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NASA NTRS1987

Algorithm Sorts Groups Of Data

For efficient sorting, algorithm finds set containing minimum or maximum most significant data. Sets of data sorted as desired. Sorting process simplified by reduction of each multielement set of data to single representative number. First, each set of data expressed as polynomial with suitably chosen base, using elements of set as coefficients. Most significant element placed in term containing largest exponent. Base selected by examining range in value of data elements. Resulting series summed to yield single representative number. Numbers easily sorted, and each such number converted back to original set of data by successive division. Program written in BASIC.

Evans, J. D.↗

NASA NTRS1998

Development of Algorithms and Error Analyses for the Short Baseline Lightning Detection and Ranging System

NASA, at the John F. Kennedy Space Center (KSC), developed and operates a unique high-precision lightning location system to provide lightning-related weather warnings. These warnings are used to stop lightning- sensitive operations such as space vehicle launches and ground operations where equipment and personnel are at risk. The data is provided to the Range Weather Operations (45th Weather Squadron, U.S. Air Force) where it is used with other meteorological data to issue weather advisories and warnings for Cape Canaveral Air Station and KSC operations. This system, called Lightning Detection and Ranging (LDAR), provides users with a graphical display in three dimensions of 66 megahertz radio frequency events generated by lightning processes. The locations of these events provide a sound basis for the prediction of lightning hazards. This document provides the basis for the design approach and data analysis for a system of radio frequency receivers to provide azimuth and elevation data for lightning pulses detected simultaneously by the LDAR system. The intent is for this direction-finding system to correct and augment the data provided by LDAR and, thereby, increase the rate of valid data and to correct or discard any invalid data. This document develops the necessary equations and algorithms, identifies sources of systematic errors and means to correct them, and analyzes the algorithms for random error. This data analysis approach is not found in the existing literature and was developed to facilitate the operation of this Short Baseline LDAR (SBLDAR). These algorithms may also be useful for other direction-finding systems using radio pulses or ultrasonic pulse data.

Starr, Stanley O.↗

NASA NTRS1988

On the Wiener-Masani algorithm for finding the generating function of multivariate stochastic processes

The algorithms developed by Wiener and Masani (1957 and 1958) and Masani (1960) for the characterization of a class of multivariate stationary stochastic processes are investigated analytically. The algorithms permit the determination of (1) the generating function, (2) the prediction-error matrix, and (3) an autoregressive representation of the linear least-squares predictor. A number of theorems and lemmas are proved, and it is shown that the range of validity of the algorithms can be extended significantly beyond that given by Wiener and Masani.

Miamee, A. G.↗

NASA NTRS1989

Power spectral estimation algorithms

Algorithms to estimate the power spectrum using Maximum Entropy Methods were developed. These algorithms were coded in FORTRAN 77 and were implemented on the VAX 780. The important considerations in this analysis are: (1) resolution, i.e., how close in frequency two spectral components can be spaced and still be identified; (2) dynamic range, i.e., how small a spectral peak can be, relative to the largest, and still be observed in the spectra; and (3) variance, i.e., how accurate the estimate of the spectra is to the actual spectra. The application of the algorithms based on Maximum Entropy Methods to a variety of data shows that these criteria are met quite well. Additional work in this direction would help confirm the findings. All of the software developed was turned over to the technical monitor. A copy of a typical program is included. Some of the actual data and graphs used on this data are also included.

Bhatia, Manjit S.↗

NASA NTRS2008

Controller for Driving a Piezoelectric Actuator at Resonance

A digital control system based partly on an extremum-seeking control algorithm tracks the changing resonance frequency of a piezoelectric actuator or an electrically similar electromechanical device that is driven by a sinusoidal excitation signal and is required to be maintained at or near resonance in the presence of uncertain, changing external loads and disturbances. Somewhat more specifically, on the basis of measurements of the performance of the actuator, this system repeatedly estimates the resonance frequency and alters the excitation frequency as needed to keep it at or near the resonance frequency. In the original application for which this controller was developed, the piezoelectric actuator is part of an ultrasonic/sonic drill/corer. Going beyond this application, the underlying principles of design and operation are generally applicable to tracking changing resonance frequencies of heavily perturbed harmonic oscillators. Resonance-frequency-tracking analog electronic circuits are commercially available, but are not adequate for the present purpose for several reasons: The input/output characteristics of analog circuits tend to drift, often necessitating recalibration, especially whenever the same controller is used in driving a different resonator. In the case of an actuator in a system that has multiple modes characterized by different resonance frequencies, an analog controller can tune erroneously to one of the higher-frequency modes. The lack of programmability of analog controllers is problematic when faults occur, and is especially problematic for preventing tuning to a higher-frequency mode. In contrast, a digital controller can be programmed to restrict itself to a specified frequency range and to maintain stability even when the affected resonator is driven at high power and subjected to uncertain disturbances and variable loads. The present digital control system (see figure) is implemented by means of an algorithm that comprises three main subalgorithms: a hill-climbing control algorithm, an estimation-based extremum-seeking control (ESC) algorithm, and a supervisory algorithm. The hill-climbing algorithm is useful for coarse tracking to find and remain within the vicinity of the resonance. The ESC algorithm is not capable of coarse resonance tracking, but is capable of fine resonance tracking once the estimates of parameters generated by the hill-climbing algorithm have converged sufficiently. On the basis of the parameter-estimation errors, the supervisory algorithm switches operation to whichever of the other two algorithms performs best at a given time.

