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At least 613 records · Page 34

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NASA NTRS2006

Mystic: Implementation of the Static Dynamic Optimal Control Algorithm for High-Fidelity, Low-Thrust Trajectory Design

Mystic software is designed to compute, analyze, and visualize optimal high-fidelity, low-thrust trajectories, The software can be used to analyze inter-planetary, planetocentric, and combination trajectories, Mystic also provides utilities to assist in the operation and navigation of low-thrust spacecraft. Mystic will be used to design and navigate the NASA's Dawn Discovery mission to orbit the two largest asteroids, The underlying optimization algorithm used in the Mystic software is called Static/Dynamic Optimal Control (SDC). SDC is a nonlinear optimal control method designed to optimize both 'static variables' (parameters) and dynamic variables (functions of time) simultaneously. SDC is a general nonlinear optimal control algorithm based on Bellman's principal.

low thrust↗

DOE OSTI2020

Distortions of the Rain Distribution With Warming, With and Without Self-Aggregation

We investigate how mesoscale circulations associated with convective aggregation can modulate the sensitivity of the hydrologic cycle to warming. We quantify changes in the full distribution of rain across radiative-convective equilibrium states in a cloud-resolving model. For a given Sea Surface Temperature (SST), the shift in mean rainfall between disorganized and organized states is associated with a shift in atmospheric radiative cooling, and is roughly analogous to the effect of a 4K SST increase. With rising temperatures, the increase in mean rain rate is insensitive to the presence of organization, while extremes can intensify faster in the aggregated state, leading to a faster amplification in the sporadic nature of rain. When convection aggregates, heavy rain is enhanced by 20%–30% and nonlinear behaviors are observed as a function of SST and strength of aggregation feedbacks. First, radiative- and surface-flux aggregation feedbacks have multiplicative effects on extremes, illustrating a non-trivial sensitivity to the degree of organization. Second, alternating Clausius-Clapeyron and super-Clausius-Clapeyron regimes in extreme rainfall are found as a function of SST, corresponding to varying thermodynamic and dynamic contributions, and a large sensitivity to precipitation efficiency variations in some SST ranges. The potential for mesoscale circulations in amplifying the hydrologic cycle is established. However, these nonlinear distortions question the quantitative relevance of idealized self-aggregation. This calls for a deeper investigation of relationships which capture the coupling between global energetics, aggregation feedbacks and local convection, and for systematic tests of their sensitivity to domain configurations, surface boundary conditions, microphysics, and turbulence schemes.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Decentralized Filtering Adaptive Neural Network Control for Uncertain Switched Interconnected Nonlinear Systems

This article presents a novel decentralized filtering adaptive neural network control framework for uncertain switched interconnected nonlinear systems. Each subsystem has its own decentralized controller based on the established decentralized state predictor. For each subsystem, the nonlinear uncertainties are approximated by a Gaussian radial basis function (GRBF) neural network incorporated with a piecewise constant adaptive law, where the adaptive law will update adaptive parameters from the error dynamics between the host system and the decentralized state predictor by discarding the unknowns, whereas a decentralized filtering control law is derived to cancel both local and mismatched uncertainties from other subsystems, as well as achieve the local objective tracking of the host system. The achievement of global objective depends on the achievement of local objective for each subsystem. The matched uncertainties are canceled directly by adopting their opposite in the control signal, whereas a dynamic inversion of the system is required to eliminate the effect of the mismatched uncertainties on the output. By exploiting the average dwell time principle, the error bounds between the real system and the virtual reference system, which defines the best performance that can be achieved by the closed-loop system, are derived. A numerical example is given to illustrate the effectiveness of the decentralized filtering adaptive neural network control architecture by comparing against the model reference adaptive control (MRAC).

Average dwell time, decentralized, filtering adapt↗

NASA NTRS1992

Membership generation using multilayer neural network

There has been intensive research in neural network applications to pattern recognition problems. Particularly, the back-propagation network has attracted many researchers because of its outstanding performance in pattern recognition applications. In this section, we describe a new method to generate membership functions from training data using a multilayer neural network. The basic idea behind the approach is as follows. The output values of a sigmoid activation function of a neuron bear remarkable resemblance to membership values. Therefore, we can regard the sigmoid activation values as the membership values in fuzzy set theory. Thus, in order to generate class membership values, we first train a suitable multilayer network using a training algorithm such as the back-propagation algorithm. After the training procedure converges, the resulting network can be treated as a membership generation network, where the inputs are feature values and the outputs are membership values in the different classes. This method allows fairly complex membership functions to be generated because the network is highly nonlinear in general. Also, it is to be noted that the membership functions are generated from a classification point of view. For pattern recognition applications, this is highly desirable, although the membership values may not be indicative of the degree of typicality of a feature value in a particular class.

