Abstract: The study on epistemic uncertainty due to the lack of knowledge has received increasing attention in risk assessment, reliability analysis, decision making, and design optimization. Different theories have been applied to model and quantify epistemic uncertainty. Research on sensitivity analysis for epistemic uncertainty has also been initialized. Sensitivity analysis can identify the contributions of individual input variables with epistemic uncertainty to the model output. It then helps guide the collection of more information to reduce the effect of epistemic uncertainty. In this paper, an effective sensitivity analysis method for epistemic uncertainty is proposed when both epistemic and aleatory uncertainties exist in model inputs. This method employs the unified uncertainty analysis framework to calculate the plausibility and belief measures. The gap between belief and plausibility measures is used as an indicator of the effect of epistemic uncertainty on the model output. The Kolmogorov-Smirnov distance between the two measures is used to quantify the main effect and the total effect of each independent variable with epistemic uncertainty. By the Kolmogorov-Smirnov distance, the importance of each variable is ranked. The feasibility and effectiveness of the proposed method is demonstrated with two engineering examples.

Abstract: [1] We present a general framework for probabilistic risk assessment (PRA) of subsurface contamination. PRA provides a natural venue for the rigorous quantification of structural (model) and parametric uncertainties inherent in predictions of subsurface flow and transport. A typical PRA starts by identifying relevant components of a subsurface system (e.g., a buried solid-waste tank, an aquitard, a remediation effort) and proceeds by using uncertainty quantification techniques to estimate the probabilities of their failure. These probabilities are then combined by means of fault-tree analyses to yield probabilistic estimates of the risk of system failure (e.g., aquifer contamination). Since PRA relies on subjective probabilities, it is ideally suited for assimilation of expert judgment and causal relationships.

Abstract: This paper presents a multi-resolution approach for the propagation of parametric uncertainty in chemical systems. It is motivated by previous studies where Galerkin formulations of Wiener-Hermite expansions were found to fail in the presence of steep dependences of the species concentrations with regard to the reaction rates. The multi-resolution scheme is based on representation of the uncertain concentration in terms of compact polynomial multi-wavelets, allowing for the control of the convergence in terms of polynomial order and resolution level. The resulting representation is shown to greatly improve the robustness of the Galerkin procedure in presence of steep dependences. However, this improvement comes with a higher computational cost which drastically increases with the number of uncertain reaction rates. To overcome this drawback an adaptive strategy is proposed to control locally (in the parameter space) and in time the resolution level. The efficiency of the method is demonstrated for an uncertain chemical system having eight random parameters.

Abstract: An improved seismic hazard model for use in performance-based earthquake engineering is presented. The model is an improved approximation from the so-called ‘power law’ model, which is linear in log–log space. The mathematics of the model and uncertainty incorporation is briefly discussed. Various means of fitting the approximation to hazard data derived from probabilistic seismic hazard analysis are discussed, including the limitations of the model. Based on these ‘exact’ hazard data for major centres in New Zealand, the parameters for the proposed model are calibrated. To illustrate the significance of the proposed model, a performance-based assessment is conducted on a typical bridge, via probabilistic seismic demand analysis. The new hazard model is compared to the current power law relationship to illustrate its effects on the risk assessment. The propagation of epistemic uncertainty in the seismic hazard is also considered. To allow further use of the model in conceptual calculations, a semi-analytical method is proposed to calculate the demand hazard in closed form. For the case study shown, the resulting semi-analytical closed form solution is shown to be significantly more accurate than the analytical closed-form solution using the power law hazard model, capturing the ‘exact’ numerical integration solution to within 7% accuracy over the entire range of exceedance rate. Copyright © 2007 John Wiley & Sons, Ltd.

Abstract: In practical engineering applications, there exist two different types of uncertainties: aleatory and epistemic uncertainties. This study attempts to develop a robust design optimization with epistemic uncertainty. For epistemic uncertainties, a possibility-based design optimization improves the failure rate, while a robust design optimization minimizes the product quality loss. In general, product quality loss is described using the first two statistical moments for aleatory uncertainty: mean and standard deviation. However, there is no metric for product quality loss defined when having epistemic uncertainty. This paper first proposes a new metric for product quality loss with epistemic uncertainty, and then a possibility-based robust design optimization. For numerical efficiency and stability, an enriched performance measure approach is employed for possibility-based robust design optimization, and the maximal possibility search is used for a possibility analysis. Three different types of robust objectives are considered for possibility-based robust design optimization: smaller-the-better type (S-Type), larger-the-better type (L-Type), and nominal-the-better type (N-Type). Examples are used to demonstrate the effectiveness of possibility-based robust design optimization using the proposed metric for product quality loss with epistemic uncertainty.

