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All sourcesNASA NTRSDOE OSTI
NASA NTRS2015

Probabilistic Fatigue Damage Prognosis Using a Surrogate Model Trained Via 3D Finite Element Analysis

Utilizing inverse uncertainty quantification techniques, structural health monitoring can be integrated with damage progression models to form probabilistic predictions of a structure's remaining useful life. However, damage evolution in realistic structures is physically complex. Accurately representing this behavior requires high-fidelity models which are typically computationally prohibitive. In the present work, a high-fidelity finite element model is represented by a surrogate model, reducing computation times. The new approach is used with damage diagnosis data to form a probabilistic prediction of remaining useful life for a test specimen under mixed-mode conditions.

Leser, Patrick E.↗
NASA NTRS2016

Application of Deterministic and Probabilistic System Design Methods and Enhancements of Conceptual Design Tools for ERA Project

This report documents work done by the Aerospace Systems Design Lab (ASDL) at the Georgia Institute of Technology, Daniel Guggenheim School of Aerospace Engineering for the National Aeronautics and Space Administration, Aeronautics Research Mission Directorate, Integrated System Research Program, Environmentally Responsible Aviation (ERA) Project. This report was prepared under contract NNL12AA12C, "Application of Deterministic and Probabilistic System Design Methods and Enhancement of Conceptual Design Tools for ERA Project". The research within this report addressed the Environmentally Responsible Aviation (ERA) project goal stated in the NRA solicitation "to advance vehicle concepts and technologies that can simultaneously reduce fuel burn, noise, and emissions." To identify technology and vehicle solutions that simultaneously meet these three metrics requires the use of system-level analysis with the appropriate level of fidelity to quantify feasibility, benefits and degradations, and associated risk. In order to perform the system level analysis, the Environmental Design Space (EDS) [Kirby 2008, Schutte 2012a] environment developed by ASDL was used to model both conventional and unconventional configurations as well as to assess technologies from the ERA and N+2 timeframe portfolios. A well-established system design approach was used to perform aircraft conceptual design studies, including technology trade studies to identify technology portfolios capable of accomplishing the ERA project goal and to obtain accurate tradeoffs between performance, noise, and emissions. The ERA goal, shown in Figure 1, is to simultaneously achieve the N+2 benefits of a cumulative noise margin of 42 EPNdB relative to stage 4, a 75 percent reduction in LTO NOx emissions relative to CAEP 6 and a 50 percent reduction in fuel burn relative to the 2005 best in class aircraft. There were 5 research task associated with this research: 1) identify technology collectors, 2) model technology collectors in EDS, 3) model and assess ERA technologies, 4) LTO and cruise emission prediction, and 5) probabilistic analysis of technology collectors and portfolios.

Mavris, Dimitri N.↗
DOE OSTI2021

Data Driven Approach to Analyzing The Impact of Power Plant Cycling on Air Preheater Degradation and Remaining Useful Life

Due to the increased penetration of renewable energy generation sources, and fluctuations of the oil and gas prices, modern coal burning power plants deal with increased variability in the demand for power generation. These varying demands result in their intermittent under-capacity operation (cycling). Periodical ramping down and back up to follow the daily power demands causes damages to the plant components reducing its operational life. In this paper we analyze the impact of cycling on a rotary Ljungstrom air preheater (APH) unit installed at a coal fire power plant in the US. An inefficient air preheater can significantly impact boiler performance. Due to the repeated boiler’s hot-cold start, the APH experiences fluctuating operating conditions that result in accelerated degradation mechanisms, such as dew-point corrosion, fouling/deposition plugging, and air heater leakage. The analysis in this paper utilizes field data related to APH basket replacement, and the number of cycles experienced by the boiler to model the life expectancy of the baskets. The data-driven model enables preventive maintenance strategies for the APH by predicting how long the APH baskets will last in a probabilistic sense. Furthermore, the analysis showed that an increase in cycling for a fixed operation time can reduce the APH basket remaining useful life by about 30%.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2025

