A Sharp Estimate on the Transient Time of Distributed Stochastic Gradient Descent
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Automation & Control Systems↗
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Results for “Distributed Estimation”
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.
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Radar-Based Bayesian Estimation of Ice Crystal Growth Parameters within a Microphysical Model
The potential for polarimetric Doppler radar measurements to improve predictions of ice microphysical processes within an idealized model–observational framework is examined. In an effort to more rigorously constrain ice growth processes (e.g., vapor deposition) with observations of natural clouds, a novel framework is developed to compare simulated and observed radar measurements, coupling a bulk adaptive-habit model of vapor growth to a polarimetric radar forward model. Bayesian inference on key microphysical model parameters is then used, via a Markov chain Monte Carlo sampler, to estimate the probability distribution of the model parameters. The statistical formalism of this method allows for robust estimates of the optimal parameter values, along with (non-Gaussian) estimates of their uncertainty. To demonstrate this framework, observations from Department of Energy radars in the Arctic during a case of pristine ice precipitation are used to constrain vapor deposition parameters in the adaptive habit model. The resulting parameter probability distributions provide physically plausible changes in ice particle density and aspect ratio during growth. A lack of direct constraint on the number concentration produces a range of possible mean particle sizes, with the mean size inversely correlated to number concentration. Consistency is found between the estimated inherent growth ratio and independent laboratory measurements, increasing confidence in the parameter PDFs and demonstrating the effectiveness of the radar measurements in constraining the parameters. Furthermore, the combined Doppler and polarimetric observations produce the highest-confidence estimates of the parameter PDFs, with the Doppler measurements providing a stronger constraint for this case.
54 ENVIRONMENTAL SCIENCES↗
Dark Energy Survey Year 3 results: calibration of lens sample redshift distributions using clustering redshifts with BOSS/eBOSS
ABSTRACT We present clustering redshift measurements for Dark Energy Survey (DES) lens sample galaxies used in weak gravitational lensing and galaxy clustering studies. To perform these measurements, we cross-correlate with spectroscopic galaxies from the Baryon Acoustic Oscillation Survey (BOSS) and its extension, eBOSS. We validate our methodology in simulations, including a new technique to calibrate systematic errors that result from the galaxy clustering bias, and we find that our method is generally unbiased in calibrating the mean redshift. We apply our method to the data, and estimate the redshift distribution for 11 different photometrically selected bins. We find general agreement between clustering redshift and photometric redshift estimates, with differences on the inferred mean redshift found to be below |Δz| = 0.01 in most of the bins. We also test a method to calibrate a width parameter for redshift distributions, which we found necessary to use for some of our samples. Our typical uncertainties on the mean redshift ranged from 0.003 to 0.008, while our uncertainties on the width ranged from 4 to 9 per cent. We discuss how these results calibrate the photometric redshift distributions used in companion papers for DES Year 3 results.
79 ASTRONOMY AND ASTROPHYSICS↗
Risk Assessment of Hydrogen Fuel Cell Electric Vehicles in Tunnels
The need to understand the risks and implications of traffic incidents involving hydrogen fuel cell electric vehicles in tunnels is increasing in importance with higher numbers of these vehicles being deployed. A risk analysis was performed to capture potential scenarios that could occur in the event of a crash and provide a quantitative calculation for the probability of each scenario occurring, with a qualitative categorization of possible consequences. The risk analysis was structured using an event sequence diagram with probability distributions on each event in the tree and random sampling was used to estimate resulting probability distributions for each end-state scenario. Here, the most likely consequence of a crash is no additional hazard from the hydrogen fuel (98.1–99.9% probability) beyond the existing hazards in a vehicle crash, although some factors need additional data and study to validate. These scenarios include minor crashes with no release or ignition of hydrogen. When the hydrogen does ignite, it is most likely a jet flame from the pressure relief device release due to a hydrocarbon fire (0.03–1.8% probability). This work represents a detailed assessment of the state-of-knowledge of the likelihood associated with various vehicle crash scenarios. This is used in an event sequence framework with uncertainty propagation to estimate uncertainty around the probability of each scenario occurring.
