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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Data-driven predictive probability density function control of fiber length stochastic distribution shaping in refining process

Pulp is the most important raw material in paper in paper industries, whose Fiber Length Stochastic Distribution (FLSD) shaping directly determines the energy consumption and paper quality of the subsequent papermaking processes. However, the mean and variance are insufficient to describe the output FLSD shaping, which display non-Gaussian distribution properties. Therefore, the traditional control, method based on the mean and variance of fiber length is difficult to control the FLSD shaping effectively. In this paper, a novel data-driven predictive probability density function (PDF) control method is proposed for output FLSD shaping in refining process. Primarily, in order to improve the approximation accuracy of the PDF employing RBF neural network, the parameters (center value and width) of each RBF basis functions are tuned via utilizing iterative learning control (ILC) law, and the corresponding estimations of weights law can be obtained. Secondly, considering that the conventional linear model of weights vector has drawbacks of low accuracy and weak generalization ability, random vector functional link networks (RVFLNs) based data driven nonlinear modelling method is employed to characterize the prediction model between the input variables and weights vector. Finally, in order to reduce the randomness of the output FLSD, a minimum entropy control method under mean constraint is employed to design the predictive PDF controller for the output FLSD shaping with the help of the established nonlinear stochastic distribution model. Both simulations and experiments are given to illustrate the effectiveness and practicability of the proposed method.

Probability debsity function, Fiber length distrib↗
NASA NTRS1986

Model reference adaptive attitude control of spacecraft using reaction wheels

A nonlinear model reference adaptive control law for large angle rotational maneuvers of spacecraft using reaction wheels in the presence of uncertainty is presented. The derivation of control law does not require any information on the values of the system parameters and the disturbance torques acting on the spacecraft. The controller includes a dynamic system in the feedback path. The control law is a nonlinear function of the attitude error, the rate of the attitude error, and the compensator state. Simulation results are prsented to show that large angle rotational maneuvers can be performed in spite of the uncertainty in the system.

Singh, Sahjendra N.↗
NASA NTRS1993

Neural net forecasting for geomagnetic activity

We use neural nets to construct nonlinear models to forecast the AL index given solar wind and interplanetary magnetic field (IMF) data. We follow two approaches: (1) the state space reconstruction approach, which is a nonlinear generalization of autoregressive-moving average models (ARMA) and (2) the nonlinear filter approach, which reduces to a moving average model (MA) in the linear limit. The database used here is that of Bargatze et al. (1985).

Hernandez, J. V.↗
NASA NTRS1985

Artificial dissipation models for the Euler equations

Various artificial dissipation models which are used with central difference algorithms for the Euler equations are analyzed for their effect on accuracy, stability and convergence rates. In particular, linear and nonlinear models are investigated using an implicit approximate factorization code (ARC2D) for transonic airfoils. Fully implicit application of the dissipation models is shown to improve robustness and convergence rates. The treatment of dissipation models at boundaries will be examined. It will be shown that accurate, error free solutions with sharp shocks can be obtained using a central difference algorithm coupled with an appropriate nonlinear artificial dissipation model.

Pulliam, T. H.↗
NASA NTRS2007

LMI-Based Generation of Feedback Laws for a Robust Model Predictive Control Algorithm

This technical note provides a mathematical proof of Corollary 1 from the paper 'A Nonlinear Model Predictive Control Algorithm with Proven Robustness and Resolvability' that appeared in the 2006 Proceedings of the American Control Conference. The proof was omitted for brevity in the publication. The paper was based on algorithms developed for the FY2005 R&TD (Research and Technology Development) project for Small-body Guidance, Navigation, and Control [2].The framework established by the Corollary is for a robustly stabilizing MPC (model predictive control) algorithm for uncertain nonlinear systems that guarantees the resolvability of the associated nite-horizon optimal control problem in a receding-horizon implementation. Additional details of the framework are available in the publication.

algorithms↗
DOE OSTI2022

Bayesian Optimization Framework for Imperfect Data or Models

Conventional Bayesian optimization methods implicitly assume that the data and model being optimized are “perfect.” This assumption leads to inaccurate posterior probability distribution functions (PDFs) when applied to “imperfect” data or models. The new Bayesian optimization framework presented in this report provides a way to parameterize the effect of imperfections usually encountered in a prior PDF of generalized data or a model on the posterior PDF. The effects of imperfections are parameterized by a set of constraints imposed on the posterior expectation values of deviations between the data and the model and on their covariance matrix elements. A particular set of values for these constraints conveys an evaluator’s best estimate of the effect of imperfections on the corresponding posterior expectation values. When a prior PDF of generalized data is assumed to be normal, an expression for a posterior PDF satisfying an arbitrary set of constraints is derived analytically for linear models. An analogous iterative algorithm is given for nonlinear models. The corresponding posterior PDF should be used to estimate any posterior expectation values in the presence of imperfections parameterized by that set of constraints. A posterior PDF of a conventional Bayesian optimization method is recovered analytically when all evaluator-specified constraints are set to zero (i.e., in the absence of any imperfections). The analytical expressions derived in this report for normal PDFs and linear models were verified numerically by a Metropolis–Hastings Monte Carlo method. The methods presented herein could be applied to any kind of data or models, including differential cross-section data or integral benchmark experiments.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

