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NASA NTRSDate not supplied

Higher-Order Statistical Moments of Predicted Sonic Boom Waveforms Through Turbulence

Sonic booms generated by supersonic aircraft are affected by turbulence in the atmospheric boundary layer through which they propagate. Turbulence effects lead to random variability of the sonic boom waveforms measured on the ground, complicating the prediction of such waveforms. As an initial effort to predict the waveform variability, the solution of the coherent or mean sonic boom waveform has previously been formulated by the author. The current paper extends the formulation to derive an expression of the second-order statistical moment necessary to calculate the variance of the spectral amplitudes. Since the derivation uses a full wave equation, results using the derived expression will be compared with those obtained using a parabolic approximation. In order to fully quantify the uncertainty of our predictions, the higher order statistical moments are also formulated and are shown to be approximately zero. Consequently, the probability density function (pdf) of the spectral amplitudes is predicted to be Gaussian. The formulation is further extended to determine the pdf of the loudness of sonic booms and quantify the uncertainties associated with the loudness prediction. Results from the formulation are compared with available flight test data.

sonic booms↗
NASA NTRSDate not supplied

Consistent Pixel Resolution Characterization of Deep Convective Clouds for Calibration

The NASA CERES project provides global TOA shortwave and longwave fluxes for climate monitoring and validation that spans over 20 years. CERES utilizes broadband fluxes derived from geostationary (GEO) imagers to estimate broadband fluxes between the CERES observations. In order for these fluxes to be viable, the GEO imager calibration must be stable over time. One such calibration method used by CERES is to evaluate ensemble sets of deep convective clouds (DCC) as invariant targets (IT) over time. DCC targets can also provide radiometric scaling between sensors. An international collaboration through GSICS is also evaluating the DCC-IT calibration methodology to provide consistent calibration coefficients across geostationary sensors. Tropical DCC are the coldest, brightest, and most Lambertian TOA Earth targets identified using a window channel brightness temperature threshold. The DCC-IT technique involves a large ensemble of TOA pixel-level reflectances, which are binned into probability density functions (PDF). The PDF structure dependency on sensor pixel resolution, which can vary greatly among sensors, is not well known. This study will identify the impact of pixel resolution on the DCC PDFs by aggregating VIIRS and Landsat OLI/TIRS pixel resolutions into various coarser pixel resolutions and comparing the shape and statistics of the resulting PDFs. This study should assist in mitigating the pixel resolution dependency in the DCC-IT approach for providing scaling factors between sensors.

Conor Haney↗
NASA NTRSDate not supplied

NASA GPM Status and Future Activities

The joint U.S.-Japan Global Precipitation Measurement (GPM) mission is approaching a decade of operations, and continues to pursue research, dataset production, and outreach related to precipitation. Key activities over the last year were the release of an improved “Version 07” of all GPM precipitation and latent heating products, boosting the orbit of the GPM Core Observatory (GPM CO) to 435 km, and improving quality control on precipitation retrievals from the GPM constellation of passive microwave satellites. This presentation summarizes key improvements to the GPM products and provides some examples of the changes between Versions 06 and 07 in algorithm performance. One important operational change that affected Version 07 is that the scanning strategy for the Ka-band radar channel changed in May 2018; all products that depend on Ka were revised to accommodate this change. For example, in Version 07 the Goddard Profiling (GPROF) algorithm has implemented improvements in regions where orographic enhancement and suppression take place and where the surface is snowy/icy, and again covers radiometers reaching back to 1987. The Combined Radar Radiometer Algorithm (CORRA) now incorporates modified drop-size distribution constraints that substantially reduce bias. Revisions to the Convective-Stratiform Heating (CSH) algorithm employ new radiative transfer retrievals as well as accounting for terrain in the vertical coordinates. Each algorithm was adjusted to ensure continuity for each product across the boundary in 2014 between the predecessor Tropical Rainfall Measuring Mission (TRMM) and the GPM CO. The U.S. Science Team’s Integrated Multi-satellitE Retrievals for GPM (IMERG) was upgraded to account for distortions in the probability density function of regional precipitation rates due to weighted averaging in the Kalman filter used for “morphing” the passive microwave data. Maintaining the GPM CO orbital altitude in the the current very active solar cycle has been forcing the use of more fuel than planned and consequently shortening the forecasted life of the mission from the early 2030's to the late 2020's. It was considered vital to regain some of this lifetime to ensure overlap with the upcoming Atmosphere Observing System mission to provide crosscalibration of instruments. To accomplish this, the orbital altitude was raised from 400 to 435 km on 7-8 November 2023. Thereafter, the primary GPM CO algorithms had to be revised to account for the change in observing parameters. By meeting time this action should be complete. Recently, a screening algorithm based on auto-encoding was developed that uncovered 162 orbits (out of the many thousands of orbits across all years and all satellites) of passive microwave retrievals that had highly anomalous values. Removing these defective retrievals has improved the integrity of both the GPROF and IMERG records. However, the nature of the IMERG processing interacted sufficiently badly with the now-discovered anomalous orbits that it was necessary to completely reprocess the IMERG Final Run record, now labeled Version 07B. The presentation also considers major issues that require continued attention, including the use of machine learning algorithms and the operational challenge of swarms of “small”, perhaps short-lived satellites.

