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Results for “equation recovery”

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 NTRS1982

An analytical technique for the analysis of airplane spin entry and recovery

The dynamic equations of motion for a spinning airplane are simplified to facilitate the analysis of spin entry and recovery maneuvers. Solutions of a nonlinear, first order equation for spin rate enable calculation of spin entry and recovery times and control required for recovery. The analysis is applied to a light airplane for which both aerodynamic data, rotory balance wind tunnel tests, and spin flight test data have been obtained. A comparison of predicted and actual transient spin responses is made which supports the validity of the analytical approach taken but which also illustrates the difficulty in obtaining accurate aerodynamic data for spinning airplanes. Certain normalized parameters of the reduced state spin equation suggest criteria for assessing the transient spin characteristics of light airplanes.

Taylor, L. W., Jr.↗
DOE OSTI2021

Data-Driven Learning of Nonautonomous Systems

In this work, we present a numerical framework for recovering unknown nonautonomous dynamical systems with time-dependent inputs. To circumvent the difficulty presented by the nonautonomous nature of the system, our method transforms the solution state into piecewise integration of the system over a discrete set of time instances. The time-dependent inputs are then locally parameterized by using a proper model, for example, polynomial regression, in the pieces determined by the time instances. This transforms the original system into a piecewise parametric system that is locally time invariant. We then design a deep neural network structure to learn the local models. Once the network model is constructed, it can be iteratively used over time to conduct global system prediction. We provide theoretical analysis of our algorithm and present a number of numerical examples to demonstrate the effectiveness of the method.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1993

The viscoplastic behavior of Hastelloy-X single crystal

A viscoplastic constitutive model for simulating the behavior of Hastelloy-X single crystal material was derived based on crystallographic slip theory. To determine the appropriate constitutive model constants and to test the predictions of the model, tests on Hastelloy-X crystals were carried out, including the rate sensitivity, cyclic hardening, nonproportional hardening, relaxation, and strain rate dip tests. It was found necessary to include cube slip in the model in order to correlate the uniaxial behavior of the single crystal, to incorporate the interaction effects in both the hardening and the dynamic recovery evolution equations for the drag stress, and to successfully capture correct strain rate sensitivity under biaxial tension-torsion loading conditions.

Jordan, Eric H.↗
NASA NTRS1992

Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method

A lattice Boltzmann model is presented which gives the complete Navier-Stokes equation and may provide an efficient parallel numerical method for solving various fluid problems. The model uses the single-time relaxation approximation and a particular Maxwell-type distribution. The model eliminates exactly (1) the non-Galilean invariance caused by a density-dependent coefficient in the convection term and (2) a velocity-dependent equation of state.

Chen, Hudong↗
NASA NTRS1988

An experimental comparison of several current viscoplastic constitutive models at elevated temperature

Four current viscoplastic models are compared experimentally for Inconel 718 at 593 C. This material system responds with apparent negative strain rate sensitivity, undergoes cyclic work softening, and is susceptible to low cycle fatigue. A series of tests were performed to create a data base from which to evaluate material constants. A method to evaluate the constants is developed which draws on common assumptions for this type of material, recent advances by other researchers, and iterative techniques. A complex history test, not used in calculating the constants, is then used to compare the predictive capabilities of the models. The combination of exponentially based inelastic strain rate equations and dynamic recovery is shown to model this material system with the greatest success. The method of constant calculation developed was successfully applied to the complex material response encountered. Backstress measuring tests were found to be invaluable and to warrant further development.

James, G. H.↗
NASA NTRS2016

Basin-Scale Assessment of the Land Surface Water Budget in the National Centers for Environmental Prediction Operational and Research NLDAS-2 Systems

