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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Comparison of Two Algebraic Methods for Curve/curve Intersection

Most geometric modeling systems use either polynomial or rational functions to represent geometry. In such systems most computational problems can be formulated as systems of polynomials in one or more variables. Classical elimination theory can be used to solve such systems. Here Cayley's method of elimination is summarized and it is shown how it can best be used to solve the curve/curve intersection problem. Cayley's method was found to be a more straightforward approach. Furthermore, it is computationally simpler, since the elements of the Cayley matrix are one variable instead of two variable polynomials. Researchers implemented and tested both methods and found Cayley's to be more efficient. Six pairs of curves, representing mixtures of lines, circles, and cubic arcs were used. Several examples had multiple intersection points. For all six cases Cayley's required less CPU time than the other method. The average time ratio of method 1 to method 2 was 3.13:1, the least difference was 2.33:1, and the most dramatic was 6.25:1. Both of the above methods can be extended to solve the surface/surface intersection problem.

Demontaudouin, Y.↗
NASA NTRS1986

Physical and numerical sources of computational inefficiency in integration of chemical kinetic rate equations: Etiology, treatment and prognosis

The design of a very fast, automatic black-box code for homogeneous, gas-phase chemical kinetics problems requires an understanding of the physical and numerical sources of computational inefficiency. Some major sources reviewed in this report are stiffness of the governing ordinary differential equations (ODE's) and its detection, choice of appropriate method (i.e., integration algorithm plus step-size control strategy), nonphysical initial conditions, and too frequent evaluation of thermochemical and kinetic properties. Specific techniques are recommended (and some advised against) for improving or overcoming the identified problem areas. It is argued that, because reactive species increase exponentially with time during induction, and all species exhibit asymptotic, exponential decay with time during equilibration, exponential-fitted integration algorithms are inherently more accurate for kinetics modeling than classical, polynomial-interpolant methods for the same computational work. But current codes using the exponential-fitted method lack the sophisticated stepsize-control logic of existing black-box ODE solver codes, such as EPISODE and LSODE. The ultimate chemical kinetics code does not exist yet, but the general characteristics of such a code are becoming apparent.

Pratt, D. T.↗
NASA NTRS1990

Computational tools for multi-linked flexible structures

A software module which designs and tests controllers and filters in Kalman Estimator form, based on a polynomial state-space model is discussed. The user-friendly program employs an interactive graphics approach to simplify the design process. A variety of input methods are provided to test the effectiveness of the estimator. Utilities are provided which address important issues in filter design such as graphical analysis, statistical analysis, and calculation time. The program also provides the user with the ability to save filter parameters, inputs, and outputs for future use.

Lee, Gordon K. F.↗
NASA NTRS1994

Correcting the distortion of images taken with the ultraviolet imaging telescope

The Ultraviolet Imaging Telescope (UIT) cameras include two-stage magnetically focused image intensifiers that introduce small but significant geometrical distortions into the data. These distortions, which create positional offsets as large as 25 arcsec at the field edges, are corrected by the procedure described here to 2-3 arcsec, approximately the resolution of the images. The distortion is measured by comparing and correcting UIT images to digitized Guidestar survey plates of the same fields. Two-dimensional third-order polynomials are used to model the distortion. The models assume that the distortion is an instrumental effect, independent of mission elapsed time and target, and that the effect of distortion is an instrumental effect, independent of mission elapsed time and target, and that the effect of distortion in the center of each field is minimal. The models are used to improve computed astrometric plate solutions and to remove the geometric distortion while transforming the image to a standard north-up, ease-left orientation.

Greason, M. R.↗
NASA NTRS2002

A Numerical Scheme for Ordinary Differential Equations Having Time Varying and Nonlinear Coefficients Based on the State Transition Matrix

A variable order method of integrating initial value ordinary differential equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. While it is more complex than most other methods, it produces exact solutions at arbitrary time step size when the time variation of the system can be modeled exactly by a polynomial. Solutions to several nonlinear problems exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with an exact solution and with solutions obtained by established methods.

