To make sound investment decisions, decision makers need accurate estimates of the uncertainties present in forecasts of reservoir performance. In this work I propose a method, the integrated mismatch method, that incorporates the misfit in the history match into the estimation of uncertainty in the prediction. I applied the integrated mismatch method, which overcomes some deficiencies of existing methods, to uncertainty estimation in two reservoir studies and compared results to estimations from existing methods. The integrated mismatch method tends to generate smaller ranges of uncertainty than many existing methods. When starting from nonoptimal reservoir models, in some cases the integrated mismatch method is able to bracket the true reserves value while other methods fail to bracket it. The results show that even starting from a nonoptimal reservoir model, but as long as the experimental designs encompass the true case parameters, the integrated mismatch method brackets the true reserves value. If the experimental designs do not encompass all the true case parameters, but the true reserves value is covered by the experiments, the integrated mismatch method may still bracket the true case. This applies if there is a strong correlation between mismatch and closeness to the true reserves value. The integrated mismatch method does not need a large number of simulation runs for the uncertainty analysis, while some other methods need hundreds of runs.

All practical control systems are subject to constraints, namely constraints aris¬ing from the actuator’s limited range and rate capacity (input constraints) or from imposed operational limits on plant variables (output constraints). A linear control system typically yields the desirable small signal performance. However, the presence of input constraints often causes undesirable large signal behavior and potential insta¬bility. An anti-windup control consists of a remedial solution that mitigates the effect of input constraints on the closed-loop without affecting the small signal behavior. Conversely, an override control addresses the control problem involving output con¬straints and also follows the idea that large signal control objectives do not alter small signal performance. Importantly, these two remedial control methodologies must in¬corporate model uncertainty into their design to be considered reliable in practice. In this dissertation, shared principles of design for the remedial compensation problem are identified which simplify the picture when analyzing, comparing and synthesiz¬ing for the variety of existing remedial schemes. Two performance objectives, each one related to a different type of remedial compensation, and a general structural representation associated with both remedial compensation problems will be consid¬ered. The effect of remedial control on the closed-loop will be evaluated in terms of two general frameworks which permit the unification and comparison of all known remedial compensation schemes. The difference systems describing the performance objectives will be further employed for comparison of remedial compensation schemes under uncertainty considerations and also for synthesis of compensators. On the ba¬sis of the difference systems and the general structure for remedial compensation, systematic remedial compensation synthesis algorithms for anti-windup and override compensation will be given and compared. Successful application of the proposed robust remedial control synthesis algorithms will be demonstrated via simulation.

All practical control systems are subject to constraints, namely constraints aris¬ing from the actuator’s limited range and rate capacity (input constraints) or from imposed operational limits on plant variables (output constraints). A linear control system typically yields the desirable small signal performance. However, the presence of input constraints often causes undesirable large signal behavior and potential insta¬bility. An anti-windup control consists of a remedial solution that mitigates the effect of input constraints on the closed-loop without affecting the small signal behavior. Conversely, an override control addresses the control problem involving output con¬straints and also follows the idea that large signal control objectives do not alter small signal performance. Importantly, these two remedial control methodologies must in¬corporate model uncertainty into their design to be considered reliable in practice. In this dissertation, shared principles of design for the remedial compensation problem are identified which simplify the picture when analyzing, comparing and synthesiz¬ing for the variety of existing remedial schemes. Two performance objectives, each one related to a different type of remedial compensation, and a general structural representation associated with both remedial compensation problems will be consid¬ered. The effect of remedial control on the closed-loop will be evaluated in terms of two general frameworks which permit the unification and comparison of all known remedial compensation schemes. The difference systems describing the performance objectives will be further employed for comparison of remedial compensation schemes under uncertainty considerations and also for synthesis of compensators. On the ba¬sis of the difference systems and the general structure for remedial compensation, systematic remedial compensation synthesis algorithms for anti-windup and override compensation will be given and compared. Successful application of the proposed robust remedial control synthesis algorithms will be demonstrated via simulation.

Accurate prediction of infill well production is crucial since the expected amount of incremental production is used in the decision-making process to choose the best infill locations. Making a good decision requires taking into account all possible outcomes and so it is necessary to quantify the uncertainty in forecasts. Many researchers have addressed the infill well location selection problem previously. Some of them used optimization algorithms, others presented empirical methods and some of them tried to solve this problem with statistical approaches. In this study, a reservoir simulation based approach was used to select infill well locations. I used multiple reservoir realizations to take different possible outcomes into consideration, generated probabilistic distributions of incremental field production and, finally, used descriptive statistical analysis to evaluate results. I quantified the uncertainty associated with infill location selection in terms of incremental field production and validated the approach on a synthetic reservoir model. Results of this work gave us the possible infill locations, which have a mean higher than the minimum economic limit, with a range of expected incremental production.

