Uncertainty-Aware Principal Component Analysis

We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to non-linear methods, linear dimensionality reduction techniques have the advantage that the characteristics of such probability distributions remain intact after projection. We derive a representation of the PCA sample covariance matrix that respects potential uncertainty in each of the inputs, building the mathematical foundation of our new method: uncertainty-aware PCA. In addition to the accuracy and performance gained by our approach over sampling-based strategies, our formulation allows us to perform sensitivity analysis with regard to the uncertainty in the data. For this, we propose factor traces as a novel visualization that enables to better understand the influence of uncertainty on the chosen principal components. We provide multiple examples of our technique using real-world datasets. As a special case, we show how to propagate multivariate normal distributions through PCA in closed form. Furthermore, we discuss extensions and limitations of our approach

Compositions and fuzzy compositions in decision-making models

In decision-making models, the compositions (Aitchison, 1986) are employed in various forms. They can represent the normalized weights of criteria in multiple-criteria decision-making models, or the probabilities of states of the world in the models of decision making under risk. The normalized weights express the relative information about the importance of criteria, while the probabilities reflect the expected incidence of the states of the world. The compositions are also the evaluations of objects according to their contributions to a common goal. This paper addresses the situation when the compositions are set expertly. This is the typical way of obtaining the normalized weights of criteria. Various methods of setting the weights were introduced in order to properly reflect the preferences of the decision maker. Direct methods where the decision maker sets the weights directly can be distinguished from indirect ones, e.g., the method of pair-wise comparison, or Saaty’s AHP

Measurements, Models, Systems and Design

531 s.

Efficient resilience analysis and decision-making for complex engineering systems