GPM↗
NASA NTRSDate not supplied

Seasonal, Spectral, and Regional Characterization of Deep Convective Clouds Top-of-Atmosphere Bidirectional Reflectance for Improved Satellite Intercalibration

The NASA CERES project provides the scientific community with regional broadband fluxes designed for long-term climate monitoring. The CERES climate quality dataset requires that the CERES instrument, as well as the MODIS and VIIRS imager records to be radiometrically stable over time. Deep Convective Clouds (DCCs) are spectrally uniform, near-Lambertian natural diffusers offering high signal-to-noise ratio and stable radiometric response in the VIS-NIR spectrum. For shortwave infrared (SWIR) wavelengths greater than 1.2µm, the DCC response is significantly influenced by cloud particle size and atmospheric absorption. Previous studies improved the characterization of the SWIR band DCC radiance, by using channel specific monthly empirical BRDFs as well as using the probability density function mean statistic to track the SWIR band stability. Also, that the DCC radiance is greater over land than over ocean and that the TWP DCC radiance has the lowest tropical DCC radiance. This study confirms and improves upon the previous studies. The study stratified the tropics regionally into land and ocean domains and applied their respective ocean-only and land-only empirical monthly BRDFs and normalized the land DCC BRDF corrected radiances with their ocean counterpart. This approach provided the most stable DCC response. The DCC BRDF corrected radiance monthly standard error was 0.24%, 0.62%, 0.59%, and 0.43% for the 1.24µm, 1.37µm, 1.61µm, and 2.25µm SWIR bands, which reduced the standard error 20%, 13%, 24%, and 26%, respectively when compared with the all-surface approach. The same approach was attempted over the Tropical Western Pacific and found not to be an improvement over the tropical domain. Further stratification of the tropical domain will need to balance sufficient sampling while accounting for regional DCC radiance differences.

Prathana Khakurel↗
NASA NTRSDate not supplied

Deep Convective Cloud Calibration Sensitivity Studies in Support of Radiometrically Scaling GEO Imagers With VIIRS

The NASA CERES SYN1deg product provides the scientific community regional hourly TOA and surface broadband fluxes and clouds. For consistent geostationary (GEO) derived fluxes and clouds the GEO imagers are radiometrically scaled to the Aqua-MODIS calibration reference. The CERES project utilizes GEO and MODIS or VIIRS analogous channel coincident, collocated, and co-angled radiance pairs as the primary method to inter-calibrate the GEO imagers. Tropical deep convective clouds (DCC) are bright, near Lambertian, top of atmosphere pseudo invariant Earth targets that do not rely on coincident ray-matched radiance pairs to radiometrically scale sensors to a common calibration reference. The DCC invariant target (DCC-IT) methodology collectively analyzes all tropical DCC identified pixel radiances by way of probability density function (PDF) distributions. Perfectly inter-calibrated sensor pairs should reveal nearly identical PDF distributions given the same DCC identification criterion. The PDF median, mean, mode, and inflection point statistics were tested as a function of DCC identification criterion using SNPP-VIIRS and Himawari-8 AHI 0.65μm channel radiances during January 2019. It was found that the PDF inflection point provided inter-calibration factors within 0.25% that were nearly independent of DCC identification criterion. The PDF median provided inter-calibration factors within 0.25% for the coldest BT and most stringent homogeneity factors. The PDF mean and mode statistics were inadequate under any DCC conditions. It is critical for the DCC pixel radiances to be anisotropically corrected. The DCC-IT methodology will also be tested for other visible and SWIR bands.