Kim, Jaeseok↗

NASA NTRS1998

Using Approximations to Accelerate Engineering Design Optimization

Optimization problems that arise in engineering design are often characterized by several features that hinder the use of standard nonlinear optimization techniques. Foremost among these features is that the functions used to define the engineering optimization problem often are computationally intensive. Within a standard nonlinear optimization algorithm, the computational expense of evaluating the functions that define the problem would necessarily be incurred for each iteration of the optimization algorithm. Faced with such prohibitive computational costs, an attractive alternative is to make use of surrogates within an optimization context since surrogates can be chosen or constructed so that they are typically much less expensive to compute. For the purposes of this paper, we will focus on the use of algebraic approximations as surrogates for the objective. In this paper we introduce the use of so-called merit functions that explicitly recognize the desirability of improving the current approximation to the objective during the course of the optimization. We define and experiment with the use of merit functions chosen to simultaneously improve both the solution to the optimization problem (the objective) and the quality of the approximation. Our goal is to further improve the effectiveness of our general approach without sacrificing any of its rigor.

Torczon, Virginia↗

NASA NTRS2009

The Principle of Energetic Consistency

A basic result in estimation theory is that the minimum variance estimate of the dynamical state, given the observations, is the conditional mean estimate. This result holds independently of the specifics of any dynamical or observation nonlinearity or stochasticity, requiring only that the probability density function of the state, conditioned on the observations, has two moments. For nonlinear dynamics that conserve a total energy, this general result implies the principle of energetic consistency: if the dynamical variables are taken to be the natural energy variables, then the sum of the total energy of the conditional mean and the trace of the conditional covariance matrix (the total variance) is constant between observations. Ensemble Kalman filtering methods are designed to approximate the evolution of the conditional mean and covariance matrix. For them the principle of energetic consistency holds independently of ensemble size, even with covariance localization. However, full Kalman filter experiments with advection dynamics have shown that a small amount of numerical dissipation can cause a large, state-dependent loss of total variance, to the detriment of filter performance. The principle of energetic consistency offers a simple way to test whether this spurious loss of variance limits ensemble filter performance in full-blown applications. The classical second-moment closure (third-moment discard) equations also satisfy the principle of energetic consistency, independently of the rank of the conditional covariance matrix. Low-rank approximation of these equations offers an energetically consistent, computationally viable alternative to ensemble filtering. Current formulations of long-window, weak-constraint, four-dimensional variational methods are designed to approximate the conditional mode rather than the conditional mean. Thus they neglect the nonlinear bias term in the second-moment closure equation for the conditional mean. The principle of energetic consistency implies that, to precisely the extent that growing modes are important in data assimilation, this term is also important.

Cohn, Stephen E.↗

DOE OSTI2022

Nonlinear dimension reduction for surrogate modeling using gradient information

We introduce a method for the nonlinear dimension reduction of a high-dimensional function $u:{\mathbb{R}}^d\rightarrow{\mathbb{R}}$, $d\gg 1$. Our objective is to identify a nonlinear feature map $g:{\mathbb{R}}^d\rightarrow{\mathbb{R}}^m$, with a prescribed intermediate dimension $m\ll d$, so that $u$ can be well approximated by $f\circ g$ for some profile function $f:{\mathbb{R}}^m\rightarrow{\mathbb{R}}$. We propose to build the feature map by aligning the Jacobian $\nabla g$ with the gradient $\nabla u$, and we theoretically analyze the properties of the resulting $g$. Once $g$ is built, we construct $f$ by solving a gradient-enhanced least squares problem. Our practical algorithm uses a sample $\{{\textbf{x}}^{(i)},u({\textbf{x}}^{(i)}),\nabla u({\textbf{x}}^{(i)})\}_{i=1}^N$ and builds both $g$ and $f$ on adaptive downward-closed polynomial spaces, using cross validation to avoid overfitting. We numerically evaluate the performance of our algorithm across different benchmarks, and explore the impact of the intermediate dimension $m$. We show that building a nonlinear feature map $g$ can permit more accurate approximation of $u$ than a linear $g$, for the same input data set.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Seismic Performance of Deeply Embedded Conceptual Advanced Reactors: Three-Dimensional Nonlinear Soil-Structure Interaction Analyses

