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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Uncertainty quantification of material parameters in modeling coupled metal and high explosive experiments

Experiments involving the coupling of metal and high explosives (HE) are of notable defense-related interest, and we seek to refine the uncertainty quantification associated with models of such experiments. In particular, our focus is on how uncertainty related to the metal constitutive model challenges our ability to infer high explosive model parameters when analyzing focused science experiments. We consider three focused experiments involving an HE accelerating metal: small plate tests with tantalum/LX-14 and tantalum/LX-17 pairings as well as a tantalum/LX-17 cylinder test. For all three models, we perform sensitivity analysis to ascertain the influence of metal strength on the coupled experimental response. Moreover, we calibrate each model in a Bayesian setting and study the quantification of metal strength on the inference of the HE parameters. Based on our results, we offer guidance for future metal/HE experiments.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Techniques for improved statistical convergence in quantification of eddy diffusivity moments

While recent approaches, such as the macroscopic forcing method (MFM) or Green's function-based approaches, can be used to compute Reynolds-averaged Navier-Stokes closure operators using forced direct numerical simulations, MFM can also be used to directly compute moments of the effective nonlocal and anisotropic eddy diffusivities. The low-order spatial and temporal moments contain limited information about the eddy diffusivity but are often sufficient for quantification and modeling of nonlocal and anisotropic effects. However, when using MFM to compute eddy diffusivity moments, the statistical convergence can be slow for higher-order moments. In this work, we demonstrate that using the same direct numerical simulation (DNS) for all forced MFM simulations improves statistical convergence of the eddy diffusivity moments. We present its implementation in conjunction with a decomposition method that handles the MFM forcing semianalytically and allows for consistent boundary condition treatment, which we develop for both scalar and momentum transport. We demonstrate that for a two-dimensional Rayleigh-Taylor instability case study, using the same DNS for all forced MFM simulations results in convergence with 𝒪⁡(100) simulations rather than 𝒪⁡(1000) simulations. In conclusion, we then demonstrate the impacts of improved convergence on the quantification of the eddy diffusivity.

general physics↗
DOE OSTI2024

Composition Quantification of SiGeSn Alloys Through Time-of-Flight Secondary Ion Mass Spectrometry: Calibration Methodologies and Validation With Atom Probe Tomography

Time-of-Flight Secondary Ion Mass Spectrometry (ToF-SIMS) is a powerful technique for elemental compositional analysis and depth profiling of materials. However, it encounters the problem of matrix effects that hinder its application. In this work, we introduce a pioneering ToF-SIMS calibration method tailored for SixGeySnz ternary alloys. SixGe1-x and Ge1-zSnz binary alloys with known compositions are used as calibration reference samples. Through a systematic SIMS quantification study of SiGe and GeSn binary alloys, we unveil a linear correlation between secondary ion intensity ratio and composition ratio for both SiGe and GeSn binary alloys, effectively mitigating the matrix effects. Extracted relative sensitivity factor (RSF) value from SixGe1-x (0.07 < x < 0.83) and Ge1-zSnz (0.066 < z < 0.183) binary alloys are subsequently applied to those of SixGeySnz (0.011 < x < 0.113, 0.863 < y < 0.935 and 0.023 < z < 0.103) ternary alloys for elemental compositions quantification. These values are cross-checked by Atom Probe Tomography (APT) analysis, an indication of the great accuracy and reliability of as-developed ToF-SIMS calibration process. Furthermore, the proposed method and its reference sample selection strategy in this work provide a low-cost as well as simple-to-follow calibration route for SiGeSn composition analysis, thus driving the development of next-generation multifunctional SiGeSn-related semiconductor devices.