33 ADVANCED PROPULSION SYSTEMS↗
Investigation of Liquid Cloud Microphysical Properties of Deep Convective Systems: 2. Parameterization of Raindrop Size Distribution and its Application for Convective Rain Estimation
The liquid cloud microphysical properties for stratiform rain (SR) have been investigated in Part 1 of this series. Since convective rain (CR) has characteristics in raindrop size distribution (DSD) and precipitation that are distinct from SR, we investigate the CR properties in this study by using 20 hr of CR samples collected by 17 Automatic Parsivel Units disdrometers during the Midlatitude Continental Convective Clouds Experiment over the Atmospheric Radiation Measurement Southern Great Plains site. A full spectrum of DSD is constructed based on a total of 23 size channels (0.321 to 9.785 mm), and both Gamma and Exponential fitted functions are applied to extract the DSD shape parameters. Compared to SR properties, CR has distinct features including broader size range and narrower exponential slope parameter (λ E ). These results indicate that the assumption of constant exponential intercept parameter ( N 0E ) is inappropriate for CR rain rate estimates. Additionally, the subsetting scheme of the CR DSD spectra also has a strong impact on the Gamma/Exponential functions. Therefore, a new CR DSD parameterization scheme is developed by choosing the appropriate spectra subset with the constraint of rain rate and using the constant λ E instead of constant N 0E . With the input of the radar reflectivity at the lowest observed height, the newly calculated CR rain rates match well with the collocated surface rain gauge measurements (127 Mesonet stations and 17 Automatic Parsivel Units), while the rain rates calculated using traditional Z-R relationship are 3–4 times larger, indicating that constant λ E is a better assumption for CR DSD.
58 GEOSCIENCES↗
Taylor approximation variance reduction for approximation errors in PDE-constrained Bayesian inverse problems
In numerous applications, surrogate models are used as a replacement for accurate parameter-to-observable mappings when solving large-scale inverse problems governed by partial differential equations (PDEs). The surrogate model may be a computationally cheaper alternative to the accurate parameter-to-observable mappings and/or may ignore additional unknowns or sources of uncertainty. The Bayesian approximation error (BAE) approach provides a means to account for the induced uncertainties and approximation errors, i.e. the errors between the accurate parameter-to-observable mapping and the surrogate. The statistics of these errors are, however, in general unknown a priori, and are thus calculated using Monte Carlo sampling. Although the sampling is typically carried out offline, i.e. before considering the data, the process can still represent a computational bottleneck. In this work, we develop a scalable computational approach for reducing the costs associated with the sampling stage of the BAE approach. Specifically, we consider the Taylor expansion of the accurate and surrogate forward models with respect to the uncertain parameter fields either as a control variate for variance reduction or as a means to directly and efficiently approximate the mean and covariance of the approximation errors. We propose efficient methods for evaluating the expressions for the mean and covariance of the Taylor approximations based on linear(-ized) PDE solves. Furthermore, the proposed approach is independent of the dimension of the uncertain parameter, depending instead on the intrinsic dimension of the data, ensuring scalability to high-dimensional problems. The potential benefits of the proposed approach are demonstrated for two high-dimensional inverse problems governed by PDE examples, namely for the estimation of a distributed Robin boundary coefficient in a linear diffusion problem, and for a coefficient estimation problem governed by a nonlinear diffusion problem.
Bayesian approximation error↗
Approximate Boltzmann distributions in quantum approximate optimization
Approaches to compute or estimate the output probability distributions from the quantum approximate optimization algorithm (QAOA) are needed to assess the likelihood it will obtain a quantum computational advantage. We analyze output from QAOA circuits solving 7200 random MaxCut instances, with $n$ = 14–23 qubits and depth parameter $p$ ≤ 12 and find that the average basis state probabilities follow approximate Boltzmann distributions: The average probabilities scale exponentially with their energy (cut value), with a peak at the optimal solution. Furthermore, we describe the rate of exponential scaling or effective temperature in terms of a series with a leading-order term $T$ ~ $C$ min /$n$ $\sqrt{p}$, with $C$ min the optimal solution energy. Using this scaling, we generate approximate output distributions with up to 38 qubits and find these give accurate accounts of important performance metrics in cases we can simulate exactly.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Ultrasonic measurement of temperature distributions in extreme environments: Electrical power plants testing in utility-scale steam generators
Thermal heterogeneities within energy conversion and storage, material processing, nuclear processes, aerospace, and military applications are often inaccessible to characterization by insertion sensors. When sensor deployment is possible, conventional pointwise temperature probes quickly degrade when inserted into harsh environments typical of such processes. We developed spatially-resolved ultrasonic thermometry to noninvasively measure the spatial distributions of thermal properties in such applications, even when sizable thermal gradients are present. Our method divides the path of ultrasonic propagation into segments bound by echogenic features, which create echoes in pulse-echo mode, encoding the information about interior temperature distributions. We use the acquired ultrasonic responses to estimate the internal temperature distributions by solving an inverse problem or concatenating segmental estimates. This work describes the implementation and industrial testing of the developed method at a coal-fired electrical power generation plant. We inserted an echogenically segmented Inconel 625 waveguide into the combustion zone of the utility-scale boiler and continuously acquired ultrasonic data while keeping sensitive components away from the damaging combustion environment. The accuracy of the time-dependent temperature distributions reconstructed from the ultrasonic measurements was comparable to that of thermocouples. The resiliency of ultrasonic thermometry to harsh combustion conditions was far superior to conventional insertion sensors. The measurements obtained during plant operation captured daily steam generation cycles in response to changing customer demand and intermittent contributions of renewable power sources to the power grid. These measurements have revealed new insights into the relationship between the dynamic power generation load and the conditions inside the steam generator. As a result, the successful industrial testing of spatially-resolved ultrasonic thermometry in solids indicates that the developed technology has matured to become an attractive alternative to conventional sensing in solving challenging problems of long-term thermal characterizations in extreme environments.