Bartels, Robert E.↗
NASA NTRS2008

Modeling State-Space Aeroelastic Systems Using a Simple Matrix Polynomial Approach for the Unsteady Aerodynamics

A simple matrix polynomial approach is introduced for approximating unsteady aerodynamics in the s-plane and ultimately, after combining matrix polynomial coefficients with matrices defining the structure, a matrix polynomial of the flutter equations of motion (EOM) is formed. A technique of recasting the matrix-polynomial form of the flutter EOM into a first order form is also presented that can be used to determine the eigenvalues near the origin and everywhere on the complex plane. An aeroservoelastic (ASE) EOM have been generalized to include the gust terms on the right-hand side. The reasons for developing the new matrix polynomial approach are also presented, which are the following: first, the "workhorse" methods such as the NASTRAN flutter analysis lack the capability to consistently find roots near the origin, along the real axis or accurately find roots farther away from the imaginary axis of the complex plane; and, second, the existing s-plane methods, such as the Roger s s-plane approximation method as implemented in ISAC, do not always give suitable fits of some tabular data of the unsteady aerodynamics. A method available in MATLAB is introduced that will accurately fit generalized aerodynamic force (GAF) coefficients in a tabular data form into the coefficients of a matrix polynomial form. The root-locus results from the NASTRAN pknl flutter analysis, the ISAC-Roger's s-plane method and the present matrix polynomial method are presented and compared for accuracy and for the number and locations of roots.

Pototzky, Anthony S.↗
NASA NTRS2018

Multifidelity Uncertainty Quantification of a Commercial Supersonic Transport

The objective of this work was to develop a multifidelity uncertainty quantification approach for efficient analysis of a commercial supersonic transport concept. An approach based on point-collocation, non-intrusive polynomial chaos was formulated in which a low-fidelity model could be corrected using multiple higher-fidelity models. The formulation and methodology also allows for the addition of uncertainty sources not present in the lower fidelity models. To demonstrate the applicability and potential computational savings of the multifidelity polynomial chaos approach, two model problems were explored. The first was a supersonic airfoil with three levels of modeling fidelity, each capturing a gradual increase in modeling of the underlying flow physics. As much as 50% computational cost reduction was observed using the mutlifidelity approach, while predicting nearly the same amount of uncertainty in drag. The second problem was a commercial supersonic transport. This model had three levels of fidelity that included two different modeling approaches and the addition of physics between the fidelity levels. Results of this analysis yielded nearly a 70% computational savings to predict a comparable amount of uncertainty in ground noise. Both problems illustrate the applicability and significant computational savings of the multifidelity method for efficient and accurate uncertainty quantification.

Thomas K. West IV↗
NASA NTRS1994

Empirical Modeling of Plant Gas Fluxes in Controlled Environments

As humans extend their reach beyond the earth, bioregenerative life support systems must replace the resupply and physical/chemical systems now used. The Controlled Ecological Life Support System (CELSS) will utilize plants to recycle the carbon dioxide (CO2) and excrement produced by humans and return oxygen (O2), purified water and food. CELSS design requires knowledge of gas flux levels for net photosynthesis (PS(sub n)), dark respiration (R(sub d)) and evapotranspiration (ET). Full season gas flux data regarding these processes for wheat (Triticum aestivum), soybean (Glycine max) and rice (Oryza sativa) from published sources were used to develop empirical models. Univariate models relating crop age (days after planting) and gas flux were fit by simple regression. Models are either high order (5th to 8th) or more complex polynomials whose curves describe crop development characteristics. The models provide good estimates of gas flux maxima, but are of limited utility. To broaden the applicability, data were transformed to dimensionless or correlation formats and, again, fit by regression. Polynomials, similar to those in the initial effort, were selected as the most appropriate models. These models indicate that, within a cultivar, gas flux patterns appear remarkably similar prior to maximum flux, but exhibit considerable variation beyond this point. This suggests that more broadly applicable models of plant gas flux are feasible, but univariate models defining gas flux as a function of crop age are too simplistic. Multivariate models using CO2 and crop age were fit for PS(sub n), and R(sub d) by multiple regression. In each case, the selected model is a subset of a full third order model with all possible interactions. These models are improvements over the univariate models because they incorporate more than the single factor, crop age, as the primary variable governing gas flux. They are still limited, however, by their reliance on the other environmental conditions under which the original data were collected. Three-dimensional plots representing the response surface of each model are included. Suitability of using empirical models to generate engineering design estimates is discussed. Recommendations for the use of more complex multivariate models to increase versatility are included.

Cornett, Jessie David↗
NASA NTRS1993

Robust stability of diamond families of polynomials with complex coefficients

Like the interval model of Kharitonov, the diamond model proves to be an alternative powerful device for taking into account the variation of parameters in prescribed ranges. The robust stability of some kinds of diamond polynomial families with complex coefficients are discussed. By exploiting the geometric characterizations of their value sets, we show that, for the family of polynomials with complex coefficients and both their real and imaginary parts lying in a diamond, the stability of eight specially selected extreme point polynomials is necessary as well as sufficient for the stability of the whole family. For the so-called simplex family of polynomials, four extreme point and four exposed edge polynomials of this family need to be checked for the stability of the entire family. The relations between the stability of various diamonds are also discussed.

