Search NASA⌕ Search

SEARCH · Search NASA

Results for “stochastic modeling”

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 NTRS2004

Validation of the Poisson Stochastic Radiative Transfer Model

A new approach to validation of the Poisson stochastic radiative transfer method is proposed. In contrast to other validations of stochastic models, the main parameter of the Poisson model responsible for cloud geometrical structure - cloud aspect ratio - is determined entirely by matching measurements and calculations of the direct solar radiation. If the measurements of the direct solar radiation is unavailable, it was shown that there is a range of the aspect ratios that allows the stochastic model to accurately approximate the average measurements of surface downward and cloud top upward fluxes. Realizations of the fractionally integrated cascade model are taken as a prototype of real measurements.

Zhuravleva, Tatiana↗
NASA NTRS1976

A reliability-based cost effective fail-safe design procedure

The authors have developed a methodology for cost-effective fatigue design of structures subject to random fatigue loading. A stochastic model for fatigue crack propagation under random loading has been discussed. Fracture mechanics is then used to estimate the parameters of the model and the residual strength of structures with cracks. The stochastic model and residual strength variations have been used to develop procedures for estimating the probability of failure and its changes with inspection frequency. This information on reliability is then used to construct an objective function in terms of either a total weight function or cost function. A procedure for selecting the design variables, subject to constraints, by optimizing the objective function has been illustrated by examples. In particular, optimum design of stiffened panel has been discussed.

Hanagud, S.↗
NASA NTRS1989

Probalistic structural analysis methods for select space propulsion system structural components

A summary of the status of this five-year project which is now in its third year of research and development is presented. The goal of the project is the development of several methodologies for probabilistic structural modeling. Probabilistic structural modeling consists of stochastic models of material properties, part geometries, boundary conditions, as well as loading conditions. The current presentation focuses on one methodology - coupling of an advanced finite element structural analysis code with probabilistic modeling strategies. The essential algorithm developments for combining the finite element and probabilistic analysis methods are reported. The validity of the resulting probabilistic structural analysis method is confirmed through a series of test problems with exact results based on Monte Carlo simulations. Additionally, the applicability of the method to a Space Propulsion System (a turbine blade) is demonstrated for static stresses.

Cruse, T. A.↗
NASA NTRS2018

Stochastic Reduced Order Models with Python (SROMPy)

Stochastic Reduced Order Models with Python (SROMPy) is a software package developed to enable user-friendly utilization of the stochastic reduced order model (SROM) approach for uncertainty quantification. A SROM is a low dimensional, discrete approximation to a random quantity that enables efficient and non-intrusive stochastic computations. With SROMPy, a user can easily generate a SROM to approximate a random variable or vector described by several different types of probability distributions using the Python programming language. Once a SROM is constructed, the software can be used to propagate uncertainty through a user-defined computational model to estimate statistics of a given quantity of interest. This report is meant to introduce the SROMPy module and brie y demonstrate its capabilities. A simple example of a spring-mass system with a random input is included to illustrate the practicality of the SROM approach to uncertainty quantification and relative ease of applying it with SROMPy. The example includes a comparison with a solution obtained using classical Monte Carlo simulation, demonstrating the similarities and advantages of using the SROM approach.

Warner, James E.↗
NASA NTRS1998

Improved Modeling of Finite-Rate Turbulent Combustion Processes in Research Combustors

