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Modeling and simulations of large-scale systems are used extensively to not only better understand a natural phenomenon, but also to predict future events. Accurate model results are critical for design optimization and policy making. They can be used effectively to reduce the impact of a natural disaster or even prevent it from happening. In reality, model predictions are often affected by uncertainties in input data and model parameters, and by incomplete knowledge of the underlying physics. A deterministic simulation assumes one set of input conditions, and generates one result without considering uncertainties. It is of great interest to include uncertainty information in the simulation. By ``Uncertainty Quantification,'' we denote the ensemble of techniques used to model probabilistically the uncertainty in model inputs, to propagate it through the system, and to represent the resulting uncertainty in the model result. This added information provides a confidence level about the model forecast. For example, in environmental modeling, the model forecast, together with the quantified uncertainty information, can assist the policy makers in interpreting the simulation results and in making decisions accordingly. Another important goal in modeling and simulation is to improve the model accuracy and to increase the model prediction power. By merging real observation data into the dynamic system through the data assimilation (DA) technique, the overall uncertainty in the model is reduced. With the expansion of human knowledge and the development of modeling tools, simulation size and complexity are growing rapidly. This poses great challenges to uncertainty analysis techniques. Many conventional uncertainty quantification algorithms, such as the straightforward Monte Carlo method, become impractical for large-scale simulations. New algorithms need to be developed in order to quantify and reduce uncertainties in large-scale simulations. This research explores novel uncertainty quantification and reduction techniques that are suitable for large-scale simulations. In the uncertainty quantification part, the non-sampling polynomial chaos (PC) method is investigated. An efficient implementation is proposed to reduce the high computational cost for the linear algebra involved in the PC Galerkin approach applied to stiff systems. A collocation least-squares method is proposed to compute the PC coefficients more efficiently. A novel uncertainty apportionment strategy is proposed to attribute the uncertainty in model results to different uncertainty sources. The apportionment results provide guidance for uncertainty reduction efforts. The uncertainty quantification and source apportionment techniques are implemented in the 3-D Sulfur Transport Eulerian Model (STEM-III) predicting pollute concentrations in the northeast region of the United States. Numerical results confirm the efficacy of the proposed techniques for large-scale systems and the potential impact for environmental protection policy making. ``Uncertainty Reduction'' describes the range of systematic techniques used to fuse information from multiple sources in order to increase the confidence one has in model results. Two DA techniques are widely used in current practice: the ensemble Kalman filter (EnKF) and the four-dimensional variational (4D-Var) approach. Each method has its advantages and disadvantages. By exploring the error reduction directions generated in the 4D-Var optimization process, we propose a hybrid approach to construct the error covariance matrix and to improve the static background error covariance matrix used in current 4D-Var practice. The updated covariance matrix between assimilation windows effectively reduces the root mean square error (RMSE) in the solution. The success of the hybrid covariance updates motivates the hybridization of EnKF and 4D-Var to further reduce uncertainties in the simulation results. Numerical tests show that the hybrid method improves the model accuracy and increases the model prediction quality. / Ph. D.

Reynolds-Averaged Navier-Stokes (RANS) simulations are widely used for engineering design and analysis involving turbulent flows. In RANS simulations, the Reynolds stress needs closure models and the existing models have large model-form uncertainties. Therefore, the RANS simulations are known to be unreliable in many flows of engineering relevance, including flows with three-dimensional structures, swirl, pressure gradients, or curvature. This lack of accuracy in complex flows has diminished the utility of RANS simulations as a predictive tool for engineering design, analysis, optimization, and reliability assessments. Recently, data-driven methods have emerged as a promising alternative to develop the model of Reynolds stress for RANS simulations. In this dissertation I explore two physics-informed, data-driven frameworks to improve RANS modeled Reynolds stresses. First, a Bayesian inference framework is proposed to quantify and reduce the model-form uncertainty of RANS modeled Reynolds stress by leveraging online sparse measurement data with empirical prior knowledge. Second, a machine-learning-assisted framework is proposed to utilize offline high-fidelity simulation databases. Numerical results show that the data-driven RANS models have better prediction of Reynolds stress and other quantities of interest for several canonical flows. Two metrics are also presented for an a priori assessment of the prediction confidence for the machine-learning-assisted RANS model. The proposed data-driven methods are also applicable to the computational study of other physical systems whose governing equations have some unresolved physics to be modeled. / Ph. D. / Reynolds-Averaged Navier–Stokes (RANS) simulations are widely used for engineering design and analysis involving turbulent flows. In RANS simulations, the Reynolds stress needs closure models and the existing models have large model-form uncertainties. Therefore, the RANS simulations are known to be unreliable in many flows of engineering relevance, including flows with three-dimensional structures, swirl, pressure gradients, or curvature. This lack of accuracy in complex flows has diminished the utility of RANS simulations as a predictive tool for engineering design, analysis, optimization, and reliability assessments. Recently, data-driven methods have emerged as a promising alternative to develop the model of Reynolds stress for RANS simulations. In this dissertation I explore two physics-informed, data-driven frameworks to improve RANS modeled Reynolds stresses. First, a Bayesian inference framework is proposed to quantify and reduce the model-form uncertainty of RANS modeled Reynolds stress by leveraging online sparse measurement data with empirical prior knowledge. Second, a machine-learning-assisted framework is proposed to utilize offline high fidelity simulation databases. Numerical results show that the data-driven RANS models have better prediction of Reynolds stress and other quantities of interest for several canonical flows. Two metrics are also presented for an a priori assessment of the prediction confidence for the machine-learning-assisted RANS model. The proposed data-driven methods are also applicable to the computational study of other physical systems whose governing equations have some unresolved physics to be modeled.

