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NASA NTRS1995

Estimation of attitude sensor timetag biases

This paper presents an extended Kalman filter for estimating attitude sensor timing errors. Spacecraft attitude is determined by finding the mean rotation from a set of reference vectors in inertial space to the corresponding observed vectors in the body frame. Any timing errors in the observations can lead to attitude errors if either the spacecraft is rotating or the reference vectors themselves vary with time. The state vector here consists of the attitude quaternion, timetag biases, and, optionally, gyro drift rate biases. The filter models the timetags as random walk processes: their expectation values propagate as constants and white noise contributes to their covariance. Thus, this filter is applicable to cases where the true timing errors are constant or slowly varying. The observability of the state vector is studied first through an examination of the algebraic observability condition and then through several examples with simulated star tracker timing errors. The examples use both simulated and actual flight data from the Extreme Ultraviolet Explorer (EUVE). The flight data come from times when EUVE had a constant rotation rate, while the simulated data feature large angle attitude maneuvers. The tests include cases with timetag errors on one or two sensors, both constant and time-varying, and with and without gyro bias errors. Due to EUVE's sensor geometry, the observability of the state vector is severely limited when the spacecraft rotation rate is constant. In the absence of attitude maneuvers, the state elements are highly correlated, and the state estimate is unreliable. The estimates are particularly sensitive to filter mistuning in this case. The EUVE geometry, though, is a degenerate case having coplanar sensors and rotation vector. Observability is much improved and the filter performs well when the rate is either varying or noncoplanar with the sensors, as during a slew. Even with bad geometry and constant rates, if gyro biases are independently known, the timetag error for a single sensor can be accurately estimated as long as its boresight is not too close to the spacecraft rotation axis.

Sedlak, J.↗

NASA NTRS1994

Two-sample discrimination of Poisson means

This paper presents a statistical test for detecting significant differences between two random count accumulations. The null hypothesis is that the two samples share a common random arrival process with a mean count proportional to each sample's exposure. The model represents the partition of N total events into two counts, A and B, as a sequence of N independent Bernoulli trials whose partition fraction, f, is determined by the ratio of the exposures of A and B. The detection of a significant difference is claimed when the background (null) hypothesis is rejected, which occurs when the observed sample falls in a critical region of (A, B) space. The critical region depends on f and the desired significance level, alpha. The model correctly takes into account the fluctuations in both the signals and the background data, including the important case of small numbers of counts in the signal, the background, or both. The significance can be exactly determined from the cumulative binomial distribution, which in turn can be inverted to determine the critical A(B) or B(A) contour. This paper gives efficient implementations of these tests, based on lookup tables. Applications include the detection of clustering of astronomical objects, the detection of faint emission or absorption lines in photon-limited spectroscopy, the detection of faint emitters or absorbers in photon-limited imaging, and dosimetry.

Lampton, M.↗

NASA NTRS1994

The rotation of photospheric magnetic fields: A random walk transport model

In an earlier study of solar differential rotation, we showed that the transport of magnetic flux across latitudes acts to establish quasi-stationary patterns, therby accounting for the observed rigid rotation of the large-scale photospheric field. In that paper, the effect of supergranular convection was represented by a continuum diffusion, limiting the applicability of the calculations to large spatial scales. Here we extend the model to scales comparable to that of the supergranulation itself by replacing the diffusive transport with a discrete random walk process. Rotation curves are derived by cross-correlating the simulated photospheric field maps for a variety of time lags and spatial resolutions. When the lag between maps is relatively short less than or approximately = 15 days), the midlatitude correlation functions show two distinct components: a broad feature associated with the large-scale unipolar patterns and a narrow feature originating from small magnetic structures encompossing from one to several supergranular cells. By fitting the broad component we obtain the rigid rotation profile of the patterns, whereas by fitting the narrow component, we recover the differential rate of the photospheric plasma itself. For time lags of 1 month or greater, only the broad feature associated with the long-lived patterns remains clearly identifiable in the simulations.

