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NASA NTRS1992

Studies on spectral analysis of randomly sampled signals: Application to laser velocimetry data

Spectral analysis is very useful in determining the frequency characteristics of many turbulent flows, for example, vortex flows, tail buffeting, and other pulsating flows. It is also used for obtaining turbulence spectra from which the time and length scales associated with the turbulence structure can be estimated. These estimates, in turn, can be helpful for validation of theoretical/numerical flow turbulence models. Laser velocimetry (LV) is being extensively used in the experimental investigation of different types of flows, because of its inherent advantages; nonintrusive probing, high frequency response, no calibration requirements, etc. Typically, the output of an individual realization laser velocimeter is a set of randomly sampled velocity data. Spectral analysis of such data requires special techniques to obtain reliable estimates of correlation and power spectral density functions that describe the flow characteristics. FORTRAN codes for obtaining the autocorrelation and power spectral density estimates using the correlation-based slotting technique were developed. Extensive studies have been conducted on simulated first-order spectrum and sine signals to improve the spectral estimates. A first-order spectrum was chosen because it represents the characteristics of a typical one-dimensional turbulence spectrum. Digital prefiltering techniques, to improve the spectral estimates from randomly sampled data were applied. Studies show that the spectral estimates can be increased up to about five times the mean sampling rate.

Sree, David↗

NASA NTRS2016

On the Calculation of Uncertainty Statistics with Error Bounds for CFD Calculations Containing Random Parameters and Fields

This chapter discusses the ongoing development of combined uncertainty and error bound estimates for computational fluid dynamics (CFD) calculations subject to imposed random parameters and random fields. An objective of this work is the construction of computable error bound formulas for output uncertainty statistics that guide CFD practitioners in systematically determining how accurately CFD realizations should be approximated and how accurately uncertainty statistics should be approximated for output quantities of interest. Formal error bounds formulas for moment statistics that properly account for the presence of numerical errors in CFD calculations and numerical quadrature errors in the calculation of moment statistics have been previously presented in [8]. In this past work, hierarchical node-nested dense and sparse tensor product quadratures are used to calculate moment statistics integrals. In the present work, a framework has been developed that exploits the hierarchical structure of these quadratures in order to simplify the calculation of an estimate of the quadrature error needed in error bound formulas. When signed estimates of realization error are available, this signed error may also be used to estimate output quantity of interest probability densities as a means to assess the impact of realization error on these density estimates. Numerical results are presented for CFD problems with uncertainty to demonstrate the capabilities of this framework.

Uncertainty↗

DOE OSTI2025

Reference Correlations for the Density and Viscosity of Molten Alkali and Alkaline Earth Fluoride Salts

While there is a significant body of literature pertaining to thermophysical property measurements of molten salts, there is often a wide degree of variability among independent measurements of the same compounds. As such, the scientific community benefits greatly from an unbiased, independent assessment of duplicate datasets, so that reference correlations which describe these thermophysical properties as functions of temperature can be determined and then commonly used by researchers, scientists, and engineers. With regard to molten fluoride compounds, a significant time has elapsed since density and viscosity reference correlations have been determined; Janz conducted the most recent effort, in 1988, to provide reference correlations for the densities and viscosities of molten fluoride compounds via the National Standard Reference Data System coordinated by the National Bureau of Standards. Since then, new data have been published for molten fluoride compounds, and a new precedent has surfaced for putting forth reference correlations that involve fitting to multiple primary datasets. In this work, reference correlations are put forth for molten alkali and alkaline earth fluoride compounds in an effort to provide updated, improved correlations for general use. For molten alkali fluoride densities, estimated uncertainties with a 95% confidence interval are summarized as follows: LiF (0.63%), NaF (0.48%), KF (0.76%), RbF (0.93%), and CsF (0.75%). For molten alkaline earth fluoride densities, an estimated uncertainty was not able to be quantified for BeF 2 because of limited data; however, estimated uncertainties with a 95% confidence interval are summarized as follows for the remaining alkaline earth fluorides: MgF 2 (1.5%), CaF 2 (0.92%), SrF 2 (1.6%), and BaF 2 (0.23%). For molten alkali fluoride viscosities, uncertainty was not able to be quantified for RbF and CsF because of limited data; however, estimated uncertainties with a 95% confidence interval are summarized as follows for the remaining alkali fluorides: LiF (4.4%), NaF (3.0%), and KF (4.0%). For molten alkaline earth fluoride viscosities, limited consistent data resulted in the recommendation of single datasets (from literature) that are deemed to be the most trustworthy based on the quality of the underlying experimental studies.

