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All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Implementation of Probabilistic Design Methodology at Tennessee State University

Engineering Design is one of the most important areas in engineering education. Deterministic Design Methodology (DDM) is the only design method that is taught in most engineering schools. This method does not give a direct account of uncertainties in design parameters. Hence, it is impossible to quantify the uncertainties in the response and the actual safety margin remains unknown. The desire for a design methodology tha can identify the primitive (random) variables that affect the structural behavior has led to a growing interest on Probabilistic Design Methodology (PDM). This method is gaining more recognition in industries than in educational institutions. Some of the reasons for the limited use of the PDM at the moment are that many are unaware of its potentials, and most of the software developed for PDM are very recent. The central goal of the PDM project at Tennessee State University is to introduce engineering students to the method. The students participating in the project learn about PDM and the computer codes that are available to the design engineer. The software being used of this project is NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) developed under NASA probabilistic structural analysis program. NESSUS has three different modules which make it a very comprehensive computer code for PDM. A research in technology transfer through course offering in PDM is in effect a Tennessee State University. The aim is to familiarize students with the problem of uncertainties in engineering design. Included in the paper are some projects on PDM carried out by some students and faculty. The areas this method is being applied at the moment include, Design of Gears (spur and worm); Design of Shafts; Design of Statistically Indeterminate Frame Structures; Design of Helical Springs; and Design of Shock Absorbers. Some of the current results of these projects are presented.

Onwubiko, Chinyere↗
NASA NTRS2010

Extracting Independent Local Oscillatory Geophysical Signals by Geodetic Tropospheric Delay

Zenith Tropospheric Delay (ZTD) due to water vapor derived from space geodetic techniques and numerical weather prediction simulated-reanalysis data exhibits non-linear and non-stationary properties akin to those in the crucial geophysical signals of interest to the research community. These time series, once decomposed into additive (and stochastic) components, have information about the long term global change (the trend) and other interpretable (quasi-) periodic components such as seasonal cycles and noise. Such stochastic component(s) could be a function that exhibits at most one extremum within a data span or a monotonic function within a certain temporal span. In this contribution, we examine the use of the combined Ensemble Empirical Mode Decomposition (EEMD) and Independent Component Analysis (ICA): the EEMD-ICA algorithm to extract the independent local oscillatory stochastic components in the tropospheric delay derived from the European Centre for Medium-Range Weather Forecasts (ECMWF) over six geodetic sites (HartRAO, Hobart26, Wettzell, Gilcreek, Westford, and Tsukub32). The proposed methodology allows independent geophysical processes to be extracted and assessed. Analysis of the quality index of the Independent Components (ICs) derived for each cluster of local oscillatory components (also called the Intrinsic Mode Functions (IMFs)) for all the geodetic stations considered in the study demonstrate that they are strongly site dependent. Such strong dependency seems to suggest that the localized geophysical signals embedded in the ZTD over the geodetic sites are not correlated. Further, from the viewpoint of non-linear dynamical systems, four geophysical signals the Quasi-Biennial Oscillation (QBO) index derived from the NCEP/NCAR reanalysis, the Southern Oscillation Index (SOI) anomaly from NCEP, the SIDC monthly Sun Spot Number (SSN), and the Length of Day (LoD) are linked to the extracted signal components from ZTD. Results from the synchronization analysis show that ZTD and the geophysical signals exhibit (albeit subtle) site dependent phase synchronization index.

Botai, O. J.↗
NASA NTRS2006

Probabilistic Classification Using Elemental Abundance Distributions and Lossless Image Compression in Apollo 17 Lunar Dust Samples from Mare Serenitatis

We have previously outlined a strategy for the detection of fossils [Storrie-Lombardi and Hoover, 2004] and extant microbial life [Storrie-Lombaudi and Hoover, 20051 during robotic missions to Mars using co-registered structural and chemical signatures. Data inputs included image lossless compression indices to estimate relative textural complexity and elemental abundance distributions. Two exploratory classification algorithms (principal component analysis and hierarchical cluster analysis) provide an initial tentative classification of all targets. Nonlinear stochastic neural networks are then trained to produce a Bayesian estimate of algorithm classification accuracy. The strategy previously has been successful in distinguishing regions of biotic and abiotic alteration of basalt glass from unaltered samples. [Storrie-Lombardi and Fisk, 2004; Storrie-Lombardi and Fisk, 2004] Such investigations of abiotic versus biotic alteration of terrestrial mineralogy on Earth are compromised by .the difficulty finding mineralogy completely unaffected by the ubiquitous presence of microbial life on the planet. The renewed interest in lunar exploration offers an opportunity to investigate geological materials that may exhibit signs of aqueous alteration, but are highly unlikely to contain contaminating biological weathering signatures. We here present an extension of our earlier data set to include lunar dust samples obtained during the Apollo 17 mission. Apollo 17 landed in the Taurus-Littrow Valley in Mare Serenitatis. Most of the rock samples from this region of the lunar highlands are basalts comprised primarily of plagioclase and pyroxene and selected examples of orange and black volcanic glass. SEM images and elemental abundances (C6, N7, O8, Na11, Mg12, Al13, Si14, P15, S16, Cll7, K19, Ca20, Fe26) for a series of targets in the lunar dust samples are compared to the extant cyanobacteria, fossil trilobites, Orgueil meteorite, and terrestrial basalt targets previously discussed. The data set provides a first step in producing a quantitative probabilistic methodology for geobiological analysis of returned lunar samples or in situ exploration.