Aldrich, Jack↗

NASA NTRS2021

Assessing CryoSat-2 Antarctic Snow Freeboard Retrievals Using Data From ICESat-2

NASA's Ice, Cloud, and land Elevation Satellite-2 (ICESat-2) laser altimeter launched in Fall 2018, providing an invaluable addition to the polar altimetry record generated by ESA's CryoSat-2 radar altimeter. The simultaneous operation of these two satellite altimeters enables unique comparison studies of sea ice altimetry, utilizing the different frequencies and profiling strategies of the two instruments. Here, we use freeboard data from ICESat-2 to assess Antarctic snow freeboard retrievals from CryoSat-2. We first discuss updates made to a previously published CryoSat-2 retrieval process and show how this Version 2 algorithm improves upon the original method by comparing the new retrievals to ICESat-2 in specific along-track profiles as well as on the basin-scale. In two near-coincident along-track profiles, we find mean snow freeboard differences (standard deviations of differences) of 0.3 (9.3) and 7.6 cm (9.6 cm) with 25 km binned correlation coefficients of 0.77 and 0.89. Monthly mean freeboard differences range between −2.9 (10.8) and 6.6 cm (16.8 cm) basin wide, with the largest differences typically occurring in Austral fall months that is hypothesized to be related to new ice growth and the use of static snow backscatter coefficients in the retrieval. Monthly mean correlation coefficients range between 0.57 and 0.80. While coincident data show good agreement between the two sensors, they highlight issues related to geometric and frequency sampling differences that can impact the freeboard distributions.

S W Fons↗

NASA NTRS2016

Thermodynamics of Gas Turbine Cycles with Analytic Derivatives in OpenMDAO

A new equilibrium thermodynamics analysis tool was built based on the CEA method using the OpenMDAO framework. The new tool provides forward and adjoint analytic derivatives for use with gradient based optimization algorithms. The new tool was validated against the original CEA code to ensure an accurate analysis and the analytic derivatives were validated against finite-difference approximations. Performance comparisons between analytic and finite difference methods showed a significant speed advantage for the analytic methods. To further test the new analysis tool, a sample optimization was performed to find the optimal air-fuel equivalence ratio, , maximizing combustion temperature for a range of different pressures. Collectively, the results demonstrate the viability of the new tool to serve as the thermodynamic backbone for future work on a full propulsion modeling tool.

Propulsion↗

NASA NTRS2019

Exploring Network-Related Optimization Problems Using Quantum Heuristics

Network-related connectivity optimization problems are underlying a wide range of applications and are also of high computational complexity. We consider studying network optimization problems using two types of quantum heuristics.One is quantum annealing, and the other Quantum Alternating Operator Ansatz, an extension of the Quantum Approximate Optimization Algorithms for gate-model quantum computation, in which a cost-function based unitary and a non-commuting mixing unitary are applied alternately. We present problem mappings for problems of finding the spanning-tree or spanning-graph of a graph that optimizes certain costs, and a variant that further requires the spanning-tree be degree-bounded. With quantum annealing, all constraints are cast into penalty terms in the cost Hamiltonian, and the solution is encoded as the ground state of the Hamiltonian. We provide three mappings to the quadratic unconstrained binary optimization (QUBO) form, compare the resource requirements, and analyze the tradeoffs. For QAOA, we give special focus on the design of mixers based on the constraints presented in the problem, such that the system evolution remains in a subspace of the full Hilbert space where all constraints are satisfied. In the spanning-tree problem, one such hard constraint is that a mixer applied to a spanning-tree needs also be a spanning tree. This involves checking the connectivity of a subgraph, which is a global condition common for most network-related problems. We show how this feature can be efficiently represented in the mixer in a quantum coherent way, based on manipulation of a descendant-matrix and an adjacent matrix. We further develop a mixer for the spanning-graphs based on the spanning-tree mixer.

