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NASA NTRSDate not supplied

Attitude Reconstruction of Free-Flight CFD Generated Trajectories Using Non-Linear Pitch Damping Coefficient Curves

Attitude history reconstruction of Free-flight CFD generated trajectories with non-linear pitch damping coefficient curves is investigated. Free-flight CFD simulations of the capsule shape used for the Genesis sample return mission and the upcoming Dragonfly mission to Titan are conducted for 1-, 2-, and 3-degree-of-freedom cases. Two different data reduction methodologies are employed to derive a pitch damping curve as a function of instantaneous angle of attack. These curves are then used to reconstruct the attitude history of the body which is compared to the raw simulation results. While both data reduction methods produce pitch damping curves that can generally reconstruct the motion seen in the Free-flight simulations, it is found that optimization of the pitch damping curve using an inverse estimation process yields superior and more generalizable results. Further refinement of this technique could allow pitch damping curves derived using CFD to serve as a capability complementary to existing techniques for dynamic stability characterization.

entry↗

NASA NTRS2004

High-Order Simulation of Non-Linear Oscillations and Shocks in the Solar Atmosphere

The solar atmosphere presents a rich source of highly non-linear magneto-hydrodynamic phenomena: strong gradients and forcing terms result in both large shocks and oscillations. The additional requirements of energy balance and initialization in hydrostatic equilibrium compound the challenge of this problem. A wealth of observational data allows us to check the results of our simulations. The problem of simulating the solar atmosphere provides, in addition to an interesting system in its own right, a challenging testbed for high-order shock-capturing methods. We discuss the challenge of simulating solar atmospheric phenomena, concentrating on various high-order central methods ranging from second to fourth order. Our method is based on the central-upwind scheme of Kurganov, Noelle and Petrova, which we extend to high order via various interpolants. We investigate various initial data for our simulations, corresponding to observed conditions in different regions of the solar surface: the normal quiet sun and sunspots. When non-oscillatory using second- and third-order methods, we are able to reproduce non-trivial observational results. In particular we find a correlation between initial data and both the shock speeds and particle oscillation spectra that match observations in the corresponding regions. When using fourth-order WENO interpolants, we find that while the individual shock profiles at any given time appear non-oscillatory, spurious oscillations appear in the fields after long time integrations. The issue of initialization in hydrostatic equilibrium raises difficult issues. Careful treatment of the gravitational source term can reduce violations of hydrostatic equilibrium, but difficulties remain, primarily due to discontinuities in the piecewise-polynomial reconstructions. In the case of the Euler equations in gravity, the use of high-order methods reduces the violation of hydrostatic equilibrium to a sufficiently low level for the above described results to be obtained. Including various energy flux terms in the equations, however, leads to severe instability when hydrostatic balance is violated. We discuss various strategies to address this problem, including adaptive grid methods.

Bryson, S.↗

NASA NTRS1996

High Reynolds number analysis of flat plate and separated afterbody flow using non-linear turbulence models

The ability of the three-dimensional Navier-Stokes method, PAB3D, to simulate the effect of Reynolds number variation using non-linear explicit algebraic Reynolds stress turbulence modeling was assessed. Subsonic flat plate boundary-layer flow parameters such as normalized velocity distributions, local and average skin friction, and shape factor were compared with DNS calculations and classical theory at various local Reynolds numbers up to 180 million. Additionally, surface pressure coefficient distributions and integrated drag predictions on an axisymmetric nozzle afterbody were compared with experimental data from 10 to 130 million Reynolds number. The high Reynolds data was obtained from the NASA Langley 0.3m Transonic Cryogenic Tunnel. There was generally good agreement of surface static pressure coefficients between the CFD and measurement. The change in pressure coefficient distributions with varying Reynolds number was similar to the experimental data trends, though slightly over-predicting the effect. The computational sensitivity of viscous modeling and turbulence modeling are shown. Integrated afterbody pressure drag was typically slightly lower than the experimental data. The change in afterbody pressure drag with Reynolds number was small both experimentally and computationally, even though the shape of the distribution was somewhat modified with Reynolds number.

