Search NASA⌕ Search

SEARCH · Search NASA

Results for “ORTHOGONAL FUNCTION”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Model orthogonalization and Bayesian forecast mixing via principal component analysis

One can improve predictability in the unknown domain by combining forecasts of imperfect complex computational models using a Bayesian statistical machine learning framework. In many cases, however, the models used in the mixing process are similar. In addition to contaminating the model space, the existence of such similar, or even redundant, models during the multimodeling process can result in misinterpretation of results and deterioration of predictive performance. In this paper we describe a method based on the principal component analysis that eliminates model redundancy. We show that by adding model orthogonalization to the proposed Bayesian model combination framework, one can arrive at better prediction accuracy and reach excellent uncertainty quantification performance.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1980

Model error estimation for large space systems

In-flight estimation of large structure model errors may have to be carried out in order to detect inevitable deficiencies in large structure controller/estimator models. These error estimates can most efficiently be obtained by the minimization of a quadratic functional of the model errors and on the subsequent analysis of the resulting optimal model error estimates. An integral operator approach to estimation leads to a geometrical interpretation of the model error estimation process. One of the significant insights gained with this interpretation is that the actual but unknown model errors can be decomposed as the sum of two distinct components that are orthogonal in some sense. One of these components is a so-called minimal error vector that retains many of the significant dynamics of the actual errors. The basic ideas in the model error estimation approach are first set forth with a two-dimensional analogy that has most of the essential features of the general estimation problem. The generalized results are then established and their application to a reference large structure model illustrated.

Rodriguez, G.↗
NASA NTRS1981

Cavity-backed, micro-strip dipole antenna array

A flush-mounted antenna assembly includes a generally rectangular, conductive, box structure open along one face to form a cavity. Within the cavity a pair of mutually orthogonal dielectric plane surfaces in an "egg crate" arrangement are mounted normal to the plane of the open face, each diagonally within the cavity. Each dielectric plane supports a pair of printed circuit dipoles typically each fed from the opposite side of the dielectric plane by a printed "cone-shaped" feed line trace which also serve as an impedance matching device and functions as a balun connected from an unbalanced strip line external feed. The open face of the conductive cavity can be flush mounted with a randome thereover, the assembly thereby being flush with the skin of a aircraft or space vehicle.

Ellis, H., Jr.↗
DOE OSTI2025

Random Phase Approximation Correlation Energy Using Real-Space Density Functional Perturbation Theory

We present a real-space method for computing the random phase approximation (RPA) correlation energy within Kohn–Sham density functional theory, leveraging the low-rank nature of the frequency-dependent density response operator. In particular, we employ a cubic-scaling formalism based on density functional perturbation theory that circumvents the calculation of the response function matrix, instead relying on the ability to compute its product with a vector through the solution of the associated Sternheimer linear systems. We develop a large-scale parallel implementation of this formalism using the subspace iteration method in conjunction with the spectral quadrature method while employing the Kronecker product-based method for the application of the Coulomb operator and the conjugate orthogonal conjugate gradient method for the solution of the linear systems. We demonstrate convergence with respect to key parameters and verify the method’s accuracy by comparing with plane-wave results. We show that the framework achieves good strong scaling to many thousands of processors, reducing the time to solution for a lithium hydride system with 128 electrons to around 150 s on 4608 processors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1995

