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All sources NASA NTRS DOE OSTI

DOE OSTI2021

A probabilistic creep model incorporating test condition, initial damage, and material property uncertainty

Uncertainty is prevalent in the creep resistance of alloys, where at elevated temperature and low pressure, rupture can range across logarithmic decades. In this study, a probabilistic continuum-damage-mechanics (CDM)-based model is derived to capture the uncertainty of creep resistance. To meet this objective, creep data for alloy 304 Stainless Steel is gathered. A constitutive model, “Sinh”, is calibrated deterministically to determine the statistical variability of the material properties. Three sources of uncertainty are injected into the model: test condition (stress and temperature), initial damage, and material properties. Probabilistic simulations are carried out by (a) calibrating probability distribution functions (pdfs) for each source of uncertainty (b) randomly sampling the pdfs using Monte Carlo methods and (c) executing simulations to replicate the uncertain creep behavior. A sensitivity analysis is performed to evaluate the relative effect of each source of uncertainty. In full probabilistic simulations, the cumulative uncertainty of creep behavior is evaluated. The probabilistic model accurately predicts the creep deformation and rupture of the available experiments. The probabilistic model is validated for interpolation but lacks extrapolation ability. Several future works are proposed to further improve the model.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Correlation between EVs and Other Loads in Probabilistic Load Flow for Distribution Systems

To date, most probabilistic studies have assumed independence between the various loads and other inputs on the distribution system. It is well know however, that this is typically not the case. The work presented in the paper expands upon a previous unbalanced three-phase probabilistic load flow study on a residential feeder with a 50 % penetration of electric vehicles, under three different charging schemes where different correlation scenarios between the load flow inputs are considered. The data for the probabilistic load flow study are derived from a voltage dependent time-variant deterministic load flow. Here the deterministic load flow data are examined further to gain a better understanding of the correlation between the customer and electric vehicle charging loads, and how different charging schemes may impact it further. Four different correlation scenarios are then created and details on how the probabilistic load flow inputs are created is also presented; demonstrating the need for better analysis on the correlation between system inputs. This paper hopes to open the discussion and start the push for future research into understanding the correlation and effects of various system inputs on the probabilistic nature of distribution systems, and how to apply this knowledge to future studies.

Melhorn, Alexander C.↗

NASA NTRS1985

Probabilistic Structural Analysis Theory Development

The objective of the Probabilistic Structural Analysis Methods (PSAM) project is to develop analysis techniques and computer programs for predicting the probabilistic response of critical structural components for current and future space propulsion systems. This technology will play a central role in establishing system performance and durability. The first year's technical activity is concentrating on probabilistic finite element formulation strategy and code development. Work is also in progress to survey critical materials and space shuttle mian engine components. The probabilistic finite element computer program NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) is being developed. The final probabilistic code will have, in the general case, the capability of performing nonlinear dynamic of stochastic structures. It is the goal of the approximate methods effort to increase problem solving efficiency relative to finite element methods by using energy methods to generate trial solutions which satisfy the structural boundary conditions. These approximate methods will be less computer intensive relative to the finite element approach.

Burnside, O. H.↗

NASA NTRS1985

Probabilistic Finite Element: Variational Theory

The goal of this research is to provide techniques which are cost-effective and enable the engineer to evaluate the effect of uncertainties in complex finite element models. Embedding the probabilistic aspects in a variational formulation is a natural approach. In addition, a variational approach to probabilistic finite elements enables it to be incorporated within standard finite element methodologies. Therefore, once the procedures are developed, they can easily be adapted to existing general purpose programs. Furthermore, the variational basis for these methods enables them to be adapted to a wide variety of structural elements and to provide a consistent basis for incorporating probabilistic features in many aspects of the structural problem. Tasks concluded include the theoretical development of probabilistic variational equations for structural dynamics, the development of efficient numerical algorithms for probabilistic sensitivity displacement and stress analysis, and integration of methodologies into a pilot computer code.

Belytschko, T.↗

NASA NTRS1987

A probabilistic Hu-Washizu variational principle

A Probabilistic Hu-Washizu Variational Principle (PHWVP) for the Probabilistic Finite Element Method (PFEM) is presented. This formulation is developed for both linear and nonlinear elasticity. The PHWVP allows incorporation of the probabilistic distributions for the constitutive law, compatibility condition, equilibrium, domain and boundary conditions into the PFEM. Thus, a complete probabilistic analysis can be performed where all aspects of the problem are treated as random variables and/or fields. The Hu-Washizu variational formulation is available in many conventional finite element codes thereby enabling the straightforward inclusion of the probabilistic features into present codes.