Storrie-Lombardi, Michael C.↗
NASA NTRS1990

Probabilistic low cycle fatigue failure analysis with application to liquid propellant rocket engines

A probabilistic Low Cycle Fatigue (LCF) failure analysis of a candidate turbine disk for use in a turbopump of a rocket engine of the Space Shuttle Main Engine class is described. A state-of-the-art LCF failure prediction method was used in a Monte Carlo simulation to generate a distribution of failure lives. A stochastic Stress/Life (S/N) model was used for materials characterization. The LCF failure model expresses fatigue life as a function of stochastic parameters including environmental parameters, loads, material properties, structural parameters, and model specification errors. The rationale for the particular characterization of each stochastic input parameter is described. The results and interpretation of the failure analysis are given.

Newlin, L.↗
NASA NTRS2018

Simulation of Stochastic Mud-Crack Damage Formation in an Environmental Barrier Coating

The integrated Finite Element Analysis–Micromechanics Analysis Code/Ceramics Analysis and Reliability Evaluation of Structures (FEAMAC/CARES) program was used to simulate the formation of mudflat-cracks from thermomechanical loading on a multi-layered Environmental Barrier Coating (EBC) system deposited on a ceramic substrate. FEAMAC/CARES combines MAC/GMC multiscale composite micromechanics code with CARES/Life probabilistic multiaxial failure criteria code and Abaqusfinite element analysis. In this work, step function elastic modulus reduction of randomly damaged finite elements was used to represent discrete cracking events. The use of many small-sized low-aspect-ratio finite elements enabled the depiction of crack boundaries and formation of mudflat patterned damage. Demonstrated examples include finite element models of button–sized disk–shaped 3-D specimen, and a 2-D model of through-the-thickness cross-section. All models were subjected to a progressive cool down from 1300oC to room temperature. Mudflat crack damage in the coating system resulted from the buildup of residual tensile stresses between the individual material constituents from thermal expansion mismatch. A 2-parameter Weibull distribution characterized the coating layer stochastic strength response and the effect of the Weibull modulus on the formation of damage was studied here.

residual tensile stress↗
NASA NTRS2003

Structural Reliability Using Probability Density Estimation Methods Within NESSUS

A reliability analysis studies a mathematical model of a physical system taking into account uncertainties of design variables and common results are estimations of a response density, which also implies estimations of its parameters. Some common density parameters include the mean value, the standard deviation, and specific percentile(s) of the response, which are measures of central tendency, variation, and probability regions, respectively. Reliability analyses are important since the results can lead to different designs by calculating the probability of observing safe responses in each of the proposed designs. All of this is done at the expense of added computational time as compared to a single deterministic analysis which will result in one value of the response out of many that make up the density of the response. Sampling methods, such as monte carlo (MC) and latin hypercube sampling (LHS), can be used to perform reliability analyses and can compute nonlinear response density parameters even if the response is dependent on many random variables. Hence, both methods are very robust; however, they are computationally expensive to use in the estimation of the response density parameters. Both methods are 2 of 13 stochastic methods that are contained within the Numerical Evaluation of Stochastic Structures Under Stress (NESSUS) program. NESSUS is a probabilistic finite element analysis (FEA) program that was developed through funding from NASA Glenn Research Center (GRC). It has the additional capability of being linked to other analysis programs; therefore, probabilistic fluid dynamics, fracture mechanics, and heat transfer are only a few of what is possible with this software. The LHS method is the newest addition to the stochastic methods within NESSUS. Part of this work was to enhance NESSUS with the LHS method. The new LHS module is complete, has been successfully integrated with NESSUS, and been used to study four different test cases that have been proposed by the Society of Automotive Engineers (SAE). The test cases compare different probabilistic methods within NESSUS because it is important that a user can have confidence that estimates of stochastic parameters of a response will be within an acceptable error limit. For each response, the mean, standard deviation, and 0.99 percentile, are repeatedly estimated which allows confidence statements to be made for each parameter estimated, and for each method. Thus, the ability of several stochastic methods to efficiently and accurately estimate density parameters is compared using four valid test cases. While all of the reliability methods used performed quite well, for the new LHS module within NESSUS it was found that it had a lower estimation error than MC when they were used to estimate the mean, standard deviation, and 0.99 percentile of the four different stochastic responses. Also, LHS required a smaller amount of calculations to obtain low error answers with a high amount of confidence than MC. It can therefore be stated that NESSUS is an important reliability tool that has a variety of sound probabilistic methods a user can employ and the newest LHS module is a valuable new enhancement of the program.

