Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “probability density function”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 307 records · Page 17

Subcloud and Cloud-Base Latent Heat Fluxes during Shallow Cumulus Convection

Doppler and Raman lidar observations of vertical velocity and water vapor mixing ratio are used to probe the physics and statistics of subcloud and cloud-base latent heat fluxes during cumulus convection at the ARM Southern Great Plains (SGP) site in Oklahoma, United States. The statistical results show that latent heat fluxes increase with height from the surface up to ~0.8 Z i (where Z i is the convective boundary layer depth) and then decrease to ~0 at Z i . Peak fluxes aloft exceeding 500 W m −2 are associated with periods of increased cumulus cloud cover and stronger jumps in the mean humidity profile. These entrainment fluxes are much larger than the surface fluxes, indicating substantial drying over the 0–0.8 Z i layer accompanied by moistening aloft as the CBL deepens over the diurnal cycle. We also show that the boundary layer humidity budget is approximately closed by computing the flux divergence across the 0–0.8 Z i layer. Composite subcloud velocity and water vapor anomalies show that clouds are linked to coherent updraft and moisture plumes. The moisture anomaly is Gaussian, most pronounced above 0.8 Z i and systematically wider than the velocity anomaly, which has a narrow central updraft flanked by downdrafts. This size and shape disparity results in downdrafts characterized by a high water vapor mixing ratio and thus a broad joint probability density function (JPDF) of velocity and mixing ratio in the upper CBL. We also show that cloud-base latent heat fluxes can be both positive and negative and that the instantaneous positive fluxes can be very large (~10 000 W m −2 ). However, since cloud fraction tends to be small, the net impact of these fluxes remains modest.

54 ENVIRONMENTAL SCIENCES↗

Breakup dynamics in a pressure-swirl injector for urea-water solution applications: A computational study

The co-optimization of in-cylinder combustion and after-treatment technology has become a major aspect in engine design and development, with the goal of meeting the increasingly restrictive emission regulations in the transportation industry. Selective Catalytic Reduction is a robust technology to control the emission of NO x , and the injection of urea in water solution is the exhaust tailpipe is a key aspect of its operation. The proposed work uses high-fidelity Computational Fluid Dynamics to characterize the atomization dynamics of the liquid jet in relevant cross-flow conditions. The study focuses on a commercial low-pressure (9 bar) pressure-swirl injector which is characterized in its internal geometry through high-resolution X-ray micro-computational tomography. The internal two-phase flow has been modeled according to the volume-of-fluid approach in a large eddy simulation framework and validated against near-nozzle X-ray radiography measurement. Moreover, characterizing the breakup dynamics for the swirling hollow cone formation, and assessing the influence of the cross-flow in the breakup dynamics was completed. The results have been reported proposing Re-Oh maps and probability density functions of the spray kinematics. Higher cross-flow momentum generates an increase in the jet intact length and a reduction of the liquid droplet diameters. The axial momentum of the jet is affected by the cross-flow already in the near-nozzle region, determining a relevant deviation of the spray velocities. In conclusion, this work aims to inform the initialization of Eulerian-Lagrangian spray models through the assignment of droplet kinematics and static one-way coupling between volume-of-fluid results and Lagrangian spray parcels, to be used for system-size domain simulations.

33 ADVANCED PROPULSION SYSTEMS↗

Bayesian Monte Carlo Evaluation Framework for Cross Sections Nuclear Data and Integral Benchmark Experiments

The new Bayesian Monte Carlo (MC) evaluation framework described in this abstract has been conceived as an attempt to improve nuclear data evaluations of differential crosssection data by removing the following two approximations conventionally employed for nuclear data evaluations: all probability density functions (PDFs) of all data and model parameters, both prior and posterior, are assumed to be normal (i.e., Gaussian) PDFs, and all uncertainties and covariances are propagated using a linear approximation. With these approximations removed, the Bayesian MC (BMC) framework could be used to account for nonlinear effects and would enable improved evaluations of differential cross sections and IBE data that are presently performed based on the assumptions itemized above. The BMC would also improve upon the uniform sampling of IBE parameters from within ranges defined by their evaluated uncertainties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Bayesian Monte Carlo Evaluation Framework for Imperfect Nuclear Data

Bayesian evaluation of resolved resonance region (RRR) nuclear data has historically been carried out using the generalized least squares (GLS) formalism, as implemented in, e.g., SAMMY. We have recently developed a prototype of Bayesian Monte Carlo (BMC) evaluation framework, implemented using a Markov Chain Monte Carlo (MCMC) method with a Metropolis-Hastings (MH) acceptance criterion. This was done in order to remove the approximations underlying the conventional GLS evaluations, namely, the linear approximation, and the approximation that all probability density functions (PDFs) are of the normal kind. Recent works by others have used similar stochastic approaches to quantify cross section uncertainties from ENDF evaluated co-variances, and/or, from integral benchmark data, but those have not been conceived as an evaluation framework like the one presented here.

