This thesis deals with the application of optimisation based Validation and Verification (V&V) analysis on aerospace vehicles in order to determine their worst case performance metrics. To this end, three aerospace models relating to satellite and launcher vehicles provided by European Space Agency (ESA) on various projects are utilised. As a means to quicken the process of optimisation based V&V analysis, surrogate models are developed using polynomial chaos method. Surro- gate models provide a quick way to ascertain the worst case directions as computation time required for evaluating them is very small. A sin- gle evaluation of a surrogate model takes less than a second. Another contribution of this thesis is the evaluation of operational safety margin metric with the help of surrogate models. Operational safety margin is a metric defined in the uncertain parameter space and is related to the distance between the nominal parameter value and the first instance of performance criteria violation. This metric can help to gauge the robustness of the controller but requires the evaluation of the model in the constraint function and hence could be computationally intensive. As surrogate models are computationally very cheap, they are utilised to rapidly compute the operational safety margin metric. But this metric focuses only on finding a safe region around the nominal parameter value and the possibility of other disjoint safe regions are not explored. In order to find other safe or failure regions in the param- eter space, the method of Bernstein expansion method is utilised on surrogate polynomial models to help characterise the uncertain param- eter space into safe and failure regions. Furthermore, Binomial failure analysis is used to assign failure probabilities to failure regions which might help the designer to determine if a re-design of the controller is required or not. The methodologies of optimisation based V&V, surrogate modelling, operational safety margin, Bernstein expansion method and risk assessment have been combined together to form the WCAT-II MATLAB toolbox.

<p><em>How do additional data of the same and/or different type contribute to reducing model parameter and predictive uncertainties?</em> This was the question addressed with two models – the HBV hydrological water balance model and the ICBM soil carbon balance model – that were used to investigate the usefulness of the Generalized Likelihood Uncertainty Estimation (GLUE) method for calibrations and uncertainty analyses.  The GLUE method is based on threshold screening of Monte Carlo simulations using so-called informal likelihood measures and subjective acceptance criterion. This method is highly appropriate for model calibrations when errors are dominated by epistemic rather than stochastic uncertainties.  The informative value of data for model calibrations was investigated with numerous calibrations aimed at conditioning posterior parameter distributions and boundaries on model predictions.  The key results demonstrated examples of: 1) redundant information in daily time series of hydrological data; 2) diminishing returns in the value of continued time series data collections of the same type; 3) the potential value of additional data of a different type; 4) a means to effectively incorporate fuzzy information in model calibrations; and 5) the robustness of estimated parameter uncertainty for portability of a soil carbon model between and tropical climate zones.  The key to obtaining these insights lied in the methods of uncertainty analysis used to produce them.  A paradigm for selecting between formal and informal likelihood measures in uncertainty analysis is presented and discussed for future use within a context of climate related environmental modeling.</p>

Groundwater is a major source of water supply, and aquifers form major storage reservoirs as well as water conveyance systems, worldwide. The viability of groundwater as a source of water to the world's population is threatened by overexploitation and contamination. The rational management of water resource systems requires an understanding of their response to existing and planned schemes of exploitation, pollution prevention and/or remediation. Such understanding requires the collection of data to help characterize the system and monitor its response to existing and future stresses. It also requires incorporating such data in models of system makeup, water flow and contaminant transport. As the collection of subsurface characterization and monitoring data is costly, it is imperative that the design of corresponding data collection schemes is cost-effective. A major benefit of new data is its potential to help improve one's understanding of the system, in large part through a reduction in model predictive uncertainty and corresponding risk of failure. Traditionally, value-of-information or data-worth analyses have relied on a single conceptual-mathematical model of site hydrology with prescribed parameters. Yet there is a growing recognition that ignoring model and parameter uncertainties render model predictions prone to statistical bias and underestimation of uncertainty. This has led to a recent emphasis on conducting hydrologic analyses and rendering corresponding predictions by means of multiple models. We develop a theoretical framework of data worth analysis considering model uncertainty, parameter uncertainty and potential sample value uncertainty. The framework entails Bayesian Model Averaging (BMA) with emphasis on its Maximum Likelihood version (MLBMA). An efficient stochastic optimization method, called Differential Evolution Method (DEM), is explored to aid in the design of optimal sampling schemes aiming at maximizing data worth. A synthetic case entailing generated log hydraulic conductivity random fields is used to illustrate the procedure. The proposed data worth analysis framework is applied to field pneumatic permeability data collected from unsaturated fractured tuff at the Apache Leap Research Site (ALRS) near Superior, Arizona.

