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NASA NTRS1991

Probabilistic simulation of the human factor in structural reliability

Many structural failures have occasionally been attributed to human factors in engineering design, analyses maintenance, and fabrication processes. Every facet of the engineering process is heavily governed by human factors and the degree of uncertainty associated with them. Factors such as societal, physical, professional, psychological, and many others introduce uncertainties that significantly influence the reliability of human performance. Quantifying human factors and associated uncertainties in structural reliability require: (1) identification of the fundamental factors that influence human performance, and (2) models to describe the interaction of these factors. An approach is being developed to quantify the uncertainties associated with the human performance. This approach consists of a multi factor model in conjunction with direct Monte-Carlo simulation.

Shah, Ashwin R.↗

DOE OSTI2017

Uncertainty in the response of terrestrial carbon sink to environmental drivers undermines carbon-climate feedback predictions

Terrestrial ecosystems play a vital role in regulating the accumulation of carbon (C) in the atmosphere. Understanding the factors controlling land C uptake is critical for reducing uncertainties in projections of future climate. The relative importance of changing climate, rising atmospheric CO2, and other factors, however, remains unclear despite decades of research. Here, we use an ensemble of land models to show that models disagree on the primary driver of cumulative C uptake for 85% of vegetated land area. Disagreement is largest in model sensitivity to rising atmospheric CO2 which shows almost twice the variability in cumulative land uptake since 1901 (1 s.d. of 212.8 PgC vs. 138.5 PgC, respectively). We find that variability in CO2 and temperature sensitivity is attributable, in part, to their compensatory effects on C uptake, whereby comparable estimates of C uptake can arise by invoking different sensitivities to key environmental conditions. Conversely, divergent estimates of C uptake can occur despite being based on the same environmental sensitivities. Together, these findings imply an important limitation to the predictability of C cycling and climate under unprecedented environmental conditions. We suggest that the carbon modeling community prioritize a probabilistic multi-model approach to generate more robust C cycle projections.

Huntzinger, D. N.↗

DOE OSTI2016

Reduced order models for assessing CO 2 impacts in shallow unconfined aquifers

Risk assessment studies of potential CO 2 sequestration projects consider many factors, including the possibility of brine and/or CO 2 leakage from the storage reservoir. Detailed multiphase reactive transport simulations have been developed to predict the impact of such leaks on shallow groundwater quality; however, these simulations are computationally expensive and thus difficult to directly embed in a probabilistic risk assessment analysis. Here we present a process for developing computationally fast reduced-order models which emulate key features of the more detailed reactive transport simulations. A large ensemble of simulations that take into account uncertainty in aquifer characteristics and CO 2 /brine leakage scenarios were performed. Twelve simulation outputs of interest were used to develop response surfaces (RSs) using a MARS (multivariate adaptive regression splines) algorithm (Milborrow, 2015). A key part of this study is to compare different measures of ROM accuracy. We then show that for some computed outputs, MARS performs very well in matching the simulation data. The capability of the RS to predict simulation outputs for parameter combinations not used in RS development was tested using cross-validation. Again, for some outputs, these results were quite good. For other outputs, however, the method performs relatively poorly. Performance was best for predicting the volume of depressed-pH-plumes, and was relatively poor for predicting organic and trace metal plume volumes. We believe several factors, including the non-linearity of the problem, complexity of the geochemistry, and granularity in the simulation results, contribute to this varied performance. The reduced order models were developed principally to be used in probabilistic performance analysis where a large range of scenarios are considered and ensemble performance is calculated. We demonstrate that they effectively predict the ensemble behavior. But, the performance of the RSs is much less accurate when used to predict time-varying outputs from a single simulation. If an analysis requires only a small number of scenarios to be investigated, computationally expensive physics-based simulations would likely provide more reliable results. Finally, if the aggregate behavior of a large number of realizations is the focus, as will be the case in probabilistic quantitative risk assessment, the methodology presented here is relatively robust.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2005

