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NASA NTRS2001

Signal-to-noise ratio comparison of encoding methods for hyperpolarized noble gas MRI

Some non-Fourier encoding methods such as wavelet and direct encoding use spatially localized bases. The spatial localization feature of these methods enables optimized encoding for improved spatial and temporal resolution during dynamically adaptive MR imaging. These spatially localized bases, however, have inherently reduced image signal-to-noise ratio compared with Fourier or Hadamad encoding for proton imaging. Hyperpolarized noble gases, on the other hand, have quite different MR properties compared to proton, primarily the nonrenewability of the signal. It could be expected, therefore, that the characteristics of image SNR with respect to encoding method will also be very different from hyperpolarized noble gas MRI compared to proton MRI. In this article, hyperpolarized noble gas image SNRs of different encoding methods are compared theoretically using a matrix description of the encoding process. It is shown that image SNR for hyperpolarized noble gas imaging is maximized for any orthonormal encoding method. Methods are then proposed for designing RF pulses to achieve normalized encoding profiles using Fourier, Hadamard, wavelet, and direct encoding methods for hyperpolarized noble gases. Theoretical results are confirmed with hyperpolarized noble gas MRI experiments. Copyright 2001 Academic Press.

Non-NASA Center↗

NASA NTRS2004

Properties of a Formal Method for Prediction of Emergent Behaviors in Swarm-based Systems

Autonomous intelligent swarms of satellites are being proposed for NASA missions that have complex behaviors and interactions. The emergent properties of swarms make these missions powerful, but at the same time more difficult to design and assure that proper behaviors will emerge. This paper gives the results of research into formal methods techniques for verification and validation of NASA swarm-based missions. Multiple formal methods were evaluated to determine their effectiveness in modeling and assuring the behavior of swarms of spacecraft. The NASA ANTS mission was used as an example of swarm intelligence for which to apply the formal methods. This paper will give the evaluation of these formal methods and give partial specifications of the ANTS mission using four selected methods. We then give an evaluation of the methods and the needed properties of a formal method for effective specification and prediction of emergent behavior in swarm-based systems.

Rouff, Christopher↗

NASA NTRS1947

A Comparison of Three Theoretical Methods of Calculating Span Load Distribution on Swept Wings

Three methods for calculating span load distribution, those developed by V.M Falkner, Wm. Mutterperl, and J. Weissinger, have been applied to five swept wings. The angles of sweep ranged from -45 degrees to +45 degrees. These methods were examined to establish their relative accuracy and case of application. Experimentally determined loadings were used as a basis for judging accuracy. For the convenience of the readers the computing forms and all information requisite to their application are included in appendixes. From the analysis it was found that the Weissinger method would be best suited to an over-all study of the effects of plan form on the span loading and associated characteristics of wings. The method gave good, but not best, accuracy and involved by far the least computing effort. The Falkner method gave the best accuracy but at a considerable expanse in computing effort and hence appeared to be most useful for a detailed study of a specific wing. The Mutterperl method offered no advantages in accuracy of facility over either of the other methods and hence is not recommended for use.

VanDorn, Nicholas H.↗

NASA NTRS1957

On the Use of the Harmonic Linearizaiton Method in the Automatic Control Theory

The method of harmonic linearization (harmonic balance), first proposed by N. M. Krylov and N. N. Bogolyubov for the approximate investigation of nonlinear vibrations, has been developed and received wide practical application to problems in the theory of automatic control. Recently, some doubt has been expressed on the legitimacy of application of the method to these problems, and assertions were made on the absence in them of a small parameter of any kind. Nevertheless, the method gives practical, acceptable results and is a simple and powerful means in engineering computations. Hence, the importance of questions arises as to its justification. The underlying principle of the method is the replacement of the given nonlinear equation by a linear equation. In establishing the method, a small parameter is considered whose presence makes it possible to speak, with some degree of approximation, of the solution of this new equation to the solution of the given nonlinear equation. In an article by the author, certain considerations were given on the presence of the small parameter, but this question has not as yet received a final answer. In the present report, a somewhat different approach to the problem is applied that permits: (a) establishing, in the clearest manner, the form of the presence of the small parameter in nonlinear problems of control theory, solvable by the method of harmonic linearization; (b) connecting it with previous intuitive physical concepts (with the "filter property") and extending the class of problems possessing this property; and (c) discussing various generalizations of the method.