The U.S. Nuclear Regulatory Commission’s functional containment concept provides advanced nuclear power plant designers with more flexibility in terms of the civil/structural design if the appropriate set of barriers for prevention of radioactive material release exist. Some of the conceptual advanced reactor structures, without the traditional pressure boundaries of large containment structures, are proposed to be deeply embedded or buried into soil. This approach is expected to provide (1) lesser seismic demands on the structures and safety-critical structures, (2) eased regulatory efforts and overall design against other external hazards such as aircraft impact, and (3) overall cost savings. Further, one of the important aspects of assessing the technical and economic viability of deeply embedding advanced reactor buildings is to assess the seismic performance with the understanding of effects with material and geometric nonlinearities. This study investigates the seismic response of deeply embedded or buried advanced reactors by conducting three-dimensional nonlinear soil-structure interaction analyses. Although the results indicate that there is a general trend of decreased seismic response with increased embedment depths, the change in the dynamic environment with different embedment depths and the nonlinear environment under high-intensity seismic inputs may result in increased peak response at increased embedment depths.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2022

Using dynamic mode decomposition to predict the dynamics of a two-time non-equilibrium Green’s function

Computing the numerical solution of the Kadanoff–Baym equations, a set of nonlinear integral differential equations satisfied by the two-time Green's functions derived from many-body perturbation theory for a quantum many-body system away from equilibrium, is a challenging task. Recently, we have successfully applied dynamic mode decomposition (DMD) to construct a data driven reduced order model that can be used to extrapolate the time-diagonal of a two-time Green's function from numerical solutions of the KBE within a small time window. In this paper, we extend the previous work and use DMD to predict off-diagonal elements of the two-time Green's function. We partition the two-time Green's function into a number of one-time functions along the diagonal and subdiagonals of the two-time window as well as in horizontal and vertical directions. We use DMD to construct separate reduced order models to predict the dynamics of these one-time functions in a two-step procedure. We extrapolate along diagonal and several subdiagonals within a subdiagonal band of a two-time window in the first step. In the second step, we use DMD to extrapolate the Green's function outside of the sub-diagonal band. In conclusion, we demonstrate the efficiency and accuracy of this approach by applying it to a two-band Hubbard model problem.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Interleaved Cuk Converter Wave Energy System With Advanced Control and Grid Support Functions for Seamless Integration

This paper presents an innovative wave energy conversion system that integrates an interleaved Cuk converter with advanced nonlinear control for seamless grid integration. The system efficiently extracts power on the DC side using the interleaved Cuk converter, while an inverter manages power transfer to the grid or load on the AC side. A nonlinear control architecture, based on the Lyapunov energy function, ensures stable and optimal operation under varying wave conditions, effectively addressing the challenges of variability and unpredictability inherent in wave energy. The proposed system also incorporates features to enhance power quality and minimize losses, making it a robust solution for renewable energy integration. The system's effectiveness in harnessing wave energy and achieving smooth grid integration is validated through comprehensive computer simulations in MATLAB/Simulink, with case study results demonstrating its capabilities.

HYDRO ENERGY,TIDAL AND WAVE POWER↗

NASA NTRS1995

Nonlinear evolution of magnetic flux ropes. 2: Finite beta plasma

In this second paper on the evolution of magnetic flux ropes we study the effects of gas pressure. We assume that the energy transport is described by a polytropic relationship and reduce the set of ideal MHD equations to a single, second-order, nonlinear, ordinary differential equation for the evolution function. For this conservative system we obtain a first integral of motion. To analyze the possible motions, we use a mechanical analogue -- a one-dimensional, nonlinear oscillator. We find that the effective potential for such an oscillator depends on two parameters: the polytropic index gamma and a dimensionless quantity kappa the latter being a function of the plasma beta, the strength of the azimuthal magnetic field relative to the axial field of the flux rope, and gamma. Through a study of this effective potential we classify all possible modes of evolution of the system. In the main body of the paper, we focus on magnetic flux ropes whose field and gas pressure increase steadily towards the symmetry axis. In this case, for gamma greater than 1 and all values of kappa, only oscillations are possible. For gamma less than 1, however, both oscillations and expansion are allowed. For gamma less than 1 and kappa below a critical value, the energy of the nonlinear oscillator determines whether the flux rope will oscillate or expand to infinity. For gamma less than 1 and kappa above critical, however, only expansion occurs. Thus by increasing kappa while keeping gamma fixed (less than 1), a phase transition occurs at kappa = kappa(sub critical) and the oscillatory mode disappears. We illustrate the above theoretical considerations by the example of a flux rope of constant field line twist evolving self-similarly. For this example, we present the full numerical MHD solution. In an appendix to the paper we catalogue all possible evolutions when (1) either the magnetic field or (2) the gas pressure decreases monotonically toward the axis. We find that in these cases critical conditions can occur for gamma greater than 1. While in most cases the flux rope collapses, there are notable exceptions when, for certain ranges of kappa and gamma, collapse may be averted.

