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At least 1,423 records · Page 79
All sourcesNASA NTRSDOE OSTI
NASA NTRS2011

Color Histogram Diffusion for Image Enhancement

Various color histogram equalization (CHE) methods have been proposed to extend grayscale histogram equalization (GHE) for color images. In this paper a new method called histogram diffusion that extends the GHE method to arbitrary dimensions is proposed. Ranges in a histogram are specified as overlapping bars of uniform heights and variable widths which are proportional to their frequencies. This diagram is called the vistogram. As an alternative approach to GHE, the squared error of the vistogram from the uniform distribution is minimized. Each bar in the vistogram is approximated by a Gaussian function. Gaussian particles in the vistoram diffuse as a nonlinear autonomous system of ordinary differential equations. CHE results of color images showed that the approach is effective.

Kim, Taemin↗
NASA NTRS2012

General Methodology for Designing Spacecraft Trajectories

A methodology for designing spacecraft trajectories in any gravitational environment within the solar system has been developed. The methodology facilitates modeling and optimization for problems ranging from that of a single spacecraft orbiting a single celestial body to that of a mission involving multiple spacecraft and multiple propulsion systems operating in gravitational fields of multiple celestial bodies. The methodology consolidates almost all spacecraft trajectory design and optimization problems into a single conceptual framework requiring solution of either a system of nonlinear equations or a parameter-optimization problem with equality and/or inequality constraints.

Condon, Gerald↗
NASA NTRS2013

Detection of Moving Targets Using Soliton Resonance Effect

The objective of this research was to develop a fundamentally new method for detecting hidden moving targets within noisy and cluttered data-streams using a novel "soliton resonance" effect in nonlinear dynamical systems. The technique uses an inhomogeneous Korteweg de Vries (KdV) equation containing moving-target information. Solution of the KdV equation will describe a soliton propagating with the same kinematic characteristics as the target. The approach uses the time-dependent data stream obtained with a sensor in form of the "forcing function," which is incorporated in an inhomogeneous KdV equation. When a hidden moving target (which in many ways resembles a soliton) encounters the natural "probe" soliton solution of the KdV equation, a strong resonance phenomenon results that makes the location and motion of the target apparent. Soliton resonance method will amplify the moving target signal, suppressing the noise. The method will be a very effective tool for locating and identifying diverse, highly dynamic targets with ill-defined characteristics in a noisy environment. The soliton resonance method for the detection of moving targets was developed in one and two dimensions. Computer simulations proved that the method could be used for detection of singe point-like targets moving with constant velocities and accelerations in 1D and along straight lines or curved trajectories in 2D. The method also allows estimation of the kinematic characteristics of moving targets, and reconstruction of target trajectories in 2D. The method could be very effective for target detection in the presence of clutter and for the case of target obscurations.

Kulikov, Igor K.↗
NASA NTRS2014

Static Aeroelastic Analysis with an Inviscid Cartesian Method

An embedded-boundary, Cartesian-mesh flow solver is coupled with a three degree-of-freedom structural model to perform static, aeroelastic analysis of complex aircraft geometries. The approach solves a nonlinear, aerostructural system of equations using a loosely-coupled strategy. An open-source, 3-D discrete-geometry engine is utilized to deform a triangulated surface geometry according to the shape predicted by the structural model under the computed aerodynamic loads. The deformation scheme is capable of modeling large deflections and is applicable to the design of modern, very-flexible transport wings. The coupling interface is modular so that aerodynamic or structural analysis methods can be easily swapped or enhanced. After verifying the structural model with comparisons to Euler beam theory, two applications of the analysis method are presented as validation. The first is a relatively stiff, transport wing model which was a subject of a recent workshop on aeroelasticity. The second is a very flexible model recently tested in a low speed wind tunnel. Both cases show that the aeroelastic analysis method produces results in excellent agreement with experimental data.

