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Results for “piecewise approximation”

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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

A finite-volume high-order ENO scheme for two-dimensional hyperbolic systems

The finite-volume approach is presently used to obtain a 2D, high-order accurate and basically nonoscillatory shock-capture method whose high-order spatial accuracy is obtained by means of a piecewise polynomial approximation of the solution from cell averages. Attention is given to a high-order spatial operator that is able to both retain high-order accuracy in smooth regions and avoid the oscillations that are associated with interpolations across steep gradients. The operator is extended to hyperbolic systems of equations and curvilinear meshes.

Casper, Jay↗
NASA NTRS2015

A Versatile Nonlinear Method for Predictive Modeling

As computational fluid dynamics techniques and tools become widely accepted for realworld practice today, it is intriguing to ask: what areas can it be utilized to its potential in the future. Some promising areas include design optimization and exploration of fluid dynamics phenomena (the concept of numerical wind tunnel), in which both have the common feature where some parameters are varied repeatedly and the computation can be costly. We are especially interested in the need for an accurate and efficient approach for handling these applications: (1) capturing complex nonlinear dynamics inherent in a system under consideration and (2) versatility (robustness) to encompass a range of parametric variations. In our previous paper, we proposed to use first-order Taylor expansion collected at numerous sampling points along a trajectory and assembled together via nonlinear weighting functions. The validity and performance of this approach was demonstrated for a number of problems with a vastly different input functions. In this study, we are especially interested in enhancing the method's accuracy; we extend it to include the second-orer Taylor expansion, which however requires a complicated evaluation of Hessian matrices for a system of equations, like in fluid dynamics. We propose a method to avoid these Hessian matrices, while maintaining the accuracy. Results based on the method are presented to confirm its validity.

nonlinear modeling↗
DOE OSTI2022

Systems and methods for direct estimation of battery parameters using only charge/discharge curves

Electrochemical models for the lithium-ion battery are useful in predicting and controlling its performance. The values of the parameters in these models are vital to their accuracy. However, not all parameters can be measured precisely, especially when destructive methods are prohibited. In some embodiments of the present disclosure, a parameter estimation approach is used to estimate the open circuit potential of the positive electrode (Up) using piecewise linear approximation together with all the other parameters of a single particle model. Up and 10 more parameters may be estimated from a single discharge curve without knowledge of the electrode chemistry using a technique such as a genetic algorithm. Different case studies were presented for estimating Up with different types of parameters of the battery model. The estimated parameters were then validated by comparing simulations at different discharge rates with experimental data.

Qi, Yanbo↗
NASA NTRS1983

Spinning mode acoustic radiation from the flight inlet

A mathematical model was developed for spinning mode acoustic radiation from a thick wall duct without flow. This model is based on a series of experiments (with and without flow). A nearly pure azimuthal spinning mode was isolated and then reflection coefficients and far field pressure (amplitude and phase) were measured. In our model the governing boundary value problem for the Helmholtz equation is first converted into an integral equation for the unknown acoustic pressure over a disk, S1, near the mouth of the duct and over the exterior surface, S2, of the duct. Assuming a pure azimuthal mode excitation, the azimuthal dependence is integrated out which yields an integral equation over the generator C1 of S1 and the generator C2 of S2. The sound pressure on C1 was approximated by a truncated modal expansion of the interior acoustic pressure. Piecewise linear spline approximation on C2 was used.

Moss, W. F.↗
NASA NTRS1985

Stresses and deformations in cross-ply composite tubes subjected to a uniform temperature change: Elasticity and Approximate Solutions

The effects of a uniform temperature change on the stresses and deformations of composite tubes are investigated. The accuracy of an approximate solution based on the principle of complementary virtual work is determined. Interest centers on tube response away from the ends and so a planar elasticity approach is used. For the approximate solution a piecewise linear variation of stresses with the radial coordinate is assumed. The results from the approximate solution are compared with the elasticity solution. The stress predictions agree well, particularly peak interlaminar stresses. Surprisingly, the axial deformations also agree well. This, despite the fact that the deformations predicted by the approximate solution do not satisfy the interface displacement continuity conditions required by the elasticity solution. The study shows that the axial thermal expansion coefficient of tubes with a specific number of axial and circumferential layers depends on the stacking sequence. This is in contrast to classical lamination theory which predicts the expansion to be independent of the stacking arrangement. As expected, the sign and magnitude of the peak interlaminar stresses depends on stacking sequence.