The purpose of this study is to evaluate the components of the land surface water budget in the four land surface models (Noah, SAC-Sacramento Soil Moisture Accounting Model, (VIC) Variable Infiltration Capacity Model, and Mosaic) applied in the newly implemented National Centers for Environmental Prediction (NCEP) operational and research versions of the North American Land Data Assimilation System version 2 (NLDAS-2). This work focuses on monthly and annual components of the water budget over 12 National Weather Service (NWS) River Forecast Centers (RFCs). Monthly gridded FLUX Network (FLUXNET) evapotranspiration (ET) from the Max-Planck Institute (MPI) of Germany, U.S. Geological Survey (USGS) total runoff (Q), changes in total water storage (dS/dt, derived as a residual by utilizing MPI ET and USGS Q in the water balance equation), and Gravity Recovery and Climate Experiment (GRACE) observed total water storage anomaly (TWSA) and change (TWSC) are used as reference data sets. Compared to these ET and Q benchmarks, Mosaic and SAC (Noah and VIC) in the operational NLDAS-2 overestimate (underestimate) mean annual reference ET and underestimate (overestimate) mean annual reference Q. The multimodel ensemble mean (MME) is closer to the mean annual reference ET and Q. An anomaly correlation (AC) analysis shows good AC values for simulated monthly mean Q and dS/dt but significantly smaller AC values for simulated ET. Upgraded versions of the models utilized in the research side of NLDAS-2 yield largely improved performance in the simulation of these mean annual and monthly water component diagnostics. These results demonstrate that the three intertwined efforts of improving (1) the scientific understanding of parameterization of land surface processes, (2) the spatial and temporal extent of systematic validation of land surface processes, and (3) the engineering-oriented aspects such as parameter calibration and optimization are key to substantially improving product quality in various land data assimilation systems.

NLDAS-2↗
DOE OSTI2022

Efficient Interdependent Systems Recovery Modeling with DeepONets

Modeling the recovery of interdependent critical infrastructure is a key component of quantifying and optimizing societal resilience to disruptive events. However, simulating the recovery of large-scale interdependent systems under random disruptive events is computationally expensive. Therefore, we propose the application of Deep Operator Networks (DeepONets) in this paper to accelerate the recovery modeling of interdependent systems. DeepONets are ML architectures which identify mathematical operators from data. The form of governing equations DeepONets identify and the governing equation of interdependent systems recovery model are similar. Therefore, we hypothesize that DeepONets can efficiently model the interdependent systems recovery with little training data. We applied DeepONets to a simple case of four interdependent systems with sixteen states. DeepONets, overall, performed satisfactorily in predicting the recovery of these interdependent systems for out of training sample data when compared to reference results.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1988

Thermoviscoplastic model with application to copper

A viscoplastic model is developed which is applicable to anisothermal, cyclic, and multiaxial loading conditions. Three internal state variables are used in the model; one to account for kinematic effects, and the other two to account for isotropic effects. One of the isotropic variables is a measure of yield strength, while the other is a measure of limit strength. Each internal state variable evolves through a process of competition between strain hardening and recovery. There is no explicit coupling between dynamic and thermal recovery in any evolutionary equation, which is a useful simplification in the development of the model. The thermodynamic condition of intrinsic dissipation constrains the thermal recovery function of the model. Application of the model is made to copper, and cyclic experiments under isothermal, thermomechanical, and nonproportional loading conditions are considered. Correlations and predictions of the model are representative of observed material behavior.

Freed, Alan D.↗
NASA NTRS1991

Sinc-Galerkin estimation of diffusivity in parabolic problems

A fully Sinc-Galerkin method for the numerical recovery of spatially varying diffusion coefficients in linear partial differential equations is presented. Because the parameter recovery problems are inherently ill-posed, an output error criterion in conjunction with Tikhonov regularization is used to formulate them as infinite-dimensional minimization problems. The forward problems are discretized with a sinc basis in both the spatial and temporal domains thus yielding an approximate solution which displays an exponential convergence rate and is valid on the infinite time interval. The minimization problems are then solved via a quasi-Newton/trust region algorithm. The L-curve technique for determining an approximate value of the regularization parameter is briefly discussed, and numerical examples are given which show the applicability of the method both for problems with noise-free data as well as for those whose data contains white noise.