Aeroelastic↗
NASA NTRS2014

Bifurcation Analysis Using Rigorous Branch and Bound Methods

For the study of nonlinear dynamic systems, it is important to locate the equilibria and bifurcations occurring within a specified computational domain. This paper proposes a new approach for solving these problems and compares it to the numerical continuation method. The new approach is based upon branch and bound and utilizes rigorous enclosure techniques to yield outer bounding sets of both the equilibrium and local bifurcation manifolds. These sets, which comprise the union of hyper-rectangles, can be made to be as tight as desired. Sufficient conditions for the existence of equilibrium and bifurcation points taking the form of algebraic inequality constraints in the state-parameter space are used to calculate their enclosures directly. The enclosures for the bifurcation sets can be computed independently of the equilibrium manifold, and are guaranteed to contain all solutions within the computational domain. A further advantage of this method is the ability to compute a near-maximally sized hyper-rectangle of high dimension centered at a fixed parameter-state point whose elements are guaranteed to exclude all bifurcation points. This hyper-rectangle, which requires a global description of the bifurcation manifold within the computational domain, cannot be obtained otherwise. A test case, based on the dynamics of a UAV subject to uncertain center of gravity location, is used to illustrate the efficacy of the method by comparing it with numerical continuation and to evaluate its computational complexity.

Smith, Andrew P.↗
NASA NTRS2010

Transforming Mean and Osculating Elements Using Numerical Methods

Mean element propagation of perturbed two body orbits has as its mathematical basis averaging theory of nonlinear dynamical systems. Averaged mean elements define the long-term evolution characteristics of an orbit. Using averaging theory, a near identity transformation can be found that transforms the mean elements back to the osculating elements that contain short period terms in addition to the secular and long period mean elements. The ability to perform the conversion is necessary so that orbit design conducted in mean elements can be converted back into osculating results. In the present work, this near identity transformation is found using the Fast Fourier Transform. An efficient method is found that is capable of recovering the osculating elements to first order

averaging↗
NASA NTRS2019

Input Constrained M-MRAC for Multirotors Operating in an Urban Environment

The paper presents a modified model reference adaptive control (M-MRAC) for multi-input multi-output nonlinear dynamical systems with time varying parametric uncertainties and bounded external disturbances. It uses a prediction model to rapidly generate adaptive estimates of the system's uncertainties with adjustable errors that converge to a small neighborhood of the origin. A sufficient condition is derived to specify the region of attraction in the space of initialization errors, design parameters and external commends. The approach is applied to thrust controlled multi-rotor air vehicles operating in an urban environment. It is shown that the designed controller can provide a good tracking of a given trajectory in the unknown urban wind field, assuming that the maximum thrust generated by the rotors is known. The performance of the algorithms are demonstrated in simulations.

Stepanyan, Vahram↗
NASA NTRS2018

CLIMATE LECTURE 5: The Role of Clouds in Climate

David Rind has played a central role in the science of the modeling of climate change. He was the scientific driving force behind the development and evaluation of the first Goddard Institute for Space Studies (GISS) global climate model (GCM), Model II. Model II was one of the three original GCMs whose projections of climate change in response to a doubling of CO2 concentration were the basis for the influential Charney Report that produced the first assessment of global climate sensitivity. David used Model II to pioneer the scientific field of climate dynamics, performing a broad range of investigations of processes controlling individual elements of the general circulation and how they changed over a wide range of past and potential future climates. The defining characteristic of Davids papers is his unique talent for tracking down the myriad links and causal chains among different parts of the nonlinear climate system. Rather than viewing climate using a simple forcing-and-response paradigm, David showed that the global energy, water, and even momentum cycles are coupled via the general circulation and its transports.

Del Genio, Anthony D.↗
NASA NTRSDate not supplied

A Moving Discontinuous Galerkin Method with Interface Condition Enforcement for Reacting Hypersonic Flows

The necessity of enforcing conservation in computational elements or cells (element conservation) for discontinuous solutions is well understood and respected for solving conservation laws in computational fluid dynamics (CFD). In contrast, interface conservation, where the conservation across cell interfaces is enforced, is long ignored, and yet is also ruled and required by the underlying physics just like element conservation. Violation of the interface conservation across discontinuities is the root cause why an exact discontinuous solution can never be achieved in shock capturing methods. The interface conservation is examined and explored in this talk. Moving discontinuous Galerkin (MDG) finite element method with interface conservation enforcement (MDG-ICE) [1],[2] are then presented for solving compressible flow problems with discontinuities based on the observation that the interface conservation can only be satisfied, only when mesh interfaces are aligned with discontinuities. In the MDG-ICE formulation, both conservative quantities and grid geometry are considered as independent variables. A space-time DG formulation is used to solve the multi-material compressible Euler equations in the standard discontinuous solution space and the discrete grid geometry is solved using a variational formulation in a continuous space. A self-adaptive Levenberg-Marquardt method is utilized to solve the resulting over-determined system of nonlinear equations arising from the MDG-ICE formulation. A number of numerical experiments for a variety of flow problems are conducted to assess the accuracy and performance of the MDG-ICE method. Numerical results obtained indicate that the MDG-ICE method is able to deliver the designed order of both h- and p-convergence even for discontinuous solutions, and detect all types of interfaces, via interface condition enforcement and satisfy, via grid movement, the compressible Euler equations and the associated interface condition.

