Daten-basierte variable-fidelity Modelle reduzierter Ordnung zur effizienten Fahrzeugform-Optimierung

Over the last decades, aerodynamics has played a more and more important role in engineering design of vehicles. Computer simulations are used to investigate the aerodynamic behavior of new geometries. In addition to scalar-valued quantities, high-dimensional field variables such as the sensitivity map, a vector-valued quantity which indicates the sensitivity of the drag coeffcient with respect to local shape variations, are of particular interest. However, the high computational effort required for high-fidelity aerodynamic flow simulations makes their use in an optimization process unfeasable. Since the design of cars is primarily driven by aesthetics, automatic optimization of the vehicle shape is also undesirable. An interactive design tool is required which enables the computation of sufficiently accurate approximations to the aerodynamic quantities via a surrogate model in real-time. This calls for the use of non-intrusive model reduction techniques, which approximate the quantity of interest based on sampled data. However, the high computational effort associated with high-fidelity flow simulations strongly limits the available sample data. In the case of scalar-valued quantities, variable-fidelity methods can be used to drastically increase the efficiency of the surrogate model. Such methods use sample data of a computationally cheaper, but also less accurate model to obtain the global trend of the quantity of interest and in this way improve the approximation of the high-fidelity model. In this thesis, a well-known variable-fidelity methodology for scalar-valued quantities is extended to the vector-valued case. It is shown that this new approach is a generalization of known variable-fidelity methods for scalar-valued qunatities and that certain properties of these approaches transfer to the new method. An error estimator is derived which can be used to adaptively improve the model. In addition, open theoretical questions associated with the Cokriging method, a well-known variable-fidelity method for scalar-valued quantities, are addressed. The applicability of the new method in industrial vehicle shape optimization is then demonstrated in two case studies on a high-resolution model of a Volkswagen Passat B6 provided by the Volkswagen AG and compared with conventional methods.In den letzten Jahrzehnten hat die Bedeutung der Aerodynamik in der Fahrzeugentwicklung immer weiter zugenommen. Zur Untersuchung des aerodynamischen Verhaltens neuer Geometrien kommen Computersimulationen zum Einsatz. Typische Zielgrößen sind dabei neben skalaren Kennwerten auch hoch-dimensionale Feldgrößen wie die Sensitivitätslandkarte, die die Sensitivität des Widerstandsbeiwertes bezüglich lokaler Formänderungen anzeigt. Allerdings macht der hohe Rechenaufwand hochgenauer aerodynamischer Strömungssimulationen ihre Verwendung in einem Optimierungsprozess unmöglich. Da das Design von Autos vor allem durch Ästhetik bestimmt wird, ist eine automatische Optimierung der Fahrzeugform zudem ungewünscht. Ferner wird ein interaktives Design-Tool benötigt, welches die Zielgröße über ein Ersatzmodell hinreichend genau in nahezu Echtzeit näherungsweise berechnet und visualisiert. Aufgrund dieser Anforderungen kommen nicht-intrusive Modellreduktions-Verfahren in Frage, welche die Zielgröße basierend auf beobachteten Stützwerten approximiert. Der hohe Rechenaufwand hochgenauer Strömungssimulationen limitiert die Anzahl der verfügbaren Stützwerte allerdings stark. Im Falle skalarer Zielgrößen kann man mithilfe von variable-fidelity Verfahren die Effizienz der Ersatzmodell-Erstellung drastisch steigern. Solche Verfahren nutzen Stützwerte eines weniger rechenintensiven, aber auch ungenaueren Modells um den globalen Trend der Zielgröße zu erfassen und so die Approximation des hochgenauen Modells zu verbessern. Im Rahmen dieser Arbeit wird eine bekannte variable-fidelity Methodik für skalare Zielgrößen auf vektorwertigen Zielgrößen erweitert. Es wird gezeigt, dass der vorgestellte neue Ansatz eine Verallgemeinerung bekannter variable-fidelity Verfahren für skalare Zielgrößen ist und sich dadurch bestimmte Eigenschaften dieser Ansätze auf die neue Methode übertragen. Ein Fehlerschätzer wird hergeleitet, der zur adaptiven Verbesserung des Modells verwendet werden kann. Außerdem werden offene theoretische Fragen zu der Cokriging-Methode, einer bekannten variable-fidelity Methode für skalare Zielgrößen, untersucht. Anschließend wird die Anwendbarkeit der neuen Methode in der industriellen Fahrzeugform-Optimierung in zwei Fallstudien am Beispiel eines hochaufgelösten Computermodells eines Volkswagen Passat B6, welches von der Volkswagen AG zur Verfügung gestellt wurde, demonstriert und mit herkömmlichen Verfahren verglichen