97 MATHEMATICS AND COMPUTING↗

Analysis of the nonlinear propagation of incoherent pulses

The nonlinear propagation of incoherent optical pulses is studied using a normalized nonlinear Schrödinger equation and statistical analysis, demonstrating various regimes that depend on the field’s coherence time and intensity. The quantification of the resulting intensity statistics using probability density functions shows that, in the absence of spatial effects, nonlinear propagation leads to an increase in the likelihood of high intensities in a medium with negative dispersion, and a decrease in a medium with positive dispersion. In the latter regime, nonlinear spatial self-focusing originating from a spatial perturbation can be mitigated, depending on the coherence time and amplitude of the perturbation. These results are benchmarked against the Bespalov–Talanov analysis applied to strictly monochromatic pulses.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Dynamical model for social distancing in the U.S. during the COVID-19 epidemic

Social distancing has led to a “flattening of the curve” in many states across the U.S. This is part of a novel, massive, global social experiment which has served to mitigate the COVID-19 pandemic in the absence of a vaccine or effective anti-viral drugs. Hence it is important to be able to forecast hospitalizations reasonably accurately. We propose on phenomenological grounds a random walk/generalized diffusion equation which incorporates the effect of social distancing to describe the temporal evolution of the probability of having a given number of hospitalizations. The probability density function is log-normal in the number of hospitalizations, which is useful in describing pandemics where the number of hospitalizations is very high. We used this insight and data to make forecasts for states using Monte Carlo methods. Back testing validates our approach, which yields good results about a week into the future. States are beginning to reopen at the time of submission of this paper and our forecasts indicate possible precursors of increased hospitalizations. However, the trends we forecast for hospitalizations as well as infections thus far show moderate growth. Additionally we studied the reproducibility in New York (Italian strain) and California (Wuhan strain). We find that even if there is a difference in the transmission of the two strains, social distancing has been able to control the progression of COVID 19.

97 MATHEMATICS AND COMPUTING↗

Beam loss modeling and mitigation due to intra-beam stripping

Intra-Beam Stripping (IBS) is a critical beam loss mechanism in high-intensity H- linacs and presents a significant limitation to increasing beam power. This work presents a computational framework to evaluate and mitigate IBS-induced beam loss along the Spallation Neutron Source (SNS) LINAC. Our calculation is based on an analytic theory and involves evaluation of a 9D integral using the Monte-Carlo technique. We first benchmarked our calculations against simplified, analytically solvable cases. We then applied our algorithm to Gaussian bunches with a known probability density function (PDF). We next expanded our algorithm to arbitrary bunch distributions using the Neural Spline Flow (NSF) models trained on PyORBIT tracking data. In the future, we plan to validate our algorithm experimentally and apply it to design IBS mitigation strategies.

Nln, Shivam [ORNL]↗

Modeling Framework for Bulk Electric Grid Impacts from HEMP E1 and E3 Effects (Tasks 3.1 Final Report)

This report presents a framework to evaluate the impact of a high-altitude electromagnetic pulse (HEMP) event on a bulk electric power grid. This report limits itself to modeling the impact of EMP E1 and E3 components. The co-simulation of E1 and E3 is presented in detail, and the focus of the paper is on the framework rather than actual results. This approach is highly conservative as E1 and E3 are not maximized with the same event characteristics and may only slightly overlap. The actual results shown in this report are based on a synthetic grid with synthetic data and a limited exemplary EMP model. The framework presented can be leveraged and used to analyze the impact of other threat scenarios, both manmade and natural disasters. This report d escribes a Monte-Carlo based methodology to probabilistically quantify the transient response of the power grid to a HEMP event. The approach uses multiple fundamental steps to characterize the system response to HEMP events, focused on the E1 and E3 components of the event. 1) Obtain component failure data related to HEMP events testing of components and creating component failure models. Use the component failure model to create component failure conditional probability density function (PDF) that is a function of the HEMP induced terminal voltage. 2) Model HEMP scenarios and calculate the E1 coupled voltage profiles seen by all system components. Model the same HEMP scenarios and calculate the transformer reactive power consumption profiles due to E3. 3) Sample each component failure PDF to determine which grid components will fail, due to the E1 voltage spike, for each scenario. 4) Perform dynamic simulations that incorporate the predicted component failures from E1 and reactive power consumption at each transformer affected by E3. These simulations allow for secondary transients to affect the relays/protection remaining in service which can lead to cascading outages. 5) Identify the locations and amount of load lost for each scenario through grid dynamic simulation. This can be an indication of the immediate grid impacts from a HEMP event. In addition, perform more detailed analysis to determine critical nodes and system trends. 6) To help realize the longer-term impacts, a security constrained alternating current optimal power flow (ACOPF) is run to maximize critical load served. This report describes a modeling framework to assess the systemic grid impacts due to a HEMP event. This stochastic simulation framework generates a large amount of data for each Monte Carlo replication, including HEMP location and characteristics, relay and component failures, E3 GIC profiles, cascading dynamics including voltage and frequency over time, and final system state. This data can then be analyzed to identify trends, e.g., unique system behavior modes or critical components whose failure is more likely to cause serious systemic effects. The proposed analysis process is demonstrated on a representative system. In order to draw realistic conclusions of the impact of a HEMP event on the grid, a significant amount of work remains with respect to modeling the impact on various grid components.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Derivation of the Future Time Equation for Analog, Non-Multiplying Monte Carlo Simulation

