Search NASA⌕ Search

SEARCH · Search NASA

Results for “random processes”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Nonstationary envelope process and first excursion probability

A definition of the envelope of nonstationary random processes is proposed. The establishment of the envelope definition makes it possible to simulate the nonstationary random envelope directly. Envelope statistics, such as the density function, joint density function, moment function, and level crossing rate, which are relevent to analyses of catastrophic failure, fatigue, and crack propagation in structures, are derived. Applications of the envelope statistics to the prediction of structural reliability under random loadings are discussed in detail.

Yang, J.↗
NASA NTRS1997

Fade Dynamics and Its Evolution: The Other Part of the Acts Rain Prediction Model

The inception of the Advanced Communication Technology Satellite (ACTS) Project has required as similarly advanced statistical mathematical modeling formalism to describe the behavior of the 30/20 GHz links emanating to and from the earth terminals through the deleterious effects of the earth's atmosphere. The resulting ACTS Rain Attenuation Prediction Model has been thoroughly described in [Manning, 1990]. In the present paper, the basic rudiments of this model will be reviewed; Section 1 covers the static or time-independent portion of the model and Section 2 covers the dynamic of time-dependent portion. The results of Section 2 are then applied to a new approximate solution of the famous problem of the time duration tau of a fade of random process below some threshold. This is known as the fade duration. The new approximate solution was published in Russian [Denisenko] and, unfortunately, was never published into English. Hence, this work is restated following [Denisenko] in Section 3 which is immediately applied to the random rain fade process. The results for all five ACTS propagation sites as well as Tampa, FL are then given.

Manning, Robert M.↗
NASA NTRS1997

Fade Dynamics and its Evolution: The Other Part of the ACTS Rain Prediction Model

The inception of the Advanced Communication Technology Satellite (ACTS) Project has required a similarly advanced statistical mathematical modeling formalism to describe the behavior of the 30/20 GHz links emanating to and from the earth terminals through the deleterious effects of the earth's atmosphere. The resulting ACTS Rain Attenuation Prediction Model has been thoroughly described in (Manning). In the present paper, the basic rudiments of this model will be reviewed; Section 1 covers the static or time-independent portion of the model and Section 2 covers the dynamic or time-dependent portion. The results of Section 2 are then applied to a new approximate solution of the famous problem of the time duration tau of a fade of a random process below some threshold. This is known as the fade duration. The new approximate solution was published in Russian (Denisenko) and, unfortunately, was never published into English. Hence, this work is restated following (Denisenko) in Section 3 which is immediately applied to the random rain fade process. The results for all five ACTS propagation sites as well as Tampa, FL are then given.

Manning, Robert M.↗
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.↗
DOE OSTI2024

Sensitivity Analysis in the Presence of Intrinsic Stochasticity for Discrete Fracture Network Simulations

Abstract Large‐scale discrete fracture network (DFN) simulators are standard fare for studies involving the sub‐surface transport of particles since direct observation of real world underground fracture networks is generally infeasible. While these simulators have successfully been used in several engineering applications, estimates of output quantities of interest (QoI) — such as breakthrough time of particles reaching the edge of the system — suffer from two distinct types of uncertainty. A run of a DFN simulator requires several parameters to be set that dictate the placement and size of fractures, the density of fractures, and the overall permeability of the system; uncertainty on the proper parameters will lead to uncertainty in the QoI, called epistemic uncertainty. Furthermore, since these input settings to DFN simulators control the stochastic processes which place fractures and govern flow, understanding how this randomness affects the QoI requires several runs of the simulator at distinct random seeds. The uncertainty in the QoI attributed to different realizations (i.e., different seeds) of the same random process (i.e., identical input parameters) leads to a second type of uncertainty, called aleatoric uncertainty. In this paper, we perform a Sensitivity Analysis, which directly attributes the uncertainty observed in the QoI to the epistemic uncertainty from each input parameter and to the aleatoric uncertainty. Beyond the specific takeaways on which input variables influence uncertainty in the QoI the most, a major contribution of this paper is the introduction of a statistically rigorous workflow for characterizing the uncertainty in DFN flow simulations that exhibit heteroskedasticity.

58 GEOSCIENCES↗
NASA NTRS1988

Periodically correlated processes and their stationary dilations

An explicit form for a stationary dilation for periodically correlated random processes is obtained. This is then used to give spectral conditions for a periodically correlated process to be non-deterministic, purely deterministic, minimal, and to have a positive angle between its past and future.

