984 research outputs found

    BOtied: Multi-objective Bayesian optimization with tied multivariate ranks

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    Many scientific and industrial applications require joint optimization of multiple, potentially competing objectives. Multi-objective Bayesian optimization (MOBO) is a sample-efficient framework for identifying Pareto-optimal solutions. We show a natural connection between non-dominated solutions and the highest multivariate rank, which coincides with the outermost level line of the joint cumulative distribution function (CDF). We propose the CDF indicator, a Pareto-compliant metric for evaluating the quality of approximate Pareto sets that complements the popular hypervolume indicator. At the heart of MOBO is the acquisition function, which determines the next candidate to evaluate by navigating the best compromises among the objectives. Multi-objective acquisition functions that rely on box decomposition of the objective space, such as the expected hypervolume improvement (EHVI) and entropy search, scale poorly to a large number of objectives. We propose an acquisition function, called BOtied, based on the CDF indicator. BOtied can be implemented efficiently with copulas, a statistical tool for modeling complex, high-dimensional distributions. We benchmark BOtied against common acquisition functions, including EHVI and random scalarization (ParEGO), in a series of synthetic and real-data experiments. BOtied performs on par with the baselines across datasets and metrics while being computationally efficient.Comment: 10 pages (+5 appendix), 9 figures. Submitted to NeurIP

    Pairwise versus mutual independence: visualisation, actuarial applications and central limit theorems

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    Accurately capturing the dependence between risks, if it exists, is an increasingly relevant topic of actuarial research. In recent years, several authors have started to relax the traditional 'independence assumption', in a variety of actuarial settings. While it is known that 'mutual independence' between random variables is not equivalent to their 'pairwise independence', this thesis aims to provide a better understanding of the materiality of this difference. The distinction between mutual and pairwise independence matters because, in practice, dependence is often assessed via pairs only, e.g., through correlation matrices, rank-based measures of association, scatterplot matrices, heat-maps, etc. Using such pairwise methods, it is possible to miss some forms of dependence. In this thesis, we explore how material the difference between pairwise and mutual independence is, and from several angles. We provide relevant background and motivation for this thesis in Chapter 1, then conduct a literature review in Chapter 2. In Chapter 3, we focus on visualising the difference between pairwise and mutual independence. To do so, we propose a series of theoretical examples (some of them new) where random variables are pairwise independent but (mutually) dependent, in short, PIBD. We then develop new visualisation tools and use them to illustrate what PIBD variables can look like. We showcase that the dependence involved is possibly very strong. We also use our visualisation tools to identify subtle forms of dependence, which would otherwise be hard to detect. In Chapter 4, we review common dependence models (such has elliptical distributions and Archimedean copulas) used in actuarial science and show that they do not allow for the possibility of PIBD data. We also investigate concrete consequences of the 'nonequivalence' between pairwise and mutual independence. We establish that many results which hold for mutually independent variables do not hold under sole pairwise independent. Those include results about finite sums of random variables, extreme value theory and bootstrap methods. This part thus illustrates what can potentially 'go wrong' if one assumes mutual independence where only pairwise independence holds. Lastly, in Chapters 5 and 6, we investigate the question of what happens for PIBD variables 'in the limit', i.e., when the sample size goes to infi nity. We want to see if the 'problems' caused by dependence vanish for sufficiently large samples. This is a broad question, and we concentrate on the important classical Central Limit Theorem (CLT), for which we fi nd that the answer is largely negative. In particular, we construct new sequences of PIBD variables (with arbitrary margins) for which a CLT does not hold. We derive explicitly the asymptotic distribution of the standardised mean of our sequences, which allows us to illustrate the extent of the 'failure' of a CLT for PIBD variables. We also propose a general methodology to construct dependent K-tuplewise independent (K an arbitrary integer) sequences of random variables with arbitrary margins. In the case K = 3, we use this methodology to derive explicit examples of triplewise independent sequences for which no CLT hold. Those results illustrate that mutual independence is a crucial assumption within CLTs, and that having larger samples is not always a viable solution to the problem of non-independent data

