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At least 217 records · Page 12

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NASA NTRS1983

Evaluation of a stochastic model of particle dispersion in a turbulent round jet

A stochastic model of particle dispersion by turbulence, proposed by Gosman and Ioannides (1981), is evaluated. The method employs a k-epsilon model to estimate turbulence properties. Dispersion is determined by computing particle motion, with random sampling to obtain instantaneous flow properties for a statistically significant number of particle trajectories. The stochastic model yields good results particularly when eddy lifetimes are evaluated. The method allows the effects of large relative velocities between the particles and the flow, drag properties at Reynolds numbers greater than the Stokes flow regime, and the variations of local turbulence properties to be readily handled, at least for boundary layer flows.

Shuen, J.-S.↗

NASA NTRS1983

A stochastic-dynamic model for the spatial structure of forecast error statistics

The present investigation is concerned with the presentation of a simplified model of the spatial structure of forecast error statistics, a comparison of the model with actual numerical weather prediction results, and the extent to which simplifying assumptions made in the model are justified. A stochastic-dynamic model is derived for the spatial structure of the global atmospheric mass-field forecast error. The model states that the relative potential vorticity of the forecast error is random. The covariance function of the model's solutions is found to be governed by a simple deterministic equation. The agreement between the stochastic model and actual mass-field forecast errors fields for 12-36 h periods validates the assumptions on which the model is derived. Within this period, the difference between the potential voriticity fields of the atmosphere and of the numerical forecasts used in the comparison is well represented by white noise.

Balgovind, R.↗

NASA NTRS1983

Stochastic three-wave interaction in flaring solar loops

A model is proposed for the dynamic structure of high-frequency microwave bursts. The dynamic component is attributed to beams of precipitating electrons which generate electrostatic waves in the upper hybrid branch. Coherent upconversion of the electrostatic waves to electromagnetic waves produces an intrinsically stochastic emission component which is superposed on the gyrosynchrotron continuum generated by stably trapped electron fluxes. The role of the density and temperature of the ambient plasma in the wave growth and the transition of the three wave upconversion to stochastic, despite the stationarity of the energy source, are discussed in detail. The model appears to reproduce the observational features for reasonable parameters of the solar flare plasma.

Vlahos, L.↗

NASA NTRS1984

Guaranteed robustness properties of multivariable nonlinear stochastic optimal regulators

The robustness of optimal regulators for nonlinear, deterministic and stochastic, multi-input dynamical systems is studied under the assumption that all state variables can be measured. It is shown that, under mild assumptions, such nonlinear regulators have a guaranteed infinite gain margin; moreover, they have a guaranteed 50 percent gain reduction margin and a 60 degree phase margin, in each feedback channel, provided that the system is linear in the control and the penalty to the control is quadratic, thus extending the well-known properties of LQ regulators to nonlinear optimal designs. These results are also valid for infinite horizon, average cost, stochastic optimal control problems.

Tsitsiklis, J. N.↗

NASA NTRS1984

Stochastic does not equal ad hoc

Some classes of influential events in solar system history are class-predictable but not event-predictable. Theories of lunar origin should not ignore class-predictable stochastic events. Impacts and close encounters with large objects during planet formation are class-predictable. These stochastic events, such as large impacts that triggered ejection of Earth-mantle material into a circum-Earth cloud, should not be rejected as ad hoc. A way to deal with such events scientifically is to investigate their consequences; if it can be shown that they might produce the Moon, they become viable concepts in theories of lunar origin.

Hartmann, W. K.↗

NASA NTRS1984

Multiobjective optimization in structural design with uncertain parameters and stochastic processes

The application of multiobjective optimization techniques to structural design problems involving uncertain parameters and random processes is studied. The design of a cantilever beam with a tip mass subjected to a stochastic base excitation is considered for illustration. Several of the problem parameters are assumed to be random variables and the structural mass, fatigue damage, and negative of natural frequency of vibration are considered for minimization. The solution of this three-criteria design problem is found by using global criterion, utility function, game theory, goal programming, goal attainment, bounded objective function, and lexicographic methods. It is observed that the game theory approach is superior in finding a better optimum solution, assuming the proper balance of the various objective functions. The procedures used in the present investigation are expected to be useful in the design of general dynamic systems involving uncertain parameters, stochastic process, and multiple objectives.

