Estimation of the parameters of sampled-data systems by means of stochastic approximation.
Stochastic approximation applied to sampled data system parameters including sampling interval
Bekey, G. A.↗
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Estimation of the mean of a discrete parameter, covariance stationary, stochastic process in rotation sampling
Constrained optimization procedure for deriving linear estimator of population mean in rotation sampling
Nishikawa, K.-Y.↗
Design techniques - Stochastic controllers
Analytic techniques aid in the design of nearly optimal linear time-varying sampled-data stochastic controllers. The techniques also aid in the simplification and automation of program designing for control computers.
Widnall, W. S.↗
Relationships Among Intrinsic Properties of Ordinary Chondrites: Oxidation State, Bulk Chemistry, Oxygen-isotopic Composition, Petrologic Type, and Chondrule Size
The properties of ordinary chondrites (OC) reflect both nebular and asteroidal processes. OC are modeled here as having acquired nebular water, probably contained within phyllosilicates, during agglomeration. This component had high Ai70 and acted like an oxidizing agent during thermal metamorphism. The nebular origin of this component is consistent with negative correlations in H, L, and LL chondrites between oxidation state (represented by olivine Fa) and bulk concentration ratios of elements involved in the metal-silicate fractionation (e.g., NdSi, Ir/Si, Ir/Mn, Ir/Cr, Ir/Mg, Ni/Mg, As/Mg, Ga/Mg). LL chondrites acquired the greatest abundance of phyllosilicates with high (delta)O-17 among OC (and thus became the most oxidized group and the one with the heaviest O isotopes); H chondrites acquired the lowest abundance, becoming the most reduced OC group with the lightest O isotopes. Chondrule precursors may have grown larger and more ferroan with time in each OC agglomeration zone. Nebular turbulence may have controlled the sizes of chondrule precursors. H-chondrite chondrules (which are the smallest among OC) formed from the smallest precursors. In each OC region, low-FeO chondrules formed before high-FeO chondrules during repeated episodes of chondrule formation. During thermal metamorphism, phyllosilicates were dehydrated; the liberated water oxidized metallic Fe-Ni. This caused correlated changes with petrologic type including decreases in the modal abundance of metal, increases in olivine Fa and low-Ca pyroxene Fs, increases in the olivine/pyroxene ratio, and increases in the kamacite Co and Ni contents. As water (with its heavy 0 isotopes) was lost during metamorphism, inverse correlations between bulk (delta)O-18 and bulk (delta)O-17 with petrologic type were produced. The H5 chondrites that were ejected from their parent body approx.7.5 Ma ago during a major impact event probably had been within a few kilometers of each other since they accreted approx.4.5 Ga ago. There are significant differences in the olivine compositional distributions among these rocks; these reflect stochastic nebular sampling of the oxidant (Le., phyllosilicates with high (delta)O-17) on a 0.1-1 km scale during agglomeration.
Rubin, Alan E.↗
Path Planning: Differential Dynamic Programming and Model Predictive Path Integral Control on VTOL Aircraft
This paper explores two optimal control approaches, widely used in robotics, to establish their viability as real-time trajectory planners for vehicle configurations envisioned for the emerging aviation sector of Urban Air Mobility (UAM). Differential Dynamic Programming (DDP) enables planning over highly nonlinear dynamics using second-order approximations along a nominal trajectory, and displays quadratic convergence to a local solution. Model Predictive Path Integral (MPPI) is a stochastic sampling-based algorithm that can optimize for general cost criteria, including potentially highly nonlinear formulations, and supports parallel computation through the use of modern GPU hardware. In this work, DDP and MPPI were implemented using model predictive control (MPC), and the results indicate they are able to successfully transition the aircraft over different flight envelopes and generate trajectories unique to UAM vehicles.
