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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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Random Sampling Process Leads to Overestimation of β-Diversity of Microbial Communities

The site-to-site variability in species composition, known as β-diversity, is crucial to understanding spatiotemporal patterns of species diversity and the mechanisms controlling community composition and structure. However, quantifying β-diversity in microbial ecology using sequencing-based technologies is a great challenge because of a high number of sequencing errors, bias, and poor reproducibility and quantification. Herein, based on general sampling theory, a mathematical framework is first developed for simulating the effects of random sampling processes on quantifying β-diversity when the community size is known or unknown. Also, using an analogous ball example under Poisson sampling with limited sampling efforts, the developed mathematical framework can exactly predict the low reproducibility among technically replicate samples from the same community of a certain species abundance distribution, which provides explicit evidences of random sampling processes as the main factor causing high percentages of technical variations. In addition, the predicted values under Poisson random sampling were highly consistent with the observed low percentages of operational taxonomic unit (OTU) overlap (<30% and <20% for two and three tags, respectively, based on both Jaccard and Bray-Curtis dissimilarity indexes), further supporting the hypothesis that the poor reproducibility among technical replicates is due to the artifacts associated with random sampling processes. Finally, a mathematical framework was developed for predicting sampling efforts to achieve a desired overlap among replicate samples. Our modeling simulations predict that several orders of magnitude more sequencing efforts are needed to achieve desired high technical reproducibility. These results suggest that great caution needs to be taken in quantifying and interpreting β-diversity for microbial community analysis using next-generation sequencing technologies.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2017

Contact Processes with Random Recovery Rates and Edge Weights on Complete Graphs

In this paper we are concerned with the contact process with random recovery rates and edge weights on the complete graph with n vertices. We show that the model has a critical value which is inversely proportional to the product of the mean of the edge weight and the mean of the inverse of the recovery rate. In the subcritical case, the process dies out before an amount of time with order O(log n) with high probability as n→+∞. In the supercritical case, the process survives for an amount of time with order exp {O(n)} with high probability as n→+∞.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1972

On the mapping associated with the complex representation of functions and processes.

The mapping between function spaces that is implied by the representation of a real 'bandpass' function by a complex 'low-pass' function is explicitly accepted. The discussion is extended to the representation of stationary random processes where the mapping is between spaces of random processes. This approach clarifies the nature of the complex representation, especially in the case of random processes and, in addition, derives the properties of the complex representation.-

Harger, R. O.↗
NASA NTRS1972

Nonstationary envelope process and first excursion probability.

The definition of stationary random envelope proposed by Cramer and Leadbetter, is extended to the envelope of nonstationary random process possessing evolutionary power spectral densities. The density function, the joint density function, the moment function, and the crossing rate of a level of the nonstationary envelope process are derived. Based on the envelope statistics, approximate solutions to the first excursion probability of nonstationary random processes are obtained. In particular, applications of the first excursion probability to the earthquake engineering problems are demonstrated in detail.

Yang, J.-N.↗
DOE OSTI2026

Experimental quantum Bernoulli factories via Bell-basis measurements

Randomness processing in the Bernoulli factory framework provides a concrete setting in which quantum resources can outperform classical ones. We experimentally demonstrate quantum randomness processing based on Bell-basis measurements of two identical input quoins prepared on IBM superconducting hardware. Using only the measurement outcomes (and no external classical randomness source), we realize the classically inconstructible Bernoulli doubling primitive f(p)=2p, and, as intermediate outputs from the same Bell-measurement statistics, an exact fair coin f(p)=1/2 and the classically inconstructible function f(p)=4p(1−p). We benchmark the measured output biases against ideal predictions and discuss the impact of device noise. Our results establish a simple resource-efficient experimental primitive for quantum-to-classical randomness processing and support the viability of quantum Bernoulli factories for quantum-enhanced stochastic simulation and sampling tasks.

Roy, Tanay [Fermilab] (ORCID:000000019442862X)↗
NASA NTRS1975

A mathematical examination of the press model for atmospheric turbulence

The random process used to model atmospheric turbulence in aircraft response problems is examined. The first, second, and higher order probability density and characteristic functions were developed. The concepts of the Press model lead to an approximate procedure for the analysis of the response of linear dynamic systems to a class of non-Gaussian random processes. The Press model accounts for both the Gaussian and non-Gaussian forms of measured turbulence data. The nonstationary aspects of measured data are explicitly described by the transition properties of the random process. The effects of the distribution of the intensity process upon calculated exceedances are examined. It is concluded that the press model with a Gaussian intensity distribution gives a conservative prediction of limit load values.