Miamee, A. G.↗
NASA NTRS1990

Periodically correlated processes and their stationary dilations

An explicit form for a stationary dilation for periodically correlated random processes is obtained. This is then used to give spectral conditions for a periodically correlated process to be non-deterministic, purely deterministic, minimal, and to have a positive angle between its past and future.

Miamee, A. G.↗
NASA NTRS1976

Reliability analysis of structures under periodic proof tests in service

A reliability analysis of structures subjected to random service loads and periodic proof tests treats gust loads and maneuver loads as random processes. Crack initiation, crack propagation, and strength degradation are treated as the fatigue process. The time to fatigue crack initiation and ultimate strength are random variables. Residual strength decreases during crack propagation, so that failure rate increases with time. When a structure fails under periodic proof testing, a new structure is built and proof-tested. The probability of structural failure in service is derived from treatment of all the random variables, strength degradations, service loads, proof tests, and the renewal of failed structures. Some numerical examples are worked out.

Yang, J.-N.↗
NASA NTRS1977

Monte Carlo turbulence simulation

The paper describes turbulence simulation experiments based on the principles of control system theory, that is, the construction of a system characterized by a system function such that upon exciting the system with prescribed noise processes the output of the system is a realization of a random processing the desired statistical attributes of turbulence. An experimental autocorrelation of Jimsphere measurements of wind velocity was approximated to simulate turbulent wind. From the approximate autocorrelation function, the required system function is obtained, and a discrete time system is designed. Another method of simulation is to solve the convolution integral by filter techniques. Other methods include discrete Fourier simulation and self-similar simulation.

Fichtl, G. H.↗
DOE OSTI2020

Vectorization techniques for probability distribution functions using VecCore

Probability distribution functions (PDFs) are very used in modeling random processes and physics simulations. Improving the performance of algorithms that generate many random numbers under complex PDFs is often a very challenging task when methods as direct functions are not available. In this work we present general strategies on how to vectorize some PDFs using VecCore library. We show the results for the Exponential, Gaussian, discrete Poisson and Gamma probability distributions.

Chaparro Amaro, Oscar R.↗
NASA NTRS1967

Concepts for a theoretical and experimental study of lifting rotor random loads and vibrations, Phase 1

A number of lifting rotor conditions with random inputs are discussed. The present state of random process theory, applicable to lifting rotor problems is sketched. Possible theories of random blade flapping and random blade flap-bending are outlined and their limitations discussed. A plan for preliminary experiments to study random flapping motions of a see-saw rotor is developed.

Hohenemser, K. H.↗
DOE OSTI2022

Random field optimization

Herein we present a new modeling paradigm for optimization that we call random field optimization. Random fields are a powerful modeling abstraction that aims to capture the behavior of random variables that live on infinite-dimensional spaces (e.g., space and time) such as stochastic processes (e.g., time series, Gaussian processes, and Markov processes), random matrices, and random spatial fields. This paradigm involves sophisticated mathematical objects (e.g., stochastic differential equations and space-time kernel functions) and has been widely used in neuroscience, geoscience, physics, civil engineering, and computer graphics. Despite of this, however, random fields have seen limited use in optimization; specifically, existing optimization paradigms that involve uncertainty (e.g., stochastic programming and robust optimization) mostly focus on the use of finite random variables. This trend is rapidly changing with the advent of statistical optimization (e.g., Bayesian optimization) and multi-scale optimization (e.g., integration of molecular sciences and process engineering). Our work extends a recently-proposed abstraction for infinite-dimensional optimization problems by capturing more general uncertainty representations. Moreover, we discuss solution paradigms for this new class of problems based on finite transformations and sampling, and identify open questions and challenges.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1982

Random element method for numerical modeling of diffusional processes

The random element method is a generalization of the random vortex method that was developed for the numerical modeling of momentum transport processes as expressed in terms of the Navier-Stokes equations. The method is based on the concept that random walk, as exemplified by Brownian motion, is the stochastic manifestation of diffusional processes. The algorithm based on this method is grid-free and does not require the diffusion equation to be discritized over a mesh, it is thus devoid of numerical diffusion associated with finite difference methods. Moreover, the algorithm is self-adaptive in space and explicit in time, resulting in an improved numerical resolution of gradients as well as a simple and efficient computational procedure. The method is applied here to an assortment of problems of diffusion of momentum and energy in one-dimension as well as heat conduction in two-dimensions in order to assess its validity and accuracy. The numerical solutions obtained are found to be in good agreement with exact solution except for a statistical error introduced by using a finite number of elements, the error can be reduced by increasing the number of elements or by using ensemble averaging over a number of solutions.

Ghoniem, A. F.↗