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Results for “Complete linearization method”

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
NASA NTRS1992

Accelerated complete-linearization method for calculating NLTE model stellar atmospheres

Two approaches to accelerating the method of complete linearization for calculating NLTE model stellar atmospheres are suggested. The first one, the so-called Kantorovich variant of the Newton-Raphson method, consists of keeping the Jacobi matrix of the system fixed, which allows us to calculate the costly matrix inversions only a few times and then keep them fixed during the subsequent computations. The second method is an application of the Ng acceleration. Both methods are extremely easy to implement with any model atmosphere code based on complete linearization. It is demonstrated that both methods, and especially their combination, yield a rapidly and globally convergent algorithm, which takes 2 to 5 times less computer time, depending on the model at hand and the required accuracy, than the ordinary complete linearization. Generally, the time gain is more significant for more complicated models. The methods were tested for a broad range of atmospheric parameters, and in all cases they exhibited similar behavior. Ng acceleration applied on the Kantorovich variant thus offers a significant improvement of the standard complete-linearization method, and may now be used for calculating relatively involved NLTE model stellar atmospheres.

Hubeny, I.↗
NASA NTRS1976

Non-LTE profiles of strong solar lines

The complete linearization method is applied to the formation of strong lines in the solar atmosphere. Transitions in Na(I), Mg(I), Ca(I), Mg(II), and Ca(II) are computed with a standard atmosphere and microturbulent velocity model. The computed profiles are compared to observations at disk center.

Schneeberger, T. J.↗
DOE OSTI2020

Development of the finite slab geometry in the NORA code

In this work we develop the complete linearization formalism for the radiation transfer equation in slab geometry. This development was motivated by an observed convergence instability arising from the NORA code’s inner boundary while modeling a suite of simple test problems in slab geometry presented at the Line Transfer Workshop held in LLNL in May of 2019. The convergence issue was seen to emerge early on in Newton-Raphson iterations. These test problems required parameters in the former NORA inner boundary to achieve the asymptotic limit of zero incoming intensity. In this work we derive the limiting case directly to gain insight into the former algorithm’s pathology.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Bayesian Framework for Multi-Timescale State Estimation in Low-Observable Distribution Systems

To support the smart grid paradigm, there has been a significant increase in sensor deployments and metering infrastructure in distribution systems. However, the measurements provided by these sensors and metering devices are typically sampled at different rates and could suffer from losses during the aggregation process. It is crucial to effectively reconcile the time-series measurements for a reliable state estimation. While weighted least squares has been the traditional approach for state estimation, sparsity-based approaches like matrix completion have become popular due to their superior performance in low-observability conditions. This paper proposes a Bayesian framework for both multi-timescale data aggregation and matrix completion based state estimation. Specifically, the multiscale time-series data aggregated from heterogenous sources are reconciled using a multitask Gaussian process that exploits the spatio-temporal correlations. Here, the resulting consistent timeseries alongwith the confidence bound on the imputations are fed into a Bayesian matrix completion method augmented with linearized power-flow constraints to accurately estimate the states in low-observability conditions. Results on three phase unbalanced IEEE 37 and IEEE 123 bus test systems reveal the superior performance of the proposed Bayesian framework. The computational complexity for the proposed Bayesian framework is also quantified.

42 ENGINEERING↗
NASA NTRS1984

Probabilistic radiative transfer

A computationally efficient method has been developed for highly nonlinear problems in which radiative transfer is an important aspect of the heating and cooling of the medium. An approximate probabilistic radiative transfer equation is derived for one-dimensional plane-parallel atmospheres of finite or semi-infinite extent, for both spectral lines and bound-free continua. Boundary conditions, accuracy, escape probabilities, and practical aspects of complete linearization, are discussed. The method is accurate to a few tens of percent of a wide variety of realistic problems in which frequency redistribution of scattered photons dominates the transfer and escape of radiation.