Carlson, John R.↗

NASA NTRS1987

Non-linear identification of a squeeze-film damper

Described is an experimental study to identify the damping laws associated with a squeeze-film vibration damper. This is achieved by using a non-linear filtering algorithm to process displacement responses of the damper ring to synchronous excitation and thus to estimate the parameters in an nth-power velocity model. The experimental facility is described in detail and a representative selection of results is included. The identified models are validated through the prediction of damper-ring orbits and comparison with observed responses.

Stanway, Roger↗

NASA NTRS1989

Non-linear cord-rubber composites

A method is presented for calculating the stress-strain relations in a multi-layer composite made up of materials whose individual stress-strain characteristics are non-linear and possibly different. The method is applied to the case of asymmetric tubes in tension, and comparisons with experimentally measured data are given.

Clark, S. K.↗

NASA NTRS2005

Failure Models and Criteria for FRP Under In-Plane or Three-Dimensional Stress States Including Shear Non-Linearity

A set of three-dimensional failure criteria for laminated fiber-reinforced composites, denoted LaRC04, is proposed. The criteria are based on physical models for each failure mode and take into consideration non-linear matrix shear behaviour. The model for matrix compressive failure is based on the Mohr-Coulomb criterion and it predicts the fracture angle. Fiber kinking is triggered by an initial fiber misalignment angle and by the rotation of the fibers during compressive loading. The plane of fiber kinking is predicted by the model. LaRC04 consists of 6 expressions that can be used directly for design purposes. Several applications involving a broad range of load combinations are presented and compared to experimental data and other existing criteria. Predictions using LaRC04 correlate well with the experimental data, arguably better than most existing criteria. The good correlation seems to be attributable to the physical soundness of the underlying failure models.

Pinho, Silvestre T.↗

NASA NTRS1986

Finite element modelling of non-linear magnetic circuits using Cosmic NASTRAN

The general purpose Finite Element Program COSMIC NASTRAN currently has the ability to model magnetic circuits with constant permeablilities. An approach was developed which, through small modifications to the program, allows modelling of non-linear magnetic devices including soft magnetic materials, permanent magnets and coils. Use of the NASTRAN code resulted in output which can be used for subsequent mechanical analysis using a variation of the same computer model. Test problems were found to produce theoretically verifiable results.

Sheerer, T. J.↗

NASA NTRS1991

Neural networks: What non-linearity to choose

Neural networks are now one of the most successful learning formalisms. Neurons transform inputs (x(sub 1),...,x(sub n)) into an output f(w(sub 1)x(sub 1) + ... + w(sub n)x(sub n)), where f is a non-linear function and w, are adjustable weights. What f to choose? Usually the logistic function is chosen, but sometimes the use of different functions improves the practical efficiency of the network. The problem of choosing f as a mathematical optimization problem is formulated and solved under different optimality criteria. As a result, a list of functions f that are optimal under these criteria are determined. This list includes both the functions that were empirically proved to be the best for some problems, and some new functions that may be worth trying.

Kreinovich, Vladik YA.↗

NASA NTRS2000

Wave Driven Non-linear Flow Oscillator for the 22-Year Solar Cycle

In the Earth's atmosphere, a zonal flow oscillation is observed with periods between 20 and 32 months, the Quasi Biennial Oscillation. This oscillation does not require external time dependent forcing but is maintained by non-linear wave momentum deposition. It is proposed that such a mechanism also drives long-period oscillations in planetary and stellar interiors. We apply this mechanism to generate a flow oscillation for the 22-year solar cycle. The oscillation would occur just below the convective envelope where waves can propagate. Using scale analysis, we present results from a simplified model that incorporates Hines' gravity wave parameterization. Wave amplitudes less than 10 m/s can produce reversing zonal flows of 25 m/s that should be sufficient to generate a corresponding oscillation in the poloidal magnetic field. Low buoyancy frequency and the associated increase in turbulence help to produce the desired oscillation period of the flow.

Mayr, Hans G.↗

NASA NTRS1985

A non-linear programming approach to the computer-aided design of regulators using a linear-quadratic formulation

A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a non-linear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer-aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer.