DCC↗
DOE OSTI2021

A REDUCED ORDER MODELING APPROACH TO PROBABILISTIC CREEP-DAMAGE PREDICTIONS IN FINITE ELEMENT ANALYSIS

This paper introduces a computationally efficient Reduced Order Modeling (ROM) approach for the probabilistic prediction of creep-damage failure. Component-level probabilistic simulations are needed to assess the reliability and safety of high-temperature components. Full-scale probabilistic creep-damage modeling in finite element (FE) approach is computationally expensive requiring many hundreds of simulations to replicate the uncertainty of component failure. To that end, ROM is proposed to minimize the elevated computational cost while controlling the loss of accuracy. It is proposed that full-scale probabilistic simulations can be completed in 1D at a reduced cost, the extremum conditions extracted, and those conditions applied for lower-cost 2D/3D probabilistic simulations of components that capture the mean and uncertainty of failure. The probabilistic Sine-hyperbolic (Sinh) model is selected which in previous work was calibrated to alloy 304 stainless steel. The Sinh model includes probability density functions (pdfs) for test condition (stress and temperature), initial damage (i.e. microstructure), and material properties uncertainty. The Sinh model is programmed into ANSYS finite element software using the USERCREEP.F material subroutine. First, the Sinh model and FE code are subject to verification and validation to ensure the accuracy of the simulations. Numerous Monte Carlo simulations are executed in a 1D model to generate probabilistic creep deformation, damage, and rupture data. This data is analyzed and the probabilistic parameters corresponding to extreme creep response are extracted. The ROM concept is applied where only the extreme conditions are applied in the 2D probabilistic prediction of a component. The probabilistic predictions between the 1D and 2D geometry is compared to assess ROM for creep. The accuracy of the probabilistic prediction employing the ROM approach will potentially reduce the time and cost of simulating complex engineering systems. Future studies will introduce multi-stage Sinh, stochasticity, and spatial uncertainty for improved prediction.

36 MATERIALS SCIENCE↗
DOE OSTI2023

FINITE ELEMENT MODEL MESH REFINEMENT EFFECTS ON QUALIFICATION OF NUCLEAR GRADE GRAPHITE COMPONENTS

The American Society of Mechanical Engineers (ASME) provides the full and simplified design-by-analysis probabilistic assessments for determining acceptance of nuclear grade graphite core components. The assessments can be characterized by three parts: (1) a component stress distribution, often determined by a finite element (FE) model; (2) a Weibull probability density function (pdf) that characterizes the experimental tensile strength distribution; and (3) the post-processor, which combines the FE model and the Weibull strength distribution in accordance with the full and simplified assessments to determine component acceptance. It is known that the level of mesh refinement in FE models can affect the modeled component’s calculated stress distribution. Depending on the component geometry, the stress distribution may converge with sufficient refinement. It was previously unknown whether the acceptance decision resulting from the full and simplified assessments might change even with sufficient mesh refinement. This study explores that question using experimental strength results for a dog-bone geometry for two graphite grades, IG-110 and PCEA. The simplified assessment has two criteria that must be met, the first limits the combined membrane stress by the allowable stress and the second limits the peak equivalent stress by the allowable stress scaled by the ratio of flexural to tensile strength. In the application of the simplified assessment, convergence of the peak equivalent stress required extreme mesh refinement, however, the acceptance decision was not affected. It is hypothesized that more complex geometries with stress concentrations may present mesh refinement effects on the simplified assessment acceptance decision. Mesh refinement did affect the acceptance decision in the full assessment for the applied pressure loadings in this study. This work suggests component stress distribution convergence is not a sufficient criteria for POF convergence in the full assessment and that mesh refinement should continue until the POF has converged, especially where the resulting POF is bordering the SRC acceptable POF limit.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Likelihood-Based Particle Identification in the Short-Baseline Near Detector