Wang, Y. -M.↗

NASA NTRS1996

Age-related alterations in the fractal scaling of cardiac interbeat interval dynamics

We postulated that aging is associated with disruption in the fractallike long-range correlations that characterize healthy sinus rhythm cardiac interval dynamics. Ten young (21-34 yr) and 10 elderly (68-81 yr) rigorously screened healthy subjects underwent 120 min of continuous supine resting electrocardiographic recording. We analyzed the interbeat interval time series using standard time and frequency domain statistics and using a fractal measure, detrended fluctuation analysis, to quantify long-range correlation properties. In healthy young subjects, interbeat intervals demonstrated fractal scaling, with scaling exponents (alpha) from the fluctuation analysis close to a value of 1.0. In the group of healthy elderly subjects, the interbeat interval time series had two scaling regions. Over the short range, interbeat interval fluctuations resembled a random walk process (Brownian noise, alpha = 1.5), whereas over the longer range they resembled white noise (alpha = 0.5). Short (alpha s)- and long-range (alpha 1) scaling exponents were significantly different in the elderly subjects compared with young (alpha s = 1.12 +/- 0.19 vs. 0.90 +/- 0.14, respectively, P = 0.009; alpha 1 = 0.75 +/- 0.17 vs. 0.99 +/- 0.10, respectively, P = 0.002). The crossover behavior from one scaling region to another could be modeled as a first-order autoregressive process, which closely fit the data from four elderly subjects. This implies that a single characteristic time scale may be dominating heartbeat control in these subjects. The age-related loss of fractal organization in heartbeat dynamics may reflect the degradation of integrated physiological regulatory systems and may impair an individual's ability to adapt to stress.

NASA Discipline Cardiopulmonary↗

NASA NTRS2003

Large-Eddy Simulation Code Developed for Propulsion Applications

A large-eddy simulation (LES) code was developed at the NASA Glenn Research Center to provide more accurate and detailed computational analyses of propulsion flow fields. The accuracy of current computational fluid dynamics (CFD) methods is limited primarily by their inability to properly account for the turbulent motion present in virtually all propulsion flows. Because the efficiency and performance of a propulsion system are highly dependent on the details of this turbulent motion, it is critical for CFD to accurately model it. The LES code promises to give new CFD simulations an advantage over older methods by directly computing the large turbulent eddies, to correctly predict their effect on a propulsion system. Turbulent motion is a random, unsteady process whose behavior is difficult to predict through computer simulations. Current methods are based on Reynolds-Averaged Navier- Stokes (RANS) analyses that rely on models to represent the effect of turbulence within a flow field. The quality of the results depends on the quality of the model and its applicability to the type of flow field being studied. LES promises to be more accurate because it drastically reduces the amount of modeling necessary. It is the logical step toward improving turbulent flow predictions. In LES, the large-scale dominant turbulent motion is computed directly, leaving only the less significant small turbulent scales to be modeled. As part of the prediction, the LES method generates detailed information on the turbulence itself, providing important information for other applications, such as aeroacoustics. The LES code developed at Glenn for propulsion flow fields is being used to both analyze propulsion system components and test improved LES algorithms (subgrid-scale models, filters, and numerical schemes). The code solves the compressible Favre-filtered Navier- Stokes equations using an explicit fourth-order accurate numerical scheme, it incorporates a compressible form of Smagorinsky s model for the subgrid-scale turbulence, and it uses generalized curvilinear coordinates to allow analysis of a wide range of geometries. The code runs in parallel on shared memory multiprocessor computers and is written in Fortran 90 with dynamic memory allocation. A sample result for a Mach-1.4 round jet is presented in the figure. Instantaneous Mach number contours in several cross-planes downstream of the nozzle exit are shown, illustrating how an LES captures the large unsteady three-dimensional turbulent structures present in the jet.

DeBonis, James R.↗

NASA NTRS2018

Discovery of Activities via Statistical Clustering of Fixation Patterns

Human behavior often consists of a series of distinct activities, each characterized by a unique pattern of interaction with the visual environment. This is true even in a restricted domain, such as a piloting an aircraft, where activities with distinct visual signatures might be things like communicating, navigating, and monitoring. We propose a novel analysis method for gaze-tracking data, to perform blind discovery of these hypothetical activities. The method is in some respects similar to recurrence analysis, but here we compare not individual fixations, but groups of fixations aggregated over a fixed time interval. The duration of this interval is a parameter that we will refer to as delta. We assume that the environment has been divided into a set of N different areas-of-interest (AOIs). For a given interval of time of duration delta, we compute the proportion of time spent fixating each AOI, resulting in an N-dimensional vector. These proportions can be converted to integer counts by multiplying by delta divided by the average fixation duration (another parameter that we fix at 280 milliseconds). We compare different intervals by computing the chi-square statistic. The p-value associated with the statistic is the likelihood of observing the data under the hypothesis that the data in the two intervals were generated by a single process with a single set of probabilities governing the fixation of each AOI. The method has been applied to approximately 100 hours of eye movement data collected from pilots in a high-fidelity B747 flight simulator, and the results have been compared to synthetic data in which the each activity is represented as first-order Markov process with random probabilities assigned to the AOIs. Randomly-generated synthetic activities can require thousands of fixations to be discriminated with statistical significance, while the human data can be clustered using averaging windows of some 10's of seconds, suggesting that the actual activities are much more narrowly focused than random Markov models.