The objective of this thesis is to further develop and test a stochastic model of turbulent combustion in recirculating flows. There is a requirement to increase the accuracy of multi-dimensional combustion predictions. As turbulence affects reaction rates, this interaction must be more accurately evaluated. In this work a more physically correct way of handling the interaction of turbulence on combustion is further developed and tested. As turbulence involves randomness, stochastic modeling is used. Averaged values such as temperature and species concentration are found by integrating the probability density function (pdf) over the range of the scalar. The model in this work does not assume the pdf type, but solves for the evolution of the pdf using the Monte Carlo solution technique. The model is further developed by including a more robust reaction solver, by using accurate thermodynamics and by more accurate transport elements. The stochastic method is used with Semi-Implicit Method for Pressure-Linked Equations. The SIMPLE method is used to solve for velocity, pressure, turbulent kinetic energy and dissipation. The pdf solver solves for temperature and species concentration. Thus, the method is partially familiar to combustor engineers. The method is compared to benchmark experimental data and baseline calculations. The baseline method was tested on isothermal flows, evaporating sprays and combusting sprays. Pdf and baseline predictions were performed for three diffusion flames and one premixed flame. The pdf method predicted lower combustion rates than the baseline method in agreement with the data, except for the premixed flame. The baseline and stochastic predictions bounded the experimental data for the premixed flame. The use of a continuous mixing model or relax to mean mixing model had little effect on the prediction of average temperature. Two grids were used in a hydrogen diffusion flame simulation. Grid density did not effect the predictions except for peak temperature and tangential velocity. The hybrid pdf method did take longer and required more memory, but has a theoretical basis to extend to many reaction steps which cannot be said of current turbulent combustion models.

VanOverbeke, Thomas J.↗
DOE OSTI2026

Identifying stochastic dynamics via finite expression methods

Modeling stochastic differential equations (SDEs) is crucial for understanding complex dynamical systems in various scientific fields. Recent methods often employ neural network-based models, which typically represent SDEs through a combination of deterministic and stochastic terms. However, these models usually lack interpretability and have difficulty in generalizing beyond their training domain. Here, this paper introduces the Finite Expression Method (FEX), a symbolic learning approach designed to derive interpretable mathematical representations of the deterministic component of SDEs. For the stochastic component, we integrate FEX with advanced generative modeling techniques to provide a comprehensive representation of SDEs. The numerical experiments on linear, nonlinear, and multidimensional SDEs demonstrate that FEX generalizes well beyond the training domain and delivers more accurate long-term predictions compared to neural network-based methods. The symbolic expressions identified by FEX not only improve prediction accuracy but also offer valuable scientific insights into the underlying dynamics of the systems.

Complex dynamical systems↗
NASA NTRS2023

Single-Band VLBI Absolute Astrometry

The ionospheric path delay impacts single-band very long baseline interferometry (VLBI) group delays, which limits their applicability for absolute astrometry. I consider two important cases: when observations are made simultaneously in two bands, but delays in only one band are available for a subset of observations and when observations are made at one band design. I developed optimal procedures of data analysis for both cases using Global Navigation Satellite System (GNSS) ionosphere maps, provided a stochastic model that describes ionospheric errors, and evaluated their impact on source position estimates. I demonstrate that the stochastic model is accurate at a level of 15%. I found that using GNSS ionospheric maps as is introduces serious biases in estimates of declination and I developed a procedure that almost eliminates them. I found serendipitously that GNSS ionospheric maps have multiplicative errors and have to be scaled by 0.85 in order to mitigate the declination bias. A similar scale factor was found in comparison of the vertical total electron content from satellite altimetry against GNSS ionospheric maps. I favor interpretation of this scaling factor as a manifestation of the inadequacy of the thin shell model of the ionosphere. I showed that we are able to model the ionospheric path delay to the extent that no noticeable systematic errors emerge and we are able to assess adequately the contribution of the ionosphere-driven random errors on source positions. This makes single-band absolute astrometry a viable option that can be used for source position determination.

Radio astrometry↗
NASA NTRS1972

Comparison of some approximations for isotropic turbulence.