Accurate particle identification is crucial in any high-energy physics experiment, allowing scientists to understand the unique interactions and mechanisms at play in a detector. In this project, I develop and study a new particle identification (PID) algorithm for the Short-Baseline Near Detector, a likelihood-based approach, different from out current $\chi^2$ method. A likelihood estimation offers a more physically motivated strategy for PID. The distribution random energy losses of charged particles traveling through a medium are described by the Vavilov probability density function. By using this model, we can account for random energy losses and construct likelihood functions specific to each particle type, potentially enabling a more accurate method for PID.

Vanderwaal, Sophia [U. Alabama, Huntsville] (ORCID↗
DOE OSTI2026

Computing the Critical Temperature of the Affine-Transformed $D=3$ Ising Model Using Masked Autoregressive Flow

The simple Ising model provides a rich environment to build and study lattice field theories. As part of an ongoing project to construct a conformal field theory (CFT) on an arbitrarily curved manifold, in this work we develop methods to measure the critical temperature $β_c$ of the affine-transformed Ising model on the face-centered cubic (FCC) lattice. The main challenge in this endeavor is finding a computationally efficient and accurate method of interpolating and extrapolating Monte Carlo observables with respect to coupling coefficients and temperature. Herein, we compare two such methods. A traditional statistical approach uses the multiple histogram (MH) method, while a newer machine learning approach uses a masked autoregressive flow (MAF) to estimate the underlying probability density function of a set of observables. While the MH method is specifically designed to interpolate and extrapolate Monte Carlo observables, we find that MAF is a viable alternative for measuring $β_c$ with a computational cost that scales more favorably. Furthermore, we comment on additional advantages of MAF relevant to our work, such as extrapolating in system volume.

Svenson, Kai [Texas U.]↗
NASA NTRS1989

Probability density and exceedance rate functions of locally Gaussian turbulence

A locally Gaussian model of turbulence velocities is postulated which consists of the superposition of a slowly varying strictly Gaussian component representing slow temporal changes in the mean wind speed and a more rapidly varying locally Gaussian turbulence component possessing a temporally fluctuating local variance. Series expansions of the probability density and exceedance rate functions of the turbulence velocity model, based on Taylor's series, are derived. Comparisons of the resulting two-term approximations with measured probability density and exceedance rate functions of atmospheric turbulence velocity records show encouraging agreement, thereby confirming the consistency of the measured records with the locally Gaussian model. Explicit formulas are derived for computing all required expansion coefficients from measured turbulence records.

Mark, W. D.↗
NASA NTRS1991

Scalar dissipation and mixing in turbulent reacting flows

The mixing term that appears in probability density function-based formulations of the statistical behavior of turbulent reacting flows was studied with the use of direct numerical simulations of an irreversible, second-order, isothermal chemical reaction between initially segregated reactants in decaying, homogeneous turbulence. Three-dimensional, time-dependent pseudospectral calculations with 64-cubed Fourier modes were made as well as were Monte Carlo simulations of the joint concentration pdf equations for coalescence-dispersion (C/D) models. It was found that the development of the scalar microscales depends largely on the initial concentration distributions (both isotropic and nonisotropic distributions were used) and is relatively independent of the reaction rate constant. Joint concentration probability density functions were compared to predictions of D/D models that make use of parameters evaluated from the nonreacting or inert system.

Leonard, Andy D.↗
NASA NTRS1985

Birds and insects as radar targets - A review

A review of radar cross-section measurements of birds and insects is presented. A brief discussion of some possible theoretical models is also given and comparisons made with the measurements. The comparisons suggest that most targets are, at present, better modeled by a prolate spheroid having a length-to-width ratio between 3 and 10 than by the often used equivalent weight water sphere. In addition, many targets observed with linear horizontal polarization have maximum cross sections much better estimated by a resonant half-wave dipole than by a water sphere. Also considered are birds and insects in the aggregate as a local radar 'clutter' source. Order-of-magnitude estimates are given for many reasonable target number densities. These estimates are then used to predict X-band volume reflectivities. Other topics that are of interest to the radar engineer are discussed, including the doppler bandwidth due to the internal motions of a single bird, the radar cross-section probability densities of single birds and insects, the variability of the functional form of the probability density functions, and the Fourier spectra of single birds and insects.

