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Results for “weighted residual methods”

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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

The effect of drying and size reduction pretreatments on recovery of inorganic crop nutrients from inedible wheat residues

Inorganic nutrients can be easily recovered from ALS crop residue solid wastes by aqueous leaching. However, oven drying and milling pretreatment of these residues has been frequently required to accommodate crop scientists and facility storage limitations. As part of a research study that will compare three different bioreactor technologies for processing these wastes, we realized that different drying and size-reduction pretreatments had been utilized for each technology. This paper compares the effects of residue pretreatment on recovery of nutrients by leaching. Pretreatments included three drying methods [fresh, oven-dried (70 degrees C overnight), and freeze-dried] and two size reduction methods [chopped (2 cm length) and milled (2 mm diameter)]. Determination of mass balances (dry weight and ash content of solids) before and after leaching indicated solubilization was least for fresh residues (23% dry weight loss and 50% for ash loss), and most for freeze-dried residues (41-47% dry weight loss and nearly 100% for ash loss). Mineral recovery of major elements (NO3, PO4, K, Ca, and Mg) in leachates was poorest for fresh residues. P and K recovery in leachates were best for oven-dried residues and Ca, Mg, and N recovery best for freeze-dried residues. The differences in recovery for N, P, and K in leachates were minimal between chopping and milling and slightly better for Ca and Mg from milled residues.

NASA Center KSC↗
NASA NTRS2011

Markov Chain Monte Carlo Bayesian Learning for Neural Networks

Conventional training methods for neural networks involve starting al a random location in the solution space of the network weights, navigating an error hyper surface to reach a minimum, and sometime stochastic based techniques (e.g., genetic algorithms) to avoid entrapment in a local minimum. It is further typically necessary to preprocess the data (e.g., normalization) to keep the training algorithm on course. Conversely, Bayesian based learning is an epistemological approach concerned with formally updating the plausibility of competing candidate hypotheses thereby obtaining a posterior distribution for the network weights conditioned on the available data and a prior distribution. In this paper, we developed a powerful methodology for estimating the full residual uncertainty in network weights and therefore network predictions by using a modified Jeffery's prior combined with a Metropolis Markov Chain Monte Carlo method.

Goodrich, Michael S.↗
DOE OSTI2024

3D Multiresolution Velocity Model Fusion with Probability Graphical Models

ABSTRACT The variability in spatial resolution of seismic velocity models obtained via tomographic methodologies is attributed to many factors, including inversion strategies, ray-path coverage, and data integrity. Integration of such models, with distinct resolutions, is crucial during the refinement of community models, thereby enhancing the precision of ground-motion simulations. Toward this goal, we introduce the probability graphical model (PGM), combining velocity models with heterogeneous resolutions and nonuniform data point distributions. The PGM integrates data relations across varying resolution subdomains, enhancing detail within low-resolution (LR) domains by utilizing information and prior knowledge from high-resolution (HR) subdomains through a maximum posterior problem. Assessment of efficacy, utilizing both 2D and 3D velocity models—consisting of synthetic checkerboard models and a fault-zone model from Ridgecrest, California—demonstrates noteworthy improvements in accuracy, compared to state-of-the-art fusion techniques. Specifically, we find reductions of 30% and 44% in computed travel-time residuals for 2D and 3D models, respectively, as compared to conventional smoothing techniques. Unlike conventional methods, the PGM’s adaptive weight selection facilitates preserving and learning details from complex, nonuniform HR models and applies the enhancements to the LR background domain.