Out-of-plane properties

This paper summarizes three areas of research which were performed to characterize out-of-plane properties of composite materials. In the first investigation, a series of tests was run to characterize the through-the-thickness tensile strength for a variety of composites that included 2D braids, 2D and 3D weaves, and prepreg tapes. A new test method based on a curved beam was evaluated. Failures were significantly different between the 2D materials and the 3D weaves. The 2D materials delaminated between layers due to out-of-plane tensile stresses while the 3D weaves failed due to the formation of radial cracks between the surface plies caused by high circumferential stresses along the inner radius. The strength of the 2D textile composites did not increase relative to the tapes. Final failure in the 3D weaves was caused by a circumferential crack similar to the 2D materials and occurred at a lower bending moment than in other materials. The early failures in the 3D weaves were caused by radial crack formation rather than a low through-the-thickness strength. The second investigation focused on the development of a standard impact test method to measure impact damage resistance. The only impact tests that currently exist are compression after impact (CAI) tests which incorporate elements of both damage resistance and damage tolerance. A new impact test method is under development which uses a quasi-static indentation (QSI) test to directly measure damage resistance. Damage resistance is quantified in terms of the contact force to produce a unit of damage where a metric for damage may be area in C-scan, depth of residual dent , penetration, damage growth, etc. A final draft of an impact standard that uses a QSI test method will be presented to the ASTM Impact Task Group on impact. In the third investigation, the impact damage resistance behavior of a variety of textile materials was studied using the QSI test method. In this study, the force where large damage initiates was measured and the delamination size as a function of force was determined. The force to initiate large damage was significantly lower in braids and weaves. The delamination diameter - impact forace relationship was quanitfied using a damage resistance parameter, Q(*), which related delamination diameter to imapct force over a range of delamination sizes. Using this Q(*) parameter to rate the materials, the stitched uniweaves, toughened epoxy tapes, and through-the-thickness orthogonal interlock weave were the most damage resistant.

Jackson, Wade C.↗
NASA NTRS2006

Semiautonomous Avionics-and-Sensors System for a UAV

Unmanned Aerial Vehicles (UAVs) autonomous or remotely controlled pilotless aircraft have been recently thrust into the spotlight for military applications, for homeland security, and as test beds for research. In addition to these functions, there are many space applications in which lightweight, inexpensive, small UAVS can be used e.g., to determine the chemical composition and other qualities of the atmospheres of remote planets. Moreover, on Earth, such UAVs can be used to obtain information about weather in various regions; in particular, they can be used to analyze wide-band acoustic signals to aid in determining the complex dynamics of movement of hurricanes. The Advanced Sensors and Electronics group at Langley Research Center has developed an inexpensive, small, integrated avionics-and-sensors system to be installed in a UAV that serves two purposes. The first purpose is to provide flight data to an AI (Artificial Intelligence) controller as part of an autonomous flight-control system. The second purpose is to store data from a subsystem of distributed MEMS (microelectromechanical systems) sensors. Examples of these MEMS sensors include humidity, temperature, and acoustic sensors, plus chemical sensors for detecting various vapors and other gases in the environment. The critical sensors used for flight control are a differential- pressure sensor that is part of an apparatus for determining airspeed, an absolute-pressure sensor for determining altitude, three orthogonal accelerometers for determining tilt and acceleration, and three orthogonal angular-rate detectors (gyroscopes). By using these eight sensors, it is possible to determine the orientation, height, speed, and rates of roll, pitch, and yaw of the UAV. This avionics-and-sensors system is shown in the figure. During the last few years, there has been rapid growth and advancement in the technological disciplines of MEMS, of onboard artificial-intelligence systems, and of smaller, faster, and smarter wireless telemetry systems. The major attraction of MEMS lies in orders-of-magnitude reductions of power requirements relative to traditional electronic components that perform equivalent functions. In addition, the compactness of MEMS, relative to functionally equivalent traditional electronics systems, makes MEMS attractive for UAV applications. Recent advances in MEMS have made it possible to produce pressure, acceleration, humidity, and temperature sensors having masses in subgram range and possessing sensitivities and accuracies comparable to those of larger devices.