Vaughn, C. R.↗
DOE OSTI2020

A Phenomenological Model for Cavitation

A phenomenological model of cavitation is presented, based on observations that both large relative negative pressures and large negative time derivatives of pressure are required for cavitation onset. We simulated two cavitation experiments to generate cavitation scaling parameters for relative pressure drop and rate of pressure drop. Our results show the model, while simple, is effective at reproducing results from laboratory experiments of cavitation. The parameters were then used in conjunction with a human surrogate computational model to predict, at any position within the head, the probability of intracranial cavitation caused by exposure to a blast event. The results suggest that the magnitude of blast overpressure observed in field data is sufficient to cause intracranial cavitation. Our analysis indicates that the helmeted head, when compared to the unhelmeted head configuration, results in a decrease but not elimination of cavitation exposure. When density functions of cavitation probability versus cumulative brain volume are combined with an injury severity model, the results show helmet efficacy at low and moderate risk levels. However, the convergence of unhelmeted and helmeted probability density functions at high-to-excessive risk thresholds indicates the helmet offers diminishing protection at elevated exposure levels, relative to the unhelmeted baseline. Future investigation and collaboration with neuroscience subject matter experts are needed to contextualize the current computational results. While the present work contributes specific and quantified predictions of intracranial cavitation location and severity, more research is required to apply our results to clinical settings with population-based brain injury subjects and controls. The relationship between our intracranial cavitation predictions with their anticipated clinical sequelae remains a topic in need of exploration.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

What Sets the Star Formation Rate of Molecular Clouds? The Density Distribution as a Fingerprint of Compression and Expansion Rates

We use a suite of 3D simulations of star-forming molecular clouds, with and without stellar feedback, magnetic fields, and driven turbulence, to study the compression and expansion rates of the gas as functions of density. We show that, around the mean density, supersonic turbulence promotes rough equilibrium between the amounts of compressing and expanding gas, consistent with continuous gas cycling between high- and low-density states. We find that the inclusion of protostellar jets produces rapidly expanding and compressing low-density gas. We find that the gas mass flux peaks at the transition between the lognormal and power-law forms of the density probability distribution function (PDF). This is consistent with the transition density tracking the post-shock density, which promotes an enhancement of mass at this density (i.e., shock compression and filament formation). At high densities, the gas dynamics are dominated by self-gravity: the compression rate in all of our runs matches the rate of the run with only gravity, suggesting that processes other than self-gravity have little effect at these densities. The net gas mass flux becomes constant at a density below the sink formation threshold, where it equals the star formation rate. The density at which the net gas mass flux equals the star formation rate is one order of magnitude lower than our sink threshold density, corresponds to the formation of the second power-law tail in the density PDF, and sets the overall star formation rates of these simulations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

An efficient method to estimate the probability density of seismic Green's functions

We present a computationally efficient method to approximate the probability distribution of seismic Green's functions given the uncertainty of an Earth model. The method is based on the Karhunen-Loève (KL) theorem and an approximation of the Green's function (or seismogram) covariance. Using Monte Carlo (MC) simulations as a control case, we demonstrate that our KL-based method can accurately reproduce a probability distribution of seismograms that results from an uncertain Earth model for a MC-derived seismogram covariance. We then describe a method to estimate the covariance of the seismograms resulting from those Earth models that is not based on MC simulations. We use the estimated Green's function covariance in conjunction with our KL-based method to produce a Green's function probability distribution, and compare that distribution to a Green's function probability distribution produced using a MC finite difference method. We find that the Green's function probability distribution approximated using our KL-based method generally mimics that produced using the MC simulations, especially for direct-arriving body waves. However the accuracy of the KL-based method generally decreases for later times in the simulated Green's function distribution.