Diagnostics: Chapter 8 of the special issue: on the path to tokamak burning plasma operation

This chapter presents the activity conducted by the ITPA topical group (TG) on Diagnostics over about the last 15 years. Following a general introduction of the ITER Diagnostics led by their measurement roles, the document is organized in several subchapters detailing the design support, research and development activity conducted by each of the specialist working groups (WGs) of the TG. Please note that the magnetic diagnostics were supported at the TG without a specific WG. Their status is included in the general introduction. In the following some highlights of the subchapter’s contents are provided. Recent advances in ITER first wall (FW) diagnostics for the measurements of plasma-metallic wall interaction in support of the ITER research plan are reported. An InfraRed imaging Video Bolometer for ITER has been developed and tested on several tokamaks to measure the radiated power loss. A laser-induced breakdown spectroscopy (LIBS) technique which utilizes a pulsed laser beam to ablate locally by forming a crater, will measure local tritium inventory in the FW material. Real-time Residual Gas Analyzers will measure the neutral gas composition in a divertor port and an equatorial port during plasma operation. Due to the full metallic FW environment, the plasma-wall interaction in ITER will face several challenges such as the compromised radiated power and divertor heat flux measurements by reflection. Ray tracing and analysis codes have been developed to eliminate and correct the effects of reflection in the measurements. The characteristics of the reflecting surfaces depending on the roughness and angle of the incidence have been measured by dedicated experiments, and the results were applied to the reflection elimination. For the measurement of the metallic impurity radiation induced by eroded metallic atoms, a vacuum ultraviolet spectrometer has been developed and tested. An extensive thermonuclear diagnostic suite will be required to support the operation of ITER and the planned experimental program for future burning plasma experiments. Due to the harsh environmental conditions, the implementation of diagnostic systems in ITER is a major challenge. These conditions include high levels of neutron and gamma fluxes, neutron heating, particle bombardment. Therefore, the selection and design of diagnostic systems must take into account a number of phenomena previously unseen in diagnostic design. For this reason, the measurement of neutrons and confined or lost fast ions, with particular emphasis on alpha particles, is critical to ITER. The diagnostics associated with these measurements will be important for future plasma-burning experiments at ITER. The high neutron emission and very large plasma size in ITER make neutron diagnostics the main diagnostic method used to measure plasma parameters such as fusion power, fusion power density, ion temperature, energy of fast ions and their spatial distributions in the plasma core. Active spectroscopy techniques are methods where a neutral particle beam is injected into the plasma and information on plasma parameters is extracted from the measurement of line emission resulting from the beam-plasma interaction, either by plasma ions or by beam atoms. Spatial localization is achieved by crossing the beamline and multiple observation lines. The ITER plasma will be a high temperature, moderately dense, fully ionized collisional plasma. The plasma facing surfaces are principally metallic being fashioned from beryllium or tungsten but many other elements, arising from either structural or from operational needs, may enter this plasma. The energy range of the emitted photons range from meV (infra-red) to multi keV (x-rays) and originate from all areas of the plasma volume. The primary role of passive emission diagnostics is to identify what is in the plasma from spectral signatures. Extracting quantitative information from these measurements such as impurity content, ion temperature, rotation, degree of detachment and radiated power depends on calibrated instruments, a physics model of the atomic and molecular processes and plasma transport and an analysis workflow that takes into account environmental effects such as reflections. The particular needs for ITER have prompted a multi-machine, many-year effort to address all these aspects and this chapter reviews the work on diagnostic design, experiments and new analysis techniques. An overview of the laser diagnostics to be implemented on ITER is also provided in this paper. This includes descriptions of the Thomson scattering in the core, edge and divertor regions, polarimetry and interferometry diagnostics used for measuring plasma density and also measurements of helium density in the divertor using Laser Induced Flourescence. Techniques which can allow improvements on current measurements are also addressed in particular expanding poloidal polarimetry measurements to measure field fluctuations and proposed use of dispersion interferometery which has a number of advantages over existing methods. This paper identifies particular areas where further research and testing on existing tokamaks is useful even at this advanced stage to inform the design of diagnostics for ITER. Outstanding areas of concern for the implementation of laser diagnostics, in particular with a view to reliable operation are identified. An overview of the latest developments of microwave diagnostic systems and techniques is given. The primary focus is the contributions for ITER—the next step burning plasma experiment—which is supplemented by describing recent progress of techniques applicable for fusion experiments beyond ITER. The contributions are intentionally kept concise, and are being supplemented by a rich list of references for further studies. Radiation induced effects are receiving continuous and well-deserved attention of the ITER diagnostic community and they are in many cases one of the primary design drivers of the ITER diagnostic systems. The paper summarizes recent progress in this area focusing primarily on the ITER