Sidwell, K.↗
NASA NTRS2002

Experimental Investigations of Non-Stationary Properties In Radiometer Receivers Using Measurements of Multiple Calibration References

Radiometers must be periodically calibrated because the receiver response fluctuates. Many techniques exist to correct for the time varying response of a radiometer receiver. An analytical technique has been developed that uses generalized least squares regression (LSR) to predict the performance of a wide variety of calibration algorithms. The total measurement uncertainty including the uncertainty of the calibration can be computed using LSR. The uncertainties of the calibration samples used in the regression are based upon treating the receiver fluctuations as non-stationary processes. Signals originating from the different sources of emission are treated as simultaneously existing random processes. Thus, the radiometer output is a series of samples obtained from these random processes. The samples are treated as random variables but because the underlying processes are non-stationary the statistics of the samples are treated as non-stationary. The statistics of the calibration samples depend upon the time for which the samples are to be applied. The statistics of the random variables are equated to the mean statistics of the non-stationary processes over the interval defined by the time of calibration sample and when it is applied. This analysis opens the opportunity for experimental investigation into the underlying properties of receiver non stationarity through the use of multiple calibration references. In this presentation we will discuss the application of LSR to the analysis of various calibration algorithms, requirements for experimental verification of the theory, and preliminary results from analyzing experiment measurements.

Racette, Paul↗
NASA NTRS1990

Correlation autoregressive processes with application to helicopter noise

This paper introduces a new class of random processes X(t), the autocorrelations R sub x (t1, t2) of which satisfy a linear relation for all t1 and t2 in some interval of the time axis. Such random processes are denoted as 'correlation-autoregressive'. This class is shown to include the familiar stationary and periodically correlated processes as well as many other, both harmonizable and nonharmonizable, nonstationary processes. When a process is correlation-autoregressive for all times and harmonizable, its two-dimensional power spectral density is shown to take a particularly simple form. The relationship of such processes to the class of stationary processes is examined. In addition, the application of such processes in the analysis of typical helicopter noise signals is described.

Hardin, J. C.↗
DOE OSTI2022

Time domain probabilistic seismic risk analysis using ground motion prediction equations of Fourier amplitude spectra

Modeling of Fourier amplitude spectra (FAS) of seismic motions has gained much attention in engineering seismology. In the past few years, several ground motion prediction equations (GMPEs) and inter-frequency correlation structure of FAS have been established. Due to many preferable characteristics of FAS, probabilistic seismic hazard/risk analysis is rapidly changing from ergodic, spectrum acceleration Sa(T 0 )-based approach to non-ergodic, site-specific, FAS-based approach. This paper presents time domain intrusive framework for probabilistic seismic risk analysis using GMPE of FAS. Herein, methodology for time domain stochastic ground motion modeling based on GMPEs of FAS is presented in some detail. The simulated uncertain motions are modeled as a random process and represented by polynomial chaos Karhunen-Loève expansion. The random process excitations are further propagated into the uncertain structural system using Galerkin stochastic finite element method (SFEM). Probabilistic evolution of structural response is solved, and such solution is used to develop seismic risk for any damage state. The presented framework is illustrated through seismic risk analysis of a four-story building subjected to possible earthquakes from two strike slip faults. The influences of the epistemic uncertainties in source stress drop Δσ and site attenuation κ0 on seismic risk are investigated. The need for non-ergodic seismic risk analysis with source-specific and site specific characterizations is emphasized.

58 GEOSCIENCES↗
NASA NTRS1976

A correlation polarimeter for noise-like signals

Optimum estimation (tracking) of the polarization plane of a linearly polarized electromagnetic wave is determined when the signal is a narrow-band Gaussian random process with a polarization plane angle which is also a Gaussian random process. This model is compared to previous work and is applicable to space communication. The estimator performs a correlation operation similar to an amplitude-comparison monopulse angle tracker, giving the name correlation polarimeter. Under large signal-to-noise ratio (SNR), the estimator is causal. Performance of the causal correlation polarimeter is evaluated for arbitrary SNR. Optimum precorrelation filtering is determined. With low SNR, the performance of this system is far better than that of previously developed systems. Practical implementation is discussed. A scheme is given to reduce the effect of linearly polarized noise.

Ohlson, J. E.↗
NASA NTRS1987

Random loading fatigue crack growth: Crack closure considerations

The prediction of fatigue crack growth is an important element of effective fracture control for metallic structures and mechanical components, especially in the aerospace industry. The prediction techniques available and applied today are mostly based on fatigue crack growth measurements determined in constant amplitude testing. However, while many service loadings are constant amplitude, many more loadings are random amplitude. An investigation to determine which statistics of random loadings are relevant to fatigue crack closure was conducted. The fundamentals of random processes and crack closure are briefly reviewed, then the relevance of certain random process parameters to the crack closure calculation are discussed qualitatively. A course for further research is outlined.

Ortiz, Keith↗
NASA NTRS1974

Square-root algorithm for evaluating mismodeled process noise

As the application of sequential filters has grown, the need has arisen to evaluate the sensitivity of these filters to mismodeling of the random process. A numerically reliable square-root algorithm is developed for calculating the covariances of estimates from a sequential filter which incorrectly models process noise. Mismodeling is restricted to the correlation time and standard deviation of a random process represented as a first-order Gauss-Markov sequence. Using a computer program which employs this algorithm, a sensitivity analysis was performed for several types of earth-based tracking data from an interplanetary spacecraft.