Fleming, P.↗

NASA NTRS2001

A Non-Linear Approach to Spacecraft Trajectory Control in the Vicinity of a Libration Point

An expanding interest in mission design strategies that exploit libration point regions demands the continued development of enhanced, efficient, control algorithms for station-keeping and formation maintenance. This paper discusses the development of a non-linear, station-keeping, control algorithm for trajectories in the vicinity of a libration point. The control law guarantees exponential convergence, based on a Lyaponov analysis. Controller performance is evaluated using FreeFlyer(R) and MATLAB(R) for a spacecraft stationed near the L2 libration point in the Earth-Moon system, tracking a pre-defined reference trajectory. Evaluation metrics are fuel usage and tracking accuracy. Simulation results are compared with a linear-based controller for a spacecraft tracking the same reference trajectory. Although the analysis is framed in the context of station-keeping, the control algorithm is equally applicable to a formation flying problem with an appropriate definition of the reference trajectory.

Luquette, Richard J.↗

NASA NTRS2002

Transient Vibration Prediction for Rotors on Ball Bearings Using Load-dependent Non-linear Bearing Stiffness

Rolling-element bearing forces vary nonlinearly with bearing deflection. Thus an accurate rotordynamic transient analysis requires bearing forces to be determined at each step of the transient solution. Analyses have been carried out to show the effect of accurate bearing transient forces (accounting for non-linear speed and load dependent bearing stiffness) as compared to conventional use of average rolling-element bearing stiffness. Bearing forces were calculated by COBRA-AHS (Computer Optimized Ball and Roller Bearing Analysis - Advanced High Speed) and supplied to the rotordynamics code ARDS (Analysis of Rotor Dynamic Systems) for accurate simulation of rotor transient behavior. COBRA-AHS is a fast-running 5 degree-of-freedom computer code able to calculate high speed rolling-element bearing load-displacement data for radial and angular contact ball bearings and also for cylindrical and tapered roller beatings. Results show that use of nonlinear bearing characteristics is essential for accurate prediction of rotordynamic behavior.

Fleming, David P.↗

NASA NTRS1987

Application of non-linear dynamics to the characterization of cardiac electrical instability

Beat-to-beat alternation in the morphology of the ECG has been previously observed in hearts susceptible to fibrillation. In addition, fibrillation has been characterized by some as a chaotic state. Period doubling phenomena, such as alternation, and the onset of chaos have been connected by non-linear dynamical systems theory. In this paper, we describe the use of a technique from nonlinear dynamics theory, the construction of a first return nap, to assess the susceptibility to fibrillation threshhold in canine experiments.

NASA Discipline Cardiopulmonary↗

NASA NTRS2001

A Non-Linear Approach to Spacecraft Formation Control in the Vicinity of a Collinear Libration Point

An expanding interest in mission design strategies that exploit libration point regions demands the continued development of enhanced, efficient, control algorithms for station-keeping and formation maintenance. This paper discusses the development of a non-linear, formation maintenance, control algorithm for trajectories in the vicinity of a libration point. However, the formulation holds for any trajectory governed by the equations of motion for the restricted three body problem. The control law guarantees exponential convergence, based on a Lyaponov analysis. FreeFlyer and MATLAB provide the simulation environment for controller performance evaluation. The simulation, modeled after the MAXIM Pathfinder mission, maintains the relative position of a "follower" spacecraft with respect to a "leader" spacecraft, stationed near the L2 libration point in the Sun-Earth system. Evaluation metrics are fuel usage and tracking accuracy.