58 GEOSCIENCES↗
NASA NTRS2003

Self-Supervised Dynamical Systems

Some progress has been made in a continuing effort to develop mathematical models of the behaviors of multi-agent systems known in biology, economics, and sociology (e.g., systems ranging from single or a few biomolecules to many interacting higher organisms). Living systems can be characterized by nonlinear evolution of probability distributions over different possible choices of the next steps in their motions. One of the main challenges in mathematical modeling of living systems is to distinguish between random walks of purely physical origin (for instance, Brownian motions) and those of biological origin. Following a line of reasoning from prior research, it has been assumed, in the present development, that a biological random walk can be represented by a nonlinear mathematical model that represents coupled mental and motor dynamics incorporating the psychological concept of reflection or self-image. The nonlinear dynamics impart the lifelike ability to behave in ways and to exhibit patterns that depart from thermodynamic equilibrium. Reflection or self-image has traditionally been recognized as a basic element of intelligence. The nonlinear mathematical models of the present development are denoted self-supervised dynamical systems. They include (1) equations of classical dynamics, including random components caused by uncertainties in initial conditions and by Langevin forces, coupled with (2) the corresponding Liouville or Fokker-Planck equations that describe the evolutions of probability densities that represent the uncertainties. The coupling is effected by fictitious information-based forces, denoted supervising forces, composed of probability densities and functionals thereof. The equations of classical mechanics represent motor dynamics that is, dynamics in the traditional sense, signifying Newton s equations of motion. The evolution of the probability densities represents mental dynamics or self-image. Then the interaction between the physical and metal aspects of a monad is implemented by feedback from mental to motor dynamics, as represented by the aforementioned fictitious forces. This feedback is what makes the evolution of probability densities nonlinear. The deviation from linear evolution can be characterized, in a sense, as an expression of free will. It has been demonstrated that probability densities can approach prescribed attractors while exhibiting such patterns as shock waves, solitons, and chaos in probability space. The concept of self-supervised dynamical systems has been considered for application to diverse phenomena, including information-based neural networks, cooperation, competition, deception, games, and control of chaos. In addition, a formal similarity between the mathematical structures of self-supervised dynamical systems and of quantum-mechanical systems has been investigated.

Zak, Michail↗
DOE OSTI2022

Data-driven Minimum Entropy Control for Stochastic Nonlinear Systems using the Cumulant-Generating Function

Here, we present a novel minimum entropy control algorithm for a class of stochastic nonlinear systems subjected to non-Gaussian noises. The entropy control can be considered as an optimization problem for the system randomness attenuation, but the mean value has to be considered separately. To overcome this disadvantage, a new representation of the system stochastic properties was given using the cumulant-generating function based on the moment-generating function, in which the mean value and the entropy was reflected by the shape of the cumulant-generating function. Based on the samples of the system output and control input, a time-variant linear model was identified, and the minimum entropy optimization was transformed to system stabilization. Then, an optimal control strategy was developed to achieve the randomness attenuation, and the boundedness of the controlled system output was analyzed. The effectiveness of the presented control algorithm was demonstrated by a numerical example. In this paper, a data-driven minimum entropy design is presented without pre-knowledge of the system model; entropy optimization is achieved by the system stabilization approach in which the stochastic distribution control and minimum entropy are unified using the same identified structure; and a potential framework is obtained since all the existing system stabilization methods can be adopted to achieve the minimum entropy objective.

42 ENGINEERING↗
NASA NTRS1994

AutoClass: A Bayesian Approach to Classification

We describe a Bayesian approach to the untutored discovery of classes in a set of cases, sometimes called finite mixture separation or clustering. The main difference between clustering and our approach is that we search for the "best" set of class descriptions rather than grouping the cases themselves. We describe our classes in terms of a probability distribution or density function, and the locally maximal posterior probability valued function parameters. We rate our classifications with an approximate joint probability of the data and functional form, marginalizing over the parameters. Approximation is necessitated by the computational complexity of the joint probability. Thus, we marginalize w.r.t. local maxima in the parameter space. We discuss the rationale behind our approach to classification. We give the mathematical development for the basic mixture model and describe the approximations needed for computational tractability. We instantiate the basic model with the discrete Dirichlet distribution and multivariant Gaussian density likelihoods. Then we show some results for both constructed and actual data.

Stutz, John↗