We develop and test a probabilistic real-time streamflow-forecasting platform, Multimodel and Multiproduct Streamflow Forecasting (MMSF), that uses information provided by a suite of hydrologic models and satellite precipitation products (SPPs). The SPPs are bias-corrected before being used as inputs to the hydrologic models, and model calibration is carried out independently for each of the model-product combinations (MPCs). Forecasts generated from the calibrated models are further bias-corrected to compensate for the deficiencies within the models, and then probabilistically merged using a variety of model averaging techniques. Use of bias-corrected SPPs in streamflow forecasting applications can overcome several issues associated with sparsely gauged basins and enable robust forecasting capabilities. Bias correction of streamflow significantly improves the forecasts in terms of accuracy and precision for all different cases considered. Results show that the merging of individual forecasts from different MPCs provides additional improvements. All the merging techniques applied in this study produce similar results, however, the Inverse Weighted Averaging (IVA) proves to be slightly superior in most cases. We demonstrate the implementation of the MMSF platform for real-time streamflow monitoring and forecasting in the Mara River basin of Africa (Kenya & Tanzania) in order to provide improved monitoring and forecasting tools to inform water management decisions.

Les chercheurs dans le domaine de la conception aérodynamique et de la fabrication des avions ont fait beaucoup d'effort pour améliorer les performances des ailes par des techniques d'optimisation. Le développement de la mécanique des fluides numérique a permis de réduire les dépenses en soufflerie tout en fournissant des résultats convaincants pour simuler des situations compliquées des aéronefs. Dans cette thèse, il a été choisi une partie spéciale et importante de l'avion, à savoir, la structure de l'aile. L'optimisation basée sur la fiabilité est une méthode plus appropriée pour les structures sous incertitudes. Il se bat pour obtenir le meilleur compromis entre le coût et la sécurité tout en tenant compte des incertitudes du système en intégrant des mesures de fiabilité au sein de l'optimisation. Malgré les avantages de l'optimisation de la fiabilité en fonction, son application à un problème d'ingénierie pratique est encore assez difficile. Dans notre travail, l'analyse de l'incertitude dans la simulation numérique est introduite et exprimée par la théorie des probabilités. La simulation de Monte Carlo comme une méthode efficace pour propager les incertitudes dans le modèle d'éléments finis de la structure est ici appliquée pour simuler les situations compliquées qui peuvent se produire. Pour améliorer l'efficacité de la simulation Monte Carlo dans le processus d'échantillonnage, la méthode de l'Hypercube Latin est effectuée. Cependant, l'énorme base de données de l'échantillonnage rend difficile le fait de fournir une évaluation explicite de la fiabilité. L'expansion polynôme du chaos est présentée et discutée. Le modèle de Kriging comme un modèle de substitution joue un rôle important dans l'analyse de la fiabilité. Les méthodes traditionnelles d'optimisation ont des inconvénients à cause du temps de calcul trop long ou de tomber dans un minimum local causant une convergence prématurée. Le recuit simulé est une méthode heuristique basée sur une recherche locale, les Algorithmes Génétiques puisent leur inspiration dans les principes et les mécanismes de la sélection naturelle, qui nous rendent capables d'échapper aux pièges des optimums locaux. Dans l'optimisation de la conception de base de la fiabilité, ces deux méthodes ont été mises en place comme procédure d'optimisation. La boucle de l'analyse de fiabilité est testée sur le modèle de substitution. / Tremendous struggles of researchers in the field of aerodynamic design and aircraft production were made to improve wing airfoil by optimization techniques. The development of computational fluid dynamic (CFD) in computer simulation cuts the expense of aerodynamic experiment while provides convincing results to simulate complicated situation of aircraft. In our work, we chose a special and important part of aircraft, namely, the structure of wing.Reliability based optimization is one of the most appropriate methods for structural design under uncertainties. It struggles to seek for the best compromise between cost