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Results for “error estimate”

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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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Effects of exposure estimation errors on estimated exposure-response relations for PM2.5

Highlights: • Recent literature has identified associations between concentrations of fine particulate matter (PM2.5) in ambient air and adverse health effects at estimated exposure concentrations below current air ambient quality standards. • The models and analyses used do not usually quantify uncertainty about exposure estimates. • Realistic errors in exposure estimates can be estimated from available air quality monitoring stations by predicting concentrations at each station from concentrations at neighboring stations. • Exposure estimation errors are large enough to obscure low-dose nonlinearities or thresholds in the true concentration-response (C-R) function, artificially making them appear to be linear at low doses. • Better estimates of C-R functions will require modeling exposure distributions and estimation errors, rather than just estimating average exposure concentrations. Associations between fine particulate matter (PM2.5) exposure concentrations and a wide variety of undesirable outcomes, from autism and auto theft to elderly mortality, suicide, and violent crime, have been widely reported. Influential articles have argued that reducing National Ambient Air Quality Standards for PM2.5 is desirable to reduce these outcomes. Yet, other studies have found that reducing black smoke and other particulate matter by as much as 70% and dozens of micrograms per cubic meter has not detectably affected all-cause mortality rates even after decades, despite strong, statistically significant positive exposure concentration-response (C-R) associations between them. This paper examines whether this disconnect between association and causation might be explained in part by ignored estimation errors in estimated exposure concentrations. We use EPA air quality monitor data from the Los Angeles area of California to examine the shapes of estimated C-R functions for PM2.5 when the true C-R functions are assumed to be step functions with well-defined response thresholds. The estimated C-R functions mistakenly show risk as smoothly increasing with concentrations even well below the response thresholds, thus incorrectly predicting substantial risk reductions from reductions in concentrations that do not affect health risks. We conclude that ignored estimation errors obscure the shapes of true C-R functions, including possible thresholds, possibly leading to unrealistic predictions of the changes in risk caused by changing exposures. Instead of estimating improvements in public health per unit reduction (e.g., per 10 µg/m{sup 3} decrease) in average PM2.5 concentrations, it may be essential to consider how interventions change the distributions of exposure concentrations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Quantifying the impact of material-model error on macroscale quantities-of-interest using multiscale a posteriori error-estimation techniques

An a posteriori error-estimation framework is introduced to quantify and reduce modeling errors resulting from approximating complex mesoscale material behavior with a simpler macroscale model. Such errors may be prevalent when modeling welds and additively manufactured structures, where spatial variations and material textures may be present in the microstructure. We consider a case where a <100> fiber texture develops in the longitudinal scanning direction of a weld. Transversely isotropic elastic properties are obtained through homogenization of a microstructural model with this texture and are considered the reference weld properties within the error-estimation framework. Conversely, isotropic elastic properties are considered approximate weld properties since they contain no representation of texture. Errors introduced by using isotropic material properties to represent a weld are assessed through a quantified error bound in the elastic regime. Lastly, an adaptive error reduction scheme is used to determine the optimal spatial variation of the isotropic weld properties to reduce the error bound.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates

In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the physical discretization error and the interpolation error in the sparse grid to enhance the sparse grid approximation and to drive adaptivity of the sparse grid. Utilizing these error estimates provides significantly more accurate functional values for random samples of the sparse grid approximation. We also demonstrate that alternative refinement strategies based upon a posteriori error estimates can lead to further increases in accuracy in the approximation over traditional hierarchical surplus based strategies. Throughout this paper we also provide and test a framework for balancing the physical discretization error with the stochastic interpolation error of the enhanced sparse grid approximation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Multiscale analysis in solids with unseparated scales: fine-scale recovery, error estimation, and coarse-scale adaptivity

There are several engineering applications in which the assumptions of homogenization and scale separation may be violated, in particular, for metallic structures constructed through additive manufacturing. Instead of resorting to direct numerical simulation of the macroscale system with an embedded fine scale, an alternative approach is to use an approximate macroscale constitutive model, but then estimate the model-form error using a posteriori error estimation techniques and subsequently adapt the macroscale model to reduce the error for a given boundary value problem and quantity of interest. Here, we investigate this approach to multiscale analysis in solids with unseparated scales using the example of an additively manufactured metallic structure consisting of a polycrystalline microstructure that is neither periodic nor statistically homogeneous. As a first step to the general nonlinear case, we focus here on linear elasticity in which each grain within the polycrystal is linear elastic but anisotropic.