Role of Probabilistic Micromechanics Modeling in Establishing Design Allowables in Composites

One of the major challenges in designing with any new material, and particularly with advanced composite materials, is the fidelity of material design allowables. In the case of composite materials, the concern arises from the inherent nature of these materials, i.e., their heterogeneous make-up and the various factors that affect their properties in a specific design environment. Composites have various scales - micro, macro, laminate and structural, as well as numerous other fabrication related parameters. Many advanced composites in aerospace applications involve complex two- and three-dimensional fiber architectures and requires high-temperature processing. Since there are uncertainties associated with each of these, the observed behavior of composite materials shows scatter. Evaluating the effect of each of these variables on the observed scatter in composite properties solely by teSting is cost and time prohibitive. One alternative is to evaluate these effects by computational simulation. The authors have developed probabilistic composite micromechanics techniques by combining woven composite micromechanics and Fast Probability Integration (FPI) techniques to address these issues. In this paper these techniques will be described and demonstrated through selected examples. Results in the form of cumulative distribution functions (CDF) of the composite properties of a MI (melt-infiltrated) SiC/SiC (silicon carbide fiber in a silicon carbide matrix) Composite will be presented. A CDF is a relationship defined by the value of the property (the response variable) with respect to the cumulative probability of occurrence. Furthermore, input variables causing scatter are identified and ranked based upon their sensitivity magnitude. Sensitivity information is very valuable in quality control. How these results can be utilized to develop design allowables so that these materials may be used by structural analysts/designers will also be discussed.

Mital, Subodh K.↗

DOE OSTI2020

Assessment of wind power scenario creation methods for stochastic power systems operations

Probabilistic scenarios of renewable energy production, such as wind, have been gaining popularity for use in stochastic variants of power systems operations scheduling problems, allowing for optimal decision-making under uncertainty. The quality of the scenarios has a direct impact on the value of the resulting decisions, but until now, methods for creating scenarios have not been compared under realistic operational conditions. Here, we compare the quality of scenario sets created using three different methods, based on a simulated re-enactment of stochastic day-ahead unit commitment and subsequent dispatch for a realistic test system. We create scenarios using a dataset of forecasted and actual wind power values, scaled to evaluate the effects of increasing wind penetration levels. We show that the choice of scenario set can significantly impact system operating cost, renewable energy use, and the ability of the system to meet demand. This result has implications for the ability of system operators to efficiently integrate renewable production into their day-ahead planning, highlighting the need for the use of performance-based assessments for scenario evaluation.

17 WIND ENERGY↗

DOE OSTI2020

Multiple Degradation Mechanisms in Reinforced Concrete Structures, Modeling and Risk Analysis

The overarching goal of this project is to complement ongoing Department of Energy (DOE) Light Water Reactor Sustainability (LWRS)-funded Grizzly concrete modeling development efforts by providing improved multi-physics models for incorporation into the Grizzly and BlackBear codes. Objectives of this work identified at the outset of this project include: 1. Coupling between mechanical damage and transport processes. The mechanical damage will be characterized by nonlinear mechanical constitutive models appropriate for concrete used in nuclear power plants (NPPs). 2. Improved representation of the coupling among the transport process, building on the current moisture and thermal transport models in Grizzly. The parameters for coupling among heat and mass transport in the multi-physics model will be experimentally determined. 3. Coupling among different scale levels of concrete constituents, fine and coarse aggregates, cement paste, hydration products, and pore structure. 4. Probabilistic analysis of the random nature of the heterogeneous concrete structure and the environmental factors (ambient temperature and humidity) and their multiple effects on concrete deterioration. 5. Benchmark verification, validation and uncertainty quantification of the thermo-hygro- chemo-mechanical (THCM) concrete formulation. The end goal of this work was to provide a comprehensive and robust simulation capability that can be applied at the engineering scale for analysis of realistic deterioration scenarios in NPP concrete structures.

