Publications

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Finding the optimal (lightest, least expensive, etc.) design for an engineered component that meets or exceeds a specified level of reliability is a problem of obvious interest across a wide spectrum of engineering fields. Various methods for this reliability-based design optimization problem have been proposed. Unfortunately, this problem is rarely solved in practice because, regardless of the method used, solving the problem is too expensive or the final solution is too inaccurate to ensure that the reliability constraint is actually satisfied. This is especially true for engineering applications involving expensive, implicit, and possibly nonlinear performance functions (such as large finite element models). The Efficient Global Reliability Analysis method was recently introduced to improve both the accuracy and efficiency of reliability analysis for this type of performance function. This paper explores how this new reliability analysis method can be used in a design optimization context to create a method of sufficient accuracy and efficiency to enable the use of reliability-based design optimization as a practical design tool.

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This report documents the results of an FY09 ASC V&V Methods level 2 milestone demonstrating new algorithmic capabilities for mixed aleatory-epistemic uncertainty quantification. Through the combination of stochastic expansions for computing aleatory statistics and interval optimization for computing epistemic bounds, mixed uncertainty analysis studies are shown to be more accurate and efficient than previously achievable. Part I of the report describes the algorithms and presents benchmark performance results. Part II applies these new algorithms to UQ analysis of radiation effects in electronic devices and circuits for the QASPR program.

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Predictive simulation of systems comprised of numerous interconnected, tightly coupled components promises to help solve many problems of scientific and national interest. However predictive simulation of such systems is extremely challenging due to the coupling of a diverse set of physical and biological length and time scales. This report investigates un-certainty quantification methods for such systems that attempt to exploit their structure to gain computational efficiency. The traditional layering of uncertainty quantification around nonlinear solution processes is inverted to allow for heterogeneous uncertainty quantification methods to be applied to each component in a coupled system. Moreover this approach allows stochastic dimension reduction techniques to be applied at each coupling interface. The mathematical feasibility of these ideas is investigated in this report, and mathematical formulations for the resulting stochastically coupled nonlinear systems are developed.

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We develop an approach for estimating model parameters which result in the "best distribution fit" between experimental and simulation data. Best distribution fit means matching moments of experimental data to those of a simulation (and possibly matching a full probability distribution). This approach extends typical nonlinear least squares methods which identify parameters maximizing agreement between experimental points and computational simulation results. Several analytic formulations for the distribution matching problem are provided, along with results for solving test problems and comparisons of this parameter estimation technique with a deterministic least squares approach. Copyright © 2008 by the American Institute of Aeronautics and Astronautics, Inc.

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This report documents the results for an FY06 ASC Algorithms Level 2 milestone combining error estimation and adaptivity, uncertainty quantification, and probabilistic design capabilities applied to the analysis and design of bistable MEMS. Through the use of error estimation and adaptive mesh refinement, solution verification can be performed in an automated and parameter-adaptive manner. The resulting uncertainty analysis and probabilistic design studies are shown to be more accurate, efficient, reliable, and convenient.

The DAKOTA (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. DAKOTA contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic finite element methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the DAKOTA toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a user's manual for the DAKOTA software and provides capability overviews and procedures for software execution, as well as a variety of example studies.

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Surfpack is a general-purpose software library of multidimensional function approximation methods for applications such as data visualization, data mining, sensitivity analysis, uncertainty quantification, and numerical optimization. Surfpack is primarily intended for use on sparse, irregularly-spaced, n-dimensional data sets where classical function approximation methods are not applicable. Surfpack is under development at Sandia National Laboratories, with a public release of Surfpack version 1.0 in August 2006. This paper provides an overview of Surfpack's function approximation methods along with some of its software design attributes. In addition, this paper provides some simple examples to illustrate the utility of Surfpack for data trend analysis, data visualization, and optimization. Copyright © 2006 by the American Institute of Aeronautics and Astronautics, Inc.

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.