Xu, Zhong Ling↗
NASA NTRS2012

Response Surface Modeling Tolerance and Inference Error Risk Specifications: Proposed Industry Standards

This paper reviews the derivation of an equation for scaling response surface modeling experiments. The equation represents the smallest number of data points required to fit a linear regression polynomial so as to achieve certain specified model adequacy criteria. Specific criteria are proposed which simplify an otherwise rather complex equation, generating a practical rule of thumb for the minimum volume of data required to adequately fit a polynomial with a specified number of terms in the model. This equation and the simplified rule of thumb it produces can be applied to minimize the cost of wind tunnel testing.

DeLoach, Richard↗
NASA NTRS1983

On the determination of airplane model structure form flight data

A procedure based on a modified stepwise regression and several selection criteria is presented for the determination of airplane model structure from flight data. The aerodynamic force and moment coefficients in an airplane model are expresed either as polynomials in output and input variables or as a combination of splines. The procedure is demonstrated in three examples by attempting to determine a local, extended and global model. Some of the resulting models are verified by using the maximum likelihood estimation or by examining model prediction capabilities.

Klein, V.↗
DOE OSTI2025

A DATA EFFICIENT SPARSE MODELING FRAMEWORK FOR POWER ESTIMATION IN WATER TREATMENT SENSING OPERATIONS

With increasing freshwater scarcity, advanced process design mechanisms such as Closed-Circuit Reverse Osmosis (CCRO) and Digital/Physical Twin systems are gaining traction in water treatment and reuse operations. While digital and physical twin models enable improved system insight and control, their development is often expensive and computationally intensive, requiring large volumes of synthetic or experimental data to characterize underlying process dynamics. This work introduces a sparse surrogate modeling framework to estimate power consumption from measured flow and pressure variables, along with their nonlinear polynomial and interaction expansions. To ensure model reliability and reduce overfitting, a two-stage pipeline is proposed. First, a dynamic data filtering algorithm is employed to remove uninformative observations and transient operational states. Second, a sparse penalized regression technique is applied to select a minimal set of parsimonious features. The proposed model achieves high sparsity, retaining only 7 out of 34 candidate features (≈79.41% sparsity) while delivering a root mean square error (RMSE) of 0.072 on the test dataset.

Mukherjee, Subrata [ORNL] (ORCID:0000000309930338)↗
NASA NTRS2004

Applications of Response Surface-Based Methods to Noise Analysis in the Conceptual Design of Revolutionary Aircraft

Due to the growing problem of noise in today's air transportation system, there have arisen needs to incorporate noise considerations in the conceptual design of revolutionary aircraft. Through the use of response surfaces, complex noise models may be converted into polynomial equations for rapid and simplified evaluation. This conversion allows many of the commonly used response surface-based trade space exploration methods to be applied to noise analysis. This methodology is demonstrated using a noise model of a notional 300 passenger Blended-Wing-Body (BWB) transport. Response surfaces are created relating source noise levels of the BWB vehicle to its corresponding FAR-36 certification noise levels and the resulting trade space is explored. Methods demonstrated include: single point analysis, parametric study, an optimization technique for inverse analysis, sensitivity studies, and probabilistic analysis. Extended applications of response surface-based methods in noise analysis are also discussed.

Hill, Geoffrey A.↗
NASA NTRS1998

Predicting lettuce canopy photosynthesis with statistical and neural network models

An artificial neural network (NN) and a statistical regression model were developed to predict canopy photosynthetic rates (Pn) for 'Waldman's Green' leaf lettuce (Latuca sativa L.). All data used to develop and test the models were collected for crop stands grown hydroponically and under controlled-environment conditions. In the NN and regression models, canopy Pn was predicted as a function of three independent variables: shootzone CO2 concentration (600 to 1500 micromoles mol-1), photosynthetic photon flux (PPF) (600 to 1100 micromoles m-2 s-1), and canopy age (10 to 20 days after planting). The models were used to determine the combinations of CO2 and PPF setpoints required each day to maintain maximum canopy Pn. The statistical model (a third-order polynomial) predicted Pn more accurately than the simple NN (a three-layer, fully connected net). Over an 11-day validation period, average percent difference between predicted and actual Pn was 12.3% and 24.6% for the statistical and NN models, respectively. Both models lost considerable accuracy when used to determine relatively long-range Pn predictions (> or = 6 days into the future).