Birri, A. [Oak Ridge National Laboratory (ORNL), O↗

DOE OSTI2021

A Novel Data-based Stochastic Distribution Control for Non-Gaussian Stochastic Systems

In this note, we present a novel data-based approach to investigate the non-Gaussian stochastic distribution control problem. As the motivation of this note, the existing methods have been summarised regarding to the drawbacks, for example, neural network weights training for unknown stochastic distribution and so on. To overcome these disadvantages, a new transformation for dynamic probability density function is given by kernel density estimation using interpolation. Based upon this transformation, a representative model has been developed while the stochastic distribution control problem has been transformed into an optimisation problem. Then, data-based direct optimisation and identification-based indirect optimisation have been proposed. In addition, the convergences of the presented algorithms are analysed and the effectiveness of these algorithms has been evaluated by numerical examples. In summary, the contributions of this note are as follows: 1) a new data-based probability density function transformation is given; 2) the optimisation algorithms are given based on the presented model; and 3) a new research framework is demonstrated as the potential extensions to the existing stochastic distribution control.

42 ENGINEERING↗

DOE OSTI2016

Muon Tomography of Deep Reservoirs

Imaging subsurface geological formations, oil and gas reservoirs, mineral deposits, cavities or magma chambers under active volcanoes has been for many years a major quest of geophysicists and geologists. Since these objects cannot be observed directly, different indirect geophysical methods have been developed. They are all based on variations of certain physical properties of the subsurface that can be detected from the ground surface or from boreholes. Electrical resistivity, seismic wave’s velocities and density are certainly the most used properties. If we look at density, indirect estimates of density distributions are performed currently by seismic reflection methods - since the velocity of seismic waves depend also on density - but they are expensive and discontinuous in time. Direct estimates of density are performed using gravimetric data looking at variations of the gravity field induced by the density variations at depth but this is not sufficiently accurate. A new imaging technique using cosmic-ray muon detectors has emerged during the last decade and muon tomography - or muography - promises to provide, for the first time, a complete and precise image of the density distribution in the subsurface. Further, this novel approach has the potential to become a direct, real-time, and low-cost method for monitoring fluid displacement in subsurface reservoirs.

borehole detector↗

DOE OSTI2017

Excess Galactic Molecular Absorption Toward the Radio Galaxy 3C 111

We show the combined spectral analysis of Chandra high-energy transmission grating and XMM-Newton reflection-grating spectrometer observations of the broad-line radio galaxy 3C 111. This source is known to show excess neutral absorption with respect to the one estimated from 21 cm radio surveys of atomic H i in the Galaxy. However, previous works were not able to constrain the origin of such an absorber as local to our Milky Way or intrinsic to the source (z = 0.0485). The high signal-to-noise grating spectra allow us to constrain the excess absorption as being due to intervening gas in the Milky Way, and we estimate a time-averaged total column density of N{sub H}=(7.4±0.1)×10{sup 21} cm{sup −2}, a factor of two higher than the tabulated H i value. We recommend using the total average Galactic column density estimated here when studying 3C 111. The origin of the extra Galactic absorption of N{sub H}=4.4×10{sup 21} cm{sup −2} is likely due to molecular gas associated with the Taurus molecular cloud complex toward 3C 111, which is our nearest star-forming region. We also detect a weak (EW = 16 ± 10 eV) and narrow (FWMH < 5500 km s{sup −1}, consistent with optical Hα) Fe Kα emission line at E = 6.4 keV, likely from the torus in the central regions of 3C 111, and we place an upper limit on the column density of a possible intrinsic warm absorber of N {sub H} < 2.5 × 10{sup 20} cm{sup −2}. These complexities make 3C 111 a very promising object for studying both the intrinsic properties of this active radio galaxy and the Galactic interstellar medium, if used as a background source.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