diagnostics but in some cases provides also outlook for the possible solutions for even more demanding radiation environment of fusion reactors beyond ITER. Despite advancements in the area of modeling and simulation of various radiation induced effects, experimental testing in a nuclear environment as close as possible to the target one is still seen as unavoidable for proper qualification of particular diagnostic functional elements. Recent advancement within three diagnostic areas: optical diagnostics, magnetics and bolometers is covered. Encouraging results on qualification of silica glass vacuum window assemblies are presented. In the area of magnetic sensors, progress of irradiation tests performed on ITER in-vessel LTCC inductive sensors is presented with outlook for novel technological approaches to inductive sensors utilizing thick printing and photolithography technologies being highlighted. Summary of advancements in the area of steady state magnetic field sensors based on Hall effect is given. New results of neutron irradiation test of the ITER borosilicate glass inserts for vacuum electrical feedthroughs are summarized finding negligible swelling at target level of neutron fluence. Off-line irradiation tests of fiber optic current sensors for plasma current measurement demonstrated that both for gamma doses up to 5 MGy and a total neutron fluence up to 10 15 cm −2 , radiation induced changes are still compatible with required measurement accuracy on ITER. The ITER bolometers are given as an example how considering radiation effects may influence the diagnostic design. Finally, outlook for future main R&D directions is outlined. All optical and laser-based diagnostics in ITER will be using mirrors to guide plasma radiation toward detectors, cameras and sensors. In the hostile plasma, radiation and particle environment the optical characteristics of diagnostic mirrors will degrade directly affecting the entire performance of involved diagnostic systems. An assessment of factors affecting mirror performance is provided. Among the prime adverse factors are deposition of plasma impurities, sputtering of mirror surface and steam ingress in the vicinity of mirrors. Within the International Tokamak Physics Activity with active support by ITER central team and domestic agencies, the structured research and development (R&D) program on mitigation of risks for diagnostic mirrors is underway. Within this program the mirror material development, the passive mitigation of mirror degradation by using diagnostic ducts and shutters along with an active mirror recovery program comprising the in-situ mirror cleaning and calibration is underway. Recent developments in diagnostic mirror R&D are described in this Chapter along with an example of their implementation of R&D solutions in ITER Infrared Thermography diagnostic. An assessment of still open engineering and physics questions, considerations on mirror risks during an early phase of ITER operation are given along with an overview of diagnostic mirror evolution in the late ITER operation stage toward the demonstration fusion power plant. Several crucial areas of diagnostic R&D outlined in ITER Research Plan are addressed. The basic control groups in a fusion reactor can be broken-down in five categories: (1) plasma position, magnetic configuration, and plasma current control, (2) profile control and confinement optimization, (3) MHD control and suppression, (4) edge dissipation control, radiation and plasma exhaust control and (5) break-down optimization. These categories are coupled via the physics (a control action in one domain will affect the other domains) and via shared actuators (e.g. ECRH for impurity accumulation avoidance, current density distribution control and MHD suppression). Consequently, a supervisory control system should determine the priority of the various control tasks, their couplings, and the interfaces with the safety and interlock system. For the systematic development of the various controllers taking the complexity of the plasma and the control system into account, a model-based approach is required. A short historical overview is given of the developments in systems and control theory and control engineering with special emphasis on those developments that are most relevant for Nuclear Fusion research and operation. An overview is given of the state of the field of fusion plasma control for the control categories. It will be shown how synthetic diagnostics are being developed in ITER and how they are used in diagnostic design and design validation and how they can be in model-based controller synthesis using relatively simple models. In modern control methods, multiple diagnostics are used to constrain relatively simple models. The constrained models provide an estimate for the state. This opens the route to state controllers, such as model predictive control. A major challenge in nuclear fusion research is the coherent combination of data from heterogeneous diagnostics and modeling codes for machine control and safety as well as physics studies. Measured data from different diagnostics often provide information about the same subset of physical parameters. Additionally, information provided by some diagnostics might be needed for the analysis of other diagnostics. A joint analysis of complementary and redundant data allows, e.g. to improve the reliability of parameter estimation, to increase the spatial and temporal resolution of profiles, to obtain synergistic effects, to consider diagnostics interdependencies and to find and resolve data inconsistencies. Physics-based modeling and parameter relationships provide additional information improving the treatment of ill-posed inversion problems. A coherent combination of all kind of available information within a probabilistic framework allows for improved data analysis results. The concept of integrated data analysis (IDA) in the framework of Bayesian probability theory is outlined and contrasted with conventional data analysis. Components of the probabilistic approach are summarized and specific ingredients beneficial for data analysis at fusion devices are discussed.