Shams, Qamar↗
NASA NTRS1992

Stability of a nonorthogonal stagnation flow to three-dimensional disturbances

A similarity solution for a low Mach number nonorthogonal flow impinging on a hot or cold plate is presented. For the constant density case, it is known that the stagnation point shifts in the direction of the incoming flow and that this shift increases as the angle of attack decreases. When the effects of density variations are included, a critical plate temperature exists; above this temperature the stagnation point shifts away from the incoming stream as the angle is decreased. This flowfield is believed to have application to the reattachment zone of certain separated flows or to a lifting body at a high angle of attack. Finally, the stability of this nonorthogonal flow to self similar, 3D disturbance is examined. Stability properties of the flow are given as a function of the parameters of this study; ratio of the plate temperature to that of the outer potential flow and angle of attack. In particular, it is shown that the angle of attack can be scaled out by a suitable definition of an equivalent wavenumber and temporal growth rate, and the stability problem for the nonorthogonal case is identical to the stability problem for the orthogonal case.

Lasseigne, D. G.↗
NASA NTRS1977

An empirical model for ocean radar backscatter and its application in inversion routine to eliminate wind speed and direction effects

Several regression models were tested to explain the wind direction dependence of the 1975 JONSWAP (Joint North Sea Wave Project) scatterometer data. The models consider the radar backscatter as a harmonic function of wind direction. The constant term accounts for the major effect of wind speed and the sinusoidal terms for the effects of direction. The fundamental accounts for the difference in upwind and downwind returns, while the second harmonic explains the upwind-crosswind difference. It is shown that a second harmonic model appears to adequately explain the angular variation. A simple inversion technique, which uses two orthogonal scattering measurements, is also described which eliminates the effect of wind speed and direction. Vertical polarization was shown to be more effective in determining both wind speed and direction than horizontal polarization.

Dome, G. J.↗
NASA NTRS1988

Flexible spacecraft maneuver - Inverse attitude control and modal stabilization

A control law is presented for three-axis rotational maneuvers of a spacecraft (orbiter)-beam-tip body (antenna or a reflector) configuration based on nonlinear inversion and modal velocity feedback. Using invertibility and functional reproducibility results, a decoupling attitude control law is presented such that, in the closed-loop system, the attitude angles of the spacecraft are independently controlled using the control moments acting on the space vehicle. This controller asymptotically decouples the flexible dynamics from the rigid one and also allows the decomposition of the elastic dynamics into two subsystems representing the transverse deflections of the beam in two orthogonal planes. These low-order subsystems are used for derivation of a modal velocity feedback stabilizer using the force and moment actuators at the end body. Simulation results are presented to show that, in the closed-loop system, attitude control and elastic mode stabilization are accomplished in spite of the parameter uncertainty and disturbance torque input in the system.

Singh, Sahjendra N.↗
DOE OSTI2024

Numerical eigen-spectrum slicing, accurate orthogonal eigen-basis, and mixed-precision eigenvalue refinement using OpenMP data-dependent tasks and accelerator offload

Performing a variety of numerical computations efficiently and, at the same time, in a portable fashion requires both an overarching design followed by a number of implementation strategies. All of these are exemplified below as we present transitioning the PLASMA numerical library from relying on dependence-driven large tasks to achieving utilization of fine grain tasking and offload to hardware accelerators while keeping its core dependence sets: OpenMP source code pragmas and runtime for most system-level functionality and basic low-level numerical kernels provided directly by hardware vendors or open source projects with vendor contributions. We also present new algorithmic methods and their efficient parallel implementations including fine grained tasking for eigen-spectrum slicing and offload for mixed-precision eigenvalue refinement. We provide performance, scaling, and numerical results showing sizable gains over the available solutions from either the open source and vendor-provided packages.

Luszczek, Piotr↗
NASA NTRS1988

ELF electric turbulence near an electron beam-emitting rocket in the auroral ionosphere - Echo 6

Orthogonal double-probes on the Echo 6 free-lying plasma diagnostic payload were used to study ELF turbulent electric fields during 36-keV beam injections. The observed characteristics of the ELF fields can best be explained by the current systems set up around the entire system rather than by a direct beam-plasma interaction. Frequency-power spectra were calculated for two different polarizations as a function of the probe-gun payload distance, and measurements were obtained of the lower hybrid waves near 8.5 kHz and whistler mode waves near 125 kHz. The dispersion of a current instability was calculated in order to investigate the generation mechanism of the observed ELF electric turbulence.

