Search NASA⌕ Search

SEARCH · Search NASA

Results for “variance”

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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Fringe biasing: A variance reduction technique for optically thick meshes

Fringe biasing is a stratified sampling scheme applicable to Monte Carlo thermal radiation transport codes. The thermal emission source in optically thick cells is partitioned into separate contributions from the cell interiors (where the likelihood of the particles escaping the cells is virtually zero) and the 'fringe' regions close to the cell boundaries. Thermal emission in the cell interiors can now be modelled with fewer particles, the remaining particles being concentrated in the fringes so that they are more likely to contribute to the energy exchange between cells. Unlike other techniques for improving the efficiency in optically thick regions (such as random walk and discrete diffusion treatments), fringe biasing has the benefit of simplicity, as the associated changes are restricted to the sourcing routines with the particle tracking routines being unaffected. This paper presents an analysis of the potential for variance reduction achieved from employing the fringe biasing technique. The aim of this analysis is to guide the implementation of this technique in Monte Carlo thermal radiation codes, specifically in order to aid the choice of the fringe width and the proportion of particles allocated to the fringe (which are interrelated) in multi-dimensional simulations, and to confirm that the significant levels of variance reduction achieved in simulations can be understood by studying the behaviour for simple test cases. The variance reduction properties are studied for a single cell in a slab geometry purely absorbing medium, investigating the accuracy of the scalar flux and current tallies on one of the interfaces with the surrounding medium. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

Variance Analysis of Wind and Natural Gas Generation under Different Market Structures: Some Observations

An important area of current research is whether large-scale penetration of variable renewable generation such as wind and solar power pose economic and operational burdens on the electricity system. In such scenarios, this issue has also raised considerable interest in the potential role and value of electricity storage as a method of mitigating variability in generation associated with the inherently variable nature of these forms of generation. At the same time, a number of studies have pointed to the potential benefits of renewable generation as a hedge against the volatility and potential escalation of fossil fuel prices. Prior research and this work suggest that the lack of correlation of renewable energy costs with fossil fuel prices means that adding large amounts of wind or solar generation may also reduce the volatility of system-wide electricity costs. Such variance reduction in overall system costs may be of significant value to consumers due to risk aversion. In contrast to this observation, other studies have focused on returns in restructured markets and noted that, in deregulated markets, baseload natural gas power generation may be relatively more attractive to investors because-unlike wind generation-peak power prices are often strongly correlated to natural gas prices. The analysis in this report recognizes that the potential value of risk mitigation associated with wind generation and natural gas generation may depend on whether one considers the consumer's perspective or the investor's perspective and whether the market is regulated or deregulated. We analyze the risk and return trade-offs for wind and natural gas generation for deregulated markets based on hourly prices and load over a 10-year period using historical data in the PJM Interconnection (PJM)2 from 1999 to 2008. Similar analysis is then simulated and evaluated for regulated markets under certain assumptions. Estimating the absolute value, as opposed to the relative value, of variance reduction will also depend on assumptions about risk aversion and other consumer preferences, such as loss aversion, and this is discussed.

03 NATURAL GAS↗
NASA NTRS2013

View-angle-dependent AIRS Cloudiness and Radiance Variance: Analysis and Interpretation

