Results for “Statistical Analysis” — Page 9

DOE OSTI2024

Atom Probe Tomography Investigation of Clustering in Model P 2 O 5 -Doped Borosilicate Glasses for Nuclear Waste Vitrification

Atom probe tomography (APT) has been utilized to investigate the microstructure of two model borosilicate glasses designed to understand the solubility limits of phosphorous pentoxide (P 2 O 5 ). This component is found in certain high-level radioactive defence wastes destined for vitrification, where phase separation can potentially lead to a number of issues relating to the processing of the glass and its long-term chemical and structural stability. The development of suitable focused ion beam (FIB)-preparation routes and APT analysis conditions were initially determined for the model glasses, before examining their detailed microstructures. In a 3.0 mol% P 2 O 5 -doped glass, both visual inspection and sensitive statistical analysis of the APT data show homogeneous microstructures, while raising the content to 4.0 mol% initiates the formation of phosphorus-enriched nanoscale precipitates. This study confirms the expected inhomogeneities and phase separation of these glasses and offers routes to characterizing these at near-atomic scale resolution using APT.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2023

X-ray absorption spectroscopy study of Mn reference compounds for Mn speciation in terrestrial surface environments

Abstract X-ray absorption spectroscopy (XAS) offers great potential to identify and quantify Mn species in surface environments by means of linear combination fit (LCF), fingerprint, and shell-fit analyses of bulk Mn XAS spectra. However, these approaches are complicated by the lack of a comprehensive and accessible spectrum library. Additionally, molecular-level information on Mn coordination in some potentially important Mn species occurring in soils and sediments is missing. Therefore, we investigated a suite of 32 natural and synthetic Mn reference compounds, including Mn oxide, oxyhydroxide, carbonate, phosphate, and silicate minerals, as well as organic and adsorbed Mn species, by Mn K-edge X-ray absorption near edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) spectroscopy. The ability of XAS to infer the average oxidation state (AOS) of Mn was assessed by comparing XANES-derived AOS with the AOS obtained from redox titrations. All reference compounds were studied for their local (<5 Å) Mn coordination environment using EXAFS shell-fit analysis. Statistical analyses were employed to clarify how well and to what extent individual Mn species (groups) can be distinguished by XAS based on spectral uniqueness. Our results show that LCF analysis of normalized XANES spectra can reliably quantify the Mn AOS within ~0.1 v.u. in the range +2 to +4. These spectra are diagnostic for most Mn species investigated, but unsuitable to identify and quantify members of the manganate and Mn(III)-oxyhydroxide groups. First-derivative XANES fingerprinting allows the unique identification of pyrolusite, ramsdellite, and potentially lithiophorite within the manganate group. However, XANES spectra of individual Mn compounds can vary significantly depending on chemical composition and/or crystallinity, which limits the accuracy of XANES-based speciation analyses. In contrast, EXAFS spectra provide a much better discriminatory power to identify and quantify Mn species. Principal component and cluster analyses of k2-weighted EXAFS spectra of Mn reference compounds implied that EXAFS LCF analysis of environmental samples can identify and quantify at least the following primary Mn species groups: (1) Phyllo- and tectomanganates with large tunnel sizes (2 × 2 and larger; hollandite sensu stricto, romanèchite, todorokite); (2) tectomanganates with small tunnel sizes (2 × 2 and smaller; cryptomelane, pyrolusite, ramsdellite); (3) Mn(III)-dominated species (nesosilicates, oxyhydroxides, organic compounds, spinels); (4) Mn(II) species (carbonate, phosphate, and phyllosilicate minerals, adsorbed and organic species); and (5) manganosite. All Mn compounds, except for members of the manganate group (excluding pyrolusite) and adsorbed Mn(II) species, exhibit unique EXAFS spectra that would allow their identification and quantification in mixtures. Therefore, our results highlight the potential of Mn K-edge EXAFS spectroscopy to assess bulk Mn speciation in soils and sediments. A complete XAS-based speciation analysis of bulk Mn in environmental samples should preferably include the determination of Mn valences following the “Combo” method of Manceau et al. (2012), EXAFS LCF analyses based on principal component and target transformation results, as well as EXAFS shell-fit analyses for the validation of LCF results. For this purpose, all 32 XAS reference spectra are provided in the Online Materials1 for further use by the scientific community.

