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Results for “Linear and nonlinear operators”

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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Optical amplifiers for coherent lidar

We examine application of optical amplification to coherent lidar for the case of a weak return signal (a number of quanta of the return optical field close to unity). We consider the option that has been explored to date, namely, incorporation of an optical amplifier operated in a linear manner located after reception of the signal and immediately prior to heterodyning and photodetection. We also consider alternative strategies where the coherent interaction, the nonlinear processes, and the amplification are not necessarily constrained to occur in the manner investigated to date. We include the complications that occur because of mechanisms that occur at the level of a few, or one, quantum excitation. Two factors combine in the work to date that limit the value of the approach. These are: (1) the weak signal tends to require operation of the amplifier in the linear regime where the important advantages of nonlinear optical processing are not accessed, (2) the linear optical amplifier has a -3dB noise figure (SN(out)/SN(in)) that necessarily degrades the signal. Some improvement is gained because the gain provided by the optical amplifier can be used to overcome losses in the heterodyned process and photodetection. The result, however, is that introduction of an optical amplifier in a well optimized coherent lidar system results in, at best, a modest improvement in signal to noise. Some improvement may also be realized on incorporating more optical components in a coherent lidar system for purely practical reasons. For example, more compact, lighter weight, components, more robust alignment, or more rapid processing may be gained. We further find that there remain a number of potentially valuable, but unexplored options offered both by the rapidly expanding base of optical technology and the recent investigation of novel nonlinear coherent interference phenomena occurring at the single quantum excitation level. Key findings are: (1) insertion of linear optical amplifiers in well optimized conventional lidar systems offers modest improvements, at best, (2) the practical advantages of optical amplifiers, especially fiber amplifiers, such as ease of alignment, compactness, efficiency, lightweight, etc., warrant further investigation for coherent lidar, (3) the possibility of more fully optical lidar systems should be explored, (4) advantages gained by use of coherent interference of optical fields at the level of one, or a few, signal quanta should be explored, (5) amplification without inversion, population trapping, and use of electromagnetic induced transparency warrant investigation in connection with coherent lidar, (6) these new findings are probably more applicable to earth related NASA work, although applications to deep space should not be excluded, and (7) our own work in the Ultrafast Laboratory at UAH along some of the above lines of investigation, may be useful.

Fork, Richard↗
DOE OSTI2020

Bilevel optimization, deep learning and fractional Laplacian regularization with applications in tomography

Here we consider a generalized bilevel optimization framework for solving inverse problems. We introduce fractional Laplacian as a regularizer to improve the reconstruction quality, and compare it with the total variation regularization. We emphasize that the key advantage of using fractional Laplacian as a regularizer is that it leads to a linear operator, as opposed to the total variation regularization which results in a nonlinear degenerate operator. Inspired by residual neural networks, to learn the optimal strength of regularization and the exponent of fractional Laplacian, we develop a dedicated bilevel optimization neural network with a variable depth for a general regularized inverse problem. We illustrate how to incorporate various regularizer choices into our proposed network. As an example, we consider tomographic reconstruction as a model problem and show an improvement in reconstruction quality, especially for limited data, via fractional Laplacian regularization. We successfully learn the regularization strength and the fractional exponent via our proposed bilevel optimization neural network. We observe that the fractional Laplacian regularization outperforms total variation regularization. This is specially encouraging, and important, in the case of limited and noisy data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A Deep Neural Network for Accurate and Robust Prediction of the Glass Transition Temperature of Polyhydroxyalkanoate Homo- and Copolymers

The purpose of this study was to develop a data-driven machine learning model to predict the performance properties of polyhydroxyalkanoates (PHAs), a group of biosourced polyesters featuring excellent performance, to guide future design and synthesis experiments. A deep neural network (DNN) machine learning model was built for predicting the glass transition temperature, Tg, of PHA homo- and copolymers. Molecular fingerprints were used to capture the structural and atomic information of PHA monomers. The other input variables included the molecular weight, the polydispersity index, and the percentage of each monomer in the homo- and copolymers. The results indicate that the DNN model achieves high accuracy in estimation of the glass transition temperature of PHAs. In addition, the symmetry of the DNN model is ensured by incorporating symmetry data in the training process. The DNN model achieved better performance than the support vector machine (SVD), a nonlinear ML model and least absolute shrinkage and selection operator (LASSO), a sparse linear regression model. The relative importance of factors affecting the DNN model prediction were analyzed. Sensitivity of the DNN model, including strategies to deal with missing data, were also investigated. Compared with commonly used machine learning models incorporating quantitative structure–property (QSPR) relationships, it does not require an explicit descriptor selection step but shows a comparable performance. The machine learning model framework can be readily extended to predict other properties.