Upper tropospheric clouds play an important role in the global energy budget and hydrological cycle. Significant view-angle asymmetry has been observed in upper-level tropical clouds derived from eight years of Atmospheric Infrared Sounder (AIRS) 15 um radiances. Here, we find that the asymmetry also exists in the extra-tropics. It is larger during day than that during night, more prominent near elevated terrain, and closely associated with deep convection and wind shear. The cloud radiance variance, a proxy for cloud inhomogeneity, has consistent characteristics of the asymmetry to those in the AIRS cloudiness. The leading causes of the view-dependent cloudiness asymmetry are the local time difference and small-scale organized cloud structures. The local time difference (1-1.5 hr) of upper-level (UL) clouds between two AIRS outermost views can create parts of the observed asymmetry. On the other hand, small-scale tilted and banded structures of the UL clouds can induce about half of the observed view-angle dependent differences in the AIRS cloud radiances and their variances. This estimate is inferred from analogous study using Microwave Humidity Sounder (MHS) radiances observed during the period of time when there were simultaneous measurements at two different view-angles from NOAA-18 and -19 satellites. The existence of tilted cloud structures and asymmetric 15 um and 6.7 um cloud radiances implies that cloud statistics would be view-angle dependent, and should be taken into account in radiative transfer calculations, measurement uncertainty evaluations and cloud climatology investigations. In addition, the momentum forcing in the upper troposphere from tilted clouds is also likely asymmetric, which can affect atmospheric circulation anisotropically.

AIRS↗
NASA NTRS2017

LMI-Based Fuzzy Optimal Variance Control of Airfoil Model Subject to Input Constraints

This paper presents a study of fuzzy optimal variance control problem for dynamical systems subject to actuator amplitude and rate constraints. Using Takagi-Sugeno fuzzy modeling and dynamic Parallel Distributed Compensation technique, the stability and the constraints can be cast as a multi-objective optimization problem in the form of Linear Matrix Inequalities. By utilizing the formulations and solutions for the input and output variance constraint problems, we develop a fuzzy full-state feedback controller. The stability and performance of the proposed controller is demonstrated through its application to the airfoil flutter suppression.

optimal variance control↗
DOE OSTI2012

VARIANCE ESTIMATION IN DOMAIN DECOMPOSED MONTE CARLO EIGENVALUE CALCULATIONS

The number of tallies performed in a given Monte Carlo calculation is limited in most modern Monte Carlo codes by the amount of memory that can be allocated on a single processor. By using domain decomposition, the calculation is now limited by the total amount of memory available on all processors, allowing for significantly more tallies to be performed. However, decomposing the problem geometry introduces significant issues with the way tally statistics are conventionally calculated. In order to deal with the issue of calculating tally variances in domain decomposed environments for the Shift hybrid Monte Carlo code, this paper presents an alternative approach for reactor scenarios in which an assumption is made that once a particle leaves a domain, it does not reenter the domain. Particles that reenter the domain are instead treated as separate independent histories. This assumption introduces a bias that inevitably leads to under-prediction of the calculated variances for tallies within a few mean free paths of the domain boundaries. However, through the use of different decomposition strategies, primarily overlapping domains, the negative effects of such an assumption can be significantly reduced to within reasonable levels.

42 ENGINEERING↗
DOE OSTI2015

A variance-based decomposition and global sensitivity index method for uncertainty quantification: Application to retrieved ice cloud properties

This study develops a novel uncertainty quantification (UQ) method for cloud microphysical property retrievals using variance-based decomposition and global sensitivity index. In this UQ framework, empirical orthogonal function (EOF) analysis is applied to the U.S. Department of Energy Atmospheric Radiation Measurement (ARM) ground-based observations, which are the inputs for the cloud retrieval studied here. The principal components (PCs) in the EOF expansion are parameterized as random input variables, and hence, the input dimension is greatly reduced (up to a factor of 50), allowing large ensemble of random samplings. The EOF expansion improves the accuracy of the uncertainty estimation by taking into account the cross correlations in the input data profiles. Here, this method enables a probabilistic representation of a retrieval process by adding normally distributed perturbations into PCs of sample means of input data profiles within a time window. Therefore, it effectively facilitates objective validation of climate models against cloud retrievals under a probabilistic framework for rigorous statistical inferences. Moreover, the variance-based global sensitivity index analysis, part of this method, attributes the output uncertainties to each individual source, thus providing directions for improving retrieval algorithms and observation strategies. For demonstration, we apply this method to quantify the uncertainties of the ARM program's baseline cloud retrieval algorithm for an ice cloud case observed at the Southern Great Plains site on 9 March 2000.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

