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Presentation slides for Nuclear Regulatory Commission Public Meeting on July 18th about advanced nuclear reactor risk metrics and data needs to support risk estimation.
This work presents a computationally-efficient inverse approach to probabilistic damage diagnosis. Given strain data at a limited number of measurement locations, Bayesian inference and Markov Chain Monte Carlo (MCMC) sampling are used to estimate probability distributions of the unknown location, size, and orientation of damage. Substantial computational speedup is obtained by replacing a three-dimensional finite element (FE) model with an efficient surrogate model. The approach is experimentally validated on cracked test specimens where full field strains are determined using digital image correlation (DIC). Access to full field DIC data allows for testing of different hypothetical sensor arrangements, facilitating the study of strain-based diagnosis effectiveness as the distance between damage and measurement locations increases. The ability of the framework to effectively perform both probabilistic damage localization and characterization in cracked plates is demonstrated and the impact of measurement location on uncertainty in the predictions is shown. Furthermore, the analysis time to produce these predictions is orders of magnitude less than a baseline Bayesian approach with the FE method by utilizing surrogate modeling and effective numerical sampling approaches.
This paper provides a coherent and efficient computational framework for stochastic multiscale analysis of material systems in the presence of parametric uncertainties and modeling errors. Uncertainty in those model parameters that are not deduced as upscaled quantities is attributed to an uncertainty “germ”. While such parameters can appear at any scale, they are predominant at the finest analysis scale. Additional uncertainties stemming from statistical estimation, attributed to lack of data and model error, are associated with each submodel contributing to the multiscale system. Here, a robust and efficient framework based on a generalized extended polynomial chaos expansion (gEPCE) is proposed to simultaneously propagate all these uncertainties in order to provide a probabilistic representation of specific quantities of interest (QoI). We characterize the full probability distribution of the QoI and the uncertainty in the failure probability pertaining to its tails. By combining gEPCE with kernel density estimation (KDE) and directional derivatives, we construct sensitivity measures that connect these statistical metrics of QoI to the various sources of uncertainty to assess their individual and combined impacts. An illustrative problem featuring three-point bending of a composite beam is investigated to demonstrate the presented approach.
The emergence of variational quantum applications has led to the development of automatic differentiation techniques in quantum computing. Existing work has formulated differentiable quantum programming with bounded loops, providing a framework for scalable gradient calculation by quantum means for training quantum variational applications. However, promising parameterized quantum applications, e.g., quantum walk and unitary implementation, cannot be trained in the existing framework due to the natural involvement of unbounded loops. To fill in the gap, we provide the first differentiable quantum programming framework with unbounded loops, including a newly designed differentiation rule, code transformation, and their correctness proof. Technically, we introduce a randomized estimator for derivatives to deal with the infinite sum in the differentiation of unbounded loops, whose applicability in classical and probabilistic programming is also discussed. We implement our framework with Python and Q# and demonstrate a reasonable sample efficiency. Through extensive case studies, we showcase an exciting application of our framework in automatically identifying close-to-optimal parameters for several parameterized quantum applications.