quantitative structure–property relationship (QSPR↗
NASA NTRS1985

A methodology for designing robust multivariable nonlinear feedback control systems

This paper presents an outline of a methodology for the design of nonlinear dynamic compensators for nonlinear multivariable systems with guarantees of closed-loop stability, robustness, and performance. The method is an extension of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery (LQG/LTR) methodology for linear systems, thus hinging upon the idea of constructing an approximate nonlinear inverse operator for the plant. A major feature of the method is a unification of both the state-space and Input-Output formulations. The major results of the paper are: (1) Properties of the solution of certain optimal control problems; (2) New results on nonlinear estimation, including a new nonlinear observer with certain guaranteed properties; (3) The Loop Operator Recovery (LOR) procedure, and (4) Inclusion of command-following and disturbance rejection with a goal of a closed-loop stable, robust system.

Grunberg, D. B.↗
NASA NTRS1991

Linear quadratic servo control of a reusable rocket engine

The paper deals with the development of a design method for a servo component in the frequency domain using singular values and its application to a reusable rocket engine. A general methodology used to design a class of linear multivariable controllers for intelligent control systems is presented. Focus is placed on performance and robustness characteristics, and an estimator design performed in the framework of the Kalman-filter formalism with emphasis on using a sensor set different from the commanded values is discussed. It is noted that loop transfer recovery modifies the nominal plant noise intensities in order to obtain the desired degree of robustness to uncertainty reflected at the plant input. Simulation results demonstrating the performance of the linear design on a nonlinear engine model over all power levels during mainstage operation are discussed.

Musgrave, Jeffrey L.↗
NASA NTRS2001

State-Dependent Pseudo-Linear Filter for Spacecraft Attitude and Rate Estimation

This paper presents the development and performance of a special algorithm for estimating the attitude and angular rate of a spacecraft. The algorithm is a pseudo-linear Kalman filter, which is an ordinary linear Kalman filter that operates on a linear model whose matrices are current state estimate dependent. The nonlinear rotational dynamics equation of the spacecraft is presented in the state space as a state-dependent linear system. Two types of measurements are considered. One type is a measurement of the quaternion of rotation, which is obtained from a newly introduced star tracker based apparatus. The other type of measurement is that of vectors, which permits the use of a variety of vector measuring sensors like sun sensors and magnetometers. While quaternion measurements are related linearly to the state vector, vector measurements constitute a nonlinear function of the state vector. Therefore, in this paper, a state-dependent linear measurement equation is developed for the vector measurement case. The state-dependent pseudo linear filter is applied to simulated spacecraft rotations and adequate estimates of the spacecraft attitude and rate are obtained for the case of quaternion measurements as well as of vector measurements.

Bar-Itzhack, Itzhack Y.↗
NASA NTRS1987

Image reconstruction from multiple 1-D scans using filtered localized projection

The spatial resolution that can be attained using scanning linear arrays (consisting of discrete IR solid-state detectors) for image acquisition is considered, and a filtered local projection (FLP) method is described which efficiently combines all available scan information into one rectangular grid without the need for explicit interpolation. Mathematically, the FLP algorithm consists of a localized summation followed by an inverse-filter operation, and it has application to nonlinear restoring techniques. The present method is applied, using a linear array, to simulated data for staggered parallel scans and to multiple scan directions. Noise effects and limitations of the technique are also considered.

Frieden, B. Roy↗
NASA NTRS1992

The European Southern Observatory-MIDAS table file system

The new and substantially upgraded version of the Table File System in MIDAS is presented as a scientific database system. MIDAS applications for performing database operations on tables are discussed, for instance, the exchange of the data to and from the TFS, the selection of objects, the uncertainty joins across tables, and the graphical representation of data. This upgraded version of the TFS is a full implementation of the binary table extension of the FITS format; in addition, it also supports arrays of strings. Different storage strategies for optimal access of very large data sets are implemented and are addressed in detail. As a simple relational database, the TFS may be used for the management of personal data files. This opens the way to intelligent pipeline processing of large amounts of data. One of the key features of the Table File System is to provide also an extensive set of tools for the analysis of the final results of a reduction process. Column operations using standard and special mathematical functions as well as statistical distributions can be carried out; commands for linear regression and model fitting using nonlinear least square methods and user-defined functions are available. Finally, statistical tests of hypothesis and multivariate methods can also operate on tables.