Smith, Ralph C.↗
NASA NTRS1984

A simple application of the Bailey-Orowan creep model to Fe-39.8 at. pct Al and gamma/gamma prime - alpha

The results of a study to determine the recovery rates and work-hardening coefficients for creep from constant cross-head speed compressive tests are presented. Stressing and straining rates are computed from measured time-load curves obtained from compression testing between 1200 and 1400 K of several B2 crystal structure Fe-39.8 Al intermetallic materials and the directionally solidified eutectic alloy gamma/gamma prime alpha. These quantities are then fitted to the universal form of the Bailey-Orowan equation for creep. The recovery rates were found to be functions of nominal strain rate, stress, and temperature, while the hardening coefficients were dependent only on temperature. While the work-hardening coefficient for gamma/gamma prime - alpha was about 0.05 of the elastic modulus, the work-hardening coefficients for Fe-39.8 at. pct Al were less than 0.002 of the modulus.

Whittenberger, J. D.↗
NASA NTRS1989

A mathematical model of physiological processes and its application to the study of aging

The behavior of a physiological system which, after displacement, returns by homeostatic mechanisms to its original condition can be described by a simple differential equation in which the "recovery time" is a parameter. Two such systems, which influence one another, can be linked mathematically by the use of "coupling" or "feedback" coefficients. These concepts are the basis for many mathematical models of physiological behavior, and we describe the general nature of such models. Next, we introduce the concept of a "fatal limit" for the displacement of a physiological system, and show how measures of such limits can be included in mathematical models. We show how the numerical values of such limits depend on the values of other system parameters, i.e., recovery times and coupling coefficients, and suggest ways of measuring all these parameters experimentally, for example by monitoring changes induced by X-irradiation. Next, we discuss age-related changes in these parameters, and show how the parameters of mortality statistics, such as the famous Gompertz parameters, can be derived from experimentally measurable changes. Concepts of onset-of-aging, critical or fatal limits, equilibrium value (homeostasis), recovery times and coupling constants are involved. Illustrations are given using published data from mouse and rat populations. We believe that this method of deriving survival patterns from model that is experimentally testable is unique.

Aging/physiology↗
NASA NTRS1988

Structure of a viscoplastic theory

The general structure of a viscoplastic theory is developed from physical and thermodynamical considerations. The flow equation is of classical form. The dynamic recovery approach is shown to be superior to the hardening function approach for incorporating nonlinear strain hardening into the material response through the evolutionary equation for back stress. A novel approach for introducing isotropic strain hardening into the theory is presented, which results in a useful simplification. In particular, the limiting stress for the kinematic saturation of state (not the drag stress) is the chosen scalar-valued state variable. The resulting simplification is that there is no coupling between dynamic and thermal recovery terms in each evolutionary equation. The derived theory of viscoplasticity has the structure of a two-surface plasticity theory when the response is plasticlike, and the structure of a Bailey-Orowan creep theory when the response is creeplike.

Freed, Alan D.↗
NASA NTRS1988

A viscoplastic theory applied to copper

A phenomenologically based viscoplastic model is derived for copper. The model is thermodynamically constrained by the condition of material dissipativity. Two internal state variables are considered. The back stress accounts for strain-induced anisotropy, or kinematic hardening. The drag stress accounts for isotropic hardening. Static and dynamic recovery terms are not coupled in either evolutionary equation. The evolution of drag stress depends on static recovery, while the evolution of back stress depends on dynamic recovery. The material constants are determined from isothermal data. Model predictions are compared with experimental data for thermomechanical test conditions. They are in good agreement at the hot end of the loading cycle, but the model overpredicts the stress response at the cold end of the cycle.

Freed, Alan D.↗
NASA NTRS2001

The Spatial Distribution of Forest Biomass in the Brazilian Amazon: A Comparison of Estimates

The amount of carbon released to the atmosphere as a result of deforestation is determined, in part, by the amount of carbon held in the biomass of the forests converted to other uses. Uncertainty in forest biomass is responsible for much of the uncertainty in current estimates of the flux of carbon from land-use change. We compared several estimates of forest biomass for the Brazilian Amazon, based on spatial interpolations of direct measurements, relationships to climatic variables, and remote sensing data. We asked three questions. First, do the methods yield similar estimates? Second, do they yield similar spatial patterns of distribution of biomass? And, third, what factors need most attention if we are to predict more accurately the distribution of forest biomass over large areas? Amazonian forests (including dead and below-ground biomass) vary by more than a factor of two, from a low of 39 PgC to a high of 93 PgC. Furthermore, the estimates disagree as to the regions of high and low biomass. The lack of agreement among estimates confirms the need for reliable determination of aboveground biomass over large areas. Potential methods include direct measurement of biomass through forest inventories with improved allometric regression equations, dynamic modeling of forest recovery following observed stand-replacing disturbances (the approach used in this research), and estimation of aboveground biomass from airborne or satellite-based instruments sensitive to the vertical structure plant canopies.