Luquette, Richard J.↗

NASA NTRS1995

Sensitivity analysis of the non-linear dynamic viscoplastic response of 2-d structures with respect to material parameters

A computational procedure is presented for evaluating the sensitivity coefficients of the viscoplastic response of structures subjected to dynamic loading. A state of plane stress is assumed to exist in the structure, a velocity strain-Cauchy stress formulation is used, and the geometric non-linearities arising from large strains are incorporated. The Jaumann rate is used as a frame indifferent stress rate. The material model is chosen to be isothermal viscoplasticity, and an associated flow rule is used with a von Mises effective stress. The equations of motion emanating from a finite element semi-discretization are integrated using an explicit central difference scheme with an implicit stress update. The sensitivity coefficients are evaluated using a direct differentiation approach. Since the domain of integration is the current configuration, the sensitivity coefficients of the spatial derivatives of the shape functions must be included. Numerical results are presented for a thin plate with a central cutout subjected to an in-plane compressive loading. The sensitivity coefficients are generated by evaluating the derivatives of the response quantities with respect to Young's modulus, and two of the material parameters characterizing the viscoplastic response. Time histories of the response and sensitivity coefficients, and spatial distributions at selected times are presented.

Kulkarni, Makarand↗

NASA NTRS2005

Development and Application of Non-Linear Image Enhancement and Multi-Sensor Fusion Techniques for Hazy and Dark Imaging

The purpose of this research was to develop enhancement and multi-sensor fusion algorithms and techniques to make it safer for the pilot to fly in what would normally be considered Instrument Flight Rules (IFR) conditions, where pilot visibility is severely restricted due to fog, haze or other weather phenomenon. We proposed to use the non-linear Multiscale Retinex (MSR) as the basic driver for developing an integrated enhancement and fusion engine. When we started this research, the MSR was being applied primarily to grayscale imagery such as medical images, or to three-band color imagery, such as that produced in consumer photography: it was not, however, being applied to other imagery such as that produced by infrared image sources. However, we felt that it was possible by using the MSR algorithm in conjunction with multiple imaging modalities such as long-wave infrared (LWIR), short-wave infrared (SWIR), and visible spectrum (VIS), we could substantially improve over the then state-of-the-art enhancement algorithms, especially in poor visibility conditions. We proposed the following tasks: 1) Investigate the effects of applying the MSR to LWIR and SWIR images. This consisted of optimizing the algorithm in terms of surround scales, and weights for these spectral bands; 2) Fusing the LWIR and SWIR images with the VIS images using the MSR framework to determine the best possible representation of the desired features; 3) Evaluating different mixes of LWIR, SWIR and VIS bands for maximum fog and haze reduction, and low light level compensation; 4) Modifying the existing algorithms to work with video sequences. Over the course of the 3 year research period, we were able to accomplish these tasks and report on them at various internal presentations at NASA Langley Research Center, and in presentations and publications elsewhere. A description of the work performed under the tasks is provided in Section 2. The complete list of relevant publications during the research periods is provided in Section 5. This research also resulted in the generation of intellectual property.

Rahman, Zia-ur↗

NASA NTRS1992

Detector noise statistics in the non-linear regime

The statistical behavior of an idealized linear detector in the presence of threshold and saturation levels is examined. It is assumed that the noise is governed by the statistical fluctuations in the number of photons emitted by the source during an exposure. Since physical detectors cannot have infinite dynamic range, our model illustrates that all devices have non-linear regimes, particularly at high count rates. The primary effect is a decrease in the statistical variance about the mean signal due to a portion of the expected noise distribution being removed via clipping. Higher order statistical moments are also examined, in particular, skewness and kurtosis. In principle, the expected distortion in the detector noise characteristics can be calibrated using flatfield observations with count rates matched to the observations. For this purpose, some basic statistical methods that utilize Fourier analysis techniques are described.

Shopbell, P. L.↗

NASA NTRS1998

Image enhancement by non-linear extrapolation in frequency space

An input image is enhanced to include spatial frequency components having frequencies higher than those in an input image. To this end, an edge map is generated from the input image using a high band pass filtering technique. An enhancing map is subsequently generated from the edge map, with the enhanced map having spatial frequencies exceeding an initial maximum spatial frequency of the input image. The enhanced map is generated by applying a non-linear operator to the edge map in a manner which preserves the phase transitions of the edges of the input image. The enhanced map is added to the input image to achieve a resulting image having spatial frequencies greater than those in the input image. Simplicity of computations and ease of implementation allow for image sharpening after enlargement and for real-time applications such as videophones, advanced definition television, zooming, and restoration of old motion pictures.

Anderson, Charles H.↗