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At least 91 records · Page 5

Stochastic robustness synthesis for a benchmark problem

Stochastic robustness analysis guides the synthesis of robust linear quadratic Gaussian (LQG) regulators for a benchmark control problem. Probabilities of exceeding allowable design limits, including stability, setting time, and control usage, are estimated by Monte Carlo evaluation. Robust, low-gain compensators that fulfill objectives are designed by numerically minimizing quadratic functions of these probabilities. The method is straightforward and makes use of uncomplicated design principles.

Stengel, Robert F.↗

Radiative transfer calculated from a Markov chain formalism

The theory of Markov chains is used to formulate the radiative transport problem in a general way by modeling the successive interactions of a photon as a stochastic process. Under the minimal requirement that the stochastic process is a Markov chain, the determination of the diffuse reflection or transmission from a scattering atmosphere is equivalent to the solution of a system of linear equations. This treatment is mathematically equivalent to, and thus has many of the advantages of, Monte Carlo methods, but can be considerably more rapid than Monte Carlo algorithms for numerical calculations in particular applications. We have verified the speed and accuracy of this formalism for the standard problem of finding the intensity of scattered light from a homogeneous plane-parallel atmosphere with an arbitrary phase function for scattering. Accurate results over a wide range of parameters were obtained with computation times comparable to those of a standard 'doubling' routine. The generality of this formalism thus allows fast, direct solutions to problems that were previously soluble only by Monte Carlo methods. Some comparisons are made with respect to integral equation methods.

Esposito, L. W.↗

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↗

Stochastic treatment of electron multiplication without scattering in dielectrics

By treating the emission of optical phonons as a Markov process, a simple analytic method is developed for calculating the electronic ionization rate per unit length for dielectrics. The effects of scattering from acoustic and optical phonons are neglected. The treatment obtains universal functions in recursive form, the theory depending on only two dimensionless energy ratios. A comparison of the present work with other numerical approaches indicates that the effect of scattering becomes important only when the electric potential energy drop in a mean free path for optical-phonon emission is less than about 25% of the ionization potential. A comparison with Monte Carlo results is also given for Teflon.

Lin, D. L.↗

A performability solution method for degradable nonrepairable systems

The present performability model-solving algorithm identifies performance with 'reward', representing the state behavior of a system S by a finite-state stochastic process and determining reward by means of reward rates that are associated with the states of the base model. A general method is obtained for determining the probability distribution function of the performance (reward) variable, and therefore the performability, of the corresponding system. This is done for bounded utilization periods, and the result is an integral expression which is either analytically or numerically solvable.

Furchtgott, D. G.↗

Probabilistic structural analysis computer code (NESSUS)

Probabilistic structural analysis has been developed to analyze the effects of fluctuating loads, variable material properties, and uncertain analytical models especially for high performance structures such as SSME turbopump blades. The computer code NESSUS (Numerical Evaluation of Stochastic Structure Under Stress) was developed to serve as a primary computation tool for the characterization of the probabilistic structural response due to the stochastic environments by statistical description. The code consists of three major modules NESSUS/PRE, NESSUS/FEM, and NESSUS/FPI. NESSUS/PRE is a preprocessor which decomposes the spatially correlated random variables into a set of uncorrelated random variables using a modal analysis method. NESSUS/FEM is a finite element module which provides structural sensitivities to all the random variables considered. NESSUS/FPI is Fast Probability Integration method by which a cumulative distribution function or a probability density function is calculated.

Shiao, Michael C.↗

A linear stochastic model of the human operator

A linear stochastic model of the human operator is developed and applied to the problem of piloted control of an aircraft. The pilot and aircraft are modeled as linear time-invariant systems containing both process and measurement noise. The loop closure by the pilot is determined by formulating the problem as an optimal stochastic control problem. The solution to the optimal control problem yields not only the pilot's optimal control output which he uses to control the vehicle, but also the optimal combination of his observations of the vehicle states upon which the pilot bases his control. A method is presented so that, using experimental pilot vehicle data, the cost functional which is minimized in the optimal control problem will be numerically equal to the pilot rating that the pilot would associate with the given vehicle and task.

Durrett, J. C.↗

Buckling of structures; Proceedings of the Symposium, Harvard University, Cambridge, Mass., June 17-21, 1974

The papers deal with such topics as the buckling and post-buckling behavior of plates and shells; methods of calculating critical buckling and collapse loads; finite element representations for thin-shell instability analysis; theory and experiment in the creep buckling of plates and shells; creep instability of thick shell structures; analytical and numerical studies of the influence of initial imperfections on the elastic buckling of columns; mode interaction in stiffened panels under compression; imperfection-sensitivity in the interactive buckling of stiffened plates; buckling of stochastically imperfect structures; and the Liapunov stability of elastic dynamic systems. A special chapter is devoted to design problems, including the design of a Mars entry 'aeroshell', and buckling design in vehicle structures. Individual items are announced in this issue.