Discontinuous Galekin↗
DOE OSTI2024

Truncated nonlinear interferometer-based sensor system

A truncated non-linear interferometer-based sensor system includes an input port that receives an optical beam and a non-linear amplifier that amplifies the optical beam with a pump beam and renders a probe beam and a conjugate beam. The system's local oscillators have a relationship with the respective beams. The system includes a sensor that transduces an input with the probe beam and the conjugate beam or their respective local oscillators. It includes one or more phase-sensitive detectors that detect a phase modulation between the respective local oscillators and the probe beam and the conjugate beam. Output from the phase-sensitive-detectors is based on the detected phase modulation. The phase-sensor-detectors include measurement circuitry that measure the phase signals. The measurement is the sum or difference of the phase signals in which the measured combination exhibit a quantum noise reduction in an intensity difference or a phase sum or an amplitude difference quadrature.

Pooser, Raphael C.↗
NASA NTRS1976

A lifting surface theory for the analysis of nonplanar lifting systems

A new nonlinear, nonplanar lifting surface theory is presented. The method is regarded as a lifting surface theory in that the effects of wing thickness are neglected, but none of the usual small perturbation assumptions inherent in most other lifting surface theories are made. The method represents nonplanar lifting systems by distributed vorticity, including the leading edge singular behavior characteristic of thin wings. The method is well suited to the computation of induced drag of nonplanar systems because leading edge suction is calculated from the leading edge singularity. The method has been used to compute the induced drag benefit of winglets (vortex diffusers), and the agreement with NASA experimental data is excellent.

Goldhammer, M. I.↗
DOE OSTI2025

Nonlinear Topological Photonics: Capturing Nonlinear Dynamics and Optical Thermodynamics

Combining multiple optical resonators or engineering dispersion of complex media has provided an effective method for demonstrating topological physics controlling photons in unprecedented ways such as unidirectional light propagation and spatially localized modes between an interface or on a corner. Further, adding nonlinear responses to those topological photonic systems has enabled achieving diverse phases of photons in both space and time, allowing for more functionalities in photonic devices that provide a new playground for studying dynamic features of nonlinear topological systems. However, most methods for describing nonlinear topological photonic systems rely on linear topological theories, making it challenging to accurately characterize the topology of nonlinear systems. Thus, substantial efforts have focused on rigorously describing nonlinear topological phases and developing effective tools to analyze nonlinear topological effects. Meanwhile, coupled multimode optical waveguides with nonlinear dynamic responses provide an excellent platform for the statistical description of photons, opening a new paradigm called “optical thermodynamics”. This review will introduce the basic concepts of nonlinear topological photonics and the recent development of theoretical approaches focusing on data-driven approaches for creating phase diagrams as well as the spectral localizer framework and the pseudospectrum method for understanding optical nonlinearities in topological systems. In addition, the new concept of optical thermodynamics will be introduced with some recent theoretical works.

Topological photonics↗
NASA NTRS1983

Influence of unbalance on the nonlinear dynamical response and stability of flexible rotor-bearing systems

In this paper, some of the effects of unbalance on the nonlinear response and stability of flexible rotor-bearing systems is presented from both a theoretical and experimental standpoint. In a linear system, operating above its stability threshold, the amplitude of motion grows exponentially with time and the orbits become unbounded. In an actual system, this is not necessarily the case. The actual amplitudes of motion may be bounded due to various nonlinear effects in the system. These nonlinear effects cause limit cycles of motion. Nonlinear effects are inherent in fluid film bearings and seals. Other contributors to nonlinear effects are shafts, couplings and foundations. In addition to affecting the threshold of stability, the nonlinear effects can cause jump phenomena to occur at not only the critical speeds, but also at stability onset or restabilization speeds.