and safety while considering system uncertainties by incorporating reliability measures within the optimization. Despite the advantages of reliability based optimization, its application to practical engineering problem is still quite challenging. In our work, uncertainty analysis in numerical simulation is introduced and expressed by probability theory. Monte Carlo simulation as an effective method to propagate the uncertainties in the finite element model of structure is applied to simulate the complicate situations that may occur. To improve efficiency of Monte Carlo simulation in sampling process, Latin Hypercube sampling is performed. However, the huge database of sampling is difficult to provide explicit evaluation of reliability. Polynomial chaos expansion is presented and discussed. Kriging model as a surrogate model play an important role in the reliability analysis.Traditional methods of optimization have disadvantages in unacceptable time-complexity or natural drawbacks of premature convergence because of finding the nearest local optima of low quality. Simulated Annealing is a local search-based heuristic, Genetic Algorithm draws inspiration from the principles and mechanisms of natural selection, that makes us capable of escaping from being trapped into a local optimum. In reliability based design optimization, these two methods were performed as the procedure of optimization. The loop of reliability analysis is running in surrogate model.

Os empreendimentos de mineração comumente demandam grande quantidade de investimentos financeiros e, na maioria das vezes, longos períodos de implantação, o que os torna altamente sujeitos a diversas fontes de incertezas. Tais incertezas comumente tendem a diminuir conforme a evolução do projeto. O objetivo deste estudo é correlacionar as incertezas associadas ao modelo de teores de cobre do depósito Sequeirinho com o volume de investimentos realizados ao longo de distintas fases da pesquisa geológica. Este depósito insere-se no contexto do Complexo de Mineração Sossego, localizado no município de Canaã dos Carajás (PA). Primeiramente, foram realizadas 100 simulações para cada domínio litológico em cada campanha de sondagem (pré-1998, 1999, 2000, 2002 e 2003) a partir do método de simulação sequencial gaussiana condicionada aos dados amostrais, totalizando 1.400 possíveis cenários. Para a avaliação das incertezas foram calculados três índices: variância condicional, coeficiente de variação condicional e intervalo interquartil. Por fim, a avaliação dos investimentos foi elaborada a partir dos custos estimados para o desenvolvimento de sondagens e análises químicas. Desde a campanha pré-1998, houve uma tendência de os teores médios do depósito aproximarem-se dos prováveis valores reais observados nas fases finais da pesquisa. No ano de 2000 ocorreu o maior investimento (cerca de 28 milhões de Reais) e a redução das incertezas atingiu o patamar de 15%. Os investimentos desenvolvidos em sondagens posteriores à campanha de 2000 foram da ordem de 9 milhões de Reais (cerca de 12 mil metros de sondagem), porém, não foram constatadas reduções significativas das incertezas. Este investimento seria melhor aproveitado caso fosse redirecionado a novas áreas de prospecção. Além do montante financeiro necessário para a redução das incertezas, foco deste estudo, as variações na interpretação geológica e a locação dos furos de sondagem são variáveis importantes na análise de incertezas associadas aos investimentos em pesquisa geológica. / Mining projects require large amount of capital investment and most cases spend long periods of implementation, which make them extremely susceptible to several sources of uncertainty. Such uncertainties commonly tend to decrease along the project development. The present study aims to correlate the uncertainties associated to the grade model of the Sequeirinho copper mine with the amount of capital investment that has been spent along different geological surveys. Sequeirinho site is included in the context of Sossego Mine Complex, located in Canaã dos Carajás (PA, Brazil). Initially, 100 simulations were carried out for each lithologic domain in each drilling campaign (pre-1998, 1999, 2000, 2002 and 2003) using sequential Gaussian simulation conditioned to the sample, resulting in 1,400 possible scenarios. Three indexes were calculated for the uncertainty analysis: conditional variance, conditional coefficient variance and interquartile range. Finally, the