Deconvolution strategies for efficient parametric variance estimation in stochastic media transport problems.
Abstract not provided.
Geraci, Gianluca↗
SEARCH · Engineering Papers
Results for “stochastic 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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Numerical Uncertainty Estimation for Stochastic Particle-in-Cell Simulations Applied to Verification and Validation.
Abstract not provided.
Cartwright, Keith↗
Deconvolution strategies for efficient parametric variance estimation in stochastic media transport problems.
Abstract not provided.
Geraci, Gianluca↗
A Bayesian Approach for Estimating Uncertainty in Stochastic Economic Dispatch considering Wind Power Penetration
The increasing penetration of renewable energy resources in power systems, represented as random processes, converts the traditional deterministic economic dispatch problem into a stochastic one. To estimate the uncertainty in this stochastic economic dispatch problem for forecasting purposes, the conventional Monte-Carlo method is prohibitively time-consuming for practical applications. To overcome this problem, here we propose a novel Gaussian-process-emulator-based approach to quantify the uncertainty in the stochastic economic dispatch considering wind power penetration. Facing high-dimensional real-world data representing the correlated uncertainties from wind generation, a manifold-learning-based Isomap algorithm is proposed to efficiently represent the low-dimensional hidden probabilistic structure of the data. In this low-dimensional latent space, with Latin hypercube sampling as the computer experimental design, a Gaussian-process emulator is used, for the first time, to serve as a nonparametric, surrogate model for the original complicated stochastic economic dispatch model. This reduced-order representative allows us to evaluate the economic dispatch solver at sampled values with a negligible computational cost while maintaining a desirable accuracy. Simulation results conducted on the IEEE 118-bus test system reveal the impressive performance of the proposed method.
17 WIND ENERGY↗
Stochastic prediction techniques for wind shear hazard assessment
The threat of low-altitude wind shear has prompted development of aircraft-based sensors that measure winds directly on the aircraft's intended flight path. Measurements from these devices are subject to turbulence inputs and measurement error, as well as to the underlying wind profile. Stochastic estimators are developed to process on-board Doppler sensor measurements, producing optimal estimates of the winds along the path. A stochastic prediction technique is described to predict the hazard to the aircraft from the estimates as well as the level of uncertainty of the hazard prediction. The stochastic prediction technique is demonstrated in a simulated microburst wind shear environment. Use of the technique in a decision-making process is discussed.
Stratton, D. A.↗
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↗
Experimental Evidence that Stochasticity Contributes to Bacterial Composition and Functioning in a Decomposer Community
ABSTRACT Stochasticity emerging from random differences in replication, death, mutation, and dispersal is thought to alter the composition of ecological communities. However, the importance of stochastic effects remains somewhat speculative because stochasticity is not directly measured but is instead inferred from unexplained variations in beta-diversity. Here, we performed a field experiment to more directly disentangle the role of stochastic processes, environmental selection, and dispersal in the composition and functioning of a natural bacterial decomposer community in the field. To increase our ability to detect these effects, we reduced initial biological and environmental heterogeneity using replicate nylon litterbags in the field. We then applied two treatments: ambient/added precipitation and bacterial and fungal dispersal using “open” litterbags (made from 18.0-μm-pore-size mesh) (“open bacterial dispersal”) versus bacterial and fungal dispersal using “closed” litterbags (made from 22.0-μm-pore-size mesh) (“closed bacterial dispersal”). After 5 months, we assayed composition and functioning by the use of three subsamples from each litterbag to disentangle stochastic effects from residual variation. Our results indicate that stochasticity via ecological drift can contribute to beta-diversity in bacterial communities. However, residual variation, which had previously been included in stochasticity estimates, accounted for more than four times as much variability. At the same time, stochastic effects on beta-diversity were not attenuated at the functional level, as measured by genetic functional potential and extracellular enzyme activity. Finally, dispersal was found to interact with precipitation availability to influence the degree to which stochasticity contributed to functional variation. Together, our results demonstrate that the ability to quantify stochastic processes is key to understanding microbial diversity and its role in ecosystem functioning. IMPORTANCE Randomness can alter the diversity and composition of ecological communities. Such stochasticity may therefore obscure the relationship between the environment and community composition and hinder our ability to predict the relationship between biodiversity and ecosystem functioning. This study investigated the role of stochastic processes, environmental selection, and dispersal in microbial composition and its functioning on an intact field community. To do this, we used a controlled and replicated experiment that was similar to that used to study population genetics in the laboratory. Our study showed that, while the stochastic effects on taxonomic composition are smaller than expected, the degree to which stochasticity contributes to variability in ecosystem processes may be much higher than previously assumed.