Canfield, R. C.↗
NASA NTRS1982

Blade loss transient dynamic analysis of turbomachinery

This paper reports on work completed to develop an analytical method for predicting the transient non-linear response of a complete aircraft engine system due to the loss of a fan blade, and to validate the analysis by comparing the results against actual blade loss test data. The solution, which is based on the component element method, accounts for rotor-to-casing rubs, high damping and rapid deceleration rates associated with the blade loss event. A comparison of test results and predicted response show good agreement except for an initial overshoot spike not observed in test. The method is effective for analysis of large systems.

Stallone, M. J.↗
NASA NTRS1993

Steady induction effects in geomagnetism. Part 1B: Geomagnetic estimation of steady surficial core motions: A non-linear inverse problem

The problem of estimating a steady fluid velocity field near the top of Earth's core which induces the secular variation (SV) indicated by models of the observed geomagnetic field is examined in the source-free mantle/frozen-flux core (SFI/VFFC) approximation. This inverse problem is non-linear because solutions of the forward problem are deterministically chaotic. The SFM/FFC approximation is inexact, and neither the models nor the observations they represent are either complete or perfect. A method is developed for solving the non-linear inverse motional induction problem posed by the hypothesis of (piecewise, statistically) steady core surface flow and the supposition of a complete initial geomagnetic condition. The method features iterative solution of the weighted, linearized least-squares problem and admits optional biases favoring surficially geostrophic flow and/or spatially simple flow. Two types of weights are advanced radial field weights for fitting the evolution of the broad-scale portion of the radial field component near Earth's surface implied by the models, and generalized weights for fitting the evolution of the broad-scale portion of the scalar potential specified by the models.

Voorhies, Coerte V.↗
NASA NTRS1975

Aircraft digital control design methods

Investigations were conducted in two main areas: the first area is control system design, and the goals were to define the limits of 'digitized S-Plane design techniques' vs. sample rate, to show the results of a 'direct digital design technique', and to compare the two methods; the second area was to evaluate the roughness of autopilot designs parametrically versus sample rate. Goals of the first area were addressed by (1) an analysis of a 2nd order example using both design methods, (2) a linear analysis of the complete 737 aircraft with an autoland obtained using the digitized S-plane technique, (3) linear analysis of a high frequency 737 approximation with the autoland from a direct digital design technique, and (4) development of a simulation for evaluation of the autopilots with disturbances and nonlinearities included. Roughness evaluation was studied by defining an experiment to be carried out on the Langley motion simulator and coordinated with analysis at Stanford.

Tashker, M. G.↗
NASA NTRS1980

A perturbation solution for transverse pressure-sensitive combustion instability in an annulus

A method for analysis of combustion instability in rocket motors based on a combination of the Galerkin method and the two-variable (or multiple-scales) perturbation method is developed. The method is illustrated by applying it to the problem of pressure-sensitive combustion instability in a liquid-fuel annular combustion chamber. To the order of approximation inherent in the method it is found that the complete linear stability analysis and most of the nonlinear stability analysis can be carried out in closed form. The results thus obtained are used to clarify several aspects of the interpretation of numerical solutions obtained by previous investigators.

Googerdy, A.↗
NASA NTRS1977

Inversion methods in temperature and aerosol remote sounding: Their commonality and differences, and some unexplored approaches

The two remote sensing problems of temperature profiling and aerosol characterization (complex refractive index, size distribution) are considered. These problems differ only in the explicit form of the source function which, for aerosols, includes contributions from both single and multiple scattering processes. When the observables are the spectral extinction or the single scattering of the source radiation, the associated problem is completely analogous to the linearized temperature inversion problem. Methods for obtaining the solution of the linear problem are classified following three main categories: (1) derivation of properties that all solutions satisfy, which must then be properties of the actual solution; (2) regularization of the ill-posed problem; and (3) data changes within their domain of uncertainty in order to avoid the basic instability. A number of unexplored methods are indicated.