Houghton, R. A.↗
NASA NTRS2011

Effect of an Additional, Parallel Capacitor on Pulsed Inductive Plasma Accelerator Performance

A model of pulsed inductive plasma thrusters consisting of a set of coupled circuit equations and a one-dimensional momentum equation has been used to study the effects of adding a second, parallel capacitor into the system. The equations were nondimensionalized, permitting the recovery of several already-known scaling parameters and leading to the identification of a parameter that is unique to the particular topology studied. The current rise rate through the inductive acceleration coil was used as a proxy measurement of the effectiveness of inductive propellant ionization since higher rise rates produce stronger, potentially better ionizing electric fields at the coil face. Contour plots representing thruster performance (exhaust velocity and efficiency) and current rise rate in the coil were generated numerically as a function of the scaling parameters. The analysis reveals that when the value of the second capacitor is much less than the first capacitor, the performance of the two-capacitor system approaches that of the single-capacitor system. In addition, as the second capacitor is decreased in value the current rise rate can grow to be twice as great as the rise rate attained in the single capacitor case.

Polzin, Kurt A.↗
DOE OSTI2023

WeakIdent: Weak formulation for identifying differential equation using narrow-fit and trimming

Data-driven identification of differential equations is an interesting but challenging problem, especially when the given data are corrupted by noise. When the governing differential equation is a linear combination of various differential terms, the identification problem can be formulated as solving a linear system, with the feature matrix consisting of linear and nonlinear terms multiplied by a coefficient vector. This product is equal to the time derivative term, and thus generates dynamical behaviors. The goal is to identify the correct terms that form the equation to capture the dynamics of the given data. We propose a general and robust framework to recover differential equations using a weak formulation with two new mechanisms, narrow-fit and trimming, for both ordinary and partial differential equations (ODEs and PDEs). The weak formulation facilitates an efficient and robust way to handle noise, and two new mechanisms, narrow-fit and trimming, improve the coefficient support and value recoveries respectively. For each sparsity level, Subspace Pursuit is utilized to find an initial set of support from the large dictionary. Then, we focus on highly dynamic regions (rows of the feature matrix), and error normalize the feature matrix in the narrow-fit step. The support is further updated via trimming the terms that contribute the least. Finally, the support set of features with the smallest Cross-Validation error is chosen as the result. A comprehensive set of numerical experiments are presented for both systems of ODEs and PDEs with various noise levels. The proposed method gives a robust recovery of the coefficients, and a significant denoising effect which can handle up to 100% noise-to-signal ratio for some equations. We compare the proposed method with several state-of-the-art algorithms for the recovery of differential equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Analytic model of dislocation density evolution in fcc polycrystals accounting for dislocation generation, storage, and dynamic recovery mechanisms

Here, an analytic model of the evolution of dislocation density in fcc polycrystals is described. The evolution equations approximately account for most known dislocation storage, dynamic recovery, and dislocation generation mechanisms in fcc polycrystals. Specifically, the model incorporates network (forest) and grain boundary storage, mobile-network and mobile–mobile annihilation, screw–screw annihilation via athermal and thermal single cross-slip, generation by double cross-slip (Koehler mechanism, including dipole formation), Frank-Read sources, grain boundary nucleation, and mobile–immobile dislocation nucleation due to shock loading. Single cross-slip is assumed to proceed through the Friedel–Escaig (FE) mechanism; the corresponding activation energy is calculated using a modified FE model. The activation energy for double cross-slip is calculated for the first time by extending the FE model. The exact evolution equations are integro-differential equations, and as such are difficult to implement in a code; hence, the evolution equations are simplified by making several approximations. Preliminary results on copper are presented, including comparisons to experimental data.

36 MATERIALS SCIENCE↗