The expected computational time required to simulate a particle from a point in phase space through a Monte Carlo history, termed the expected future time, is found by solving the Future Time Equation (FTE). The expected future time may be useful when generating variance reduction parameters for a Monte Carlo simulation with a method such as Consistent Adjoint Driven Importance Sampling (CADIS). This report presents a detailed derivation of the Future Time Probability Density Function (FTPDF) and FTE for neutral particle Monte Carlo transport to aid future researchers. For simplicity, this derivation only considers analog transport in non-multiplying media.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Proof that Combining the Forced-collision and DXTRAN Monte Carlo Variance-reduction Techniques is Fair

This report provides mathematical proof that the MCNP DXTRAN (also known in other codes as forced-flight) and forced-collision variance-reduction techniques do not bias the expected value of Monte Carlo simulation estimates when combined. Proof is also provided that the techniques are unbiased when used independently. To prove that the techniques are unbiased, this report derives the first History Score Moment Equation (HSME) for non-multiplying media employing only forced collisions, only DXTRAN, and then both the variance-reduction techniques combined, as defined next. The HSMEs are found by forming the History Score Probability Density Functions (HSPDFs) and then taking the first score moment. Following its derivation, each HSME with a variance-reduction technique employed is reduced to the HSME for an analog simulation. Because the HSME represents the expected contribution to estimators in the simulation, reducing the HSME with variance reduction to the analog HSME shows that the simulation is unbiased despite the variance-reduction technique considered in the HSME. Analysis regarding higher-score moments of each technique is the subject of prior work and is not addressed herein. Throughout this work, the phase space p is defined to be the particle position x, direction-of-flight unit vector $\hat{Ω}$, energy E, and statistical weight w, $$p ≡ (x; \hat{Ω}; E; w).$$ A reduced phase-space excluding the statistical weight of the particle, $$r ≡ (x; \hat{Ω}; E),$$ is also used.

97 MATHEMATICS AND COMPUTING↗

Modeling Urban Acoustic Noise in the Las Vegas, NV Region

Ambient infrasound noise in quiet, rural environments has been extensively studied and well-characterized through noise models for several decades. More recently, creating noise models for high-noise rural environments has also become an area of active research. However, far less work has been done to create generalized low-frequency noise models for urban areas. The high ambient noise levels expected in cities and other highly populated areas means that these environments are regarded as poor locations for acoustic sensors, and historically, sensor deployment in urban areas were avoided for this reason. However, there are several advantages to placing sensors in urban environments, including convenience of deployment and maintenance, and increasingly, necessity, as more previously rural areas become populated. This study seeks to characterize trends in low-frequency urban noise by creating a background noise model for Las Vegas, NV, using the Las Vegas Infrasound Array (LVIA): a network of eleven infrasound sensors deployed throughout the city. Data included in this study spans from 2019 to 2021 and provides a largely uninterrupted record of noise levels in the city from 0.1–500 Hz, with only minor discontinuities on individual stations. We organize raw data from the LVIA sensors into hourly power spectral density (PSD) averages for each station and select from these PSDs to create frequency distributions for time periods of interest . These frequency distributions are converted into probability density functions (PDFs), which are then used to evaluate variations in frequency and amplitude over daily to seasonal timescale s. In addition to PDFs, the median, 5 th percentile, and 95 th percentile amplitude values are calculated across the entire frequency range. This methodology follows a well-established process for noise model creation.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗

Improving the Nomenclature Around Uncertainty [Slides]