evaluation of capital investment was elaborated from the costs estimated for drilling and chemical analysis. Since pre-1998 drilling campaign, deposit average grades have showed a trend to get closer to the possible real values observed in the final research surveys. In 2000, there was the biggest capital investment (about R$ 28 millions) and the uncertainty reduction has reached the maximum level of 15%. Investments performed in drilling programs after 2000 were around R$ 9 million (around 12,000 meters of drill holes), but the uncertainty reduction was not significant. Therefore, such investments might be used to discover new targets. Besides the correlation of uncertainty reduction and amount of capital investment, the main focus of this study, the uncertainty of geological model and the drillhole locations are important variables to be considered in investment analysis of geological survey.

A formulação e o uso de modelos matemáticos complexos têm recebido grande atenção no estudo da ecologia nos últimos anos. Questões relacionadas à exploração de espaços de parâmetros destes modelos - executada de forma eficiente, sistemática e à prova de erros - são de grande importância para melhor compreender, avaliar a confiabilidade e interpretar o resultado destes modelos. Neste trabalho, apresentamos uma investigação de métodos existentes para responder as questões relevantes da área, com ênfase na técnica conhecida como Hipercubo Latino e com foco na análise quantitativa dos resultados, e realizamos a comparação entre resultados analíticos de incerteza e sensibilidade e resultados obtidos do Hipercubo. Ainda, examinamos a proposta de uma metodologia paralela baseada no paradigma estatístico da verossimilhança. O capítulo 1 introduz uma investigação a respeito dos conceitos históricos sobre a natureza da probabilidade, situando o conceito da verossimilhança como componente central da inferência estatística. O capítulo 2 (em inglês) traz uma revisão bibliográfica sobre o estado da arte em análises de incerteza e sensibilidade, apresentando dois exemplos de aplicação das técnicas descritas a problemas de crescimento populacional estruturado. O capítulo 3 examina a proposta de uma metodologia baseada na verossimilhança dos dados como uma abordagem integrativa entre a estimação de parâmetros e a análise de incerteza, apresentando resultados preliminares. Durante o progresso do presente trabalho, um pacote de funções na linguagem R foi desenvolvido para facilitar o emprego na prática das ferramentas teóricas expostas acima. Os apêndices deste texto trazem um tutorial e exemplos de uso deste pacote, pensado para ser ao mesmo tempo conveniente e de fácil extensão, e disponível livremente na internet, no endereço http://cran.r-project.org/web/packages/pse. / There is a growing trend in the use of mathematical modeling tools in the study of many areas of the biological sciences. The use of computer models in science is increasing, specially in fields where laboratory experiments are too complex or too costly, like ecology. Questions of efficient, systematic and error-proof exploration of parameter spaces are are of great importance to better understand, estimate confidences and make use of the output from these models. We present a survey of the proposed methods to answer these questions, with emphasis on the Latin Hypercube Sampling and focusing on quantitative analysis of the results. We also compare analytical results for sensitivity and uncertainty, where relevant, to LHS results. Finally, we examine the proposal of a methodology based on the likelihood statistical paradigm. Chapter 1 introduces a brief investigation about the historical views about the nature of probability, in order to situate the concept of likelihood as a central component in statistical inference. Chapter 2 (in English) shows a revision about the state-of-art uncertainty and sensitivity analyses, with a practical example of applying the described techniques to two models of structured population growth. Chapter 3 examines the proposal of a likelihood based approach as an integrative procedure between parameter value estimation and uncertainty analyses, with preliminary results. During the progress of this work, a package of R functions was developed to facilitate the real world use of the above theoretical tools. The appendices of this text bring a tutorial and examples of using this package, freely available on the Internet at http://cran.r-project.org/web/packages/pse.