Modern societies around the world are increasingly dependent on the smooth functionality of progressively more complex systems, such as infrastructure systems, digital systems like the internet, and sophisticated machinery. They form the cornerstones of our technologically advanced world and their efficiency is directly related to our well-being and the progress of society. However, these important systems are constantly exposed to a wide range of threats of natural, technological, and anthropogenic origin. The emergence of global crises such as the COVID-19 pandemic and the ongoing threat of climate change have starkly illustrated the vulnerability of these widely ramified and interdependent systems, as well as the impossibility of predicting threats entirely. The pandemic, with its widespread and unexpected impacts, demonstrated how an external shock can bring even the most advanced systems to a standstill, while the ongoing climate change continues to produce unprecedented risks to system stability and performance. These global crises underscore the need for systems that can not only withstand disruptions, but also, recover from them efficiently and rapidly. The concept of resilience and related developments encompass these requirements: analyzing, balancing, and optimizing the reliability, robustness, redundancy, adaptability, and recoverability of systems -- from both technical and economic perspectives. This cumulative dissertation, therefore, focuses on developing comprehensive and efficient tools for resilience-based analysis and decision-making of complex engineering systems. The newly developed resilience decision-making procedure is at the core of these developments. It is based on an adapted systemic risk measure, a time-dependent probabilistic resilience metric, as well as a grid search algorithm, and represents a significant innovation as it enables decision-makers to identify an optimal balance between different types of resilience-enhancing measures, taking into account monetary aspects. Increasingly, system components have significant inherent complexity, requiring them to be modeled as systems themselves. Thus, this leads to systems-of-systems with a high degree of complexity. To address this challenge, a novel methodology is derived by extending the previously introduced resilience framework to multidimensional use cases and synergistically merging it with an established concept from reliability theory, the survival signature. The new approach combines the advantages of both original components: a direct comparison of different resilience-enhancing measures from a multidimensional search space leading to an optimal trade-off in terms of system resilience, and a significant reduction in computational effort due to the separation property of the survival signature. It enables that once a subsystem structure has been computed -- a typically computational expensive process -- any characterization of the probabilistic failure behavior of components can be validated without having to recompute the structure. In reality, measurements, expert knowledge, and other sources of information are loaded with multiple uncertainties. For this purpose, an efficient method based on the combination of survival signature, fuzzy probability theory, and non-intrusive stochastic simulation (NISS) is proposed. This results in an efficient approach to quantify the reliability of complex systems, taking into account the entire uncertainty spectrum. The new approach, which synergizes the advantageous properties of its original components, achieves a significant decrease in computational effort due to the separation property of the survival signature. In addition, it attains a dramatic reduction in sample size due to the adapted NISS method: only a single stochastic simulation is required to account for uncertainties. The novel methodology not only represents an innovation in the field of reliability analysis, but can also be integrated into the resilience framework. For a resilience analysis of existing systems, the consideration of continuous component functionality is essential. This is addressed in a further novel development. By introducing the continuous survival function and the concept of the Diagonal Approximated Signature as a corresponding surrogate model, the existing resilience framework can be usefully extended without compromising its fundamental advantages. In the context of the regeneration of complex capital goods, a comprehensive analytical framework is presented to demonstrate the transferability and applicability of all developed methods to complex systems of any type. The framework integrates the previously developed resilience, reliability, and uncertainty analysis methods. It provides decision-makers with the basis for identifying resilient regeneration paths in two ways: first, in terms of regeneration paths with inherent resilience, and second, regeneration paths that lead to maximum system resilience, taking into account technical and monetary factors affecting the complex capital good under analysis. In summary, this dissertation offers innovative contributions to efficient resilience analysis and decision-making for complex engineering systems. It presents universally applicable methods and frameworks that are flexible enough to consider system types and performance measures of any kind. This is demonstrated in numerous case studies ranging from arbitrary flow networks, functional models of axial compressors to substructured infrastructure systems with several thousand individual components.Moderne Gesellschaften sind weltweit zunehmend von der reibungslosen Funktionalität immer komplexer werdender Systeme, wie beispielsweise Infrastruktursysteme, digitale Systeme wie das Internet oder hochentwickelten Maschinen, abhängig. Sie bilden die Eckpfeiler unserer technologisch fortgeschrittenen Welt, und ihre