Peron, M.↗
NASA NTRS1979

Generation of linear dynamic models from a digital nonlinear simulation

The results and methodology used to derive linear models from a nonlinear simulation are presented. It is shown that averaged positive and negative perturbations in the state variables can reduce numerical errors in finite difference, partial derivative approximations and, in the control inputs, can better approximate the system response in both directions about the operating point. Both explicit and implicit formulations are addressed. Linear models are derived for the F 100 engine, and comparisons of transients are made with the nonlinear simulation. The problem of startup transients in the nonlinear simulation in making these comparisons is addressed. Also, reduction of the linear models is investigated using the modal and normal techniques. Reduced-order models of the F 100 are derived and compared with the full-state models.

Daniele, C. J.↗
DOE OSTI2026

Experimental Studies of Nonlinear Integrable Optics with Elliptic Potentials

The stable transport of charged particle beams is the core challenge in designing and operating accelerators. The current paradigm for transverse focusing is based on quadrupole and dipole elements, described as a linear integrable Hamiltonian by Courant and Snyder. The operational limits of high intensity accelerators are often determined by collective instabilities within the beam. Nonlinear elements may be added to suppress certain forms of these collective effects, but restrict the range of stable trajectories. These shortcomings motivate extending to a nonlinear integrable system which can offer the benefits of suppressing collective instabilities without limiting the stable trajectories. Danilov and Nagaitsev proposed a novel nonlinear integrable system with elliptical potentials, which could be implemented as magnetic elements in an accelerator. Such a system has been implemented for practical verification in the integrable optics test accelerator (IOTA), a small storage ring constructed for beam dynamics studies. Electron beam studies in IOTA treat the low-emittance beam as a macroparticle for detailed probing of the expected single particle dynamics. This dissertation details new measurements of the nonlinear integrable system relevant for practical implementation. Turn-by-turn measurements of the kicked beam responses are used for phase space reconstruction and analysis of the predicted nonlinear dynamics. The stability and aperture for various nonlinear configurations are measured with beam losses. Amplitude dependent detuning, a core figure of merit for suppressing instabilities, is measured and compared with high fidelity particle tracking simulations. The synchrotron radiation images of circulating beam allow direct measurements of the topology and lifetime in configurations where nonlinear focusing terms dominate.

Wieland, John [Michigan U.] (ORCID:000000028971852↗
NASA NTRS1993

Optimal fixed-finite-dimensional compensator for Burgers' equation with unbounded input/output operators

The problem of using reduced order dynamic compensators to control a class of nonlinear parabolic distributed parameter systems was considered. Concentration was on a system with unbounded input and output operators governed by Burgers' equation. A linearized model was used to compute low-order-finite-dimensional control laws by minimizing certain energy functionals. Then these laws were applied to the nonlinear model. Standard approaches to this problem employ model/controller reduction techniques in conjunction with linear quadratic Gaussian (LQG) theory. The approach used is based on the finite dimensional Bernstein/Hyland optimal projection theory which yields a fixed-finite-order controller.

Burns, John A.↗
DOE OSTI2023

A Probabilistic Scheme for Semilinear Nonlocal Diffusion Equations with Volume Constraints

This work presents a probabilistic scheme for solving semilinear nonlocal diffusion equations with volume constraints and integrable kernels. The nonlocal model of interest is defined by a time-dependent semilinear partial integro-differential equation (PIDE), in which the integro-differential operator consists of both local convection-diffusion and nonlocal diffusion operators. Here, our numerical scheme is based on the direct approximation of the nonlinear Feynman–Kac formula that establishes a link between nonlinear PIDEs and stochastic differential equations. The exploitation of the Feynman–Kac representation avoids solving dense linear systems arising from nonlocal operators. Compared with existing stochastic approaches, our method can achieve first-order convergence after balancing the temporal and spatial discretization errors, which is a significant improvement of existing probabilistic/stochastic methods for nonlocal diffusion problems. Error analysis of our numerical scheme is established. The effectiveness of our approach is shown in two numerical examples. The first example considers a three-dimensional nonlocal diffusion equation to numerically verify the error analysis results. The second example presents a physics problem motivated by the study of heat transport in magnetically confined fusion plasmas.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Charge Conservation beyond Uniformity: Spatially Inhomogeneous Electromagnetic Response in Periodic Solids

