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NASA NTRS1990

A probabilistic approach to the dynamic analysis of ducts subjected to multibase harmonic and random excitation

The dynamic behavior of the discharge duct of the high-pressure oxidizer turbopump of a cryogenic rocket motor is investigated analytically. The probabilistic analysis program NESSUS (Numerical Evaluation of Stochastic Structures Under Stress; Cruse et al., 1988) is used to treat the uncertainties due to random and harmonic excitation (e.g., pump noise, pump-induced harmonics, and combustion noise), variations in engine inlet pressure, and changes in system damping. The load modeling procedure, the variation in power-spectral density in different zones of the engine structure, and the dynamic structural-analysis technique are described, and the numerical results of the NESSUS analysis are presented in extensive tables and graphs and discussed in detail.

Debchaudhury, Amit↗

NASA NTRS1996

Effect of Dust Coagulation Dynamics on the Geometry of Aggregates

Master equation gives a more fundamental description of stochastic coagulation processes rather than popular Smoluchowski's equation. In order to examine the effect of the dynamics on the geometry of resulting aggregates, we study Master equation with a rigorous Monte Carlo algorithm. It is found that Cluster-Cluster aggregation model is a good approximation of orderly growth and the aggregates have fluffy structures with a fractal dimension approx. 2. A scaling analysis of Smoluchowski's equation also supports this conclusion.

Nakamura, R.↗

NASA NTRS1996

Possible effects of protracted exposure on the additivity of risks from space radiations

Conventional radiation risk assessments are presently based on the additivity assumption. This assumption states that risks from individual components of a complex radiation field involving many different types of radiation can be added to yield the total risk of the complex radiation field. If the assumption is not correct, the summations and integrations performed to obtain the presently quoted risk estimates are not appropriate. This problem is particularly important in the area of space radiation risk evaluation because of the many different types of high- and low-LET radiation present in the galactic cosmic ray environment. For both low- and high-LET radiations at low enough dose rates, the present convention is that the addivity assumption holds. Mathematically, the total risk, Rtot is assumed to be Rtot = summation (i) Ri where the summation runs over the different types of radiation present. If the total dose (or fluence) from each component is such that the interaction between biological lesions caused by separate single track traversals is negligible within a given cell, it is presently considered to be reasonable to accept the additivity assumption. However, when the exposure is protracted over many cell doubling times (as will be the case for extended missions to the moon or Mars), the possibility exists that radiation effects that depend on multiple cellular events over a long time period, such as is probably the case in radiation-induced carcinogenesis, may not be additive in the above sense and the exposure interval may have to be included in the evaluation procedure. It is shown, however, that "inverse" dose-rate effects are not expected from intermediate LET radiations arising from the galactic cosmic ray environment due to the "sensitive-window-in-the-cell-cycle" hypothesis.

NASA Discipline Number 45-10↗

NASA NTRSDate not supplied

Co-Optimization of Navigation System Requirements and Trajectory Design Using a Sweeping Gradient Method and Linear Covariance Analysis

We describe the application of a sweeping gradient method for ordinary differential equations with events (SGM) and linear covariance analysis (LinCov) to the co-optimization of navigation system requirement generation and robust trajectory design. SGM is a method for computing the gradient of trajectory analyses defined by performance indices over initial value problems with events with respect to static parameters. LinCov is an analytic technique for predicting stochastic behavior of dynamical systems. By combining SGM and LinCov, it is possible use efficient, off-the-shelf, gradient-based optimizers to solve a combined robust optimal trajectory and navigation system design problem. In this paper, we formulate the required models to apply the combined SGM and LinCov techniques to a Near-Rectilinear Halo Orbit rendezvous approach scenario and show results for several intermediate problems.

Benjamin W L Margolis↗

NASA NTRS1992

Distance estimation and collision prediction for on-line robotic motion planning

An efficient method for computing the minimum distance and predicting collisions between moving objects is presented. This problem is incorporated into the framework of an in-line motion-planning algorithm to satisfy collision avoidance between a robot and moving objects modeled as convex polyhedra. In the beginning, the deterministic problem where the information about the objects is assumed to be certain is examined. L(1) or L(infinity) norms are used to represent distance and the problem becomes a linear programming problem. The stochastic problem is formulated where the uncertainty is induced by sensing and the unknown dynamics of the moving obstacles. Two problems are considered: First, filtering of the distance between the robot and the moving object at the present time. Second, prediction of the minimum distance in the future in order to predict the collision time.