Wang, Zhihui↗

NASA NTRS2019

Study network-related optimization problems using quantum alternating optimization ansatz

Network-related connectivity optimization problems are underlying a wide range of applications and are also of high computational complexity. We consider studying network optimization problems using two types of quantum heuristics. One is quantum annealing, and the other Quantum Alternating Operator Ansatz, an extension of the Quantum Approximate Optimization Algorithms for gate-model quantum computation, in which a cost-function based unitary and a non-commuting mixing unitary are applied alternately. We present problem mappings for problems of finding the spanning-tree or spanning-graph of a graph that optimizes certain costs, and a variant that further requires the spanning-tree be degree-bounded. With quantum annealing, all constraints are cast into penalty terms in the cost Hamiltonian, and the solution is encoded as the ground state of the Hamiltonian. We provide three mappings to the quadratic unconstrained binary optimization (QUBO) form, compare the resource requirements, and analyze the tradeoffs. For QAOA, we give special focus on the design of mixers based on the constraints presented in the problem, such that the system evolution remains in a subspace of the full Hilbert space where all constraints are satisfied. In the spanning-tree problem, one such hard constraint is that a mixer applied to a spanning-tree needs also be a spanning tree. This involves checking the connectivity of a subgraph, which is a global condition common for most network-related problems. We show how this feature can be efficiently represented in the mixer in a quantum coherent way, based on manipulation of a descendant-matrix and an adjacent matrix. We further develop a mixer for the spanning-graphs based on the spanning-tree mixer.

Zhihui Wang↗

NASA NTRS1977

Objective tropical cyclone analysis and forecasting technique using conventional and Nimbus-5 electrically scanning microwave radiometer measurements

The ADAPT empirical analysis programs, based on finding an optimal representation of the data in the Karhunen-Loeve sense, were applied to 120 observations of twenty-nine 1973 and 1974 Pacific tropical cyclones. Each observation consists of NIMBUS-5 electrically scanning microwave radiometer (ESMR) radiation measurements at 267 grid points covering and surrounding the tropical cyclone plus nine other non-satellite derived descriptors. Analysis and forecast algorithms to estimate storm motion and intensity were developed for times ranging from the observation time up to 72 hours later. The 24 hr wind speed forecasts with an accuracy of 11.7 knots and position forecasts with accuracies 15% better than persistence were demonstrated using independent tests.

Hunter, H. E.↗

NASA NTRS2004

Best of Breed

No team of engineers, no matter how much time they took or how many bottles of cabernet they consumed, would dream up an antenna that looked like a deer antler on steroids. Yet that's what a group at NASA Ames Research Center came up with-thanks to a little help from Darwin. NASA's Space Technology 5 nanosatellites, which are scheduled to start measuring Earth's magnetosphere in late 2004, requires an antenna that can receive a wide range of frequencies regardless of the spacecraft's orientation. Rather than leave such exacting requirements in the hands of a human, the engineers decided to breed a design using genetic algorithms and 32 Linux PCs. The computers generated small antenna-constructing programs (the genotypes) and executed them to produce designs (the phenotypes). Then the designs were evaluated using an antenna simulator. The team settled on the form pictured here. You won't find this kind of antenna in any textbook, design guide, or research paper. But its innovative structure meets a challenging set of specifications. If successfully deployed, it will be the first evolved antenna to make it out of the lab and the first piece of evolved hardware ever to fly in space.