Nonlinear electromagnetic response functions have reemerged as a crucial tool for studying quantum materials, due to recently appreciated connections between optical response functions, quantum geometry, and band topology. Most attention has been paid to responses to spatially uniform electric fields, relevant to low-energy optical experiments in conventional solid state materials. However, magnetic and magnetoelectric phenomena are naturally connected by responses to spatially varying electric fields due to Maxwell’s equations. Furthermore, in the emerging field of moiré materials, characteristic lattice scales are much longer, allowing spatial variation of optical electric fields to potentially have a measurable effect in experiments. In order to address these issues, we develop a formalism for computing linear and nonlinear responses to spatially inhomogeneous electromagnetic fields. Starting with the continuity equation, we derive an expression for the second-quantized current operator that is manifestly conserved and model independent. Crucially, our formalism makes no assumptions on the form of the microscopic Hamiltonian and so is applicable to model Hamiltonians derived from tight-binding or calculations. We then develop a diagrammatic Kubo formalism for computing the wave vector dependence of linear and nonlinear conductivities, using Ward identities to fix the value of the diamagnetic current order by order in the vector potential. We apply our formula to compute the magnitude of the Kerr effect at oblique incidence for a model of a moiré-Chern insulator and demonstrate the experimental relevance of spatially inhomogeneous fields in these systems. We further show how our formalism allows us to compute the (orbital) magnetic multipole moments and magnetic susceptibilities in insulators. Turning to nonlinear response, we use our formalism to compute the second-order transverse response to spatially varying transverse electric fields in our moiré-Chern insulator model, with an eye toward the next generation of experiments in these systems. Published by the American Physical Society 2024

Physics↗
NASA NTRS1994

Fuzzy self-learning control for magnetic servo system

It is known that an effective control system is the key condition for successful implementation of high-performance magnetic servo systems. Major issues to design such control systems are nonlinearity; unmodeled dynamics, such as secondary effects for copper resistance, stray fields, and saturation; and that disturbance rejection for the load effect reacts directly on the servo system without transmission elements. One typical approach to design control systems under these conditions is a special type of nonlinear feedback called gain scheduling. It accommodates linear regulators whose parameters are changed as a function of operating conditions in a preprogrammed way. In this paper, an on-line learning fuzzy control strategy is proposed. To inherit the wealth of linear control design, the relations between linear feedback and fuzzy logic controllers have been established. The exercise of engineering axioms of linear control design is thus transformed into tuning of appropriate fuzzy parameters. Furthermore, fuzzy logic control brings the domain of candidate control laws from linear into nonlinear, and brings new prospects into design of the local controllers. On the other hand, a self-learning scheme is utilized to automatically tune the fuzzy rule base. It is based on network learning infrastructure; statistical approximation to assign credit; animal learning method to update the reinforcement map with a fast learning rate; and temporal difference predictive scheme to optimize the control laws. Different from supervised and statistical unsupervised learning schemes, the proposed method learns on-line from past experience and information from the process and forms a rule base of an FLC system from randomly assigned initial control rules.

Tarn, J. H.↗
NASA NTRS1992

An approximately factored incremental strategy for calculating consistent discrete aerodynamic sensitivity derivatives

An incremental strategy is presented for iteratively solving very large systems of linear equations, which are associated with aerodynamic sensitivity derivatives for advanced CFD codes. It is shown that the left-hand side matrix operator and the well-known factorization algorithm used to solve the nonlinear flow equations can also be used to efficiently solve the linear sensitivity equations. Two airfoil problems are considered as an example: subsonic low Reynolds number laminar flow and transonic high Reynolds number turbulent flow.

Korivi, V. M.↗
NASA NTRS1997

Linearized Poststall Aerodynamic and Control Law Models of the X-31A Aircraft and Comparison with Flight Data

The X-31A aircraft has a unique configuration that uses thrust-vector vanes and aerodynamic control effectors to provide an operating envelope to a maximum 70 deg angle of attack, an inherently nonlinear portion of the flight envelope. This report presents linearized versions of the X-31A longitudinal and lateral-directional control systems, with aerodynamic models sufficient to evaluate characteristics in the poststall envelope at 30 deg, 45 deg, and 60 deg angle of attack. The models are presented with detail sufficient to allow the reader to reproduce the linear results or perform independent control studies. Comparisons between the responses of the linear models and flight data are presented in the time and frequency domains to demonstrate the strengths and weaknesses of the ability to predict high-angle-of-attack flight dynamics using linear models. The X-31A six-degree-of-freedom simulation contains a program that calculates linear perturbation models throughout the X-31A flight envelope. The models include aerodynamics and flight control system dynamics that are used for stability, controllability, and handling qualities analysis. The models presented in this report demonstrate the ability to provide reasonable linear representations in the poststall flight regime.

Stoliker, Patrick C.↗