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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.

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At least 145 records · Page 8

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NASA NTRS1988

Optical communication with semiconductor laser diodes

Slot timing recovery in a direct detection optical PPM communication system can be achieved by processing the photodetector waveform with a nonlinear device whose output forms the input to a phase lock group. The choice of a simple transition detector as the nonlinearity is shown to give satisfactory synchronization performance. The rms phase error of the recovered slot clock and the effect of slot timing jitter on the bit error probability were directly measured. The experimental system consisted of an AlGaAs laser diode (lambda = 834 nm) and a silicon avalanche photodiode (APD) photodetector and used Q=4 PPM signaling operated at a source data rate of 25 megabits/second. The mathematical model developed to characterize system performance is shown to be in good agreement with actual performance measurements. The use of the recovered slot clock in the receiver resulted in no degradation in receiver sensitivity compared to a system with perfect slot timing. The system achieved a bit error probability of 10 to the minus 6 power at received signal energies corresponding to an average of less than 60 detected photons per information bit.

Davidson, F.↗

NASA NTRS1993

An onboard star identification algorithm

The paper presents the autonomous Initial Stellar Acquisition (ISA) algorithm developed for the X-Ray Timing Explorer for prividing the attitude quaternion within the desired accuracy, based on the one-axis attitude knowledge (through the use of the Digital Sun Sensor, CCD Star Trackers, and the onboard star catalog, OSC). Mathematical analysis leads to an accurate measure of the performance of the algorithm as a function of various parameters, such as the probability of a tracked star being in the OSC, the sensor noise level, and the number of stars matched. It is shown that the simplicity, tractability, and robustness of the ISA algorithm, compared to a general three-axis attiude determination algorithm, make it a viable on-board solution.

Ha, Kong↗

NASA NTRS1996

Physical Meaning of the Optimum Measurement Process in Quantum Detection Theory

The optimum measurement processes are represented as the optimum detection operators in the quantum detection theory. The error probability by the optimum detection operators goes beyond the standard quantum limit automatically. However the optimum detection operators are given by pure mathematical descriptions. In order to realize a communication system overcoming the standard quantum limit, we try to give the physical meaning of the optimum detection operators.

Osaki, Masao↗

NASA NTRS1988

Heat Flow and Magnetization in the Oceanic Lithosphere

Two aspects of the processing and interpretation of satellite measurements of the geomagnetic field are described. One deals with the extraction of the part of the geomagnetic field that originates from sources in the earth's atmosphere. The other investigates the possibility of using the thermal state of the oceanic lithosphere to further constrain modelling and interpretation of magnetic anomalies. It is shown that some of the magnetic signal in crustal anomaly maps can be an artifact of the mathematical algorithms that have been used to separate the crustal field from the observed data. Strong magnetic anomalies can be distorted but are probably real, but weak magnetic anomalies can arise from leakage of power from short wavelengths, and will also appear in anomaly maps as repetitions of the strong crustal anomaly. The distortion and the ghost anomalies follow the magnetic dip lines in a way that is similar to actual MAGSAT anomaly fields. This phenomenon will also affect the lower degree spherical harmonic terms in the power spectrum of the crustal field. A model of the magnetic properties of the oceanic crust that has been derived from direct measurements of the rock magnetic properties of oceanic rocks is presented. The average intensity of magnetization in the oceanic crust is not strong enough to explain magnetic anomalies observed over oceanic areas. This is the case for both near surface observations (ship and aeromagnetic data) and satellite altitude observations. It is shown that magnetic sources in the part of the upper mantle that is situated above the Curie isotherm, if sufficiently strong, can produce satellite magnetic anomalies that are comparable to MAGSAT data. The method developed for the study of depth to the Curie isotherm and magnetic anomalies can also be used in inverse modelling of satellite magnetic anomalies when the model is to be adjusted with an annihilator.

Hayling, Kjell Lennart↗

NASA NTRS1994

AutoClass: A Bayesian Approach to Classification

We describe a Bayesian approach to the untutored discovery of classes in a set of cases, sometimes called finite mixture separation or clustering. The main difference between clustering and our approach is that we search for the "best" set of class descriptions rather than grouping the cases themselves. We describe our classes in terms of a probability distribution or density function, and the locally maximal posterior probability valued function parameters. We rate our classifications with an approximate joint probability of the data and functional form, marginalizing over the parameters. Approximation is necessitated by the computational complexity of the joint probability. Thus, we marginalize w.r.t. local maxima in the parameter space. We discuss the rationale behind our approach to classification. We give the mathematical development for the basic mixture model and describe the approximations needed for computational tractability. We instantiate the basic model with the discrete Dirichlet distribution and multivariant Gaussian density likelihoods. Then we show some results for both constructed and actual data.

Stutz, John↗

NASA NTRS1948

Planing of Watercraft

The present report deals with the processes accompanying the planing of a planing boat or a seaplane on water . The study is largely based upon theoretical investigations; mathematical problems and proofs are not discussed. To analyze theoreticaly actual planing processes, giving due consideration to all aspects of the problem, is probably not possible. The theories therefore treat various simple limiting cases, which in their entirety give a picture of the planing processes and enable the interpretation of the experimental results. The discussion is concerned with the stationary planing attitude: the boat planes at a constant speed V on an originally smooth surface.