In the Task 1 report for the U.S. Nuclear Regulatory Commission (NRC) funded Local Intense Precipitation (LIP) Probabilistic Flood Hazard Assessment (PFHA) Pilot Study, the Pacific Northwest National Laboratory (PNNL) reviewed hydrologic and hydraulic modeling approaches for estimation of LIP flooding and their implementation in readily available simulation software packages (Prasad and Yuan 2020). NRC’s interest is in developing guidance for performing LIP PFHA at nuclear power plant (NPP) sites. This report describes the work done under Task 2 of the study that focused on describing uncertainties associated with LIP flood modeling. Two main types of uncertainties exist in LIP flood modeling: (1) aleatory uncertainties that arise from the inherent natural variability of the hydrometeorological system and (2) epistemic uncertainties that arise from the analysts’ incomplete knowledge of the hydrometeorological and site configuration. Principal sources for aleatory variability in LIP flood simulations at NPP sites include precipitation (i.e., magnitude, duration, and temporal distribution of LIP events), initial conditions (e.g., soil moisture content, stormwater drainage discharge, surface storage), boundary conditions (e.g., upstream discharge, downstream water surface elevations), and long-term temporal trends (e.g., climate change). This report describes approaches used for estimating the aleatory variability in precipitation including precipitation-frequency analysis, numerical weather prediction, and stochastic weather generation. Data sources that can be used to estimate aleatory variability in initial and boundary conditions are also described. Approaches to include effects of long-term trends like those from climate change into estimation of aleatory variability are summarized. Sources of epistemic uncertainty in LIP flood simulations at NPP sites include process representation (e.g., multiple approaches to represent runoff generation, stormwater drainage, and hydraulic routing), site configurations (e.g., site layout, flow features, status of temporary flood protection, blockage of drains), model resolution, and long-term temporal trends (e.g., known/planned site alterations, land-use changes at and in the vicinity of the site). The report describes alternative process representations (methods and models), particularly those implemented in the LIP flood simulation software packages reviewed in Task 1 report, and lists the associated model parameters. Approaches for estimating model parameters when surface and subsurface water exchanges occur are also described.
We evaluated the implications of different approaches to characterize the uncertainty of calibrated parameters of microsimulation decision models (DMs) and quantified the value of such uncertainty in decision making. We calibrated the natural history model of CRC to simulated epidemiological data with different degrees of uncertainty and obtained the joint posterior distribution of the parameters using a Bayesian approach. We conducted a probabilistic sensitivity analysis (PSA) on all the model parameters with different characterizations of the uncertainty of the calibrated parameters. We estimated the value of uncertainty of the various characterizations with a value of information analysis. We conducted all analyses using high-performance computing resources running the Extreme-scale Model Exploration with Swift (EMEWS) framework. The posterior distribution had a high correlation among some parameters. The parameters of the Weibull hazard function for the age of onset of adenomas had the highest posterior correlation of -0.958. When comparing full posterior distributions and the maximum-a-posteriori estimate of the calibrated parameters, there is little difference in the spread of the distribution of the CEA outcomes with a similar expected value of perfect information (EVPI) of $\$$653 and $\$$685, respectively, at a willingness-to-pay (WTP) threshold of $\$$66,000 per quality-adjusted life year (QALY). Ignoring correlation on the calibrated parameters’ posterior distribution produced the broadest distribution of CEA outcomes and the highest EVPI of $\$$809 at the same WTP threshold. Different characterizations of the uncertainty of calibrated parameters affect the expected value of eliminating parametric uncertainty on the CEA. Ignoring inherent correlation among calibrated parameters on a PSA overestimates the value of uncertainty.
After the Fukushima Daiichi Accident, the safety features such as accident tolerant fuel (ATF) and diverse and flexible coping strategies (FLEX) for existing nuclear fleets are being investigated by the US Department of Energy under the Light Water Reactor Sustainability Program. This research is being conducted to quantify the risk-benefit of these safety features. Dynamic probabilistic risk assessment (DPRA)-based response-surface approach has been presented to quantify the FLEX and ATF benefits by estimating the risk associated with each option. ATFs with multilayered silicon carbide (SiC), iron-chromium-aluminum, and chromium-coated zirconium cladding were considered in this study. While these ATF candidates perform better than the current zirconium cladding (Zr), they may introduce additional failure modes in some operating conditions. The fuel failure analysis modules (FAMs) were developed to investigate ATF performance. The dynamic risk assessments were performed using RAVEN, a DPRA tool, coupled with RELAP5 and FAMs. A cumulative distribution function-based index provided a mean of comparing the benefits of safety enhancements. For medium break loss of coolant accidents, FLEX operational timing window for each fuel type was estimated. Among these ATF candidates, SiC-type ATF was the most beneficial candidate for an increased safety margin than Zr-based fuel and was found to complement FLEX strategies in terms of risk and coping time.