42 ENGINEERING↗
Bayesian Assimilation of Multiscale Precipitation Data and Sparse Ground Gauge Observations in Mountainous Areas
Estimating the spatial distribution of precipitation is important for understanding ecohydrological processes at catchment scales. However, this estimation is difficult in mountainous areas because ground-based observation stations are often sparsely located and do not represent the spatial variability of precipitation. In this study, we develop a Bayesian assimilation method based on data collected on the Tibetan Plateau from 1980 to 2014 to estimate monthly and daily precipitation. To accomplish this, point-scale ground meteorological observations are combined with large-scale precipitation data such as satellite observations or reanalysis data. First, we remove the terrain effects from ground observations by fitting the precipitation data as functions of elevation, and then we spatially interpolate the residuals to 5-km-resolution grids to obtain monthly and daily precipitation. Additionally, we use Tropical Rainfall Measuring Mission (TRMM) satellite observations and ERA-Interim reanalysis data. Cross-validation methods are used to evaluate our method; the results show that our method not only captures the change in precipitation with terrain but also significantly reduces the associated uncertainty. The improvements are more evident in the main river source areas on the edge of the Tibetan Plateau, where elevation changes dramatically, and in high-altitude areas, where the ground gauges are sparse compared with those in low-altitude areas. Our assimilation method is applicable to other regions and is particularly useful for mountainous watersheds where ground meteorological stations are sparse and precipitation is considerably influenced by terrain.
54 ENVIRONMENTAL SCIENCES↗
Radiation Protection Around High-intensity Laser Interactions with Solid Targets
Interaction of a high-intensity optical laser with a solid target can generate an ionizing radiation hazard in the form of high-energy "hot" electrons and bremsstrahlung, resulting from hot electrons interacting with the target itself and the surrounding target chamber. Previous studies have characterized the bremsstrahlung dose yields generated by such interactions for lasers in the range of 10 17 to 10 22 W cm -2 using particle-in-cell code EPOCH and Monte Carlo code FLUKA. Electron measurements based on a depth-dose approach are presented for two laser intensities, which indicate a Maxwellian distribution is more suitable for estimating the hot electrons' energy distribution. Also, transmission factors for the resulting bremsstrahlung for common shielding materials are calculated with FLUKA, and shielding tenth-value-layer thicknesses are also derived. In combination with the bremsstrahlung dose yield, the tenth-value layers provide radiation protection programs the means to evaluate radiation hazards and design shielding for high-intensity laser facilities.
61 RADIATION PROTECTION AND DOSIMETRY↗
Probabilistic Zonal Reserve Requirements for Improved Energy Deliverability with Wind Power
In power systems with high penetration of renewable energy resources, uncertainty and variability of these stochastic resources introduce additional challenges for the operation of power systems. To improve the power system's reliability in the face of uncertainty, reserves are required as additional generation capacity to rebalance the power system following random disturbances. However, reserve deliverability is not guaranteed, because it may encounter potential transmission line congestion. Zonal reserve requirements can address this issue, but operators lack efficient ways to allocate reserves to zones while accounting for wind power forecast uncertainty. Herein we propose a methodology for probabilistic zonal reserve requirements to address wind power forecast uncertainties. This method estimates the probability distribution of line flows based on the system generation margin and injection shift factor. This estimate is then used to construct pre-defined and post-zonal reserve requirements. Case studies demonstrate that the proposed method efficiently schedules energy and reserves to balance energy and manage deliverability with wind power forecast uncertainty.We also discuss operational implications of the proposed method.