Geochemistry & Geophysics↗

DOE OSTI2021

Machine learning-based analysis of COVID-19 pandemic impact on US research networks

Here in this study we explore how fallout from the changing public health policy around COVID-19 has changed how researchers access and process their science experiments. Using a combination of techniques from statistical analysis and machine learning, we conduct a retrospective analysis of historical network data for a period around the stay-at-home orders that took place in March 2020. Our analysis takes data from the entire ESnet infrastructure to explore DOE high-performance computing (HPC) resources at OLCF, ALCF, and NERSC, as well as User sites such as PNNL and JLAB. We look at detecting and quantifying changes in site activity using a combination of t-Distributed Stochastic Neighbor Embedding (t-SNE) and decision tree analysis. Our findings bring insights into the working patterns and impact on data volume movements, particularly during late-night hours and weekends.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Total Moisture Analysis of Salts by Dissolution

This report discusses recent efforts within TA-48 in developing a robust, defensible, and straightforward procedure for determining the moisture content of alkali and alkaline metal halide salts utilizing a total dissolution Karl-Fischer titration method. Utilizing statistical analysis of blank and dissolved salt samples, we determine a (3 sigma) detection limit of 67 micrograms H 2 O/g salt, and a (10 sigma) quantification limit of 160 micrograms H 2 O/g salt. Several salts are analyzed, and suggestions for future efforts are given.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Assessment of task‐based performance from five clinical DBT systems using an anthropomorphic breast phantom

Purpose Digital breast tomosynthesis (DBT) is a limited‐angle tomographic breast imaging modality that can be used for breast cancer screening in conjunction with full‐field digital mammography (FFDM) or synthetic mammography (SM). Currently, there are five commercial DBT systems that have been approved by the U.S. FDA for breast cancer screening, all varying greatly in design and imaging protocol. Because the systems are different in technical specifications, there is a need for a quantitative approach for assessing them. In this study, the DBT systems are assessed using a novel methodology with an inkjet‐printed anthropomorphic phantom and four alternative forced choice (4AFC) study scheme. Method A breast phantom was fabricated using inkjet printing and parchment paper. The phantom contained 5‐mm spiculated masses fabricated with potassium iodide (KI)‐doped ink and microcalcifications (MCs) made with calcium hydroxyapatite. Images of the phantom were acquired on all five systems with DBT, FFDM, and SM modalities where available using beam settings under automatic exposure control. A 4AFC study was conducted to assess reader performance with each signal under each modality. Statistical analysis was performed on the data to determine proportion correct (PC), standard deviations, and levels of significance. Results For masses, overall detection was highest with DBT. The difference in PC was statistically significant between DBT and SM for most systems. A relationship was observed between increasing PC and greater gantry span. For MCs, performance was highest with DBT and FFDM compared to SM. The difference between PC of DBT and PC of SM was statistically significant for all manufacturers. Conclusions This methodology represents a novel approach for evaluating systems. This study is the first of its kind to use an inkjet‐printed anthropomorphic phantom with realistic signals to assess performance of clinical DBT imaging systems.

Ikejimba, Lynda C.↗

DOE OSTI2023

Compilation of a Solar Mirror Materials Database and an Analysis of Natural and Accelerated Mirror Exposure and Degradation

The National Renewable Energy Laboratory (NREL) has been conducting exposure experiments on solar reflectors for over four decades. Thousands of mirror samples from over one hundred suppliers have been exposed to and monitored in a range of relevant environments. These test conditions include outdoor test settings and several controlled laboratory environments. These samples have been rigorously individually characterized using a series of reflectance measurements, visual inspections, and in some cases, in-depth composition analysis to identify degradation modes, reflectance losses, and other mirror properties integral to understanding the solar reflector's life cycle. Here, this paper compiles the decades of measurement data into a concise statistical analysis. It includes exposure and degradation data for numerous reflector types, including secondary-surface reflector permutations of polymer and glass superstrates with silver and aluminum reflectors as well as front-surface reflectors. The results herein are intended to analyze environmental stressors and degradation trends among various historical and state-of-the-art solar reflectors. It may be used to support solar reflector design, effective testing methodology, and inform manufacturing decisions moving forward. Presented are the results of the compiled database and an initial analysis for degradation rate modeling using full-spectrum and wavelength-dependent approaches. The database is a growing resource hosted on a live, publicly accessible website. In conjunction with the analysis presented here, it provides a valuable resource to the solar reflector manufacturing and testing industry.