Wagner, Herbert↗

NASA NTRS1982

Viscoelastic Properties of Polymer Blends

Viscosity, shear modulus and other viscoelastic properties of multicomponent polymer blends are predicted from behavior of individual components, using a mathematical model. Model is extension of two-component-blend model based on Rouse-Bueche-Zimm theory of polymer viscoelasticity. Extension assumes that probabilities of forming various possible intracomponent and intercomponent entanglements among polymer molecules are proportional to relative abundances of components.

Hong, S. D.↗

NASA NTRS1988

Predicting debris

The probable amount, sizes, and relative velocities of debris are discussed, giving examples of the damage caused by debris, and focusing on the use of mathematical models to forecast the debris environment and solar activity now and in the future. Most debris are within 2,000 km of the earth's surface. The average velocity of spacecraft-debris collisions varies from 9 km/sec at 30 degrees of inclination to 13 km/sec near polar orbits. Mathematical models predict a 5 percent per year increase in the large-fragment population, producing a small-fragment population increase of 10 percent per year until the year 2060, the time of critical density. A 10 percent increase in the large population would cause the critical density to be reached around 2025.

Kessler, Donald J.↗

NASA NTRS1989

Slot clock recovery in optical PPM communication systems with avalanche photodiode photodetectors

Slot timing recovery in a direct-detection optical PPM communication system can be achieved by processing the photodetector output waveform with a nonlinear device whose output forms the input to a phase-locked loop. The choice of a simple transition detector as the nonlinearity is shown to give satisfactory synchronization performance. The rms phase error of the recovered slot clock and the effect of slot timing jitter on the bit error probability were directly measured. The experimental system consisted of an AlGaAs laser diode (wavelength = 834 nm) and a silicon avalanche photodiode photodetector. The system used Q = 4 PPM signaling and operated at a source data rate of 25 Mbits/s. The mathematical model developed to compute the rms phase error of the recovered clock is shown to be in good agreement with results of actual measurements of phase errors. The use of the recovered slot clock in the receiver resulted in no significant degradation in receiver sensitivity compared to a system with perfect slot timing. The system achieved a bit error probability of 10 to the -6th at a received optical signal energy of 55 detected photons per information bit.

Davidson, Frederic M.↗

NASA NTRS2003

Modeling, Analyzing, and Mitigating Dissonance Between Alerting Systems

Alerting systems are becoming pervasive in process operations, which may result in the potential for dissonance or conflict in information from different alerting systems that suggests different threat levels and/or actions to resolve hazards. Little is currently available to help in predicting or solving the dissonance problem. This thesis presents a methodology to model and analyze dissonance between alerting systems, providing both a theoretical foundation for understanding dissonance and a practical basis from which specific problems can be addressed. A state-space representation of multiple alerting system operation is generalized that can be tailored across a variety of applications. Based on the representation, two major causes of dissonance are identified: logic differences and sensor error. Additionally, several possible types of dissonance are identified. A mathematical analysis method is developed to identify the conditions for dissonance originating from logic differences. A probabilistic analysis methodology is developed to estimate the probability of dissonance originating from sensor error, and to compare the relative contribution to dissonance of sensor error against the contribution from logic differences. A hybrid model, which describes the dynamic behavior of the process with multiple alerting systems, is developed to identify dangerous dissonance space, from which the process can lead to disaster. Methodologies to avoid or mitigate dissonance are outlined. Two examples are used to demonstrate the application of the methodology. First, a conceptual In-Trail Spacing example is presented. The methodology is applied to identify the conditions for possible dissonance, to identify relative contribution of logic difference and sensor error, and to identify dangerous dissonance space. Several proposed mitigation methods are demonstrated in this example. In the second example, the methodology is applied to address the dissonance problem between two air traffic alert and avoidance systems: the existing Traffic Alert and Collision Avoidance System (TCAS) vs. the proposed Airborne Conflict Management system (ACM). Conditions on ACM resolution maneuvers are identified to avoid dynamic dissonance between TCAS and ACM. Also included in this report is an Appendix written by Lee Winder about recent and continuing work on alerting systems design. The application of Markov Decision Process (MDP) theory to complex alerting problems is discussed and illustrated with an abstract example system.

Song, Lixia↗

NASA NTRS1982

An automated approach to the design of decision tree classifiers

An automated technique is presented for designing effective decision tree classifiers predicated only on a priori class statistics. The procedure relies on linear feature extractions and Bayes table look-up decision rules. Associated error matrices are computed and utilized to provide an optimal design of the decision tree at each so-called 'node'. A by-product of this procedure is a simple algorithm for computing the global probability of correct classification assuming the statistical independence of the decision rules. Attention is given to a more precise definition of decision tree classification, the mathematical details on the technique for automated decision tree design, and an example of a simple application of the procedure using class statistics acquired from an actual Landsat scene.