17 WIND ENERGY↗
Estimation of extreme temperatures in direct solar methane pyrolysis within a porous medium
Porous media have wide application in renewable energy conversion processes, such as solar-thermal fuels production and decarbonization. Heat transport mechanisms within porous media can be highly complex, particularly under extreme conditions encountered in concentrated solar thermal reactors in which direct measurement of temperature is challenging. Here, we implement and report an inverse heat conduction model to estimate the temperature distribution throughout a porous substrate domain in a direct solar methane pyrolysis process. By solving a two-dimensional heat transfer problem and applying an inverse optimization algorithm, we estimate the quasi-steady state spatial temperature distribution in a fibrous porous carbon substrate. The results are validated indirectly by experimentally measured graphite deposition and a simplified reaction kinetic model.
finite difference method↗
Dynamic signal recovery in distribution grids using compressive lossy measurements
Distribution system state estimation requires reliable aggregation of the measured data. However, the large volume of the measured data imposes a significant stress on the underlying communication infrastructure. With the challenges associated with measurement availability, current distribution systems are typically unobservable. To cope with the unobservability issue, compressive sensing theory allows us to recover system state information from a small number of measurements provided the states of the distribution system exhibit sparsity. In this paper, we evaluate the robustness of an updated Kalman filtered modified compressive sensing (KF-ModCS) technique that dynamically estimates the grid states using a small fraction of measured data. In practice, measurements used for sparsity based state estimation may also be intermittent due to communication network induced losses. Further, to understand the effect of packet losses on KF-ModCS, we provide an upper bound for the expected variances of the state estimation error for a given rate of information loss. This upper bound is further improved if the support set of the sparse signal that characterizes the state dynamics does not change over time and/or the reduced model is observable. Simulations based on two practical data sets collected from actual customers in a distribution grid validate the theoretical results.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Adversarial sampling of unknown and high-dimensional conditional distributions
Many engineering problems require the prediction of realization-to-realization variability or a refined description of modeled quantities. In that case, it is necessary to sample elements from unknown high-dimensional spaces with possibly millions of degrees of freedom. While there exist methods able to sample elements from probability density functions (PDF) with known shapes, several approximations need to be made when the distribution is unknown. In this paper the sampling method, as well as the inference of the underlying distribution, are both handled with a data-driven method known as generative adversarial networks (GAN), which trains two competing neural networks to produce a network that can effectively generate samples from the training set distribution. In practice, it is often necessary to draw samples from conditional distributions. When the conditional variables are continuous, only one (if any) data point corresponding to a particular value of a conditioning variable may be available, which is not sufficient to estimate the conditional distribution. This work handles this problem using an a priori estimation of the conditional moments of a PDF. Herein, two approaches, stochastic estimation, and an external neural network are compared for computing these moments; however, any preferred method can be used. The algorithm is demonstrated in the case of the deconvolution of a filtered turbulent flow field. It is shown that all the versions of the proposed algorithm effectively sample the target conditional distribution with minimal impact on the quality of the samples compared to state-of-the-art methods. Additionally, the procedure can be used as a metric for the diversity of samples generated by a conditional GAN (cGAN) conditioned with continuous variables.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
A baseline for ensemble-based, time-resolved inflow reconstruction for a single turbine using large-eddy simulations and latent diffusion models
We are interested in reconstructing winds flowing through a turbine on a second-by-second basis over a 10 min window. Previously, we developed a machine learning algorithm that takes in a snapshot of wind speed measurements and generates ensembles of three-dimensional wind field estimates. Here, we use these estimates as initial conditions in large-eddy simulations and reconstruct atmospheric and turbine response dynamic quantities in a synthetic field campaign. In doing so, we establish a baseline for model validation that future time-aware data assimilation techniques will be compared to. In turbine-free case studies, ground truth wind speeds consistently fall within our estimated wind speed distribution for the first 100 s after the simulation start. In simulations with turbines, the wind estimates show a small bias of 0.10 m s 1 and good correlation of 0.80 during the first 100 s. During this window, our estimates of the Blade 1 bending moment and generator power typically span the ground truth, with the estimate of the former performing better overall. In summary, this approach shows promise as a stand-alone technique for reconstructing real-world inflow and turbine dynamics in 1-2 min windows and as a foundation for future time-aware data assimilation techniques.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
A stochastic sampling approach to zircon eruption age interpretation
The accessory mineral zircon is widely used to constrain the timing of igneous processes such as magma crystallisation or eruption. However, zircon U-Pb ages record zircon crystallisation, which is not an instantaneous process. Zircon saturation calculations link zircon crystallisation, temperature, and melt fraction, allowing for the estimation of zircon crystallisation distributions as a function of time or temperature. Such distributions provide valuable prior information, enabling Bayesian estimates of magma eruption time and allowing for comparison of the relative accuracy of common weighted-mean and youngest-zircon age interpretations with synthetic datasets. We find that both traditional interpretations carry a risk of underestimating the uncertainty in eruption age; a low mean square of weighted deviates (MSWD) does not guarantee the accuracy of weighted-mean interpretations. In the absence of independent confirmation that crystallisation timescale is short relative to analytical uncertainties, a Bayesian approach frequently provides the most accurate results and is least likely to underestimate uncertainty. Finally, since U-Pb zircon studies now routinely resolve geological age dispersion due to increasing analytical precision, such considerations are increasingly critical to future progress in resolving rates and dates of Earth processes.
