Publications

Abstract not provided.

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.

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 reference manual for the commands specification for the DAKOTA software, providing input overviews, option descriptions, and example specifications.

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 developers manual for the DAKOTA software and describes the DAKOTA class hierarchies and their interrelationships. It derives directly from annotation of the actual source code and provides detailed class documentation, including all member functions and attributes.

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Importance sampling is an unbiased sampling method used to sample random variables from different densities than originally defined. These importance sampling densities are constructed to pick 'important' values of input random variables to improve the estimation of a statistical response of interest, such as a mean or probability of failure. Conceptually, importance sampling is very attractive: for example one wants to generate more samples in a failure region when estimating failure probabilities. In practice, however, importance sampling can be challenging to implement efficiently, especially in a general framework that will allow solutions for many classes of problems. We are interested in the promises and limitations of importance sampling as applied to computationally expensive finite element simulations which are treated as 'black-box' codes. In this paper, we present a customized importance sampler that is meant to be used after an initial set of Latin Hypercube samples has been taken, to help refine a failure probability estimate. The importance sampling densities are constructed based on kernel density estimators. We examine importance sampling with respect to two main questions: is importance sampling efficient and accurate for situations where we can only afford small numbers of samples? And does importance sampling require the use of surrogate methods to generate a sufficient number of samples so that the importance sampling process does increase the accuracy of the failure probability estimate? We present various case studies to address these questions.

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Extensive experimentation over the past decade has shown that fabricated physical systems that are intended to be identical, and are nominally identical, in fact, differ from one another, and sometimes substantially. This fact makes it difficult to validate a mathematical model for any system and results in the requirement to characterize physical system behavior using the tools of uncertainty quantification. Further, because of the existence of system, component, and material uncertainty, the mathematical models of these elements sometimes seek to reflect the uncertainty. This presentation introduces some of the methods of probability and statistics, and shows how they can be applied in engineering modeling and data analysis. The ideas of randomness and some basic means for measuring and modeling it are presented. The ideas of random experiment, random variable, mean, variance and standard deviation, and probability distribution are introduced. The ideas are introduced in the framework of a practical, yet simple, example; measured data are included. This presentation is the third in a sequence of tutorial discussions on mathematical model validation. The example introduced here is also used in later presentations. © 2009 Society for Experimental Mechanics Inc.

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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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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Gaussian processes are used as emulators for expensive computer simulations. Recently, Gaussian processes have also been used to model the "error field" or "code discrepancy" between a computer simulation code and experimental data, and the delta term between two levels of computer simulation (multi-fidelity codes). This work presents the use of Gaussian process models to approximate error or delta fields, and examines how one calculates the parameters governing the process. In multi-fidelity modeling, the delta term is used to correct a lower fidelity model to match or approximate a higher fidelity model. The terms governing the Gaussian process (e.g., the parameters of the covariance matrix) are updated using a Bayesian approach. We have found that use of Gaussian process models requires a good understanding of the method itself and an understanding of the problem in enough detail to identify reasonable covariance parameters. The methods are not "black-box" methods that can be used without some statistical understanding. However, Gaussian processes offer the ability to account for uncertainties in prediction. This approach can help reduce the number of high-fidelity function evaluations necessary in multi-fidelity optimization.

This project focused on research and algorithmic development in optimization under uncertainty (OUU) problems driven by earth penetrator (EP) designs. While taking into account uncertainty, we addressed three challenges in current simulation-based engineering design and analysis processes. The first challenge required leveraging small local samples, already constructed by optimization algorithms, to build effective surrogate models. We used Gaussian Process (GP) models to construct these surrogates. We developed two OUU algorithms using 'local' GPs (OUU-LGP) and one OUU algorithm using 'global' GPs (OUU-GGP) that appear competitive or better than current methods. The second challenge was to develop a methodical design process based on multi-resolution, multi-fidelity models. We developed a Multi-Fidelity Bayesian Auto-regressive process (MF-BAP). The third challenge involved the development of tools that are computational feasible and accessible. We created MATLAB{reg_sign} and initial DAKOTA implementations of our algorithms.

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 reference manual for the commands specification for the DAKOTA software, providing input overviews, option descriptions, and example specifications.

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 developers manual for the DAKOTA software and describes the DAKOTA class hierarchies and their interrelationships. It derives directly from annotation of the actual source code and provides detailed class documentation, including all member functions and attributes.