Study of several related turbulence approximations with regard to dynamical properties and agreement of numerical predictions with laboratory and computer experiments. The approximations considered include the direct-interaction equations (Kraichnan, 1964), Herring's (1966) self-consistent-field theory, a generalization of Edwards' (1964) theory, the abridged Lagrangian-history, direct-interaction approximation (Kraichnan, 1966), the test-field model (Kraichnan, 1971), and an approximation, not previously described, in which one velocity field passively suffers convection by another. Most of the cited approximations are representable by stochastic model equations for the velocity amplitude. Explicit constructions are given for the stochastic models, in a form that can be approximated on a digital computer. These constructions are used to discuss the physical and mathematical differences between the model dynamics and actual Navier-Stokes dynamics.-

Herring, J. R.↗
NASA NTRS1977

Reliability based fatigue design and maintenance procedures

A stochastic model has been developed to describe a probability for fatigue process by assuming a varying hazard rate. This stochastic model can be used to obtain the desired probability of a crack of certain length at a given location after a certain number of cycles or time. Quantitative estimation of the developed model was also discussed. Application of the model to develop a procedure for reliability-based cost-effective fail-safe structural design is presented. This design procedure includes the reliability improvement due to inspection and repair. Methods of obtaining optimum inspection and maintenance schemes are treated.

Hanagud, S.↗
NASA NTRS1997

Stochastic-Dynamical Modeling of Space Time Rainfall

The focus of this research work is the elucidation of the physical origins of the observed extreme-rainfall variability over tropical oceans. The quantitative results of this work may be used to establish links between deterministic models of the mesoscale and synoptic scale with statistical descriptions of the temporal variability of local tropical oceanic rainfall. In addition, they may be used to quantify the influence of measurement error in large-scale forcing and cloud scale observations on the accuracy of local rainfall variability inferences, important for hydrologic studies. A simple statistical-dynamical model, suitable for use in repetitive Monte Carlo experiments, is formulated as a diagnostic tool for this purpose. Stochastic processes with temporal structure and parameters estimated from observed large-scale data represent large-scale forcing.

Georgankakos, Konstantine P.↗
NASA NTRS1990

Frequency-wavenumber spectrum for GATE phase I rainfields

The oceanic rainfall frequency-wavenumber spectrum and its associated space-time correlation have been evaluated from subsets of GATE phase I data. The records, of a duration of four days, were sampled at 15 minutes intervals in 4 x 4 km grid boxes over a 400 km diameter hexagon. In the low frequencies-low wavenumber region the results coincide with those obtained by using the stochastic model proposed by North and Nakomoto (1989). From the derived spectrum the inherent time and space scales of the stochastic model were determined to be approximately 13 hours and 36 km. The formalism proposed by North and Nakamoto was taken together with the derived spectrum to compute the mean square sampling error due to intermittent visits of a spaceborne sensor.

Nakamoto, Shoichiro↗
DOE OSTI2025

Elucidation of Local Ordering and Atomic-Scale Structure in Polymer-Derived SiOC

Silicon oxycarbide (SiOC) is a versatile ceramic material with tunable microstructure and compositions that can be modulated through precursor chemistry and processing conditions. Though there are several noteworthy uses of SiOC across a range of application spaces, the difficulties in elucidating the short- to medium-range order within these materials have limited the maturation of strategies to precisely control SiC x O 4–x compositions for user-tailored applications. In this contribution, we implement a range of synchrotron scattering and spectroscopy methods coupled with stochastic modeling techniques to elucidate changes in local chemistry and structure associated with the pyrolysis of a commercially available SiOC polymer precursor. Stochastic modeling approaches provide valuable insights into decoupling local Si–O and Si–C environments while confirming predominate heterogeneous phases in materials. Using pyrolysis temperatures between 250 to 800 °C results in a heterogeneous material predominately composed of SiOC and amorphous SiO 2 domains. At 1100 °C, redistribution of Si–C pairs in the SiOC network and Si–O from the SiO 2 domains create a more ordered SiOC phase with local cubic SiC-like ordering. In addition, residual carbon leads to a detectable carbon phases at 1100 °C that persist at higher temperatures. These efforts address the difficulties of obtaining atomic-scale insights into the local structure and nanoscale heterogeneities in SiOC, providing pathways toward establishing structure–property relationships for future materials development.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2017