Fymat, A. L.↗
NASA NTRS1994

Active control of instabilities in laminar boundary-layer flow. Part 1: An overview

This paper (the first in a series) focuses on using active-control methods to maintain laminar flow in a region of the flow in which the natural instabilities, if left unattended, lead to turbulent flow. The authors review previous studies that examine wave cancellation (currently the most prominent method) and solve the unsteady, nonlinear Navier-Stokes equations to evaluate this method of controlling instabilities. It is definitely shown that instabilities are controlled by the linear summation of waves (i.e., wave cancellation). Although a mathematically complete method for controlling arbitrary instabilities has been developed (but not yet tested), the review, duplication, and physical explanation of previous studies are important steps for providing an independent verification of those studies, for establishing a framework for subsequent work which will involve automated transition control, and for detailing the phenomena by which the automated studies can be used to expand knowledge of flow control.

Joslin, Ronald D.↗
NASA NTRS1997

Active Control of Instabilities in Laminar Boundary Layers-Overview and Concept Validation

This paper (the first in a series) focuses on using active-control methods to maintain laminar flow in a region of the flow in which the natural instabilities, if left unattended, lead to turbulent flow. The authors review previous studies that examine wave cancellation (currently the most prominent method) and solve the unsteady, nonlinear Navier-Stokes equations to evaluate this method of controlling instabilities. It is definitively shown that instabilities are controlled by the linear summation of waves (i.e., wave cancellation). Although a mathematically complete method for controlling arbitrary instabilities has been developed, the review, duplication, and physical explanation of previous studies are important steps for providing an independent verification of those studies, for establishing a framework for the work which will involve automated transition control, and for detailing the phenomena by-which the automated studies can be used to expand knowledge of flow control.

Joslin, Ronald D.↗
DOE OSTI2024

Predicting ptychography probe positions using single-shot phase retrieval neural network

Ptychography is a powerful imaging technique that is used in a variety of fields, including materials science, biology, and nanotechnology. However, the accuracy of the reconstructed ptychography image is highly dependent on the accuracy of the recorded probe positions which often contain errors. These errors are typically corrected jointly with phase retrieval through numerical optimization approaches. When the error accumulates along the scan path or when the error magnitude is large, these approaches may not converge with satisfactory result. We propose a fundamentally new approach for ptychography probe position prediction for data with large position errors, where a neural network is used to make single-shot phase retrieval on individual diffraction patterns, yielding the object image at each scan point. The pairwise offsets among these images are then found using a robust image registration method, and the results are combined to yield the complete scan path by constructing and solving a linear equation. We show that our method can achieve good position prediction accuracy for data with large and accumulating errors on the order of 10 2 pixels, a magnitude that often makes optimization-based algorithms fail to converge. For ptychography instruments without sophisticated position control equipment such as interferometers, our method is of significant practical potential.

47 OTHER INSTRUMENTATION↗
NASA NTRS1997

Controls/CFD Interdisciplinary Research Software Generates Low-Order Linear Models for Control Design From Steady-State CFD Results

The NASA Lewis Research Center is developing analytical methods and software tools to create a bridge between the controls and computational fluid dynamics (CFD) disciplines. Traditionally, control design engineers have used coarse nonlinear simulations to generate information for the design of new propulsion system controls. However, such traditional methods are not adequate for modeling the propulsion systems of complex, high-speed vehicles like the High Speed Civil Transport. To properly model the relevant flow physics of high-speed propulsion systems, one must use simulations based on CFD methods. Such CFD simulations have become useful tools for engineers that are designing propulsion system components. The analysis techniques and software being developed as part of this effort are an attempt to evolve CFD into a useful tool for control design as well. One major aspect of this research is the generation of linear models from steady-state CFD results. CFD simulations, often used during the design of high-speed inlets, yield high resolution operating point data. Under a NASA grant, the University of Akron has developed analytical techniques and software tools that use these data to generate linear models for control design. The resulting linear models have the same number of states as the original CFD simulation, so they are still very large and computationally cumbersome. Model reduction techniques have been successfully applied to reduce these large linear models by several orders of magnitude without significantly changing the dynamic response. The result is an accurate, easy to use, low-order linear model that takes less time to generate than those generated by traditional means. The development of methods for generating low-order linear models from steady-state CFD is most complete at the one-dimensional level, where software is available to generate models with different kinds of input and output variables. One-dimensional methods have been extended somewhat so that linear models can also be generated from two- and three-dimensional steady-state results. Standard techniques are adequate for reducing the order of one-dimensional CFD-based linear models. However, reduction of linear models based on two- and three-dimensional CFD results is complicated by very sparse, ill-conditioned matrices. Some novel approaches are being investigated to solve this problem.