Lohn, Jason↗

NASA NTRS2008

Using Hyperspectral Imagery to Identify Turfgrass Stresses

The use of a form of remote sensing to aid in the management of large turfgrass fields (e.g. golf courses) has been proposed. A turfgrass field of interest would be surveyed in sunlight by use of an airborne hyperspectral imaging system, then the raw observational data would be preprocessed into hyperspectral reflectance image data. These data would be further processed to identify turfgrass stresses, to determine the spatial distributions of those stresses, and to generate maps showing the spatial distributions. Until now, chemicals and water have often been applied, variously, (1) indiscriminately to an entire turfgrass field without regard to localization of specific stresses or (2) to visible and possibly localized signs of stress for example, browning, damage from traffic, or conspicuous growth of weeds. Indiscriminate application is uneconomical and environmentally unsound; the amounts of water and chemicals consumed could be insufficient in some areas and excessive in most areas, and excess chemicals can leak into the environment. In cases in which developing stresses do not show visible signs at first, it could be more economical and effective to take corrective action before visible signs appear. By enabling early identification of specific stresses and their locations, the proposed method would provide guidance for planning more effective, more economical, and more environmentally sound turfgrass-management practices, including application of chemicals and water, aeration, and mowing. The underlying concept of using hyperspectral imagery to generate stress maps as guides to efficient management of vegetation in large fields is not new; it has been applied in the growth of crops to be harvested. What is new here is the effort to develop an algorithm that processes hyperspectral reflectance data into spectral indices specific to stresses in turfgrass. The development effort has included a study in which small turfgrass plots that were, variously, healthy or subjected to a variety of controlled stresses were observed by use of a hand-held spectroradiometer. The spectroradiometer readings in the wavelength range from 350 to 1,000 nm were processed to extract hyperspectral reflectance data, which, in turn, were analyzed to find correlations with the controlled stresses. Several indices were found to be correlated with drought stress and to be potentially useful for identifying drought stress before visible symptoms appear.

Hutto, Kendall↗

NASA NTRS2021

Modeling Snow Ablation over the Western United States Mountains: Patterns and Controlling Factors

When compared with differences in snow accumulation predicted by widely used hydrological models, there is a much greater divergence among otherwise “good” models in their simulation of the snow ablation process. Here, we explore differences in the performance of the Variable Infiltration Capacity model (VIC), Noah land surface model with multiparameterization options (Noah-MP), the Catchment model, and the third-generation Simplified Simple Biosphere model (SiB3) in their ability to reproduce observed snow water equivalent (SWE) during the ablation season at 10 Snowpack Telemetry (SNOTEL) stations over 1992–2012. During the ablation period, net radiation generally has stronger correlations with observed melt rates than does air temperature. Average ablation rates tend to be higher (in both model predictions and observations) at stations with a large accumulation of SWE. The differences in the dates of last snow between models and observations range from several days to approximately a month (on average 5.1 days earlier than in observations). If the surface cover in the models is changed from observed vegetation to bare soil in all of the models, only the melt rate of the VIC model increases. The differences in responses of models to canopy removal are directly related to snowpack energy inputs, which are further affected by different algorithms for surface albedo and energy allocation across the models. We also find that the melt rates become higher in VIC and lower in Noah-MP if the shrub/grass present at the observation sites is switched to trees.

Snow↗

NASA NTRS1994

Vision based object pose estimation for mobile robots

Mobile robot navigation using visual sensors requires that a robot be able to detect landmarks and obtain pose information from a camera image. This paper presents a vision system for finding man-made markers of known size and calculating the pose of these markers. The algorithm detects and identifies the markers using a weighted pattern matching template. Geometric constraints are then used to calculate the position of the markers relative to the robot. The selection of geometric constraints comes from the typical pose of most man-made signs, such as the sign standing vertical and the dimensions of known size. This system has been tested successfully on a wide range of real images. Marker detection is reliable, even in cluttered environments, and under certain marker orientations, estimation of the orientation has proven accurate to within 2 degrees, and distance estimation to within 0.3 meters.

Wu, Annie↗

NASA NTRS2014

Carbon Monitoring System Flux Estimation and Attribution: Impact of ACOS-GOSAT X(CO2) Sampling on the Inference of Terrestrial Biospheric Sources and Sinks

Using an Observing System Simulation Experiment (OSSE), we investigate the impact of JAXA Greenhouse gases Observing SATellite 'IBUKI' (GOSAT) sampling on the estimation of terrestrial biospheric flux with the NASA Carbon Monitoring System Flux (CMS-Flux) estimation and attribution strategy. The simulated observations in the OSSE use the actual column carbon dioxide (X(CO2)) b2.9 retrieval sensitivity and quality control for the year 2010 processed through the Atmospheric CO2 Observations from Space algorithm. CMS-Flux is a variational inversion system that uses the GEOS-Chem forward and adjoint model forced by a suite of observationally constrained fluxes from ocean, land and anthropogenic models. We investigate the impact of GOSAT sampling on flux estimation in two aspects: 1) random error uncertainty reduction and 2) the global and regional bias in posterior flux resulted from the spatiotemporally biased GOSAT sampling. Based on Monte Carlo calculations, we find that global average flux uncertainty reduction ranges from 25% in September to 60% in July. When aggregated to the 11 land regions designated by the phase 3 of the Atmospheric Tracer Transport Model Intercomparison Project, the annual mean uncertainty reduction ranges from 10% over North American boreal to 38% over South American temperate, which is driven by observational coverage and the magnitude of prior flux uncertainty. The uncertainty reduction over the South American tropical region is 30%, even with sparse observation coverage. We show that this reduction results from the large prior flux uncertainty and the impact of non-local observations. Given the assumed prior error statistics, the degree of freedom for signal is approx.1132 for 1-yr of the 74 055 GOSAT X(CO2) observations, which indicates that GOSAT provides approx.1132 independent pieces of information about surface fluxes. We quantify the impact of GOSAT's spatiotemporally sampling on the posterior flux, and find that a 0.7 gigatons of carbon bias in the global annual posterior flux resulted from the seasonally and diurnally biased sampling when using a diagonal prior flux error covariance.