This presentation finds that defining the marginal probability density function (PDF) for nuclear data is important. Additionally, the vocabulary of “means and covariances” and new GNDS 2.0 formats are limited to Gaussian (normal) representations— always incorrect—but clearly of practical significance when uncertainties are large (>40%). Finally, the Triage Solution: declare our current data as containing best estimate (mode) plus variance for a truncated normal or lognormal.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Modeling and Simulation of Fuel Dispersal During the Loss-of-Coolant Accident

This document is the compilation of the milestone portion to a larger end of project NEUP report. The executive summary of the modeling portion is provided below: In the event of cladding rupture during a postulated LOCA in a pressurized water reactor, fuel particles, along with fission gases, can be expelled into the reactor core from the fractured fuel rod, a phenomenon referred to as fuel dispersal. The initial stage of fuel dispersal is strongly influenced by the high-pressure ejection of fuel fragments, the size and geometry of the ruptured cladding, and the depressurization history of the fuel rod during the postulated LOCA transient. Depending on the location of the burst orifice relative to the quench front, the dispersal event represents an intricate three-phase flow and heat transfer phenomenon, where high-temperature fuel particles carried by the fission gases interact with the coolant within the narrow subchannels of the fuel assemblies, inducing localized phase change. Given the unique multiphysics nature of this phenomena, the current study develops a dedicated computational framework to predict the mass distribution and cooling of dispersing fuel particles, facilitating post-accident assessment and management of the fuel assemblies. Considering the scale of nuclear reactor applications, a continuum three-fluid model is proposed for simulating the transport of solids within the reactor core. With high-temperature fuel fragments within the liquid media, nucleation sites inducing phase changes are dispersed within the flow domain. Coupled with the fact that the transient dispersal event occurs on different time scales than other three-phase flow applications, this study derives a time-averaged three-fluid flow model without losing generality. The assumptions regarding the continuum treatment of the solid phase and the modeling of fuel dispersal behavior are incorporated to simplify the governing equations and derive applicable closure relations. The computational validation of the model was conducted using adiabatic experimental results obtained from ongoing research at Oregon State University, focusing on characterizing fuel dispersal behavior during simulated LOCA conditions. Settlement characteristics of the solids, quantified by the probability distribution of equivalent particles, closely matched the probability density functions reported in experimental studies. The transport of fuel particles within a scaled 5 × 5 lattice of a pressurized-water reactor rod bundle geometry was modeled through a two-fluid Eulerian framework. The required boundary conditions were evaluated from the fuel performance code BISON in a postulated large-break LOCA scenario. The modeling framework considered solid fuel particles as granular matter, interacting with the gaseous dry steam phase and fission gases through the governing interfacial momentum exchange between the participating fluids. The simulation results provided the volume fraction of the solids obtained at the bottom surface of the enclosing tank geometry. Postulated LOCA leading to fuel dispersal phenomena involves the strong coupling between fuel thermomechanics, cladding deformation, thermal-hydraulics, and fuel particle transport. Incorporation of such a strong coupling in numerical simulation is performed by coupling the multiphysics solvers. In the case of fuel dispersal, a strong coupled simulation can be performed by coupling the BISON code for fuel performance, the TRACE code for system-level thermal hydraulics, and fuel particle transport in Multiphysics Object-Oriented Simulation Environment (MOOSE). For such intricate infrastructure, the MOOSE Framework eases the data transfer between codes. The recent version of MOOSE has incorporated the Navier-Stokes module for the fluid flow. An exploratory exercise was done to gain familiarity with finite volume capabilities in the MOOSE framework to incorporate the Spalart-Allmaras (SA) turbulence model. New finite-volume and auxiliary kernels were introduced to assemble the SA transport equation, compute turbulent viscosity, and evaluate wall distance and diagnostic turbulence terms, fully integrated with existing Navier-Stokes modules. A turbulent lid-driven cavity at a Reynolds number of approximately 10,000 is used for verification. MOOSE shows the robust solver convergence and produces the turbulent features. But it underpredicts the velocity profile and turbulent quantities, emphasizing the need to develop improved SA near-wall treatments (e.g., low-Re corrections or wall functions) as a key direction for future work.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Determining SMEFT and PDF parameters simultaneously based on the CTEQ-TEA framework

The SM effective field theory (SMEFT) provides a model-independent and systematically improvable framework for new physics searches. In this talk, we outline our approach of simultaneously fitting SMEFT parameters and Probability Density Functions (PDFs) in an extension of the CT18 global analysis framework. To enhance the efficiency of our global fitting and Lagrange multiplier scans, we leverage machine-learning techniques. We focus on several representative operators relevant to top-quark pair production and jet production. Through this approach, we establish self-consistent limitations on the associated Wilson coefficients, and explore the correlations between these Wilson coefficients and the PDFs.