Abstract: We propose a way of accounting for the lack of detailed knowledge about material shapes in computational time-domain electromagnetics. We use Legendre-Gauss-Lobatto, Stroud-2 and Stroud-3 quadrature formulas to solve the resulting stochastic equation and we show the efficiency of the proposed method over statistical Monte Carlo simulations. We also show how the radar cross section (RCS) in scattering is affected by the uncertainty in shape of the objects and by the direction of the incident field

Abstract: This paper deals with the use of Bayesian Networks to compute system reliability of complex systems under epistemic uncertainty. In the context of incompleteness of reliability data and inconsistencies between the reliability model and the system modeled, the evidence theory is more suitable to manage this epistemic uncertainty. We propose to adapt the Bayesian Network model of reliability in order to integrate the evidence theory and then to produce an Evidential Network. Three examples are proposed to observe the propagation mechanism of the uncertainty through the network and its influence on the system reliability.

Abstract: Today's computers allow us to simulate large, complex physical problems. Many times the mathematical models describing such problems are based on a relatively small amount of available information ...

Abstract: A method for forecasting production from a hydrocarbon producing reservoir, the method includes defining an objective function and characteristics of a history-matched model of a reservoir and acceptable error E. At least one geological realization of the reservoir is created representing a probable geological setting. For each geological realization, a global optimization technique is used to perform history matching in a series of iterative steps to obtain acceptable models. Production of the reservoir is forecasted based upon simulation runs of the respective models.

Abstract: Most computer models for engineering applications are developed to help assess a design or regulatory requirement. As part of this task, the capability to quantify the impact of variability and uncertainty in the decision context is critical. The requirement is often stated as: the probability that some system response quantity exceeds a threshold value is less than some required probability. This presentation will provide an outline and comparison of methods that are used for analyzing and propagating aleatory and epistemic uncertainties. The methods are all available in a software tool called DAKOTA. We will specifically focus on five classes of methods: Latin Hypercube sampling, analytic reliability methods, polynomial chaos expansions, Dempster-Shafer theory of evidence, and “second-order” probability analysis. Examples of each of the methods as applied to a simple engineering model will be provided.

Abstract: [1] Predictions of reactive transport in the subsurface are routinely compromised by both model (structural) and parametric uncertainties. We present a set of computational tools for quantifying these two types of uncertainties. The model uncertainty is resolved at the molecular scale where epistemic uncertainty incorporates aleatory uncertainty. The parametric uncertainty is resolved at both molecular and continuum (Darcy) scales. We use the proposed approach to quantify uncertainty in modeling the sorption of neptunium through a competitive ion exchange. This radionuclide is of major concern for various high-level waste storage projects because of its relatively long half-life and its high-solubility and low-sorption properties. We demonstrate how parametric and model uncertainties affect one's ability to estimate the distribution coefficient. The uncertainty quantification tools yield complete probabilistic descriptions of key parameters affecting the fate and migration of neptunium in the subsurface rather than the lower statistical moments. This is important, since these distributions are highly skewed.

Abstract: A method for quantifying uncertainty in conceptual-level design via a computationally- efficient probabilistic method is presented. The investigated method is applied to estimating the maximum-expected temperature of several critical components on a spacecraft. The variables of the design are first classified and assigned appropriate probability density functions. To characterize the thermal control system of the spacecraft, Subset Simulation, an efficient simulation technique originally developed for reliability analysis of civil engineering structures, is used. The results of Subset Simulation are compared with traditional Monte Carlo simulation. The investigated method allows uncertainty in the maximum-expected temperatures to be quantified based on the risk tolerance of the decision maker. For the spacecraft thermal control problem presented, Subset Simulation successfully replicated Monte Carlo simulation results for estimating the maximum-expected temperatures of several critical components yet required significantly less computational effort, in particular for risk-averse decision makers. Nomenclature

Abstract: A variety of analysis strategies and design methodologies are widely applied to accommodate uncertainties in engineering design. Generally there exist two different types of uncertainties in practice, aleatory uncertainty and epistemic uncertainty. When data and information are very limited, the probabilistic methodology may not be appropriate. Among several alternative tools, possibility theory is proved to be a computationally efficient and stable tool to handle incomplete information. In this paper, we first introduce two issues concerned with possibilistic approaches: reliability analysis and design optimization. Then the type of uncertainties in these issues are explained with emphasis on the epistemic uncertainty. After that, this paper presents both theoretical development and computational improvement of possibility theory in recent years. More details are given to reveal the capability and characteristics of quantified uncertainty from different aspects. In the end, future research directions are summarized.