Chamis, Chrisos C.↗
NASA NTRS1988

Particle-laden weakly swirling free jets: Measurements and predictions

A theoretical and experimental investigation of particle-laden, weakly swirling, turbulent free jets was conducted. Glass particles, having a Sauter mean diameter of 39 microns with a standard deviation of 15 microns, were used. A single loading ratio of 0.2 was used in the experiments. Measurements are reported for three swirl numbers, ranging from 0.0 to 0.3. The measurements included mean and fluctuating velocities of both phases, and particle mass flux distributions. Measurements were compared with predictions from three types of multiphase flow analysis: locally homogeneous flow (LHF); deterministic separated flow (DSF); and stochastic separated flow (SSF). For the particle-laden jets, the LHF and DSF models did not provide very satisfactory predictions. The LHF model generally overestimated the rate of decay of particle mean axial and angular velocities with streamwise distance, due to the neglect of particle inertia. The LHF model predictions of particle mass flux also showed poor agreement with measurements due to the assumption of no-slip between phases. The DSF model also performed quite poorly for predictions of particle mass flux, because turbulent dispersion of the particles was neglected. The SSF model, which accounts for both particle inertia and turbulent dispersion of the particles, yielded reasonably good predictions throughout the flow field for the particle-laden jets.

Bulzan, Daniel L.↗
NASA NTRS1988

Particle-laden weakly swirling free jets - Measurements and predictions

A theoretical and experimental investigation of particle-laden, weakly swirling, turbulent free jets was conducted. Glass particles, having a Sauter mean diameter of 39 microns with a standard deviation of 15 microns, were used. A single loading ratio of 0.2 was used in the experiments. Measurements are reported for three swirl numbers, ranging from 0.0 to 0.3. The measurements included mean and fluctuating velocities of both phases, and particle mass flux distributions. Measurements were compared with predictions from three types of multiphase flow analysis: locally homogeneous flow (LHF); deterministic separated flow (DSF); and stochastic separated flow (SSF). For the particle-laden jets, the LHF and DSF models did not provide very satisfactory predictions. The LHF model generally overestimated the rate of decay of particle mean axial and angular velocities with streamwise distance, due to the neglect of particle inertia. The LHF model predictions of particle mass flux also showed poor agreement with measurements due to the assumption of no-slip between phases. The DSF model also performed quite poorly for predictions of particle mass flux, because turbulent dispersion of the particles was neglected. The SSF model, which accounts for both particle inertia and turbulent disperison of the particles, yielded reasonably good predictions throughout the flow field for the particle-laden jets.

Bulzan, Daniel L.↗
NASA NTRS1990

A methodology for evaluating the reliability and risk of structures under complex service environments

The theoretical basis and numerical implementation of NESSUS (Numerical Evaluation of Stochastic Structures Under Stress), a computer code for probabilistic structural analysis of aerospace components, are described, with an emphasis on the use of NESSUS for reliability and risk assessment. Topics addressed include the structure of probabilistic models of fatigue-crack initiation, risk/cost evaluation, fatigue-fracture analysis, and fatigue-crack initiation. Numerical results from typical applications are presented in graphs and briefly characterized. The usefulness of NESSUS predictions for establishing inspection and retirement schedules and for component certification is indicated.

Shiao, Michael C.↗
NASA NTRS1993

Probabilistic finite elements for fatigue and fracture analysis

An overview of the probabilistic finite element method (PFEM) developed by the authors and their colleagues in recent years is presented. The primary focus is placed on the development of PFEM for both structural mechanics problems and fracture mechanics problems. The perturbation techniques are used as major tools for the analytical derivation. The following topics are covered: (1) representation and discretization of random fields; (2) development of PFEM for the general linear transient problem and nonlinear elasticity using Hu-Washizu variational principle; (3) computational aspects; (4) discussions of the application of PFEM to the reliability analysis of both brittle fracture and fatigue; and (5) a stochastic computational tool based on stochastic boundary element (SBEM). Results are obtained for the reliability index and corresponding probability of failure for: (1) fatigue crack growth; (2) defect geometry; (3) fatigue parameters; and (4) applied loads. These results show that initial defect is a critical parameter.

