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NASA NTRS1983

Lagged average forecasting, an alternative to Monte Carlo forecasting

A 'lagged average forecast' (LAF) model is developed for stochastic dynamic weather forecasting and used for predictions in comparison with the results of a Monte Carlo forecast (MCF). The technique involves the calculation of sample statistics from an ensemble of forecasts, with each ensemble member being an ordinary dynamical forecast (ODF). Initial conditions at a time lagging the start of the forecast period are used, with varying amounts of time for the lags. Forcing by asymmetric Newtonian heating of the lower layer is used in a two-layer, f-plane, highly truncated spectral model in a test forecasting run. Both the LAF and MCF are found to be more accurate than the ODF due to ensemble averaging with the MCF and the LAF. When a regression filter is introduced, all models become more accurate, with the LAF model giving the best results. The possibility of generating monthly or seasonal forecasts with the LAF is discussed.

Hoffman, R. N.↗

NASA NTRS2017

Improved Reference Sampling and Subtraction: A Technique for Reducing the Read Noise of Near-Infrared Detector Systems

Near-infrared array detectors, like the James Webb Space Telescope (JWST) NIRSpec's Teledyne's H2RGs, often provide reference pixels and a reference output. These are used to remove correlated noise. Improved reference sampling and subtraction (IRS(exp 2)) is a statistical technique for using this reference information optimally in a leastsquares sense. Compared with the traditional H2RG readout, IRS(exp 2) uses a different clocking pattern to interleave many more reference pixels into the data than is otherwise possible. Compared with standard reference correction techniques, IRS(exp 2) subtracts the reference pixels and reference output using a statistically optimized set of frequency dependent weights. The benefits include somewhat lower noise variance and much less obvious correlated noise. NIRSpec's IRS(exp 2) images are cosmetically clean, with less 1/f banding than in traditional data from the same system. This article describes the IRS(exp 2) clocking pattern and presents the equations needed to use IRS(exp 2) in systems other than NIRSpec. For NIRSpec, applying these equations is already an option in the calibration pipeline. As an aid to instrument builders, we provide our prototype IRS(exp 2) calibration software and sample JWST NIRSpec data. The same techniques are applicable to other detector systems, including those based on Teledyne's H4RG arrays. The H4RG's interleaved reference pixel readout mode is effectively one IRS(exp 2) pattern.

Methods-statistical↗

NASA NTRS1995

Chemical studies of H chondrites. 5: Temporal variations of sources

We report Cl-36 (301-kyr half-life) data obtained by accelerator mass spectrometry allowing nominal terrestrial ages to be determined for 39 Antarctic H4-6 chondrites for which contents of volatile trace elements are known. The compositional difference between these Antarctic meteorites and 58 non-Antarctic falls increases with terrestrial age and, using multivariate statistical techniques, becomes highly significant for Antarctic samples with ages greater than 50 kyr. The compositional difference is inconsistent with trivial causes such as weathering and seems to reflect differences in thermal histories of parent sources. Temporal source variations for the H chondrite flux on Earth thus exist not only on a short-term, 40 years, basis (Dodd et al., 1993) but also on a long-term, greater than 50 kyr, basis.

Michlovich, Edward S.↗

NASA NTRS2006

Calculating Statistical Orbit Distributions Using GEO Optical Observations with the Michigan Orbital Debris Survey Telescope (MODEST)

