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All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

The reality of comet groups and pairs

Although the common genetic origin of the Kreutz family of sun-grazing comets has generally been accepted, there remains uncertainty with regard to genetic identity among other groups of comets whose orbital elements are nearly alike. Porter (1952) has listed a number of such groups, and Opik (1971) has made a statistical study of the orbits of 472 comets with aphelion distances beyond Saturn. Opik lists 97 groups that show similarities among their three angular elements, calculates an overall probability of some 10 to the -39th power that these similarities could have occurred by chance, and thus concludes that 60% or more of such comets fall into genetic groups containing from two to seven members. This paper explores the statistical reality of Opik's groups utilizing the Monte Carlo method of statistics as well as ordinary probability theory. The conclusion is reached that except for a few pairs, the similarity among orbital elements within the groups is no greater than random expectation.

Whipple, F. L.↗
NASA NTRS1977

Extending radiative transfer models by use of Bayes rule

This paper presents a procedure that extends some existing radiative transfer modeling techniques to problems in atmospheric science where curvature and layering of the medium and dynamic range and angular resolution of the signal are important. Example problems include twilight and limb scan simulations. Techniques that are extended include successive orders of scattering, matrix operator, doubling, Gauss-Seidel iteration, discrete ordinates and spherical harmonics. The procedure for extending them is based on Bayes' rule from probability theory.

Whitney, C.↗
NASA NTRS1982

Introduction to SIMRAND: Simulation of research and development project

SIMRAND: SIMulation of Research ANd Development Projects is a methodology developed to aid the engineering and management decision process in the selection of the optimal set of systems or tasks to be funded on a research and development project. A project may have a set of systems or tasks under consideration for which the total cost exceeds the allocated budget. Other factors such as personnel and facilities may also enter as constraints. Thus the project's management must select, from among the complete set of systems or tasks under consideration, a partial set that satisfies all project constraints. The SIMRAND methodology uses analytical techniques and probability theory, decision analysis of management science, and computer simulation, in the selection of this optimal partial set. The SIMRAND methodology is truly a management tool. It initially specifies the information that must be generated by the engineers, thus providing information for the management direction of the engineers, and it ranks the alternatives according to the preferences of the decision makers.

Miles, R. F., Jr.↗
NASA NTRS1983

Range reference atmosphere models

A description is given of the methods used to establish the statistical parameters and models for wind and various thermodynamic quantities at an altitude of 0-70 km for nine geographical locations. It is noted that wind is modeled as a vector quantity using the bivariate normal probability function. With the five parameters of the bivariate normal distribution, the distribution for wind speed is derived as a generalized Rayleigh distribution. In addition, the frequency of wind direction is derived, and the conditional distribution of wind speed given the wind direction is derived. It is pointed out that these and other wind models are consistent with the rigorous mathematical properties of the bivariate normal probability theory. The thermodynamic quantities are consistent with the hydrostatic equation and the equation of state for the mean values. With these methods, many statistical relationships can be derived.

Smith, O. E.↗
NASA NTRS1986

Manipulation of Numbers With Many Digits

PRECISION designed for manipulation of numbers with accurate retention of up to thousands of digits per number. Use of PRECISION prevents underflow and overflow in programs that generate extreme numbers such as probability theory, statistics, and scientific applications.

Howell, L. W.↗
NASA NTRS1985

Circuit analysis method for thin-film solar cell modules

The design of a thin-film solar cell module is dependent on the probability of occurrence of pinhole shunt defects. Using known or assumed defect density data, dichotomous population statistics can be used to calculate the number of defects expected in a module. Probability theory is then used to assign the defective cells to individual strings in a selected series-parallel circuit design. Iterative numerical calculation is used to calcuate I-V curves using cell test values or assumed defective cell values as inputs. Good and shunted cell I-V curves are added to determine the module output power and I-V curve. Different levels of shunt resistance can be selected to model different defect levels.

Burger, D. R.↗
NASA NTRS1988

Dispositional logic

The applicability of conventional mathematical analysis (based on the combination of two-valued logic and probability theory) to problems in which human judgment, perception, or emotions play significant roles is considered theoretically. It is shown that dispositional logic, a branch of fuzzy logic, has particular relevance to the common-sense reasoning typical of human decision-making. The concepts of dispositionality and usuality are defined analytically, and a dispositional conjunctive rule and dispositional modus ponens are derived.