activity analysis↗

DOE OSTI2023

Operation Optimization Using Reinforcement Learning with Integrated Artificial Reasoning Framework

In large and complex systems, operational decision-making requires a systematic analysis with a vast amount of data from both process parameters and component status monitoring. In this paper, we present an integrated artificial reasoning approach for system state transition models that can help operational decision-making with explainable and traceable reasoning. The integrated artificial reasoning framework is a physics-based approach of defining the system structure in a Bayesian network, so we leveraged it in a Markov decision process (MDP) for finding optimal operational solutions. In our proposed framework, the MDP is implemented on a dynamic Bayesian network (DBN), which represents causalities in a system. The multilevel flow modeling was utilized in order to extract these causalities in a more efficient and objective manner. Since multilevel flow modeling is based on the fundamental energy and mass conservation laws, the target system is decomposed into several mass, energy, and information structures, which serve as the basis for a DBN. The MDP consists of the processes of finding a solution for the Bellman equation, which can be derived from the conditional probability equations of the constructed DBN. System operators can capture stochastic system dynamics as multiple subsystem state transitions based on their physical relations and uncertainties coming from the component degradation process or random failures. We analyzed a simplified example system to illustrate finding an optimal operational policy with this approach.

Kim, Junyung↗

DOE OSTI2022

Evaluating the performance of random forest and iterative random forest based methods when applied to gene expression data

Gene-to-gene networks, such as Gene Regulatory Networks (GRN) and Predictive Expression Networks (PEN) capture relationships between genes and are beneficial for use in downstream biological analyses. There exists multiple network inference tools to produce these gene-to-gene networks from matrices of gene expression data. Random Forest-Leave One Out Prediction (RF-LOOP) is a method that has been shown to be efficient at producing these gene-to-gene networks, frequently known as GEne Network Inference with Ensemble of trees (GENIE3). Random Forest can be replaced in this process by iterative Random Forest (iRF), which performs variable selection and boosting. Here we validate that iterative Random Forest-Leave One Out Prediction (iRF-LOOP) produces higher quality networks than GENIE3 (RF-LOOP). We use both synthetic and empirical networks from the Dialogue for Reverse Engineering Assessment and Methods (DREAM) Challenges by Sage Bionetworks, as well as two additional empirical networks created from Arabidopsis thaliana and Populus trichocarpa expression data.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS2012

A Parameterized Inversion Model for Soil Moisture and Biomass from Polarimetric Backscattering Coefficients

A semi-empirical algorithm for the retrieval of soil moisture, root mean square (RMS) height and biomass from polarimetric SAR data is explained and analyzed in this paper. The algorithm is a simplification of the distorted Born model. It takes into account the physical scattering phenomenon and has three major components: volume, double-bounce and surface. This simplified model uses the three backscattering coefficients ( sigma HH, sigma HV and sigma vv) at low-frequency (P-band). The inversion process uses the Levenberg-Marquardt non-linear least-squares method to estimate the structural parameters. The estimation process is entirely explained in this paper, from initialization of the unknowns to retrievals. A sensitivity analysis is also done where the initial values in the inversion process are varying randomly. The results show that the inversion process is not really sensitive to initial values and a major part of the retrievals has a root-mean-square error lower than 5% for soil moisture, 24 Mg/ha for biomass and 0.49 cm for roughness, considering a soil moisture of 40%, roughness equal to 3cm and biomass varying from 0 to 500 Mg/ha with a mean of 161 Mg/ha