36 MATERIALS SCIENCE↗
DOE OSTI2026

3D Deep Learning Joint Inversion of Active Seismic Full Waveform and Passive Seismic Traveltime Data for Reservoir Imaging and Uncertainty Quantification

Here, we present deep learning (DL) networks for three-dimensional (3D) joint inversion of active seismic full waveform and passive seismic traveltime data to image reservoirs and their properties and quantify imaging uncertainties. Active seismic full-waveform data can provide high-resolution monitoring images but are collected only intermittently because of their high acquisition cost. In contrast, passive seismic data can be gathered at relatively low cost between regular active surveys, although their imaging quality can be compromised by factors such as low signal-to-noise ratios and limited ray coverage of the target. Although these datasets are routinely acquired together at CO 2 storage sites, their combined inversion within a 3D DL framework has not been previously demonstrated. To our knowledge, this is the first study to address this gap, combining the strength of both data types. For efficient data storage and DL training with large 3D seismic datasets, we use a 3D data matrix in which a random number of passive seismic traveltime data are stored as parabolic envelopes using one-hot encoding and a 3D full-waveform data matrix in which multiple shot gathers are summed. Two network architectures are evaluated: a single-encoder U-Net for single-data type inversion and a dual-encoder U-Net for joint inversion of active and passive seismic data. We also evaluate the single-encoder U-Net for joint inversion by concatenating full-waveform data and traveltime data. We propose a systematic approach for selecting an optimal dropout rate that balances regularization during training and Monte Carlo dropout-based uncertainty quantification during prediction by examining the correlation coefficient between standard deviation and prediction error, along with the training misfit, across a range of dropout rates. 3D DL inversion experiments include five different network configurations, with evaluations under ideal, noisy and dropout-enabled conditions. Both model and data uncertainties are assessed, as well as their combined effects. Across all conditions, the networks consistently predict accurate CO 2 saturation models with low prediction errors, such as a structural similarity index of 0.993 and CO 2 difference of 1.1%. Uncertainty estimates show strong spatial correlation with prediction errors, confirming the effectiveness of the proposed dropout selection approach. The results demonstrate that our DL approach, utilizing compact data representations and appropriate uncertainty quantification, yields accurate subsurface images under various inversion conditions and provides valuable insights into the reliability of predictions.

Um, Evan Schankee [Lawrence Berkeley National Labo↗
DOE OSTI2025

Integrated System for Methane Emissions Monitoring, Mapping, and Quantification

This report presents the work completed under the DOE iM4 project for the development of a methane emission monitoring system for detection, location, and quantification of methane in oil and gas industries. The task was divided into four main areas including: 1) Sensors and Input, 2) Centralized Cloud Information Center, 3) Algorithms, and 4) Testing and Validation. Task 1 focused on researching and developing an understanding of the current, or soon to be, available methane sensing technologies. Task 2 consisted of developing the architecture, selecting hardware, software and elements for the methane monitoring system. Task 3 focused on the algorithms used for the complex inverse model of going from measured methane signatures to the detection, localization, and quantification of sources that are desired. Finally, Task 4 focused on the methods of testing and validating the operation of the system. Attention was also given to the development method and cost breakdown of the system.

03 NATURAL GAS↗
DOE OSTI2025

Uncertainty Quantification for Smooth Functional Data with Application to Material Properties

This document outlines a method for processing functional output (i.e., curves) for the ultimate purpose of sampling curves under specified input conditions for use in modeling and simulation uncertainty quantification (UQ) studies. A set of benchmark curves sufficiently representative of the relevant scenario(s) being simulated are provided to the process and formatted as described in Section 1. Principal Component Analysis (PCA) is utilized to discover the components of uncertainty in the benchmark curves and is outlined in Section 2. Section 3 describes the application of uncertainty quantification to the PCA results for the purpose of sampling curves to be used in UQ analysis. Section 4 applies these techniques to an example benchmark dataset. Concluding remarks are provided in the final section.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Probabilistic Predictions for Fastener Failure in the Sandia Mechanics Challenge Using the Discrete-Direct Uncertainty Quantification Approach