14 SOLAR ENERGY↗

DOE OSTI2022

Rapid attribution analysis of the extraordinary heat wave on the Pacific coast of the US and Canada in June 2021

Towards the end of June 2021, temperature records were broken by several degrees Celsius in several cities in the Pacific Northwest areas of the US and Canada, leading to spikes in sudden deaths and sharp increases in emergency calls and hospital visits for heat-related illnesses. Here we present a multi-model, multi-method attribution analysis to investigate the extent to which human-induced climate change has influenced the probability and intensity of extreme heat waves in this region. Based on observations, modelling and a classical statistical approach, the occurrence of a heat wave defined as the maximum daily temperature (TXx) observed in the area 45–52 °N, 119–123 °W, was found to be virtually impossible without human-caused climate change. The observed temperatures were so extreme that they lay far outside the range of historical temperature observations. This makes it hard to state with confidence how rare the event was. Using a statistical analysis that assumes that the heat wave is part of the same distribution as previous heat waves in this region led to a first-order estimation of the event frequency of the order of once in 1000 years under current climate conditions. Using this assumption and combining the results from the analysis of climate models and weather observations, we found that such a heat wave event would be at least 150 times less common without human-induced climate change. Also, this heat wave was about 2 °C hotter than a 1-in-1000-year heat wave would have been in 1850–1900, when global mean temperatures were 1.2 °C cooler than today. Looking into the future, in a world with 2 °C of global warming (0.8 °C warmer than today), a 1000-year event would be another degree hotter. Our results provide a strong warning: our rapidly warming climate is bringing us into uncharted territory with significant consequences for health, well-being and livelihoods. Adaptation and mitigation are urgently needed to prepare societies for a very different future.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Estimating reaction parameters in mechanism-enabled population balance models of nanoparticle size distributions: A Bayesian inverse problem approach

In order to quantitatively predict nano- as well as other particle-size distributions, one needs to have both a mathematical model and estimates of the parameters that appear in these models. Here, we show how one can use Bayesian inversion to obtain statistical estimates for the parameters that appear in recently derived mechanism-enabled population balance models (ME-PBM) of nanoparticle growth. The Bayesian approach addresses the question of “how well do we know our parameters, along with their uncertainties?.” The results reveal that Bayesian inversion statistical analysis on an example, prototype $\mathrm{lr(0)_n}$ nanoparticle formation system allows one to estimate not just the most likely rate constants and other parameter values, but also their SDs, confidence intervals, and other statistical information. Moreover, knowing the reliability of the mechanistic model's parameters in turn helps inform one about the reliability of the proposed mechanism, as well as the reliability of its predictions. Importantly, the paper can also be seen as a tutorial with the additional goal of achieving a “Gold Standard” Bayesian inversion ME-PBM benchmark that others can use as a control to check their own use of this methodology for other systems of interest throughout nature. Overall, the results provide strong support for the hypothesis that there is substantial value in using a Bayesian inversion methodology for parameter estimation in particle formation systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Utilizing Advanced Statistics to Determine Anomalistic Conditions in Pebble-Bed Reactors

Pebble-bed reactors (PBRs) utilize hundreds of thousands of fuel pebbles, which continuously circulate through the core, in lieu of traditional fuel assemblies to generate fissions and produce power. The use of unmarked fuel pebbles presents a challenge for international safeguards verification that nuclear material is not being diverted. To ensure pebble diversion is not taking place, new methods for accounting for and monitoring the pebbles should be examined to determine an appropriate methodology for performing bulk accountancy with pebbles. Here, this work examines the use of statistical methods for determining if the reactor is within a declared range of operation by examining the statistical distribution of pebble burnup as they are discharged from the core. Using this methodology, we created a model that detects diversion over 95% of the time, over multiple diversion pathways, if the reactor core maintains a constant power density during the diversion process and only falsely labels a diversion case nominal 2% of the time. For a diversion scenario where the reactor is maintained at a constant power, the statistical analysis can correctly identify if diversion is occurring over 80% of the time; however, nearly 20% of specific diversion pathways are mislabeled nominal. These results provide a basis and framework for exploring the further use of statistical methods to determine where these methods could be most useful and where additional methods, such as machine learning, could be used to capture if diversion is occurring in pebble-bed reactors.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Investigation into the instantaneous centre of rotation for enhanced design of floating offshore wind turbines

