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NASA NTRS1989

Parallel and vector computation for stochastic optimal control applications

A general method for parallel and vector numerical solutions of stochastic dynamic programming problems is described for optimal control of general nonlinear, continuous time, multibody dynamical systems, perturbed by Poisson as well as Gaussian random white noise. Possible applications include lumped flight dynamics models for uncertain environments, such as large scale and background random atmospheric fluctuations. The numerical formulation is highly suitable for a vector multiprocessor or vectorizing supercomputer, and results exhibit high processor efficiency and numerical stability. Advanced computing techniques, data structures, and hardware help alleviate Bellman's curse of dimensionality in dynamic programming computations.

Hanson, F. B.↗
NASA NTRS1989

Simultaneous stochastic inversion for geomagnetic main field and secular variation. II - 1820-1980

With the aim of producing readable time-dependent maps of the geomagnetic field at the core-mantle boundary, the method of simultaneous stochastic inversion for the geomagnetic main field and secular variation, described by Bloxham (1987), was applied to survey data from the period 1820-1980 to yield two time-dependent geomagnetic-field models, one for the period 1900-1980 and the other for 1820-1900. Particular consideration was given to the effect of crustal fields on observations. It was found that the existing methods of accounting for these fields as sources of random noise are inadequate in two circumstances: (1) when sequences of measurements are made at one particular site, and (2) for measurements made at satellite altitude. The present model shows many of the features in the earth's magnetic field at the core-mantle boundary described by Bloxham and Gubbins (1985) and supports many of their earlier conclusions.

Bloxham, Jeremy↗
NASA NTRS1991

Structural reliability methods: Code development status

The Probabilistic Structures Analysis Method (PSAM) program integrates state of the art probabilistic algorithms with structural analysis methods in order to quantify the behavior of Space Shuttle Main Engine structures subject to uncertain loadings, boundary conditions, material parameters, and geometric conditions. An advanced, efficient probabilistic structural analysis software program, NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) was developed as a deliverable. NESSUS contains a number of integrated software components to perform probabilistic analysis of complex structures. A nonlinear finite element module NESSUS/FEM is used to model the structure and obtain structural sensitivities. Some of the capabilities of NESSUS/FEM are shown. A Fast Probability Integration module NESSUS/FPI estimates the probability given the structural sensitivities. A driver module, PFEM, couples the FEM and FPI. NESSUS, version 5.0, addresses component reliability, resistance, and risk.

Millwater, Harry R.↗
NASA NTRS2017

Non-Pharmacological Countermeasure to Decrease Landing Sickness and Improve Functional Performance

Upon return from long-duration spaceflight, 100% of crewmembers experience motion sickness (MS) symptoms. The interactions between crewmembers' adaptation to a gravitational transition, the performance decrements resulting from MS and/or use of promethazine (PMZ), and the constraints imposed by mission task demands could significantly challenge and limit an astronaut's ability to perform functional tasks during gravitational transitions. Stochastic resonance (SR) is "noise benefit": adding noise to a system might increase the information (examples to the left and above). Stochastic vestibular stimulation (SVS), or low levels of noise applied to the vestibular system, improves balance and locomotor performance (Goel et al. 2015, Mulavara et al. 2011, 2015). In hemi-lesioned rat models, Samoudi et al. 2012 found that SVS increased GABA release on the lesioned, but not the intact side. Activation of the GABA pathway is important in modulating MS and promoting adaptability (Cohen 2008) and was seen to reverse MS symptoms in rats after unilateral labyrinthectomy (Magnusson et al. 2000). Thus, SVS could be used to promote GABA pathways to reduce MS and promote adaptability, eliminate the need for PMZ or other performance-inhibiting drugs.