Geochemistry & Geophysics↗
DOE OSTI2020

Benzene homologues contaminants in a former herbicide factory site: distribution, attenuation, risk, and remediation implication

Benzene homologues often used as organic raw materials or as detergents in chemical industry are prone to accidental release into the environment which can cause serious long-term soil pollutions. In a large former herbicide factory site, we investigated 43 locations for benzene homologues contaminations in soil, soil gas, and groundwater; and studied the hydrogeological conditions. An inverse distance weighted interpolation method was employed to determine the pollutants three-dimensional spatial distribution in the soils. Results showed that benzene homologues residues were mainly originated from the herbicide production workshop; and that the pollution had horizontally expanded at the deeper soil layer. Contaminants had already migrated 15m downward from ground surface. Contaminant phase distribution study showed that NAPL was the primary phase (>99%) for the pollutants accumulated in the unsaturated zone; while it had not migrated to groundwater. The primary mechanism for contaminant transport and attenuation included dissolution of “occluded” NAPL into pore water and pollutant volatilization into soil pore space. Risk assessment revealed that the pollutants brought unacceptable high carcinogenic and non-carcinogenic risks to public health. In order to convert this former chemical processing factory site into a residential area, a remediation to the polluted production workshop sites is urgently required.

Yang, Shuo↗
NASA NTRS1995

Combining Comparison Functions and Finite Element Approximations in CFD

In a variety of potential flow applications, the modal element method has been shown to significantly reduce the numerical grid, employ a more precise grid termination boundary condition, and give theoretical insight to the flow physics. The method employs eigenfunctions to replace the numerical grid over significant portions of the flow field. Generally, a numerical grid is employed around obstacles with complex geometry while eigenfunctions are applied to regions in the flow field where the boundary conditions can easily be satisfied. To handle a wider class of computational fluid dynamics (CFD) problems, the present paper extends the modal element to include function approximations which do not satisfy the governing differential equation. To accomplish this task, a double modal series approximation and weighted residual constraints are developed to force the comparison functions to satisfy the governing differential equation and to interface properly with the finite element solution. As an example, the method is applied to the problem of potential flow in a channel with two-dimensional cylindrical like obstacles. The calculated flow fields are in excellent agreement with exact analytical solutions.

Baumeister, Kenneth J.↗
NASA NTRS2002

Coupling Finite Element and Meshless Local Petrov-Galerkin Methods for Two-Dimensional Potential Problems

A coupled finite element (FE) method and meshless local Petrov-Galerkin (MLPG) method for analyzing two-dimensional potential problems is presented in this paper. The analysis domain is subdivided into two regions, a finite element (FE) region and a meshless (MM) region. A single weighted residual form is written for the entire domain. Independent trial and test functions are assumed in the FE and MM regions. A transition region is created between the two regions. The transition region blends the trial and test functions of the FE and MM regions. The trial function blending is achieved using a technique similar to the 'Coons patch' method that is widely used in computer-aided geometric design. The test function blending is achieved by using either FE or MM test functions on the nodes in the transition element. The technique was evaluated by applying the coupled method to two potential problems governed by the Poisson equation. The coupled method passed all the patch test problems and gave accurate solutions for the problems studied.

Chen, T.↗
DOE OSTI2021

A multi-center quadrature scheme for the molecular continuum

We report a common way to evaluate electronic integrals for polyatomic molecules is to use Becke’s partitioning scheme (Becke and Chem, 1988) in conjunction with overlapping grids centered at each atomic site. The Becke scheme was designed for integrands that fall off rapidly at large distances, such as those approximating bound electronic states. When applied to states in the electronic continuum, however, Becke scheme exhibits slow convergence and it is highly redundant. Here, we present a modified version of Becke scheme that is applicable to functions of the electronic continuum, such as those involved in molecular photoionization and electron–molecule scattering, and which ensures convergence and efficiency comparable to those realized in the calculation of bound states. In this modified scheme, the atomic weights already present in Becke’s partition are smoothly switched off within a range of few bond lengths from their respective nuclei, and complemented by an asymptotically unitary weight. The atomic integrals are evaluated on small spherical grids, centered on each atom, with size commensurate to the support of the corresponding atomic weight. The residual integral of the interstitial and long-range region is evaluated with a central master grid. The accuracy of the method is demonstrated by evaluating integrals involving integrands containing Gaussian Type Orbitals and Yukawa potentials, on the atomic sites, as well as spherical Bessel functions centered on the master grid. These functions are representative of those encountered in realistic electron-scattering and photoionization calculations in polyatomic molecules.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Hybrid Cyber-attack Detection in Photovoltaic Farms