Abe, Y.↗
NASA NTRS2017

Laser Pulse Bidirectional Reflectance from CALIPSO Mission

In this Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) study, we present a simple way of determining laser pulse bidirectional reflectance over snow/ice surface using the Cloud-Aerosol LIdar with Orthogonal Polarization (CALIOP) 532 nanometer polarization channels' measurements. The saturated laser pulse returns from snow and ice surfaces are recovered based on surface tail information. The method overview and initial assessment of the method performance will be presented. The retrieved snow surface bidirectional reflectance is compared with reflectance from both CALIOP cloud cover regions and Moderate Resolution Imaging Spectroradiometer (Earth Observing System (EOS)) (MODIS) Bi-directional Reflectance Distribution Function (BRDF) / Albedo model parameters. The comparisons show that the snow surface bidirectional reflectance over Antarctica for saturation region are generally reliable with a mean value of about 0.90 plus or minus 0.10, while the mean surface reflectance from cloud cover region is about 0.84 plus or minus 0.13 and the calculated MODIS reflectance at 555 nanometers from the BRDF / Albedo model with near nadir illumination and viewing angles is about 0.96 plus or minus 0.04. The comparisons here demonstrate that the snow surface reflectance underneath the cloud with cloud optical depth of about 1 is significantly lower than that for a clear sky condition.

Lu, Xiaomei↗
NASA NTRS2022

Regression Bias in using Solar Wind Measurements

Simultaneous solar wind measurements from the solar wind monitors, WIND and ACE, differ due to the spatial and temporal structure of the solar wind. Correlation studies that use these measurements as input may infer an incorrect correlation due to uncertainties arising from this spatial and temporal structure, especially at extreme and rare solar wind values. In particular, regression analysis will lead to a regression function whose slope is biased towards the mean value of the measurement parameter. This article demonstrates this regression bias by comparing simultaneous ACE and WIND solar wind measurements. A non-linear regression analysis between them leads to a perception of underestimation of extreme values of one measurement on average over the other. Using numerical experiments, we show that popular regression analysis techniques such as linear least-squares, orthogonal least-squares, and non-linear regression are not immune to this bias. Hence while using solar wind parameters as an independent variable in a correlation or regression analysis, random uncertainty in the independent variable can create unintended biases in the response of the dependent variable. More generally, the regression to the mean effect can impact both event-based, statistical studies of magnetospheric response to solar wind forcing.

magnetosphere↗
NASA NTRS1981

Dual differential interferometer for measurements of broadband surface acoustic waves

A simple duel interferometer which uses two pairs of orthogonally polarized optical beams to measure both the amplitude and direction of propagation of broadband ultrasonic surface waves is described. Each pair of focused laser probe beams is used in a separate wideband differential interferometer to independently detect the component of surface wave motion along one direction on the surface. By combining the two output signals corresponding to both components, the two dimensional surface profile and its variation as a function of time is determined.

Turner, T. M.↗
NASA NTRS2000

CVS Decomposition of 3D Homogeneous Turbulence Using Orthogonal Wavelets

This paper compares the filtering used in Coherent Vortex Simulation (CVS) decomposition with an orthogonal wavelet basis, with the Proper Orthogonal Decomposition (POD) or Fourier filtering. Both methods are applied to a field of Direct Numerical Simulation (DNS) data of 3D forced homogeneous isotropic turbulence at microscale Reynolds number R(sub lambda) = 168. We show that, with only 3%N retained modes, CVS filtering separates the coherent vortex tubes from the incoherent background flow. The latter is structureless, has an equipartition energy spectrum, and has a Gaussian velocity probability distribution function (PDF) and an exponential vorticity PDF. On the other hand, the Fourier basis does not extract the coherent vortex tubes cleanly and leaves organized structures in the residual high wavenumber modes whose PDFs are stretched exponentials for both the velocity and the vorticity.