This paper documents the blind and post-blind analysis predictions for the 2023 Sandia Mechanics Challenge (SMC), which involved predicting the behavior of a threaded fastener joint structure subjected to shock loading. Utilizing repeat sets of fastener calibration data from various experimental configurations including tension, double shear, and joint tension, we developed a library of calibrated models which were propagated through the application model using the Discrete-Direct (DD) uncertainty quantification (UQ) approach. Although the initial blind predictions did not incorporate spare-sample processing to quantify fastener failure probabilities, the analyses yielded reasonable conclusions aligned with experimental results. In the post-blind analysis phase, we focused on enhancing the fidelity of the aluminum constitutive model and innovating the DD approach to obtain probabilistic predictions for fastener failure, particularly when quantities of interest (QoIs) approach their bounds. The improved aluminum model captures the behavior of the cantilever under shock loading more accurately, predicting both partial and complete cracks, although it tends to underpredict failure propagation. The enhanced DD approach facilitates probabilistic predictions that reflect the interdependent failure mechanisms of the fasteners and the cantilever, revealing that while certain fasteners are more likely to fail, the failure does not necessarily follow a progressive pattern. Overall, the post-blind analyses significantly improved the predictive capabilities of the model, providing valuable insights into the SMC application and establishing a robust foundation for informed engineering decisions. The methodology demonstrates a cost-effective and extensible approach suitable for a wide range of applications, highlighting the importance of uncertainty quantification to provide context for engineering decision making.

42 ENGINEERING↗
DOE OSTI2026

New approaches to Bayesian uncertainty quantification for Nuclear Science (Final Technical Report)

Inverse problems play a central role in experimentation and theory/data comparisons for many areas of modern Nuclear Physics (NP) and High-Energy Physics (HEP). Bayes’s Theorem is a powerful tool for solving Inverse Problems, providing conceptually transparent and unbiased constraints on theoretical parameters and their uncertainties (“Bayesian Inference”) and enabling the quantification of agreement or tension between models and data. However, analyses based on Bayesian Inference are often challenging for NP and HEP applications, either because of the large number of parameters in the problem, the high computational cost, or both. We propose a multi-institutional collaboration to develop and deploy novel Bayesian analysis tools that advance the scientific scope of a broad range of current and future NP experiments. This project brings together NP domain scientists working on several high-profile NP projects for which new, high-performance Bayesian Uncertainty Quantification (“Bayesian UQ”) methods are essential to carry out the science, and data scientists who are developing state-of-the-art methods applicable to these problems. The NP projects in this proposal comprise measurements of the mass and fundamental nature of the neutrino; study of the Quark-Gluon Plasma that filled the early universe; and mapping of natural and anthropogenic radiation environments. While these NP projects have very different scientific goals, with datasets and analysis approaches that differ significantly, they share common requirements for improving computationally intensive Bayesian analyses using advanced Machine Learning algorithms and will benefit strongly from a coherent effort to develop general solutions. This proposal brings together these projects and forefront ML-based data science algorithms to develop such general solutions. The methods developed in this project will also be more widely applicable, thereby advancing science in the larger Nuclear Physics portfolio.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Leveraging design of experiments to build chemometric models for the quantification of uranium (VI) and HNO3 by Raman spectroscopy

Partial least squares regression (PLSR) and support vector regression (SVR) models were optimized for the quantification of U(VI) (10–320 g L −1 ) and HNO 3 (0.6–6 M) by Raman spectroscopy with optimized calibration sets chosen by optimal design of experiments. The designed approach effectively minimized the number of samples in the calibration set for PLSR and SVR by selecting sample concentrations with a quadratic process model, despite complex confounding and covarying spectral features in the spectra. The top PLS2 model resulted in percent root mean square errors of prediction for U(VI), HNO 3 , and NO 3 − of 3.7%, 3.6%, and 2.9%, respectively. PLS1 models performed similarly despite modeling an analyte with a majority linear response (i.e., uranyl symmetric stretch) and another with more covarying vibrational modes (i.e., HNO 3 ). Partial least squares (PLS) model loadings and regression coefficients were evaluated to better understand the relationship between weaker Raman bands and covarying spectral features. Support vector machine models outperformed PLS1 models, resulting in percent root mean square error of prediction values for U(VI) and HNO 3 of 1.5% and 3.1%, respectively. The optimal nonlinear SVR model was trained using a similar number of samples (11) compared with the PLSR model, even though PLS is a linear modeling approach. The generic D-optimal design presented in this work provides a robust statistical framework for selecting training set samples in disparate two-factor systems. This approach reinforces Raman spectroscopy for the quantification of species relevant to the nuclear fuel cycle and provides a robust chemometric modeling approach to bolster online monitoring in challenging process environments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