Popov, E. P.↗

NASA NTRS2005

Comparison of Response Surface Construction Methods for Derivative Estimation Using Moving Least Squares, Kriging and Radial Basis Functions

Response construction methods using Moving Least Squares (MLS), Kriging and Radial Basis Functions (RBF) are compared with the Global Least Squares (GLS) method in three numerical examples for derivative generation capability. Also, a new Interpolating Moving Least Squares (IMLS) method adopted from the meshless method is presented. It is found that the response surface construction methods using the Kriging and RBF interpolation yields more accurate results compared with MLS and GLS methods. Several computational aspects of the response surface construction methods also discussed.

Krishnamurthy, Thiagarajan↗

NASA NTRS2003

New Method Developed To Purify Single Wall Carbon Nanotubes for Aerospace Applications

Single wall carbon nanotubes have attracted considerable attention because of their remarkable mechanical properties and electrical and thermal conductivities. Use of these materials as primary or secondary reinforcements in polymers or ceramics could lead to new materials with significantly enhanced mechanical strength and electrical and thermal conductivity. Use of carbon-nanotube-reinforced materials in aerospace components will enable substantial reductions in component weight and improvements in durability and safety. Potential applications for single wall carbon nanotubes include lightweight components for vehicle structures and propulsion systems, fuel cell components (bipolar plates and electrodes) and battery electrodes, and ultra-lightweight materials for use in solar sails. A major barrier to the successful use of carbon nanotubes in these components is the need for methods to economically produce pure carbon nanotubes in large enough quantities to not only evaluate their suitability for certain applications but also produce actual components. Most carbon nanotube synthesis methods, including the HiPCO (high pressure carbon monoxide) method developed by Smalley and others, employ metal catalysts that remain trapped in the final product. These catalyst impurities can affect nanotube properties and accelerate their decomposition. The development of techniques to remove most, if not all, of these impurities is essential to their successful use in practical applications. A new method has been developed at the NASA Glenn Research Center to purify gram-scale quantities of single wall carbon nanotubes. This method, a modification of a gas phase purification technique previously reported by Smalley and others, uses a combination of high-temperature oxidations and repeated extractions with nitric and hydrochloric acid. This improved procedure significantly reduces the amount of impurities (catalyst and nonnanotube forms of carbon) within the nanotubes, increasing their stability significantly. The onset of decomposition of the purified nanotubes (determined by thermal gravimetric analysis in air) is more than 300 C higher than that of the crude nanotubes. Transmission electron microscopy analysis of nanotubes purified by this method reveals near complete removal of iron catalyst particles. Analysis of the nanotubes using inductively coupled plasma spectroscopy revealed that the iron content of the nanotubes was reduced from 22.7 wt% in the crude nanotubes to less than 0.02 wt%. X-ray photoelectron spectroscopy revealed a decrease in iron content after purification as well as an increase in oxygen content due to the formation of carboxylic acid groups on the surface of the nanotubes. Nanotubes purified by this improved method can be readily dispersed in common organic solvents, in particular N,N-dimethylformamide, using prolonged ultrasonic treatment. These dispersions can then be used to incorporate single wall carbon nanotubes into polymer films.