SU-G-JeP2-02: A Unifying Multi-Atlas Approach to Electron Density Mapping Using Multi-Parametric MRI for Radiation Treatment Planning

Purpose: MRI has a number of advantages over CT as a primary modality for radiation treatment planning (RTP). However, one key bottleneck problem still remains, which is the lack of electron density information in MRI. In the work, a reliable method to map electron density is developed by leveraging the differential contrast of multi-parametric MRI. Methods: We propose a probabilistic Bayesian approach for electron density mapping based on T1 and T2-weighted MRI, using multiple patients as atlases. For each voxel, we compute two conditional probabilities: (1) electron density given its image intensity on T1 and T2-weighted MR images, and (2) electron density given its geometric location in a reference anatomy. The two sources of information (image intensity and spatial location) are combined into a unifying posterior probability density function using the Bayesian formalism. The mean value of the posterior probability density function provides the estimated electron density. Results: We evaluated the method on 10 head and neck patients and performed leave-one-out cross validation (9 patients as atlases and remaining 1 as test). The proposed method significantly reduced the errors in electron density estimation, with a mean absolute HU error of 138, compared with 193 for the T1-weighted intensity approach and 261 without density correction. For bone detection (HU>200), the proposed method had an accuracy of 84% and a sensitivity of 73% at specificity of 90% (AUC = 87%). In comparison, the AUC for bone detection is 73% and 50% using the intensity approach and without density correction, respectively. Conclusion: The proposed unifying method provides accurate electron density estimation and bone detection based on multi-parametric MRI of the head with highly heterogeneous anatomy. This could allow for accurate dose calculation and reference image generation for patient setup in MRI-based radiation treatment planning.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2013

Plasma relaxation mechanics of pulsed high power microwave surface flashover

Microwave transmission and reflection characteristics of pulsed radio frequency field generated plasmas are elucidated for air, N{sub 2}, and He environments under pressure conditions ranging from 10 to 600 torr. The pulsed, low temperature plasma is generated along the atmospheric side of the dielectric boundary between the source (under vacuum) and the radiating environment with a thickness on the order of 5 mm and a cross sectional area just smaller than that of the waveguide. Utilizing custom multi-standard waveguide couplers and a continuous low power probing source, the scattering parameters were measured before, during, and after the high power microwave pulse with emphasis on the latter. From these scattering parameters, temporal electron density estimations (specifically the longitudinal integral of the density) were calculated using a 1D plane wave-excited model for analysis of the relaxation processes associated. These relaxation characteristics ultimately determine the maximum repetition rate for many pulsed electric field applications and thus are applicable to a much larger scope in the plasma community than just those related to high power microwaves. This manuscript discusses the diagnostic setup for acquiring the power measurements along with a detailed description of the kinematic and chemical behavior of the plasma as it decays down to its undisturbed state under various gas type and pressure conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

Photoluminescence characteristics of polariton condensation in a CuBr microcavity

We have investigated the photoluminescence (PL) properties of a CuBr microcavity at 10 K, including the temporal profiles, from the viewpoint of cavity-polariton condensation. The excitation energy density dependence of the PL intensity (band width) of the lower polariton branch at an in-plane wave vector of k{sub //} = 0 exhibits a threshold-like increase (decrease). A large blueshift in the PL energy of ∼10 meV caused by the cavity-polariton renormalization is correlated with the excitation energy density dependence of the PL intensity. The estimated density of photogenerated electron-hole pairs at the threshold is two orders lower than the Mott transition density. These results consistently demonstrate the occurrence of cavity-polariton condensation. In addition, we found that the PL rise and decay times are shortened dramatically by the cavity-polariton condensation, which reflects the bosonic final state stimulation in the relaxation process and the intrinsic cavity-polariton lifetime in the decay process.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1994