Rosenberg, M. J. F.↗
NASA NTRSDate not supplied

A Model for Ice Accretion Roughness Evolution and Spatial Variations

Over the past decade, multiple investigations of ice accretion roughness and spatial variations have been performed in the Icing Research Tunnel (IRT) at the NASA Glenn Research Center. The early investigations used models of NACA 0012 airfoils with different chord sizes and focused on temporal scaling and primary cloud scaling parameters such as stagnation point collection efficiency. Subsequent investigations included the effects of model sweep, airfoil shape, airfoil lifting condition, and freestream static temperature. To develop a predictive model for roughness evolution in generalized icing situations, the maximum roughness values for the airfoils and conditions used in the angle of attack and freestream temperature investigations were scaled to eliminate the temporal variations. LEWICE simulations were employed to identify the local collection efficiency at the locations of maximum roughness, and a two-dimensional panel-method code was used to identify the local static pressure at the location of the maximum roughness. Because of the stochastic nature of ice accretion roughness, a physics-directed approach was employed to develop a multi-dimensional correlation based on the local pressure coefficient, the local total temperature, the cloud properties, and the cloud exposure time. The resulting correlation predictions are compared to ice shapes measured in the IRT for both a 21-in. NACA 0012 airfoil model and a 60-in. HAARP-II model. The resulting predictions indicate that the local freezing fraction must be included in the roughness predictive model. Implications regarding icing heat transfer predictions using the resulting roughness model are also discussed.

Icing↗
NASA NTRS2025

Gaussian Process for Flight Delay Prediction: Learning a Stochastic Process

This paper presents a machine-learning approach to predict flight delays. Whereas neural networks are extensively studied for predictive capabilities, they involve non-intuitive design and extensive analysis, particularly in training and optimization processes. Instead, the proposed framework employs Gaussian Processes as a supervised learning technique for flight delay prediction. This data-driven approach trains the model using prior information, specifically the mean and covariance tied to existing data. The proposed Gaussian Process Regression (GPR) model employs the day of flight as a pivotal feature for delay forecasting. We analyze flights from various routes and gauge the accuracy of the presented learning technique by comparing the predicted delays with the actual ones. Given the inherent challenges in precisely forecasting delays, we predict the delays with a 95 % confidence interval. Also, an error propagation analysis in the prediction horizon is carried out to determine the optimal time frame for prediction. The proposed method for flight delay prediction is important as airlines can strategize flight operations and issue timely advisories.

stochastic↗
NASA NTRS1976

Terminal area guidance along curved paths: A stochastic control approach

Stochastic control theory is applied to the problem of designing a digital flight compensator for terminal guidance along a helical flight path as a prelude to landing. The development of aircraft, wind, and measurement models is discussed along with a control scheme consisting of feedback gains multiplying estimate of the aircraft and wind states obtained from a Kalman one step predictor. Preliminary results are presented which indicate that the compensator performs satisfactorily in the presence of both steady winds and gusts.

Quaranta, J. E.↗
NASA NTRS1977

Set-point control of nonlinear systems

A method of nonlinear stochastic control is applied to the problem of providing set-point control. The procedure is illustrated for a nonlinear second-order plant. The controller design uses a variation of the 'multiple-model adaptive control' approach. Specific problems related to the design are investigated, including learning time and set-point accuracy dependence on the number of approximating models, chord versus tangent approximations, and the a priori Markov switching parameter values. Simulations are provided for different situations under various levels of measurement noise.

Vanlandingham, H. F.↗
NASA NTRS1993

Frequency distributions and correlations of solar X-ray flare parameters

Frequency distributions of flare parameters are determined from over 12,000 solar flares. The flare duration, the peak counting rate, the peak hard X-ray flux, the total energy in electrons, and the peak energy flux in electrons are among the parameters studied. Linear regression fits, as well as the slopes of the frequency distributions, are used to determine the correlations between these parameters. The relationship between the variations of the frequency distributions and the solar activity cycle is also investigated. Theoretical models for the frequency distribution of flare parameters are dependent on the probability of flaring and the temporal evolution of the flare energy build-up. The results of this study are consistent with stochastic flaring and exponential energy build-up. The average build-up time constant is found to be 0.5 times the mean time between flares.

Crosby, Norma B.↗
NASA NTRS1993

The quasi-periodic oscillations and very low frequency noise of Scorpius X-1 as transient chaos - A dripping handrail?

We present evidence that the quasi-periodic oscillations (QPO) and very low frequency noise (VLFN) characteristic of many accretion sources are different aspects of the same physical process. We analyzed a long, high time resolution EXOSAT observation of the low-mass X-ray binary (LMXB) Sco X-1. The X-ray luminosity varies stochastically on time scales from milliseconds to hours. The nature of this variability - as quantified with both power spectrum analysis and a new wavelet technique, the scalegram - agrees well with the dripping handrail accretion model, a simple dynamical system which exhibits transient chaos. In this model both the QPO and VLFN are produced by radiation from blobs with a wide size distribution, resulting from accretion and subsequent diffusion of hot gas, the density of which is limited by an unspecified instability to lie below a threshold.