Multilevel Delayed Acceptance MCMC with Applications to Hydrogeological Inverse Problems

Quantifying the uncertainty of model predictions is a critical task for engineering decision support systems. This is a particularly challenging effort in the context of statistical inverse problems, where the model parameters are unknown or poorly constrained, and where the data is often scarce. Many such problems emerge in the fields of hydrology and hydro--environmental engineering in general, and in hydrogeology in particular. While methods for rigorously quantifying the uncertainty of such problems exist, they are often prohibitively computationally expensive, particularly when the forward model is high--dimensional and expensive to evaluate. In this thesis, I present a Metropolis--Hastings algorithm, namely the Multilevel Delayed Acceptance (MLDA) algorithm, which exploits a hierarchy of forward models of increasing computational cost to significantly reduce the total cost of quantifying the uncertainty of high--dimensional, expensive forward models. The algorithm is shown to be in detailed balance with the posterior distribution of parameters, and the computational gains of the algorithm is demonstrated on multiple examples. Additionally, I present an approach for exploiting a deep neural network as an ultra--fast model approximation in an MLDA model hierarchy. This method is demonstrated in the context of both 2D and 3D groundwater flow modelling. Finally, I present a novel approach to adaptive optimal design of groundwater surveying, in which MLDA is employed to construct the posterior Monte Carlo estimates. This method utilises the posterior uncertainty of the primary problem in conjunction with the expected solution to an adjoint problem to sequentially determine the optimal location of the next datapoint.Engineering and Physical Sciences Research Council (EPSRC)Alan Turing InstituteEngineering and Physical Sciences Research Council (EPSRC

Model-data interaction in groundwater studies: Review of methods, applications and future directions

This manuscript version is made available under the CC-BY-NC-ND 4.0 license: http://creativecommons.org/licenses/by-nc-nd/4.0/ which permits use, distribution and reproduction in any medium, provided the original work is properly cited. This author accepted manuscript is made available following 24 month embargo from date of publication (Sept 2018) in accordance with the publisher’s archiving policyWe define model-data interaction (MDI) as a two way process between models and data, in which on one hand data can serve the modeling purpose by supporting model discrimination, parameter refinement, uncertainty analysis, etc., and on the other hand models provide a tool for data fusion, interpretation, interpolation, etc. MDI has many applications in the realm of groundwater and has been the topic of extensive research in the groundwater community for the past several decades. This has led to the development of a multitude of increasingly sophisticated methods. The progress of data acquisition technologies and the evolution of models are continuously changing the landscape of groundwater MDI, creating new challenges and opportunities that must be properly understood and addressed. This paper aims to review, analyze and classify research on MDI in groundwater applications, and discusses several related aspects including: (1) basic theoretical concepts and classification of methods, (2) sources of uncertainty and how they are commonly addressed, (3) specific characteristics of groundwater models and data that affect the choice of methods, (4) how models and data can interact to provide added value in groundwater applications, (5) software and codes for MDI, and (6) key issues that will likely form future research directions. The review shows that there are many tools and techniques for groundwater MDI, and this diversity is needed to support different MDI objectives, assumptions, model and data types and computational constraints. The study identifies eight categories of applications for MDI in the groundwater literature, and highlights the growing gap between MDI practices in the research community and those in consulting, industry and government.Behzad Ataie-Ashtiani and Craig T. Simmons acknowledge support from the National Centre for Groundwater Research and Training, Australia. Behzad Ataie-Ashtiani also appreciates the support of the Research Office of the Sharif University of Technology, Iran