59 BASIC BIOLOGICAL SCIENCES↗
Discrete-time demodulation of continuous-time signals.
Nonlinear stochastic estimation theory is applied to the problem of obtaining discrete-time demodulator structures for the common types of analog communication signals. A stochastic communication model is presented that can be treated with current results in estimation theory. Approximate algorithms are developed for the estimation problem that yield mathematically realizable receiver structures for the cases of AM, PC, and FM. The digital receivers yield performance characteristics that compare favorably with those of their analog counterparts.
Kelly, C. N.↗
Underlying Fundamentals of Kalman Filtering for River Network Modeling
The grand challenge of producing hydrometeorological estimates every time and everywhere has motivated the fusion of sparse observations with dense numerical models, with a particular interest on discharge in river modeling. Ensemble methods are largely preferred as they enable the estimation of error properties, but at the expense of computational load and generally with underestimations. These imperfect stochastic estimates motivate the use of correction methods, that is, error localization and inflation, although the physical justifications for their optimality are limited. The purpose of this study is to use one of the simplest forms of data assimilation when applied to river modeling and reveal the underlying mechanisms impacting its performance. Our framework based on assimilating daily averaged in situ discharge measurements to correct daily averaged runoff was tested over a 4-yr case study of two rivers in Texas. Results show that under optimal conditions of inflation and localization, discharge simulations are consistently improved such that the mean values of Nash–Sutcliffe efficiency are enhanced from211.32 to 0.55 at observed gauges and from212.24 to21.10 at validation gauges. Yet, parameters controlling the inflation and the localization have a large impact on the performance. Further investigations of these sensitivities showed that optimal inflation occurs when compensating exactly for discrepancies in the magnitude of errors while optimal localization matches the distance traveled during one assimilation window. These results may be applicable to more advanced data assimilation methods as well as for larger applications motivated by upcoming river-observing satellite missions, such as NASA’s Surface Water and Ocean Topography mission.
Streamflow↗
Probing for the Trace Estimation of a Permuted Matrix Inverse Corresponding to a Lattice Displacement
We report thatpProbing is a general technique that is used to reduce the variance of the Hutchinson stochastic estimator for the trace of the inverse of a large, sparse matrix A. The variance of the estimator is the sum of the squares of the off-diagonal elements of A -1 . Therefore, this technique computes probing vectors that when used in the estimator annihilate the largest off-diagonal elements. For matrices that display decay of the magnitude of |A$^{-1}_{ij}$| with the graph distance between nodes i and j, this is achieved through graph coloring of increasing powers A k . Equivalently, when a matrix stems from a lattice discretization, it is computationally beneficial to find a distance-k coloring of the lattice. Previously, a hierarchical coloring was proposed so that k can be increased at runtime as needed without discarding previous work. In this work, we study probing for the more general problem of computing the trace of a permutation of A -1 , say PA -1 . The motivation comes from lattice quantum chromodynamics (QCD), where we need to construct “disconnected diagrams” to extract flavor-separated generalized parton functions. In lattice QCD, where the matrix has a four-dimensional toroidal lattice structure, these nonlocal operators correspond to a PA -1 , where P is the permutation relating to some displacement $\vec{p}$ in one or more dimensions. We focus on a single dimension displacement (p), but our methods are general. We show that probing on A k or (PA) k does not annihilate the largest magnitude elements. To resolve this issue, our displacement-based probing works on PA k using a new coloring scheme that works directly on appropriately displaced neighborhoods on the lattice. We prove lower bounds on the number of colors needed and study the effect of this scheme on variance reduction, both theoretically and experimentally on a real-world lattice QCD calculation. We achieve orders of magnitude speedup over the unprobed or the naively probed methods.