Liu, W. K.↗

NASA NTRS1989

Probabilistic structural analysis: Introductory remarks

The development of probabilistic structural analysis methodology consists of the following program elements: (1) composite load spectra models, (2) computational probabilistic structural analysis methods, and (3) probabilistic constitutive relationships. The development of the probabilistic structural analysis methodology is a joint program of NASA Lewis in-house and sponsored research. The objective of this session is to illustrate recent progress on the application of this methodology to determine the reliability of structural components for rocket propulsion systems. The session contains descriptions of and progress reports on the following specific activities: (1) The NESSUS computer code, (2) approximate methods, (3) advanced methods, (4) composite load spectra applications, (5) probabilistic fracture mechanisms, and (6) probability of failure and risk analysis. Collectively, the progress to date demonstrates that the structural durability of hot engine structural components can be effectively evaluated in a formal probabilistic/reliability framework.

Chamis, Christos C.↗

NASA NTRS1992

Recent developments of the NESSUS probabilistic structural analysis computer program

The NESSUS probabilistic structural analysis computer program combines state-of-the-art probabilistic algorithms with general purpose structural analysis methods to compute the probabilistic response and the reliability of engineering structures. Uncertainty in loading, material properties, geometry, boundary conditions and initial conditions can be simulated. The structural analysis methods include nonlinear finite element and boundary element methods. Several probabilistic algorithms are available such as the advanced mean value method and the adaptive importance sampling method. The scope of the code has recently been expanded to include probabilistic life and fatigue prediction of structures in terms of component and system reliability and risk analysis of structures considering cost of failure. The code is currently being extended to structural reliability considering progressive crack propagation. Several examples are presented to demonstrate the new capabilities.

Millwater, H.↗

NASA NTRS1993

Probabilistic sizing of laminates with uncertainties

A reliability based design methodology for laminate sizing and configuration for a special case of composite structures is described. The methodology combines probabilistic composite mechanics with probabilistic structural analysis. The uncertainties of constituent materials (fiber and matrix) to predict macroscopic behavior are simulated using probabilistic theory. Uncertainties in the degradation of composite material properties are included in this design methodology. A multi-factor interaction equation is used to evaluate load and environment dependent degradation of the composite material properties at the micromechanics level. The methodology is integrated into a computer code IPACS (Integrated Probabilistic Assessment of Composite Structures). Versatility of this design approach is demonstrated by performing a multi-level probabilistic analysis to size the laminates for design structural reliability of random type structures. The results show that laminate configurations can be selected to improve the structural reliability from three failures in 1000, to no failures in one million. Results also show that the laminates with the highest reliability are the least sensitive to the loading conditions.

Shah, A. R.↗

NASA NTRS1993

Global/local methods for probabilistic structural analysis

A probabilistic global/local method is proposed to reduce the computational requirements of probabilistic structural analysis. A coarser global model is used for most of the computations with a local more refined model used only at key probabilistic conditions. The global model is used to establish the cumulative distribution function (cdf) and the Most Probable Point (MPP). The local model then uses the predicted MPP to adjust the cdf value. The global/local method is used within the advanced mean value probabilistic algorithm. The local model can be more refined with respect to the g1obal model in terms of finer mesh, smaller time step, tighter tolerances, etc. and can be used with linear or nonlinear models. The basis for this approach is described in terms of the correlation between the global and local models which can be estimated from the global and local MPPs. A numerical example is presented using the NESSUS probabilistic structural analysis program with the finite element method used for the structural modeling. The results clearly indicate a significant computer savings with minimal loss in accuracy.

Millwater, H. R.↗

NASA NTRS1994

Probabilistic Simulation of Stress Concentration in Composite Laminates

A computational methodology is described to probabilistically simulate the stress concentration factors (SCF's) in composite laminates. This new approach consists of coupling probabilistic composite mechanics with probabilistic finite element structural analysis. The composite mechanics is used to probabilistically describe all the uncertainties inherent in composite material properties, whereas the finite element is used to probabilistically describe the uncertainties associated with methods to experimentally evaluate SCF's, such as loads, geometry, and supports. The effectiveness of the methodology is demonstrated by using is to simulate the SCF's in three different composite laminates. Simulated results match experimental data for probability density and for cumulative distribution functions. The sensitivity factors indicate that the SCF's are influenced by local stiffness variables, by load eccentricities, and by initial stress fields.

Chamis, C. C.↗

NASA NTRS1995

Probabilistic Fatigue And Flaw-Propagation Analysis

Probabilistic Failure Assessment for Fatigue and Flaw Propagation (PFAFAT II) package of software utilizing probabilistic failure-assessment (PFA) methodology to model flaw-propagation and low-cycle-fatigue modes of failure of structural components. Comprises one program for performing probabilistic crack-growth analysis and two programs for performing probabilistic low-cycle-fatigue analysis. These programs perform probabilistic fatigue and crack-propagation analysis by means of Monte Carlo simulation. PFAFAT II is extension of, rather than replacement for, PFAFAT software (NPO-18965). Written in FORTRAN 77.

