiebung von Mittelwert und Kovarianz online überwachen kann. / This dissertation focuses on the high dimensional financial engineering, especially in dependence modeling and sequential surveillance. In aspect of dependence modeling, an introduction of high dimensional copula concentrating on state-of-the-art research in copula is presented. A more complex application in financial engineering using high dimensional copula is concentrated on the pricing of the portfolio-like credit derivative, i.e. credit default swap index (CDX) tranches. In this part, the convex combination of copulas is proposed in CDX tranche pricing with components stemming from elliptical copula family (Gaussian and Student-t), Archimedean copula family (Frank, Gumbel, Clayton and Joe) and hierarchical Archimedean copula family used in some publications. In financial surveillance part, the chapter focuses on the monitoring of high dimensional portfolios (in 5, 29 and 90 dimensions) by development of a nonparametric multivariate statistical process control chart, i.e. energy test based control chart (ETCC). In order to support the further research and practice of nonparametric multivariate statistical process control chart devised in this dissertation, an R package "EnergyOnlineCPM" is developed. At moment, this package has been accepted and published in the Comprehensive R Archive Network (CRAN), which is the first package that can online monitor the shift in mean and covariance jointly.