The HD 220 program was created as part of the space shuttle solid rocket booster recovery system definition. The model was generated to investigate the damage to SRB components under water impact loads. The random nature of environmental parameters, such as ocean waves and wind conditions, necessitates estimation of the relative frequency of occurrence for these parameters. The nondeterministic nature of component strengths also lends itself to probabilistic simulation. The Monte Carlo technique allows the simultaneous perturbation of multiple independent parameters and provides outputs describing the probability distribution functions of the dependent parameters. This allows the user to determine the required statistics for each output parameter.
In countries with long historical tradition in thermal water therapy and with several mineral-medicinal thermal sources, workplaces within thermal centers may be a source of radon exposure which may be intensified if these are located in regions of high level of natural radiation. According to the EU Directive 96/29/Euratom (repealed by the Directive 2013/59/EURATOM) each Member State shall identify, by means of survey or any other adequate mean, the work activities where a significant increase in the exposure from natural radiation sources may occur, including thermal centers where the exposure to thoron/radon daughters or gamma radiation may occur. The purpose of this work was to perform a radiological characterization of selected thermal centers based on indoor dosimetry. The effective doses received by workers due to radon inhalation were estimated and gamma dose rates were measured through continuous periods. The radon risk for indoor exposure was assessed on a probabilistic basis both on thermal centers and workers' dwellings. Radon levels within the thermal centers ranged from 73 to 4335 Bq/m{sup 3} and the values within the workers dwellings are of the same order of magnitude, 68-4051 Bq/m{sup 3}. Approximately 66 % of indoor radon concentration values are above the maximum EU reference (300 Bq/m{sup 3}) and 94 % of the effective dose is higher than 1 mSv/year. In some situations, radon levels at residential environments are much higher than at workplaces and effective doses are higher than 6 mSv/year, both at residential and work environments. (authors)
In facilities that process special nuclear material (SNM) it is important to account accurately for the fissile material that enters and leaves the plant. Although there are many stages and processes through which materials must be traced and measured, the focus of this project is material that is “held-up” in equipment, pipes, and ducts during normal operation and that can accumulate over time into significant quantities. Accurately estimating the holdup is essential for proper SNM accounting (vis-à-vis nuclear non-proliferation), criticality and radiation safety, waste management, and efficient plant operation. Usually it is not possible to directly measure the holdup quantity and location, so these must be inferred from measured radiation fields, primarily gamma and less frequently neutrons. Current methods to quantify holdup, i.e. Generalized Geometry Holdup (GGH), primarily rely on simple source configurations and crude radiation transport models aided by ad hoc correction factors. This project seeks an alternate method of performing measurement-based holdup calculations using a predictive model that employs state-of-the-art radiation transport codes capable of accurately simulating such situations. Inverse and data assimilation methods use the forward transport model to search for a source configuration that best matches the measured data and simultaneously provide an estimate of the level of confidence in the correctness of such configuration. In this work the holdup problem is re-interpreted as an inverse problem that is under-determined, hence may permit multiple solutions. A probabilistic approach is applied to solving the resulting inverse problem. This approach rates possible solutions according to their plausibility given the measurements and initial information. This is accomplished through the use of Bayes’ Theorem that resolves the issue of multiple solutions by giving an estimate of the probability of observing each possible solution. To use Bayes’ Theorem, one must have a model y(x) that maps the state variables x (the solution in this case) to the measurements y. In this case, the unknown state variables are the configuration and composition of the heldup SNM. The measurements are the detector readings. Thus, the natural model is neutral-particle radiation transport where a wealth of computational tools exists for performing these simulations accurately and efficiently. The combination of predictive model and Bayesian inference forms the Data Integration with Modeled Predictions (DIMP) method that serves as foundation for this project. The cost functional describing the model-to-data misfit is computed via a norm created by the inverse of the covariance matrix of the model parameters and responses. Since the model y(x) for the holdup problem is nonlinear, a nonlinear optimization on Q is conducted via Newton-type iterative methods to find the optimal values of the model parameters x. This project comprised a collaboration between NC State University (NCSU), the University of South Carolina (USC), and Oak Ridge National Laboratory (ORNL). The project was originally proposed in seven main tasks with an eighth contingency task to be performed if time and funding permitted; in fact time did not permit commencement of the contingency task and it was not performed. The remaining tasks involved holdup analysis with gamma detection strategies and separately with neutrons based on coincidence counting. Early in the project, and upon consultation with experts in coincidence counting it became evident that this approach is not viable for holdup applications and this task was replaced with an alternative, but valuable investigation that was carried out by the USC partner. Nevertheless, the experimental 4 measurements at ORNL of both gamma and neutron sources for the purpose of constructing Detector Response Functions (DRFs) with the associated uncertainties were indeed completed.