Farge, Marie↗
NASA NTRS2015

Nearly a Decade of CALIPSO Observations of Asian and Saharan Dust Properties Near Source and Transport Regions

The lidar on the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) mission, makes robust measurements of dust and has generated a length of record that is significant both seasonally and inter-annually. We exploit this record to determine a multi-year climatology of the properties of Asian and Saharan dust, in particular seasonal optical depths, layer frequencies, and layer heights of dust gridded in accordance with the Level 3 data products protocol, between 2006-2015. The data are screened using standard CALIPSO quality assurance flags, cloud aerosol discrimination (CAD) scores, overlying features and layer properties. To evaluate the effects of transport on the morphology, vertical extent and size of the dust layers, we compare probability distribution functions of the layer integrated volume depolarization ratios, geometric depths and integrated attenuated color ratios near the source to the same distributions in the far field or transport region. CALIPSO is collaboration between NASA and Centre National D'études Spatiales (CNES), was launched in April 2006 to provide vertically resolved measurements of cloud and aerosol distributions. The primary instrument on the CALIPSO satellite is the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP), a near-nadir viewing two-wavelength polarization-sensitive instrument. The unique nature of CALIOP measurements make it quite challenging to validate backscatter profiles, aerosol type, and cloud phase, all of which are used to retrieve extinction and optical depth. To evaluate the uncertainty in the lidar ratios, we compare the values computed from dust layers overlying opaque water clouds, considered nominal, with the constant lidar ratio value used in the CALIOP algorithms for dust. We also explore the effects of noise on the CALIOP retrievals at daytime by comparing the distributions of the properties at daytime to the nighttime distributions.

Omar, Ali H.↗
DOE OSTI2025

Exact spectral gaps of random one-dimensional quantum circuits

The spectral gap of local random quantum circuits is a fundamental property that determines how close the moments of the circuit's unitaries match those of a Haar random distribution. When studying spectral gaps, it is common to bound these quantities using tools from statistical mechanics or via quantum information-based inequalities. Here, by focusing on the second moment of one-dimensional unitary circuits where nearest-neighboring gates act on sets of qudits (with open and closed boundary conditions), we show that one can exactly compute the associated spectral gaps. Indeed, having access to their functional form allows us to prove several important results, such as the fact that the spectral gap for closed boundary condition is exactly the square of the gap for open boundaries, as well as improve on previously known bounds for approximate design convergence. Finally, we verify our theoretical results by numerically computing the spectral gap for systems of up to 70 qubits, as well as comparing them to gaps of random orthogonal and symplectic circuits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1992

Cell volume control at a surface for three-dimensional grid generation packages

An alternate method of calculating the cell size for orthogonality control in the solution of Poisson's 3D space equations is presented. The method provides the capability to enforce a better initial guess for the grid distribution required for boundary layer resolution. This grid point distribution is accomplished by enforcing grid spacing from a grid block boundary where orthogonality is required. The actual grid spacing or cell size for that boundary is determined by the two or four adjacent boundaries in the grid block definition, which are two dimensional grids. These two dimensional grids are in turn defined by the user using insight into the flow field and boundary layer characteristics. The adjoining boundaries are extended using a multifunctional blending scheme, with user control of the blending and interpolating functions to be used. This grid generation procedure results in an enhanced computational fluid dynamics calculation by allowing a quicker resolution of the configuration's boundary layer and flow field and by limiting the number of grid re-adaptations. The cell size specification calculation was applied to a variety of configurations ranging from axisymmetric to complex three-dimensional configurations. Representative grids are shown for the Space Shuttle and the Langley Lifting Body (HL-20).

Alter, Stephen J.↗