NASA's Orbital Debris measurements program has a goal to characterize the small debris environment in the geosynchronous Earth-orbit (GEO) region using optical telescopes ("small" refers to objects too small to catalog and track with current systems). Traditionally, observations of GEO and near-GEO objects involve following the object with the telescope long enough to obtain an orbit suitable for tracking purposes. Telescopes operating in survey mode, however, randomly observe objects that pass through their field of view. Typically, these short-arc observation are inadequate to obtain detailed orbits, but can be used to estimate approximate circular orbit elements (semimajor axis, inclination, and ascending node). From this information, it should be possible to make statistical inferences about the orbital distributions of the GEO population bright enough to be observed by the system. The Michigan Orbital Debris Survey Telescope (MODEST) has been making such statistical surveys of the GEO region for four years. During that time, the telescope has made enough observations in enough areas of the GEO belt to have had nearly complete coverage. That means that almost all objects in all possible orbits in the GEO and near- GEO region had a non-zero chance of being observed. Some regions (such as those near zero inclination) have had good coverage, while others are poorly covered. Nevertheless, it is possible to remove these statistical biases and reconstruct the orbit populations within the limits of sampling error. In this paper, these statistical techniques and assumptions are described, and the techniques are applied to the current MODEST data set to arrive at our best estimate of the GEO orbit population distribution.

Matney, M.↗

NASA NTRS1994

The optical and near-infrared colors of galaxies, 1: The photometric data

We present optical and near-infrared photometry and spectroscopic redshifts of a well defined sample of 171 field galaxies selected from three high galactic latitude fields. This data set forms the basis for subsequent studies to characterize the trends, dispersion, and evolution of rest-frame colors and image structure. A subset of 143 galaxies constitutes a magnitude-limited sample to B approx. 19.9-20.75 (depending on field), with a median redshift of 0.14, and a maximum redshift of 0.54. This subset is statistically representative in its sampling of the apparent color distribution of galaxies. Thirty six galaxies were selected to have the reddest red-optical colors in two redshift intervals between 0.2 less than z less than 0.3. Photometric passbands are similar to U, B, V, I, and K, and sample galaxy spectral energy distributions between 0.37 and 2.2 micrometers in the observed frame, or down to 0.26 micrometers in the rest frame for the most distant galaxies. B and K images of the entire sample are assembled to form the first optical and near-infrared atlas of a statistically-representative sample of field galaxies. We discuss techniques for faint field-galaxy photometry, including a working definition of a total magnitude, and a method for matching magnitudes in different passbands and different seeing conditions to ensure reliable, integrated colors. Photographic saturation, which substantially affects the brightest 12% of our sample in the optical bands, is corrected with a model employing measured plate-density distributions for each galaxy, calibrated via similar measurements for stars as a function of known saturation level. Both the relative and absolute calibration of our photometry are demonstrated.

Bershady, Matthew A.↗

NASA NTRS1980

Time domain period determination techniques

Two simple period determination schemes are discussed. They are well suited to problems involving non-sinusoidal periodic phenomena sampled at a few irregularly spaced points. Statistical properties are discussed. The techniques are applied to the double mode Cepheids BK Cen and TU Cas as test cases.

Stellingwerf, R. F.↗

NASA NTRS2006

Exploring the Connection Between Sampling Problems in Bayesian Inference and Statistical Mechanics

The Bayesian and statistical mechanical communities often share the same objective in their work - estimating and integrating probability distribution functions (pdfs) describing stochastic systems, models or processes. Frequently, these pdfs are complex functions of random variables exhibiting multiple, well separated local minima. Conventional strategies for sampling such pdfs are inefficient, sometimes leading to an apparent non-ergodic behavior. Several recently developed techniques for handling this problem have been successfully applied in statistical mechanics. In the multicanonical and Wang-Landau Monte Carlo (MC) methods, the correct pdfs are recovered from uniform sampling of the parameter space by iteratively establishing proper weighting factors connecting these distributions. Trivial generalizations allow for sampling from any chosen pdf. The closely related transition matrix method relies on estimating transition probabilities between different states. All these methods proved to generate estimates of pdfs with high statistical accuracy. In another MC technique, parallel tempering, several random walks, each corresponding to a different value of a parameter (e.g. "temperature"), are generated and occasionally exchanged using the Metropolis criterion. This method can be considered as a statistically correct version of simulated annealing. An alternative approach is to represent the set of independent variables as a Hamiltonian system. Considerab!e progress has been made in understanding how to ensure that the system obeys the equipartition theorem or, equivalently, that coupling between the variables is correctly described. Then a host of techniques developed for dynamical systems can be used. Among them, probably the most powerful is the Adaptive Biasing Force method, in which thermodynamic integration and biased sampling are combined to yield very efficient estimates of pdfs. The third class of methods deals with transitions between states described by rate constants. These problems are isomorphic with chemical kinetics problems. Recently, several efficient techniques for this purpose have been developed based on the approach originally proposed by Gillespie. Although the utility of the techniques mentioned above for Bayesian problems has not been determined, further research along these lines is warranted