Hyer, M. W.↗
NASA NTRS1986

Stresses and deformations in cross-ply composite tubes subjected to a uniform temperature change

This study investigates the effects of a uniform temperature change on the stresses and deformations of composite tubes and determines the accuracy of an approximate solution based on the principle of complementary virtual work. Interest centers on tube response away from the ends and so a planar elasticity approach is used. For the approximate solution a piecewise linear variation of stresses with the radial coordinate is assumed. The results from the approximate solution are compared with the elasticity solution. The stress predictions agree well, particularly peak interlaminar stresses. Surprisingly, the axial deformations also agree well, despite the fact that the deformations predicted by the approximate solution do not satisfy the interface displacement continuity conditions required by the elasticity solution. The study shows that the axial thermal expansion coefficient of tubes with a specific number of axial and circumferential layers depends on the stacking sequence. This is in contrast to classical lamination theory, which predicts that the expansion will be independent of the stacking arrangement. As expected, the sign and magnitude of the peak interlaminar stresses depend on stacking sequence. For tubes with a specific number of axial and circumferential layers, thermally induced interlaminar stresses can be controlled by altering stacking arrangement.

Hyer, M. W.↗
DOE OSTI2023

Reduced-Order Models of Static Power Grids based on Spectral Clustering

For large-scale interconnected power systems that cover large geographical areas, certain electrical studies are required so that appropriate decisions ensure system reliability and low cost. For such studies, it is often neither practical nor necessary to model in detail the entire power system, which is increasingly complex due to a more diverse range of grid assets to choose from in both short and long-term planning. The goal of this paper is to present a methodology to reduce the order of large-scale power networks based on spectral graph theory given that current methods for static network reduction are not scalable. A brief analysis of some spectral clustering properties to determine which graph Laplacian matrix should be used and why is included. The analysis shows that the utilization of the normalized graph Laplacian is more advantageous for clustering purposes. Techniques are proposed to approximate cost functions for the aggregated generators. This is done via linear regression. The reduced-order model obtained with the proposed methodology has an accuracy above 94% and solves the scalability issue commonly present in other reduction methods. If the utilization of the reduced-order model is either constrained to load levels above mid-peak demand, or cost functions of aggregated units are approximated via a piecewise quadratic approach, then the error distribution is in the order of 10^-3. .

Baquedano-Aguilar, Mario D.↗
NASA NTRS1971

A variable-step-size robust delta modulator.

Description of an analytically obtained optimum adaptive delta modulator-demodulator configuration. The device utilizes two past samples to obtain a step size which minimizes the mean square error for a Markov-Gaussian source. The optimum system is compared, using computer simulations, with a linear delta modulator and an enhanced Abate delta modulator. In addition, the performance is compared to the rate distortion bound for a Markov source. It is shown that the optimum delta modulator is neither quantization nor slope-overload limited. The highly nonlinear equations obtained for the optimum transmitter and receiver are approximated by piecewise-linear equations in order to obtain system equations which can be transformed into hardware. The derivation of the experimental system is presented.

Song, C. L.↗
NASA NTRS1981

Time-temperature effect in adhesively bonded joints

The viscoelastic analysis of an adhesively bonded lap joint was reconsidered. The adherends are approximated by essentially Reissner plates and the adhesive is linearly viscoelastic. The hereditary integrals are used to model the adhesive. A linear integral differential equations system for the shear and the tensile stress in the adhesive is applied. The equations have constant coefficients and are solved by using Laplace transforms. It is shown that if the temperature variation in time can be approximated by a piecewise constant function, then the method of Laplace transforms can be used to solve the problem. A numerical example is given for a single lap joint under various loading conditions.

Delale, F.↗
NASA NTRS1989

Optimal moving grids for time-dependent partial differential equations

Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of partial differential equation solutions in the least squares norm.

Wathen, A. J.↗
NASA NTRS1992

Optimal moving grids for time-dependent partial differential equations

Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of PDE solutions in the least-squares norm are reported.