42 ENGINEERING↗
NASA NTRS1983

Model error estimation for distributed systems described by elliptic equations

A function space approach is used to develop a theory for estimation of the errors inherent in an elliptic partial differential equation model for a distributed parameter system. By establishing knowledge of the inevitable deficiencies in the model, the error estimates provide a foundation for updating the model. The function space solution leads to a specification of a method for computation of the model error estimates and development of model error analysis techniques for comparison between actual and estimated errors. The paper summarizes the model error estimation approach as well as an application arising in the area of modeling for static shape determination of large flexible systems.

Rodriguez, G.↗
NASA NTRS1991

Parallel computers - Estimate errors caused by imprecise data

A new approach to the problem of estimating errors caused by imprecise data is proposed in the context of software engineering. A software device is used to produce an ideal solution to the problem, when the computer is capable of computing errors of arbitrary programs. The software engineering aspect of this problem is to describe a device for computing the error estimates in software terms and then to provide precise numbers with error estimates to the user. The feasibility of the program capable of computing both some quantity and its error estimate in the range of possible measurement errors is demonstrated.

Kreinovich, Vladik↗
DOE OSTI2019

Sensor Error Estimation for Reactor Coolant System with Generalization Error Equations

We consider a simplified version of the sensor error estimation problem in pressure sensors in the primary coolant system of a nuclear power plant under the condition that a majority of sensors are error-free. We present a sensor fusion method to estimate sensor errors in the primary coolant system of a power reactor by using measurements collected by multiple sensors. The underlying relationship between the measured and estimated parameters is inferred using measurements collected under controlled no-error conditions of the plant. We propose a machine learning approach to train fusers that provide an estimate of the sensor measurement by using measurements from other sensors, and the difference between the actual sensor measurement and its estimate provides the sensor estimate. We present generalization error equations for these methods that characterize the performance of their sensor error estimates on future measurements using the distribution-free machine learning formulation.

Rao, Nageswara S.↗
DOE OSTI2025

A note on the reliability of goal-oriented error estimates for Galerkin finite element methods with nonlinear functionals

Here, we consider estimating the discretization error in a nonlinear functional J (u) in the setting of an abstract variational problem: find u ϵ $\mathscr{V}$ such that B (u, φ) = L (φ) ∀φ ϵ $\mathscr{V}$, as approximated by a Galerkin finite element method. Here, $\mathscr{V}$ is a Hilbert space, B (. , .) is a bilinear form, and L (∙) is a linear functional. We consider well-known error estimates η of the form J (u) - J (u h ) ≈ η = L (z) - B (u h , z), where u h denotes a finite element approximation to u, and z denotes the solution to an auxiliary adjoint variational problem. We show that there exist nonlinear functionals for which error estimates of this form are not reliable, even in the presence of an exact adjoint solution z. An estimate η is said to be reliable if there exists a constant C ϵ $\mathbb{R}$ >0 independent of u h such that |J (u) - J (u h )| ≤ C|η|. We present several example pairs of bilinear forms and nonlinear functionals where reliability of η is not achieved.

A posteriori↗
DOE OSTI2013

A posteriori error estimators for the discrete ordinates approximation of the one-speed neutron transport equation

When calculating numerical solutions of the neutron transport equation it is important to have a measure of the accuracy of the solution. As the true solution is generally not known, a suitable estimation of the error must be made. The steady state transport equation possesses discretization errors in all its independent variables: angle, energy and space. In this work only spatial discretization errors are considered. An exact transport solution, in which the degree of regularity of the exact flux across the singular characteristic is controlled, is manufactured to determine the numerical solutions true discretization error. This solution is then projected onto a Legendre polynomial space in order to form an exact solution on the same basis space as the numerical solution, Discontinuous Galerkin Finite Element Method (DGFEM), to enable computation of the true error. Over a series of test problems the true error is compared to the error estimated by: Ragusa and Wang (RW), residual source (LER) and cell discontinuity estimators (JD). The validity and accuracy of the considered estimators are primarily assessed by considering the effectivity index and global L2 norm of the error. In general RW excels at approximating the true error distribution but usually under-estimates its magnitude; the LER estimator emulates the true error distribution but frequently over-estimates the magnitude of the true error; the JD estimator poorly captures the true error distribution and generally under-estimates the error about singular characteristics but over-estimates it elsewhere. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Linearization errors in discrete goal-oriented error estimation