Effizienz steht in direktem Zusammenhang mit unserem Wohlbefinden sowie dem Fortschritt der Gesellschaft. Diese wichtigen Systeme sind jedoch einer ständigen und breiten Palette von Bedrohungen natürlichen, technischen und anthropogenen Ursprungs ausgesetzt. Das Auftreten globaler Krisen wie die COVID-19-Pandemie und die anhaltende Bedrohung durch den Klimawandel haben die Anfälligkeit der weit verzweigten und voneinander abhängigen Systeme sowie die Unmöglichkeit einer Gefahrenvorhersage in voller Gänze eindrücklich verdeutlicht. Die Pandemie mit ihren weitreichenden und unerwarteten Auswirkungen hat gezeigt, wie ein externer Schock selbst die fortschrittlichsten Systeme zum Stillstand bringen kann, während der anhaltende Klimawandel immer wieder beispiellose Risiken für die Systemstabilität und -leistung hervorbringt. Diese globalen Krisen unterstreichen den Bedarf an Systemen, die nicht nur Störungen standhalten, sondern sich auch schnell und effizient von ihnen erholen können. Das Konzept der Resilienz und die damit verbundenen Entwicklungen umfassen diese Anforderungen: Analyse, Abwägung und Optimierung der Zuverlässigkeit, Robustheit, Redundanz, Anpassungsfähigkeit und Wiederherstellbarkeit von Systemen -- sowohl aus technischer als auch aus wirtschaftlicher Sicht. In dieser kumulativen Dissertation steht daher die Entwicklung umfassender und effizienter Instrumente für die Resilienz-basierte Analyse und Entscheidungsfindung von komplexen Systemen im Mittelpunkt. Das neu entwickelte Resilienz-Entscheidungsfindungsverfahren steht im Kern dieser Entwicklungen. Es basiert auf einem adaptierten systemischen Risikomaß, einer zeitabhängigen, probabilistischen Resilienzmetrik sowie einem Gittersuchalgorithmus und stellt eine bedeutende Innovation dar, da es Entscheidungsträgern ermöglicht, ein optimales Gleichgewicht zwischen verschiedenen Arten von Resilienz-steigernden Maßnahmen unter Berücksichtigung monetärer Aspekte zu identifizieren. Zunehmend weisen Systemkomponenten eine erhebliche Eigenkomplexität auf, was dazu führt, dass sie selbst als Systeme modelliert werden müssen. Hieraus ergeben sich Systeme aus Systemen mit hoher Komplexität. Um diese Herausforderung zu adressieren, wird eine neue Methodik abgeleitet, indem das zuvor eingeführte Resilienzrahmenwerk auf multidimensionale Anwendungsfälle erweitert und synergetisch mit einem etablierten Konzept aus der Zuverlässigkeitstheorie, der Überlebenssignatur, zusammengeführt wird. Der neue Ansatz kombiniert die Vorteile beider ursprünglichen Komponenten: Einerseits ermöglicht er einen direkten Vergleich verschiedener Resilienz-steigernder Maßnahmen aus einem mehrdimensionalen Suchraum, der zu einem optimalen Kompromiss in Bezug auf die Systemresilienz führt. Andererseits ermöglicht er durch die Separationseigenschaft der Überlebenssignatur eine signifikante Reduktion des Rechenaufwands. Sobald eine Subsystemstruktur berechnet wurde -- ein typischerweise rechenintensiver Prozess -- kann jede Charakterisierung des probabilistischen Ausfallverhaltens von Komponenten validiert werden, ohne dass die Struktur erneut berechnet werden muss. In der Realität sind Messungen, Expertenwissen sowie weitere Informationsquellen mit vielfältigen Unsicherheiten belastet. Hierfür wird eine effiziente Methode vorgeschlagen, die auf der Kombination von Überlebenssignatur, unscharfer Wahrscheinlichkeitstheorie und nicht-intrusiver stochastischer Simulation (NISS) basiert. Dadurch entsteht ein effizienter Ansatz zur Quantifizierung der Zuverlässigkeit komplexer Systeme unter Berücksichtigung des gesamten Unsicherheitsspektrums. Der neue Ansatz, der die vorteilhaften Eigenschaften seiner ursprünglichen Komponenten synergetisch zusammenführt, erreicht eine bedeutende Verringerung des Rechenaufwands aufgrund der Separationseigenschaft der Überlebenssignatur. Er erzielt zudem eine drastische Reduzierung der Stichprobengröße aufgrund der adaptierten NISS-Methode: Es wird nur eine einzige stochastische Simulation benötigt, um Unsicherheiten zu berücksichtigen. Die neue Methodik stellt nicht nur eine Neuerung auf dem Gebiet der Zuverlässigkeitsanalyse dar, sondern kann auch in das Resilienzrahmenwerk integriert werden. Für eine Resilienzanalyse von real existierenden Systemen ist die Berücksichtigung kontinuierlicher Komponentenfunktionalität unerlässlich. Diese wird in einer weiteren Neuentwicklung adressiert. Durch die Einführung der kontinuierlichen Überlebensfunktion und dem Konzept der Diagonal Approximated Signature als entsprechendes Ersatzmodell kann das bestehende Resilienzrahmenwerk sinnvoll erweitert werden, ohne seine grundlegenden Vorteile zu beeinträchtigen. Im Kontext der Regeneration komplexer Investitionsgüter wird ein umfassendes Analyserahmenwerk vorgestellt, um die Übertragbarkeit und Anwendbarkeit aller entwickelten Methoden auf komplexe Systeme jeglicher Art zu demonstrieren. Das Rahmenwerk integriert die zuvor entwickelten Methoden der Resilienz-, Zuverlässigkeits- und Unsicherheitsanalyse. Es bietet Entscheidungsträgern die Basis für die Identifikation resilienter Regenerationspfade in zweierlei Hinsicht: Zum einen im Sinne von Regenerationspfaden mit inhärenter Resilienz und zum anderen Regenerationspfade, die zu einer maximalen Systemresilienz unter Berücksichtigung technischer und monetärer Einflussgrößen des zu analysierenden komplexen Investitionsgutes führen. Zusammenfassend bietet diese Dissertation innovative Beiträge zur effizienten Resilienzanalyse und Entscheidungsfindung für komplexe Ingenieursysteme. Sie präsentiert universell anwendbare Methoden und Rahmenwerke, die flexibel genug sind, um beliebige Systemtypen und Leistungsmaße zu berücksichtigen. Dies wird in zahlreichen Fallstudien von willkürlichen Flussnetzwerken, funktionalen Modellen von Axialkompressoren bis hin zu substrukturierten Infrastruktursystemen mit mehreren tausend Einzelkomponenten demonstriert