Thornton, C. L.↗
DOE OSTI2016

Radiation Transport in Random Media With Large Fluctuations

Strongly heterogeneous media arise in several applications that include radiation shields, nuclear fuel, BWR moderators, clouds, planetary and stellar atmospheres, turbulent gases and plasmas. Neutral and charged particle transport computations in such media have relied heavily on formulating transport equations with spatially random coefficients (physical data) and developing solution methods to deal with the additional stochastic dimensions. Attempts at developing approximate closures that yield only low order statistical information (e.g., mean and variance of the flux) have proved to be highly restrictive under real physics conditions or rely on techniques that require fluctuation amplitudes to be small for robustness. Recently, stochastic spectral methods such as polynomial chaos and stochastic collocation have been developed for aleatoric uncertainty quantification and sensitivity analysis, and successfully applied in radiation transport work. Advances in UQ techniques have tended to focus on efficiently handling large numbers of uncertain variables but the rigorous stochastic basis of the approach also promotes its use in situations where stochasticity is due to spatial heterogeneity and the associated uncertainty is large. Here we apply these techniques to radiation transport in media with spatially randomly varying cross sections without restriction on fluctuation amplitudes. Specifically, we represent the cross sections as a lognormal spatial random process with specified mean, variance and covariance function and use a Karhunen-Loeve (KL) decomposition to generate cross section realizations that are strictly positive. Woodcock Monte Carlo (WMC) is then used to simulate transport using random sampling of cross sections and deterministic sampling based on a stochastic collocation technique. Numerical results for the mean and variance in the scalar flux and leakage currents are obtained for weak and strong random variations. We focus in this work on demonstrating the approach and defer application to specific problems to a future investigation. We have demonstrated that a combination of stochastic spectral representation and Woodcock Monte Carlo simulation allows efficient computation of radiation transport in strongly random media. The use of a lognormal distribution to represent the fluctuations in medium properties facilitates enforcement of strict positivity of cross section realizations, a condition that has challenged standard approaches that assume Gaussian fluctuations. The fact that the lognormal random process is a memoryless nonlinear transformation of a Gaussian process further enables efficient and accurate reconstruction of the random cross section realizations using a Karhunen-Loeve representation of the cross section. Finally, the robustness of this model enables fluctuations of arbitrarily large amplitude to be studied, using both random sampling Monte Carlo and more efficient stochastic collocation techniques. The present work is being extended to allow reconstruction of probability density functions of output variables using polynomial chaos representation, and to accommodate general cross section covariance functions. Also, techniques are being explored to more judiciously select ceiling cross sections to enhance the efficiency of Woodcock Monte Carlo for transport in random media. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1976

Three-level sampler having automated thresholds

A three-level sampler is described that has its thresholds controlled automatically so as to track changes in the statistics of the random process being sampled. In particular, the mean value is removed and the ratio of the standard deviation of the random process to the threshold is maintained constant. The system is configured in such a manner that slow drifts in the level comparators and digital-to-analog converters are also removed. The ratio of the standard deviation to threshold level may be chosen within the constraints of the ratios of two integers N and M. These may be chosen to minimize the quantizing noise of the sampled process.

Jurgens, R. F.↗
NASA NTRS1977

The human as a detector of changes in variance and bandwidth

The detection of changes in random process variance and bandwidth was studied. Psychophysical thresholds for these two parameters were determined using an adaptive staircase technique for second order random processes at two nominal periods (1 and 3 seconds) and damping ratios (0.2 and 0.707). Thresholds for bandwidth changes were approximately 9% of nominal except for the (3sec,0.2) process which yielded thresholds of 12%. Variance thresholds averaged 17% of nominal except for the (3sec,0.2) process in which they were 32%. Detection times for suprathreshold changes in the parameters may be roughly described by the changes in RMS velocity of the process. A more complex model is presented which consists of a Kalman filter designed for the nominal process using velocity as the input, and a modified Wald sequential test for changes in the variance of the residual. The model predictions agree moderately well with the experimental data. Models using heuristics, e.g. level crossing counters, were also examined and are found to be descriptive but do not afford the unification of the Kalman filter/sequential test model used for changes in mean.

Curry, R. E.↗
DOE OSTI2018

Non-stationary Almost Sure Invariance Principle for Hyperbolic Systems with Singularities

We investigate a wide class of two-dimensional hyperbolic systems with singularities, and prove the almost sure invariance principle (ASIP) for the random process generated by sequences of dynamically Hölder observables. The observables could be unbounded, and the process may be non-stationary and need not have linearly growing variances. Our results apply to Anosov diffeomorphisms, Sinai dispersing billiards and their perturbations. The random processes under consideration are related to the fluctuation of Lyapunov exponents, the shrinking target problem, etc.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