This paper provides an overview of several approaches to formulating and solving optimization under uncertainty (OUU) engineering design problems. In addition, the topic of high-performance computing and OUU is addressed, with a discussion of the coarse- and fine-grained parallel computing opportunities in the various OUU problem formulations. The OUU approaches covered here are: sampling-based OUU, surrogate model-based OUU, analytic reliability-based OUU (also known as reliability-based design optimization), polynomial chaos-based OUU, and stochastic perturbation-based OUU.
The thermal challenge problem has been developed at Sandia National Laboratories as a testbed for demonstrating various types of validation approaches and prediction methods. This report discusses one particular methodology to assess the validity of a computational model given experimental data. This methodology is based on Bayesian Belief Networks (BBNs) and can incorporate uncertainty in experimental measurements, in physical quantities, and model uncertainties. The approach uses the prior and posterior distributions of model output to compute a validation metric based on Bayesian hypothesis testing (a Bayes' factor). This report discusses various aspects of the BBN, specifically in the context of the thermal challenge problem. A BBN is developed for a given set of experimental data in a particular experimental configuration. The development of the BBN and the method for ''solving'' the BBN to develop the posterior distribution of model output through Monte Carlo Markov Chain sampling is discussed in detail. The use of the BBN to compute a Bayes' factor is demonstrated.
This work focuses on different methods to generate confidence regions for nonlinear parameter identification problems. Three methods for confidence region estimation are considered: a linear approximation method, an F-test method, and a Log-Likelihood method. Each of these methods are applied to three case studies. One case study is a problem with synthetic data, and the other two case studies identify hydraulic parameters in groundwater flow problems based on experimental well-test results. The confidence regions for each case study are analyzed and compared. Although the F-test and Log-Likelihood methods result in similar regions, there are differences between these regions and the regions generated by the linear approximation method for nonlinear problems. The differing results, capabilities, and drawbacks of all three methods are discussed.
This report is a white paper summarizing the literature and different approaches to the problem of calibrating computer model parameters in the face of model uncertainty. Model calibration is often formulated as finding the parameters that minimize the squared difference between the model-computed data (the predicted data) and the actual experimental data. This approach does not allow for explicit treatment of uncertainty or error in the model itself: the model is considered the %22true%22 deterministic representation of reality. While this approach does have utility, it is far from an accurate mathematical treatment of the true model calibration problem in which both the computed data and experimental data have error bars. This year, we examined methods to perform calibration accounting for the error in both the computer model and the data, as well as improving our understanding of its meaning for model predictability. We call this approach Calibration under Uncertainty (CUU). This talk presents our current thinking on CUU. We outline some current approaches in the literature, and discuss the Bayesian approach to CUU in detail.
This document is a reference guide for the UNIX Library/Standalone version of the Latin Hypercube Sampling Software. This software has been developed to generate Latin hypercube multivariate samples. This version runs on Linux or UNIX platforms. This manual covers the use of the LHS code in a UNIX environment, run either as a standalone program or as a callable library. The underlying code in the UNIX Library/Standalone version of LHS is almost identical to the updated Windows version of LHS released in 1998 (SAND98-0210). However, some modifications were made to customize it for a UNIX environment and as a library that is called from the DAKOTA environment. This manual covers the use of the LHS code as a library and in the standalone mode under UNIX.
This report summarizes the results of a three-year LDRD project on prognostics and health management. System failure over some future time interval (an alternative definition is the capability to predict the remaining useful life of a system). Prognostics are integrated with health monitoring (through inspections, sensors, etc.) to provide an overall PHM capability that optimizes maintenance actions and results in higher availability at a lower cost. Our goal in this research was to develop PHM tools that could be applied to a wide variety of equipment (repairable, non-repairable, manufacturing, weapons, battlefield equipment, etc.) and require minimal customization to move from one system to the next. Thus, our approach was to develop a toolkit of reusable software objects/components and architecture for their use. We have developed two software tools: an Evidence Engine and a Consequence Engine. The Evidence Engine integrates information from a variety of sources in order to take into account all the evidence that impacts a prognosis for system health. The Evidence Engine has the capability for feature extraction, trend detection, information fusion through Bayesian Belief Networks (BBN), and estimation of remaining useful life. The Consequence Engine involves algorithms to analyze the consequences of various maintenance actions. The Consequence Engine takes as input a maintenance and use schedule, spares information, and time-to-failure data on components, then generates maintenance and failure events, and evaluates performance measures such as equipment availability, mission capable rate, time to failure, and cost. This report summarizes the capabilities we have developed, describes the approach and architecture of the two engines, and provides examples of their use. 'Prognostics' refers to the capability to predict the probability of
This paper examines the modeling accuracy of finite element interpolation, kriging, and polynomial regression used in conjunction with the Progressive Lattice Sampling (PLS) incremental design-of-experiments approach. PLS is a paradigm for sampling a deterministic hypercubic parameter space by placing and incrementally adding samples in a manner intended to maximally reduce lack of knowledge in the parameter space. When combined with suitable interpolation methods, PLS is a formulation for progressive construction of response surface approximations (RSA) in which the RSA are efficiently upgradable, and upon upgrading, offer convergence information essential in estimating error introduced by the use of RSA in the problem. The three interpolation methods tried here are examined for performance in replicating an analytic test function as measured by several different indicators. The process described here provides a framework for future studies using other interpolation schemes, test functions, and measures of approximation quality.
This paper presents a graph-based approach to network vulnerability analysis. The method is flexible, allowing analysis of attacks from both outside and inside the network. It can analyze risks to a specific network asset, or examine the universe of possible consequences following a successful attack. The graph-based tool can identify the set of attack paths that have a high probability of success (or a low effort cost) for the attacker. The system could be used to test the effectiveness of making configuration changes, implementing an intrusion detection system, etc. The analysis system requires as input a database of common attacks, broken into atomic steps, specific network configuration and topology information, and an attacker profile. The attack information is matched with the network configuration information and an attacker profile to create a superset attack graph. Nodes identify a stage of attack, for example the class of machines the attacker has accessed and the user privilege level he or she has compromised. The arcs in the attack graph represent attacks or stages of attacks. By assigning probabilities of success on the arcs or costs representing level-of-effort for the attacker, various graph algorithms such as shortest-path algorithms can identify the attack paths with the highest probability of success.
This paper presents a graph based approach to network vulnerability analysis. The method is flexible, allowing analysis of attacks from both outside and inside the network. It can analyze risks to a specific network asset, or examine the universe of possible consequences following a successful attack. The analysis system requires as input a database of common attacks, broken into atomic steps, specific network configuration and topology information, and an attacker profile. The attack information is matched with the network configuration information and an attacker profile to create a superset attack graph. Nodes identify a stage of attack, for example the class of machines the attacker has accessed and the user privilege level he or she has compromised. The arcs in the attack graph represent attacks or stages of attacks. By assigning probabilities of success on the arcs or costs representing level of effort for the attacker, various graph algorithms such as shortest path algorithms can identify the attack paths with the highest probability of success.
