Publications

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Response surface functions are often used as simple and inexpensive replacements for computationally expensive computer models that simulate the behavior of a complex system over some parameter space. "Progressive" response surfaces are built up incrementally as global information is added from new sample points added to the previous points in the parameter space. As the response surfaces are globally upgraded, indicators of the convergence of the response surface approximation to the exact (fitted) function can be inferred. Sampling points can be incrementally added in a structured or unstructured fashion. Whatever the approach, it is usually desirable to sample the entire parameter space uniformly (at least in early stages of sampling). At later stages of sampling, depending on the nature of the quantity being resolved, it may be desirable to continue sampling uniformly (progressive response surfaces), or to switch to a focusing/economizing strategy of preferentially sampling certain regions of the parameter space based on information gained in previous stages of sampling ("adaptive" response surfaces). Here we consider progressive response surfaces where a balanced representation of global response over the parameter space is desired. We use Kriging and Moving-Least-Squares methods to fit Halton quasi-Monte-Carlo data samples and interpolate over the parameter space. On 2-D test problems we use the response surfaces to compute various response measures and assess the accuracy/applicability of heuristic error estimates based on convergence behavior of the computed response quantities. Where applicable we apply Richardson Extrapolation for estimates of error, and assess the accuracy of these estimates. We seek to develop a robust methodology for constructing progressive response surface approximations with reliable error estimates.

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 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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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.

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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.

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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.

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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.

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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.