36 MATERIALS SCIENCE↗

NASA NTRS1986

Dynamic remapping decisions in multi-phase parallel computations

The effectiveness of any given mapping of workload to processors in a parallel system is dependent on the stochastic behavior of the workload. Program behavior is often characterized by a sequence of phases, with phase changes occurring unpredictably. During a phase, the behavior is fairly stable, but may become quite different during the next phase. Thus a workload assignment generated for one phase may hinder performance during the next phase. We consider the problem of deciding whether to remap a paralled computation in the face of uncertainty in remapping's utility. Fundamentally, it is necessary to balance the expected remapping performance gain against the delay cost of remapping. This paper treats this problem formally by constructing a probabilistic model of a computation with at most two phases. We use stochastic dynamic programming to show that the remapping decision policy which minimizes the expected running time of the computation has an extremely simple structure: the optimal decision at any step is followed by comparing the probability of remapping gain against a threshold. This theoretical result stresses the importance of detecting a phase change, and assessing the possibility of gain from remapping. We also empirically study the sensitivity of optimal performance to imprecise decision threshold. Under a wide range of model parameter values, we find nearly optimal performance if remapping is chosen simply when the gain probability is high. These results strongly suggest that except in extreme cases, the remapping decision problem is essentially that of dynamically determining whether gain can be achieved by remapping after a phase change; precise quantification of the decision model parameters is not necessary.

Nicol, D. M.↗

NASA NTRS1996

Probabilistic Simulation of Progressive Fracture in Bolted-Joint Composite Laminates

This report describes computational methods to probabilistically simulate fracture in bolted composite structures. An innovative approach that is independent of stress intensity factors and fracture toughness was used to simulate progressive fracture. The effect of design variable uncertainties on structural damage was also quantified. A fast probability integrator assessed the scatter in the composite structure response before and after damage. Then the sensitivity of the response to design variables was computed. General-purpose methods, which are applicable to bolted joints in all types of structures and in all fracture processes-from damage initiation to unstable propagation and global structure collapse-were used. These methods were demonstrated for a bolted joint of a polymer matrix composite panel under edge loads. The effects of the fabrication process were included in the simulation of damage in the bolted panel. Results showed that the most effective way to reduce end displacement at fracture is to control both the load and the ply thickness. The cumulative probability for longitudinal stress in all plies was most sensitive to the load; in the 0 deg. plies it was very sensitive to ply thickness. The cumulative probability for transverse stress was most sensitive to the matrix coefficient of thermal expansion. In addition, fiber volume ratio and fiber transverse modulus both contributed significantly to the cumulative probability for the transverse stresses in all the plies.

Minnetyan, L.↗

NASA NTRS1997

Probabilistic Evaluation of Bolted Joints in Polymer Matrix Composites

Computational methods are described to probabilistically simulate fracture in bolted composite structures. Progressive fracture is simulated via an innovative approach independent of stress intensity factors and fracture toughness. The effect on structure damage of design variable uncertainties is quantified. The Fast Probability Integrator is used to assess the scatter in the composite structure response before and after damage. Sensitivity of the response to design variables is evaluated. The methods are demonstrated for bolted joint polymer matrix composite panels under end loads. The effects of fabrication process are included in the simulation of damage in the bolted panel. The results show that the most effective way to reduce the end displacement at fracture is to control the load and ply thickness.

Chamis, C. C.↗

NASA NTRS2016

Application of Interval Predictor Models to Space Radiation Shielding

This paper develops techniques for predicting the uncertainty range of an output variable given input-output data. These models are called Interval Predictor Models (IPM) because they yield an interval valued function of the input. This paper develops IPMs having a radial basis structure. This structure enables the formal description of (i) the uncertainty in the models parameters, (ii) the predicted output interval, and (iii) the probability that a future observation would fall in such an interval. In contrast to other metamodeling techniques, this probabilistic certi cate of correctness does not require making any assumptions on the structure of the mechanism from which data are drawn. Optimization-based strategies for calculating IPMs having minimal spread while containing all the data are developed. Constraints for bounding the minimum interval spread over the continuum of inputs, regulating the IPMs variation/oscillation, and centering its spread about a target point, are used to prevent data over tting. Furthermore, we develop an approach for using expert opinion during extrapolation. This metamodeling technique is illustrated using a radiation shielding application for space exploration. In this application, we use IPMs to describe the error incurred in predicting the ux of particles resulting from the interaction between a high-energy incident beam and a target.

