Showing papers on "Uncertainty quantification published in 2004"

Flood risk assessment and associated uncertainty

Abstract: . Flood disaster mitigation strategies should be based on a comprehensive assessment of the flood risk combined with a thorough investigation of the uncertainties associated with the risk assessment procedure. Within the "German Research Network of Natural Disasters" (DFNK) the working group "Flood Risk Analysis" investigated the flood process chain from precipitation, runoff generation and concentration in the catchment, flood routing in the river network, possible failure of flood protection measures, inundation to economic damage. The working group represented each of these processes by deterministic, spatially distributed models at different scales. While these models provide the necessary understanding of the flood process chain, they are not suitable for risk and uncertainty analyses due to their complex nature and high CPU-time demand. We have therefore developed a stochastic flood risk model consisting of simplified model components associated with the components of the process chain. We parameterised these model components based on the results of the complex deterministic models and used them for the risk and uncertainty analysis in a Monte Carlo framework. The Monte Carlo framework is hierarchically structured in two layers representing two different sources of uncertainty, aleatory uncertainty (due to natural and anthropogenic variability) and epistemic uncertainty (due to incomplete knowledge of the system). The model allows us to calculate probabilities of occurrence for events of different magnitudes along with the expected economic damage in a target area in the first layer of the Monte Carlo framework, i.e. to assess the economic risks, and to derive uncertainty bounds associated with these risks in the second layer. It is also possible to identify the contributions of individual sources of uncertainty to the overall uncertainty. It could be shown that the uncertainty caused by epistemic sources significantly alters the results obtained with aleatory uncertainty alone. The model was applied to reaches of the river Rhine downstream of Cologne.

Uncertainty Quantification in Aeroelasticity: Recent Results and Research Challenges

Abstract: Static and dynamic aeroelasticity considerations are a particularly important component of airframe design because they often control safety and performance. Consequently, the impact of uncertainty on aeroelastic response prediction has begun to receive substantial attention in the research literature. In this paper, general sources of uncertainty that complicate airframe design and testing are briefly described. Recent applications of uncertainty quantification to various aeroelastic problems, for example, flutter flight testing, prediction of limit-cycle oscillations, and design optimization with aeroelastic constraints, are reviewed with an emphasis on new physical insights and promising paths toward improved design methods that have resulted from these studies. Several challenges and needs are explored to suggest future steps that will enable practical application of uncertainty quantification in aeroelasticity design and certification.

Expanded uncertainty quantification in inverse problems: Hierarchical Bayes and empirical Bayes

Abstract: A common way to account for uncertainty in inverse problems is to apply Bayes' rule and obtain a posterior distribution of the quantities of interest given a set of measurements. A conventional Bayesian treatment, however, requires assuming specific values for parameters of the prior distribution and of the distribution of the measurement errors (e.g., the standard deviation of the errors). In practice, these parameters are often poorly known a priori, and choosing a particular value is often problematic. Moreover, the posterior uncertainty is computed assuming that these parameters are fixed; if they are not well known a priori, the posterior uncertainties have dubious value.This paper describes extensions to the conventional Bayesian treatment that assign uncertainty to the parameters defining the prior distribution and the distribution of the measurement errors. These extensions are known in the statistical literature as “empirical Bayes” and “hierarchical Bayes.” We demonstrate the practical applicati...

Uncertainty Assessment of Well-Placement Optimization

Abstract: Summary Determining the best location for new wells is a complex problem that depends on reservoir and fluid properties, well and surfaceequipment specifications, and economic criteria. Numerical simulation is often the most appropriate tool to evaluate the feasibility of well configurations. However, because the data used to establish numerical models have uncertainty, so do the model forecasts. The uncertainties in the model reflect themselves in the uncertainties of the outcomes of well-configuration decisions. We never possess the true and deterministic information about the reservoir, but we may have geostatistical realizations of the truth constructed from the information available. An approach that can translate the uncertainty in the data to uncertainty in the wellplacement decision in terms of monetary value was developed in this study. The uncertainties associated with well placement were addressed within the utility-theory framework using numerical simulation as the evaluation tool. The methodology was evaluated by use of the Production forecasting with UNcertainty Quantification (PUNQ)-S3 model, which is a standard test case that was based on a real field. Experiments were carried out on 23 historymatched realizations, and a truth case was also available. The results were verified by comparison to exhaustive simulations. Utility theory not only offered the framework to quantify the influence of uncertainties in the reservoir description in terms of monetary value, but it also provided the tools to quantify the otherwise arbitrary notion of the risk attitude of the decision maker. A hybrid genetic algorithm (HGA) was used for optimization. In addition, a computationally cheaper alternative was also investigated. The well-placement problem was formulated as the optimization of a random function. The genetic algorithm (GA) was used as the optimization tool. Each time a well configuration was to be evaluated, a different realization of the reservoir properties was selected randomly from the set of realizations, all of which honored the geologic and dynamic data available from the reservoir. Numerical simulation was then carried out with this randomly selected realization to calculate the objective function value. This approach has the potential to incorporate the risk attitudes of the decision maker and was observed to be approximate but computationally feasible.

Spectral stochastic uncertainty quantification in chemical systems

Abstract: Uncertainty quantification (UQ) in the computational modelling of physical systems is important for scientific investigation, engineering design, and model validation. We have implemented an ‘intru...

Quantifying uncertainty in chemical systems modeling.