Shen, XiaoMin↗

Stochastic Distribution Control Theory-Its Potential Application in Risk Management in Financial Systems

Stochastic Distribution Control (SDC) theory [1], originated by the author in 1996, aims at developing modeling and control strategies for dynamic and non-Gaussian stochastic systems by controlling the shape of the probability density functions of some concerned variables and parameters in stochastic systems. It generalizes the capability of standard stochastic differential equations and can therefore be applied to generic non-Gaussian systems. Since it was established in 1996, it has found a wide spectrum of applications in non-Gaussian stochastic system control, data mining, filtering and optimization for uncertain systems. In this short opinion article, discussions will be made on potential applications of SDC theory to financial systems in terms of risk analysis and management.

97 MATHEMATICS AND COMPUTING↗

Non-Parametric Statistical Analysis of Current Waveforms through Power System Sensors

The protection, control, and monitoring of the power grid is not possible without accurate measurement devices. As the percentage of renewable energy sources penetrating the existing grid infrastructure increases, so do uncertainties surrounding their effects on the everyday operation of the power system. Many of these devices are sources of high-frequency transients. These transients may be useful for identifying certain events or behaviors otherwise not seen in traditional analysis techniques. Therefore, the ability of sensors to accurately capture these phenomena is paramount. In this work, two commercial-grade power system distribution sensors are investigated in terms of their ability to replicate high-frequency phenomena by studying their responses to three events: a current inrush, a microgrid “close-in”, and a fault on the terminals of a wind turbine. Kernel density estimation is used to derive the non-parametric probability density functions of these error distributions and their adequateness is quantified utilizing the commonly used root mean square error (RMSE) metric. It is demonstrated that both sensors exhibit characteristics in the high harmonic range that go against the assumption that measurement error is normally distributed.

47 OTHER INSTRUMENTATION↗

Large-scale Gravitational Lens Modeling with Bayesian Neural Networks for Accurate and Precise Inference of the Hubble Constant

We investigate the use of approximate Bayesian neural networks (BNNs) in modeling hundreds of time delay gravitational lenses for Hubble constant (H 0 ) determination. Here, our BNN was trained on synthetic Hubble Space Telescope quality images of strongly lensed active galactic nuclei with lens galaxy light included. The BNN can accurately characterize the posterior probability density functions (PDFs) of model parameters governing the elliptical power-law mass profile in an external shear field. We then propagate the BNN-inferred posterior PDFs into an ensemble H 0 inference, using simulated time delay measurements from a plausible dedicated monitoring campaign. Assuming well-measured time delays and a reasonable set of priors on the environment of the lens, we achieve a median precision of 9.3% per lens in the inferred H 0 . A simple combination of a set of 200 test lenses results in a precision of 0.5 km s –1 Mpc –1 (0.7%), with no detectable bias in this H 0 recovery test. The computation time for the entire pipeline—including the generation of the training set, BNN training and H0 inference—translates to 9 minutes per lens on average for 200 lenses and converges to 6 minutes per lens as the sample size is increased. Being fully automated and efficient, our pipeline is a promising tool for exploring ensemble-level systematics in lens modeling for H 0 inference.

79 ASTRONOMY AND ASTROPHYSICS↗

Constraints on White Dwarf Hydrogen Layer Masses Using Gravitational Redshifts

The hydrogen envelope is the outermost layer of a DA white dwarf; it makes up the entirety of the stellar photosphere, and yet its typical extent is difficult to model theoretically and remains poorly observationally constrained. As a result, hydrogen envelope mass is a substantial source of systematic uncertainty in the physical properties of white dwarfs, including overall masses and cooling ages. In this work, we fit a Gaussian mixture model to gravitational redshifts from high-resolution spectroscopy, paired with radius measurements from Gaia BP/RP spectra, to measure the mass–radius relation for a sample of 468 white dwarfs. Our results are in excellent agreement with the predicted mass–radius relations of state-of-the-art evolutionary models, including those from the MESA Isochrones and Stellar Tracks (MIST) library. We find that mass–radius relations such as those from MIST that assume a thick and mass-dependent hydrogen envelope are preferred by the observed probability density function over models that assume a hydrogen envelope of constant mass. Proper treatment of the evolution of white dwarf progenitors is thus important for accurately modeling the mass–radius relation. Our results indicate that gravitational redshift measurements of large samples of white dwarfs in wide binaries are promising probes of the hydrogen envelope masses of DA white dwarfs.

Astronomy and AstroPhysics↗