Abstract: The general stochastic problem involves the propagation of input uncertainties through a computation model to arrive at a random output vector. This paper presents the application of the multi-dimensional Hermite polynomials to reduce an unknown random output vector into a significantly simpler unknown vector of numbers. The unknown numbers are evaluated using a collocation method because it has the important practical advantage of allowing existing deterministic numerical codes to be used as “black boxes”. A simple laterally loaded pile example involving two input random variables demonstrated that a third- or fourth-order Hermite expansion is adequate to reproduce probabilities of failure between 10 -3 and 10 -4 . A simple and efficient 2-term recurrence method for obtaining Hermite polynomials of any order in the case of two random dimensions is proposed. To our knowledge, this proposal appears to be original.

Abstract: Computer simulation based design processes are being extensively used in complex systems like scramjet powered hypersonic vehicles. The computational demands associated with the high-fidelity analysis tools for predicting the system performance restrict the number of simulations that are possible within the design cycle time. Hence, analysis tools of lower fidelity are generally used for design studies. To enable the designer to make better design decisions in such situations, the lower fidelity analysis tool is complemented with an uncertainty model. An approach based on ranks is proposed in this study to aggregate high-fidelity information in a cost effective manner. Based on this information, a cumulative distribution function for the difference between high-fidelity response and low-fidelity response is constructed. The approach is explained initially for uncertainty quantification in a synthetic example. Subsequently an uncertainty model for estimating the mass flow capture of air, a typical disciplinary performance metric in hypersonic vehicle design, is presented.

Abstract: Galerkin polynomial chaos and collocation methods have been widely adopted for uncertainty quantification purpose. However, when the stiff system is involved, the computational cost can be prohibitive, since stiff numerical integration requires the solution of a nonlinear system of equations at every time step. Applying the Galerkin polynomial chaos to stiff system will cause a computational cost increase from O(n3) to O(S3n3). This paper explores uncertainty quantification techniques for stiff chemical systems using Galerkin polynomial chaos, collocation and collocation least-square approaches. We propose a modification in the implicit time stepping process. The numerical test results show that with the modified approach, the run time of the Galerkin polynomial chaos is reduced. We also explore different methods of choosing collocation points in collocation implementations and propose a collocation least-square approach. We conclude that the collocation least-square for uncertainty quantification is at least as accurate as the Galerkin approach, and is more efficient with a well-chosen set of collocation points.

Abstract: Coupled fire-environment/thermal-response models were validated using data for an object engulfed in a JP8 hydrocarbon fuel fire. Fire model predictions of heat flux were used as boundary conditions in the thermal response calculations of the object. Predictions of transient external shell temperatures as well as the surface temperatures of the embedded mass were averaged spatially and compared to data. The solution sensitivity to mesh size, time step, nonlinear iterations, and radiation rays were assessed and the uncertainties in the predictions were quantified using a Latin Hypercube Sampling (LHS) technique. The comparisons showed that the response variable was more sensitive to fire model parameters than to thermal model parameters. The observed relative difference in measurements and model predictions was also compared to the model uncertainty. The comparisons showed that the model plus uncertainty bounded the experimental data. I. Introduction Sandia National Laboratories has been engaged in testing weapon system safety in fire environments since the 1950s. Due to the high consequences involved, system safety has traditionally been demonstrated through full scale system tests, albeit with a limited number of tests. Historically developed standardized tests include the placement of a system in a fully engulfing fire for 1 hour. Systems are declared qualified and ready for production based on passage of these standardized tests and with reference to the testing and analysis during development. Beginning in the early to mid 1990’s, the DOE began a program of Science Based Stockpile Stewardship. A significant part of this program is the Advanced Simulation and Computing (ASC) program, in which modeling and simulation, through high performance computing has been applied to system development and qualification. As part of the ASC program, Sandia engaged in developing the capability to model fire environments coupled to system response in those environments. An important thrust area within the ASC program includes the advancement of the verification and validation (V&V) methodologies and uncertainty quantification techniques. Sandia National Laboratories has made strides in developing new capabilities in this area and applying them to current applications. A best estimate plus uncertainty approach has been fully adopted and incorporated into safety themes for system qualification. Providing uncertainty estimates along with deterministic results has provided value to Sandia programs and gives more insight into predictive capability. The direct contribution of this study to current and future systems is an understanding of the uncertainties in predicting internal system temperatures when an object is engulfed in a JP8 fire environment. The uncertainty in input parameters can be used with other scenarios and configurations to evaluate situations that challenge safety themes. Confidence gained in validation processes such as discussed in the current work is crucial when evaluating system qualification activities that include modeling and simulation. II. Numerical Modeling