A Review of Offshore Methane Quantification Methodologies

Since pre-industrial times, anthropogenic methane emissions have increased and are partly responsible for a changing global climate. Natural gas and oil extraction activities are one significant source of anthropogenic methane. While methods have been developed and refined to quantify onshore methane emissions, the ability of methods to directly quantify emissions from offshore production facilities remains largely unknown. Here, we review recent studies that have directly measured emissions from offshore production facilities and critically evaluate the suitability of these measurement strategies for emission quantification in a marine environment. The average methane emissions from production platforms measured using downwind dispersion methods were 32 kg h−1 from 188 platforms; 118 kg h−1 from 104 platforms using mass balance methods; 284 kg h−1 from 151 platforms using aircraft remote sensing; and 19,088 kg h−1 from 10 platforms using satellite remote sensing. Upon review of the methods, we suggest the unusually large emissions, or zero emissions observed could be caused by the effects of a decoupling of the marine boundary layer (MBL). Decoupling can happen when the MBL becomes too deep or when there is cloud cover and results in a stratified MBL with air layers of different depths moving at different speeds. Decoupling could cause: some aircraft remote sensing observations to be biased high (lower wind speed at the height of the plume); the mass balance measurements to be biased high (narrow plume being extrapolated too far vertically) or low (transects miss the plume); and the downwind dispersion measurements much lower than the other methods or zero (plume lofting in a decoupled section of the boundary layer). To date, there has been little research on the marine boundary layer, and guidance on when decoupling happens is not currently available. We suggest an offshore controlled release program could provide a better understanding of these results by explaining how and when stratification happens in the MBL and how this affects quantification methodologies.

Riddick, Stuart N. (ORCID:0000000316841843)↗
NASA NTRS1977

Analysis of laser fluorosensor systems for remote algae detection and quantification

The development and performance of single- and multiple-wavelength laser fluorosensor systems for use in the remote detection and quantification of algae are discussed. The appropriate equation for the fluorescence power received by a laser fluorosensor system is derived in detail. Experimental development of a single wavelength system and a four wavelength system, which selectively excites the algae contained in the four primary algal color groups, is reviewed, and test results are presented. A comprehensive error analysis is reported which evaluates the uncertainty in the remote determination of the chlorophyll a concentration contained in algae by single- and multiple-wavelength laser fluorosensor systems. Results of the error analysis indicate that the remote quantification of chlorophyll a by a laser fluorosensor system requires optimum excitation wavelength(s), remote measurement of marine attenuation coefficients, and supplemental instrumentation to reduce uncertainties in the algal fluorescence cross sections.

Browell, E. V.↗
NASA NTRS1982

Psychoacoustic considerations for helicopter noise quantification: Metrics, human response and criteria

The purpose of this paper is to examine several aspects of helicopter noise quantification from the standpoint of psychoacoustics. Noise metrics in common use to describe far-field aircraft noise and the noise characteristics which they consider are discussed. Some findings of recent psychoacoustic research related specifically to helicopter noise quantification are presented. Criteria for the accuracy of noise metrics to quantify helicopter noise are discussed. Finally, the prospects for improved metrics and research needed to develop and validate improved metrics or existing metrics are discussed.

Powell, C. A.↗
NASA NTRS1992

Rapid detection and quantification of features such as damage or flaws in composite and metallic structures

An apparatus, system, and method for non-destructible evaluation (NDE) of a material use thermography to rapidly detect and/or generally locate a feature such as, for example, damage or a defect in the material. The apparatus, system, and method also use ultrasound to specifically locate the feature in the material for quantification and/or evaluation either by an operator or by an external device suited for such purpose. Accordingly, the apparatus, system and method are particularly useful for NDE in applications such as the analysis of the structure of an aircraft, for example, in which the scale of the material to be analyzed is large, thus requiring the rapid NDE afforded by thermography, and in which quantification and/or evaluation of a feature must be performed with precision, thus requiring the relatively high-resolution NDE afforded by ultrasound.