Crespo, Luis G.↗

DOE OSTI2017

Smart Sampling and HPC-based Probabilistic Look-ahead Contingency Analysis Implementation and its Evaluation with Real-world Data

This paper describes a probabilistic look-ahead contingency analysis application that incorporates smart sampling and high-performance computing (HPC) techniques. Smart sampling techniques are implemented to effectively represent the structure and statistical characteristics of uncertainty introduced by different sources in the power system. They can significantly reduce the data set size required for multiple look-ahead contingency analyses, and therefore reduce the time required to compute them. High-performance-computing (HPC) techniques are used to further reduce computational time. These two techniques enable a predictive capability that forecasts the impact of various uncertainties on potential transmission limit violations. The developed package has been tested with real world data from the Bonneville Power Administration. Case study results are presented to demonstrate the performance of the applications developed.

high performance computing↗

DOE OSTI2016

Multivariate Predictive Analytics of Wind Power Data for Robust Control of Energy Storage

Short-term forecasting is frequently identified as an important tool for the effective management of wind generation. However, forecasting errors, inherent to the point forecasts, increase requirements for energy storage and can affect optimal system operation. Probabilistic forecasts can help tackle this issue by providing a proper characterization of forecasting errors in the optimization process. This paper proposes a multivariate model of forecasting data for wind generation. Predictive uncertainty intervals of wind power can be obtained by sampling from the proposed model. The main goal is to use empirical data models without linear or Gaussian approximations of the distributional or temporal variations. The predictive modeling is utilized within a case study of an energy storage system. Finally, a modified robust convex programming is used to maintain the practical robustness and feasibility of the solution based on the sampled scenarios from the model.

17 WIND ENERGY↗

NASA NTRS2002

An Overview of PRA with Applications to Aerospace Systems

Probabilistic Risk Assessment (PRA) is a systematic process for evaluating the probabilities and consequences of undesirable events that can occur in a process or system along with providing a measure of the uncertainty associated with these probability estimates. In the past it was looked at with suspicion by many at NASA, perhaps because of bad experiences with unsuccessful quantitative methods during the Apollo era, but since the Challenger accident NASA has mandated that it be used, and it has been very successful. With NASA's new "faster, better, cheaper" philosophy, it is vital that a tool be in place that can help to achieve these goals in the reliability area. This paper describes the history of PRA, gives examples of its aerospace applications to date, and gives suggestions for how it can be used in the future, both for space shuttle upgrades and for totally new technologies such as the Second Generation Reusable Launch Vehicle.

Sharon E. Navard↗

NASA NTRS2021

Self-Consistent Implementation of a Zero-Equation Transport Model Into a Predictive Model for a Hall Effect Thruster

The performance of an axisymmetric multi-fluid Hall thruster code that incorporates a self-consistent, data-driven closure model for the anomalous electron transport is investigated. Five different operating conditions of the H9 magnetically shielded Hall thruster are simulated with the Jet Propulsion Laboratory’s Hall2De. In order to capture the inherent uncertainty associated with the closure model, O(100) simulations are run for each condition, each of using a coefficient set sampled randomly from a probability distribution. The results of these simulations provide probabilistic predictions of thruster performance quantities including thrust, and discharge current, as well as several component efficiencies and centerline plasma properties. The model is found to yield converged solutions at all conditions, with large 10 kHzrange oscillations and performance trends with voltage and flow rate similar to experiment. The model under-predicts the thrust by 15-25% and over-predicts the discharge current by 20% on average compared to experiments at the same discharge voltage and mass flow rate. This performance discrepancy is due to lower beam utilization, mass utilization, and divergence efficiency than experiment, resulting from high Hall parameters in the acceleration region, which lead to a protracted ion acceleration region. The physical processes underlying this result are discussed in the context of future data-driven modeling efforts.