Kyriakopoulos, K. J.↗

NASA NTRS2016

Uncertainty Assessment of the NASA Earth Exchange Global Daily Downscaled Climate Projections (NEX-GDDP) Dataset

The NASA Earth Exchange Global Daily Downscaled Projections (NEX-GDDP) dataset is comprised of downscaled climate projections that are derived from 21 General Circulation Model (GCM) runs conducted under the Coupled Model Intercomparison Project Phase 5 (CMIP5) and across two of the four greenhouse gas emissions scenarios (RCP4.5 and RCP8.5). Each of the climate projections includes daily maximum temperature, minimum temperature, and precipitation for the periods from 1950 through 2100 and the spatial resolution is 0.25 degrees (approximately 25 km x 25 km). The GDDP dataset has received warm welcome from the science community in conducting studies of climate change impacts at local to regional scales, but a comprehensive evaluation of its uncertainties is still missing. In this study, we apply the Perfect Model Experiment framework (Dixon et al. 2016) to quantify the key sources of uncertainties from the observational baseline dataset, the downscaling algorithm, and some intrinsic assumptions (e.g., the stationary assumption) inherent to the statistical downscaling techniques. We developed a set of metrics to evaluate downscaling errors resulted from bias-correction ("quantile-mapping"), spatial disaggregation, as well as the temporal-spatial non-stationarity of climate variability. Our results highlight the spatial disaggregation (or interpolation) errors, which dominate the overall uncertainties of the GDDP dataset, especially over heterogeneous and complex terrains (e.g., mountains and coastal area). In comparison, the temporal errors in the GDDP dataset tend to be more constrained. Our results also indicate that the downscaled daily precipitation also has relatively larger uncertainties than the temperature fields, reflecting the rather stochastic nature of precipitation in space. Therefore, our results provide insights in improving statistical downscaling algorithms and products in the future.

climate projection↗

NASA NTRS1997

Visual signal detection in structured backgrounds. II. Effects of contrast gain control, background variations, and white noise

Studies of visual detection of a signal superimposed on one of two identical backgrounds show performance degradation when the background has high contrast and is similar in spatial frequency and/or orientation to the signal. To account for this finding, models include a contrast gain control mechanism that pools activity across spatial frequency, orientation and space to inhibit (divisively) the response of the receptor sensitive to the signal. In tasks in which the observer has to detect a known signal added to one of M different backgrounds grounds due to added visual noise, the main sources of degradation are the stochastic noise in the image and the suboptimal visual processing. We investigate how these two sources of degradation (contrast gain control and variations in the background) interact in a task in which the signal is embedded in one of M locations in a complex spatially varying background (structured background). We use backgrounds extracted from patient digital medical images. To isolate effects of the fixed deterministic background (the contrast gain control) from the effects of the background variations, we conduct detection experiments with three different background conditions: (1) uniform background, (2) a repeated sample of structured background, and (3) different samples of structured background. Results show that human visual detection degrades from the uniform background condition to the repeated background condition and degrades even further in the different backgrounds condition. These results suggest that both the contrast gain control mechanism and the background random variations degrade human performance in detection of a signal in a complex, spatially varying background. A filter model and added white noise are used to generate estimates of sampling efficiencies, an equivalent internal noise, an equivalent contrast-gain-control-induced noise, and an equivalent noise due to the variations in the structured background.

NASA Discipline Space Human Factors↗

NASA NTRS1990

A methodology for evaluating the reliability and risk of structures under complex service environments

The theoretical basis and numerical implementation of NESSUS (Numerical Evaluation of Stochastic Structures Under Stress; Cruse et al., 1988), a computer code for probabilistic structural analyses of aerospace components, are described, with an emphasis on the use of NESSUS for reliability and risk assessment. Topics addressed include the structure of NESSUS, the material-properties model, computational procedures, probabilistic models of fatigue-crack initiation, risk/cost evaluation, fatigue-fracture analyses, and fatigue-crack propagation. Numerical results from typical applications are presented in extensive graphs and briefly characterized; the usefulness of NESSUS predictions for establishing inspection and retirement schedules and for component certification is indicated.