Le Balleur, J. C.↗
NASA NTRS1989

Multiresolutional models of uncertainty generation and reduction

Kolmogorov's axiomatic principles of the probability theory, are reconsidered in the scope of their applicability to the processes of knowledge acquisition and interpretation. The model of uncertainty generation is modified in order to reflect the reality of engineering problems, particularly in the area of intelligent control. This model implies algorithms of learning which are organized in three groups which reflect the degree of conceptualization of the knowledge the system is dealing with. It is essential that these algorithms are motivated by and consistent with the multiresolutional model of knowledge representation which is reflected in the structure of models and the algorithms of learning.

Meystel, A.↗
NASA NTRS1989

Infrared-fiber-optic fire sensor developments - Role of measurement uncertainty in evaluation of background limited range

Fire-detector systems based on distributed infrared fiber-sensors have been investigated for potential applications in the aerospace industry. Responsivities to blackbody and flame radiations were measured with various design configurations of an infrared fiber-optic sensor. Signal processing techniques were also investigated, and the results show significant differences in the fire-sensor performance depending on the design configuration. Measurement uncertainties were used to determine the background-limited ranges for the various fire-sensor concepts, and the probability of producing false alarms caused by fluctuations in the background signals were determined using extreme probability theory. The results of the research show that infrared fiber-optic fire sensors are feasible for application on manned spacecraft; however, additional development work will be required to eliminate false alarms caused by high temperature objects such as incandescent lamps.

Tapphorn, Ralph M.↗
NASA NTRS1992

The influence of finite impurity size on heterogeneous nucleation

The effects of the finite size of impurities upon the heterogeneous nucleation rate is examined. Simple arguments based upon probability theory are used to find the relative nucleation rate, p(j), on particles containing j nuclei. The expression for p(j) is used in turn to compute the overall nucleation rate and average number of nuclei on an impurity as a function of time.

Weinberg, Michael C.↗
NASA NTRS1992

Quantification of human responses

Human perception is a complex phenomenon which is difficult to quantify with instruments. For this reason, large panels of people are often used to elicit and aggregate subjective judgments. Print quality, taste, smell, sound quality of a stereo system, softness, and grading Olympic divers and skaters are some examples of situations where subjective measurements or judgments are paramount. We usually express what is in our mind through language as a medium but languages are limited in available choices of vocabularies, and as a result, our verbalizations are only approximate expressions of what we really have in mind. For lack of better methods to quantify subjective judgments, it is customary to set up a numerical scale such as 1, 2, 3, 4, 5 or 1, 2, 3, ..., 9, 10 for characterizing human responses and subjective judgments with no valid justification except that these scales are easy to understand and convenient to use. But these numerical scales are arbitrary simplifications of the complex human mind; the human mind is not restricted to such simple numerical variations. In fact, human responses and subjective judgments are psychophysical phenomena that are fuzzy entities and therefore difficult to handle by conventional mathematics and probability theory. The fuzzy mathematical approach provides a more realistic insight into understanding and quantifying human responses. This paper presents a method for quantifying human responses and subjective judgments without assuming a pattern of linear or numerical variation for human responses. In particular, quantification and evaluation of linguistic judgments was investigated.

Steinlage, R. C.↗
NASA NTRS1992

A new method for the detection of a periodic signal of unknown shape and period

A method was developed for the detection and measurement of a periodic signal with unknown characteristics in a data set where the existence of such signal was not known. The method detects a signal by using Bayesian probability theory to compare a constant model for the signal to members of a class of models with periodic structure. The method was applied to simulated data generated with both stepwise and sinusoidal light curves, demonstrating that such signals can be sensitively detected and the signal frequency and its shape can be accurately estimated.

