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NASA NTRS1987

NESSUS/expert and NESSUS/FPI in the Probabilistic Structural Analysis Methods (PSAM) program

The Numerical Evaluation of Stochastic Structures under Stress (NESSUS) is the primary computer code being developed in the NASA Probabilistic Structural Analysis Methods (PSAM) project. It consists of four modules NESSUS/EXPERT, NESSUS/FPI, NESSUS/PRE and NESSUS/FEM. This presentation concentrates on EXPERT and FPI. To provide an effective interface between NESSUS and the user, an expert system module called NESSUS/EXPERT is being developed. That system uses the CLIPS artificial intelligence code developed to NASA-JSC. The code is compatible with FORTRAN, the standard language for codes in PSAM. The user interacts with the CLIPS inference engine, which is linked to the knowledge database. The perturbation database generated by NESSUS/FEM and managed in EXPERT is used to develop the so-called response or performance model in the random variables. Two independent probabilistic methods are available in PSAM for the computation of the probabilistic structural response. These are the Fast Probability Integration (FPI) method and Monte Carlo simulation. FPI is classified as an advanced reliability method and has been developed over the past ten years by researchers addressing the reliability of civil engineering structures. Monte Carlo is a well-established technique for computing probabilities by conducting a number of deterministic analyses with specified input distributional information.

Burnside, O. H.↗

NASA NTRS1998

Attitude/attitude-rate estimation from GPS differential phase measurements using integrated-rate parameters

A sequential filtering algorithm is presented for attitude and attitude-rate estimation from Global Positioning System (GPS) differential carrier phase measurements. A third-order, minimal-parameter method for solving the attitude matrix kinematic equation is used to parameterize the filter's state, which renders the resulting estimator computationally efficient. Borrowing from tracking theory concepts, the angular acceleration is modeled as an exponentially autocorrelated stochastic process, thus avoiding the use of the uncertain spacecraft dynamic model. The new formulation facilitates the use of aiding vector observations in a unified filtering algorithm, which can enhance the method's robustness and accuracy. Numerical examples are used to demonstrate the performance of the method.

Oshman, Yaakov↗

NASA NTRS1997

Vector Observation-Aided/Attitude-Rate Estimation Using Global Positioning System Signals

Oshman, Yaakov↗

NASA NTRS2003

The Aeronautical Data Link: Decision Framework for Architecture Analysis

A decision analytic approach that develops optimal data link architecture configuration and behavior to meet multiple conflicting objectives of concurrent and different airspace operations functions has previously been developed. The approach, premised on a formal taxonomic classification that correlates data link performance with operations requirements, information requirements, and implementing technologies, provides a coherent methodology for data link architectural analysis from top-down and bottom-up perspectives. This paper follows the previous research by providing more specific approaches for mapping and transitioning between the lower levels of the decision framework. The goal of the architectural analysis methodology is to assess the impact of specific architecture configurations and behaviors on the efficiency, capacity, and safety of operations. This necessarily involves understanding the various capabilities, system level performance issues and performance and interface concepts related to the conceptual purpose of the architecture and to the underlying data link technologies. Efficient and goal-directed data link architectural network configuration is conditioned on quantifying the risks and uncertainties associated with complex structural interface decisions. Deterministic and stochastic optimal design approaches will be discussed that maximize the effectiveness of architectural designs.

Morris, A. Terry↗

NASA NTRS2009

Extending Newtonian Dynamics to Include Stochastic Processes

A paper presents further results of continuing research reported in several previous NASA Tech Briefs articles, the two most recent being Stochastic Representations of Chaos Using Terminal Attractors (NPO-41519), [Vol. 30, No. 5 (May 2006), page 57] and Physical Principle for Generation of Randomness (NPO-43822) [Vol. 33, No. 5 (May 2009), page 56]. This research focuses upon a mathematical formalism for describing post-instability motions of a dynamical system characterized by exponential divergences of trajectories leading to chaos (including turbulence as a form of chaos). The formalism involves fictitious control forces that couple the equations of motion of the system with a Liouville equation that describes the evolution of the probability density of errors in initial conditions. These stabilizing forces create a powerful terminal attractor in probability space that corresponds to occurrence of a target trajectory with probability one. The effect in configuration space (ordinary three-dimensional space as commonly perceived) is to suppress exponential divergences of neighboring trajectories without affecting the target trajectory. As a result, the post-instability 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.