Pohorille, Andrew↗

NASA NTRS1978

Statistical sampling analysis for stratospheric measurements from satellite missions

Earth orbiting satellite experiments can be designed to measure stratospheric constituents such as ozone by utilizing remote sensing techniques. Statistical analysis techniques, mission simulation and model development have been utilized to develop a method for analyzing various mission/sensor combinations. Existing and planned NASA satellite missions such as Nimbus-4 and G, and Stratospheric Aerosol and Gas Experiment-Application Explorer Mission (SAGE-AEM) have been analyzed to determine the ability of the missions to adequately sample the global field.

Drewry, J. W.↗

NASA NTRS1974

Light beams and radiation patterns in random media

The purpose of this paper is to apply a numerical technique in solving problems involving light beams in a random medium. The technique starts by generating numerically sample media with prescribed statistical properties. Rays are then traced in these sample media, and the ray statistics are compiled. These statistics are utilized to find the mean square displacement and distribution of a beam. Problems on beam broadening and distortion of radiation patterns are considered. Fluctuations in wave amplitude and phase are also investigated. When possible, the numerical results are compared with the analytical results and experimental results.

Youakim, M. Y.↗

NASA NTRS2002

Maximizing Macromolecule Crystal Size for Neutron Diffraction Experiments

A challenge in neutron diffraction experiments is growing large (greater than 1 cu mm) macromolecule crystals. In taking up this challenge we have used statistical experiment design techniques to quickly identify crystallization conditions under which the largest crystals grow. These techniques provide the maximum information for minimal experimental effort, allowing optimal screening of crystallization variables in a simple experimental matrix, using the minimum amount of sample. Analysis of the results quickly tells the investigator what conditions are the most important for the crystallization. These can then be used to maximize the crystallization results in terms of reducing crystal numbers and providing large crystals of suitable habit. We have used these techniques to grow large crystals of Glucose isomerase. Glucose isomerase is an industrial enzyme used extensively in the food industry for the conversion of glucose to fructose. The aim of this study is the elucidation of the enzymatic mechanism at the molecular level. The accurate determination of hydrogen positions, which is critical for this, is a requirement that neutron diffraction is uniquely suited for. Preliminary neutron diffraction experiments with these crystals conducted at the Institute Laue-Langevin (Grenoble, France) reveal diffraction to beyond 2.5 angstrom. Macromolecular crystal growth is a process involving many parameters, and statistical experimental design is naturally suited to this field. These techniques are sample independent and provide an experimental strategy to maximize crystal volume and habit for neutron diffraction studies.

Judge, R. A.↗

NASA NTRS1987

Statistical evaluation of vibration analysis techniques

An evaluation methodology is presented for a selection of candidate vibration analysis techniques applicable to machinery representative of the environmental control and life support system of advanced spacecraft; illustrative results are given. Attention is given to the statistical analysis of small sample experiments, the quantification of detection performance for diverse techniques through the computation of probability of detection versus probability of false alarm, and the quantification of diagnostic performance.

Milner, G. Martin↗

NASA NTRS1974

A Monte Carlo investigation of thrust imbalance of solid rocket motor pairs

A technique is described for theoretical, statistical evaluation of the thrust imbalance of pairs of solid-propellant rocket motors (SRMs) firing in parallel. Sets of the significant variables, determined as a part of the research, are selected using a random sampling technique and the imbalance calculated for a large number of motor pairs. The performance model is upgraded to include the effects of statistical variations in the ovality and alignment of the motor case and mandrel. Effects of cross-correlations of variables are minimized by selecting for the most part completely independent input variables, over forty in number. The imbalance is evaluated in terms of six time - varying parameters as well as eleven single valued ones which themselves are subject to statistical analysis. A sample study of the thrust imbalance of 50 pairs of 146 in. dia. SRMs of the type to be used on the space shuttle is presented. The FORTRAN IV computer program of the analysis and complete instructions for its use are included. Performance computation time for one pair of SRMs is approximately 35 seconds on the IBM 370/155 using the FORTRAN H compiler.

