Publications

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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.

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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This document provides verification test results for normal, lognormal, and uniform distributions that are used in Sandia's Latin Hypercube Sampling (LHS) software. The purpose of this testing is to verify that the sample values being generated in LHS are distributed according to the desired distribution types. The testing of distribution correctness is done by examining summary statistics, graphical comparisons using quantile-quantile plots, and format statistical tests such as the Chisquare test, the Kolmogorov-Smirnov test, and the Anderson-Darling test. The overall results from the testing indicate that the generation of normal, lognormal, and uniform distributions in LHS is acceptable.

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.