Moore, Nicholas↗

NASA NTRS1999

Probabilistic Structural Analysis Methods (PSAM) for Select Space Propulsion System Components

Probabilistic Structural Analysis Methods (PSAM) are described for the probabilistic structural analysis of engine components for current and future space propulsion systems. Components for these systems are subjected to stochastic thermomechanical launch loads. Uncertainties or randomness also occurs in material properties, structural geometry, and boundary conditions. Material property stochasticity, such as in modulus of elasticity or yield strength, exists in every structure and is a consequence of variations in material composition and manufacturing processes. Procedures are outlined for computing the probabilistic structural response or reliability of the structural components. The response variables include static or dynamic deflections, strains, and stresses at one or several locations, natural frequencies, fatigue or creep life, etc. Sample cases illustrates how the PSAM methods and codes simulate input uncertainties and compute probabilistic response or reliability using a finite element model with probabilistic methods.

Source record↗

NASA NTRS2001

Probabilistic Structural Analysis and Reliability Using NESSUS With Implemented Material Strength Degradation Model

This project included both research and education objectives. The goal of this project was to advance innovative research and education objectives in theoretical and computational probabilistic structural analysis, reliability, and life prediction for improved reliability and safety of structural components of aerospace and aircraft propulsion systems. Research and education partners included Glenn Research Center (GRC) and Southwest Research Institute (SwRI) along with the University of Texas at San Antonio (UTSA). SwRI enhanced the NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) code and provided consulting support for NESSUS-related activities at UTSA. NASA funding supported three undergraduate students, two graduate students, a summer course instructor and the Principal Investigator. Matching funds from UTSA provided for the purchase of additional equipment for the enhancement of the Advanced Interactive Computational SGI Lab established during the first year of this Partnership Award to conduct the probabilistic finite element summer courses. The research portion of this report presents the cumulation of work performed through the use of the probabilistic finite element program, NESSUS, Numerical Evaluation and Structures Under Stress, and an embedded Material Strength Degradation (MSD) model. Probabilistic structural analysis provided for quantification of uncertainties associated with the design, thus enabling increased system performance and reliability. The structure examined was a Space Shuttle Main Engine (SSME) fuel turbopump blade. The blade material analyzed was Inconel 718, since the MSD model was previously calibrated for this material. Reliability analysis encompassing the effects of high temperature and high cycle fatigue, yielded a reliability value of 0.99978 using a fully correlated random field for the blade thickness. The reliability did not change significantly for a change in distribution type except for a change in distribution from Gaussian to Weibull for the centrifugal load. The sensitivity factors determined to be most dominant were the centrifugal loading and the initial strength of the material. These two sensitivity factors were influenced most by a change in distribution type from Gaussian to Weibull. The education portion of this report describes short-term and long-term educational objectives. Such objectives serve to integrate research and education components of this project resulting in opportunities for ethnic minority students, principally Hispanic. The primary vehicle to facilitate such integration was the teaching of two probabilistic finite element method courses to undergraduate engineering students in the summers of 1998 and 1999.

Bast, Callie C.↗

NASA NTRS2010

Probabilistic Design and Analysis Framework

PRODAF is a software package designed to aid analysts and designers in conducting probabilistic analysis of components and systems. PRODAF can integrate multiple analysis programs to ease the tedious process of conducting a complex analysis process that requires the use of multiple software packages. The work uses a commercial finite element analysis (FEA) program with modules from NESSUS to conduct a probabilistic analysis of a hypothetical turbine blade, disk, and shaft model. PRODAF applies the response surface method, at the component level, and extrapolates the component-level responses to the system level. Hypothetical components of a gas turbine engine are first deterministically modeled using FEA. Variations in selected geometrical dimensions and loading conditions are analyzed to determine the effects of the stress state within each component. Geometric variations include the cord length and height for the blade, inner radius, outer radius, and thickness, which are varied for the disk. Probabilistic analysis is carried out using developing software packages like System Uncertainty Analysis (SUA) and PRODAF. PRODAF was used with a commercial deterministic FEA program in conjunction with modules from the probabilistic analysis program, NESTEM, to perturb loads and geometries to provide a reliability and sensitivity analysis. PRODAF simplified the handling of data among the various programs involved, and will work with many commercial and opensource deterministic programs, probabilistic programs, or modules.