biased sampling↗

NASA NTRS2011

Automated Verification of Spatial Resolution in Remotely Sensed Imagery

Image spatial resolution characteristics can vary widely among sources. In the case of aerial-based imaging systems, the image spatial resolution characteristics can even vary between acquisitions. In these systems, aircraft altitude, speed, and sensor look angle all affect image spatial resolution. Image spatial resolution needs to be verified with estimators that include the ground sample distance (GSD), the modulation transfer function (MTF), and the relative edge response (RER), all of which are key components of image quality, along with signal-to-noise ratio (SNR) and dynamic range. Knowledge of spatial resolution parameters is important to determine if features of interest are distinguishable in imagery or associated products, and to develop image restoration algorithms. An automated Spatial Resolution Verification Tool (SRVT) was developed to rapidly determine the spatial resolution characteristics of remotely sensed aerial and satellite imagery. Most current methods for assessing spatial resolution characteristics of imagery rely on pre-deployed engineered targets and are performed only at selected times within preselected scenes. The SRVT addresses these insufficiencies by finding uniform, high-contrast edges from urban scenes and then using these edges to determine standard estimators of spatial resolution, such as the MTF and the RER. The SRVT was developed using the MATLAB programming language and environment. This automated software algorithm assesses every image in an acquired data set, using edges found within each image, and in many cases eliminating the need for dedicated edge targets. The SRVT automatically identifies high-contrast, uniform edges and calculates the MTF and RER of each image, and when possible, within sections of an image, so that the variation of spatial resolution characteristics across the image can be analyzed. The automated algorithm is capable of quickly verifying the spatial resolution quality of all images within a data set, enabling the appropriate use of those images in a number of applications.

Davis, Bruce↗

NASA NTRS2003

Enhanced Weather Radar (EWxR) System

An airborne weather radar system, the Enhanced Weather Radar (EWxR), with enhanced on-board weather radar data processing was developed and tested. The system features additional weather data that is uplinked from ground-based sources, specialized data processing, and limited automatic radar control to search for hazardous weather. National Weather Service (NWS) ground-based Next Generation Radar (NEXRAD) information is used by the EWxR system to augment the on-board weather radar information. The system will simultaneously display NEXRAD and on-board weather radar information in a split-view format. The on-board weather radar includes an automated or hands-free storm-finding feature that optimizes the radar returns by automatically adjusting the tilt and range settings for the current altitude above the terrain and searches for storm cells near the atmospheric 0-degree isotherm. A rule-based decision aid was developed to automatically characterize cells as hazardous, possibly-hazardous, or non-hazardous based upon attributes of that cell. Cell attributes are determined based on data from the on-board radar and from ground-based radars. A flight path impact prediction algorithm was developed to help pilots to avoid hazardous weather along their flight plan and their mission. During development the system was tested on the NASA B757 aircraft and final tests were conducted on the Rockwell Collins Sabreliner.

Kronfeld, Kevin M.↗

NASA NTRS1992

Solder creep-fatigue interactions with flexible leaded parts

With flexible leaded parts, the solder-joint failure process involves a complex interplay of creep and fatigue mechanisms. To better understand the role of creep in typical multi-hour cyclic loading conditions, a specialized non-linear finite-element creep simulation computer program has been formulated. The numerical algorithm includes the complete part-lead-solder-PWB system, accounting for strain-rate dependence of creep on applied stress and temperature, and the role of the part-lead dimensions and flexibility that determine the total creep deflection (solder strain range) during stress relaxation. The computer program has been used to explore the effects of various solder creep-fatigue parameters such as lead height and stiffness, thermal-cycle test profile, and part/board differential thermal expansion properties. One of the most interesting findings is the strong presence of unidirectional creep-ratcheting that occurs during thermal cycling due to temperature dominated strain-rate effects. To corroborate the solder fatigue model predictions, a number of carefully controlled thermal-cycle tests have been conducted using special bimetallic test boards.

Ross, R. G., Jr.↗