Random parameter models of human controllers
Random variables to use in modeling manual control performance
MANUAL CONTROL↗
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The SIMRAND methodology: Theory and application for the simulation of research and development projects
A research and development (R&D) project often involves a number of decisions that must be made concerning which subset of systems or tasks are to be undertaken to achieve the goal of the R&D project. To help in this decision making, SIMRAND (SIMulation of Research ANd Development Projects) is a methodology for the selection of the optimal subset of systems or tasks to be undertaken on an R&D project. Using alternative networks, the SIMRAND methodology models the alternative subsets of systems or tasks under consideration. Each path through an alternative network represents one way of satisfying the project goals. Equations are developed that relate the system or task variables to the measure of reference. Uncertainty is incorporated by treating the variables of the equations probabilistically as random variables, with cumulative distribution functions assessed by technical experts. Analytical techniques of probability theory are used to reduce the complexity of the alternative networks. Cardinal utility functions over the measure of preference are assessed for the decision makers. A run of the SIMRAND Computer I Program combines, in a Monte Carlo simulation model, the network structure, the equations, the cumulative distribution functions, and the utility functions.
Miles, R. F., Jr.↗
Auxiliary estimating functions for doubly truncated normal samples
Probability density function of random variable taken from normally distributed population for estimating maximum likelihood - estimation curve and tables for doubly truncated normal samples
POPULATION↗
Relative Radiometric Calibration of LANDSAT TM Reflective Bands
The characterization of the relative radiometric calibration of the protoflight Thematic Mapper sensor (TM/PF) is considered with focus on the variability and uncertainty of TM relative radiometry, including total variability as well as its systematic and random components. Emphasis is placed on identifying the magnitude and types of systematic errors, since these have the potential for being reduced during ground processing. Estimates of innate random variability, such as the standard deviation of a signal or its signal to noise ratio, are also important. The processing effects of radiometry are explored. Recommendations are given for engineering characterization, flight segment operations and ground processing.
Barker, J. L.↗
Reliability of COPVs Accounting for Margin of Safety on Design Burst
In this paper, the stress rupture reliability of Carbon/Epoxy Composite Overwrapped Pressure Vessels (COPVs) is examined utilizing the classic Phoenix model and accounting for the differences between the design and the actual burst pressure, and the liner contribution effects. Stress rupture life primarily depends upon the fiber stress ratio which is defined as the ratio of stress in fibers at the maximum expected operating pressure to actual delivered fiber strength. The actual delivered fiber strength is calculated using the actual burst pressures of vessels established through burst tests. However, during the design phase the actual burst pressure is generally not known and to estimate the reliability of the vessels calculations are usually performed based upon the design burst pressure only. Since the design burst is lower than the actual burst, this process yields a much higher value for the stress ratio and consequently a conservative estimate for the reliability. Other complications arise due to the fact that the actual burst pressure and the liner contributions have inherent variability and therefore must be treated as random variables in order to compute the stress rupture reliability. Furthermore, the model parameters, which have to be established based on stress rupture tests of subscale vessels or coupons, have significant variability as well due to limited available data and hence must be properly accounted for. In this work an assessment of reliability of COPVs including both parameter uncertainties and physical variability inherent in liner and overwrap material behavior is made and estimates are provided in terms of degree of uncertainty in the actual burst pressure and the liner load sharing.
Murthy, Pappu L.N.↗
Probabilistic methods for structural response analysis
This paper addresses current work to develop probabilistic structural analysis methods for integration with a specially developed probabilistic finite element code. The goal is to establish distribution functions for the structural responses of stochastic structures under uncertain loadings. Several probabilistic analysis methods are proposed covering efficient structural probabilistic analysis methods, correlated random variables, and response of linear system under stationary random loading.
Wu, Y.-T.↗
The algebra of probability density functions
Algebra of probability density functions of variable known as arbitrary function of one or more random variables
Grunebaum, B. G.↗
A First and Second Order Moment Approach to Probabilistic Control Synthesis
This paper presents a robust control design methodology based on the estimation of the first two order moments of the random variables and processes that describe the controlled response. Synthesis is performed by solving an multi-objective optimization problem where stability and performance requirements in time- and frequency domains are integrated. The use of the first two order moments allows for the efficient estimation of the cost function thus for a faster synthesis algorithm. While reliability requirements are taken into account by using bounds to failure probabilities, requirements related to undesirable variability are implemented by quantifying the concentration of the random outcome about a deterministic target. The Hammersley Sequence Sampling and the First- and Second-Moment- Second-Order approximations are used to estimate the moments, whose accuracy and associated computational complexity are compared numerically. Examples using output-feedback and full-state feedback with state estimation are used to demonstrate the ideas proposed.