ITER↗
NASA NTRS1994

Data Analysis with Graphical Models: Software Tools

Probabilistic graphical models (directed and undirected Markov fields, and combined in chain graphs) are used widely in expert systems, image processing and other areas as a framework for representing and reasoning with probabilities. They come with corresponding algorithms for performing probabilistic inference. This paper discusses an extension to these models by Spiegelhalter and Gilks, plates, used to graphically model the notion of a sample. This offers a graphical specification language for representing data analysis problems. When combined with general methods for statistical inference, this also offers a unifying framework for prototyping and/or generating data analysis algorithms from graphical specifications. This paper outlines the framework and then presents some basic tools for the task: a graphical version of the Pitman-Koopman Theorem for the exponential family, problem decomposition, and the calculation of exact Bayes factors. Other tools already developed, such as automatic differentiation, Gibbs sampling, and use of the EM algorithm, make this a broad basis for the generation of data analysis software.

Buntine, Wray L.↗
NASA NTRS1995

Implementation of probabilistic design methodology at Tennessee State University

The fact that Deterministic Design Method no longer satisfies most design needs calls for methods that will cope with the high trend in technology. The advance in computer technology has reduced the rigors that normally accompany many design analysis methods that account for uncertainties in design parameters. Probabilistic Design Methodology (PDM) is beginning to make impact in engineering design. 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 this 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 for 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. Since this method is new to the students, its introduction into the engineering curriculum is to be in stages. These range from the introduction of PDM and its software to the applications. While this program is being developed for its eventual inclusion into the engineering curriculum, some graduate and undergraduate students are already carrying out some projects using this method. As the students are increasing their understanding on PDM, they are at the same time applying it to some common design problems. The areas this method is being applied at the moment include, Design of Gears (spur and worm); Design of Brakes; Design of Heat Exchangers Design of Helical Springs; and Design of Shock Absorbers. Some of the current results of these projects are presented.