Zak, Michail↗

NASA NTRS1988

A few parts in 10 to the 8th geodetic baseline repeatablity in the Gulf of California using the Global Positioning System

GPS geodetic measurements of 350-650 km baselines across the Pacific-North America plate boundary in the Gulf of California are presented. The analysis employs a four-station U.S. fiducial network and combined carrier phase and pseudorange data. Water vapor radiometer data at the Gulf sites are used to calibrate the GPS signal for wet tropospheric path delays. Residual tropospheric delays are modeled as first-order exponentially correlated stochastic processes. The measurement precision for horizontal components is a few parts in 10 to the 8th or better.

Tralli, David M.↗

NASA NTRS1999

GCR Transport in the Brain: Assessment of Self-Shielding, Columnar Damage, and Nuclear Reactions on Cell Inactivation Rates

Radiation shield design is driven by the need to limit radiation risks while optimizing risk reduction with launch mass/expense penalties. Both limitation and optimization objectives require the development of accurate and complete means for evaluating the effectiveness of various shield materials and body-self shielding. For galactic cosmic rays (GCR), biophysical response models indicate that track structure effects lead to substantially different assessments of shielding effectiveness relative to assessments based on LET-dependent quality factors. Methods for assessing risk to the central nervous system (CNS) from heavy ions are poorly understood at this time. High-energy and charge (HZE) ion can produce tissue events resulting in damage to clusters of cells in a columnar fashion, especially for stopping heavy ions. Grahn (1973) and Todd (1986) have discussed a microlesion concept or model of stochastic tissue events in analyzing damage from HZE's. Some tissues, including the CNS, maybe sensitive to microlesion's or stochastic tissue events in a manner not illuminated by either conventional dosimetry or fluence-based risk factors. HZE ions may also produce important lateral damage to adjacent cells. Fluences of high-energy proton and alpha particles in the GCR are many times higher than HZE ions. Behind spacecraft and body self-shielding the ratio of protons, alpha particles, and neutrons to HZE ions increases several-fold from free-space values. Models of GCR damage behind shielding have placed large concern on the role of target fragments produced from tissue atoms. The self-shielding of the brain reduces the number of heavy ions reaching the interior regions by a large amount and the remaining light particle environment (protons, neutrons, deuterons. and alpha particles) may be the greatest concern. Tracks of high-energy proton produce nuclear reactions in tissue, which can deposit doses of more than 1 Gv within 5 - 10 cell layers. Information on rates of cell killing from GCR, including patterns of cell killing from single particle tracks. can provide useful information on expected differences between proton and HZE tracks and clinical experiences with photon irradiation. To model effects on cells in the brain, it is important that transport models accurately describe changes in the GCR due to interactions in the cranium and proximate tissues. We describe calculations of the attenuated GCR particle fluxes at three dose-points in the brain and associated patterns of cell killing using biophysical models. The effects of the brain self-shielding and bone-tissue interface of the skull in modulating the GCR environment are considered. For each brain dose-point, the mass distribution in the surrounding 4(pi) solid angle is characterized using the CAM model to trace 512 rays. The CAM model describes the self-shielding by converting the tissue distribution to mass-equivalent aluminum, and nominal values of spacecraft shielding is considered. Particle transport is performed with the proton, neutron, and heavy-ion transport code HZETRN with the nuclear fragmentation model QMSFRG. The distribution of cells killed along the path of individual GCR ions is modeled using in vitro cell inactivation data for cells with varying sensitivity. Monte Carlo simulations of arrays of inactivated cells are considered for protons and heavy ions and used to describe the absolute number of cell killing events of various magnitude in the brain from the GCR. Included are simulations of positions of inactivated cells from stopping heavy ions and nuclear stars produced by high-energy ions most importantly, protons and neutrons.