Crespo, Luis G.↗
Droplet Growth or Evaporation Does Not Buffer the Variability in Supersaturation in Clean Clouds
Abstract Water vapor supersaturation in clouds is a random variable that drives activation and growth of cloud droplets. The Pi Convection–Cloud Chamber generates a turbulent cloud with a microphysical steady state that can be varied from clean to polluted by adjusting the aerosol injection rate. The supersaturation distribution and its moments, e.g., mean and variance, are investigated for varying cloud microphysical conditions. High-speed and collocated Eulerian measurements of temperature and water vapor concentration are combined to obtain the temporally resolved supersaturation distribution. This allows quantification of the contributions of variances and covariances between water vapor and temperature. Results are consistent with expectations for a convection chamber, with strong correlation between water vapor and temperature; departures from ideal behavior can be explained as resulting from dry regions on the warm boundary, analogous to entrainment. The saturation ratio distribution is measured under conditions that show monotonic increase of liquid water content and decrease of mean droplet diameter with increasing aerosol injection rate. The change in liquid water content is proportional to the change in water vapor concentration between no-cloud and cloudy conditions. Variability in the supersaturation remains even after cloud droplets are formed, and no significant buffering is observed. Results are interpreted in terms of a cloud microphysical Damköhler number (Da), under conditions corresponding to , i.e., the slow-microphysics regime. This implies that clouds with very clean regions, such that is satisfied, will experience supersaturation fluctuations without them being buffered by cloud droplet growth. Significance Statement The saturation ratio (humidity) in clouds controls the growth rate and formation of cloud droplets. When air in a turbulent cloud mixes, the humidity varies in space and time throughout the cloud. This is important because it means cloud droplets experience different growth histories, thereby resulting in broader size distributions. It is often assumed that growth and evaporation of cloud droplets buffers out some of the humidity variations. Measuring these variations has been difficult, especially in the field. The purpose of this study is to measure the saturation ratio distribution in clouds with a range of conditions. We measure the in-cloud saturation ratio using a convection cloud chamber with clean to polluted cloud properties. We found in clouds with low concentrations of droplets that the variations in the saturation ratio are not suppressed.
54 ENVIRONMENTAL SCIENCES↗
Primal and Dual Integrated Force Methods Used for Stochastic Analysis
At the NASA Glenn Research Center, the primal and dual integrated force methods are being extended for the stochastic analysis of structures. The stochastic simulation can be used to quantify the consequence of scatter in stress and displacement response because of a specified variation in input parameters such as load (mechanical, thermal, and support settling loads), material properties (strength, modulus, density, etc.), and sizing design variables (depth, thickness, etc.). All the parameters are modeled as random variables with given probability distributions, means, and covariances. The stochastic response is formulated through a quadratic perturbation theory, and it is verified through a Monte Carlo simulation.
Patnaik, Surya N.↗
Digital simulation of dynamic processes in radiometer systems
The development and application of several computer programs for simulating different classes of microwave radiometers are described. The programs are dynamic in nature, and they may be used to determine the instantaneous behavior of system variables as a function of time. Some of the programs employ random variable models in the simulations so that the statistical nature of the results may be investigated. The programs have been developed to utilize either the Continuous System Modeling Program or the Advanced Continuous System Language. The validity of most of the programs was investigated using statistical tests, and the results show excellent correlation with theoretical predictions. The programs are currently being used in the investigation of new design techniques for microwave radiometers.
Stanley, W. D.↗
Information transmission with continuous variable quantum erasure channels
Quantum capacity, as the key figure of merit for a given quantum channel, upper bounds the channel's ability in transmitting quantum information. Identifying different types of channels, evaluating the corresponding quantum capacity, and finding the capacity-approaching coding scheme are the major tasks in quantum communication theory. Quantum channel in discrete variables has been discussed enormously based on various error models, while error model in the continuous variable channel has been less studied due to the infinite dimensional problem. In this paper, we investigate a general continuous variable quantum erasure channel. By defining an effective subspace of the continuous variable system, we find a continuous variable random coding model. We then derive the quantum capacity of the continuous variable erasure channel in the framework of decoupling theory. The discussion in this paper fills the gap of a quantum erasure channel in continuous variable setting and sheds light on the understanding of other types of continuous variable quantum channels.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Probabilities and statistics for backscatter estimates obtained by a scatterometer
Methods for the recovery of winds near the surface of the ocean from measurements of the normalized radar backscattering cross section must recognize and make use of the statistics (i.e., the sampling variability) of the backscatter measurements. Radar backscatter values from a scatterometer are random variables with expected values given by a model. A model relates backscatter to properties of the waves on the ocean, which are in turn generated by the winds in the atmospheric marine boundary layer. The effective wind speed and direction at a known height for a neutrally stratified atmosphere are the values to be recovered from the model. The probability density function for the backscatter values is a normal probability distribution with the notable feature that the variance is a known function of the expected value. The sources of signal variability, the effects of this variability on the wind speed estimation, and criteria for the acceptance or rejection of models are discussed. A modified maximum likelihood method for estimating wind vectors is described. Ways to make corrections for the kinds of errors found for the Seasat SASS model function are described, and applications to a new scatterometer are given.