Wathen, A. J.↗
NASA NTRS1993

A multigrid algorithm for the cell-centered finite difference scheme

In this article, we discuss a non-variational V-cycle multigrid algorithm based on the cell-centered finite difference scheme for solving a second-order elliptic problem with discontinuous coefficients. Due to the poor approximation property of piecewise constant spaces and the non-variational nature of our scheme, one step of symmetric linear smoothing in our V-cycle multigrid scheme may fail to be a contraction. Again, because of the simple structure of the piecewise constant spaces, prolongation and restriction are trivial; we save significant computation time with very promising computational results.

Ewing, Richard E.↗
NASA NTRS2003

Hybrid Discrete-Continuous Markov Decision Processes

This paper proposes a Markov decision process (MDP) model that features both discrete and continuous state variables. We extend previous work by Boyan and Littman on the mono-dimensional time-dependent MDP to multiple dimensions. We present the principle of lazy discretization, and piecewise constant and linear approximations of the model. Having to deal with several continuous dimensions raises several new problems that require new solutions. In the (piecewise) linear case, we use techniques from partially- observable MDPs (POMDPS) to represent value functions as sets of linear functions attached to different partitions of the state space.

Feng, Zhengzhu↗
DOE OSTI2024

Learning Functions Varying along a Central Subspace

Many functions of interest are in a high-dimensional space but exhibit low-dimensional structures. This paper studies regression of an s-Hölder function in $R^D$ which varies along a central subspace of dimension $d$ while $d \ll D$. A direct approximation of $f$ in $R^D$ with an accuracy $\varepsilon$ requires the number of samples in the order of $\varepsilon^{-(2s+D)/s}$. In this paper, we analyze the generalized contour regression (GCR) algorithm for the estimation of the central subspace and use piecewise polynomials for function approximation. GCR is among the best estimators for the central subspace, but its sample complexity is an open question. In this paper, we partially answer this questions by proving that if a variance quantity is exactly known, GCR leads to a mean squared estimation error of $O(n^{-1})$ for the central subspace. The estimation error of this variance quantity is also given in this paper. The mean squared regression error of $f$ is proved to be in the order of $(n/\log n)^{-\frac{2s}{2s+d}}$, where the exponent depends on the dimension of the central subspace instead of the ambient space . This result demonstrates that GCR is effective in learning the low-dimensional central subspace. We also propose a modified GCR with improved efficiency. Here, the convergence rate is validated through several numerical experiments.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1986

Entropy conservative finite element schemes

The question of entropy stability for discrete approximations to hyperbolic systems of conservation laws is studied. The amount of numerical viscosity present in such schemes is quantified and related to their entropy stability by means of comparison. To this end, two main ingredients are used: entropy variables and the construction of certain entropy conservative schemes in terms of piecewise-linear finite element approximations. It is then shown that conservative schemes are entropy stable, if and (for three-point schemes) only if, they contain more numerical viscosity than the abovementioned entropy conservation ones.

Tadmor, E.↗
NASA NTRS1985

The Definition and Computation of a Metric on Plane Curves. The Meaning of a Face on a Geometric Model

Two topics in topology, the comparison of plane curves and faces on geometric models, are discussed. With regard to the first problem, a curve is defined to be a locus of points without any underlying parameterization. A metric on a class of plane curves is defined, a finite computation of this metric is given for the case of piecewise linear curves, and it is shown how to approximate curves that have bounded curvature by piecewise linear curves. In this way a bound on the distance between two curves can be computed. With regard to the second problem, the questions to be discussed are under what circumstances do geometrical faces make sense; how can they be explicity defined; and when are these geometrical faces homeomorphic to the realization of the abstract (topological) face.

Emery, J. D.↗
DOE OSTI2024

A Data-Driven Approach for High-Impedance Fault Localization in Distribution Systems [SWR-24-13]

This software provides a data-driven approach for efficiently identifying high impedance faults (HIFs) in distribution systems. To tackle the nonlinearity of the voltage current trajectory of HIFs, we first formulate linear least squares problems to approximate the trajectory with piecewise functions. Then we collect the function features of all segments as inputs and use the support vector machine approach to efficiently identify HIFs at different locations.

Zhou, Yuqi↗