This study aimed to investigate the impact of uncertainties in treatment planning related to the setup and range uncertainties. Three locations of targets were chosen, one in the head, one in the abdomen, and one in the pelvis. The treatment planning was assembled by utilising a CT image of a full body anthropomorphic phantom that was implemented into the treatment planning system RayStation (version 10, RaySearch Laboratories AB). A total of five regions of interest for the target were delineated as well as the associated organs at risks. The initial treatment plan considered the objective functions that aimed to achieve coverage of the CTV according to the clinical goal whilst minimising the dose reviewed by the organs at risk. In order to take the uncertainties into account for the treatment plan robustness optimization was applied with a predetermined set of setup and range uncertainties for each target. Dose histograms for the different cases of setup and range uncertainties were used to evaluate the significance of setup and range uncertainties onto the targets and the organs at risk. In addition, dose volume histograms and the difference in dose distribution aided to visualise the greatest deviation between the different cases. For the targets located in the head the small structures and the tissue heterogeneity resulted in being more affected by the range uncertainty rather than the setup uncertainty. The targets located in the abdomen and pelvic were on the other hand more affected by the setup uncertainties. This was a result related to structures adjacent to the target with different dose constraints and tissue heterogeneities. A comparison of the dose distribution showed the effect of setup uncertainties in the two aforementioned regions. For all cases the target coverage with the robust optimisation was as expected achieved. / Syftet med denna studie var att undersöka påverkan av osäkerheterna för protonernas utbredning och patienternas positionering med avseende på planeringen av en behandlingsplan. Totalt valdes tre områden som valdes att fokusera på var av två tumörer som var placerade i huvudet, en tumör som var placerad i abdomen och en tumör som var placerad i pelvis. Behandlingsplanen konstruerades med hjälp av en CT bild för en antropomorf helkropps fantom som överfördes till behandlingsteamet RayStation (version 10, RaySearch Laboratories AB). Samtliga tumörer och relevanta organ som anses vara i riskzonen för strålning fick definierade konturer. Därefter infördes funktioner för att optimera strålning till tumörer och funktioner för att begränsa strålningen till organen som var placerade i riskzonen enligt de kliniska önskemålen. För att beakta de ingående osäkerheterna i behandlingsplanen användes optimeringsalgoritmer för att säkerhetsställa att behandlingsplanen var robust gentemot ett antal förbestämda värde på de angivna osäkerheterna. Resultaten för osäkerheterna påverkas redovisades med histograms som påvisade den erhållna dosen för tumörer respektive organ i riskzonen. Utöver histogrammen redovisades differens mellan olika tillstånd av osäkerheterna med avseende på fördelning av dos. Tumörer som var placerade i huvudet hade större påverkan av protonernas utbredning på grund av de strukturer som är små till storlek relativt tumören, men även på grund av den heterogena omgivningen i det området. Däremot var tumörer som var placerade i abdomen och i pelvis mer påverkade av patientens position. Detta på grund av att närliggande organ och strukturer hade en diskrepans i de begränsade dosnivåerna samt på grund av heterogena omgivningar. Dessa fenomen påvisades även i de jämförelser som gjordes med avseende på fördelning av dos mellan olika tillstånd av osäkerheter. Slutligen visade denna studie att robust optimering gav samtliga tumörer en dosfördelning, vilket stämmer överens med vad som var förväntat.