Gregory, P. C.↗
NASA NTRS1999

Behavior of Filters and Smoothers for Strongly Nonlinear Dynamics

The Kalman filter is the optimal filter in the presence of known gaussian error statistics and linear dynamics. Filter extension to nonlinear dynamics is non trivial in the sense of appropriately representing high order moments of the statistics. Monte Carlo, ensemble-based, methods have been advocated as the methodology for representing high order moments without any questionable closure assumptions. Investigation along these lines has been conducted for highly idealized dynamics such as the strongly nonlinear Lorenz model as well as more realistic models of the means and atmosphere. A few relevant issues in this context are related to the necessary number of ensemble members to properly represent the error statistics and, the necessary modifications in the usual filter situations to allow for correct update of the ensemble members. The ensemble technique has also been applied to the problem of smoothing for which similar questions apply. Ensemble smoother examples, however, seem to be quite puzzling in that results state estimates are worse than for their filter analogue. In this study, we use concepts in probability theory to revisit the ensemble methodology for filtering and smoothing in data assimilation. We use the Lorenz model to test and compare the behavior of a variety of implementations of ensemble filters. We also implement ensemble smoothers that are able to perform better than their filter counterparts. A discussion of feasibility of these techniques to large data assimilation problems will be given at the time of the conference.

Zhu, Yanqui↗
NASA NTRS1999

The Behavior of Filters and Smoothers for Strongly Nonlinear Dynamics

The Kalman filter is the optimal filter in the presence of known Gaussian error statistics and linear dynamics. Filter extension to nonlinear dynamics is non trivial in the sense of appropriately representing high order moments of the statistics. Monte Carlo, ensemble-based, methods have been advocated as the methodology for representing high order moments without any questionable closure assumptions (e.g., Miller 1994). Investigation along these lines has been conducted for highly idealized dynamics such as the strongly nonlinear Lorenz (1963) model as well as more realistic models of the oceans (Evensen and van Leeuwen 1996) and atmosphere (Houtekamer and Mitchell 1998). A few relevant issues in this context are related to the necessary number of ensemble members to properly represent the error statistics and, the necessary modifications in the usual filter equations to allow for correct update of the ensemble members (Burgers 1998). The ensemble technique has also been applied to the problem of smoothing for which similar questions apply. Ensemble smoother examples, however, seem to quite puzzling in that results of state estimate are worse than for their filter analogue (Evensen 1997). In this study, we use concepts in probability theory to revisit the ensemble methodology for filtering and smoothing in data assimilation. We use Lorenz (1963) model to test and compare the behavior of a variety implementations of ensemble filters. We also implement ensemble smoothers that are able to perform better than their filter counterparts. A discussion of feasibility of these techniques to large data assimilation problems will be given at the time of the conference.

Zhu, Yanqiu↗
NASA NTRS2000

Probabilistic Risk Assessment: A Bibliography

Probabilistic risk analysis is an integration of failure modes and effects analysis (FMEA), fault tree analysis and other techniques to assess the potential for failure and to find ways to reduce risk. This bibliography references 160 documents in the NASA STI Database that contain the major concepts, probabilistic risk assessment, risk and probability theory, in the basic index or major subject terms, An abstract is included with most citations, followed by the applicable subject terms.

Source record↗
NASA NTRS2000

Fault Tree Analysis: A Bibliography

Fault tree analysis is a top-down approach to the identification of process hazards. It is as one of the best methods for systematically identifying an graphically displaying the many ways some things can go wrong. This bibliography references 266 documents in the NASA STI Database that contain the major concepts. fault tree analysis, risk an probability theory, in the basic index or major subject terms. An abstract is included with most citations, followed by the applicable subject terms.

Source record↗
NASA NTRS2001

Mathematical Analysis of Space Radiator Segmenting for Increased Reliability and Reduced Mass

Spacecraft for long duration deep space missions will need to be designed to survive micrometeoroid bombardment of their surfaces some of which may actually be punctured. To avoid loss of the entire mission the damage due to such punctures must be limited to small, localized areas. This is especially true for power system radiators, which necessarily feature large surface areas to reject heat at relatively low temperature to the space environment by thermal radiation. It may be intuitively obvious that if a space radiator is composed of a large number of independently operating segments, such as heat pipes, a random micrometeoroid puncture will result only in the loss of the punctured segment, and not the entire radiator. Due to the redundancy achieved by independently operating segments, the wall thickness and consequently the weight of such segments can be drastically reduced. Probability theory is used to estimate the magnitude of such weight reductions as the number of segments is increased. An analysis of relevant parameter values required for minimum mass segmented radiators is also included.

Juhasz, Albert J.↗