Strack, William C.↗

DOE OSTI2015

Initial Probabilistic Evaluation of Reactor Pressure Vessel Fracture with Grizzly and Raven

The Grizzly code is being developed with the goal of creating a general tool that can be applied to study a variety of degradation mechanisms in nuclear power plant components. The first application of Grizzly has been to study fracture in embrittled reactor pressure vessels (RPVs). Grizzly can be used to model the thermal/mechanical response of an RPV under transient conditions that would be observed in a pressurized thermal shock (PTS) scenario. The global response of the vessel provides boundary conditions for local models of the material in the vicinity of a flaw. Fracture domain integrals are computed to obtain stress intensity factors, which can in turn be used to assess whether a fracture would initiate at a pre-existing flaw. These capabilities have been demonstrated previously. A typical RPV is likely to contain a large population of pre-existing flaws introduced during the manufacturing process. This flaw population is characterized stastistically through probability density functions of the flaw distributions. The use of probabilistic techniques is necessary to assess the likelihood of crack initiation during a transient event. This report documents initial work to perform probabilistic analysis of RPV fracture during a PTS event using a combination of the RAVEN risk analysis code and Grizzly. This work is limited in scope, considering only a single flaw with deterministic geometry, but with uncertainty introduced in the parameters that influence fracture toughness. These results are benchmarked against equivalent models run in the FAVOR code. When fully developed, the RAVEN/Grizzly methodology for modeling probabilistic fracture in RPVs will provide a general capability that can be used to consider a wider variety of vessel and flaw conditions that are difficult to consider with current tools. In addition, this will provide access to advanced probabilistic techniques provided by RAVEN, including adaptive sampling and parallelism, which can dramatically decrease run times.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2016

Probabilistic Fracture Mechanics of Reactor Pressure Vessels with Populations of Flaws

This report documents recent progress in developing a tool that uses the Grizzly and RAVEN codes to perform probabilistic fracture mechanics analyses of reactor pressure vessels in light water reactor nuclear power plants. The Grizzly code is being developed with the goal of creating a general tool that can be applied to study a variety of degradation mechanisms in nuclear power plant components. Because of the central role of the reactor pressure vessel (RPV) in a nuclear power plant, particular emphasis is being placed on developing capabilities to model fracture in embrittled RPVs to aid in the process surrounding decision making relating to life extension of existing plants. A typical RPV contains a large population of pre-existing flaws introduced during the manufacturing process. The use of probabilistic techniques is necessary to assess the likelihood of crack initiation at one or more of these flaws during a transient event. This report documents development and initial testing of a capability to perform probabilistic fracture mechanics of large populations of flaws in RPVs using reduced order models to compute fracture parameters. The work documented here builds on prior efforts to perform probabilistic analyses of a single flaw with uncertain parameters, as well as earlier work to develop deterministic capabilities to model the thermo-mechanical response of the RPV under transient events, and compute fracture mechanics parameters at locations of pre-defined flaws. The capabilities developed as part of this work provide a foundation for future work, which will develop a platform that provides the flexibility needed to consider scenarios that cannot be addressed with the tools used in current practice.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2019

A two-step short-term probabilistic wind forecasting methodology based on predictive distribution optimization

With increasing wind penetrations into electric power systems, probabilistic wind forecasting becomes more critical to power system operations because of its capability of quantifying wind uncertainties. In this paper, a two-step probabilistic wind forecasting approach based on pinball loss optimization is developed. First, a multimodel machine learning-based ensemble deterministic forecasting framework is adopted to generate deterministic forecasts. The deterministic forecast is assumed to be the mean value of the predictive distribution at each forecasting time stamp. Then, the optimal unknown parameter (i.e., standard deviation) of the predictive distribution is estimated by a support vector regression surrogate model based on the deterministic forecasts. Lastly, probabilistic forecasts are generated from the predictive distribution. Numerical results of case studies at eight locations show that the developed two-step probabilistic forecasting methodology has improved the pinball loss metric score by up to 35% compared to a baseline quantile regression forecasting model.

17 WIND ENERGY↗

DOE OSTI2016

A real-time probabilistic channel flood-forecasting model based on the Bayesian particle filter approach

Reliable real-time probabilistic flood forecasting is critical for effective water management and flood protection all over the world. In this study, we develop a real-time probabilistic channel flood-forecasting model by combining a channel hydraulic model with the Bayesian particle filter approach. The new model is tested in the upstream river reach of Three Gorges Dam (TGD) on the Yangtze River, China. Stage observations at seven hydrological stations are used simultaneously to adjust the Manning's roughness coefficients and to update discharges and stages along the river reach to attain reliable probabilistic flood forecasting. The synthetic experiments are applied to demonstrate the new model's correction and forecasting performances. The real-world experiments show that the new model can make accurate flood forecasting as well as derive reliable intervals for different confidence levels. The new probabilistic flood forecasting model not only outperforms the existing deterministic channel flood-forecasting models in accuracy, but also provides a more robust tool with which to incorporate uncertainty into flood-control efforts.

54 ENVIRONMENTAL SCIENCES↗