Non-NASA Center↗
DOE OSTI2021

An extended polynomial chaos expansion for PDF characterization and variation with aleatory and epistemic uncertainties

This paper presents an extended polynomial chaos formalism for epistemic uncertainties and a new framework for evaluating sensitivities and variations of output probability density functions (PDF) to uncertainty in probabilistic models of input variables. An ”extended” polynomial chaos expansion (PCE) approach is developed that accounts for both aleatory and epistemic uncertainties, modeled as random variables, thus allowing a unified treatment of both types of uncertainty. We explore in particular epistemic uncertainty associated with the choice of prior probabilistic models for input parameters. A PCE-based Kernel Density (KDE) construction provides a composite map from the PCE coefficients and germ to the PDF of quantities of interest (QoI). Here, the sensitivities of these PDF with respect to the input parameters are then evaluated. Input parameters of the probabilistic models are considered. By sampling over the epistemic random variable, a family of PDFs is generated and the failure probability is itself estimated as a random variable with its own PCE. Integrating epistemic uncertainties within the PCE framework results in a computationally efficient paradigm for propagation and sensitivity evaluation. Two typical illustrative examples are used to demonstrate the proposed approach.

Aleatory uncertainty↗
DOE OSTI2025

Uncertainty quantification and sensitivity analysis of a nuclear thermal propulsion reactor startup sequence

The research presented in this article describes progress in applying stochastic methods, uncertainty quantification, parametric studies, and variance-based sensitivity analysis (also known as Sobol sensitivity analysis) to a full-core model of a nuclear thermal propulsion (NTP) system simulated via the radiation transport code Griffin to simulate neutronics. Our goal is to develop a reduced-order (surrogate) model that can be rapidly sampled with perturbations to multiple input parameters. In this NTP system, reactivity and power feedback affect the rotation of control drums (CDs), which is itself controlled by a hybrid proportional-integral-derivative (PID) controller actuated by the power demand and reactivity feedback from the numerical model. This model uses reactor kinetic feedback (mean generation time [Λ] and effective delayed neutron fraction [ β eff ] from a transient Griffin simulation executed via Griffin’s improved quasi-static solver to provide the kinetic parameters) as inputs to functions that control the CD rotation angle. By investigating numerous stochastic approaches, we developed a dual-purpose surrogate model of the NTP system, using polynomial regression in the Multiphysics Object-Oriented Simulation Environment (MOOSE) Stochastic Tools Module (STM). The trained model can be rapidly sampled while simultaneously perturbing various input parameters, such as coefficients on the PID control or temperature (directly affecting the neutron cross section). The surrogate model delivers accurate (within 5%) results at speeds orders of magnitude faster (minutes, not days of computational time) than the base model. Once the surrogate model has been trained, distributions of the uncertain parameters can be changed at will to investigate the effects of perturbing multiple inputs as well as the effects of these inputs on the model output. For example, coefficients used in the PID control system may vary due to some type of physical interference, or uncertainty may exist in the temperature of the neutron cross sections in various regions of the reactor. A distribution can be placed on these parameters, and operational boundaries can be determined. The goal of this work is to support development of an advanced control system for operating CDs in a functioning NTP system. This work is a scoping study of the MOOSE STM.

21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗
DOE OSTI2022

Field Sensitivity Analysis of Turbulence Model Parameters for Flow Over a Wing

Reynolds-averaged-Navier-Stokes (RANS) turbulence models are a critical tool in computational-fluid-dynamics simulations of aerodynamic systems, but simulation results can be highly sensitive to RANS-model parameter choices. Sensitivity analysis can be used to quantify these impacts, and the objective of this study is to demonstrate field sensitivity analysis with respect to ten parameters in the 2003 Menter shear-stress-transport (SST) turbulence model. Here, the analysis is demonstrated for an application relevant to wind energy, namely, flow over a NACA 0015 wing at 12 degree angle of attack and a Reynolds number of 1.5 x 10 6 . We quantify sensitivity using Sobol indices and the mean-squared gradient, which are estimated using polynomial chaos and active subspace models, respectively. Our results indicate that there are substantial spatial variations in parameter sensitivities, with different sets of most-sensitive parameters near the wing, as well as in the downstream wake, consistent with the physical interpretations of the turbulence model inputs. We show that, for this particular turbulence model and flow, simultaneous dimension reduction is possible across all quantities of interest, enabling efficient exploration of model outcomes. Ultimately, this analysis provides new insights into turbulence model parameter sensitivities in incompressible flows, and also demonstrates the implementation of field sensitivity analysis for applications relevant to aerodynamics simulations.

17 WIND ENERGY↗
NASA NTRS1983

Determination of airplane model structure from flight data using splines and stepwise regression

A procedure for the determination of airplane model structure from flight data is presented. The model is based on a polynomial spline representation of the aerodynamic coefficients, and the procedure is implemented by use of a stepwise regression. First, a form of the aerodynamic force and moment coefficients amenable to the utilization of splines is developed. Next, expressions for the splines in one and two variables are introduced. Then the steps in the determination of an aerodynamic model structure and the estimation of parameters are discussed briefly. The focus is on the application to flight data of the techniques developed.

Klein, V.↗