Belytschko, Ted↗
NASA NTRS1995

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↗
NASA NTRS1999

Scaling in nature: from DNA through heartbeats to weather

The purpose of this report is to describe some recent progress in applying scaling concepts to various systems in nature. We review several systems characterized by scaling laws such as DNA sequences, heartbeat rates and weather variations. We discuss the finding that the exponent alpha quantifying the scaling in DNA in smaller for coding than for noncoding sequences. We also discuss the application of fractal scaling analysis to the dynamics of heartbeat regulation, and report the recent finding that the scaling exponent alpha is smaller during sleep periods compared to wake periods. We also discuss the recent findings that suggest a universal scaling exponent characterizing the weather fluctuations.

Review↗
NASA NTRS1989

Probabilistic design analysis using Composite Loads Spectra (CLS) coupled with Probabilistic Structural Analysis Methodologies (PSAM)

Composite loads spectra (CLS) were applied to generate probabilistic loads for use in the PSAM nonlinear evaluation of stochastic structures under stress (NESSUS) finite element code. The CLS approach allows for quantifying loads as mean values and distributions around a central value rather than maximum or enveloped values typically used in deterministic analysis. NESSUS uses these loads to determine mean and perturbation responses. These results are probabilistically evaluated with the distributional information from CLS using a fast probabilistic integration (FPI) technique to define response distributions. The main example discussed describes a method of obtaining load descriptions and stress response of the second-stage turbine blade of the Space Shuttle Main Engine (SSME) high-pressure fuel turbopump (HPFTP). Additional information is presented on the on-going analysis of the high pressure oxidizer turbopump discharge duct (HPOTP) where probabilistic dynamic loads have been generated and are in the process of being used for dynamic analysis. Example comparisons of load analysis and engine data are furnished for partial verification and/or justification for the methodology.

Newell, J. F.↗
NASA NTRS2016

FEAMAC/CARES Stochastic-Strength-Based Damage Simulation Tool for Ceramic Matrix Composites

Reported here is a coupling of two NASA developed codes: CARES (Ceramics Analysis and Reliability Evaluation of Structures) with the MAC/GMC (Micromechanics Analysis Code/ Generalized Method of Cells) composite material analysis code. The resulting code is called FEAMAC/CARES and is constructed as an Abaqus finite element analysis UMAT (user defined material). Here we describe the FEAMAC/CARES code and an example problem (taken from the open literature) of a laminated CMC in off-axis loading is shown. FEAMAC/CARES performs stochastic-strength-based damage simulation response of a CMC under multiaxial loading using elastic stiffness reduction of the failed elements.

composite structures↗
NASA NTRS2015

Stochastic-Strength-Based Damage Simulation Tool for Ceramic Matrix Composite

Reported here is a coupling of two NASA developed codes: CARES (Ceramics Analysis and Reliability Evaluation of Structures) with the MAC/GMC (Micromechanics Analysis Code/ Generalized Method of Cells) composite material analysis code. The resulting code is called FEAMAC/CARES and is constructed as an Abaqus finite element analysis UMAT (user defined material). Here we describe the FEAMAC/CARES code and an example problem (taken from the open literature) of a laminated CMC in off-axis loading is shown. FEAMAC/CARES performs stochastic-strength-based damage simulation response of a CMC under multiaxial loading using elastic stiffness reduction of the failed elements.

ceramic matrix composites↗
NASA NTRS2018

Weibull-Based Stochastic Simulation of Mud-Crack Damage Formation in an Environmental Barrier Coating

The integrated Finite Element Analysis Micromechanics Analysis Code/Ceramics Analysis and Reliability Evaluation of Structures (FEAMAC/CARES) program was used to simulate the formation of mudflat-cracks from thermomechanical loading on a multi-layered Environmental Barrier Coating (EBC) system deposited on a ceramic substrate. FEAMAC/CARES combines MAC/GMC (Micromechanics Analysis Code/Generalized Method of Cells) multiscale composite micromechanics code with CARES/Life probabilistic multiaxial failure criteria code and Abaqusfinite element analysis. In this work, step function elastic modulus reduction of randomly damaged finite elements was used to represent discrete cracking events. The use of many small-sized low-aspect-ratio finite elements enabled the depiction of crack boundaries and formation of mudflat patterned damage. Demonstrated examples include finite element models of button-sized disk-shaped 3-D specimen, and a 2-D model of through-the-thickness cross-section. All models were subjected to a progressive cool down from 1300 degrees Centigrade to room temperature. Mudflat crack damage in the coating system resulted from the buildup of residual tensile stresses between the individual material constituents from thermal expansion mismatch. A 2-parameter Weibull distribution characterized the coating layer stochastic strength response and the effect of the Weibull modulus on the formation of damage was studied here.

Residual Tensile Stress↗