Towards development of fuzzy spatial datacubes : fundamental concepts with example for multidimensional coastal erosion risk assessment and representation

Les systèmes actuels de base de données géodécisionnels (GeoBI) ne tiennent généralement pas compte de l'incertitude liée à l'imprécision et le flou des objets; ils supposent que les objets ont une sémantique, une géométrie et une temporalité bien définies et précises. Un exemple de cela est la représentation des zones à risque par des polygones avec des limites bien définies. Ces polygones sont créés en utilisant des agrégations d'un ensemble d'unités spatiales définies sur soit des intérêts des organismes responsables ou les divisions de recensement national. Malgré la variation spatio-temporelle des multiples critères impliqués dans l’analyse du risque, chaque polygone a une valeur unique de risque attribué de façon homogène sur l'étendue du territoire. En réalité, la valeur du risque change progressivement d'un polygone à l'autre. Le passage d'une zone à l'autre n'est donc pas bien représenté avec les modèles d’objets bien définis (crisp). Cette thèse propose des concepts fondamentaux pour le développement d'une approche combinant le paradigme GeoBI et le concept flou de considérer la présence de l’incertitude spatiale dans la représentation des zones à risque. En fin de compte, nous supposons cela devrait améliorer l’analyse du risque. Pour ce faire, un cadre conceptuel est développé pour créer un model conceptuel d’une base de donnée multidimensionnelle avec une application pour l’analyse du risque d’érosion côtier. Ensuite, une approche de la représentation des risques fondée sur la logique floue est développée pour traiter l'incertitude spatiale inhérente liée à l'imprécision et le flou des objets. Pour cela, les fonctions d'appartenance floues sont définies en basant sur l’indice de vulnérabilité qui est un composant important du risque. Au lieu de déterminer les limites bien définies entre les zones à risque, l'approche proposée permet une transition en douceur d'une zone à une autre. Les valeurs d'appartenance de plusieurs indicateurs sont ensuite agrégées basées sur la formule des risques et les règles SI-ALORS de la logique floue pour représenter les zones à risque. Ensuite, les éléments clés d'un cube de données spatiales floues sont formalisés en combinant la théorie des ensembles flous et le paradigme de GeoBI. En plus, certains opérateurs d'agrégation spatiale floue sont présentés. En résumé, la principale contribution de cette thèse se réfère de la combinaison de la théorie des ensembles flous et le paradigme de GeoBI. Cela permet l’extraction de connaissances plus compréhensibles et appropriées avec le raisonnement humain à partir de données spatiales et non-spatiales. Pour ce faire, un cadre conceptuel a été proposé sur la base de paradigme GéoBI afin de développer un cube de données spatiale floue dans le system de Spatial Online Analytical Processing (SOLAP) pour évaluer le risque de l'érosion côtière. Cela nécessite d'abord d'élaborer un cadre pour concevoir le modèle conceptuel basé sur les paramètres de risque, d'autre part, de mettre en œuvre l’objet spatial flou dans une base de données spatiales multidimensionnelle, puis l'agrégation des objets spatiaux flous pour envisager à la représentation multi-échelle des zones à risque. Pour valider l'approche proposée, elle est appliquée à la région Perce (Est du Québec, Canada) comme une étude de cas.Current Geospatial Business Intelligence (GeoBI) systems typically do not take into account the uncertainty related to vagueness and fuzziness of objects; they assume that the objects have well-defined and exact semantics, geometry, and temporality. Representation of fuzzy zones by polygons with well-defined boundaries is an example of such approximation. This thesis uses an application in Coastal Erosion Risk Analysis (CERA) to illustrate the problems. CERA polygons are created using aggregations of a set of spatial units defined by either the stakeholders’ interests or national census divisions. Despite spatiotemporal variation of the multiple criteria involved in estimating the extent of coastal erosion risk, each polygon typically has a unique value of risk attributed homogeneously across its spatial extent. In reality, risk value changes gradually within polygons and when going from one polygon to another. Therefore, the transition from one zone to another is not properly represented with crisp object models. The main objective of the present thesis is to develop a new approach combining GeoBI paradigm and fuzzy concept to consider the presence of the spatial uncertainty in the representation of risk zones. Ultimately, we assume this should improve coastal erosion risk assessment. To do so, a comprehensive GeoBI-based conceptual framework is developed with an application for Coastal Erosion Risk Assessment (CERA). Then, a fuzzy-based risk representation approach is developed to handle the inherent spatial uncertainty related to vagueness and fuzziness of objects. Fuzzy membership functions are defined by an expert-based vulnerability index. Instead of determining well-defined boundaries between risk zones, the proposed approach permits a smooth transition from one zone to another. The membership values of multiple indicators (e.g. slop and elevation of region under study, infrastructures, houses, hydrology network and so on) are then aggregated based on risk formula and Fuzzy IF-THEN rules to represent risk zones. Also, the key elements of a fuzzy spatial datacube are formally defined by combining fuzzy set theory and GeoBI paradigm. In this regard, some operators of fuzzy spatial aggregation are also formally defined. The main contribution of this study is combining fuzzy set theory and GeoBI. This makes spatial knowledge discovery more understandable with human reasoning and perception. Hence, an analytical conceptual framework was proposed based on GeoBI paradigm to develop a fuzzy spatial datacube within Spatial Online Analytical Processing (SOLAP) to assess coastal erosion risk. This necessitates developing a framework to design a conceptual model based on risk parameters, implementing fuzzy spatial objects in a spatial multi-dimensional database, and aggregating fuzzy spatial objects to deal with multi-scale representation of risk zones. To validate the proposed approach, it is applied to Perce region (Eastern Quebec, Canada) as a case study