Melcher, Kevin J.↗
NASA NTRS1989

Direct numerical study of leading-edge contamination

Instability, turbulence, and relaminarization in the attachment-line region of swept and unswept cylindrical bodies are studied by numerical solution of the full Navier-Stokes equations. The flow is simulated over a strip containing the attachment-line and treated as homogeneous in the spanwise direction; the disturbances decay exponentially upstream. Transpiration through the wall may be prescribed. The new method, which admits completely general disturbance, agrees with published linear-stability results, which were limited to an apparently restrictive form of disturbance. Fully developed turbulent solutions with sweep are generated and compare well with the experiment. The turbulence is subcritical (except for blowing), resulting in large hysteresis loops. By lowering the sweep Reynolds number, or increasing the suction, the turbulent flow is made to relaminarize. The relaminarization Reynolds number is much less sensitive to suction than the linear-stability Reynolds number. Extensive attempts to detect the postulated nonlinear instability of the unswept flow failed, suggesting that this flow is linearly and nonlinearly stable.

Spalart, P. R.↗
NASA NTRS2007

Compatibility Condition in Theory of Solid Mechanics (Elasticity, Structures, and Design Optimization)

The strain formulation in elasticity and the compatibility condition in structural mechanics have neither been understood nor have they been utilized. This shortcoming prevented the formulation of a direct method to calculate stress. We have researched and understood the compatibility condition for linear problems in elasticity and in finite element analysis. This has lead to the completion of the method of force with stress (or stress resultant) as the primary unknown. The method in elasticity is referred to as the completed Beltrami-Michell formulation (CBMF), and it is the integrated force method (IFM) in structures. The dual integrated force method (IFMD) with displacement as the primary unknown has been formulated. IFM and IFMD produce identical responses. The variational derivation of the CBMF yielded the new boundary compatibility conditions. The CBMF can be used to solve stress, displacement, and mixed boundary value problems. The IFM in structures produced high-fidelity response even with a modest finite element model. The IFM has influenced structural design considerably. A fully utilized design method for strength and stiffness limitation has been developed. The singularity condition in optimization has been identified. The CBMF and IFM tensorial approaches are robust formulations because of simultaneous emphasis on the equilibrium equation and the compatibility condition.

Patnaik, Surya N.↗
NASA NTRS1980

An independent Cepheid distance scale: Current status

An independent distance scale for Cepheid variables is discussed. The apparent magnitude and the visual surface brightness, inferred from an appropriate color index, are used to determine the angular diameter variation of the Cepheid. When combined with the linear displacement curve obtained from the integrated radial velocity curve, the distance and linear radius are determined. The attractiveness of the method is its complete independence of all other stellar distance scales, even though a number of practical difficulties currently exist in implementing the technique.

Barnes, T. G., III↗
NASA NTRS1982

A general method to determine the stability of compressible flows

Several problems were studied using two completely different approaches. The initial method was to use the standard linearized perturbation theory by finding the value of the individual small disturbance quantities based on the equations of motion. These were serially eliminated from the equations of motion to derive a single equation that governs the stability of fluid dynamic system. These equations could not be reduced unless the steady state variable depends only on one coordinate. The stability equation based on one dependent variable was found and was examined to determine the stability of a compressible swirling jet. The second method applied a Lagrangian approach to the problem. Since the equations developed were based on different assumptions, the condition of stability was compared only for the Rayleigh problem of a swirling flow, both examples reduce to the Rayleigh criterion. This technique allows including the viscous shear terms which is not possible in the first method. The same problem was then examined to see what effect shear has on stability.

Guenther, R. A.↗