Lebron, Marisabel↗

NASA NTRS2003

Neural Network and Regression Methods Demonstrated in the Design Optimization of a Subsonic Aircraft

The neural network and regression methods of NASA Glenn Research Center s COMETBOARDS design optimization testbed were used to generate approximate analysis and design models for a subsonic aircraft operating at Mach 0.85 cruise speed. The analytical model is defined by nine design variables: wing aspect ratio, engine thrust, wing area, sweep angle, chord-thickness ratio, turbine temperature, pressure ratio, bypass ratio, fan pressure; and eight response parameters: weight, landing velocity, takeoff and landing field lengths, approach thrust, overall efficiency, and compressor pressure and temperature. The variables were adjusted to optimally balance the engines to the airframe. The solution strategy included a sensitivity model and the soft analysis model. Researchers generated the sensitivity model by training the approximators to predict an optimum design. The trained neural network predicted all response variables, within 5-percent error. This was reduced to 1 percent by the regression method. The soft analysis model was developed to replace aircraft analysis as the reanalyzer in design optimization. Soft models have been generated for a neural network method, a regression method, and a hybrid method obtained by combining the approximators. The performance of the models is graphed for aircraft weight versus thrust as well as for wing area and turbine temperature. The regression method followed the analytical solution with little error. The neural network exhibited 5-percent maximum error over all parameters. Performance of the hybrid method was intermediate in comparison to the individual approximators. Error in the response variable is smaller than that shown in the figure because of a distortion scale factor. The overall performance of the approximators was considered to be satisfactory because aircraft analysis with NASA Langley Research Center s FLOPS (Flight Optimization System) code is a synthesis of diverse disciplines: weight estimation, aerodynamic analysis, engine cycle analysis, propulsion data interpolation, mission performance, airfield length for landing and takeoff, noise footprint, and others.

Hopkins, Dale A.↗

NASA NTRS2005

Issues and Methods Concerning the Evaluation of Hypersingular and Near-Hypersingular Integrals in BEM Formulations

It is known that higher order modeling of the sources and the geometry in Boundary Element Modeling (BEM) formulations is essential to highly efficient computational electromagnetics. However, in order to achieve the benefits of hIgher order basis and geometry modeling, the singular and near-singular terms arising in BEM formulations must be integrated accurately. In particular, the accurate integration of near-singular terms, which occur when observation points are near but not on source regions of the scattering object, has been considered one of the remaining limitations on the computational efficiency of integral equation methods. The method of singularity subtraction has been used extensively for the evaluation of singular and near-singular terms. Piecewise integration of the source terms in this manner, while manageable for bases of constant and linear orders, becomes unwieldy and prone to error for bases of higher order. Furthermore, we find that the singularity subtraction method is not conducive to object-oriented programming practices, particularly in the context of multiple operators. To extend the capabilities, accuracy, and maintainability of general-purpose codes, the subtraction method is being replaced in favor of the purely numerical quadrature schemes. These schemes employ singularity cancellation methods in which a change of variables is chosen such that the Jacobian of the transformation cancels the singularity. An example of the sin,oularity cancellation approach is the Duffy method, which has two major drawbacks: 1) In the resulting integrand, it produces an angular variation about the singular point that becomes nearly-singular for observation points close to an edge of the parent element, and 2) it appears not to work well when applied to nearly-singular integrals. Recently, the authors have introduced the transformation u(x(prime))= sinh (exp -1) x(prime)/Square root of ((y prime (exp 2))+ z(exp 2) for integrating functions of the form I = Integral of (lambda(r(prime))((e(exp -jkR))/(4 pi R) d D where A (r (prime)) is a vector or scalar basis function and R = Square root of( (x(prime)(exp2) + (y(prime)(exp2) + z(exp 2)) is the distance between source and observation points. This scheme has all of the advantages of the Duffy method while avoiding the disadvantages listed above. In this presentation we will survey similar approaches for handling singular and near-singular terms for kernels with 1/R(exp 2) type behavior, addressing potential pitfalls and offering techniques to efficiently handle special cases.