97 MATHEMATICS AND COMPUTING↗
A stochastic approximation algorithm for estimating mixture proportions
A stochastic approximation algorithm for estimating the proportions in a mixture of normal densities is presented. The algorithm is shown to converge to the true proportions in the case of a mixture of two normal densities.
Sparra, J.↗
Trace Element Mass Flow Rates from U.S. Coal Fired Power Plants
Trace elements (TEs) exit coal-fired power plants (CFPPs) via solid, liquid, and gaseous waste streams. Estimating the TE concentrations of these waste streams is essential to selecting pollution controls and estimating emission reduction benefits. Our report presents a generalizable mass balance model for estimating TE mass flow rates in CFPP waste streams and evaluates model accuracy for the U.S. coal fleet given current data constraints. We stochastically estimate, using a bootstrapping approach, the 2015 plant-level mass flow rates of Hg, Se, As, and Cl to solid, liquid, and gas phase waste streams by combining publicly available data for combusted coal TE concentrations with estimates of TE partitioning within installed air pollution control processes. When compared with measured and reported data on TE mass flow rates, this model generally overestimates masses by 30–50%, with larger errors for Hg. The partitioning estimates are consistent for Se, As, and Cl removal from flue gas, but tend to underestimate Hg removal. While our model is suitable for first-order estimates of TE mass flows, future work to enhance model performance should focus on collecting and using new data on TE concentrations in the coal blend, where data quality is the weakest.
01 COAL, LIGNITE, AND PEAT↗
Improved Sampling Algorithms in the Risk-Informed Safety Margin Characterization Toolkit
The RISMC approach is developing advanced set of methodologies and algorithms in order to perform Probabilistic Risk Analyses (PRAs). In contrast to classical PRA methods, which are based on Event-Tree and Fault-Tree methods, the RISMC approach largely employs system simulator codes applied to stochastic analysis tools. The basic idea is to randomly perturb (by employing sampling algorithms) timing and sequencing of events and internal parameters of the system codes (i.e., uncertain parameters) in order to estimate stochastic parameters such as core damage probability. This approach applied to complex systems such as nuclear power plants requires to perform a series of computationally expensive simulation runs given a large set of uncertain parameters. These types of analysis are affected by two issues. Firstly, the space of the possible solutions (a.k.a., the issue space or the response surface) can be sampled only very sparsely, and this precludes the ability to fully analyze the impact of uncertainties on the system dynamics. Secondly, large amounts of data are generated and tools to generate knowledge from such data sets are not yet available. This report focuses on the first issue and in particular employs novel methods that optimize the information generated by the sampling process by sampling unexplored and risk-significant regions of the issue space: adaptive (smart) sampling algorithms. They infer system response from surrogate models constructed from existing samples and predict the most relevant location of the next sample. It is therefore possible to understand features of the issue space with a small number of carefully selected samples. In this report, we will present how it is possible to perform adaptive sampling using the RISMC toolkit and highlight the advantages compared to more classical sampling approaches such Monte-Carlo. We will employ RAVEN to perform such statistical analyses using both analytical cases but also another RISMC code: RELAP-7.
21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
Some tests of wet tropospheric calibration for the CASA Uno Global Positioning System experiment
Wet tropospheric path delay can be a major error source for Global Positioning System (GPS) geodetic experiments. Strategies for minimizing this error are investigted using data from CASA Uno, the first major GPS experiment in Central and South America, where wet path delays may be both high and variable. Wet path delay calibration using water vapor radiometers (WVRs) and residual delay estimation is compared with strategies where the entire wet path delay is estimated stochastically without prior calibration, using data from a 270-km test baseline in Costa Rica. Both approaches yield centimeter-level baseline repeatability and similar tropospheric estimates, suggesting that WVR calibration is not critical for obtaining high precision results with GPS in the CASA region.