Jorns, Benjamin A.↗

NASA NTRSDate not supplied

Probabalistic Risk Analysis and Thermal Margin Process for an Inflatable Aeroshell

Uncertainties always exist in atmospheric entry aeroheating environments and the thermal response of thermal protection system (TPS) material. These uncertainties are mitigated in the design by ap-plying margin and factors of safety to the TPS. Entry vehicle TPS is often conservatively over-sized for the heat loads that are experienced along the entry trajectory by stacking worst-case scenarios together. Additionally, the current TPS design and margin process used by NASA offers very little insight into the risk of over-temperature during flight and the reliability of the heat shield performance [1,3]. A probabilistic margin process can be used to calculate the amount of TPS margin necessary to survive a given entry heat load at a specified level of risk [2,3,4]. The vehicle’s initial entry state (entry velocity, flight path angle, and entry mass) determines the expected atmospheric entry environmental conditions and resulting heat load that the entry vehicle will experience. If there is flexibility in the entry state, then this process can be used to select an appropriate combination of entry state parameters and TPS size to target a desired reentry reliability. This probabilistic margin process allows engineers to make informed aeroshell design, entry-trajectory design, and TPS performance risk trades while preventing excessive TPS margin from being applied. The probabilistic TPS margin process has been performed to determine TPS thickness and entry heating constraints given an acceptable risk level for the Low Earth Orbit Flight Experiment of an Inflatable Decelerator (LOFTID) flight project. The process is used in a manner to size the entry heat load for a given flexible TPS (FTPS) thickness so that it meets project reliability standards while allowing the FTPS and the underlying inflatable structure (IS) to be pushed to adequately high temperatures. Since the LOFTID project is an experimental flight demonstration, it is de-sired to drive the FTPS and IS to temperatures that cover a large range of their thermal response models’ applicability. This will allow the thermal response models to be better improved and validated post-flight using LOFTID’s extensive instrumentation embedded within the aeroshell. The presentation demonstrates how uncertainty analysis is carried out using an end-to-end Monte Carlo process where three separate Monte Carlo simulations are run in sequence. The first Monte Carlo simulation operates on the entry trajectory model to generate trajectory parameter dispersions that are fed into the second Monte Carlo simulation. The second Monte Carlo simulation operates on the aerothermodynamics model to generate aeroheating parameter dispersions that are fed into the third Monte Carlo simulation. The third Monte Carlo simulation operates on the FTPS material thermal response model to generate the final FTPS/IS thermal response dispersions. The end-to-end Monte Carlo simulation propagates the uncertainties of each model into the next to quantify the resulting uncertainty of the FTPS/IS thermal response. The fractional contributions of the uncertain parameters in the trajectory, aerothermal, and thermal response models to the variance in the FTPS/IS thermal response is determined as a byproduct of the Monte Carlo analysis. The structural uncertainty of the FTPS thermal response model is evaluated by flight relevant ground testing and model error analysis using test measurements. This probabilistic TPS margin process had never been applied to an entry vehicle and it is one of the LOFTID project’s goals to demonstrate its merits.

Steven A. Tobin↗

DOE OSTI2023

Beyond Expected Values Evolving Metrics for Resource Adequacy Assessment

Resource adequacy analysis quantifies the likelihood of capacity shortfall on a power system in a probabilistic manner. Using a combination of statistical techniques and power system fundamentals, the analysis typically evaluates hundreds or thousands of stochastic random samples (replications) of varying load, generator outages, variable renewable energy availability, and other aspects of power system uncertainty. In this range of uncertainty, there are - at times - periods where the power system's available resources are insufficient to meet system demand, referred to as a shortfall event. Today's power systems' rapidly evolving generation mix is changing the types of data needed by system planners and regulators, which can often render traditional resource adequacy metrics insufficient for ensuring resource adequacy for tomorrow's grid. In this paper we provide a critical assessment of traditional measures of shortfall risk in power systems, discussing their shortcomings and how they compare to metrics used in other domains. From this analysis we propose four steps forward for improving power system resource adequacy risk metrics in the future.