Environmental Barrier Coating Fracture, Fatigue and High-Heat-Flux Durability Modeling and Stochastic Progressive Damage Simulation

Advanced environmental barrier coatings will play an increasingly important role in future gas turbine engines because of their ability to protect emerging light-weight SiC/SiC ceramic matrix composite (CMC) engine components, further raising engine operating temperatures and performance. Because the environmental barrier coating systems are critical to the performance, reliability and durability of these hot-section ceramic engine components, a prime-reliant coating system along with established life design methodology are required for the hot-section ceramic component insertion into engine service. In this paper, we have first summarized some observations of high temperature, high-heat-flux environmental degradation and failure mechanisms of environmental barrier coating systems in laboratory simulated engine environment tests. In particular, the coating surface cracking morphologies and associated subsequent delamination mechanisms under the engine level high-heat-flux, combustion steam, and mechanical creep and fatigue loading conditions will be discussed. The EBC compostion and archtechture improvements based on advanced high heat flux environmental testing, and the modeling advances based on the integrated Finite Element Analysis Micromechanics Analysis Code/Ceramics Analysis and Reliability Evaluation of Structures (FEAMAC/CARES) program will also be highlighted. The stochastic progressive damage simulation successfully predicts mud flat damage pattern in EBCs on coated 3-D specimens, and a 2-D model of through-the-thickness cross-section. A 2-parameter Weibull distribution was assumed in characterizing the coating layer stochastic strength response and the formation of damage was therefore modeled. The damage initiation and coalescence into progressively smaller mudflat crack cells was demonstrated. A coating life prediction framework may be realized by examining the surface crack initiation and delamination propagation in conjunction with environmental degradation under high-heat-flux and environment load test conditions.

Mechanical creep and fatigue loading condition↗
NASA NTRS1997

Parameterizing Grid-Averaged Longwave Fluxes for Inhomogeneous Marine Boundary Layer Clouds

This paper examines the relative impacts on grid-averaged longwave flux transmittance (emittance) for Marine Boundary Layer (MBL) cloud fields arising from horizontal variability of optical depth tau and cloud sides, First, using fields of Landsat-inferred tau and a Monte Carlo photon transport algorithm, it is demonstrated that mean all-sky transmittances for 3D variable MBL clouds can be computed accurately by the conventional method of linearly weighting clear and cloudy transmittances by their respective sky fractions. Then, the approximations of decoupling cloud and radiative properties and assuming independent columns are shown to be adequate for computation of mean flux transmittance. Since real clouds have nonzero geometric thicknesses, cloud fractions A'(sub c) presented to isotropic beams usually exceed the more familiar vertically projected cloud fractions A(sub c). It is shown, however, that when A(sub c)less than or equal to 0.9, biases for all-sky transmittance stemming from use of A(sub c) as opposed to A'(sub c) are roughly 2-5 times smaller than, and opposite in sign to, biases due to neglect of horizontal variability of tau. By neglecting variable tau, all-sky transmittances are underestimated often by more than 0.1 for A(sub c) near 0.75 and this translates into relative errors that can exceed 40% (corresponding errors for all-sky emittance are about 20% for most values of A(sub c). Thus, priority should be given to development of General Circulation Model (GCM) parameterizations that account for the effects of horizontal variations in unresolved tau, effects of cloud sides are of secondary importance. On this note, an efficient stochastic model for computing grid-averaged cloudy-sky flux transmittances is furnished that assumes that distributions of tau, for regions comparable in size to GCM grid cells, can be described adequately by gamma distribution functions. While the plane-parallel, homogeneous model underestimates cloud transmittance by about an order of magnitude when 3D variable cloud transmittances are less than or equal to 0.2 and by approx. 20% to 100% otherwise, the stochastic model reduces these biases often by more than 80%.