It is well known that the standard canonical uncertainty relation does not apply to the angular variable ? and its conjugate LZ. That is, the relation ? ø ? L Z > h/2 is false. The break down of the result has to do with difference in topology between the line and the circle. It is thus desirable to generalize the standard uncertainty relation topologically and find satisfactory results for the non-Euclidean spaces. This problem is intimately related to the issue of finding a consistent definition for quantum mechanics on "curved spaces". Just as the Heisenberg uncertainty relation was pivotal in understanding the basic structure of standard quantum mechanics, a solution to this problem should shine some light onto the proper conduct of quantum mechanics on general topological spaces. In this study we explore in detail how the standard uncertainty relation may breakdown. We also address the importance of topological considerations in quantum mechanics in general - we shall show how a change in topological character can change the nature of the quantum mechanics for a system and how the consideration of the topology of a system can greatly organize the solution of a problem and in some cases even be necessary for a. full understanding of the problem. We then discuss the derivation of satisfactory uncertainty relations for the compact, homogeneous spaces of the circle, the n-torus and the n-sphere. Finally, we draw out any implications to the issue of properly defining quantum mechanics on the non- Euclidean spaces.

The following thesis deals with methods to increase the reliability of the results in life cycle assessment. The paper is divided into two parts. The first part points out the typologies and sources of uncertainty in LCA and summarises the existing methods dealing with it. The methods are critically discussed and pros and cons are contrasted. Within the second part a case study is carried out. This study calculates the carbon footprint of a cosmetic product of Li-iL GmbH. Thereby the whole life cycle of the powder bath Blaue Traube is analysed. To increase the reliability of the result a procedure, derived from the first part, is applied. Recommendations to enhance the product´s sustainability are then given to the decision-makers of the company. Finally the applied procedure for dealing with uncertainty in LCAs is evaluated. The aims of the thesis are to make a contribution to the understanding of uncertainty in life cycle assessment and to deal with it in a more consistent manner. As well, the carbon footprint of the powder bath shall be based on appropriate assumptions and shall consider occurring uncertainties. Basing on discussed problems, a method is introduced to avoid the problematic merging of variability uncertainty and data uncertainty to generate probability distributions. The introduced uncertainty importance analysis allows a consistent differentiation of these types of uncertainty. Furthermore an assessment of the used data of LCA studies is possible. The method is applied at a PCF study of the bath powder Blaue Traube of Li-iL GmbH. Thereby the analysis is carried out over the whole life cycle (cradle-to-grave) as well as cradle-to-gate. The study gives a practical example to the company determining the carbon footprint of products. In addition, it meets the requirements of ISO guidelines of publishing the study and comparing it with other products. Within the PCF study the introduced method allows a differentiation of variability uncertainty and knowledge uncertainty. The included uncertainty importance analysis supports the assessment of each aggregated unit process within the analysed product system. Finally this analysis can provide a basis to collect additional, more reliable or uncertain data for critical processes.

The purpose of this paper is to increase the understanding of how knowledge and uncertainty can affect relationship commitment between companies in the international market. Therefore, knowledge accumulation, the various levels of uncertainties and the creation of business relationships will be examined. In order to achieve the purpose of the study the main research problem is formulated: How do Knowledge and uncertainty levels related to relationship commitment of internationalized firms?This thesis is based on the qualitative method since the aim of this study is to understand and analyse a phenomenon not quantitatively to measure it. This research is further based on the deductive approach since we have formulated our main research question on the basis of previous theory and apply it on real life cases. The empirical data is collected through a multiple case study with three companies active on the international market.The study's conclusion indicates that relationship commitment has an impact on knowledge and uncertainty in the international context. We demonstrate this by proving that companies can through relationships accumulate the necessary knowledge needed to reduce uncertainty in international business. Thus reducing the gap between knowledge possessed by the firm and knowledge needed to perform an international activity.