Onwubiko, Chinyere↗
DOE OSTI2020

UQpy: A general purpose Python package and development environment for uncertainty quantification

In this paper, we present the UQpy software toolbox, an open-source Python package for general uncertainty quantification (UQ) in mathematical and physical systems. The software serves as both a user-ready toolbox that includes many of the latest methods for UQ in computational modeling and a convenient development environment for Python programmers advancing the field of UQ. The paper presents an introduction to the software's architecture and existing capabilities, divided in the code in a set of modules centered around different UQ tasks such as sampling methods, generation of random processes and random fields, probabilistic inverse modeling, reliability analysis, surrogate modeling, and active learning. The paper also highlights the importance of the RunModel module, which is used to drive simulations in the uncertainty analyses performed in UQpy. This module conveniently allows the user to define computational models directly in Python, or to run simulations from a third-party software in serial or in parallel. To illustrate the various capabilities, two examples are tracked throughout the paper and analyzed repeatedly for various UQ tasks. The first is a Python model solving a nonlinear structural dynamics problem, used to illustrate UQpy's capabilities in sampling and forward propagation of high dimensional random vectors (stochastic processes), and probabilistic inference. The second model is a third-party Abaqus finite element model solving the thermomechanical response of a beam structure. This example is used to illustrate UQpy's capabilities in variance reduction sampling techniques, reliability analysis, surrogate modeling and active learning techniques.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Determination of proton PDF uncertainties with Markov chain Monte Carlo

We present an analysis of parton distribution functions (PDFs) of the proton using Markov chain Monte Carlo (MCMC) methods. The MCMC approach naturally implements Bayes’ theorem and, thus, provides a means to directly sample the underlying probability distribution—in this case, the probability distribution of the PDF parameters. This allows for a straightforward propagation of the resulting uncertainties into any PDF-dependent observable, preserving their simple probabilistic interpretation. In our analysis we include a broad set of deep inelastic scattering data from HERA, BCDMS and NMC experiments along with the Drell-Yan, 𝑊 and 𝑍 boson data from LHC and Tevatron experiments, which combined with theoretical calculations at next-to-next-to-leading order in QCD allow for realistic determination of PDFs. The main focus of this analysis is to explore alternative methods for PDF uncertainty estimation that are more firmly grounded in statistical principles. We show that the flexibility of the Bayes framework, allowing one, e.g., to account for non-Gaussianity or inconsistencies of datasets, is crucial to extract realistic uncertainties when such assumptions are not fulfilled. We also demonstrate that MCMC allows one to determine the Δ⁢𝜒 2 value corresponding to a given confidence level in the sample, which can, in turn, be used as a statistically well-founded tolerance criterion used in the Hessian method, thus addressing one of its main long-standing drawbacks.

Risse, Peter Clemens [Universität Münster (Germany↗
DOE OSTI2025

Risk Analysis of Radiological Release from Pu-238 Targets During Manual Handling

Pu-238 Isotope Production Targets are routinely installed in the Advanced Test Reactor (ATR) core, transferred, and stored in the spent fuel canal. These evolutions involve manual handling and manipulation of the targets underwater using long handled tools. The ATR Safety Analysis Report (SAR) postulates a design basis accident which results in damage from manual manipulation of targets, and radiological consequences must be determined for receptors inside the reactor facility, as well as public receptors. This presentation presents the analysis used to determine the radiological consequences due to potential target damage in the ATR canal. The analysis considered radionuclide release fractions, damage ratios for handling evolutions, and entrainment of radionuclides in the canal water.

Advanced Test Reactor↗
DOE OSTI2020

Distribution Development for the RDX Regional Model at Los Alamos National Laboratory - 20385