ENERGY PLANNING, POLICY, AND ECONOMY↗

NASA NTRSDate not supplied

Validation of a Probabilistic Continuity Assessment Method for Earth Observation Portfolios

With the increased reliance on spaceborne Earth observation data among the Earth science community and other end users, it is important that efforts are made to promote data continuity for a range of parameters of interest. Continuity gaps may occur between missions measuring like parameters due to mission development delays or early termination and introduce the potential of increased uncertainty for retrieved parameters. To inform portfolio-level decisions for Earth observing missions, Ivanco et al. developed a method that enables the assessment of the probability of continuity gaps for multi-mission architectures and provides a framework to assess this probability in the context of multiple scenarios that represent possible future states of the architecture [Ivanco et al., “A Scenario-Based Approach to Assess Continuity Gaps in Earth Observations,” IEEE Aerospace Conf., 2024]. While this method was previously applied to assess continuity gaps for a specific multi-mission architecture, it had not yet been validated with historical data. This paper outlines the process of validating the probabilistic gap assessment method by utilizing data obtained from past NASA Earth Science mission formulation documents and provides a discussion of the results and takeaways from the validation. Future areas of improvement pertaining to both the modeling and simulation methodologies and underlying assumptions are identified and discussed.

Katharine Burn↗

DOE OSTI2015

Branch-and-Bound algorithm applied to uncertainty quantification of a Boiling Water Reactor Station Blackout

Evaluation of the impacts of uncertainty and sensitivity in modeling presents a significant set of challenges in particular to high fidelity modeling. Computational costs and validation of models creates a need for cost effective decision making with regards to experiment design. Experiments designed to validate computation models can be used to reduce uncertainty in the physical model. In some cases, large uncertainty in a particular aspect of the model may or may not have a large impact on the final results. For example, modeling of a relief valve may result in large uncertainty, however, the actual effects on final peak clad temperature in a reactor transient may be small and the large uncertainty with respect to valve modeling may be considered acceptable. Additionally, the ability to determine the adequacy of a model and the validation supporting it should be considered within a risk informed framework. Low fidelity modeling with large uncertainty may be considered adequate if the uncertainty is considered acceptable with respect to risk. In other words, models that are used to evaluate the probability of failure should be evaluated more rigorously with the intent of increasing safety margin. Probabilistic risk assessment (PRA) techniques have traditionally been used to identify accident conditions and transients. Traditional classical event tree methods utilize analysts’ knowledge and experience to identify the important timing of events in coordination with thermal-hydraulic modeling. These methods lack the capability to evaluate complex dynamic systems. In these systems, time and energy scales associated with transient events may vary as a function of transition times and energies to arrive at a different physical state. Dynamic PRA (DPRA) methods provide a more rigorous analysis of complex dynamic systems. Unfortunately DPRA methods introduce issues associated with combinatorial explosion of states. This study presents a methodology to address combinatorial explosion using a Branch-and-Bound algorithm applied to Dynamic Event Trees (DET), which utilize LENDIT (L – Length, E – Energy, N – Number, D – Distribution, I – Information, and T – Time) as well as a set theory to describe system, state, resource, and response (S2R2) sets to create bounding functions for the DET. The optimization of the DET in identifying high probability failure branches is extended to create a Phenomenological Identification and Ranking Table (PIRT) methodology to evaluate modeling parameters important to safety of those failure branches that have a high probability of failure. The PIRT can then be used as a tool to identify and evaluate the need for experimental validation of models that have the potential to reduce risk. Finally, in order to demonstrate this methodology, a Boiling Water Reactor (BWR) Station Blackout (SBO) case study is presented.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