Shiao, Michael C.↗

NASA NTRS1989

Probability of failure and risk assessment of propulsion structural components

The probabilistic structural analysis method (PSAM) was developed to analyze the effects of fluctuating loads, variable material properties, and uncertain analytical models especially for high performance structures such as the Space Shuttle Main Engine turbopump blades. Risk is calculated after expensive service experience. However, probabilistic structural analysis provides a rational alternative method to quantify uncertainties in the structural performance and durability. NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) was developed as a probabilistic structural analysis computer code which integrates finite element methods and reliability algorithms, capable to predicting the probability distributions of structural response variables such as stress, displacement, natural frequencies, and buckling loads. This computer code is detailed.

Shiao, Michael C.↗

NASA NTRS1996

Fluid Stochastic Petri Nets: Theory, Applications, and Solution

In this paper we introduce a new class of stochastic Petri nets in which one or more places can hold fluid rather than discrete tokens. We define a class of fluid stochastic Petri nets in such a way that the discrete and continuous portions may affect each other. Following this definition we provide equations for their transient and steady-state behavior. We present several examples showing the utility of the construct in communication network modeling and reliability analysis, and discuss important special cases. We then discuss numerical methods for computing the transient behavior of such nets. Finally, some numerical examples are presented.

Horton, Graham↗

NASA NTRS1998

Ocean Turbulence V: Mesoscale Modeling in Level Coordinates. The Effect of Random Nature of Density

The main result of this paper is the derivation of a new expression for the tracer subgrid term in level coordinates S(l) to be employed in O-GCM. The novel feature is the proper account of the random nature of the density field which strongly affects the transformation from isopycnal to level coordinates of the variables of interest, velocity and tracer fields, their correlation functions and ultimately the subgrid terms. In deriving our result we made use of measured properties of vertical ocean turbulence. The major new results are: 1) the new subgrid expression is different from that of the heuristic GM model, 2) u++(tracer)=1/2u+(thickness), where u++ and u+ are the tracer and thickness bolus velocities. In previous models, u++ = u+, 2) the subgrid for a tracer tau is not the same as that for the density rho even when one accounts for the obvious absence of a diffusion term in the latter. The difference stems from a new treatment of the stochastic nature of the density, 3) the mesoscale diffusivity enters both locally and non-locally, as the integral over all z's from the bottom of the ocean to the level z.

Canuto, V. M.↗

NASA NTRS2010

VLBI Analysis with the Multi-Technique Software GEOSAT

GEOSAT is a multi-technique geodetic analysis software developed at Forsvarets Forsknings Institutt (Norwegian defense research establishment). The Norwegian Mapping Authority has now installed the software and has, together with Forsvarets Forsknings Institutt, adapted the software to deliver datum-free normal equation systems in SINEX format. The goal is to be accepted as an IVS Associate Analysis Center and to provide contributions to the IVS EOP combination on a routine basis. GEOSAT is based on an upper diagonal factorized Kalman filter which allows estimation of time variable parameters like the troposphere and clocks as stochastic parameters. The tropospheric delays in various directions are mapped to tropospheric zenith delay using ray-tracing. Meteorological data from ECMWF with a resolution of six hours is used to perform the ray-tracing which depends both on elevation and azimuth. Other models are following the IERS and IVS conventions. The Norwegian Mapping Authority has submitted test SINEX files produced with GEOSAT to IVS. The results have been compared with the existing IVS combined products. In this paper the outcome of these comparisons is presented.

Kierulf, Halfdan Pascal↗

NASA NTRS2011

Mesh-Based Entry Vehicle and Explosive Debris Re-Contact Probability Modeling

The risk to a crewed vehicle arising from potential re-contact with fragments from an explosive breakup of any jettisoned spacecraft segments during entry has long sought to be quantified. However, great difficulty lies in efficiently capturing the potential locations of each fragment and their collective threat to the vehicle. The method presented in this paper addresses this problem by using a stochastic approach that discretizes simulated debris pieces into volumetric cells, and then assesses strike probabilities accordingly. Combining spatial debris density and relative velocity between the debris and the entry vehicle, the strike probability can be calculated from the integral of the debris flux inside each cell over time. Using this technique it is possible to assess the risk to an entry vehicle along an entire trajectory as it separates from the jettisoned segment. By decoupling the fragment trajectories from that of the entry vehicle, multiple potential separation maneuvers can then be evaluated rapidly to provide an assessment of the best strategy to mitigate the re-contact risk.