Nebular properties from far-infrared spectrosopy

We describe a semiempirical methodology-based on measurements of far-infrared (FIR) lines-that yields information on electron densities in regions where various ionic species exist, effective temperatures (T(sub eff)) for stars ionizing H II regions, and gas-phase heavy element abundances. Although this capability has long been available via optical data, the special features of FIR lines-relative insensitivity to extinction and electron temperature variations-extend the analysis ability. Several line ratios serve as diagnostics of electron density, N(sub e), probing different ionization conditions and different density regimes. The more N(sub e)-diagnostic observations made, the more reliable will be the deciphering of the actual variation in density throughout a nebula. A method to estimate T(sub eff) from the FIR (N III)/(N II) line ratio requires that the nebula be ionization bounded and that substantially all of the flux from the revevant lines be observed. However, to estimate T(sub eff) by a second method that uses the ratio of FIR (S III)/(O III) lines, an ionization-bounded nebula is a sufficient, but not necessary, condition. These restrictions are unnecessary for estimating densities and heavy element abundances. We show that a fairly general determination of metallicity, via the S/H ratio, may be made for H II regions with observations of just two lines-(S III) 19 micron and a hydrogen recombination line (or appropriate substitute). These techniques are applied to recent FIR data for the G333.6-0.2 H II region, including application to the recently measured (N II) 122 and 205 micron lines.

Rubin, Robert H.↗

DOE OSTI2022

A functional global sensitivity measure and efficient reliability sensitivity analysis with respect to statistical parameters

Sensitivity analysis and reliability assessment are two important aspects of structural and system safety. Epistemic uncertainty with respect to probabilistic model of input parameters due to lack of knowledge is present in many scarce-data applications and complicates the characterization of uncertainty in model response. In this article, we present two importance measures to evaluate the impact of distribution parameters on the probability distribution function (PDF) of the output and the failure probability. The epistemic uncertainty associated with the distribution parameters is modeled as random variables. Additionally, a modified extended polynomial chaos expansion (MEPCE) approach is introduced in which aleatory and epistemic random variables are modeled and propagated simultaneously while allowing the separate assessment for any single epistemic variable. A MEPCE-based kernel density estimation (KDE) construction provides a composite map from each epistemic variable to the response PDF. The functional global sensitivity index of the PDF with respect to the distribution parameters is thus derived, as a function of output, which is both more informative and more efficient than standard scalar sensitivity measures. Reliability sensitivity indices can be readily evaluated by integrating the global sensitivity index function over the failure zone. Three illustrative examples are used to demonstrate the proposed methodology.

42 ENGINEERING↗

DOE OSTI2011

Using Surface Remote Sensors to Derive Radiative Characteristics of Mixed-Phase Clouds: An Example from M-PACE

Measurements from ground-based cloud radar, high spectral resolution lidar and microwave radiometer are used in conjunction with a column version of the Rapid Radiative Transfer Model (RRTMG) and radiosonde measurements to derive the surface radiative properties under mixed-phase cloud conditions. These clouds were observed during the United States Department of Energy (US DOE) Atmospheric Radiation Measurement (ARM) Mixed-Phase Arctic Clouds Experiment (M-PACE) between September and November of 2004. In total, sixteen half hour time periods are reviewed due to their coincidence with radiosonde launches. Cloud liquid (ice) water paths are found to range between 11.0-366.4 (0.5-114.1) gm-2, and cloud physical thicknesses fall between 286-2075 m. Combined with temperature and hydrometeor size estimates, this information is used to calculate surface radiative flux densities using RRTMG, which are demonstrated to generally agree with measured flux densities from surface-based radiometric instrumentation. Errors in longwave flux density estimates are found to be largest for thin clouds, while shortwave flux density errors are generally largest for thicker clouds. A sensitivity study is performed to understand the impact of retrieval assumptions and uncertainties on derived surface radiation estimates. Cloud radiative forcing is calculated for all profiles, illustrating longwave dominance during this time of year, with net cloud forcing generally between 50 and 90 Wm-2.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Improved Data Interpretation through Identification of Time Series Periodicity Changes