Here, to address the cyber-physical security in PV farms, a hybrid cyber-attack detection is proposed in this manuscript. To secure PV farms, the proposed method integrates model-based and data-driven methods by fusing the detection score at the device and system levels. First, a model-based cyber-attack detection method is developed for each PV inverter. A residual between the estimation of the Kalman filter and measurement is calculated. By leveraging the calculated residual from all inverters, a squared Mahalanobis distance is developed for device detection score generation. At the system level, a convolutional neural network (CNN) is proposed to detect cyber-attack using the waveform data at the point of common coupling (PCC) in PV farms. To improve the CNN detection accuracy, a set of well-designed features are extracted from the raw waveform data. Finally, a weighted detection score fusion method is proposed to combine device and system detection scores by using their complementary strength. The feasibility and robustness of the proposed method are validated by testing cases and a comparative experiment.

14 SOLAR ENERGY↗
NASA NTRS1998

An Astronomical Test of CCD Photometric Precision

This article considers a posteriori error estimation of specified functionals for first-order systems of conservation laws discretized using the discontinuous Galerkin (DG) finite element method. Using duality techniques. we derive exact error representation formulas for both linear and nonlinear functionals given an associated bilinear or nonlinear variational form. Weighted residual approximations of the exact error representation formula are then proposed and numerically evaluated for Ringleb flow, an exact solution of the 2-D Euler equations.

Koch, David↗
NASA NTRS1999

A Posteriori Error Estimation for Discontinuous Galerkin Approximations of Hyperbolic Systems

This article considers a posteriori error estimation of specified functionals for first-order systems of conservation laws discretized using the discontinuous Galerkin (DG) finite element method. Using duality techniques, we derive exact error representation formulas for both linear and nonlinear functionals given an associated bilinear or nonlinear variational form. Weighted residual approximations of the exact error representation formula are then proposed and numerically evaluated for Ringleb flow, an exact solution of the 2-D Euler equations.

Larson, Mats G.↗
NASA NTRS1990

Reduced size first-order subsonic and supersonic aeroelastic modeling

Various aeroelastic, aeroservoelastic, dynamic-response, and sensitivity analyses are based on a time-domain first-order (state-space) formulation of the equations of motion. The formulation of this paper is based on the minimum-state (MS) aerodynamic approximation method, which yields a low number of aerodynamic augmenting states. Modifications of the MS and the physical weighting procedures make the modeling method even more attractive. The flexibility of constraint selection is increased without increasing the approximation problem size; the accuracy of dynamic residualization of high-frequency modes is improved; and the resulting model is less sensitive to parametric changes in subsequent analyses. Applications to subsonic and supersonic cases demonstrate the generality, flexibility, accuracy, and efficiency of the method.

Karpel, Mordechay↗
DOE OSTI2020

Matrix-free subcell residual distribution for Bernstein finite elements: Monolithic limiting

This paper is focused on the aspects of limiting in residual distribution (RD) schemes for high-order finite element approximations to advection problems. Both continuous and discontinuous Galerkin methods are considered in this work. Discrete maximum principles are enforced using algebraic manipulations of element contributions to the global nonlinear system. The required modifications can be carried out without calculating the element matrices and assembling their global counterparts. The components of element vectors associated with the standard Galerkin discretization are manipulated directly using localized subcell weights to achieve optimal accuracy. Low-order nonlinear RD schemes of this kind were originally developed to calculate local extremum diminishing predictors for flux-corrected transport (FCT) algorithms. In the present paper, we incorporate limiters directly into the residual distribution procedure, which makes it applicable to stationary problems and leads to well-posed nonlinear discrete problems. To circumvent the second-order accuracy barrier, the correction factors of monolithic limiting approaches and FCT schemes are adjusted using smoothness sensors based on second derivatives. Finally, the convergence behavior of presented methods is illustrated by numerical studies for two-dimensional test problems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1992