A surface layer variance heat budget for ENSO

Abstract Characteristics of the El Niño–Southern Oscillation (ENSO), such as frequency, propagation, spatial extent, and amplitude, strongly depend on the climatological background state of the tropical Pacific. Multidecadal changes in the ocean mean state are hence likely to modulate ENSO properties. To better link background state variations with low‐frequency amplitude changes of ENSO, we develop a diagnostic framework that determines locally the contributions of different physical feedback terms on the ocean surface temperature variance. Our analysis shows that multidecadal changes of ENSO variance originate from the delicate balance between the background‐state‐dependent positive thermocline feedback and the atmospheric damping of sea surface temperatures anomalies. The role of higher‐order processes and atmospheric and oceanic nonlinearities is also discussed. The diagnostic tool developed here can be easily applied to other tropical ocean areas and climate phenomena.

Boucharel, Julien↗
DOE OSTI2013

Clock Synchronization in High-end Computing Environments: A Strategy for Minimizing Clock Variance at Runtime

We present a new software-based clock synchronization scheme that provides high precision time agreement among distributed memory nodes. The technique is designed to minimize variance from a reference chimer during runtime and with minimal time-request latency. Our scheme permits initial unbounded variations in time and corrects both slow and fast chimers (clock skew). An implementation developed within the context of the MPI message passing interface is described, and time coordination measurements are presented. Among our results, the mean time variance for a set of nodes improved from 20.0 milliseconds under standard Network Time Protocol (NTP) down to 2.29 secs under our scheme.

clock synchronization↗
DOE OSTI2013

Continuous-Time Mean-Variance Portfolio Selection with Random Horizon

This paper examines the continuous-time mean-variance optimal portfolio selection problem with random market parameters and random time horizon. Treating this problem as a linearly constrained stochastic linear-quadratic optimal control problem, I explicitly derive the efficient portfolios and efficient frontier in closed forms based on the solutions of two backward stochastic differential equations. Some related issues such as a minimum variance portfolio and a mutual fund theorem are also addressed. All the results are markedly different from those in the problem with deterministic exit time. A key part of my analysis involves proving the global solvability of a stochastic Riccati equation, which is interesting in its own right.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Mean-Variance Hedging on Uncertain Time Horizon in a Market with a Jump

In this work, we study the problem of mean-variance hedging with a random horizon T∧τ, where T is a deterministic constant and τ is a jump time of the underlying asset price process. We first formulate this problem as a stochastic control problem and relate it to a system of BSDEs with a jump. We then provide a verification theorem which gives the optimal strategy for the mean-variance hedging using the solution of the previous system of BSDEs. Finally, we prove that this system of BSDEs admits a solution via a decomposition approach coming from filtration enlargement theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Uncertainty quantification for radiation measurements: Bottom-up error variance estimation using calibration information