Shavers, M. R.↗

NASA NTRSDate not supplied

Computational Investigation of Oxidative Etch Pitting in FiberForm and Its Impact on Material Properties

Oxidation-driven carbon erosion does not occur uniformly but rather through the development of localized etch pits at active surface sites. These active sites form due to atomic defects on the carbon surface, making them significantly more reactive than the surrounding, non-defective areas. As a result, these sites are the first to react during ablation, leading to their removal. This process creates new defects in neighboring atoms, increasing their reactivity and causing localized carbon removal around these active sites. In this way, the highly reactive defective areas serve as nucleation points for the formation and growth of etch pits, which can have adverse effects on structural integrity of FiberForm. To better understand how these etch pits impact the material properties of carbon fiber microstructures, we have developed a new capability within the direct simulation Monte Carlo (DSMC) framework to capture the etch pit formation process. This capability, integrated into the DSMC code SPARTA (Stochastic Parallel Rarefied-gas Time-accurate Analyzer), models material removal in the presence of active sites, leading to the formation of etch pits. The current work focuses on studying the effects of these etch pits on the material properties of FiberForm, a widely used base material in thermal protection systems (TPS). The microstructure of virgin FiberForm, obtained via X-ray microtomography, is imported into SPARTA to generate the ablated geometries with etch pits. These modified microstructures are then analyzed using the Porous Microstructure Analysis (PuMA) software to compute various material properties, including elasticity, thermal conductivity, and permeability. We investigate the variation of these properties due to the complex surface topology changes caused by etch pit formation. Additionally, we compare the effects of pitting with the conventional model of shrinking fibers, traditionally used to simulate the ablation of carbon structures. Significant differences emerge between the two approaches. Consequently, this physically realistic model of material removal through etch pit formation offers improved accuracy in predicting the degradation of carbon-based TPS during oxidation. It also provides insights into other mechanisms, such as spallation, where chunks of material are removed into the flow due to etch pit growth. Ultimately, this model enhances our understanding of failure modes in these materials during ablation.

PuMA↗

NASA NTRSDate not supplied

Uncertainty Quantification using Deep Ensembles for Decision Making in Cyber-Physical-Human Systems

In this paper and its companion, Differential Equation Approximation Using Gradient-Boosted Quantile Regression, Robison et al., we examine an approach to quantifying model uncertainty with the aim of increasing the trustworthiness of computational models in human-machine interactions. In Differential Equation Approximation Using Gradient-Boosted Quantile Regression, we focus on gradient-boosted decision trees, while in this one, we give more details about deep ensembles. Uncertainty quantification is crucial for building trustworthy autonomous decision-making agents in human-machine teams. There are two types of uncertainties: aleatoric and epistemic. The former is related to the inherent stochasticity (noise) of the process, whereas the latter is associated with the lack of knowledge or representation capability of models, such as neural networks. By lack of knowledge, we mean the model’s inability to accurately predict outputs for all possible inputs. The aleatory uncertainty can be estimated fairly easily with, for example, filters, whereas epistemic uncertainty is challenging to compute. This paper uses deep ensembles to quantify both aleatory and epistemic uncertainty. It can act as an uncertainty-aware surrogate transition model for decision-making frameworks. "Uncertainty-aware" means that the surrogate transition model should make predictions along with confidence in those predictions. In the context of decision-making, the transition models are ordinary differential equations (ODEs). Since ODEs can be simulated to make one-step or multi-step predictions, a good surrogate model for them should perform reasonably well in both modes. In a multi-step approach, the trajectory sampling method TS∞ was used to propagate uncertainty over multiple steps. The cartpole dynamical system was selected to demonstrate the ability of deep ensembles as good surrogate transition models for decision-making frameworks. The deep ensembles modeled the dynamics of cartpole ODEs and made uncertainty-aware predictions in single-step and multi-step transition modes.