Dixon, T. H.↗
The augmentation algorithm and molecular phylogenetic trees
Moore's (1977) augmentation procedure is discussed, and it is concluded that the procedure is valid for obtaining estimates of the total number of fixed nucleotide substitutions both theoretically and in practice, for both simulated and real data, and in agreement, for experimentally dense data sets, with stochastic estimates of the divergence, provided the restrictions on codon mutability resulting from natural selection are explicitly allowed for. Tateno and Nei's (1978) critique that the augmentation procedure has a systematic bias toward overestimation of the total number of nucleotide replacements is disputed, and a data analysis suggests that ancestral sequences inferred by the method of parsimony contain a large number of incorrectly assigned nucleotides.
Holmquist, R.↗
Electron thermal confinement in a partially stochastic magnetic structure
Using a high-repetition-rate Thomson scattering diagnostic, we observe a peak in electron temperature $T_e$ coinciding with the location of a large magnetic island in the Madison Symmetric Torus. Magnetohydrodynamic modeling of this quasi-single helicity plasma indicates that smaller adjacent islands overlap with and destroy the large island flux surfaces. The estimated stochastic electron thermal conductivity (≈30 m 2 /s) is consistent with the conductivity inferred from the observed $T_e$ gradient and ohmic heating power. Island-shaped $T_e$ peaks can result from partially stochastic magnetic islands.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Isovector and isoscalar tensor charges of the nucleon from lattice QCD
We present results for the iso-vector and flavor diagonal tensor charges $g$$^{u−d}_{T}$, $g$$^{u}_{T}$, $g$$^{d}_{T}$, and $g$$^{s}_{T}$ needed to probe novel tensor interactions at the TeV scale in neutron and nuclear β-decays and the contribution of the quark electric dipole moment (EDM) to the neutron EDM. The lattice QCD calculations were done using nine ensembles of gauge configurations generated by the MILC collaboration using the HISQ action with 2+1+1 dynamical flavors. These ensembles span three lattice spacings a ≈ 0.06, 0.09 and 0.12 fm and three quark masses corresponding to the pion masses M π ≈ 130, 220 and 310 MeV. Using estimates from these ensembles, we quantify all systematic uncertainties and perform a simultaneous extrapolation in the lattice spacing, volume and light quark masses for the connected contributions. The final estimates of the connected nucleon (proton) tensor charge for the iso-vector combination is $g$$^{u−d}_{T}$ = 1.020(76) in the MS scheme at 2 GeV. The additional disconnected quark loop contributions needed for the flavor-diagonal matrix elements are calculated using a stochastic estimator employing the truncated solver method with the all-mode-averaging technique. We find that the size of the disconnected contribution is smaller than the statistical error in the connected contribution. This allows us to bound the disconnected contribution and include it as an additional uncertainty in the flavor-diagonal charges. After a continuum extrapolation, we find $g$$^{u}_{T}$ = 0.774(66), $g$$^{d}_{T}$ = −0.233(28) and $g$$^{u+d}_{T}$ = 0.541(67). The strangeness tensor charge, that can make a significant contribution to the neutron EDM due to the large ratio ms/mu,d, is $g$$^{s}_{T}$ = 0.008(9) in the continuum limit.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Multigrid deflation for Lattice QCD
Computing the trace of the inverse of large matrices is typically addressed through statistical methods. Deflating out the lowest eigenvectors or singular vectors of the matrix reduces the variance of the trace estimator. This work summarizes our efforts to reduce the computational cost of computing the deflation space while achieving the desired variance reduction for Lattice QCD applications. Previous efforts computed the lower part of the singular spectrum of the Dirac operator by using an eigensolver preconditioned with a multigrid linear system solver. Despite the improvement in performance in those applications, as the problem size grows the runtime and storage demands of this approach will eventually dominate the stochastic estimation part of the computation. In this work, we propose to compute the deflation space in one of the following two ways. First, by using an inexact eigensolver on the Hermitian, but maximally indefinite, operator. Second, by exploiting the fact that the multigrid prolongator for this operator is rich in components toward the lower part of the singular spectrum. We show experimentally that the inexact eigensolver can approximate the lower part of the spectrum even for ill-conditioned operators. Also, the deflation based on the multigrid prolongator is more efficient to compute and apply, and, despite its limited ability to approximate the fine level spectrum, it obtains similar variance reduction on the trace estimator as deflating with approximate eigenvectors from the fine level operator.
97 MATHEMATICS AND COMPUTING↗