The dynamic behaviour of floating offshore wind turbines (FOWTs) involves complex interactions of multivariate loads from wind, waves, and currents, which result in complex motion characteristics. Although methods for analysing global motion responses are well-established, the time- and location-dependent kinematics remain underexplored. This paper investigates the instantaneous centre of rotation (ICR), a point of zero velocity at a time instance of general plane motion. Understanding and strategically positioning the ICR can reduce the dynamic motion in critical structural locations, enhancing the performance and structural robustness of FOWTs. The paper presents a method for computing the ICR using time-domain simulation results and proposes a statistical analysis approach suitable for design studies. Building on prior research, it examines the sensitivity of the ICR to external loading and design features, providing insights into how these factors influence motion response and how the motion response influences the statistics of the ICR, structural loads, and other performance metrics of interest. The study explores two FOWT configurations, a spar and a semisubmersible, identifying design variables that most effectively control the ICR statistics and identifying the ICR statistics most correlated with the responses of interest. Finally, through two case studies, we demonstrate how to apply these new insights in a practical design scenario. By adjusting the design variables most correlated with the ICR (fairlead vertical position and centre of mass for the spar and mooring line length and offset column diameter for the semisubmersible), we successfully modified the designs of the floating support structures to reduce the loads in the mooring lines, tower base, and blade roots, improving the ultimate strength and fatigue characteristics compared to the original designs.

17 WIND ENERGY↗

DOE OSTI2024

Assessment of BQ-9000 Biodiesel Properties for 2023

This is the seventh in a series of reports documenting the quality of biodiesel from U.S.- and Canadian-based producers that participate in the BQ-9000 program, the biodiesel industry’s voluntary quality assurance program. Participants provided monthly data on critical quality parameters for calendar year 2023 with quality data provided to a team of experts, who removed any identifying company information and provided anonymized data to the National Renewable Energy Laboratory (NREL) for statistical analysis. New for 2023, data on kinematic viscosity, sulfated ash, distillation temperature, carbon residue, and cetane were collected, as well as individual levels of sodium, potassium, calcium, and magnesium. Critical quality parameters analyzed are listed in Table ES-1 with descriptive statistics.

09 BIOMASS FUELS↗

DOE OSTI2025

Concentration-Discharge Relationships in the Six Largest Arctic Rivers, 2003-2019

This dataset provides the results of the analysis of the relationship of dissolved analyte concentrations and river discharges in the six largest Arctic rivers across the global panarctic region (see Figure 1 in documentation file *.pdf). Long-term measurements of dissolved analyte concentrations and river discharge have been collected for each of the Kolyma, Lena, Mackenzie, Ob, Yenisey, and Yukon rivers by the Arctic Great Rivers Observatory (ArcticGRO) project from ~2003-present (Shiklomanov, 2021). The relationship of dissolved analyte concentrations and discharges in each river was characterized by statistical analysis of the slope of the log(concentration) vs log(discharge) (b), the coefficient of variation ratio (CVc/CVq), the 2.5% and 97.5% confidence intervals of b, and assigning a chemostatic, flushing, diluting, or non-systematic behavior category according to Koger (2018). The summary of these analyses for all six rivers is provided in one .csv file. The concentrations of 20 dissolved analytes and discharge measurement data for the individual Kolyma, Lena, Mackenzie, Ob, Yenisey, and Yukon rivers are also provided with this dataset. There are seven *.csv files; one for each river plus the statistical summary. These public ArcticGRO data at "https://www.arcticgreatrivers.org" (Shiklomanov, 2021) were downloaded on Feb 13, 2020, but each river has different measurement dates over the sampling and analysis period. The ArcticGRO metadata document (*.pdf) downloaded on Feb 13, 2020 is also included in this dataset. The Next-Generation Ecosystem Experiments: Arctic (NGEE Arctic), was a research effort to reduce uncertainty in Earth System Models by developing a predictive understanding of carbon-rich Arctic ecosystems and feedbacks to climate. NGEE Arctic was supported by the Department of Energy's Office of Biological and Environmental Research. The NGEE Arctic project had two field research sites: 1) located within the Arctic polygonal tundra coastal region on the Barrow Environmental Observatory (BEO) and the North Slope near Utqiagvik (Barrow), Alaska and 2) multiple areas on the discontinuous permafrost region of the Seward Peninsula north of Nome, Alaska. Through observations, experiments, and synthesis with existing datasets, NGEE Arctic provided an enhanced knowledge base for multi-scale modeling and contributed to improved process representation at global pan-Arctic scales within the Department of Energy's Earth system Model (the Energy Exascale Earth System Model, or E3SM), and specifically within the E3SM Land Model component (ELM).