One example of top-down uncertainty quantification (UQ) involves comparing two or more measurements on each of multiple items. One example of bottom-up UQ expresses a measurement result as a function of one or more input variables that have associated errors, such as a measured count rate, which individually (or collectively) can be evaluated for impact on the uncertainty in the resulting measured value. In practice, it is often found that top-down UQ exhibits larger error variances than bottom-up UQ because some error sources are present in the fielded assay methods used in top-down UQ that are not present (or not recognized) in the assay studies used in bottom-up UQ One would like better consistency between the two approaches in order to claim understanding of the measurement process. The purpose of this paper is to refine bottom-up uncertainty estimation by using calibration information so that if there are no unknown error sources, the refined bottom-up uncertainty estimate will agree with the top-down uncertainty estimate to within a specified tolerance. Then, in practice, if the top-down uncertainty estimate is larger than the refined bottom-up uncertainty estimate by more than the specified tolerance, there must be omitted sources of error beyond those predicted from calibration uncertainty. The paper develops a refined bottom-up uncertainty approach for four cases of simple linear calibration: (1) inverse regression with negligible error in predictors, (2) inverse regression with non negligible error in predictors, (3) classical regression followed by inversion with negligible error in predictors, and (4) classical regression followed by inversion with non-negligible errors in predictors. Our illustrations are of general interest, but are drawn from our experience with nuclear material assay by non-destructive assay. The main example we use is gamma spectroscopy that applies the enrichment meter principle. Previous papers that ignore error in predictors have shown a tendency for inverse regression to have lower error variance than classical regression followed by inversion. Our paper supports that tendency both with and without error in predictors. Furthermore, the paper shows that calibration parameter estimates using error in predictor methods perform worse than without using error in predictor methods in the case of inverse regression, but perform better than without using error in predictor methods in the case of classical regression followed by inversion. Both inverse and classical regression involve the ratio of dependent random variables; therefore, the assumed error distribution(s) will matter in parameter estimation and in uncertainty calculations. Mainly for that reason, calibration using a single predictor is distinct from simple regression, and it has not been thoroughly treated in the literature, nor in the ISO Guide to the Expression of Uncertainty in Measurements (GUM). This refined approach is based on simulation, because we illustrate that analytical approximations are not adequate when there are, for example, 10 or fewer calibration measurements, which is common in calibration applications, each consisting of measured responses from known quantities.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2015

Variance reduction through robust design of boundary conditions for stochastic hyperbolic systems of equations

We consider a hyperbolic system with uncertainty in the boundary and initial data. Our aim is to show that different boundary conditions give different convergence rates of the variance of the solution. This means that we can with the same knowledge of data get a more or less accurate description of the uncertainty in the solution. A variety of boundary conditions are compared and both analytical and numerical estimates of the variance of the solution are presented. As an application, we study the effect of this technique on Maxwell's equations as well as on a subsonic outflow boundary for the Euler equations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Variance reduction for Fokker–Planck based particle Monte Carlo schemes

Recently, Fokker–Planck based particle Monte Carlo schemes have been proposed and evaluated for simulations of rarefied gas flows [1–3]. In this paper, the variance reduction for particle Monte Carlo simulations based on the Fokker–Planck model is considered. First, deviational based schemes were derived and reviewed, and it is shown that these deviational methods are not appropriate for practical Fokker–Planck based rarefied gas flow simulations. This is due to the fact that the deviational schemes considered in this study lead either to instabilities in the case of two-weight methods or to large statistical errors if the direct sampling method is applied. Motivated by this conclusion, we developed a novel scheme based on correlated stochastic processes. The main idea here is to synthesize an additional stochastic process with a known solution, which is simultaneously solved together with the main one. By correlating the two processes, the statistical errors can dramatically be reduced; especially for low Mach numbers. To assess the methods, homogeneous relaxation, planar Couette and lid-driven cavity flows were considered. For these test cases, it could be demonstrated that variance reduction based on parallel processes is very robust and effective.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Importance sampling variance reduction for the Fokker–Planck rarefied gas particle method

The Fokker–Planck approximation to the Boltzmann equation, solved numerically by stochastic particle schemes, is used to provide estimates for rarefied gas flows. This paper presents a variance reduction technique for a stochastic particle method that is able to greatly reduce the uncertainty of the estimated flow fields when the characteristic speed of the flow is small in comparison to the thermal velocity of the gas. The method relies on importance sampling, requiring minimal changes to the basic stochastic particle scheme. We test the importance sampling scheme on a homogeneous relaxation, planar Couette flow and a lid-driven-cavity flow, and find that our method is able to greatly reduce the noise of estimated quantities. Significantly, we find that as the characteristic speed of the flow decreases, the variance of the noisy estimators becomes independent of the characteristic speed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Girsanov's transformation based variance reduced Monte Carlo simulation schemes for reliability estimation in nonlinear stochastic dynamics

