Nearly every decision must be made with a degree of uncertainty regarding the outcome. Decision making based on modeling and simulation predictions needs to incorporate and aggregate uncertain evidence. To validate multiscale simulation models, it may be necessary to consider evidence collected at a length scale that is different from the one at which a model predicts. In addition, traditional methods of uncertainty analysis do not distinguish between two types of uncertainty: uncertainty due to inherently random inputs, and uncertainty due to lack of information about the inputs. This thesis examines and applies a Bayesian approach for model parameter validation that uses generalized interval probability to separate these two types of uncertainty. A generalized interval Bayes’ rule (GIBR) is used to combine the evidence and update belief in the validity of parameters. The sensitivity of completeness and soundness for interval range estimation in GIBR is investigated. Several approaches to represent complete ignorance of probabilities’ values are tested. The result from the GIBR method is verified using Monte Carlo simulations. The method is first applied to validate the parameter set for a molecular dynamics simulation of defect formation due to radiation. Evidence is supplied by the comparison with physical experiments. Because the simulation includes variables whose effects are not directly observable, an expanded form of GIBR is implemented to incorporate the uncertainty associated with measurement in belief update. In a second example, the proposed method is applied to combining the evidence from two models of crystal plasticity at different length scales.

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In 1988, the US Nuclear Regulatory Commission approved an amendment that allowed the use of best-estimate methods. This led to an increased development, and application of Best Estimate Plus Uncertainty (BEPU) safety analyses. However, a greater burden was placed on the licensee to justify all uncertainty estimates. A review of the current state of the BEPU methods indicate that there exists a number of significant criticisms, which limits the BEPU methods from reaching its full potential as a comprehensive licensing basis. The most significant criticism relates to the lack of a formal framework for distinguishing between aleatory and epistemic uncertainties. This has led to a prevalent belief that such separation of uncertainties is for convenience, rather than one out of necessity. In this thesis, we address the above concerns by developing a statistically rigorous framework to characterize the different uncertainty types. This framework is grounded on the philosophical concepts of knowledge. Considering the Plato problem, we explore the use of probability as a means to gain knowledge, which allows us to relate the inherent distinctness in knowledge with the different uncertaintytypesforanycomplexphysicalsystem. Thisframeworkis demonstrated using nuclear analysis problems, and we show through the use of structural models that the separation of these uncertainties leads to more accurate tolerance limits relative to existing BEPU methods. In existing BEPU methods, where such a distinction is not applied, the total uncertainty is essentially treated as the aleatory uncertainty. Thus, the resulting estimated percentile is much larger than the actual (true) percentile of the system's response. Our results support the premise that the separation of these two distinct uncertainty types is necessary and leads to more accurate estimates of the reactor safety margins. / Thesis / Doctor of Philosophy (PhD)