soil moisture↗

DOE OSTI2024

RGM: Random Geological Model Generation Package

This Fortran code is to accompany a manuscript to be submitted to Computers & Geosciences, a high-impact, peer-reviewed journal in computer methods for geosciences research. This Fortran code focuses on generation of synthetic geological models using a multi-randomization strategy. Generating high-fidelity synthetic geological models, including realistic seismic reflector migration images, faults, salt bodies, and relative geological time images, is the key for many supervised machine learning methods that aim to delineate faults and other geological properties of interest from seismic migration images. Our package contains two major functionalities: generating 2D synthetic random geological models and generating 3D synthetic random geological models. In each step of the generation process, we set random values for key properties of a geological model to improve the fidelity of the resulting geological model. The package also includes example codes on how to use the random geological model generation subroutines. We name this package RGM – Random Geological Model generation package.

Gao, Kai↗

DOE OSTI2025

Enhancing Gaussian Process Surrogates for Optimization and Posterior Approximation via Random Exploration

This paper proposes novel noise-free Bayesian optimization strategies that rely on a random exploration step to enhance the accuracy of Gaussian process surrogate models. The new algorithms retain the ease of implementation of the classical GP-UCB algorithm, but the additional random exploration step accelerates their convergence, nearly achieving the optimal convergence rate. Furthermore, to facilitate Bayesian inference with intractable likelihoods, we propose to utilize optimization iterates for maximum a posteriori estimation to build a Gaussian process surrogate model for the unnormalized log-posterior density. We provide bounds for the Hellinger distance between the true and the approximate posterior distributions in terms of the number of design points. We demonstrate the effectiveness of our Bayesian optimization algorithms in nonconvex benchmark objective functions, in a machine learning hyperparameter tuning problem, and in a black-box engineering design problem. The effectiveness of our posterior approximation approach is demonstrated in two Bayesian inference problems for parameters of dynamical systems.

Bayesian inference↗

NASA NTRS1972

Control theory for random systems

A survey is presented of the current knowledge available for designing and predicting the effectiveness of controllers for dynamic systems which can be modeled by ordinary differential equations. A short discussion of feedback control is followed by a description of deterministic controller design and the concept of system state. The need for more realistic disturbance models led to the use of stochastic process concepts, in particular the Gauss-Markov process. A compensator controlled system, with random forcing functions, random errors in the measurements, and random initial conditions, is treated as constituting a Gauss-Markov random process; hence the mean-square behavior of the controlled system is readily predicted. As an example, a compensator is designed for a helicopter to maintain it in hover in a gusty wind over a point on the ground.

Bryson, A. E., Jr.↗

NASA NTRS1993

Fuzzy sets predict flexural strength and density of silicon nitride ceramics

In this work, we utilize fuzzy sets theory to evaluate and make predictions of flexural strength and density of NASA 6Y silicon nitride ceramic. Processing variables of milling time, sintering time, and sintering nitrogen pressure are used as an input to the fuzzy system. Flexural strength and density are the output parameters of the system. Data from 273 Si3N4 modulus of rupture bars tested at room temperature and 135 bars tested at 1370 C are used in this study. Generalized mean operator and Hamming distance are utilized to build the fuzzy predictive model. The maximum test error for density does not exceed 3.3 percent, and for flexural strength 7.1 percent, as compared with the errors of 1.72 percent and 11.34 percent obtained by using neural networks, respectively. These results demonstrate that fuzzy sets theory can be incorporated into the process of designing materials, such as ceramics, especially for assessing more complex relationships between the processing variables and parameters, like strength, which are governed by randomness of manufacturing processes.

Cios, Krzysztof J.↗

NASA NTRS1976

Modeling laser velocimeter signals as triply stochastic Poisson processes

Previous models of laser Doppler velocimeter (LDV) systems have not adequately described dual-scatter signals in a manner useful for analysis and simulation of low-level photon-limited signals. At low photon rates, an LDV signal at the output of a photomultiplier tube is a compound nonhomogeneous filtered Poisson process, whose intensity function is another (slower) Poisson process with the nonstationary rate and frequency parameters controlled by a random flow (slowest) process. In the present paper, generalized Poisson shot noise models are developed for low-level LDV signals. Theoretical results useful in detection error analysis and simulation are presented, along with measurements of burst amplitude statistics. Computer generated simulations illustrate the difference between Gaussian and Poisson models of low-level signals.