CPH systems↗

NASA NTRS1982

Design of analytical failure detection using secondary observers

The problem of designing analytical failure-detection systems (FDS) for sensors and actuators, using observers, is addressed. The use of observers in FDS is related to the examination of the n-dimensional observer error vector which carries the necessary information on possible failures. The problem is that in practical systems, in which only some of the components of the state vector are measured, one has access only to the m-dimensional observer-output error vector, with m or = to n. In order to cope with these cases, a secondary observer is synthesized to reconstruct the entire observer-error vector from the observer output error vector. This approach leads toward the design of highly sensitive and reliable FDS, with the possibility of obtaining a unique fingerprint for every possible failure. In order to keep the observer's (or Kalman filter) false-alarm rate under a certain specified value, it is necessary to have an acceptable matching between the observer (or Kalman filter) models and the system parameters. A previously developed adaptive observer algorithm is used to maintain the desired system-observer model matching, despite initial mismatching or system parameter variations. Conditions for convergence for the adaptive process are obtained, leading to a simple adaptive law (algorithm) with the possibility of an a priori choice of fixed adaptive gains. Simulation results show good tracking performance with small observer output errors, while accurate and fast parameter identification, in both deterministic and stochastic cases, is obtained.

Sisar, M.↗

NASA NTRS1991

Generalized Covariance Analysis For Remote Estimators

Technique developed to predict true covariance of stochastic process at remote location when control applied to process both by autonomous (local-estimator) control subsystem and remote (non-local-estimator) control subsystem. Intended orginally for design and evaluation of ground-based schemes for estimation of gyro parameters of Magellan spacecraft. Applications include variety of remote-control systems with and without delays. Potential terrestrial applications include navigation and control of industrial processes.

Boone, Jack N.↗

NASA NTRS1998

Empirical correction for earth sensor horizon radiance variation

A major limitation on the use of infrared horizon sensors for attitude determination is the variability of the height of the infrared Earth horizon. This variation includes a climatological component and a stochastic component of approximately equal importance. The climatological component shows regular variation with season and latitude. Models based on historical measurements have been used to compensate for these systematic changes. The stochastic component is analogous to tropospheric weather. It can cause extreme, localized changes that for a period of days, overwhelm the climatological variation. An algorithm has been developed to compensate partially for the climatological variation of horizon height and at least to mitigate the stochastic variation. This method uses attitude and horizon sensor data from spacecraft to update a horizon height history as a function of latitude. For spacecraft that depend on horizon sensors for their attitudes (such as the Total Ozone Mapping Spectrometer-Earth Probe-TOMS-EP) a batch least squares attitude determination system is used. It is assumed that minimizing the average sensor residual throughout a full orbit of data results in attitudes that are nearly independent of local horizon height variations. The method depends on the additional assumption that the mean horizon height over all latitudes is approximately independent of season. Using these assumptions, the method yields the latitude dependent portion of local horizon height variations. This paper describes the algorithm used to generate an empirical horizon height. Ideally, an international horizon height database could be established that would rapidly merge data from various spacecraft to provide timely corrections that could be used by all.

Hashmall, Joseph A.↗

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

Optimal Control via Self-Generated Stochasticity

The problem of global maxima of functionals has been examined. Mathematical roots of local maxima are the same as those for a much simpler problem of finding global maximum of a multi-dimensional function. The second problem is instability even if an optimal trajectory is found, there is no guarantee that it is stable. As a result, a fundamentally new approach is introduced to optimal control based upon two new ideas. The first idea is to represent the functional to be maximized as a limit of a probability density governed by the appropriately selected Liouville equation. Then, the corresponding ordinary differential equations (ODEs) become stochastic, and that sample of the solution that has the largest value will have the highest probability to appear in ODE simulation. The main advantages of the stochastic approach are that it is not sensitive to local maxima, the function to be maximized must be only integrable but not necessarily differentiable, and global equality and inequality constraints do not cause any significant obstacles. The second idea is to remove possible instability of the optimal solution by equipping the control system with a self-stabilizing device. The applications of the proposed methodology will optimize the performance of NASA spacecraft, as well as robot performance.