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Comparative Analyses of Bioequivalence Assessment Methods for In Vitro Permeation Test Data

ABSTRACT For topical, dermatological drug products, an in vitro option to determine bioequivalence (BE) between test and reference products is recommended. In particular, in vitro permeation test (IVPT) data analysis uses a reference‐scaled approach for two primary endpoints, cumulative penetration amount (AMT) and maximum flux ( J max ), which takes the within donor variability into consideration. In 2022, the Food and Drug Administration (FDA) published a draft IVPT guidance that includes statistical analysis methods for both balanced and unbalanced cases of IVPT study data. This work presents a comprehensive evaluation of various methodologies used to estimate critical parameters essential in assessing BE. Specifically, we investigate the performance of the FDA draft IVPT guidance approach alongside alternative empirical and model‐based methods utilizing mixed‐effects models. Our analyses include both simulated scenarios and real‐world studies. In simulated scenarios, empirical formulas consistently demonstrate robustness in approximating the true model, particularly in effectively addressing treatment–donor interactions. Conversely, the effectiveness of model‐based approaches heavily relies on precise model selection, which significantly influences their results. The research emphasizes the importance of accurate model selection in model‐based BE assessment methodologies. It sheds light on the advantages of empirical formulas, highlighting their reliability compared to model‐based approaches and offers valuable implications for BE assessments. Our findings underscore the significance of robust methodologies and provide essential insights to advance their understanding and application in the assessment of BE, employed in IVPT data analysis.

Leon, Sami↗

DOE OSTI2020

Soil microbial function and fungal community data along an ectomycorrhizal basal area gradient, Vermont, May 2019

Mycorrhizal fungi can affect soil organic matter cycling through several mechanisms including priming, nutrient competition, and direct enzyme production. Differences in nutrient foraging strategies between ectomycorrhizal (EcM) and arbuscular mycorrhizal (AM) fungi produce divergent belowground dynamics: where EcM can take up organic nitrogen and directly break down SOM by producing enzymes, AM fungi are limited to scavenging mineral N. EcM-associated tree species also have leaf litter with relatively higher ratios of carbon to nitrogen (C:N), and belowground saprotrophic communities more dominated by fungi. Consequently, free-living microbes in EcM-dominated soils should experience nitrogen limitation, with subsequent increases in enzyme production and decreased carbon use efficiency (CUE). However, the relative importance of the effects of substrate quality and fungal community composition on enzyme production and CUE are unclear. To assess this distinction, we sampled the organic horizon and 10 cm of the mineral horizon in northern temperate forest soils along a gradient of EcM dominance (see SCxTS_DBH.csv for full tree species information). We characterized fungal community composition by measuring EcM relative abundances from extracted fungal DNA (To run raw ASV data through R code, use SCxTS_ASV_taxonomy.csv, and R code ITS_processing.Rmd; to see processed data with EcM relative abundance, use file SCxTS_sum_afitch_Feb18.20.csv) and the fungal to bacterial ratios (see data file SCxTS_plfa.csv) from phospholipid fatty acid analysis. Soil microbial functions were measured as potential activities of five hydrolytic and two oxidative enzymes ( To run raw data through R code us SCxTS_metadata.csv, hydrolytic_oxidative_raw.csv, MUBraw.csv, Enzyme_soilweight.csv, and incubationtime.csv, and R code SCxTS_enzymes.Rmd; to use Enzyme data ready to run through statistics code, use file Enzyme.data.csv) and microbial carbon use efficiency (see file SCxTS_CUE.csv and for full calculations file 18O_CUEcalcs_SCxTS_2019.xlsx). We assessed soil substrate quality as the soil carbon:nitrogen ratio (See file Organic_CN.csv). Statistical analysis can be run using R code from file SCxTS_analysis.Rmd.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Dakota A Multilevel Parallel Object-Oriented Framework for Design Optimization Parameter Estimation Uncertainty Quantification and Sensitivity Analysis: Version 6.12 Theory Manual

The Dakota 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 expansion 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 theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Dakota A Multilevel Parallel Object-Oriented Framework for Design Optimization Parameter Estimation Uncertainty Quantification and Sensitivity Analysis (V.6.14) (Theory Manual)

The Dakota 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 expansion 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 theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 6.13 Theory Manual

The Dakota 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 expansion 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 theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Theory Manual (V.6.15)

The Dakota 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 expansion 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 theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