Mayo, W. T., Jr.↗

DOE OSTI2018

Stationary Distribution of a Stochastic Process

We find a stationary distribution of a stochastic process with delay at the origin. The trajectories of the process have linear growth and random jumps at random times. We use known results for regenerative processes and factorization technique for the study in boundary crossing problems for random walks.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1996

Random root movements in weightlessness

The dynamics of root growth was studied in weightlessness. In the absence of the gravitropic reference direction during weightlessness, root movements could be controlled by spontaneous growth processes, without any corrective growth induced by the gravitropic system. If truly random of nature, the bending behavior should follow so-called 'random walk' mathematics during weightlessness. Predictions from this hypothesis were critically tested. In a Spacelab ESA-experiment, denoted RANDOM and carried out during the IML-2 Shuttle flight in July 1994, the growth of garden cress (Lepidium sativum) roots was followed by time lapse photography at 1-h intervals. The growth pattern was recorded for about 20 h. Root growth was significantly smaller in weightlessness as compared to gravity (control) conditions. It was found that the roots performed spontaneous movements in weightlessness. The average direction of deviation of the plants consistently stayed equal to zero, despite these spontaneous movements. The average squared deviation increased linearly with time as predicted theoretically (but only for 8-10 h). Autocorrelation calculations showed that bendings of the roots, as determined from the 1-h photographs, were uncorrelated after about a 2-h interval. It is concluded that random processes play an important role in root growth. Predictions from a random walk hypothesis as to the growth dynamics could explain parts of the growth patterns recorded. This test of the hypothesis required microgravity conditions as provided for in a space experiment.

STS-65 Shuttle Project↗

NASA NTRS1999

Fidelity Analysis of Sampled Imaging Systems

Many modeling, simulation and performance analysis studies of sampled imaging systems are inherently incomplete because they are conditioned on a discrete-input, discrete-output model that only accounts for blurring during image acquisition and additive noise. For those sampled imaging systems where the effects of digital image acquisition, digital filtering and reconstruction are significant, the modeling, simulation and performance analysis should be based on a more comprehensive continuous-input, discrete-processing, continuous-output end-to-end model. This more comprehensive model should properly account for the low-pass filtering effects of image acquisition prior to sampling, the potentially important noiselike effects of the aliasing caused by sampling, additive noise due to device electronics and quantization, the generally high-boost filtering effects of digital processing, and the low-pass filtering effects of image reconstruction. This model should not, however, be so complex as to preclude significant mathematical analysis, particularly the mean-square (fidelity) type of analysis so common in linear system theory. We demonstrate that, although the mathematics of such a model is more complex, the increase in complexity is not so great as to prevent a complete fidelity-metric analysis at both the component level and at the end-to-end system level: that is, computable mean-square-based fidelity metrics are developed by which both component-level and system-level performance can be quantified. In addition, we demonstrate that system performance can be assessed qualitatively by visualizing the output image as the sum of three component images, each of which relates to a corresponding fidelity metric. The cascaded, or filtered, component accounts for the end-to-end system filtering of image acquisition, digital processing, and image reconstruction; the random noise component accounts for additive random noise, modulated by digital processing and image reconstruction filtering; and the aliased noise component accounts for the frequency folding effect of sampling, modulated by digital processing and image reconstruction filtering.

Park, Stephen K.↗

DOE OSTI2023

Influence of energy density on the microstructure, growth orientation, and anisotropy of magnetic properties in additively manufactured Fe-3.8wt%Si transformer steels

Fe-3.8wt%Si transformer steels were processed using two different additive manufacturing (AM) techniques, laser powder bed fusion (LPBF) and directed energy deposition (DED). While the LPBF processed samples exhibited a strong <001> orientation of the BCC grains along the build axis, the DED processed samples exhibited a randomized texture along the build axis. DED processed samples showed substantially coarser columnar grains as compared to their LPBF counterparts. Here, the columnar grains exhibited a substantial number of low-angle sub-grain boundaries. All samples exhibited very good soft magnetic properties, with saturation magnetization (M s ) values ranging from 205 - 232 emu/gm, and coercivity (H c ) values ranging from 1.2 – 4.2 Oe. The Coercivity (H c ) values were significantly lower when the magnetic field was applied parallel to the build axis, as compared to being perpendicular, which can be rationalized based on the columnar nature of the grains, resulting in a higher number density of grain boundaries in case of the field applied perpendicular to the build axis.

36 MATERIALS SCIENCE↗