Analysis and interpretation of time series data is easiest when the data values occur at uniform intervals in time, but actual data may have differing data sampling frequencies, such as monthly and daily readings. Applying data analysis techniques, such as smoothing, to such a data set may not give a representative result between time segments. The ability to automatically distinguish time segments of differing data frequency would provide a means for applying data analysis independently to each segment, though a suitable blending at segment boundaries would be required. A method for detecting frequency changes was developed and applied to Gaussian and median smoothing of hydraulic head data from groundwater wells at the U.S. Department of Energy Hanford Site in southeastern Washington state. The process identifies time segments of high-frequency (daily) or low-frequency (greater than daily) data using adjusted-bandwidth Gaussian kernel density estimation and a threshold value, which are further refined to address small blocks of low-frequency data within larger blocks of high-frequency data. User-selectable levels of smoothing are then applied independently to the time segments prior to combining the segment results for a single smoothed data set. This time segment identification approach provides effective low- and high-frequency data separation, which provides a method to apply data analysis independently to each time segment.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2015

Cauchy Drag Estimation For Low Earth Orbiters

Recent work on minimum variances estimators based on Cauchy distributions appear relevant to orbital drag estimation. Samples form Cauchy distributions which are part of a class of heavy-tailed distributions, are characterized by long stretches of fairly small variation, punctuated by large variations that are many times larger than could be expected from a Gaussian. Such behavior can occur when solar storms perturb the atmosphere. In this context, the present work describes an embedding of the scalar Idan-Speyer Cauchy Estimator to estimate density corrections, within an Extended Kalman Filter that estimates the state of a low Earth orbiter. In contrast to the baseline Kalman approach, the larger formal errors of the present approach fully and conservatively bound the predictive error distribution, even in the face of unanticipated density disturbances of hundreds of percent.

Low Earth↗

DOE OSTI2019

A Probabilistic Data-Driven Method for Photovoltaic Pseudo-Measurement Generation in Distribution Systems

This paper presents a probabilistic data-driven method to model the uncertainty of distributed photovoltaic (PV) generation to enhance the observability of distribution grids with a high penetration of renewable resources. The proposed method employs a kernel density estimation (KDE) technique to develop the conditional probability density function (PDF) of PV outputs given the time of the day, using the measurement data from observed PV systems. Then time series of output power of unmeasured PV generators, located at the same grid, are generated according to the corresponding PDF and used as pseudo-measurements in distribution system state estimation (DSSE). The proposed model has been tested and verified using real PV data and utility networks.

Yuan, Yuxuan↗

DOE OSTI2025

Conformal Hierarchical Simulation-Based Inference with Local Validity

Trustworthy and interpretable uncertainty quantification is a long-standing challenge in artificial intelligence. Simulation-based inference (SBI) comprises a broad swath of approaches for estimating latent parameters with uncertainties. Although flexible neural density estimators in SBI can be remark- ably expressive capturing highly structured, high-dimensional posteriors their credible regions can be badly mis-calibrated and are often only accompanied by heuristic coverage checks. We present the first SBI framework that delivers finite-sample local valid coverage guarantees that hold in the neighborhood of each observation. Our framework can couple any off-the-shelf hierarchical SBI engine with a confor- mal Bayesian post-processing step that operates on the posterior predictive density. A kernel-weighted conformity score adapts the conformal quantile to the local geometry of the data, yielding prediction sets that are simultaneously (i) marginally calibrated, (ii) locally valid, and (iii) hierarchical, handling global and observation-specific parameters in a single pass. Through experiments on synthetic data and benchmarks from neuroscience and physics, we show that our approach attains 1 − α coverage, where prior SBI methods under- or over-cover. Our approach also maintains a competitive, credible set size with minimal computational overhead. Finally, our approach can be used to make predictions on real data and give valid credible regions modulo weight-initialization-based model mis-specification.