Differential Dynamic Programming↗
Sampling error study for rainfall estimate by satellite using a stochastic model
In a parameter study of satellite orbits, sampling errors of area-time averaged rain rate due to temporal sampling by satellites were estimated. The sampling characteristics were studied by accounting for the varying visiting intervals and varying fractions of averaging area on each visit as a function of the latitude of the grid box for a range of satellite orbital parameters. The sampling errors were estimated by a simple model based on the first-order Markov process of the time series of area averaged rain rates. For a satellite of nominal Tropical Rainfall Measuring Mission (Thiele, 1987) carrying an ideal scanning microwave radiometer for precipitation measurements, it is found that sampling error would be about 8 to 12 pct of estimated monthly mean rates over a grid box of 5 X 5 degrees. It is suggested that an observation system based on a low inclination satellite combined with a sunsynchronous satellite simultaneously might be the best candidate for making precipitation measurements from space.
Shin, Kyung-Sup↗
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↗
A Fast Monte Carlo Method for Model-Based Prognostics Based on Stochastic Calculus
This work proposes a fast Monte Carlo method to solve differential equations utilized in model-based prognostics. The methodology is derived from the theory of stochastic calculus, and the goal of such a method is to speed up the estimation of the probability density functions describing the independent variable evolution over time. In the prognostic scenarios presented in this paper, the stochastic differential equations describe variables directly or indirectly related to the degradation of a monitored system. The method allows the estimation of the probability density functions by solving the deterministic equation and approximating the stochastic integrals using samples of the model noise. By so doing, the prognostic problem is solved without the Monte Carlo simulation based on Euler's forward method, which is typically the most time consuming task of the prediction stage. Three different prognostic scenarios are presented as proof of concept: (i) life prediction of electrolytic capacitors, (ii) remaining time to discharge of Lithium-ion batteries, and (iii) prognostic of cracked structures under fatigue loading. The paper shows how the method produces probability density functions that are statistically indistinguishable from the distributions estimated with Euler's forward Monte Carlo simulation. However, the proposed solution is orders of magnitude faster when computing the time-to-failure distribution of the monitored system. The approach may enable complex real-time prognostics and health management solutions with limited computing power.
stochastic calculus↗
On the representation of a continuous stochastic intensity by Poisson shot noise
Poisson shot noise process relationship with continuous stochastic intensity as sample function
Gagliardi, R. M.↗
Application of multipoint measurements for flow characterization
Some of the possibilities for inferring the structure of complicated flows from simultaneous measurements at many points are reviewed. Conditional sampling, pseudoflow visualization, stochastic estimation, and the proper orthogonal decomposition are briefly reviewed and illustrated by example. Resolution criteria for multipoint spatial arrays are proposed that minimize the possibilities for misinterpreting the data.
Glauser, Mark N.↗
Resilience: Concepts and Measures
Inertia, the resistance of an ecosystem property to change under stress, is distinguished from resilience, which refers to the degree, manner. and pace of change or recovery in ecosystem properties following disturbance. In turn, these two terms are differentiated from 'stability'. which is used here to refer to the pattern of natural fluctuation in ecosystem properties in the absence of major exogenous disturbance. Four component attributes of resilience are reviewed in the context of Mediterranean-climate examples. The elasticity component concerns the rate of recovery of an ecosystem property following disturbance; amplitude, the threshold of stress beyond which recovery to the initial state does not occur; hysteresis, the degree to which the pattern of recovery after stress differs from that of deterioration under chronic stress, and malleability the ease with which the ecosystem can become permanently altered. Each ecosystem property will typically reveal a different level of resilience to a given stress and stressor. The degree of recovery should not be expected to be complete in any event, due to sample variability and stochastic events. In cyclicallystable ecosystems, the pattern of recovery should be measured in light of this periodicity, and short-term (within-cycle) recovery distinguished from long-term (between-cycle) recovery. The prediction of resilience properties of ecosystems can be approached through a knowledge of the modular structure of foodwebs, through knowledge of the autecological adaptations of key species to the stressor, or through cumulative experience of the response to disturbance at the community level. At present there is much room for investigation of each of these approaches in Mediterranean-climate ecosystems.