Gunter, E. J.↗
DOE OSTI2022

Characterization of nonlinear ultrasonic waves behavior while interacting with poor interlayer bonds in large-scale additive manufactured materials

Over the past decades, researchers have developed several nonlinear ultrasonic techniques for quality control of materials commonly used in different applications. Owing to the superior sensitivity of nonlinear ultrasound waves to small defects such as micro-cracks, their applicability in different nondestructive testing (NDT) problems has been investigated in numerous studies. These studies utilize frequency domain analysis to detect the generation of higher harmonics because of the formation of defects in the inspected medium. Frequency domain analysis based on the Fourier transform is a significant approach used in linear systems; however, it may not perform adequately on nonlinear systems. Hence, studies on nonlinear dynamics and physics consider analyzing systems' behavior in the phase-space domain. In contrast to the frequency domain analysis, which can result in information loss, analysis in the phase-space domain retains all the information regarding a system's states. Here, we investigate the nonlinearities induced by poor interlayer bonding in polymer-based additive manufactured parts in the phase-space domain. It is convenient to characterize the nonlinearity in the phase-space domain because it provides a geometrical representation of a system's states. Two types of low quality interlayer bond are considered. The first type is simulated artificially while the second type is manufactured by reducing the bond quality during the printing process. The analysis verified that the received ultrasonic signals exhibit classical nonlinear behavior in the phase-space domain while interacting with simulated poor interlayer bonds. In addition, the results showed that the behavior of ultrasonic waves is amplitude-dependent and evolves into models that have not been previously reported. Furthermore, Largest Lyapunov Exponent (LLE) is used to quantify the behavior of nonlinear ultrasonic waves while interacting with poor interlayer bonds. Using LLE, it was observed that the divergence rate of the phase-space trajectories depends on the amplitude of the excitation. This observation quantitatively proves that nonlinear behavior of ultrasound while interacting with poor interlayer bonds can be amplitude-dependent. The results of both simulated and inherent poor interlayer bond cases showed that LLE can be used as a reliable quantitative damage-sensitive feature to detect and potentially characterize weak bonds, which are difficult to detect using conventional approaches. Additionally, the reported results in the phase-space domain provide a basis for proposing a new mathematical model for ultrasonic waves interacting with poor interlayer bonds.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Learning Distributed Geometric Koopman Operator for Sparse Networked Dynamical Systems

Koopman operator theory provides an alternative to study nonlinear networked dynamical systems by mapping the state space to an abstract higher dimensional space where the system evolution is linear. Recent works show the application of graph neural networks (GNNs) to learn state to object-centric embeddings and achieve centralized block-wise computation of Koopman operator (KO) under additional assumptions on the underlying agents properties and constraints on the KO structure. However, the computational complexity of learning the Koopman increases exponentially for networked systems where the number of possible system states grows in a combinatorial fashion with the number of nodes. The learning challenge is further amplified for sparse networks by two factors: 1) sample sparsity for learning the Koopman operator in the non-linear space, and 2) the divergence in the dynamics of individual nodes or from one subgraph to another. Our work aims to address these challenge by formulating the representation learning of networked dynamical systems into a multi-agent paradigm and learning the Koopman operator in a distributive manner. The computational as well as performance advantages of distributed Koopman is predominant for sparse networks whereas for fully connected networks, it is shown to coincide with the centralized one. The empirical study on rope system, network of oscillators and a synthetic power system show comparable and superior performance along with computational benefits with the state-of-the-art methods.

Mukherjee, Sayak↗
NASA NTRS1994

Control strategies for systems with limited actuators

This work investigates the effects of actuator saturation in multi-input, multi-output (MIMO) control systems. The adverse system behavior introduced by the saturation nonlinearity is viewed here as resulting from two mechanisms: controller windup - a problem caused by the discrepancy between the limited actuator commands and the corresponding control signals, and directionality - the problem of how to use nonlimited actuators when a limited condition exists. The tracking mode and Hanus methods are two common strategies for dealing with the windup problem. It is seen that while these methods alleviate windup, performance problems remain due to plant directionality. Though high gain conventional antiwindup as well as more general linear methods have the potential to address both windup and directionality, no systematic design method for these schemes has emerged; most approaches used in practice are application driven. An alternative method of addressing the directionality problem is presented which involves the introduction of a control direction preserving nonlinearity to the Hanus antiwindup system. A nonlinearity is subsequently proposed which reduces the conservation inherent in the former direction-preserving approach, improving performance. The concept of multivariable sensitivity is seen to play a key role in the success of the new method.

Marcopoli, Vincent R.↗