Representing uncertainty in model inputs often means finding a balance between uncertainty and physical reality. Developing wide distributions may seem conservative in principle, but this approach may lead to unrealistic model results. Characterizing the current state of knowledge of stochastic inputs presents many challenges, especially if the data available are limited or have limited relevance to the site. Relationships among these inputs may also be important to represent but are typically complex or difficult to define. Often special adjustments must be made to account for reduced credibility in particular data. If parameters are strongly related to one another, a correlation structure may be developed for input to the model. Other techniques such as regression models may be used to incorporate relationships between the information available and the desired parameters. The process of developing distributions must consider details of the model in terms of what the distribution is meant to represent. This paper uses the example of a probabilistic fate and transport model for hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX) in the regional aquifer at Los Alamos National Laboratory (LANL). For many parameters, a single draw is applied to all space and time over which the model is run, for a single iteration. This simplification is often made for many reasons, and can often be beneficial, but also adds additional complexity in the distribution development process. Defining the distributional goals as they relate to the modeling process is an important step, which should take place prior to evaluation of the data. Usually, the distributions developed are meant to characterize the average value of the parameter over the spatial and temporal domain of the model. Distribution development requires consideration of many sources of information on the parameter where available, ideally from multiple references. Examples of different sources include data from different references but also from different conditions, measurement methods, or experimental types. Depending on these conditions and the reliability or relevance of particular references, different sources of data may each contribute valuable information but have varying relevance to the site. In these cases, weighting data unequally is a useful way to incorporate this information. As an example, aqueous dispersivity data are available for a variety of rock types. Only a few values are available for the desired rock type, and this is not enough to develop a distribution. Therefore, dispersivity values from other rock types are included in distribution development but are down-weighted such that the best data have the most influence on the distribution developed. In another case, K{sub d} distributions in the model are meant to represent a known composition of multiple soil types. Data from these materials are weighted accordingly to develop a distribution for the weighted average K{sub d} across soil types. Other cases include varying reliability of different sources, and weighting data according to the confidence in these sources. In some cases, input parameters are correlated with one another. An example is advective porosity, which is positively correlated with total porosity and must be less than total porosity. Paired data with both parameters must exist to discern the relationship between the two parameters and if it is necessary to build a correlation structure into the model. In general, correlated parameters may be represented in the model by a multivariate distribution, or perhaps more desirably, capturing the correlation within the developed distributions which may be treated as independent from one another. In the example of porosity, this can be done by transforming advective porosity into a proportion of total porosity which may be drawn independently from the distribution of total porosity. This paper explores how complex data and correlations can be incorporated to meet the distributional goals of the model, using the RDX regional model as a detailed example. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

A Bayesian Deep Learning Approach to Near-Term Climate Prediction

Since model bias and associated initialization shock are serious shortcomings that reduce prediction skills in state-of-the-art decadal climate prediction efforts, we pursue a complementary machine-learning-based approach to climate prediction. The example problem setting we consider consists of predicting natural variability of the North Atlantic sea surface temperature on the interannual timescale in the pre-industrial control simulation of the Community Earth System Model. While previous works have considered the use of recurrent networks such as convolutional LSTMs and reservoir computing networks in this and other similar problem settings, we currently focus on the use of feedforward convolutional networks. In particular, we find that a feedforward convolutional network with a Densenet architecture is able to outperform a convolutional LSTM in terms of predictive skill. Next, we go on to consider a probabilistic formulation of the same network based on Stein variational gradient descent and find that in addition to providing useful measures of predictive uncertainty, the probabilistic (Bayesian) version improves on its deterministic counterpart in terms of predictive skill. Finally, we characterize the reliability of the ensemble of machine learning models obtained in the probabilistic setting by using analysis tools developed in the context of ensemble numerical weather prediction.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Probabilistic Data-Driven Sampling via Multi-Criteria Importance Analysis

Although supercomputers are becoming increasingly powerful, their components have thus far not scaled proportionately. Compute power is growing enormously and is enabling finely resolved simulations that produce never-before-seen features. However, I/O capabilities lag by orders of magnitude, which means only a fraction of the simulation data can be stored for post hoc analysis. Prespecified plans for saving features and quantities of interest do not work for features that have not been seen before. Data-driven intelligent sampling schemes are needed to detect and save important parts of the simulation while it is running. Here, we propose a novel sampling scheme that reduces the size of the data by orders-of-magnitude while still preserving important regions. The approach we develop selects points with unusual data values and high gradients. Finally, we demonstrate that our approach outperforms traditional sampling schemes on a number of tasks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Hydrogen Extremely Low Probability of Rupture Version 1