Rao, S. S.↗

NASA NTRS1984

Analog simulation of stochastic satellite response

A numerical study was performed on the effects of stochastic geometry and random environmental torques on the pointing accuracy of spinning and three-axis stabilized satellites. The Euler equations for the motions of satellites yielded the stochastic principal moments and a Fokker-Planck analog simulation was employed to model the response vector of a rigid satellite. White noise inputs were obtained from a random number generator. Attention was given to both fast and slow spin satellites. Responses grew with time in all cases. The growth was initially exponential and eventually reached stable values. In comparison with other theoretical techniques, the Fokker-Planck model detailed the most responses and showed that spin-stabilization is preferable for satellites with low inertial noise levels.

Huang, T. C.↗

NASA NTRS1985

On the evaluation of expected performance cost for partially observed closed-loop stochastic systems

New methods are presented for evaluating the expected performance cost of partially observed closed-loop stochastic systems. When the variances of the process statistics are small, a linearized model of the closed-loop stochastic system is defined for which the expected cost can be evaluated by recursion on a set of purely deterministic difference equations. When the variances of the process statistics are large, the linearized model can be used in the control variate method of variance reduction for reducing the number of sample paths required for effective Monte Carlo estimation.

Bayard, D. S.↗

NASA NTRS1986

Can stochastic, dissipative wave fields be treated as random walk generators

A suggestion by Meek et al. (1985) that the gravity wave field be viewed as stochastic, with significant nonlinearities, is applied to calculate diffusivities. The purpose here is to calculate the diffusivity for stochastic wave model and compare it with previous diffusivity estimates. The researchers do this for an idealized case in which the wind velocity changes but slowly, and for which saturation is the principal mechanism by which wave energy is lost. A related calculation was given in a very brief way (Weinstock, 1976), but the approximations were not fully justified, nor were the physical pre-suppositions clearly explained. The observations of Meek et al. (1985) have clarified the pre-suppositions for the researchers and provided a rationalization and improvement of the approximations employed.

Weinstock, J.↗

NASA NTRS1987

Active stability augmentation of large space structures: A stochastic control problem

A problem in SCOLE is that of slewing an offset antenna on a long flexible beam-like truss attached to the space shuttle, with rather stringent pointing accuracy requirements. The relevant methodology aspects in robust feedback-control design for stability augmentation of the beam using on-board sensors is examined. It is framed as a stochastic control problem, boundary control of a distributed parameter system described by partial differential equations. While the framework is mathematical, the emphasis is still on an engineering solution. An abstract mathematical formulation is developed as a nonlinear wave equation in a Hilbert space. That the system is controllable is shown and a feedback control law that is robust in the sense that it does not require quantitative knowledge of system parameters is developed. The stochastic control problem that arises in instrumenting this law using appropriate sensors is treated. Using an engineering first approximation which is valid for small damping, formulas for optimal choice of the control gain are developed.

Balakrishnan, A. V.↗

NASA NTRS1987

Stochastic and hybrid-stress plate/shell finite elements for hot-section components

The research effort in the Center for the Advancement of Computational Mechanics at Georgia Tech has two main thrusts. The first of these is the development of special approaches for the numerical stress analysis of solids and structures whose material and geometric properties are uncertain. The second seeks to develop and implement high-efficiency plate and shell elements. The stochastic element method, currently being implemented, will be able to more accurately portray the probabilistic nature of stress, strain, and displacement in actual structures. Current research has provided a hybrid-stress shell element whose behavior is acceptable for aspect ratios as high as 30 to 1. Thus, substantially more complex analyses will be practicable as soon as this element is fully implemented. An additional advantage of the hybrid approach is that it permits more accurate stress-recovery at the upper and lower surfaces of the shell, an important consideration in high thickness-gradient applications. The software associated with the above research is being implemented in the form of extensions to the Nessus code. The hybrid shell element has been successfully tested in several small-deformation elastic analyses. The theoretical formulation of the stochastic elements is essentially complete; its implementation is just beginning.

Atluri, S. N.↗

NASA NTRS1986

A study of the stochastic energization of charged particles with and without synchrotron energy loss

A momentum-diffusion formulation that takes the initial values of the particle distribution functions and momentum-space boundary conditions is presently employed for the computational and analytical study of the stochastic energization of charged particles by plasma waves. The nature of the particle distribution functions resulting from stochastic energization and the validity of the momentum-diffusion formulation for the energization are determined. The validity of the momentum-diffusion formulation with power law diffusion coefficients is assessed.