Space Shuttle Main Engine structural analysis and data reduction/evaluation. Volume 1: Aft Skirt analysis

Using the ANSYS finite element program, a global model of the aft skirt and a detailed nonlinear model of the failure region was made. The analysis confirmed the area of failure in both STA-2B and STA-3 tests as the forging heat affected zone (HAZ) at the aft ring centerline. The highest hoop strain in the HAZ occurs in this area. However, the analysis does not predict failure as defined by ultimate elongation of the material equal to 3.5 percent total strain. The analysis correlates well with the strain gage data from both the Wyle influence test of the original design aft sjirt and the STA-3 test of the redesigned aft skirt. it is suggested that the sensitivity of the failure area material strength and stress/strain state to material properties and therefore to small manufacturing or processing variables is the most likely cause of failure below the expected material ultimate properties.

Berry, David M.↗
NASA NTRS2003

Coupled Attitude and Orbit Dynamics and Control in Formation Flying Systems

Formation flying systems can range from global constellations offering extended service coverage to clusters of highly coordinated vehicles that perform distributed sensing. Recently, the use of groups of micro-satellites in the areas of near Earth explorations, deep space explorations, and military applications has received considerable attention by researchers and practitioners. To date, most proposed control strategies are based on linear models (e.g., Hill-Clohessy-Wiltshire equations) or nonlinear models that are restricted to circular reference orbits. Also, all models in the literature are uncoupled between relative position and relative attitude. In this paper, a generalized dynamic model is proposed. The reference orbit is not restricted to the circular case. In this formulation, the leader or follower satellite can be in either a circular or an elliptic orbit. In addition to maintaining a specified relative position, the satellites are also required to maintain specified relative attitudes. Thus the model presented couples vehicle attitude and orbit requirements. Orbit perturbations are also included. In particular, the J(sub 2) effects are accounted in the model. Finally, a sliding mode controller is developed and used to control the relative attitude of the formation and the simulation results are presented.

Yunjun Xu↗
NASA NTRS1987

Numerical simulation of polar lows and comma clouds using simple dry models

Linear and nonlinear numerical channel models are used to simulate polar low/comma cloud evolution. The basic state of the model is idealized and can be specified analytically. It has strong horizontal as well as vertical wind shear and implicitly includes the effect of sensible heat fluxes from the lower boundary. This is done by having a layer of reduced stability present in the lower troposphere. The results of the linear model study are presented and used to provide input for the nonlinear model integration. It is shown that, given sufficient horizontal resolution, many features of polar low/comma clouds can be simulated by the nonlinear primitive equations model and the idealized basic state, in particular a rapidly growing disturbance with a wavelength on the order of 1000 km.

Mudrick, Stephen E.↗
NASA NTRS1997

Nonlinear Spectral Mixture Modeling of Lunar Multispectral: Implications for Lateral Transport

Linear and nonlinear spectral mixture models applied to Clementine multispectral images of the Moon result in roughly similar spatial distributions of endmember abundances. However, there are important differences in the absolute values of the predicted abundances. The magnitude of these differences and the implications for understanding geological processes are investigated across a geologic contact between mare and highland in the Grimaldi Basin on the western nearside of the Moon. Vertical and lateral mass transport due to impact cratering has redistributed mare and highland materials across the contact, creating a gradient in composition. Solutions to linear and nonlinear spectral mixture models for identical spectral endmembers of mare, highland, and fresh crater materials are compared across this simple geologic contact in the Grimaldi Basin. Profiles of mare abundance across the contact are extracted and compared quantitatively. Profiles from the linear mixture models indicate that the geologic contact has an average mare abundance of 60%, and the compositional boundary is asymmetric with more mare transported onto the highland side of the contact than highland onto the mare side of the contact. In contrast the nonlinear abundance profiles indicate that the geologic contact has an average mare abundance of 50%, and the compositional boundary is remarkably symmetric. Given the expectation that materials will be intimately mixed on the surface of the Moon, and that the asymmetries implied by the linear model are not consistent with our understanding of lunar surface processes, the nonlinear spectral mixture model is preferred and should be applied whenever quantitative abundance information is required. The remarkable symmetry in the compositional gradients across this contact indicate that lateral mass transport dominates over vertical transport at this boundary.