Farley, Gary L.↗
NASA NTRS1995

Coral Pigments: Quantification Using HPLC and Detection by Remote Sensing

Widespread coral bleaching (loss of pigments of symbiotic dinoflagellates), and the corresponding decline in coral reef health worldwide, mandates the monitoring of coral pigmentation. Samples of the corals Porites compressa and P. lobata were collected from a healthy reef at Puako, Hawaii, and chlorophyll (chl) a, peridinin, and Beta-carotene (Beta-car) were quantified using reverse-phase high performance liquid chromatography (HPLC). Detailed procedures are presented for the extraction of the coral pigments in 90% acetone, and the separation, identification, and quantification of the major zooxanthellar pigments using spectrophotometry and a modification of the HPLC system described by Mantoura and Llewellyn (1983). Beta-apo-8-carotenal was found to be inadequate as in internal standard, due to coelution with chl b and/or chl a allomer in the sample extracts. Improvements are suggested, which may result in better resolution of the major pigments and greater accuracy in quantification. Average concentrations of peridinin, chl a, and Beta-car in corals on the reef were 5.01, 8.59, and 0.29, micro-grams/cm(exp 2), respectively. Average concentrations of peridinin and Beta-car did not differ significantly between the two coral species sampled; however, the mean chl a concentration in P. compressa specimens (7.81 ,micro-grams/cm(exp 2) was significantly lower than that in P. lobata specimens (9.96 11g/cm2). Chl a concentrations determined spectrophotometrically were significantly higher than those generated through HPLC, suggesting that spectrophotometry overestimates chl a concentrations. The average ratio of chl a-to-peridinin concentrations was 1.90, with a large (53%) coefficient of variation and a significant difference between the two species sampled. Additional data are needed before conclusions can be drawn regarding average pigment concentrations in healthy corals and the consistency of the chl a/peridinin ratio. The HPLC pigment concentration values contribute to the limited database of pigment concentrations in healthy corals, from which quantitative definitions of 'healthy' vs. 'bleached' coral may emerge. They also serve as ground-truth, corresponding to fluorescence data collected from the reef at Puako using airborne remote sensing of laser induced fluorescence. Fluorescence spectra from several overflights using the NASA AOL (airborne oceanographic lidar) system show consistent chlorphyll fluorescence peaks around 685 nm, as well as consistence peaks in the 400-600 nm range which may emanate from granules in the coral tissue. These data, along with results from previous studies of coral fluorescence, suggest that remote sensing of laser-induced fluorescence may become a rapid and efficient means of monitoring coral pigmentation and coral reef bleaching.

Cottone, Mary C.↗
NASA NTRS1998

Quantification of mitral regurgitation by automated cardiac output measurement: experimental and clinical validation

OBJECTIVES: To develop and validate an automated noninvasive method to quantify mitral regurgitation. BACKGROUND: Automated cardiac output measurement (ACM), which integrates digital color Doppler velocities in space and in time, has been validated for the left ventricular (LV) outflow tract but has not been tested for the LV inflow tract or to assess mitral regurgitation (MR). METHODS: First, to validate ACM against a gold standard (ultrasonic flow meter), 8 dogs were studied at 40 different stages of cardiac output (CO). Second, to compare ACM to the LV outflow (ACMa) and inflow (ACMm) tracts, 50 normal volunteers without MR or aortic regurgitation (44+/-5 years, 31 male) were studied. Third, to compare ACM with the standard pulsed Doppler-two-dimensional echocardiographic (PD-2D) method for quantification of MR, 51 patients (61+/-14 years, 30 male) with MR were studied. RESULTS: In the canine studies, CO by ACM (1.32+/-0.3 liter/min, y) and flow meter (1.35+/-0.3 liter/min, x) showed good correlation (r=0.95, y=0.89x+0.11) and agreement (deltaCO(y-x)=0.03+/-0.08 [mean+/-SD] liter/min). In the normal subjects, CO measured by ACMm agreed with CO by ACMa (r=0.90, p < 0.0001, deltaCO=-0.09+/-0.42 liter/min), PD (r=0.87, p < 0.0001, deltaCO=0.12+/-0.49 liter/min) and 2D (r=0.84, p < 0.0001, deltaCO=-0.16+/-0.48 liter/min). In the patients, mitral regurgitant volume (MRV) by ACMm-ACMa agreed with PD-2D (r= 0.88, y=0.88x+6.6, p < 0.0001, deltaMRV=2.68+/-9.7 ml). CONCLUSIONS: We determined that ACM is a feasible new method for quantifying LV outflow and inflow volume to measure MRV and that ACM automatically performs calculations that are equivalent to more time-consuming Doppler and 2D measurements. Additionally, ACM should improve MR quantification in routine clinical practice.