Climate change is probably the most challenging threat to mankind. International agreements have acknowledged the fact that anthropogenic GHG emissions must be reduced significantly to adhere to a maximum global warming of 2°C. The livestock sector plays a key role in achieving this target as it is a significant source of GHG emissions. While the livestock sector offers significant GHG reduction potential, it is currently neglected in international and national mitigation efforts. Therefore, scientific research must guide mitigation policy decisions with evidence of cost-efficient abatement potential that can be achieved through various mitigation technologies. Marginal Abatement Cost Curves (MACC) are an analytical tool for informing policy makers about the cost-effectiveness (CE) of mitigation. MACCs provide a relatively clear representation of a complicated issue based on their graphical design that prioritises various mitigation options in terms of their CE of abatement and enables assessment of total GHG reduction under a budget constraint. However, developing a MACC involves considerable data collection, depends on various interdisciplinary information sources and the methodology is subject to several limitations. These factors can result in uncertainties in marginal abatement cost (MAC) results, the assessment of which is often neglected in MACC literature. This research shows the main GHG emission sources in livestock production and possible mitigation options to reduce GHG emissions from these sources. After elaborating the MACC methodology, advantages, disadvantages and limitation of the engineering MACC are shown. This allows understanding the relevance of assessing and reporting uncertainty of MACCs. Two engineering MACCs are developed that show the CE abatement potentials available in the Chinese livestock sector and European Union 15 (EU-15) dairy sector in 2020, with emphasis on dietary mitigation options. The requirement of assessing CE of abatement for individual mitigation options is highlighted by separate derivation of technical and economic abatement potential for the EU-15 dairy sector. For the Chinese MACC, a scenario analysis (SA) and for the European MACC, a Monte Carlo (MC) simulation are utilised to show the relevance of assessing uncertainty in MACCs. To provide further evidence, the overall range of CE estimates for eight mitigation options found in relevant MACC literature is presented. This allows the generation of probability distribution functions of CE for each mitigation option with kernel density estimation (KDE). The results from this study show the significance of livestock and dairy production related GHG emissions in China and Europe, respectively. In China, baseline GHG emissions of livestock production are projected to increase significantly, while these of the EU-15 dairy production are predicted to decrease by 2020. It was found that enteric fermentation is the largest GHG emission source from dairy production and should be focus of mitigation policies. Both case studies showed mitigation options that offer abatement potential at high CE. Priorities should be given to biomass gasification, breeding techniques and feed supplements as tea saponins and probiotics for the Chinese livestock sector, and to animal selection, reduced tillage and dietary probiotics for the EU-15 dairy sector. The scenario analysis reveals that mid-term projections for the Chinese livestock sector are varying strongly, and utilising key variables from different projections has a significant impact on MAC results which changes the ranking of the mitigation options. The MC simulation shows the contribution of some model inputs to the uncertainty of abatement at negative cost and a high model output uncertainty regarding measure’s CE for most mitigation options. However, the ranking of the mitigation options remains stable. The range of MAC estimates for 8 mitigation options in the agricultural sector is high and variables like ‘study quality’ or ‘study location’ do not change this. The KDE was further used to rank the mitigations options based on their probability of being reported as cost-negative and shows that measures affecting soil N2O and carbon sequestration are reported to be more cost-efficient as compared to measures focusing on manure management. Based on these finding, the impact of study designs on MAC estimates and lack of communication uncertainty in MACC literature are discussed. Uncertainties that are underpinning MACC results can have significant impacts on CE and abatement potentials. To increase utilisation of MACCs by knowledge users, MACC research must prioritise assessment, quantification and report of uncertainties, compare results within the scientific literature and publish data and assumption of the MACC transparently.