Osherovich, V. A.↗

NASA NTRS1973

High speed flow past wings

The analytical solution to the transonic small perturbation equation which describes steady compressible flow past finite wings at subsonic speeds can be expressed as a nonlinear integral equation with the perturbation velocity potential as the unknown function. This known formulation is substituted by a system of nonlinear algebraic equations to which various methods are applicable for its solution. Due to the presence of mathematical discontinuities in the flow solutions, however, a main computational difficulty was to ensure uniqueness of the solutions when local velocities on the wing exceeded the speed of sound. For continuous solutions this was achieved by embedding the algebraic system in an one-parameter operator homotopy in order to apply the method of parametric differentiation. The solution to the initial system of equations appears then as a solution to a Cauchy problem where the initial condition is related to the accompanying incompressible flow solution. In using this technique, however, a continuous dependence of the solution development on the initial data is lost when the solution reaches the minimum bifurcation point. A steepest descent iteration technique was therefore, added to the computational scheme for the calculation of discontinuous flow solutions. Results for purely subsonic flows and supersonic flows with and without compression shocks are given and compared with other available theoretical solutions.

Norstrud, H.↗

NASA NTRS1991

Formulation of the linear model from the nonlinear simulation for the F18 HARV

The F-18 HARV is a modified F-18 Aircraft which is capable of flying in the post-stall regime in order to achieve superagility. The onset of aerodynamic stall, and continued into the post-stall region, is characterized by nonlinearities in the aerodynamic coefficients. These aerodynamic coefficients are not expressed as analytic functions, but rather in the form of tabular data. The nonlinearities in the aerodynamic coefficients yield a nonlinear model of the aircraft's dynamics. Nonlinear system theory has made many advances, but this area is not sufficiently developed to allow its application to this problem, since many of the theorems are existance theorems and that the systems are composed of analytic functions. Thus, the feedback matrices and the state estimators are obtained from linear system theory techniques. It is important, in order to obtain the correct feedback matrices and state estimators, that the linear description of the nonlinear flight dynamics be as accurate as possible. A nonlinear simulation is run under the Advanced Continuous Simulation Language (ACSL). The ACSL simulation uses FORTRAN subroutines to interface to the look-up tables for the aerodynamic data. ACSL has commands to form the linear representation for the system. Other aspects of this investigation are discussed.

Hall, Charles E., Jr.↗

NASA NTRS1984

In Search of a Visual-cortical Describing Function: a Summary of Work in Progress

The thrust of the present work is to explore the utility of using a sum of sinusoids (seven or more) to obtain an evoked response and, furthermore, to see if the response is sensitive to changes in cognitive processing. Within the field of automatic control system technology, a mathematical input/output relationship for a sinusoidally stimulated nonlinear system is defined as describing function. Applying this technology, sum of sines inputs to yield describing functions for the visual-cortical response have been designed. What follows is a description of the method used to obtain visual-cortical describing functions. A number of measurement system redesigns were necessary to achieve the desired frequency resolution. Results that guided and came out of the redesigns are presented. Preliminary results of stimulus parameter effects (average intensity and depth of modulation) are also shown.