Infrastructures are the most fundamental facilities and systems serving the society. Due to the existence of infrastructures in economic, social, and environmental contexts, all lifecycle phases of such fundamental facilities should maximize utility for the designers, occupants, and the society. With respect to the nature of the decision problem, two main types of uncertainties may exist: 1) the aleatory uncertainty associated with the nature of the built environment (i.e., the economic, social, and environmental impacts of infrastructures must be described as probabilistic); and 2) the epistemic uncertainty associated with the lack of knowledge of decision maker utilities. Although a number of decision analysis models exist that consider the uncertainty associated with the nature of the built environment, they do not provide a systematic framework for including aleatory and epistemic uncertainties, and decision maker utilities in the decision analysis process. In order to address the identified knowledge gap, a three-phase modular decision analysis methodology is proposed. Module one uses a formal preference assessment methodology (i.e., utility function/indifference curve) for assessing decision maker utility functions with respect to a range of alternative design configurations. Module two utilizes the First Order Reliability Method (FORM) in a systems reliability approach for assessing the reliability of alternative infrastructure design configurations with respect to the probabilistic decision criteria and decision maker defined utility functions (indifference curves), and provides a meaningful feedback loop for improving the reliability of the alternative design configurations. Module three provides a systematic framework to incorporate both aleatory and epistemic uncertainties in the decision analysis methodology (i.e., uncertain utility functions and group decision making). The multi-criteria, probabilistic decision analysis framework is tested on a nine-story office building in a seismic zone with the probabilistic decision criteria of: building damage and business interruption costs, casualty costs, and CO2 emission costs. Twelve alternative design configurations and four decision maker utility functions under aleatory and epistemic uncertainties are utilized. The results of the decision analysis methodology revealed that the high-performing design configurations with an initial cost of up to $3.2M (in a cost range between $1.7M and $3.2M), a building damage and business interruption cost as low as $303K (in a cost range between $303K and $6.2M), a casualty cost as low as $43K (in a cost range between $43K and $1.2M), and a CO2 emission as low as $146K (in a cost range between $133K to $150K) can be identified by having a higher probability (i.e., up to 80%) of meeting the decision makers' preferences. The modular, holistic, decision analysis framework allows decision makers to make more informed performance-based design decisions—and allows designers to better incorporate the preferences of the decision makers—during the early design process. / PHD / Infrastructures, including buildings, roads, and bridges, are the most fundamental facilities and systems serving the society. Because infrastructures exist in economic, social, and environmental contexts, the design, construction, operations, and maintenance phases of such fundamental facilities should maximize value and usability for the designers, occupants, and the society. Identifying infrastructure configurations that maximize value and usability is challenged by two sources of uncertainty: 1) the nature of the built environment is variable (i.e., whether or not a natural hazard will occur during the infrastructure lifetime, or how costs might change over time); and 2) there is lack of knowledge of decision maker preferences and values (e.g., design cost versus social impact tradeoffs). Although a number of decision analysis models exist that consider the uncertainty associated with the nature of the built environment (e.g., natural hazard events), they do not provide a systematic framework for including the uncertainties associated with the decision analysis process (e.g., lack of knowledge about decision maker preferences), and decision maker requirements in the decision analysis process. In order to address the identified knowledge gap, a three-phase modular decision analysis methodology is proposed. Module one uses a formal preference assessment methodology for assessing decision maker values with respect to a range of alternative design configurations. Module two utilizes an algorithm for assessing the reliability of alternative infrastructure design configurations with respect to the probabilistic decision criteria and decision maker requirements, and provides a meaningful feedback loop for understanding the decision analysis results (i.e., improving the value and usability of the alternative design configurations). Module three provides a systematic framework to incorporate both the random uncertainty associated with the built environment and the knowledge uncertainty associated with lack of knowledge of decision maker preferences, and tests the reliability of the decision analysis results under random and knowledge uncertainties (i.e., uncertain decision maker preferences and group decision making). The holistic decision analysis framework is tested on a nine-story office building in a seismic zone with the probabilistic decision criteria of: building damage and business interruption costs, casualty costs, and CO2 emission costs. Twelve alternative design configurations, four decision makers, and random and knowledge sources of uncertainty are considered in the decision analysis methodology. Results indicate that the modular, holistic, decision analysis framework allows decision makers to make more informed design decisions—and allows designers to better incorporate the preferences of the decision makers—during the early design process.

Afin d'obtenir des simulations plus prédictives et plus précises du comportement mécanique des structures, des modèles matériau de plus en plus complexes ont été développés. Aujourd'hui, la caractérisation des propriétés des matériaux est donc un objectif prioritaire. Elle exige des méthodes et des tests d'identification dédiés dans des conditions les plus proches possible des cas de service. Cette thèse vise à développer une méthodologie d'identification efficace pour trouver les paramètres des propriétés matériau, en tenant compte de toutes les informations disponibles. L'information utilisée pour l'identification est à la fois théorique, expérimentale et empirique : l'information théorique est liée aux modèles mécaniques dont l'incertitude est épistémique; l'information expérimentale provient ici de la mesure de champs cinématiques obtenues pendant l'essai ct dont l'incertitude est aléatoire; l'information empirique est liée à l'information à priori associée à une incertitude épistémique ainsi. La difficulté principale est que l'information disponible n'est pas toujours fiable et que les incertitudes correspondantes sont hétérogènes. Cette difficulté est surmontée par l'utilisation de la théorie des fonctions de croyance. En offrant un cadre général pour représenter et quantifier les incertitudes hétérogènes, la performance de l'identification est améliorée. Une stratégie basée sur la théorie des fonctions de croyance est proposée pour identifier les propriétés élastiques macro et micro des matériaux multi-structures. Dans cette stratégie, les incertitudes liées aux modèles et aux mesures sont analysées et quantifiées. Cette stratégie est ensuite étendue pour prendre en compte l'information à priori et quantifier l'incertitude associée. / In order to obtain more predictive and accurate simulations of mechanical behaviour in the practical environment, more and more complex material models have been developed. Nowadays, the characterization of material properties remains a top-priority objective. It requires dedicated identification methods and tests in conditions as close as possible to the real ones. This thesis aims at developing an effective identification methodology to find the material property parameters, taking advantages of all available information. The information used for the identification is theoretical, experimental, and empirical: the theoretical information is linked to the mechanical models whose uncertainty is epistemic; the experimental information consists in the full-field measurement whose uncertainty is aleatory; the empirical information is related to the prior information with epistemic uncertainty as well. The main difficulty is that the available information is not always reliable and its corresponding uncertainty is heterogeneous. This difficulty is overcome by the introduction of the theory of belief functions. By offering a general framework to represent and quantify the heterogeneous uncertainties, the performance of the identification is improved. The strategy based on the belief function is proposed to identify macro and micro elastic properties of multi-structure materials. In this strategy, model and measurement uncertainties arc analysed and quantified. This strategy is subsequently developed to take prior information into consideration and quantify its corresponding uncertainty.