Integrated performance prediction and quality control in manufacturing systems

textPredicting the condition of a degrading dynamic system is critical for implementing successful control and designing the optimal operation and maintenance strategies throughout the lifetime of the system. In many situations, especially in manufacturing, systems experience multiple degradation cycles, failures, and maintenance events throughout their lifetimes. In such cases, historical records of sensor readings observed during the lifecycle of a machine can yield vital information about degradation patterns of the monitored machine, which can be used to formulate dynamic models for predicting its future performance. Besides the ability to predict equipment failures, another major component of cost effective and high-throughput manufacturing is tight control of product quality. Quality control is assured by taking periodic measurements of the products at various stages of production. Nevertheless, quality measurements of the product require time and are often executed on costly measurement equipment, which increases the cost of manufacturing and slows down production. One possible way to remedy this situation is to utilize the inherent link between the manufacturing equipment condition, mirrored in the readings of sensors mounted on that machine, and the quality of products coming out of it. The concept of Virtual Metrology (VM) addresses the quality control problem by using data-driven models that relate the product quality to the equipment sensors, enabling continuous estimation of the quality characteristics of the product, even when physical measurements of product quality are not available. VM can thus bring significant production benefits, including improved process control, reduced quality losses and higher productivity. In this dissertation, new methods are formulated that will combine long-term performance prediction of sensory signatures from a degrading manufacturing machine with VM quality estimation, which enables integration of predictive condition monitoring (prediction of sensory signatures) with predictive manufacturing process control (predictive VM model). The recently developed algorithm for prediction of sensory signatures is capable of predicting the system condition by comparing the similarity of the most recent performance signatures with the known degradation patterns available in the historical records. The method accomplishes the prediction of non-Gaussian and non-stationary time-series of relevant performance signatures with analytical tractability, which enables calculations of predicted signature distributions with significantly greater speeds than what can be found in literature. VM quality estimation is implemented using the recently introduced growing structure multiple model system paradigm (GSMMS), based on the use of local linear dynamic models. The concept of local models enables representation of complex, non-linear dependencies with non-Gaussian and non-stationary noise characteristics, using a locally tractable model representation. Localized modeling enables a VM that can detect situations when the VM model is not adequate and needs to be improved, which is one of the main challenges in VM. Finally, uncertainty propagation with Monte Carlo simulation is pursued in order to propagate the predicted distributions of equipment signatures through the VM model to enable prediction of distributions of the quality variables using the readily available sensor readings streaming from the monitored manufacturing machine. The newly developed methods are applied to long-term production data coming from an industrial plasma-enhanced chemical vapor deposition (PECVD) tool operating in a major semiconductor manufacturing fab.Mechanical Engineerin

New Methods to Improve Large-Scale Microscopy Image Analysis with Prior Knowledge and Uncertainty

Multidimensional imaging techniques provide powerful ways to examine various kinds of scientific questions. The routinely produced data sets in the terabyte-range, however, can hardly be analyzed manually and require an extensive use of automated image analysis. The present work introduces a new concept for the estimation and propagation of uncertainty involved in image analysis operators and new segmentation algorithms that are suitable for terabyte-scale analyses of 3D+t microscopy images

New Methods to Improve Large-Scale Microscopy Image Analysis with Prior Knowledge and Uncertainty

Multidimensional imaging techniques provide powerful ways to examine various kinds of scientific questions. The routinely produced datasets in the terabyte-range, however, can hardly be analyzed manually and require an extensive use of automated image analysis. The present thesis introduces a new concept for the estimation and propagation of uncertainty involved in image analysis operators and new segmentation algorithms that are suitable for terabyte-scale analyses of 3D+t microscopy images.Comment: 218 pages, 58 figures, PhD thesis, Department of Mechanical Engineering, Karlsruhe Institute of Technology, published online with KITopen (License: CC BY-SA 3.0, http://dx.doi.org/10.5445/IR/1000057821