Trivedi, Shubhendu [Fermilab]↗

DOE OSTI2019

A Novel Statistical Method for Measuring the Temperature–Density Relation in the IGM Using the b – N Hi Distribution of Absorbers in the Ly α Forest

We propose a new method for determining the thermal state of the intergalactic medium based on Voigt profile decomposition of the Lyα forest. The distribution of Doppler parameter and column density (b–N H i distribution) is sensitive to the temperature–density relation T = T 0 (ρ/ρ 0 ) γ-1 , and previous work has inferred T 0 and γ by fitting its low-b cutoff. This approach discards the majority of available data and is susceptible to systematics related to cutoff determination. We introduce an approach that exploits all information encoded in the b – N H i distribution by modeling its entire shape. We apply kernel density estimation to discrete absorption lines to generate model probability density functions, and then we use principal component decomposition to create an emulator that can be evaluated anywhere in thermal parameter space. We introduce a Bayesian likelihood based on these models enabling parameter inference via Markov Chain Monte Carlo. The method's robustness is tested by applying it to a large grid of thermal history simulations. By conducting 160 mock measurements, we establish that our approach delivers unbiased estimates and valid uncertainties for a 2D ( T 0 , γ) measurement. Furthermore, we conduct a pilot study applying this methodology to real observational data at z = 2. Using 200 absorbers, equivalent in path length to a single Lya forest spectrum, we measure $\mathrm{log}{T}_{0}={4.092}_{-0.055}^{+0.050}$ and $\gamma ={1.49}_{-0.074}^{+0.073}$ in excellent agreement with cutoff fitting determinations using the same data. Our method is far more sensitive than cutoff fitting, enabling measurements of log T 0 and γ with precision on $\mathrm{log}{T}_{0}$ (γ) nearly two (three) times higher for current data set sizes.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

Evaluating the functional importance of secretive species: A case study of aquatic snake predators in isolated wetlands

Abstract Although the need to prioritize limited conservation resources has prompted increased interest in understanding the functional importance of species within ecosystems, species that are infrequently observed are often written off as being unimportant. In this study, we use aquatic snakes as a case study for examining the importance of secretive predators. Most snakes are extremely cryptic and secretive, traits that not only lead to the perception that they are rare, and of minor importance, but also impede attempts to quantify densities. We used high sampling effort and robust‐design capture–recapture analyses to estimate density of aquatic snakes inhabiting an isolated 5.4‐ha wetland in South Carolina, USA . We assessed snake diets and coupled field measurements of growth rates with laboratory‐derived data on mass conversion efficiency to estimate prey consumption by snakes over a 1‐year period. We found a peak density 171 snakes ha −1 of wetland habitat, corresponding to a standing biomass of 7.77 kg ha −1 . We calculated that snakes within the wetland consumed a total of over 200 kg (>55 000 individuals) of amphibian prey annually, translating into >150 000 kJ ha −1 of energy flow from secondary to tertiary consumers within the wetland food web. Further, because many amphibians are primarily terrestrial as adults and are consumed by aquatic snakes only when they return to wetlands to breed, snakes can be responsible for substantial transfer of energy and biomass between terrestrial and aquatic habitats. Our study is one of the first comprehensive evaluations of the importance of snakes as predators and underscores the need to consider snakes in initiatives aimed at preserving overall ecosystem integrity.

Willson, J. D.↗