To make sound investment decisions, decision makers need accurate estimates of the uncertainties present in forecasts of reservoir performance. In this work I propose a method, the integrated mismatch method, that incorporates the misfit in the history match into the estimation of uncertainty in the prediction. I applied the integrated mismatch method, which overcomes some deficiencies of existing methods, to uncertainty estimation in two reservoir studies and compared results to estimations from existing methods. The integrated mismatch method tends to generate smaller ranges of uncertainty than many existing methods. When starting from nonoptimal reservoir models, in some cases the integrated mismatch method is able to bracket the true reserves value while other methods fail to bracket it. The results show that even starting from a nonoptimal reservoir model, but as long as the experimental designs encompass the true case parameters, the integrated mismatch method brackets the true reserves value. If the experimental designs do not encompass all the true case parameters, but the true reserves value is covered by the experiments, the integrated mismatch method may still bracket the true case. This applies if there is a strong correlation between mismatch and closeness to the true reserves value. The integrated mismatch method does not need a large number of simulation runs for the uncertainty analysis, while some other methods need hundreds of runs.

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Analysis of uncertainty in ore reserves impacts investment decisions, mine planning and sampling. Uncertainty is evaluated by geostatistical simulation and is affected by the amount of data and the modeling parameters. Incomplete uncertainty is given because the parameter uncertainty is ignored. Also, greater spatial continuity leads to more uncertainty. This increase is unreasonable in earth science. To address these problems, two approaches are proposed. The first approach is based on multiGaussian simulation where many realizations are performed at translated and/or rotated configurations and conditioned to the data. Variable configurations give different mean values that define uncertainty. The second approach is based on a stochastic trend; this approach randomizes the trend coefficients accounting for the fitted coefficients correlation. Variable set of coefficients provide different mean values. Furthermore, a methodology to account for parameter uncertainty is proposed. The uncertainty in the mean is transferred through simulation to deliver a more complete uncertainty. / Mining Engineering

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.

Backward erosion piping (BEP) is one of the major causes of seepage failures in levees. Seepage fields dictate the BEP behaviors and are influenced by the heterogeneity of soil properties. To investigate the effects of the heterogeneity on the seepage failures, we develop a numerical algorithm and conduct simulations to study BEP progressions in geologic media with spatially stochastic parameters. Specifically, the void ratio e, the hydraulic conductivity k, and the ratio of the particle contents r of the media are represented as the stochastic variables. They are characterized by means and variances, the spatial correlation structures, and the cross correlation between variables. Results of the simulations reveal that the heterogeneity accelerates the development of preferential flow paths, which profoundly increase the likelihood of seepage failures. To account for unknown heterogeneity, we define the probability of the seepage instability (PI) to evaluate the failure potential of a given site. Using Monte-Carlo simulation (MCS), we demonstrate that the PI value is significantly influenced by the mean and the variance of ln k and its spatial correlation scales. But the other parameters, such as means and variances of e and r, and their cross correlation, have minor impacts. Based on PI analyses, we introduce a risk rating system to classify the field into different regions according to risk levels. This rating system is useful for seepage failures prevention and assists decision making when BEP occurs.

This thesis aims to use general assertions of moral uncertainty as a perspective by which to explore and illuminate contemporary strands of liberal theory. It examines the work of the earlier contemporary liberal theorists, including John Rawls, Robert Nozick, Ronald Dworkin and Bruce Ackerman, as well as the more recent accounts of liberalism that express ideas of pluralism (Michael Walzer, Joseph Raz, John Gray, William Galston, George Crowder), political liberalism (John Rawls, Charles Larmore), public reason (Amy Gutmann & Dennis Thompson, Gerald Gaus), multiculturalism (Charles Taylor, Will Kymlicka, Brian Barry, James Tully, and Bikhu Parekh), and postmodernism (Richard Rorty). The development from the earlier to more recent liberal theories represents a fundamental shift in justificatory strategy: where earlier liberal conceptions aim at universality, and at overcoming or transcending uncertainty, later approaches make this uncertainty, usually in the form of pluralism or difference, central to the liberal project. In order to achieve this, these latter theories tended to presuppose the circumstances of western society, or western democratic values. Generally speaking, these approaches fail to respond adequately to moral uncertainty, and to meet their own justificatory aims. This manifests, in the earlier theories, as plausible but contestable central conceptions, and, in the more recent theories, as the inability to justify particular liberal conceptions in the face of persistence difference. This is an important result, and suggests the need for further developments in liberal justificatory strategies. I suggest that one viable approach would be for liberal theory to accept moral uncertainty, and work from a model of society and self towards a more successful liberal conception.