Scargle, Jeffrey D.↗
NASA NTRS1995

A new approach to the formulation of scalar flux closure

This report shows that if a stochastic differential equation (Langevin equation) for velocity fluctuation vector is known, it is possible to derive the equations for scalar flux transport. Durbin and Speziale (1994) showed that the second moment of this stochastic differential equation gives an equation for the evolution of Reynolds stress tensor. Similarly, the stochastic equation will give an equation for scalar flux. Therefore, a coupling between these two is present. The basis for the present work is that there should be Langevin equations that can produce acceptable models for both the Reynolds stress tensor and the scalar flux vector. Having found this basic Langevin equation, the amount of work needed to model the second order closure problems is reduced; using the well developed models for Reynolds stress equations, it will be possible to derive corresponding models for scalar flux equation.

Shabany, Y.↗
NASA NTRS2017

MS Non-Pharmacological Countermeasure to Decrease Landing Sickness and Improve Functional Performance While Disorientad

Upon return from spaceflight, a majority of crewmembers experience motion sickness (MS) symptoms. The interactions between crewmembers' adaptation to a gravitational transition, the performance decrements resulting from MS and/or use of promethazine (PMZ), and the constraints imposed by mission task demands could significantly challenge and limit an astronaut's ability to perform functional tasks during gravitational transitions. No operational countermeasure currently exists to mitigate the risks associated with these sensorimotor disturbances. Stochastic resonance (SR) can be thought of simply as "noise benefit" or an increase in information transfer by a system when in the presence of a non-zero level of noise. We have shown that low levels of stochastic vestibular stimulation (SVS) improve balance and locomotor performance due to SR (Goel et al. 2015, Mulavara et al. 2011, 2015). Additionally, a study in a 6-hydroxydopamine (6-OHDA) hemi-lesioned rat model of Parkinson's disease demonstrated improvements in locomotor activity after low-level SVS delivery possibly due to an increase in nigral gamma-aminobutyric acid (GABA) release in a dopamine independent way (Samoudi et al. 2012). SVS specifically increased GABA release on the lesioned, but not the intact side. These results suggest that SVS can cause targeted alterations of GABA release to affect performance of functional tasks. Activation of the GABA pathway is important in modulating MS and promoting adaptability (Cohen 2008). Magnusson et al. (2000) supported this finding by showing that the administration of a GABAB agonist caused a reversal of the symptoms that is normally seen after unilateral labyrinthectomy. Thus, GABA could play a significant role in reducing MS and promoting adaptability. We have taken advantage of the SR mechanism as a modulator of neurotransmitters to develop a unique SVS countermeasure system to mitigate MS symptoms and improve functional performance after landing. Healthy subjects (n=20) participated in two test sessions, one in which they received +/-400 microA of SVS and one where they received no stimulation (0 microA); the study design was counterbalanced. Subjects began by performing a series of four functional tasks 3-5 times as baseline measurements of task performance. Then, to induce MS, subjects walked an obstacle course with up-down reversing prisms. If they completed the course before achieving our pre-determined level of MS, they were asked to read a poster while making large up-down head movements to a metronome while still wearing the reversing prism goggles. Subjects were stopped every two minutes and asked to report their MS symptoms. Using the Pensacola Scale for motion sickness, test operators evaluated the level of MS of each subject. Once a subject reached an 8 on this scale, which is equivalent to mild malaise, or 30 minutes had passed since the start of the MS induction, this protocol was stopped. Finally, immediately after MS induction, subjects were asked to complete the four functional tasks again. Although, 100% of our subjects experienced at least one MS symptom, only 55% of our subjects experienced stomach awareness to any degree. Without SVS, only 40% of subjects lasted the full 30-minute MS induction protocol, while 65% of subjects lasted the full 30 minutes with SVS, which is nearly a significant increase (p=0.056). In addition, subjects showed significant improvement from baseline when performing a tandem walk and a prone-to-stand test immediately after the MS induction protocol was stopped but the stimulation level was continued. The results are promising and future work includes comparing MS progression between PMZ and SVS directly in subjects that are provoked to a minimum of nausea. Low levels of SVS stimulation may serve as a non-pharmacological countermeasure to replace or reduce the PMZ dosage requirements and concurrently improve functional performance during transitions to new gravitational environments after spaceflight.