Abstract: This study compares two techniques for uncertainty quantification in chemistry computations, one based on sensitivity analysis and error propagation, and the other on stochastic analysis using polynomial chaos techniques. The two constructions are studied in the context of H{sub 2}-O{sub 2} ignition under supercritical-water conditions. They are compared in terms of their prediction of uncertainty in species concentrations and the sensitivity of selected species concentrations to given parameters. The formulation is extended to one-dimensional reacting-flow simulations. The computations are used to study sensitivities to both reaction rate pre-exponentials and enthalpies, and to examine how this information must be evaluated in light of known, inherent parametric uncertainties in simulation parameters. The results indicate that polynomial chaos methods provide similar first-order information to conventional sensitivity analysis, while preserving higher-order information that is needed for accurate uncertainty quantification and for assigning confidence intervals on sensitivity coefficients. These higher-order effects can be significant, as the analysis reveals substantial uncertainties in the sensitivity coefficients themselves.

Experimental validation of a nonparametric probabilistic model of nonhomogeneous uncertainties for dynamical systems.

Abstract: The paper deals with an experimental validation of a nonparametric probabilistic model of nonhomogeneous uncertainties for dynamical systems. The theory used, recently introduced, allows model uncertainties and data uncertainties to be simultaneously taken into account. An experiment devoted to this validation was specifically developed. The experimental model is constituted of two simple dural rectangular plates connected together with a complex joint. In the mean mechanical model, the complex joint, which is constituted of two additional plates attached with 40 screw-bolts, is modeled by a homogeneous orthotropic continuous plate with constant thickness, as usual. Consequently, the mean model introduces a region (the joint) which has a high level of uncertainties. The objective of the paper is to present the experiment and the comparisons of the theoretical prediction with the experiments.

Nonparametric Modeling of Random Uncertainties for Dynamic Response of Mistuned Bladed Disks

Abstract: The random character of blade mistuning is a motivation to construct probability models of random uncertainties. Recently, a new approach known as a nonparametric model of random uncertainties, based on the entropy optimization principle, was introduced for modeling random uncertainties in linear and nonlinear elastodynamics. This paper presents an extension of this nonparametric model for vibration analysis of structures with cyclic geometry. In particular this probability model allows the blade eigenfrequencies uncertainties and the blade-modal-shape uncertainties to be modeled.

Non‐parametric–parametric model for random uncertainties in non‐linear structural dynamics: application to earthquake engineering

Abstract: This paper deals with the transient response of a non-linear dynamical system with random uncertainties. The non-parametric probabilistic model of random uncertainties recently published and extended to nonlinear dynamical system analysis is used in order to model random uncertainties related to the linear part of the finite element model. The non-linearities are due to restoring forces whose parameters are uncertain and are modeled by the parametric approach. Jayne's maximum entropy principle with the constraints defined by the available information allows the probabilistic model of such random variables to be constructed. Therefore, a non-parametric-parametric formulation is developed in order to model all the sources of uncertainties in such a non-linear dynamical system. Finally, a numerical application for earthquake engineering analysis is proposed concerning a reactor cooling system under seismic loads.

Structural safety–issues and progress

Abstract: A major aspect of ensuring safe structures is the management of uncertainty. The nature of safety, risk and uncertainty is discussed. Three types of uncertainty are considered: aleatoric, epistemic and ontological. The first is readily described in terms of probability distributions, so within this type of uncertainty, safety involves achieving less than a particular failure probability. The second cannot so easily be described by probability distributions, though the uncertainty can be estimated. The third type of uncertainty is essentially unknown. The different kinds of uncertainty call for different strategies. Probabilistic structural analysis deals with aleatoric uncertainty and to some extent epistemic uncertainty. Ontological uncertainty requires different strategies such as quality assurance or indicator methods. In addition, the traditional narrow focus on structural analysis is now broadening to include economic analysis and the social and environmental context of safety. This requires a different way of looking at safety. There is a shift from a narrow technical focus to the broader systemic viewpoint required for modern problems. The paper ends with a summary of problems needing to be addressed.

Spatial decisions under uncertainty: fuzzy inference in urban water management

Abstract: The endogenous complexity and spatial nature of the problems encountered in the urban water management environment present decision-makers with three major problems: (a) in the urban environment, every decision is site-specific, almost on a case-by-case basis, (b) the decision-maker must access, simultaneously, a large amount of information, increasing with rising spatial resolution and (c) the information to be evaluated is heterogeneous, including engineering, economical and social characteristics and constraints. The first two problems indicate that urban water management is an ideal field to develop and use spatial decision support systems (SDSS), while the latter promotes the use of fuzzy inference systems as a key mathematical framework. This research discusses the nature of uncertainty in environmental management in general and urban water management in particular, argues that fuzzy, rule-based, inference systems can be an invaluable tool for uncertainty quantification and presents the relevant elements of a prototype SDSS for urban water management. The examples presented in this paper are based on an application of the SDSS in water demand management.

A033 practical methods for uncertainty assessment of flow predictions for reservoirs with significant history -af ield case study

Abstract: This paper discusses two practical strategies to quantify the uncertainty in production and injection forecasts for a field with a long and complex production history with poor quality measurements. These methods are applied to a large offshore field in Africa that has been on production for more than 30 years. The first method follows an advanced Experimental Design framework and requires the use of non-linear Response Surfaces such as kriging. The second method uses sensitivity coefficients; it can be considered as a first pass to evaluate uncertainty before embarking in a more comprehensive analysis. Both methods lead to multiple acceptable representations of the history of the reservoir. The range of outcomes obtained with production forecasts allows for uncertainty quantification. In this case, both methods delivered similar prediction results.