McPherson, Mark A.↗

NASA NTRS1979

Aircraft adaptive learning control

The optimal control theory of stochastic linear systems is discussed in terms of the advantages of distributed-control systems, and the control of randomly-sampled systems. An optimal solution to longitudinal control is derived and applied to the F-8 DFBW aircraft. A randomly-sampled linear process model with additive process and noise is developed.

Lee, P. S. T.↗

NASA NTRS1993

Q-Markov covariance equivalent realization and its application to flexible structure identification

The Q-Markov covariance equivalent realization algorithm is applied to NASA's Minimast structure to identify state-space models for the purpose of designing closed-loop controllers, and laboratory test results are shown for the identification and for the closed-loop performance. The paper also presents for the first time a deterministic formulation of covariance parameters from a pulse response, a stochastic formulation of Markov parameters from a white-noise response, and a simple Q-Markov covariance equivalent realization formulation. This requires only pulse laboratory tests or only white-noise laboratory tests to generate Q-Markov covariance equivalent realizations.

Liu, Ketao↗

NASA NTRS1991

A Scheduling Algorithm for Replicated Real-Time Tasks

We present an algorithm for scheduling real-time periodic tasks on a multiprocessor system under fault-tolerant requirement. Our approach incorporates both the redundancy and masking technique and the imprecise computation model. Since the tasks in hard real-time systems have stringent timing constraints, the redundancy and masking technique are more appropriate than the rollback techniques which usually require extra time for error recovery. The imprecise computation model provides flexible functionality by trading off the quality of the result produced by a task with the amount of processing time required to produce it. It therefore permits the performance of a real-time system to degrade gracefully. We evaluate the algorithm by stochastic analysis and Monte Carlo simulations. The results show that the algorithm is resilient under hardware failures.

Yu, Albert C.↗

NASA NTRS2003

Transition-Sensitized Turbulence Models for Compressible and Incompressible Flows

During the grant period from January 1,2002 to December 31,2002 work was carried out on three projects to extend the range of applicability of advanced turbulence models. First, a new transition-sensitized turbulence model was tested and refined. Second, the influence of compressibility on the pressure-strain rate correlation was studied. Third, the relationship between time-filtered large eddy simulation (TLES) and Reynolds-averaged Navier Stokes (RANS) modeling was investigated leading to submission of the article. The transition-sensitized turbulence model encompasses the early-stage transition and turbulent flow regimes describing the evolution of the ensemble mean disturbance energy and dissipation rate. It is founded on a consistent mathematical description of the laminar regime with its linear disturbances and the fully turbulent regime with its stochastic fluctuations. The unified description is provided by the ensemble viewpoint.

Thacker, William D.↗

NASA NTRS1994

Statistical mechanics in biology: how ubiquitous are long-range correlations?

The purpose of this opening talk is to describe examples of recent progress in applying statistical mechanics to biological systems. We first briefly review several biological systems, and then focus on the fractal features characterized by the long-range correlations found recently in DNA sequences containing non-coding material. We discuss the evidence supporting the finding that for sequences containing only coding regions, there are no long-range correlations. We also discuss the recent finding that the exponent alpha characterizing the long-range correlations increases with evolution, and we discuss two related models, the insertion model and the insertion-deletion model, that may account for the presence of long-range correlations. Finally, we summarize the analysis of long-term data on human heartbeats (up to 10(4) heart beats) that supports the possibility that the successive increments in the cardiac beat-to-beat intervals of healthy subjects display scale-invariant, long-range "anti-correlations" (a tendency to beat faster is balanced by a tendency to beat slower later on). In contrast, for a group of subjects with severe heart disease, long-range correlations vanish. This finding suggests that the classical theory of homeostasis, according to which stable physiological processes seek to maintain "constancy," should be extended to account for this type of dynamical, far from equilibrium, behavior.

Non-NASA Center↗