Zak, Michail↗

NASA NTRS1977

Information distribution in distributed microprocessor based flight control systems

This paper presents an optimal control theory that accounts for variable time intervals in the information distribution to control effectors in a distributed microprocessor based flight control system. The theory is developed using a linear process model for the aircraft dynamics and the information distribution process is modeled as a variable time increment process where, at the time that information is supplied to the control effectors, the control effectors know the time of the next information update only in a stochastic sense. An optimal control problem is formulated and solved that provides the control law that minimizes the expected value of a quadratic cost function. An example is presented where the theory is applied to the control of the longitudinal motions of the F8-DFBW aircraft. Theoretical and simulation results indicate that, for the example problem, the optimal cost obtained using a variable time increment Markov information update process where the control effectors know only the past information update intervals and the Markov transition mechanism is almost identical to that obtained using a known uniform information update interval.

Montgomery, R. C.↗

NASA NTRS1985

H I properties of dwarf irregular galaxies in the Virgo Cluster

A neutral hydrogen survey was carried out at Arecibo on 91 dwarf irregular galaxies, with morphological types Sdm through Im, in and around the direction of the Virgo Cluster. Only nine of these were found to be background galaxies, and 19 remain undetected, i.e., most of the candidate galaxies are indeed members of the Virgo Cluster or Supercluster. The distribution of positions and systemic velocities (compared with large spirals) shows no evidence for mass segregation. The H I depletion for dwarfs in the cluster core is only moderate, no more than for spirals. The magnitude-velocity width correlation is continous from spirls to dwarfs. Satistics on H I masses agree only partially with a simple stochastic star formation model.

Hoffman, G. L.↗

NASA NTRS1987

A statistical rain attenuation prediction model with application to the advanced communication technology satellite project. Part 2: Theoretical development of a dynamic model and application to rain fade durations and tolerable control delays for fade countermeasures

A dynamic rain attenuation prediction model is developed for use in obtaining the temporal characteristics, on time scales of minutes or hours, of satellite communication link availability. Analagous to the associated static rain attenuation model, which yields yearly attenuation predictions, this dynamic model is applicable at any location in the world that is characterized by the static rain attenuation statistics peculiar to the geometry of the satellite link and the rain statistics of the location. Such statistics are calculated by employing the formalism of Part I of this report. In fact, the dynamic model presented here is an extension of the static model and reduces to the static model in the appropriate limit. By assuming that rain attenuation is dynamically described by a first-order stochastic differential equation in time and that this random attenuation process is a Markov process, an expression for the associated transition probability is obtained by solving the related forward Kolmogorov equation. This transition probability is then used to obtain such temporal rain attenuation statistics as attenuation durations and allowable attenuation margins versus control system delay.

Manning, Robert M.↗

NASA NTRS1993

Solar flux forecasting using mutual information with an optimal delay

Solar flux F(sub 10.7) directly affects the atmospheric density, thereby changing the lifetime and prediction of satellite orbits. For this reason, accurate forecasting of F(sub 10.7) is crucial for orbit determination of spacecraft. Our attempts to model and forecast F(sub 10.7) uncovered highly entangled dynamics. We concluded that the general lack of predictability in solar activity arises from its nonlinear nature. Nonlinear dynamics allow us to predict F(sub 10.7) more accurately than is possible using stochastic methods for time scales shorter than a characteristic horizon, and with about the same accuracy as using stochastic techniques when the forecasted data exceed this horizon. The forecast horizon is a function of two dynamical invariants: the attractor dimension and the Lyapunov exponent. In recent years, estimation of the attractor dimension reconstructed from a time series has become an important tool in data analysis. In calculating the invariants of the system, the first necessary step is the reconstruction of the attractor for the system from the time-delayed values of the time series. The choice of the time delay is critical for this reconstruction. For an infinite amount of noise-free data, the time delay can, in principle, be chosen almost arbitrarily. However, the quality of the phase portraits produced using the time-delay technique is determined by the value chosen for the delay time. Fraser and Swinney have shown that a good choice for this time delay is the one suggested by Shaw, which uses the first local minimum of the mutual information rather than the autocorrelation function to determine the time delay. This paper presents a refinement of this criterion and applies the refined technique to solar flux data to produce a forecast of the solar activity.

Ashrafi, S.↗