Argentiero, P.↗

NASA NTRS2014

A Statistical Treatment of Bioassay Pour Fractions

The binomial probability distribution is used to treat the statistics of a microbiological sample that is split into two parts, with only one part evaluated for spore count. One wishes to estimate the total number of spores in the sample based on the counts obtained from the part that is evaluated (pour fraction). Formally, the binomial distribution is recharacterized as a function of the observed counts (successes), with the total number (trials) an unknown. The pour fraction is the probability of success per spore (trial). This distribution must be renormalized in terms of the total number. Finally, the new renormalized distribution is integrated and mathematically inverted to yield the maximum estimate of the total number as a function of a desired level of confidence ( P(<n)=LOC ). Selected results of the indicated numerical calculations are presented. For LOC=0.5, or the likely value, the estimates differ little from the usual calculation: the number of spores counted divided by the pour fraction. The extension to recovery efficiency corrections is also presented. Now the product of recovery efficiency and pour fraction may be small enough that the likely value may be much larger than the usual calculation: the number of spores divided by that product. The use of this analysis would not be limited to microbiological data.

000000↗

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 NTRS1973

Estimating the number of terrestrial organisms on the moon.

Methods used to obtain estimates for the biological loadings on moon bound spacecraft prior to launch are reviewed, along with the mathematical models used to calculate the microorganism density on the lunar surface (such as it results from contamination deposited by manned and unmanned flights) and the probability of lunar soil sample contamination. Some of the results obtained by the use of a lunar inventory system based on these models are presented.

Dillon, R. T.↗

NASA NTRS1966

Log-normal model for microbial survival in heat sterilization

An analytical model is developed for the survival times of organisms in heat sterilization in which the probability of inactivation as a function of exposure time is log-normally distributed. Experimental data is examined relative to this model and it is concluded that the model is valid except during the initial period of heating when an additional interaction between the organisms and their surrounding medium appears to be present. At long heating times, the log-normal model appears more accurate for extrapolating to low survival probabilities than the usual logarithmic survivor curves and is generally more conservative.

SURVIVAL↗

DOE OSTI2024

Yet Another Discriminant Analysis (YADA): A Probabilistic Model for Machine Learning Applications

This paper presents a probabilistic model for various machine learning (ML) applications. While deep learning (DL) has produced state-of-the-art results in many domains, DL models are complex and over-parameterized, which leads to high uncertainty about what the model has learned, as well as its decision process. Further, DL models are not probabilistic, making reasoning about their output challenging. In contrast, the proposed model, referred to as Yet Another Discriminate Analysis(YADA), is less complex than other methods, is based on a mathematically rigorous foundation, and can be utilized for a wide variety of ML tasks including classification, explainability, and uncertainty quantification. YADA is thus competitive in most cases with many state-of-the-art DL models. Ideally, a probabilistic model would represent the full joint probability distribution of its features, but doing so is often computationally expensive and intractable. Hence, many probabilistic models assume that the features are either normally distributed, mutually independent, or both, which can severely limit their performance. YADA is an intermediate model that (1) captures the marginal distributions of each variable and the pairwise correlations between variables and (2) explicitly maps features to the space of multivariate Gaussian variables. Numerous mathematical properties of the YADA model can be derived, thereby improving the theoretic underpinnings of ML. Validation of the model can be statistically verified on new or held-out data using native properties of YADA. However, there are some engineering and practical challenges that we enumerate to make YADA more useful.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1988

SURE reliability analysis: Program and mathematics

The SURE program is a new reliability analysis tool for ultrareliable computer system architectures. The computational methods on which the program is based provide an efficient means for computing accurate upper and lower bounds for the death state probabilities of a large class of semi-Markov models. Once a semi-Markov model is described using a simple input language, the SURE program automatically computes the upper and lower bounds on the probability of system failure. A parameter of the model can be specified as a variable over a range of values directing the SURE program to perform a sensitivity analysis automatically. This feature, along with the speed of the program, makes it especially useful as a design tool.

Butler, Ricky W.↗

NASA NTRS2010

Turbulence and the Stabilization Principle

Further results of research, reported in several previous NASA Tech Briefs articles, were obtained on a mathematical formalism for postinstability motions of a dynamical system characterized by exponential divergences of trajectories leading to chaos (including turbulence). To recapitulate: Fictitious control forces are introduced to couple the dynamical equations with a Liouville equation that describes the evolution of the probability density of errors in initial conditions. These forces create a powerful terminal attractor in probability space that corresponds to occurrence of a target trajectory with probability one. The effect in ordinary perceived three-dimensional space is to suppress exponential divergences of neighboring trajectories without affecting the target trajectory. Con sequently, the postinstability motion is represented by a set of functions describing the evolution of such statistical quantities as expectations and higher moments, and this representation is stable. The previously reported findings are analyzed from the perspective of the authors Stabilization Principle, according to which (1) stability is recognized as an attribute of mathematical formalism rather than of underlying physics and (2) a dynamical system that appears unstable when modeled by differentiable functions only can be rendered stable by modifying the dynamical equations to incorporate intrinsic stochasticity.

Zak, Michail↗