    Power system adequacy: on two-area models and the capacity procurement decision process

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    In this work, we explore methodological extensions to modelling practices in power system adequacy for single-area and two-area systems. Specifically, we build on top of some of the practices currently in use in Great Britain (GB) by National Grid, framing this in the context of the current technological transition in which renewable capacity is gradually replacing a considerable share of fossil-fuel-based capacity. We explore two-area extensions of the methodology currently used in GB to quantify risk in single-area models. By doing this, we also explore the impact of shortfall-sharing policies and wind capacity on risk indices and on the value of interconnection. Furthermore, we propose a model based on the statistical theory of extreme values to characterise statistical dependence across systems in both net demand (defined as power demand minus renewable generation) and capacity surpluses/deficits (defined as power supply minus demand), looking at how statistical dependence strength influences post-interconnection risk and the capacity value of interconnection. Lastly, we analyse the risk profile of a single-area system as reliance on wind capacity grows, looking at risk beyond the standard set of risk indices, which are based on long-term averages. In doing this, we look at trends which are overlooked by the latter, yet are of considerable importance for decision-makers. Moreover, we incorporate a measure of the decision-maker's degree of risk aversion into the current capacity procurement methodology in GB, and look at the impact of this and other parameters on the amount of procured capacity. We find that shortfall-sharing policies can have a sizeable impact on the interconnector's valuation in terms of security of supply, specially for systems that are significantly smaller than their neighbours. Moreover, this valuation also depends strongly on the risk indices chosen to measure it. We also find that the smoothing effect of parametric extreme value models on tail regions can have a material effect on practical adequacy calculations for post-interconnection risks, and that assumed independence between conventional generation fleets makes capacity shortfall co-occurrences only weakly dependent (in a precisely defined sense) across areas despite much stronger statistical dependence between system net demands. Lastly, as more wind capacity is installed, we find multiple relevant changes in the (single-area) system's risk profile that are not expressed by the standard risk indices: in particular, we find a substantial increase in the frequency of severe events, extreme year-to-year variability of outturn, and a progression to a system with fewer days of potentially much larger shortfalls. Moreover, we show that a high reliance on wind introduces a substantial amount of uncertainty into the calculations due to the limited number of available historic years, which cannot account for the wide range of possible weather conditions the system could experience in the future. Lastly, we also find that the a higher reliance on wind generation also impact the capacity procurement decision process, potentially making the amount of procured capacity considerably more sensitive to parameters such as the value of lost load

    Efficient resilience analysis and decision-making for complex engineering systems

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    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

    Joint Probability Analysis of Extreme Precipitation and Water Level for Chicago, Illinois

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    A compound flooding event occurs when there is a combination of two or more extreme factors that happen simultaneously or in quick succession and can lead to flooding. In the Great Lakes region, it is common for a compound flooding event to occur with a high lake water level and heavy rainfall. With the potential of increasing water levels and an increase in precipitation under climate change, the Great Lakes coastal regions could be at risk for more frequent and severe flooding. The City of Chicago which is located on Lake Michigan has a high population and dense infrastructure and is very vulnerable to a compound flooding event, even with the implementation of its water control structures. For this case study, annual maximum precipitation and corresponding lake water level data were analyzed to examine the bivariate return period of a compound flood event using a copula function. The results show that under climate change if the water level were to rise by 0.2, 0.45, or 0.8 m, compound flooding events due to heavy precipitation and high water level will be more likely in the future. By documenting the joint risk of potential compound flooding in this area, preventative measures and planning can be implemented

    Comprehensive bias correction of regional climate model boundary conditions for simulation of hydrologic extremes.