Abstract: Because of dynamic, complex and competitive environments, many information technology (IT) projects are plagued by significant cost overruns and unexpected schedule slips. Research suggests that a major reason for project failures is management's inability to address uncertainty during the development of a new management information system. Dealing with project uncertainty consists of three main segments: identifying sources of project development uncertainty, quantifying project uncertainty, and using such uncertainty measure for improving decision making process with respect to projects. While the first segment has been a major concern for researchers and practitioners, very little progress in the way of theoretical development has been achieved in the areas of uncertainty quantification and its use in project management. This paper explores various aspects of project uncertainties and offers three entropy-based uncertainty measures: aggregate uncertainty, weighted aggregate uncertainty, and deviation uncertainty. Aggregate uncertainty incorporates a list of unknown risk factors into a single entropy-based measure. Weighted aggregate uncertainty considers the relative importance of unknown uncertainty factors. Deviation uncertainty is a relative uncertainty measure which indicates the degree of deviation of a given project from an ideal project in which all factors are certain. An actual project is used to demonstrate our measures. The paper also discusses managerial implications of such measure. INTRODUCTION In our global competitive economy, information technology has become a primary resource for competitive advantage. In particular, the successful development of computer-based systems that support a firm's competitive strategy is critical to organizational success. Yet, for the last three decades, projects have suffered from high failure rates (Mayer 1998, Jiang et al., 2002). Turner (1982) indicates that between one third and one half of all information systems projects never reached the implementation stage. Other evidence is provided by an IBM study which suggests that 55 percent of projects exceeded their planned budget, 58 percent exceeded their planned schedule, and 88 percent had to be significantly redesigned (Gibbs, 1994). Recent studies by the Government Accountability Office and the National Institute of Standards and Technology show that 31.1% of all software projects will be cancelled before they ever get completed. Further results indicate that 52.7% of projects will cost over 189% of their original estimates (Rensin, 2005). Research suggests that a major reason for projects failures is management's inability to address uncertainty during the development of new management information systems (Kydd, 1989, Mazzola & McCardle, 1996). Other sources suggest that information systems requirements uncertainty has a direct negative effect on project performance (Nidumolu, 1996) and development risk affects budgets, schedules, and system quality of projects (Jiang et al., 2002). Traditional techniques of project management have become inadequate to monitor project uncertainty (Lycett & Paul, 1999, Meyer at al. 2002). Practitioners and researchers have developed and utilized a variety of system development tools, such as prototyping, data modeling, structured and object-oriented design, and computer-assisted software engineering. Unfortunately, even with these efforts, the failure rates remain high. In a recent study, only 37 percent of major projects were completed on time and only 42 percent were completed on budget (Gordon, 1999). Two major areas of uncertainty management consist of uncertainty identification and uncertainty quantification. Identifying uncertainty sources during the development of IT related projects has been a major concern for researchers and practitioners (Chapman & Ward, 1997). However, current research is focused on empirical studies that investigate the impact of uncertainty reduction on project success (Rai and Al-Hindi, 2000, Jiang et al. …

Abstract: This work examines uncertainties in the back end fuel cycle metrics of isotopic composition, decay heat, radioactivity, and radiotoxicity. Most advanced fuel cycle scenarios, including the ones represented in this work, are limited by one or more of these metrics, so that quantification of them becomes of great importance in order to optimize or select one of these scenarios. Uncertainty quantification, in this work, is performed by propagating cross-section covariance data, and later number density covariance data, through a reactor physics and depletion code sequence. Propagation of uncertainty is performed primarily via the Efficient Subspace Method (ESM). ESM decomposes the covariance data into singular pairs and perturbs input data along independent directions of the uncertainty and only for the most significant values of that uncertainty. Results of these perturbations being collected, ESM directly calculates the covariance of the observed output posteriori. By exploiting the rank deficient nature of the uncertainty data, ESM works more efficiently than traditional stochastic sampling, but is shown to produce equivalent results. ESM is beneficial for very detailed models with large amounts of input data that make stochastic sampling impractical. In this study various fuel cycle scenarios are examined. Simplified, representative models of pressurized water reactormore » (PWR) and boiling water reactor (BWR) fuels composed of both uranium oxide and mixed oxides are examined. These simple models are intended to give a representation of the uncertainty that can be associated with open uranium oxide fuel cycles and closed mixed oxide fuel cycles. The simplified models also serve as a demonstration to show that ESM and stochastic sampling produce equivalent results, because these models require minimum computer resources and have amounts of input data small enough such that either method can be quickly implemented and a numerical experiment performed. The simplified models are followed by more rigorous reactor physics and depletion models showing a PWR uranium oxide fuel and various metal fast reactor fuels composed of transuranics. The more rigorous models include multi-group cross sections, multiple burnup steps, neutron transport calculations to update cross sections, and multi-scale multi-physics code sequences to simulate a complete fuel lifetime. Finally, the fast reactor and PWR fuels are combined in a closed fast reactor recycle fuel cycle, and uncertainties on the resulting equilibrium cycle examined.« less