Sforzini, R. H.↗

NASA NTRS1964

Monte Carlo techniques for solving transport problems

The Monte Carlo procedure is a model sampling technique. A model is established, and the behavior of sample units in this model is followed. A sufficient number of sample units are followed to obtain a statistical average or macroscopic quantities, which are the quantities of interest. This technique was used in crude form by Fermi in connection with the building of the first atomic pile. Later, Von Neumann and Ulam developed and used the Monte Carlo procedure extensively in developing the atomic bomb. Since then this technique has gained considerable use in nuclear reactor problems (refs. 1 and 2), and we at the Lewis Research Center have been extending it to thermal radiation (refs. 3 and 4), rarefied gas flows, and plasma flow problems (ref. 5). This technique, which requires a large number of sample histories to obtain solutions with small variances, is receiving greater use because of the development of the high-speed electronic computers.

SAMPLED DATA SYSTEM↗

NASA NTRS1998

New AFM Techniques for Investigating Molecular Growth Mechanisms of Protein Crystals

Atomic Force Microscopy (AFM) has emerged as a powerful technique for investigating protein crystal growth. Earlier AFM studies were among the first to demonstrate that these crystals grew by dislocation and 2D nucleation growth mechanisms [1]. These investigations were restricted to the micron range where only surface features, such as dislocation hillocks and 2D islands are visible. Most AFM instruments can scan at higher resolutions and have the potential to resolve individual protein molecules at nanometer ranges. Such scans are essential for determining the molecular packing arrangements on crystal faces and for probing the growth process at the molecular level. However, at this resolution the AFM tip influences the image produced, with the resulting image being a convolution of the tip shape and the surface morphology [2]. In most studies this problem is resolved by deconvoluting the image to obtain the true surface morphology. Although deconvolution routines work reasonably well for simple one- dimensional shapes, for complex surfaces this approach does not produce accurate results. In this study we devised a new approach which takes advantage of the precise molecular order of crystal surfaces, combined with the knowledge of individual molecular shapes from the crystallographic data of the protein and the AFM tip shape. This information is used to construct expected theoretical AFM images by convoluting the tip shape with the constructed crystal surface shape for a given surface packing arrangement. By comparing the images from actual AFM scans with the constructed ones for different possible surface packing arrangements, the correct packing arrangement can be conclusively determined. This approach was used in this study to determine the correct one from two possible packing arrangements on (I 10) faces of tetragonal lysozyme crystals. Another novel AFM technique was also devised to measure the dimension of individual growth units of the crystal faces. Measuring these units was not attempted before and most studies have assumed that the growth unit consisted of individual protein molecules. The linescan mode of AFM instruments allows the crystal surface to be scanned along a single line. By scanning across a growth step an image showing the motion of the step is obtained. Normally such an image shows a straight line for continuous and constant step velocity. In this study by increasing the scan rate and by decreasing the step velocity (by decreasing the supersaturation), we were able to capture images of individual growth events, shown by jump discontinuities in the step line. By suitable integration of the image the growth unit dimension in the scanned direction can be obtained. Since multiple units can be involved in the growth process it is necessary to collect a statistically relevant sample before drawing conclusions about the growth mechanism. This technique was successfully employed to obtain the dimensions of growth units for the (110) face, showing that they consisted of various aggregates corresponding to the 43 helices in the crystal structure.