Westman, Walter E.↗
A Fast Monte Carlo Method for Model-Based Prognostics Based on Stochastic Calculus
This work proposes a fast Monte Carlo method to solve differential equations utilized in model-based prognostics. The methodology is derived from the theory of stochastic calculus, and the goal of such a method is to speed up the estimation of the probability density functions describing the independent variable evolution over time. In the prognostic scenarios presented in this paper, the stochastic differential equations describe variables directly or indirectly related to the degradation of a monitored system. The method allows the estimation of the probability density functions by solving the deterministic equation and approximating the stochastic integrals using samples of the model noise. By so doing, the prognostic problem is solved without the Monte Carlo simulation based on Euler's forward method, which is typically the most time consuming task of the prediction stage. Three different prognostic scenarios are presented as proof of concept: (i) life prediction of electrolytic capacitors, (ii) remaining time to discharge of Lithium-ion batteries, and (iii) prognostic of cracked structures under fatigue loading. The paper shows how the method produces probability density functions that are statistically indistinguishable from the distributions estimated with Euler's forward Monte Carlo simulation. However, the proposed solution is orders of magnitude faster when computing the time-to-failure distribution of the monitored system. The approach may enable complex real-time prognostics and health management solutions with limited computing power.
Corbetta, M.↗
Interplanetary dust particles collected from the stratosphere: Physical, chemical, and mineralogical properties and implications for their sources
The suggestion that significant quantities of interplanetary dust are produced by both main-belt asteroids and comets is based on the Infrared Astronomical Satellite (IRAS) detection of dust trails or bands associated with these objects. Gravitational focusing strongly biases all near-Earth collections of interplanetary dust in favor of particles with the lowest geocentric velocities, that is the dust from main-belt asteroids spiraling into the Sun under the influence of Poynting-Robertson radiation drag. The major dust bands in the main-belt appear to be associated with the catastrophic disruptions which produced the Eos, Themis and Koronis families of asteroids. If dust particles are produced in the catastrophic collision process, then Poynting-Robertson radiation drag is such an efficient transport mechanism from the main-belt to 1 AU that near-Earth collections of interplanetary dust should include, and perhaps be dominated by, this material. Interplanetary dust particles from 5 to 100 micrometers in diameter have been recovered from the stratosphere of the Earth by NASA sampling aircraft since the mid-1970s. The densities of a large fraction of these interplanetary dust particles are significantly lower than the densities of their constituent silicate mineral phases, indicating significant porosites. The majority of the particles are chemically and mineralogically similar to, but not identical to, the carbonaceous chondrite meteorites. Most stony interplanetary dust particles have carbon contents exceeding those of Allende, a carbonaceous chondrite meteorite having a low albedo. Higher albedo particles corresponding to S-type asteroids are underrepresented or absent from the stratospheric collections, and primitive carbonaceous particles seem to be overrepresented in the stratospheric collections compared to the fraction of main-belt asteroids classified as primitive. This suggests that much of the interplanetary dust may be generated by a stochastic process, probably preferentially sampling a few most recent collisional events.
Flynn, George J.↗
Modeling Common-Sense Decisions in Artificial Intelligence
A methodology has been conceived for efficient synthesis of dynamical models that simulate common-sense decision- making processes. This methodology is intended to contribute to the design of artificial-intelligence systems that could imitate human common-sense decision making or assist humans in making correct decisions in unanticipated circumstances. This methodology is a product of continuing research on mathematical models of the behaviors of single- and multi-agent systems known in biology, economics, and sociology, ranging from a single-cell organism at one extreme to the whole of human society at the other extreme. Earlier results of this research were reported in several prior NASA Tech Briefs articles, the three most recent and relevant being Characteristics of Dynamics of Intelligent Systems (NPO -21037), NASA Tech Briefs, Vol. 26, No. 12 (December 2002), page 48; Self-Supervised Dynamical Systems (NPO-30634), NASA Tech Briefs, Vol. 27, No. 3 (March 2003), page 72; and Complexity for Survival of Living Systems (NPO- 43302), NASA Tech Briefs, Vol. 33, No. 7 (July 2009), page 62. The methodology involves the concepts reported previously, albeit viewed from a different perspective. One of the main underlying ideas is to extend the application of physical first principles to the behaviors of living systems. Models of motor dynamics are used to simulate the observable behaviors of systems or objects of interest, and models of mental dynamics are used to represent the evolution of the corresponding knowledge bases. For a given system, the knowledge base is modeled in the form of probability distributions and the mental dynamics is represented by models of the evolution of the probability densities or, equivalently, models of flows of information. Autonomy is imparted to the decisionmaking process by feedback from mental to motor dynamics. This feedback replaces unavailable external information by information stored in the internal knowledge base. Representation of the dynamical models in a parameterized form reduces the task of common-sense-based decision making to a solution of the following hetero-associated-memory problem: store a set of m predetermined stochastic processes given by their probability distributions in such a way that when presented with an unexpected change in the form of an input out of the set of M inputs, the coupled motormental dynamics converges to the corresponding one of the m pre-assigned stochastic process, and a sample of this process represents the decision.