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    High-impact extreme weather and climate events result that threaten society and ecosystems worldwide, from multiple interactions of atmospheric variables linked in dynamic ways. Ongoing global warming necessitates new ways of assessing how extreme events may change in the future. While global climate models (GCMs) have been utilised to assess the simulation of extreme events, the coarse spatial and temporal scales limit their effectiveness at regional or hydrological catchment scales. Regional climate models (RCMs) that use GCM datasets as input boundary conditions are commonly used to improve model predictability for extreme events. Although analyses of extreme events at the regional scale have evolved, systematic bias still exists and is passed onto the RCM simulation through biased boundary conditions simulated using coarser scale GCMs. Despite using various bias correction alternatives to address biases, these approaches often assume that inter-variable bias is not of key importance and that diurnal patterns are properly simulated by the GCM. However, such assumptions can result in substantial anomalies in the simulation of extreme events. Thus, this thesis investigates the impact that several bias correction alternatives can have on RCM boundary conditions with a focus on (1) Precipitation extremes; (2) Spatial, temporal, and multivariate aspects; (3) Multivariate relationships for extreme events; (4) Compound events; (5) Diurnal precipitation cycle; and develops a (6) Software tool for bias correction. The univariate techniques show improvement in precipitation extremes, but the discrepancies in inter-variable relationships are not adequately reduced through RCM boundaries. To address this issue, this study corrects the cross-dependence attributes of these fields, leading to substantial improvements in the statistics used. This study also shows that multivariate bias correction broadly represents the frequency of compound events better. The method is further developed to provide sub-daily corrections that are shown to improve the diurnal cycle of precipitation. Finally, a Python package has been developed as a software tool that simplifies the correction of systematic bias in RCM input boundary conditions. In conclusion, the work in this thesis demonstrates a significant improvement in the regional climate model simulation capacity, thereby enhancing water security and enabling more accurate forecasting of drought and flood events under climate change

    Application of machine learning and deep neural networks for spatial prediction of groundwater nitrate concentration to improve land use management practices

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    The prediction of groundwater nitrate concentration\u27s response to geo-environmental and human-influenced factors is essential to better restore groundwater quality and improve land use management practices. In this paper, we regionalize groundwater nitrate concentration using different machine learning methods (Random forest (RF), unimodal 2D and 3D convolutional neural networks (CNN), and multi-stream early and late fusion 2D-CNNs) so that the nitrate situation in unobserved areas can be predicted. CNNs take into account not only the nitrate values of the grid cells of the observation wells but also the values around them. This has the added benefit of allowing them to learn directly about the influence of the surroundings. The predictive performance of the models was tested on a dataset from a pilot region in Germany, and the results show that, in general, all the machine learning models, after a Bayesian optimization hyperparameter search and training, achieve good spatial predictive performance compared to previous studies based on Kriging and numerical models. Based on the mean absolute error (MAE), the random forest model and the 2DCNN late fusion model performed best with an MAE (STD) of 9.55 (0.367) mg/l, R2 = 0.43 and 10.32 (0.27) mg/l, R2 = 0.27, respectively. The 3DCNN with an MAE (STD) of 11.66 (0.21) mg/l and largest resources consumption is the worst performing model. Feature importance learning from the models was used in conjunction with partial dependency analysis of the most important features to gain greater insight into the major factors explaining the nitrate spatial variability. Large uncertainties in nitrate prediction have been shown in previous studies. Therefore, the models were extended to quantify uncertainty using prediction intervals (PIs) derived from bootstrapping. Knowledge of uncertainty helps the water manager reduce risk and plan more reliably

    Bayesian joint quantile autoregression

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    Quantile regression continues to increase in usage, providing a useful alternative to customary mean regression. Primary implementation takes the form of so-called multiple quantile regression, creating a separate regression for each quantile of interest. However, recently, advances have been made in joint quantile regression, supplying a quantile function which avoids crossing of the regression across quantiles. Here, we turn to quantile autoregression (QAR), offering a fully Bayesian version. We extend the initial quantile regression work of Koenker and Xiao (J Am Stat Assoc 101(475):980–990, 2006. https://doi.org/10.1198/016214506000000672) in the spirit of Tokdar and Kadane (Bayesian Anal 7(1):51–72, 2012. https://doi.org/10.1214/12-BA702). We offer a directly interpretable parametric model specification for QAR. Further, we offer a pth-order QAR(p) version, a multivariate QAR(1) version, and a spatial QAR(1) version. We illustrate with simulation as well as a temperature dataset collected in Aragón, Spain

    Időjárás 2023

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