Fink, P. W.↗

NASA NTRS2009

Local-in-Time Adjoint-Based Method for Optimal Control/Design Optimization of Unsteady Compressible Flows

.We study local-in-time adjoint-based methods for minimization of ow matching functionals subject to the 2-D unsteady compressible Euler equations. The key idea of the local-in-time method is to construct a very accurate approximation of the global-in-time adjoint equations and the corresponding sensitivity derivative by using only local information available on each time subinterval. In contrast to conventional time-dependent adjoint-based optimization methods which require backward-in-time integration of the adjoint equations over the entire time interval, the local-in-time method solves local adjoint equations sequentially over each time subinterval. Since each subinterval contains relatively few time steps, the storage cost of the local-in-time method is much lower than that of the global adjoint formulation, thus making the time-dependent optimization feasible for practical applications. The paper presents a detailed comparison of the local- and global-in-time adjoint-based methods for minimization of a tracking functional governed by the Euler equations describing the ow around a circular bump. Our numerical results show that the local-in-time method converges to the same optimal solution obtained with the global counterpart, while drastically reducing the memory cost as compared to the global-in-time adjoint formulation.

Yamaleev, N. K.↗

NASA NTRS2008

Using Optically Stimulated Electron Emission as an Inspection Method to Monitor Surface Contamination

During redesign of the Space Shuttle reusable solid rocket motor (RSRM), NASA amended the contract with ATK Launch Systems (then Morton Thiokol Inc.) with Change Order 966 to implement a contamination control and cleanliness verification method. The change order required: (1) A quantitative inspection method (2) A written record of actual contamination levels versus a known reject level (3) A method that is more sensitive than existing methods of visual and black light inspection. Black light inspection is only useful for inspection of contaminants that fluoresce near the 365 nm spectral line and is not useful for inspection of most silicones that will not produce strong fluorescence. Black light inspection conducted by a qualified inspector under controlled light is capable of detecting Conoco HD-2 grease in gross amounts and is very subjective due to operator sensitivity. Optically stimulated electron emission (OSEE), developed at the Materials and Process Laboratory at Marshall Space Flight Center (MSFC), was selected to satisfy Change Order 966. OSEE offers several important advantages over existing laboratory methods with similar sensitivity, e.g., spectroscopy and nonvolatile residue sampling, which provide turn around time, real time capability, and full coverage inspection capability. Laboratory methods require sample gathering and in-lab analysis, which sometimes takes several days to get results. This is not practical in a production environment. In addition, these methods do not offer full coverage inspection of the large components

Lingbloom, Mike S.↗

NASA NTRS2008

Integrated Force Method for Indeterminate Structures

Two methods of solving indeterminate structural-mechanics problems have been developed as products of research on the theory of strain compatibility. In these methods, stresses are considered to be the primary unknowns (in contrast to strains and displacements being considered as the primary unknowns in some prior methods). One of these methods, denoted the integrated force method (IFM), makes it possible to compute stresses, strains, and displacements with high fidelity by use of modest finite-element models that entail relatively small amounts of computation. The other method, denoted the completed Beltrami Mitchell formulation (CBMF), enables direct determination of stresses in an elastic continuum with general boundary conditions, without the need to first calculate displacements as in traditional methods. The equilibrium equation, the compatibility condition, and the material law are the three fundamental concepts of the theory of structures. For almost 150 years, it has been commonly supposed that the theory is complete. However, until now, the understanding of the compatibility condition remained incomplete, and the compatibility condition was confused with the continuity condition. Furthermore, the compatibility condition as applied to structures in its previous incomplete form was inconsistent with the strain formulation in elasticity.

Hopkins, Dale A.↗

NASA NTRS2003

Flight-Test Evaluation of Flutter-Prediction Methods

The flight-test community routinely spends considerable time and money to determine a range of flight conditions, called a flight envelope, within which an aircraft is safe to fly. The cost of determining a flight envelope could be greatly reduced if there were a method of safely and accurately predicting the speed associated with the onset of an instability called flutter. Several methods have been developed with the goal of predicting flutter speeds to improve the efficiency of flight testing. These methods include (1) data-based methods, in which one relies entirely on information obtained from the flight tests and (2) model-based approaches, in which one relies on a combination of flight data and theoretical models. The data-driven methods include one based on extrapolation of damping trends, one that involves an envelope function, one that involves the Zimmerman-Weissenburger flutter margin, and one that involves a discrete-time auto-regressive model. An example of a model-based approach is that of the flutterometer. These methods have all been shown to be theoretically valid and have been demonstrated on simple test cases; however, until now, they have not been thoroughly evaluated in flight tests. An experimental apparatus called the Aerostructures Test Wing (ATW) was developed to test these prediction methods.