Junker, A. M.↗

DOE OSTI2021

Similarity properties in capacitive radio frequency plasmas with nonlinear collision processes

Abstract Similarity laws (SL) are essential for correlating the characteristics of plasmas at different dimensional scales, which have been validated for radio frequency (rf) discharges at low pressure but under limited conditions. In this work, we evaluate the effects of nonlinear collisions (e.g. stepwise ionization) on the similarity properties in capacitive rf discharges in argon across a wide range of pressure regimes via fully kinetic particle-in-cell simulations. The SL scalings of fundamental discharge parameters, e.g. the electron power absorption and electron energy probability function, are examined with and without nonlinear collisions, respectively. Without the nonlinear collisions, the similarity scalings are found to be rigorously valid. When the nonlinear collisions are considered, the similarity properties in rf discharges still exist approximately, which indicates that the violations caused by the nonlinear collisions are still minor in the studied cases. The reasons for the effectiveness of SL scalings with nonlinear collision processes are also discussed. The results from this study confirmed the validity of similarity transformations with more complex reaction kinetics, which may promote the applicability of the SL scalings for the design and fabrications of plasma devices.

Physics↗

NASA NTRS1975

Combustion instability with partial length acoustic liners

The development is discussed of analytical techniques and numerical methods for the prediction of the stability behavior of liquid propellant rocket combustors with partial length acoustic liners, injector face baffles, and nonlinear combustion responses. Three primary objectives included: (1) extension of the Green's Function integral-iteration technique previously developed so that nonlinear three dimensional wave propagation effects could be included in stability predictions; (2) development of an analytical technique and a computer program for the prediction of the damping effects caused by injector face baffles; and (3) inclusion of a nonlinear, wave distortation dependent, combustion response model in the global stability analysis and determination of its effect on combustor stability.

Mitchell, C. E.↗

DOE OSTI2024

Proximal Galerkin: A Structure-Preserving Finite Element Method for Pointwise Bound Constraints

The proximal Galerkin finite element method is a high-order, low iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of pointwise bound constraints in infinite-dimensional function spaces. This paper introduces the proximal Galerkin method and applies it to solve free boundary problems, enforce discrete maximum principles, and develop a scalable, mesh-independent algorithm for optimal design with pointwise bound constraints. This paper also introduces the latent variable proximal point (LVPP) algorithm, from which the proximal Galerkin method derives. When analyzing the classical obstacle problem, we discover that the underlying variational inequality can be replaced by a sequence of second-order partial differential equations (PDEs) that are readily discretized and solved with, e.g., the proximal Galerkin method. Throughout this work, we arrive at several contributions that may be of independent interest. These include (1) a semilinear PDE we refer to as the entropic Poisson equation; (2) an algebraic/geometric connection between high-order positivity-preserving discretizations and certain infinite-dimensional Lie groups; and (3) a gradient-based, bound-preserving algorithm for two-field, density-based topology optimization. The complete proximal Galerkin methodology combines ideas from nonlinear programming, functional analysis, tropical algebra, and differential geometry and can potentially lead to new synergies among these areas as well as within variational and numerical analysis. Open-source implementations of our methods accompany this work to facilitate reproduction and broader adoption.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Focusing Ions at Atmospheric Pressure using Nonlinear DC Voltage Sequences Applied to a Stacked Ring Ion Guide

Many modern ion mobility (IM) and mass spectrometers (MS) operate under low pressure (= 10 Torr) and employ high voltage radiofrequencies (RF) to provide ion confinement. Unfortunately, RF effectiveness drastically decreases as pressure increases, and few techniques for focusing ions at elevated pressures exist. Here we demonstrate a new approach for focusing ions at atmospheric pressure (AP) by applying nonlinear DC voltage sequences following quadratic and power (exponential) functions to a stacked ring ion guide. We used ion trajectory simulations to rigorously explore how ions react to nonlinear electric fields and validate the simulations with a set of ion current measurements performed at AP. Ion trajectory simulations show that ions initially defocus near the entrance of the device but then become intensely focused as they travel through the device. Contour plots for both nonlinear voltage sequences show electric field lines that increasingly curve inwards as a function of distance, resulting in spatial ion focusing. Experimental ion current and spot size measurements were performed at AP using a 10-cm stacked ring ion guide and a segmented Faraday cup detector. Quadratic sequences produced ~5% smaller spot sizes (~22.8 mm) and ~25% higher ion current compared to a linear voltage sequence (~24.0 mm). Alternatively, power sequences produced ~64% smaller spot sizes (~8.7 mm), albeit with ~10x lower ion current. However, both nonlinear voltage sequences produced similar ion currents at the center of the Faraday cup detector, indicating that higher ion densities are achieved when using nonlinear voltage gradients. These results demonstrate a new way to focus ions at AP, and the capabilities demonstrated here provide fundamental insights on how to keep ions inside analytical devices at elevated pressures without RF.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