Li, Huayu↗

NASA NTRS1971

Extensions of the space trajectories error analysis programs

A generalized covariance analysis technique which permits the study of the sensitivity of linear estimation algorithms to errors in a priori statistics has been developed and programed. Several sample cases are presented to illustrate the use of this technique. Modifications to the Simulated Trajectories Error Analysis Program (STEAP) to enable targeting a multiprobe mission of the Planetary Explorer type are discussed. The logic for the mini-probe targeting is presented. Finally, the initial phases of the conversion of the Viking mission Lander Trajectory Reconstruction (LTR) program for use on Venus missions is discussed. An integrator instability problem is discussed and a solution proposed.

Adams, G. L.↗

NASA NTRS2008

The Integrated Medical Model: Statistical Forecasting of Risks to Crew Health and Mission Success

The Integrated Medical Model (IMM) helps capture and use organizational knowledge across the space medicine, training, operations, engineering, and research domains. The IMM uses this domain knowledge in the context of a mission and crew profile to forecast crew health and mission success risks. The IMM is most helpful in comparing the risk of two or more mission profiles, not as a tool for predicting absolute risk. The process of building the IMM adheres to Probability Risk Assessment (PRA) techniques described in NASA Procedural Requirement (NPR) 8705.5, and uses current evidence-based information to establish a defensible position for making decisions that help ensure crew health and mission success. The IMM quantitatively describes the following input parameters: 1) medical conditions and likelihood, 2) mission duration, 3) vehicle environment, 4) crew attributes (e.g. age, sex), 5) crew activities (e.g. EVA's, Lunar excursions), 6) diagnosis and treatment protocols (e.g. medical equipment, consumables pharmaceuticals), and 7) Crew Medical Officer (CMO) training effectiveness. It is worth reiterating that the IMM uses the data sets above as inputs. Many other risk management efforts stop at determining only likelihood. The IMM is unique in that it models not only likelihood, but risk mitigations, as well as subsequent clinical outcomes based on those mitigations. Once the mathematical relationships among the above parameters are established, the IMM uses a Monte Carlo simulation technique (a random sampling of the inputs as described by their statistical distribution) to determine the probable outcomes. Because the IMM is a stochastic model (i.e. the input parameters are represented by various statistical distributions depending on the data type), when the mission is simulated 10-50,000 times with a given set of medical capabilities (risk mitigations), a prediction of the most probable outcomes can be generated. For each mission, the IMM tracks which conditions occurred and decrements the pharmaceuticals and supplies required to diagnose and treat these medical conditions. If supplies are depleted, then the medical condition goes untreated, and crew and mission risk increase. The IMM currently models approximately 30 medical conditions. By the end of FY2008, the IMM will be modeling over 100 medical conditions, approximately 60 of which have been recorded to have occurred during short and long space missions.

Fitts, M. A.↗

NASA NTRS1985

Preliminary design of an Earth-based debris detection system using current technology and existing installations

Assessment of debris hazard requires the determination of debris down to mm sizes for near-Earth orbits and near-stationary points. It is necessary to obtain reasonable orbits for a statistically significant sample of the debris population. Several ground-based techniques for detection are available. Radar detection was used to obtain information of existing debris population. Another technique is optical detection. The possibilities and application of optical detection with state-of-the-art instrumentation is studied.

Morgan, T. H.↗

NASA NTRS2011

Shuttle Hypervelocity Impact Database

With three missions outstanding, the Shuttle Hypervelocity Impact Database has nearly 3000 entries. The data is divided into tables for crew module windows, payload bay door radiators and thermal protection system regions, with window impacts compromising just over half the records. In general, the database provides dimensions of hypervelocity impact damage, a component level location (i.e., window number or radiator panel number) and the orbiter mission when the impact occurred. Additional detail on the type of particle that produced the damage site is provided when sampling data and definitive analysis results are available. Details and insights on the contents of the database including examples of descriptive statistics will be provided. Post flight impact damage inspection and sampling techniques that were employed during the different observation campaigns will also be discussed. Potential enhancements to the database structure and availability of the data for other researchers will be addressed in the Future Work section. A related database of returned surfaces from the International Space Station will also be introduced.

Hyde, James L.↗