58 GEOSCIENCES↗
Characterization of runaway electron impact on instrumented sacrificial limiters on DIII-D
Instrumented sacrificial limiter heads, both domed (proud) and flat (flush) are used in DIII-D runaway electron (RE) wall strikes to study the wall impact dynamics with high spatial and time resolution. The approximate structure of the RE wetted area and heating depth on the domed limiter heads were predicted qualitatively using orbit-tracking simulations, although a strong left–right asymmetry (about the magnetic field direction) was not captured well by the simulations. It is hypothesized that this difference is perhaps due to the local 3D magnetic field perturbation of the dome limiter head. The average kinetic energy K and pitch angle θ of REs striking the limiter head were estimated from the spatial distribution of local HXR emission and were estimated to be roughly K ≈ 4 MeV and θ ≈ 0.2 rad. These values are roughly consistent with in-plasma values estimated before the loss event, indicating that RE kinetic energy and pitch angle are not drastically altered when transporting to the wall. Large shot–shot variations (1–10 kJ) in energy deposition into the limiter head were observed and were explained by shot–shot variations in locked magneto-hydrodynamics mode toroidal phase. For the largest deposited energies (10 kJ), graphite material failure and explosive dust release was observed, and the depth of material failure at higher energy deposition was successfully reproduced using modelling of volumetric energy deposition and brittle failure. The presence of energetic (keV) level ion impact during the RE wall strike was confirmed by three different surface analysis techniques. The ratio of energetic ion to RE flux appears to be larger on flat surfaces within the RE wetted area, although the energetic ion flux and total energy flux due to energetic ions have not yet been quantified.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Multimodal fission from self-consistent calculations
When multiple fission modes coexist in a given nucleus, distinct fragment yield distributions appear. Multimodal fission has been observed in a number of fissioning nuclei spanning the nuclear chart, and this phenomenon is expected to affect the nuclear abundances synthesized during the rapid neutron-capture process (𝑟-process). In this study, we generalize the previously proposed hybrid model for fission-fragment yield distributions to predict competing fission modes and estimate the resulting yield distributions. Here, our framework allows for a comprehensive large-scale calculation of fission-fragment yields suited for 𝑟-process nuclear network studies. Nuclear density functional theory is employed to obtain the potential energy and collective inertia tensor on a multidimensional collective space defined by mass multipole moments. Fission pathways and their relative probabilities are determined using the nudged elastic band method. Based on this information, mass and charge fission yields are predicted using the recently developed hybrid model. Fission properties of fermium isotopes are calculated in the axial quadrupole-octupole collective space for three energy density functionals (EDFs). Disagreement between the EDFs appears when multiple fission modes are present. Within our framework, the UNEDF1 HFB EDF agrees best with experimental data. Calculations in the axial quadrupole-octupole-hexadecapole collective space improve the agreement with the experiment for SkM*. We also discuss the sensitivity of fission predictions on the choice of EDF for several superheavy nuclei. Fission-fragment yield predictions for nuclei with multiple fission modes are sensitive to the underlying EDF. For large-scale calculations in which a minimal number of collective coordinates is considered, UNEDF1 HFB provides the best description of experimental data, though the sensitivity motivates robust quantification of the uncertainties of the theoretical model.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