Pierson, Willard J., Jr.↗
Estimating the signal-to-noise ratio of AVIRIS data
To make the best use of narrowband airborne visible/infrared imaging spectrometer (AVIRIS) data, an investigator needs to know the ratio of signal to random variability or noise (signal-to-noise ratio or SNR). The signal is land cover dependent and varies with both wavelength and atmospheric absorption; random noise comprises sensor noise and intrapixel variability (i.e., variability within a pixel). The three existing methods for estimating the SNR are inadequate, since typical laboratory methods inflate while dark current and image methods deflate the SNR. A new procedure is proposed called the geostatistical method. It is based on the removal of periodic noise by notch filtering in the frequency domain and the isolation of sensor noise and intrapixel variability using the semi-variogram. This procedure was applied easily and successfully to five sets of AVIRIS data from the 1987 flying season and could be applied to remotely sensed data from broadband sensors.
Curran, Paul J.↗
Estimation of signal-to-noise - A new procedure applied to AVIRIS data
To make the best use of narrowband airborne visible/infrared imaging spectrometer (AVIRIS) data, an investigator needs to know the ratio of signal to random variability or noise (signal-to-noise ratio or SNR). The signal is land cover dependent and varies with both wavelength and atmospheric absorption; random noise comprises sensor noise and intrapixel variability (i.e., variability within a pixel). The three existing methods for estimating the SNR are inadequate, since typical laboratory methods inflate while dark current and image methods deflate the SNR. A new procedure is proposed called the geostatistical method. It is based on the removal of periodic noise by notch filtering in the frequency domain and the isolation of sensor noise and intrapixel variability using the semi-variogram. This procedure was applied easily and successfully to five sets of AVIRIS data from the 1987 flying season and could be applied to remotely sensed data from broadband sensors.
Curran, Paul J.↗
Zones of information in the AVIRIS spectra
To make the best use of Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) data an investigator needs to know the ratio of signal to random variability or noise (S/N ratio). The signal is land-cover dependent and decreases with both wavelength and atmospheric absorption and random noise comprises sensor noise and intra-pixel variability. The three existing methods for estimating the S/N ratio are inadequate as typical laboratory methods inflate, while dark current and image methods deflate the S/N ratio. We propose a new procedure called the geostatistical method. It is based on the removal of periodic noise by notch filtering in the frequency domain and the isolation of sensor noise and intra-pixel variability using the semi-variogram. This procedure was applied easily and successfully to five sets of AVIRIS data from the 1987 flying season.
Curran, Paul J.↗
SMC X-1 variability observed from HEAO 1
Studies are reported of the slow variability of SMC X-1 and its spectrum. An analysis of red-noise random variability is based on a method discussed by Deeter and Boynton (1982). The 0.7 s X-ray pulsar SMC X-1 is in a 3.89 day eclipsing binary system with a B0 I supergiant companion. Observations of the pulsar were conducted with the aid of the UCSD/MIT instrument on HEAO 1 from 1977 August through 1979 January. A light curve was constructed for the period 1977 September to 1978 December. The apparent tendency of SMC X-1 to be in one of two states, high or low, suggests the acquisition of average spectra separately for each state. The total (steady plus pulsed) emission from SMC X-1 displays a continuum spectrum with a dominant exponential form which implies a temperature of 17 keV for thin thermal bremsstrahlung emission or 5 keV if the other limit of a Wien spectrum is assumed.
Gruber, D. E.↗
Probabilistic Physics-Based Risk Tools Used to Analyze the International Space Station Electrical Power System Output
This paper describes the methods employed to apply probabilistic modeling techniques to the International Space Station (ISS) power system. These techniques were used to quantify the probabilistic variation in the power output, also called the response variable, due to variations (uncertainties) associated with knowledge of the influencing factors called the random variables. These uncertainties can be due to unknown environmental conditions, variation in the performance of electrical power system components or sensor tolerances. Uncertainties in these variables, cause corresponding variations in the power output, but the magnitude of that effect varies with the ISS operating conditions, e.g. whether or not the solar panels are actively tracking the sun. Therefore, it is important to quantify the influence of these uncertainties on the power output for optimizing the power available for experiments.
Patel, Bhogila M.↗