Zak, Michail↗
Wind power prediction models
Investigations were performed to predict the power available from the wind at the Goldstone, California, antenna site complex. The background for power prediction was derived from a statistical evaluation of available wind speed data records at this location and at nearby locations similarly situated within the Mojave desert. In addition to a model for power prediction over relatively long periods of time, an interim simulation model that produces sample wind speeds is described. The interim model furnishes uncorrelated sample speeds at hourly intervals that reproduce the statistical wind distribution at Goldstone. A stochastic simulation model to provide speed samples representative of both the statistical speed distributions and correlations is also discussed.
Levy, R.↗
Sampling errors for satellite-derived tropical rainfall - Monte Carlo study using a space-time stochastic model
Estimates of monthly average rainfall based on satellite observations from a low earth orbit will differ from the true monthly average because the satellite observes a given area only intermittently. This sampling error inherent in satellite monitoring of rainfall would occur even if the satellite instruments could measure rainfall perfectly. The size of this error is estimated for a satellite system being studied at NASA, the Tropical Rainfall Measuring Mission (TRMM). First, the statistical description of rainfall on scales from 1 to 1000 km is examined in detail, based on rainfall data from the Global Atmospheric Research Project Atlantic Tropical Experiment (GATE). A TRMM-like satellite is flown over a two-dimensional time-evolving simulation of rainfall using a stochastic model with statistics tuned to agree with GATE statistics. The distribution of sampling errors found from many months of simulated observations is found to be nearly normal, even though the distribution of area-averaged rainfall is far from normal. For a range of orbits likely to be employed in TRMM, sampling error is found to be less than 10 percent of the mean for rainfall averaged over a 500 x 500 sq km area.
Bell, Thomas L.↗
Identification of human operator models by stochastic approximation
Human operator models parameter estimation by stochastic approximation, considering continuous and sampled data models
Bekey, G. A.↗
Metal-Poor, Strongly Star-Forming Galaxies in the DEEP2 Survey: The Relationship Between Stellar Mass, Temperature-Based Metallicity, and Star Formation Rate
We report on the discovery of 28 redshift (z) approximately equal to 0.8 metal-poor galaxies in DEEP2. These galaxies were selected for their detection of the weak [O (sub III)] lambda 4363 emission line, which provides a "direct" measure of the gas-phase metallicity. A primary goal for identifying these rare galaxies is to examine whether the fundamental metallicity relation (FMR) between stellar mass, gas metallicity, and star formation rate (SFR) holds for low stellar mass and high SFR galaxies. The FMR suggests that higher SFR galaxies have lower metallicity (at fixed stellar mass). To test this trend, we combine spectroscopic measurements of metallicity and dust-corrected SFR with stellar mass estimates from modeling the optical photometry. We find that these galaxies are 1.05 plus or minus 0.61 dex above the redshift (z) approximately 1 stellar mass-SFR relation and 0.23 plus or minus 0.23 dex below the local mass-metallicity relation. Relative to the FMR, the latter offset is reduced to 0.01 dex, but significant dispersion remains dex with 0.16 dex due to measurement uncertainties). This dispersion suggests that gas accretion, star formation, and chemical enrichment have not reached equilibrium in these galaxies. This is evident by their short stellar mass doubling timescale of approximately equal to 100 (sup plus 310) (sub minus 75) million years which suggests stochastic star formation. Combining our sample with other redshift (z) of approximately 1 metal-poor galaxies, we find a weak positive SFR-metallicity dependence (at fixed stellar mass) that is significant at 94.4 percent confidence. We interpret this positive correlation as recent star formation that has enriched the gas but has not had time to drive the metal-enriched gas out with feedback mechanisms.
Metal-Poor↗