Borovsky, J. E.↗

NASA NTRS1987

Proof of quasi-adaptivity for the m-measurement feedback class of stochastic control policies

Bounds on expected performance are established which show that the m-measurement feedback (mM) policy for nonlinear stochastic control performs as well or better than the open-loop optimal control policy, and thus is quasi-adaptive in the sense of Witenhausen (1966). The chain of performance inequalities indicate a tendency for the mM policy performance to improve with increasing m. It is suggested that the present analytical method, based on the construction of artificial control sequences denoted as utility controls, can be used to establish performance bounds on other well-known policies, avoiding the extensive Monte Carlo simulations necessary in comparing stochastic control policies.

Bayard, David S.↗

NASA NTRS1987

Stochastic estimation of conditional eddies in turbulent channel flow

Several long-standing issues regarding linear estimation and coherent structures are addressed, and some questions that were addressed partially, but never with the benefit of full, three-dimensional information are answered. The objectives were to: determine how well linear estimates approximate the field obtained by true conditional averaging, using events such as those in quadrant analysis; determine the extent to which the three-dimensional linearly estimated fields correspond to coherent structures, and the degree and manner in which they differ; evaluate the type and nature of the structural information gained by employing several different types of events; and learn more about the 3-D structure of important coherent motions that occur in wall turbulence. The results indicate that linear stochastic estimation can be used effectively in the study of numerical data bases consisting of three-dimensional vector fields, both velocity and vorticity. Two-point stochastic estimation yields more structural information and more detail than single-point estimation. The structures observed occurred repeatedly within the flow, but much can not be said about their dominance or the probability of their occurrence without further systematic studies of their frequency.

Adrian, R. J.↗

NASA NTRS1988

Cometary water on Venus - Implications of stochastic impacts

Attention is given to a Venus water abundance model, incorporating a stochastic cometary source and nonthermal hydrogen escape, that reproduces both the near-steady-state balance between escape loss and infall replenishment implied by Venus' short water lifetime, and the consistency of the observed deuterium-to-hydrogen ratio with a steady state. It is shown that the stochastic variability of each of these quantities is large. Water's quasi-steady state on Venus is judged to be mediated by comet impacts, leading to an obscuration of the early water history of Venus by the history of random impacts.

Grinspoon, David H.↗

NASA NTRS1989

Design Of Combined Stochastic Feedforward/Feedback Control

Methodology accommodates variety of control structures and design techniques. In methodology for combined stochastic feedforward/feedback control, main objectives of feedforward and feedback control laws seen clearly. Inclusion of error-integral feedback, dynamic compensation, rate-command control structure, and like integral element of methodology. Another advantage of methodology flexibility to develop variety of techniques for design of feedback control with arbitrary structures to obtain feedback controller: includes stochastic output feedback, multiconfiguration control, decentralized control, or frequency and classical control methods. Control modes of system include capture and tracking of localizer and glideslope, crab, decrab, and flare. By use of recommended incremental implementation, control laws simulated on digital computer and connected with nonlinear digital simulation of aircraft and its systems.

Halyo, Nesim↗

NASA NTRS1989

Stochastic modeling of crack initiation and short-crack growth under creep and creep-fatigue conditions

A simplified stochastic model is proposed for crack initiation and short-crack growth under creep and creep-fatigue conditions. Material inhomogeneity provides the random nature of crack initiation and early growth. In the model, the influence of microstructure is introduced by the variability of: (1) damage accumulation along grain boundaries, (2) critical damage required for crack initiation or growth, and (3) the grain-boundary length. The probabilities of crack initiation and growth are derived by using convolution integrals. The model is calibrated and used to predict the crack density and crack-growth rate of short cracks of 304 stainless steel under creep and creep-fatigue conditions. The mean-crack initiation lives are predicted to be within an average deviation of about 10 percent from the experimental results. The predicted cumulative distributions of crack-growth rate follow the experimental data closely. The applicability of the simplified stochastic model is discussed and the future research direction is outlined.

Kitamura, Takayuki↗

NASA NTRS1988

Stochastic time-optimal control problems

Two types of stochastic time-optimal controls in a one-dimensional setting are considered. Multidimensional problems, in the case of complete state information available and the system modeled by stochastic differential equations, are studied under the formulation of minimizing the expected transient-response time. The necessary condition of optimality is the satisfaction for the value function of a parabolic partial differential equation with boundary conditions. The sufficient condition of optimality is also provided, based on Dynkin's formula. Finally, three examples are given.

Zhang, W.↗