The study considers the problem of simulation based time variant reliability analysis of nonlinear randomly excited dynamical systems. Attention is focused on importance sampling strategies based on the application of Girsanov's transformation method. Controls which minimize the distance function, as in the first order reliability method (FORM), are shown to minimize a bound on the sampling variance of the estimator for the probability of failure. Two schemes based on the application of calculus of variations for selecting control signals are proposed: the first obtains the control force as the solution of a two-point nonlinear boundary value problem, and, the second explores the application of the Volterra series in characterizing the controls. The relative merits of these schemes, vis-à-vis the method based on ideas from the FORM, are discussed. Illustrative examples, involving archetypal single degree of freedom (dof) nonlinear oscillators, and a multi-degree of freedom nonlinear dynamical system, are presented. The credentials of the proposed procedures are established by comparing the solutions with pertinent results from direct Monte Carlo simulations. - Highlights: • The distance minimizing control forces minimize a bound on the sampling variance. • Establishing Girsanov controls via solution of a two-point boundary value problem. • Girsanov controls via Volterra's series representation for the transfer functions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A TKE-Based Framework for Studying Disturbed Atmospheric Surface Layer Flows and Application to Vertical Velocity Variance Over Canopies

We propose an approach to study disturbed surface layer flows based on a simplified form of the turbulent kinetic energy (TKE) budget equation (the reduced TKE budget), which can be represented by a two-dimensional phase space. The phase space provides a way to quantify relative contributions of shear and buoyancy production/destruction of TKE, as well as the local imbalance between local production and dissipation. In this framework, Monin-Obukhov Similarity Theory represents one possible approach to reduce the dimensionality of the phase space. We apply this framework to study the vertical velocity variance in the canonical surface layer and in the canopy roughness sublayer above the Amazon forest. Results reveal interesting insight into the behavior of the vertical velocity variance over forests, linking its magnitude to the imbalance between local production and dissipation of TKE.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2013

Variance of the quantum dwell time for a nonrelativistic particle

Munoz, Seidel, and Muga [Phys. Rev. A 79, 012108 (2009)], following an earlier proposal by Pollak and Miller [Phys. Rev. Lett. 53, 115 (1984)] in the context of a theory of a collinear chemical reaction, showed that suitable moments of a two-flux correlation function could be manipulated to yield expressions for the mean quantum dwell time and mean square quantum dwell time for a structureless particle scattering from a time-independent potential energy field between two parallel lines in a two-dimensional spacetime. The present work proposes a generalization to a charged, nonrelativistic particle scattering from a transient, spatially confined electromagnetic vector potential in four-dimensional spacetime. The geometry of the spacetime domain is that of the slab between a pair of parallel planes, in particular, those defined by constant values of the third (z) spatial coordinate. The mean Nth power, N= 1, 2, 3, Horizontal-Ellipsis , of the quantum dwell time in the slab is given by an expression involving an N-flux-correlation function. All these means are shown to be nonnegative. The N= 1 formula reduces to an S-matrix result published previously [G. E. Hahne, J. Phys. A 36, 7149 (2003)]; an explicit formula for N= 2, and of the variance of the dwell time in terms of the S-matrix, is worked out. A formula representing an incommensurability principle between variances of the output-minus-input flux of a pair of dynamical variables (such as the particle's time flux and others) is derived.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Excitation variance matching with limited configuration interaction expansions in variational Monte Carlo

In the regime where traditional approaches to electronic structure cannot afford to achieve accurate energy differences via exhaustive wave function flexibility, rigorous approaches to balancing different states’ accuracies become desirable. As a direct measure of a wave function’s accuracy, the energy variance offers one route to achieving such a balance. Here, we develop and test a variance matching approach for predicting excitation energies within the context of variational Monte Carlo and selective configuration interaction. In a series of tests on small but difficult molecules, we demonstrate that the approach it is effective at delivering accurate excitation energies when the wave function is far from the exhaustive flexibility limit. Results in C3, where we combine this approach with variational Monte Carlo orbital optimization, are especially encouraging.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