Determination of orbits of comets: P/Kearns-Kwee, P/Gunn, including nongravitational effects in the comets' motion

To improve the orbits, all the positional observations of the comets were collected. The observations were selected and weighted according to objective mathematical criteria and the mean residuals a priori were calculated for both comets. We took into account nongravitational effects in the comets' motion using Marsden's method applied in two ways: either determining the three constant parameters, A(sub 1), A(sub 2), A(sub 3) or the four parameters A, eta, I, phi connected with the rotating nucleus of the comet. To link successfully all the observations, we had to assume for both comets that A(t) = A(sub O)exp(-B x t) where B was an additional nongravitational parameter.

Todorovic-Juchniewicz, Bozenna↗
NASA NTRS2009

Precision Cleaning of Oxygen Systems and Components

Currently, NASA uses Dichloropentafluoropropane (HCFC-225), a Class II ozone depleting substance (ODs), to clean contaminated oxygen systems. Starting in 20 15, the Montreal Protocols and Clean Air Act prohibit the production and importation of all hydrochlorofluorocarbons (HCFC), except for limited use in refrigeration applications. Thus, a new non-ozone depleting solvent needs to be developed for use in cleaning. Optimally, such a solvent should also be environmentally benign or green to avoid needing to replace the new solvent with yet another solvent in the future due to other environmental concerns. Work for the first year consisted of two parts. The first part was developing a method of testing the cleaning efficiency of potential solvents. Stainless steel coupons were contaminated with a known weight of various contaminants and contaminant combinations and then immersed in solvent for ten minutes. The coupons were then removed and dried in an oven until all solvent had evaporated. Once dry, the coupons were weighed and the mass of the non-volatile residue (NVR) left on the coupon was determined. The cleaning efficiency of the solvents is reported as percent cleaning, with 100% cleaning being zero NVR left on the test coupon. The second half of the first goal was to use the develop method to perform baseline testing on current solvents. The second part of the work was to begin exploring alternative cleaning solvents. A variety of hydrofluorocarbons (HFCs) were tested. Preliminary testing was also performed with ionic liquids and aqueous surfactant solutions. Once potential solvents were identified, an analysis of the performance and environmental characteristics of each was to be conducted. Four contaminants were specified for use in testing. These are Mil-Spec-H-5606 (5606), a hydraulic fluid, Mil-H-83282B (83282), another hydraulic fluid, diethylhexyl sebacate (Sebacate), and WD-40. The structures of these contaminants are all similar, with long aliphatic hydrocarbon chains of lengths between fifteen and fifty. Contaminants were tested both individually and in combination. All combinations were done with equal weights of the constituent contaminants.

McLaughlin, Russell↗
DOE OSTI2025

Fast-RF-Shimming: Accelerate RF shimming in 7T MRI using deep learning

Ultrahigh field (UHF) Magnetic Resonance Imaging (MRI) offers an elevated signal-to-noise ratio (SNR), enabling exceptionally high spatial resolution that benefits both clinical diagnostics and advanced research. However, the jump to higher fields introduces complications, particularly transmit radiofrequency (RF) field ($B^{+}_{1}$) inhomogeneities, manifesting as uneven flip angles and image intensity irregularities. These artifacts can degrade image quality and impede broader clinical adoption. Traditional RF shimming methods, such as Magnitude Least Squares (MLS) optimization, effectively mitigate $B^{+}_{1}$ inhomogeneity, but remain time-consuming. Recent machine learning approaches, including RF Shim Prediction by Iteratively Projected Ridge Regression and other deep learning architectures, suggest alternative pathways. Although these approaches show promise, challenges such as extensive training periods, limited network complexity, and practical data requirements persist. In this paper, we introduce a holistic learning-based framework called Fast-RF-Shimming, which achieves a 5000 ​× ​speed-up compared to the traditional MLS method. In the initial phase, we employ random-initialized Adaptive Moment Estimation (Adam) to derive the desired reference shimming weights from multi-channel $B^{+}_{1}$ fields. Next, we train a Residual Network (ResNet) to map $B^{+}_{1}$ fields directly to the ultimate RF shimming outputs, incorporating the confidence parameter into its loss function. Finally, we design Non-uniformity Field Detector (NFD), an optional post-processing step, to ensure the extreme non-uniform outcomes are identified. Comparative evaluations with standard MLS optimization underscore notable gains in both processing speed and predictive accuracy, which indicates that our technique shows a promising solution for addressing persistent inhomogeneity challenges.