Budiansky, B.↗

LES, DNS and RANS for the analysis of high-speed turbulent reacting flows

The purpose of this research is to continue our efforts in advancing the state of knowledge in large eddy simulation (LES), direct numerical simulation (DNS), and Reynolds averaged Navier Stokes (RANS) methods for the computational analysis of high-speed reacting turbulent flows. In the second phase of this work, covering the period 1 Sep. 1993 - 1 Sep. 1994, we have focused our efforts on two research problems: (1) developments of 'algebraic' moment closures for statistical descriptions of nonpremixed reacting systems, and (2) assessments of the Dirichlet frequency in presumed scalar probability density function (PDF) methods in stochastic description of turbulent reacting flows. This report provides a complete description of our efforts during this past year as supported by the NASA Langley Research Center under Grant NAG1-1122.

Givi, Peyman↗

Creep life prediction based on stochastic model of microstructurally short crack growth

A nondimensional model of microstructurally short crack growth in creep is developed based on a detailed observation of the creep fracture process of 304 stainless steel. In order to deal with the scatter of small crack growth rate data caused by microstructural inhomogeneity, a random variable technique is used in the model. A cumulative probability of the crack length at an arbitary time, G(bar a, bar t), and that of the time when a crack reaches an arbitary length, F(bar t, bar a), are obtained numerically by means of a Monte Carlo method. G(bar a, bar t), and F(bar t, bar a) are the probabilities for a single crack. However, multiple cracks generally initiate on the surface of a smooth specimen from the early stage of creep life to the final stage. TAking into account the multiple crack initiations, the actual crack length distribution observed on the surface of a specimen is predicted by the combination of probabilities for a single crack. The prediction shows a fairly good agreement with the experimental result for creep of 304 stainless steel at 923 K. The probability of creep life is obtained from an assumption that creep fracture takes place when the longest crack reaches a critical length. The observed and predicted scatter of the life is fairly small for the specimens tested.

Kitamura, Takayuki↗

Creep life prediction based on stochastic model of microstructurally short crack growth

A nondimensional model of microstructurally short crack growth in creep is developed based on a detailed observation of the creep fracture process of 304 stainless steel. In order to deal with the scatter of small crack growth rate data caused by microstructural inhomogeneity, a random variable technique is used in the model. A cumulative probability of the crack length at an arbitrary time, G(bar a, bar t), and that of the time when a crack reaches an arbitrary length, F(bar t, bar a), are obtained numerically by means of a Monte Carlo method. G(bar a, bar t), and F(bar t, bar a) are the probabilities for a single crack. However, multiple cracks generally initiate on the surface of a smooth specimen from the early stage of creep life to the final stage. Taking into account the multiple crack initiations, the actual crack length distribution observed on the surface of a specimen is predicted by the combination of probabilities for a single crack. The prediction shows a fairly good agreement with the experimental result for creep of 304 stainless steel at 923 K. The probability of creep life is obtained from an assumption that creep fracture takes place when the longest crack reaches a critical length. The observed and predicted scatter of the life is fairly small for the specimens tested.

Kitamura, Takayuki↗

Alterations of the climate of a primitive equation model produced by filtering approximations and subsequent tuning and stochastic forcing

A comparison is made of the simulated climates of nonlinear models based on the primitive equations (PE), balance equations (BE), and quasi-geostrophic (QG) equations. The models and numerical procedures are identical in all possible respects. The models are highly truncated spectral forms of Lorenz's (1960) energy preserving two-layer model. Two means of making use of the information contained in the (presumed known) short-term prediction error statistics are investigated. An unrealistically high level of thermal forcing is used so that the model climates are sufficiently different to allow any improvements due to the empirical methods to be observed. The general tuning problem is outlined and the QG model is tuned, using data obtained from a PE model run, to minimize the mean squared short term prediction error.

Hoffman, R. N.↗

Towards Comprehensive Variation Models for Designing Vehicle Monitoring Systems

When designing vehicle vibration monitoring systems for aerospace devices, it is common to use well-established models of vibration features to determine whether failures or defects exist. Most of the algorithms used for failure detection rely on these models to detect significant changes in a flight environment. In actual practice, however, most vehicle vibration monitoring systems are corrupted by high rates of false alarms and missed detections. This crucial roadblock makes their implementation in real vehicles (e.g., helicopter transmissions and aircraft engines) difficult, making their operation costly and unreliable. Research conducted at the NASA Ames Research Center has determined that a major reason for the high rates of false alarms and missed detections is the numerous sources of statistical variations that are not taken into account in the modeling assumptions. In this paper, we address one such source of variations, namely, those caused during the design and manufacturing of rotating machinery components that make up aerospace systems. We present a novel way of modeling the vibration response by including design variations via probabilistic methods. Using such models, we develop a methodology to account for design and manufacturing variations, and explore the changes in the vibration response to determine its stochastic nature. We explore the potential of the methodology using a nonlinear cam-follower model, where the spring stiffness values are assumed to follow a normal distribution. The results demonstrate initial feasibility of the method, showing great promise in developing a general methodology for designing more accurate aerospace vehicle monitoring systems.