SAND2024-08511O The Hydrogen Extremely Low Probability of Rupture (HELPR) software toolkit provides probabilistic fracture assessments of natural gas infrastructure for transporting hydrogen. Using probabilistic sampling and sensitivity analysis—along with engineering fatigue and fracture mechanics— the software develops models that can predict structural integrity measures for natural gas pipelines under stress. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Schroeder, Benjamin↗
NASA NTRS1978

Costing the satellite power system

The paper presents a methodology for satellite power system costing, places approximate limits on the accuracy possible in cost estimates made at this time, and outlines the use of probabilistic cost information in support of the decision-making process. Reasons for using probabilistic costing or risk analysis procedures instead of standard deterministic costing procedures are considered. Components of cost, costing estimating relationships, grass roots costing, and risk analysis are discussed. Risk analysis using a Monte Carlo simulation model is used to estimate future costs.

Hazelrigg, G. A., Jr.↗
NASA NTRS1992

A probabilistic fracture mechanics approach for structural reliability assessment of space flight systems

A probabilistic fracture mechanics approach for predicting the failure life distribution due to subcritical crack growth is presented. A state-of-the-art crack propagation method is used in a Monte Carlo simulation to generate a distribution of failure lives. The crack growth failure model expresses failure life as a function of stochastic parameters including environment, loads, material properties, geometry, and model specification errors. A stochastic crack growth rate model that considers the uncertainties due to scatter in the data and mode misspecification is proposed. The rationale for choosing a particular type of probability distribution for each stochastic input parameter and for specifying the distribution parameters is presented. The approach is demonstrated through a probabilistic crack growth failure analysis of a welded tube in the Space Shuttle Main Engine. A discussion of the results from this application of the methodology is given.

Sutharshana, S.↗
NASA NTRS1995

Novel composites for wing and fuselage applications

Probabilistic predictions based on the IPACS code are presented for the material and structural response of unnotched and notched, IM6/3501-6 Gr/Ep laminates. Comparisons of predicted and measured modulus and strength distributions are given for unnotched unidirectional, cross-ply and quasi-isotropic laminates. The predicted modulus distributions were found to correlate well with the test results for all three unnotched laminates. Correlations of strength distributions for the unnotched laminates are judged good for the unidirectional laminate and fair for the cross-ply laminate, whereas the strength correlation for the quasi-isotropic laminate is judged poor because IPACS did not have a progressive failure capability at the time this work was performed. The report also presents probabilistic and structural reliability analysis predictions for the strain concentration factor (SCF) for an open-hole, quasi-isotropic laminate subjected to longitudinal tension. A special procedure was developed to adapt IPACS for the structural reliability analysis. The reliability results show the importance of identifying the most significant random variables upon which the SCF depends, and of having accurate scatter values for these variables.

Sobel, L. H.↗
NASA NTRS2005

Bidirectional Classical Stochastic Processes with Measurements and Feedback

A measurement on a quantum system is said to cause the "collapse" of the quantum state vector or density matrix. An analogous collapse occurs with measurements on a classical stochastic process. This paper addresses the question of describing the response of a classical stochastic process when there is feedback from the output of a measurement to the input, and is intended to give a model for quantum-mechanical processes that occur along a space-like reaction coordinate. The classical system can be thought of in physical terms as two counterflowing probability streams, which stochastically exchange probability currents in a way that the net probability current, and hence the overall probability, suitably interpreted, is conserved. The proposed formalism extends the . mathematics of those stochastic processes describable with linear, single-step, unidirectional transition probabilities, known as Markov chains and stochastic matrices. It is shown that a certain rearrangement and combination of the input and output of two stochastic matrices of the same order yields another matrix of the same type. Each measurement causes the partial collapse of the probability current distribution in the midst of such a process, giving rise to calculable, but non-Markov, values for the ensuing modification of the system's output probability distribution. The paper concludes with an analysis of a classical probabilistic version of the so-called grandfather paradox.

Hahne, G. E.↗