Deep learning↗
NASA NTRS2014

Diagnosability-Based Sensor Placement through Structural Model Decomposition

Systems health management, and in particular fault diagnosis, is important for ensuring safe, correct, and efficient operation of complex engineering systems. The performance of an online health monitoring system depends critically on the available sensors of the system. However, the set of selected sensors is subject to many constraints, such as cost and weight, and hence, these sensors must be selected judiciously. This paper presents an offline design-time sensor placement approach for complex systems. Our diagnosis method is built upon the analysis of model-based residuals, which are computed using structural model decomposition. Sensor placement in this framework manifests as a residual selection problem, and we aim to find the set of residuals that achieves single-fault diagnosability of the system, uses the minimum number of sensors, and corresponds to the best model decomposition for the best distribution of the diagnosis system. We present a set of algorithms for solving this problem and compare their performance in terms of computational complexity and optimality of solutions. We demonstrate the approach using a benchmark multi-tank system.

Daigle, Matthew↗
DOE OSTI2025

Optimizing transmit field inhomogeneity of parallel RF transmit design in 7T MRI using deep learning

Ultrahigh field (UHF) Magnetic Resonance Imaging (MRI) provides a higher signal-to-noise ratio and, thereby, higher spatial resolution. However, UHF MRI introduces challenges such as transmit radiofrequency (RF) field (B+1) inhomogeneities, leading to uneven flip angles and image intensity anomalies. These issues can significantly degrade imaging quality and its medical applications. This study addresses B+1 field homogeneity through a novel deep learning-based strategy. Traditional methods like Magnitude Least Squares (MLS) optimization have been effective but are time-consuming and dependent on the patient’s presence. Recent machine learning approaches, such as RF Shim Prediction by Iteratively Projected Ridge Regression and deep learning frameworks, have shown promise but face limitations like extensive training times and oversimplified architectures. We propose a two-step deep learning strategy. First, we obtain the desired reference RF shimming weights from multi-channel B+1 fields using random-initialized Adaptive Moment Estimation. Then, we employ Residual Networks (ResNets) to train a model that maps B+1 fields to target RF shimming outputs. Our approach does not rely on pre-calculated reference optimizations for the testing process and efficiently learns residual functions. Comparative studies with traditional MLS optimization demonstrate our method’s advantages in terms of speed and accuracy. The proposed strategy achieves a faster and more efficient RF shimming design, significantly improving imaging quality at UHF. This advancement holds potential for broader applications in medical imaging and diagnostics.

Lu, Zhengyi [Vanderbilt University]↗
NASA NTRS1981

A multigrid method for the transonic full potential equation discretized with finite elements on an arbitrary body fitted mesh

A multigrid method for the acceleration of transonic potential flow calculations based on a Galerkin finite element approach is described. In order to allow the use of arbitrary body fitted meshes it is necessary to introduce nonuniform interpolation and residual weighting. Emphasis is put on the construction of these operators consistent with the finite element approximation, while standard successive line overrelaxation is used as a smoothing step. Substantial convergence acceleration is obtained and results are presented for different transonic flow configurations including shocks.

Deconinck, H.↗