McAdams, Daniel A.↗

Numerical simulation of a turbulent flame stabilized behind a rearward-facing step

Flow of combustible mixtures in a plane channel past a smooth contraction followed by an abrupt expansion, in a typical dump combustor configuration, is modeled by a two-dimensional numerical technique based on the random vortex method. Both the inert and the reacting case are considered. In the latter, the flame is treated as an interface, self-advancing at a prescribed normal burning speed, while the dynamic effects of expansion due to the exothermicity of combustion are expressed by volumetric source lines delineated by its front. Solutions are shown to be in satisfactory agreement with experimental results, especially with respect to global properties such as the average velocity profiles and the reattachment length. The stochastic turbulent velocity components manifest interesting differences, especially near the walls where three-dimensional effects of turbulence are expected to be of importance.

Hsiao, C. C.↗

Distributed state-space generation of discrete-state stochastic models

High-level formalisms such as stochastic Petri nets can be used to model complex systems. Analysis of logical and numerical properties of these models of ten requires the generation and storage of the entire underlying state space. This imposes practical limitations on the types of systems which can be modeled. Because of the vast amount of memory consumed, we investigate distributed algorithms for the generation of state space graphs. The distributed construction allows us to take advantage of the combined memory readily available on a network of workstations. The key technical problem is to find effective methods for on-the-fly partitioning, so that the state space is evenly distributed among processors. In this paper we report on the implementation of a distributed state-space generator that may be linked to a number of existing system modeling tools. We discuss partitioning strategies in the context of Petri net models, and report on performance observed on a network of workstations, as well as on a distributed memory multi-computer.

Ciardo, Gianfranco↗

Feedback control for unsteady flow and its application to the stochastic Burgers equation

The study applies mathematical methods of control theory to the problem of control of fluid flow with the long-range objective of developing effective methods for the control of turbulent flows. Model problems are employed through the formalism and language of control theory to present the procedure of how to cast the problem of controlling turbulence into a problem in optimal control theory. Methods of calculus of variations through the adjoint state and gradient algorithms are used to present a suboptimal control and feedback procedure for stationary and time-dependent problems. Two types of controls are investigated: distributed and boundary controls. Several cases of both controls are numerically simulated to investigate the performances of the control algorithm. Most cases considered show significant reductions of the costs to be minimized. The dependence of the control algorithm on the time-descretization method is discussed.

Choi, Haecheon↗

A general rough-surface inversion algorithm: Theory and application to SAR data

Rough-surface inversion has significant applications in interpretation of SAR data obtained over bare soil surfaces and agricultural lands. Due to the sparsity of data and the large pixel size in SAR applications, it is not feasible to carry out inversions based on numerical scattering models. The alternative is to use parameter estimation techniques based on approximate analytical or empirical models. Hence, there are two issues to be addressed, namely, what model to choose and what estimation algorithm to apply. Here, a small perturbation model (SPM) is used to express the backscattering coefficients of the rough surface in terms of three surface parameters. The algorithm used to estimate these parameters is based on a nonlinear least-squares criterion. The least-squares optimization methods are widely used in estimation theory, but the distinguishing factor for SAR applications is incorporating the stochastic nature of both the unknown parameters and the data into formulation, which will be discussed in detail. The algorithm is tested with synthetic data, and several Newton-type least-squares minimization methods are discussed to compare their convergence characteristics. Finally, the algorithm is applied to multifrequency polarimetric SAR data obtained over some bare soil and agricultural fields. Results will be shown and compared to ground-truth measurements obtained from these areas. The strength of this general approach to inversion of SAR data is that it can be easily modified for use with any scattering model without changing any of the inversion steps. Note also that, for the same reason it is not limited to inversion of rough surfaces, and can be applied to any parameterized scattering process.

Moghaddam, M.↗

An APL program for the distribution of energy deposition by charged particles passing through thin absorbers

An APL program which numerically evaluates the probability density function (PDF) for the energy deposited in a thin absorber by a charged particle is proposed, with application to the construction, pointing, and control of spacecraft. With this program, the PDF of the restricted energy loss distribution of Watts (1973) is derived, and Vavilov's (1957) distribution is obtained by proper parameter selection. The method is demonstrated with the example of the effect of charged particle induced radiation on the Hubble Space Telescope (HST) pointing accuracy. A Monte Carlo study simulates the photon noise caused by charged particles passing through the photomultiplier tube window, and the stochastic variation of energy loss is introduced into the simulation by generating random energy losses from a power law distribution. The program eliminates annoying loop procedures, and model parameter sensitivity can be studied using the graphical output.

Howell, L. W.↗