Lind, RIck↗

NASA NTRS2012

Model-Based Method for Sensor Validation

Fault detection, diagnosis, and prognosis are essential tasks in the operation of autonomous spacecraft, instruments, and in situ platforms. One of NASA s key mission requirements is robust state estimation. Sensing, using a wide range of sensors and sensor fusion approaches, plays a central role in robust state estimation, and there is a need to diagnose sensor failure as well as component failure. Sensor validation can be considered to be part of the larger effort of improving reliability and safety. The standard methods for solving the sensor validation problem are based on probabilistic analysis of the system, from which the method based on Bayesian networks is most popular. Therefore, these methods can only predict the most probable faulty sensors, which are subject to the initial probabilities defined for the failures. The method developed in this work is based on a model-based approach and provides the faulty sensors (if any), which can be logically inferred from the model of the system and the sensor readings (observations). The method is also more suitable for the systems when it is hard, or even impossible, to find the probability functions of the system. The method starts by a new mathematical description of the problem and develops a very efficient and systematic algorithm for its solution. The method builds on the concepts of analytical redundant relations (ARRs).

Vatan, Farrokh↗

NASA NTRS2012

Validation of Satellite-Based Objective Overshooting Cloud-Top Detection Methods Using CloudSat Cloud Profiling Radar Observations

Two satellite infrared-based overshooting convective cloud-top (OT) detection methods have recently been described in the literature: 1) the 11-mm infrared window channel texture (IRW texture) method, which uses IRW channel brightness temperature (BT) spatial gradients and thresholds, and 2) the water vapor minus IRW BT difference (WV-IRW BTD). While both methods show good performance in published case study examples, it is important to quantitatively validate these methods relative to overshooting top events across the globe. Unfortunately, no overshooting top database currently exists that could be used in such study. This study examines National Aeronautics and Space Administration CloudSat Cloud Profiling Radar data to develop an OT detection validation database that is used to evaluate the IRW-texture and WV-IRW BTD OT detection methods. CloudSat data were manually examined over a 1.5-yr period to identify cases in which the cloud top penetrates above the tropopause height defined by a numerical weather prediction model and the surrounding cirrus anvil cloud top, producing 111 confirmed overshooting top events. When applied to Moderate Resolution Imaging Spectroradiometer (MODIS)-based Geostationary Operational Environmental Satellite-R Series (GOES-R) Advanced Baseline Imager proxy data, the IRW-texture (WV-IRW BTD) method offered a 76% (96%) probability of OT detection (POD) and 16% (81%) false-alarm ratio. Case study examples show that WV-IRW BTD.0 K identifies much of the deep convective cloud top, while the IRW-texture method focuses only on regions with a spatial scale near that of commonly observed OTs. The POD decreases by 20% when IRW-texture is applied to current geostationary imager data, highlighting the importance of imager spatial resolution for observing and detecting OT regions.

Bedka, Kristopher M.↗

NASA NTRS2014

High-Order Implicit-Explicit Multi-Block Time-stepping Method for Hyperbolic PDEs