Mustard, John F.↗
NASA NTRS1989

Nonlinear triggered lightning models for use in finite difference calculations

Two nonlinear triggered lightning models have been developed for use in finite difference calculations. Both are based on three species of air chemistry physics and couple nonlinearly calculated air conductivity to Maxwell's equations. The first model is suitable for use in three-dimensional modeling and has been applied to the analysis of triggered lightning on the NASA F106B Thunderstorm Research Aircraft. The model calculates number densities of positive ions, negative ions, and electrons as a function of time and space through continuity equations, including convective derivative terms. The set of equations is closed by using experimentally determined mobilities, and the mobilities are also used to determine the air conductivity. Results from the model's application to the F106B are shown. The second model is two-dimensional and incorporates an enhanced air chemistry formulation. Momentum conservation equations replace the mobility assumption of the first model. Energy conservation equations for neutrals, heavy ions, and electrons are also used. Energy transfer into molecular vibrational modes is accounted for. The purpose for the enhanced model is to include the effects of temperature into the air breakdown, a necessary step if the model is to simulate more than the very earliest stages of breakdown. Therefore, the model also incorporates a temperature-dependent electron avalanche rate. Results from the model's application to breakdown around a conducting ellipsoid placed in an electric field are shown.

Rudolph, Terence↗
DOE OSTI2023

Applications of the Dulmage–Mendelsohn decomposition for debugging nonlinear optimization problems

Nonlinear modeling and optimization is a valuable tool for aiding decisions by engineering practitioners, but programming an optimization problem based on a complex electrical, mechanical, or chemical process is a time-consuming and error-prone activity. Therefore, there is a need for model analysis and debugging tools that can detect and diagnose modeling errors. One such tool is the Dulmage–Mendelsohn decomposition, which identifies structurally under- and over-determined subsets in systems of equations and variables by partitioning the bipartite graph of the system. This work provides the necessary background to understand the Dulmage–Mendelsohn decomposition and its application to the analysis of nonlinear optimization problems, demonstrates its use in diagnosing a variety of modeling errors, and introduces software implementations for analyzing nonlinear optimization problems in the Pyomo and JuMP algebraic modeling languages.

42 ENGINEERING↗
DOE OSTI2023

Explainability and extrapolation of machine learning models for predicting the glass transition temperature of polymers

Abstract Machine learning (ML) offers promising tools to develop surrogate models for polymers' structure–property relations. Surrogate models can be built upon existing polymer data and are useful for rapidly predicting the properties of unknown polymers. The accuracy of such ML models appears to depend on the feature space representation of polymers, the range of training data, and learning algorithms. Here, we establish connections between these factors for predicting the glass transition temperature (T g ) of polymers. Our analysis suggests linear models with fewer fitting parameters are as accurate as nonlinear models with many hidden and unexplainable parameters. Also, the performance of a monomer topology‐based ML model is found to be qualitatively identical to that of a physicochemical descriptor‐based ML model. We find that the ML models's performance in the extrapolative region is enhanced as the property range of the training data increases. Moreover, we establish newT g – polymer chemistry correlations via ML. Our work illustrates how ML can advance the fundamental understanding of polymer structure–property correlations and its efficacy for extrapolation problems.

Polymer Science↗
NASA NTRS1987

Structural Error and Identifiability in Mathematical Models

Errors and previously implicit assumptions treated explicitly. Paper discusses errors in mathematical models of physical systems and problem of identifying model from system input and output. Problem approached by explicitly taking account of erroneous choices of model structure. Paper concerned specifically with linear or weakly nonlinear models.

Hadaegh, F. Y.↗
NASA NTRS1988

The dynamics and control of large-flexible space structures, part 10

A mathematical model is developed to predict the dynamics of the proposed orbiting Spacecraft Control Laboratory Experiment (SCOLE) during the station keeping phase. The equations of motion are derived using a Newton-Euler formulation. The model includes the effects of gravity, flexibility, and orbital dynamics. The control is assumed to be provided to the system through the Shuttle's three torquers, and through six actuators located by pairs at two points on the mast and at the mass center of the reflector. The modal shape functions are derived using the fourth order beam equation. The generic mode equations are derived to account for the effects of the control forces on the modal shape and frequencies. The equations are linearized about a nominal equilibrium position. The linear regulator theory is used to derive control laws for both the linear model of the rigidized SCOLE as well as that of the actual SCOLE including the first four flexible modes. The control strategy previously derived for the linear model of the rigidized SCOLE is applied to the nonlinear model of the same configuration of the system and preliminary single axis slewing maneuvers conducted. The results obtained confirm the applicability of the intuitive and appealing two-stage control strategy which would slew the SCOLE system, as if rigid to its desired position and then concentrate on damping out the residual flexible motions.

Bainum, Peter M.↗