Non-NASA Center↗
NASA NTRS2007

The Roles of Verification, Validation and Uncertainty Quantification in the NASA Standard for Models and Simulations

The National Aeronautics and Space Administration (NASA) recently issued an interim version of the Standard for Models and Simulations (M&S Standard) [1]. The action to develop the M&S Standard was identified in an internal assessment [2] of agency-wide changes needed in the wake of the Columbia Accident [3]. The primary goal of this standard is to ensure that the credibility of M&S results is properly conveyed to those making decisions affecting human safety or mission success criteria. The secondary goal is to assure that the credibility of the results from models and simulations meets the project requirements (for credibility). This presentation explains the motivation and key aspects of the M&S Standard, with a special focus on the requirements for verification, validation and uncertainty quantification. Some pilot applications of this standard to computational fluid dynamics applications will be provided as illustrations. The authors of this paper are the members of the team that developed the initial three drafts of the standard, the last of which benefited from extensive comments from most of the NASA Centers. The current version (number 4) incorporates modifications made by a team representing 9 of the 10 NASA Centers. A permanent version of the M&S Standard is expected by December 2007. The scope of the M&S Standard is confined to those uses of M&S that support program and project decisions that may affect human safety or mission success criteria. Such decisions occur, in decreasing order of importance, in the operations, the test & evaluation, and the design & analysis phases. Requirements are placed on (1) program and project management, (2) models, (3) simulations and analyses, (4) verification, validation and uncertainty quantification (VV&UQ), (5) recommended practices, (6) training, (7) credibility assessment, and (8) reporting results to decision makers. A key component of (7) and (8) is the use of a Credibility Assessment Scale, some of the details of which were developed in consultation with William Oberkampf, David Peercy and Timothy Trocano of Sandia National Laboratories. The focus of most of the requirements, including those for VV&UQ, is on the documentation of what was done and the reporting, using the Credibility Assessment Scale, of the level of rigor that was followed. The aspects of one option for the Credibilty Assessment Scale are (1) code verification, (2) solution verification, (3) validation, (4) predictive capability, (5) technical review, (6) process control, and (7) operator and analyst qualification.

Zang, Thomas A.↗
NASA NTRS2014

Advanced Modeling and Uncertainty Quantification for Flight Dynamics; Interim Results and Challenges

As part of the NASA Vehicle Systems Safety Technologies (VSST), Assuring Safe and Effective Aircraft Control Under Hazardous Conditions (Technical Challenge #3), an effort is underway within Boeing Research and Technology (BR&T) to address Advanced Modeling and Uncertainty Quantification for Flight Dynamics (VSST1-7). The scope of the effort is to develop and evaluate advanced multidisciplinary flight dynamics modeling techniques, including integrated uncertainties, to facilitate higher fidelity response characterization of current and future aircraft configurations approaching and during loss-of-control conditions. This approach is to incorporate multiple flight dynamics modeling methods for aerodynamics, structures, and propulsion, including experimental, computational, and analytical. Also to be included are techniques for data integration and uncertainty characterization and quantification. This research shall introduce new and updated multidisciplinary modeling and simulation technologies designed to improve the ability to characterize airplane response in off-nominal flight conditions. The research shall also introduce new techniques for uncertainty modeling that will provide a unified database model comprised of multiple sources, as well as an uncertainty bounds database for each data source such that a full vehicle uncertainty analysis is possible even when approaching or beyond Loss of Control boundaries. Methodologies developed as part of this research shall be instrumental in predicting and mitigating loss of control precursors and events directly linked to causal and contributing factors, such as stall, failures, damage, or icing. The tasks will include utilizing the BR&T Water Tunnel to collect static and dynamic data to be compared to the GTM extended WT database, characterizing flight dynamics in off-nominal conditions, developing tools for structural load estimation under dynamic conditions, devising methods for integrating various modeling elements into a real-time simulation capability, generating techniques for uncertainty modeling that draw data from multiple modeling sources, and providing a unified database model that includes nominal plus increments for each flight condition. This paper presents status of testing in the BR&T water tunnel and analysis of the resulting data and efforts to characterize these data using alternative modeling methods. Program challenges and issues are also presented.

Hyde, David C.↗