Barker, Howard W.↗
NASA NTRS1989

Comparison of parameterized nitric acid rainout rates using a coupled stochastic-photochemical tropospheric model

A major tropospheric loss of soluble species such as nitric acid results from scavenging by water droplets. Several theoretical formulations have been advanced which relate an effective time-independent loss rate for soluble species to statistical properties of precipitation such as the wet fraction and length of a precipitation cycle. In this paper, various 'effective' loss rates that have been proposed are compared with the results of detailed time-dependent model calculations carried out over a seasonal time scale. The model is a stochastic precipitation model coupled to a tropospheric photochemical model. The results of numerous time-dependent seasonal model runs are used to derive numerical values for the nitric acid residence time for several assumed sets of preciptation statistics. These values are then compared with the results obtained by utilizing theoretical 'effective' loss rates in time-independent models.

Stewart, Richard W.↗
NASA NTRS2015

Simulation of DNA Damage in Human Cells from Space Radiation Using a Physical Model of Stochastic Particle Tracks and Chromosomes

The formation of double-strand breaks (DSBs) and chromosomal aberrations (CAs) is of great importance in radiation research and, specifically, in space applications. We are presenting a recently developed model, in which chromosomes simulated by NASARTI (NASA Radiation Tracks Image) is combined with nanoscopic dose calculations performed with the Monte-Carlo simulation by RITRACKS (Relativistic Ion Tracks) in a voxelized space. The model produces the number of DSBs, as a function of dose for high-energy iron, oxygen, and carbon ions, and He ions. The combined model calculates yields of radiation-induced CAs and unrejoined chromosome breaks in normal and repair deficient cells. The merged computational model is calibrated using the relative frequencies and distributions of chromosomal aberrations reported in the literature. The model considers fractionated deposition of energy to approximate dose rates of the space flight environment. The merged model also predicts of the yields and sizes of translocations, dicentrics, rings, and more complex-type aberrations formed in the G0/G1 cell cycle phase during the first cell division after irradiation.

Ponomarev, Artem↗
NASA NTRS1992

Climatology of Station Storm Rainfall in the Continental United States: Parameters of the Bartlett-Lewis and Poisson Rectangular Pulses Models

The parameters of two stochastic models of point rainfall, the Bartlett-Lewis model and the Poisson rectangular pulses model, are estimated for each month of the year from the historical records of hourly precipitation at more than seventy first-order stations in the continental United States. The parameters are presented both in tabular form and as isopleths on maps. The Poisson rectangular pulses parameters are useful in implementing models of the land surface water balance. The Bartlett-Lewis parameters are useful in disaggregating precipitation to a time period shorter than that of existing observations. Information is also included on a floppy disk.

Hawk, Kelly Lynn↗
NASA NTRS2013

North American Tropical Cyclone Landfall and SST: A Statistical Model Study

A statistical-stochastic model of the complete life cycle of North Atlantic (NA) tropical cyclones (TCs) is used to examine the relationship between climate and landfall rates along the North American Atlantic and Gulf Coasts. The model draws on archived data of TCs throughout the North Atlantic to estimate landfall rates at high geographic resolution as a function of the ENSO state and one of two different measures of sea surface temperature (SST): 1) SST averaged over the NA subtropics and the hurricane season and 2) this SST relative to the seasonal global subtropical mean SST (termed relSST). Here, the authors focus on SST by holding ENSO to a neutral state. Jackknife uncertainty tests are employed to test the significance of SST and relSST landfall relationships. There are more TC and major hurricane landfalls overall in warm years than cold, using either SST or relSST, primarily due to a basinwide increase in the number of storms. The signal along the coast, however, is complex. Some regions have large and significant sensitivity (e.g., an approximate doubling of annual major hurricane landfall probability on Texas from -2 to +2 standard deviations in relSST), while other regions have no significant sensitivity (e.g., the U.S. mid-Atlantic and Northeast coasts). This geographic structure is due to both shifts in the regions of primary TC genesis and shifts in TC propagation.

El Nino↗