Os empreendimentos de mineração comumente demandam grande quantidade de investimentos financeiros e, na maioria das vezes, longos períodos de implantação, o que os torna altamente sujeitos a diversas fontes de incertezas. Tais incertezas comumente tendem a diminuir conforme a evolução do projeto. O objetivo deste estudo é correlacionar as incertezas associadas ao modelo de teores de cobre do depósito Sequeirinho com o volume de investimentos realizados ao longo de distintas fases da pesquisa geológica. Este depósito insere-se no contexto do Complexo de Mineração Sossego, localizado no município de Canaã dos Carajás (PA). Primeiramente, foram realizadas 100 simulações para cada domínio litológico em cada campanha de sondagem (pré-1998, 1999, 2000, 2002 e 2003) a partir do método de simulação sequencial gaussiana condicionada aos dados amostrais, totalizando 1.400 possíveis cenários. Para a avaliação das incertezas foram calculados três índices: variância condicional, coeficiente de variação condicional e intervalo interquartil. Por fim, a avaliação dos investimentos foi elaborada a partir dos custos estimados para o desenvolvimento de sondagens e análises químicas. Desde a campanha pré-1998, houve uma tendência de os teores médios do depósito aproximarem-se dos prováveis valores reais observados nas fases finais da pesquisa. No ano de 2000 ocorreu o maior investimento (cerca de 28 milhões de Reais) e a redução das incertezas atingiu o patamar de 15%. Os investimentos desenvolvidos em sondagens posteriores à campanha de 2000 foram da ordem de 9 milhões de Reais (cerca de 12 mil metros de sondagem), porém, não foram constatadas reduções significativas das incertezas. Este investimento seria melhor aproveitado caso fosse redirecionado a novas áreas de prospecção. Além do montante financeiro necessário para a redução das incertezas, foco deste estudo, as variações na interpretação geológica e a locação dos furos de sondagem são variáveis importantes na análise de incertezas associadas aos investimentos em pesquisa geológica. / Mining projects require large amount of capital investment and most cases spend long periods of implementation, which make them extremely susceptible to several sources of uncertainty. Such uncertainties commonly tend to decrease along the project development. The present study aims to correlate the uncertainties associated to the grade model of the Sequeirinho copper mine with the amount of capital investment that has been spent along different geological surveys. Sequeirinho site is included in the context of Sossego Mine Complex, located in Canaã dos Carajás (PA, Brazil). Initially, 100 simulations were carried out for each lithologic domain in each drilling campaign (pre-1998, 1999, 2000, 2002 and 2003) using sequential Gaussian simulation conditioned to the sample, resulting in 1,400 possible scenarios. Three indexes were calculated for the uncertainty analysis: conditional variance, conditional coefficient variance and interquartile range. Finally, the evaluation of capital investment was elaborated from the costs estimated for drilling and chemical analysis. Since pre-1998 drilling campaign, deposit average grades have showed a trend to get closer to the possible real values observed in the final research surveys. In 2000, there was the biggest capital investment (about R$ 28 millions) and the uncertainty reduction has reached the maximum level of 15%. Investments performed in drilling programs after 2000 were around R$ 9 million (around 12,000 meters of drill holes), but the uncertainty reduction was not significant. Therefore, such investments might be used to discover new targets. Besides the correlation of uncertainty reduction and amount of capital investment, the main focus of this study, the uncertainty of geological model and the drillhole locations are important variables to be considered in investment analysis of geological survey.

In this thesis we modify an existing model for the spread of resistant bacteria in a hospital. The existing model does not account for some of the trends seen in the data found in literature. The new model takes some of these trends into account. For the new model, we examine issues relating to identifiability, sensitivity analysis, parameter estimation, uncertainty analysis, and equilibrium stability.