Rosenberg, M. J. F.↗
NASA NTRS1979

Gravitational collapse in dust lanes and the appearance of spiral structure in galaxies

The possibility is considered that there are two types of spiral for each spiral galaxy: an underlying spiral of relatively old stars seen in red and IR photographs and a spiral outlined by H II regions and young bright blue stars. The origin of the first spiral is attributed to large-scale spiral density waves, and the second spiral is identified as a stochastic spiral. It is suggested that there is a physical or causal connection between the two spirals and that dust lanes play the role of intermediary. An analysis is performed which shows that such a model can account for the formation and destruction of giant molecular cloud complexes and for observed spiral structure in one simple unified theory.

Elmegreen, B. G.↗
NASA NTRS1982

On-line methods for rotorcraft aeroelastic mode identification

The requirements for the on-line identification of rotorcraft aeroelastic blade modes from random response test data are presented. A recursive maximum likelihood (RML) technique is used in conjunction with a bandpass filter to identify isolated blade mode damping and frequency. The RML technique is demonstrated to have excellent convergence characteristics in random measurement noise and random process noise excitation. The RML identification technique uses an ARMA representation for the aeroelastic stochastic system and requires virtually no user interaction while providing accurate confidence bands on the parameter estimates. Comparisons are made with an off-line Newton type maximum likelihood algorithm which uses a state variable model representation. Results are presented from simulation random response data which quantify the identifed parameter convergence behavior for various levels of random excitation which is typical of wind tunnel turbulence levels. The RML technique is applied to hingless rotor test data from the NASA Langley Research Center Helicopter Hover Facility.

Molusis, J. A.↗
NASA NTRS1993

On the structure of solar and stellar coronae - Loops and loop heat transport

We discuss the principal constraints on mechanisms for structuring and heating the outer atmospheres - the coronae - of stars. We argue that the essential cause of highly localized heating in the coronae of stars like the sun is the spatially intermittent nature of stellar surface magnetic fields, and that the spatial scale of the resulting coronal structures is related to the spatial structure of the photospheric fields. We show that significant constraints on coronal heating mechanisms derive from the observed variations in coronal emission, and, in addition, show that the observed structuring perpendicular to coronal magnetic fields imposes severe constraints on mechanisms for heat dispersal in the low-beta atmosphere. In particular, we find that most of commonly considered mechanisms for heat dispersal, such as anomalous diffusion due to plasma turbulence or magnetic field line stochasticity, are much too slow to account for the observed rapid heating of coronal loops. The most plausible mechanism appears to be reconnection at the interface between two adjacent coronal flux bundles. Based on a model invoking hyperresistivity, we show that such a mechanism naturally leads to dominance of isolated single bright coronal loops and to bright coronal plasma structures whose spatial scale transverse to the local magnetic field is comparable to observed dimensions of coronal X-ray loops.

Litwin, Christof↗
NASA NTRS1995

Research of Stochastic Robustness: Results and conclusions

With stochastic robustness we are creating tools to design robust compensators for practical systems. During this year, the stochastic robustness research achieved the following results: refined the search tools needed for synthesis; successfully designed robust compensators for the American Controls Conference benchmark problem; and successfully designed robust compensators for a nonlinear hypersonic aircraft model with uncertainties in 28 parameters.

Marrison, Chris↗
NASA NTRS1975

Stochastic process approximation for recursive estimation with guaranteed bound on the error covariance

An approach, is proposed for the design of approximate, fixed order, discrete time realizations of stochastic processes from the output covariance over a finite time interval, was proposed. No restrictive assumptions are imposed on the process; it can be nonstationary and lead to a high dimension realization. Classes of fixed order models are defined, having the joint covariance matrix of the combined vector of the outputs in the interval of definition greater or equal than the process covariance; (the difference matrix is nonnegative definite). The design is achieved by minimizing, in one of those classes, a measure of the approximation between the model and the process evaluated by the trace of the difference of the respective covariance matrices. Models belonging to these classes have the notable property that, under the same measurement system and estimator structure, the output estimation error covariance matrix computed on the model is an upper bound of the corresponding covariance on the real process. An application of the approach is illustrated by the modeling of random meteorological wind profiles from the statistical analysis of historical data.

Menga, G.↗
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), a computer code for probabilistic structural analysis of aerospace components, are described, with an emphasis on the use of NESSUS for reliability and risk assessment. Topics addressed include the structure of probabilistic models of fatigue-crack initiation, risk/cost evaluation, fatigue-fracture analysis, and fatigue-crack initiation. Numerical results from typical applications are presented in graphs and briefly characterized. The usefulness of NESSUS predictions for establishing inspection and retirement schedules and for component certification is indicated.

Shiao, Michael C.↗