This work seeks to explore and improve the current time-stepping schemes used in computational fluid dynamics (CFD) in order to reduce overall computational time. A high-order scheme has been developed using a combination of implicit and explicit (IMEX) time-stepping Runge-Kutta (RK) schemes which increases numerical stability with respect to the time step size, resulting in decreased computational time. The IMEX scheme alone does not yield the desired increase in numerical stability, but when used in conjunction with an overlapping partitioned (multi-block) domain significant increase in stability is observed. To show this, the Overlapping-Partition IMEX (OP IMEX) scheme is applied to both one-dimensional (1D) and two-dimensional (2D) problems, the nonlinear viscous Burger's equation and 2D advection equation, respectively. The method uses two different summation by parts (SBP) derivative approximations, second-order and fourth-order accurate. The Dirichlet boundary conditions are imposed using the Simultaneous Approximation Term (SAT) penalty method. The 6-stage additive Runge-Kutta IMEX time integration schemes are fourth-order accurate in time. An increase in numerical stability 65 times greater than the fully explicit scheme is demonstrated to be achievable with the OP IMEX method applied to 1D Burger's equation. Results from the 2D, purely convective, advection equation show stability increases on the order of 10 times the explicit scheme using the OP IMEX method. Also, the domain partitioning method in this work shows potential for breaking the computational domain into manageable sizes such that implicit solutions for full three-dimensional CFD simulations can be computed using direct solving methods rather than the standard iterative methods currently used.

Nielsen, Tanner B.↗

NASA NTRS2015

Experimental Validation of the Dynamic Inertia Measurement Method to Find the Mass Properties of an Iron Bird Test Article

The mass properties of an aerospace vehicle are required by multiple disciplines in the analysis and prediction of flight behavior. Pendulum oscillation methods have been developed and employed for almost a century as a means to measure mass properties. However, these oscillation methods are costly, time consuming, and risky. The NASA Armstrong Flight Research Center has been investigating the Dynamic Inertia Measurement, or DIM method as a possible alternative to oscillation methods. The DIM method uses ground test techniques that are already applied to aerospace vehicles when conducting modal surveys. Ground vibration tests would require minimal additional instrumentation and time to apply the DIM method. The DIM method has been validated on smaller test articles, but has not yet been fully proven on large aerospace vehicles.

moments of inertia↗

NASA NTRS2011

On Calculation Methods and Results for Straight Cylindrical Roller Bearing Deflection, Stiffness, and Stress

The purpose of this study was to assess some calculation methods for quantifying the relationships of bearing geometry, material properties, load, deflection, stiffness, and stress. The scope of the work was limited to two-dimensional modeling of straight cylindrical roller bearings. Preparations for studies of dynamic response of bearings with damaged surfaces motivated this work. Studies were selected to exercise and build confidence in the numerical tools. Three calculation methods were used in this work. Two of the methods were numerical solutions of the Hertz contact approach. The third method used was a combined finite element surface integral method. Example calculations were done for a single roller loaded between an inner and outer raceway for code verification. Next, a bearing with 13 rollers and all-steel construction was used as an example to do additional code verification, including an assessment of the leading order of accuracy of the finite element and surface integral method. Results from that study show that the method is at least first-order accurate. Those results also show that the contact grid refinement has a more significant influence on precision as compared to the finite element grid refinement. To explore the influence of material properties, the 13-roller bearing was modeled as made from Nitinol 60, a material with very different properties from steel and showing some potential for bearing applications. The codes were exercised to compare contact areas and stress levels for steel and Nitinol 60 bearings operating at equivalent power density. As a step toward modeling the dynamic response of bearings having surface damage, static analyses were completed to simulate a bearing with a spall or similar damage.

Krantz, Timothy L.↗

NASA NTRS2015

Leak Rate Quantification Method for Gas Pressure Seals with Controlled Pressure Differential

An enhancement to the pressure decay leak rate method with mass point analysis solved deficiencies in the standard method. By adding a control system, a constant gas pressure differential across the test article was maintained. As a result, the desired pressure condition was met at the onset of the test, and the mass leak rate and measurement uncertainty were computed in real-time. The data acquisition and control system were programmed to automatically stop when specified criteria were met. Typically, the test was stopped when a specified level of measurement uncertainty was attained. Using silicone O-ring test articles, the new method was compared with the standard method that permitted the downstream pressure to be non-constant atmospheric pressure. The two methods recorded comparable leak rates, but the new method recorded leak rates with significantly lower measurement uncertainty, statistical variance, and test duration. Utilizing this new method in leak rate quantification, projects will reduce cost and schedule, improve test results, and ease interpretation between data sets.

seal↗