Model based techniques for automated condition monitoring of HVAC systems have been under development for some years. Results from the application of these methods to systems installed in real buildings have highlighted robustness and sensitivity issues. The generation of false alarms has been identified as a principal factor affecting the potential usefulness of condition monitoring in HVAC applications. The robustness issue is a direct result of the uncertain measurements and the lack of experimental control that axe characteristic of HVAC systems. This thesis investigates the uncertainties associated with implementing a condition monitoring scheme based on simple first principles models in HVAC subsystems installed in real buildings. The uncertainties present in typical HVAC control system measurements are evaluated. A sensor validation methodology is developed and applied to a cooling coil subsystem installed in a real building. The uncertainty in steady-state analysis based on transient data is investigated. The uncertainties in the simplifications and assumptions associated with the derivation of simple first principles based models of heat-exchangers are established. A subsystem model is developed and calibrated to the test system. The relationship between the uncertainties in the calibration data and the parameter estimates are investigated. The uncertainties from all sources are evaluated and used to generate a robust indication of the subsystem condition. The sensitivity and robustness of the scheme is analysed based on faults implemented in the test system during summer, winter and spring conditions.

The dissertation focuses on estimating the uncertainty associated with stress/strain prediction procedures from dynamic test data used in turbine blade analysis. An accurate prediction of the maximum response levels for physical components during in-field operating conditions is essential for evaluating their performance and life characteristics, as well as for investigating how their behavior critically impacts system design and reliability assessment. Currently, stress/strain inference for a dynamic system is based on the combination of experimental data and results from the analytical/numerical model of the component under consideration. Both modeling challenges and testing limitations, however, contribute to the introduction of various sources of uncertainty within the given estimation procedure, and lead ultimately to diminished accuracy and reduced confidence in the predicted response. The objective of this work is to characterize the uncertainties present in the current response estimation process and provide a means to assess them quantitatively. More specifically, proposed in this research is a statistical methodology based on a Bayesian-network representation of the modeling process which allows for a statistically rigorous synthesis of modeling assumptions and information from experimental data. Such a framework addresses the problem of multi-directional uncertainty propagation, where standard techniques for unidirectional propagation from inputs' uncertainty to outputs' variability are not suited. Furthermore, it allows for the inclusion within the analysis of newly available test data that can provide indirect evidence on the parameters of the structure's analytical model, as well as lead to a reduction of the residual uncertainty in the estimated quantities. As part of this work, key uncertainty sources (i.e., material and geometric properties, sensor measurement and placement, as well as noise due data processing limitations) are investigated, and their impact upon the system response estimates is assessed through sensitivity studies. The results are utilized for the identification of the most significant contributors to uncertainty to be modeled within the developed Bayesian inference scheme. Simulated experimentation, statistically equivalent to specified real tests, is also constructed to generate the data necessary to build the appropriate Bayesian network, which is then infused with actual experimental information for the purpose of explaining the uncertainty embedded in the response predictions and quantifying their inherent accuracy.

[pt] Este trabalho tem um duplo objetivo. Em primeiro lugar, investiga qual o efeito da incerteza sobre a atividade econômica no Brasil. Para isso, são construídas diversas proxies que buscam captar o nível de incerteza vigente no Brasil (incerteza doméstica) e em vários de seus principais parceiros comerciais (incerteza externa). Em seguida, são estimados modelos de vetores autorregressivos (SVAR), em linha com Baker, Bloom e Davis (2016). Os resultados obtidos sugerem que a incerteza tem efeitos contracionistas relevantes sobre a economia brasileira. Em segundo lugar, estuda qual o efeito da incerteza sobre o poder da política monetária no Brasil. Para tanto, são construídos diversos modelos de vetores autorregressivos interativos (IVAR), tal como proposto por Aastveit, Natvik e Sola (2013), porém estimados por LASSO Adaptativo. As estimativas obtidas não corroboram a hipótese de que sob alta incerteza os efeitos da política monetária sobre a atividade são menores do que sob baixa incerteza. Este resultado, no entanto, não é robusto. / [en] This work has a dual purpose. First of all, we investigate the effect of uncertainty on economic activity in Brazil. In order to do that, we construct several proxies which seek to capture the uncertainty level prevailing in Brazil (domestic uncertainty) and in several of our major trading partners (external uncertainty). Next, we estimate vector autoregressive (SVAR) models, in line with Baker, Bloom and Davis (2016). The results suggest that uncertainty has, in fact, contractionary effects on the activity in Brazil. Second, we study the effect of uncertainty on effectiveness of monetary policy in Brazil. Thus, we make use of interacted vector autoregressive (IVAR) models, as proposed by Aastveit, Natvik and Sola (2013), estimated, however, by Adaptive LASSO. Our estimates do not corroborate the hypothesis that under high uncertainty the effects of monetary policy on the activity are lower than under low uncertainty.