This paper is concerned with goal-oriented a posteriori error estimation for nonlinear functionals in the context of nonlinear variational problems solved with continuous Galerkin finite element discretizations. A two-level, or discrete, adjoint-based approach for error estimation is considered. The traditional method to derive an error estimate in this context requires linearizing both the nonlinear variational form and the nonlinear functional of interest which introduces linearization errors into the error estimate. In this paper, we investigate these linearization errors. In particular, we develop a novel discrete goal-oriented error estimate that accounts for traditionally neglected nonlinear terms at the expense of greater computational cost. We demonstrate how this error estimate can be used to drive mesh adaptivity. Here, we show that accounting for linearization errors in the error estimate can improve its effectivity for several nonlinear model problems and quantities of interest. We also demonstrate that an adaptive strategy based on the newly proposed estimate can lead to more accurate approximations of the nonlinear functional with fewer degrees of freedom when compared to uniform refinement and traditional adjoint-based approaches.

42 ENGINEERING↗
NASA NTRS1980

Model error estimation for large space systems

In-flight estimation of large structure model errors may have to be carried out in order to detect inevitable deficiencies in large structure controller/estimator models. These error estimates can most efficiently be obtained by the minimization of a quadratic functional of the model errors and on the subsequent analysis of the resulting optimal model error estimates. An integral operator approach to estimation leads to a geometrical interpretation of the model error estimation process. One of the significant insights gained with this interpretation is that the actual but unknown model errors can be decomposed as the sum of two distinct components that are orthogonal in some sense. One of these components is a so-called minimal error vector that retains many of the significant dynamics of the actual errors. The basic ideas in the model error estimation approach are first set forth with a two-dimensional analogy that has most of the essential features of the general estimation problem. The generalized results are then established and their application to a reference large structure model illustrated.

Rodriguez, G.↗
DOE OSTI2013

Residual a posteriori error estimation of a mimetic/virtual element method

A posteriori error estimation and adaptivity are very useful in the context of the mimetic finite difference method due to the flexibility of the meshes to which this family of numerical schemes can be applied. Nevertheless, developing error estimators for mimetic methods is not a straightforward task due to the lack of knowledge of the basis functions. This issue is tackled by the virtual element method recently introduced in [4], which can be interpreted as a Galerkin reformulation of the mimetic finite difference method. In the new virtual element setting, we develop a residual based a posteriori error estimator that immediately applies to its mimetic counterpart. For such estimator we prove the reliability and we show the numerical performance when it is combined with an adaptive strategy for the mesh refinement. For the lowest-regular approximation we also developed an hp-adaptive strategy based on the comparison between the numerical solution on a base mesh and on a reference mesh.

a posteriori error estimation↗
DOE OSTI2017

Stochastic goal-oriented error estimation with memory

We propose a stochastic dual-weighted error estimator for the viscous shallow-water equation with boundaries. For this purpose, previous work on memory-less stochastic dual-weighted error estimation is extended by incorporating memory effects. The memory is introduced by describing the local truncation error as a sum of time-correlated random variables. The random variables itself represent the temporal fluctuations in local truncation errors and are estimated from high-resolution information at near-initial times. The resulting error estimator is evaluated experimentally in two classical ocean-type experiments, the Munk gyre and the flow around an island. In these experiments, the stochastic process is adapted locally to the respective dynamical flow regime. Our stochastic dual-weighted error estimator is shown to provide meaningful error bounds for a range of physically relevant goals. We prove, as well as show numerically, that our approach can be interpreted as a linearized stochastic-physics ensemble.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2002

Finite Element A Posteriori Error Estimation for Heat Conduction

This research investigates residual-based a posteriori error estimates for finite element approximations of heat conduction in single-layer and multi-layered materials. The finite element approximation, based upon hierarchical modelling combined with p-version finite elements, is described with specific application to a two-dimensional, steady state, heat-conduction problem. Element error indicators are determined by solving an element equation for the error with the element residual as a source, and a global error estimate in the energy norm is computed by collecting the element contributions. Numerical results of the performance of the error estimate are presented by comparisons to the actual error. Two methods are discussed and compared for approximating the element boundary flux. The equilibrated flux method provides more accurate results for estimating the error than the average flux method. The error estimation is applied to multi-layered materials with a modification to the equilibrated flux method to approximate the discontinuous flux along a boundary at the material interfaces. A directional error indicator is developed which distinguishes between the hierarchical modeling error and the finite element error. Numerical results are presented for single-layered materials which show that the directional indicators accurately determine which contribution to the total error dominates.

Lang, Christapher G.↗