The current project develops a novel approach that uses a probabilistic description to capture the current state of knowledge about the computational solution. To effectively spread the computational effort over multiple nodes, the global computational domain is split into many subdomains. Computational uncertainty in the solution translates into uncertain boundary conditions for the equation system to be solved on those subdomains, and many independent, concurrent subdomain simulations are used to account for this bound- ary condition uncertainty. By relying on the fact that solutions on neighboring subdomains must agree with each other, a more accurate estimate for the global solution can be achieved. Statistical approaches in this update process make it possible to account for the effect of system faults in the probabilistic description of the computational solution, and the associated uncertainty is reduced through successive iterations. By combining all of these elements, the probabilistic reformulation allows splitting the computational work over very many independent tasks for good scalability, while being robust to system faults.
For long duration missions outside of the protection of the Earth s magnetic field, space radiation presents significant health risks including cancer mortality. Space radiation consists of solar particle events (SPEs), comprised largely of medium energy protons (less than several hundred MeV); and galactic cosmic ray (GCR), which include high energy protons and heavy ions. While the frequency distribution of SPEs depends strongly upon the phase within the solar activity cycle, the individual SPE occurrences themselves are random in nature. We estimated the probability of SPE occurrence using a non-homogeneous Poisson model to fit the historical database of proton measurements. Distributions of particle fluences of SPEs for a specified mission period were simulated ranging from its 5 th to 95th percentile to assess the cancer risk distribution. Spectral variability of SPEs was also examined, because the detailed energy spectra of protons are important especially at high energy levels for assessing the cancer risk associated with energetic particles for large events. We estimated the overall cumulative probability of GCR environment for a specified mission period using a solar modulation model for the temporal characterization of the GCR environment represented by the deceleration potential (^). Probabilistic assessment of cancer fatal risk was calculated for various periods of lunar and Mars missions. This probabilistic approach to risk assessment from space radiation is in support of mission design and operational planning for future manned space exploration missions. In future work, this probabilistic approach to the space radiation will be combined with a probabilistic approach to the radiobiological factors that contribute to the uncertainties in projecting cancer risks.
Customer-level rooftop photovoltaic (PV) has been widely integrated into distribution systems. In most cases, PVs are installed behind-the-meter (BTM), and only the net demand is recorded. Therefore, the native demand and PV generation are unknown to utilities. Separating native demand and solar generation from net demand is critical for improving grid-edge observability. In this paper, a novel approach is proposed for disaggregating customer-level BTM PV generation using low-resolution but widely available hourly smart meter data. The proposed approach exploits the strong correlation between monthly nocturnal and diurnal native demands and the high similarity among PV generation profiles. First, a joint probability density function (PDF) of monthly nocturnal and diurnal native demands is constructed for customers without PVs, using Gaussian mixture modeling (GMM). Deviation from the constructed PDF is utilized to probabilistically assess the monthly solar generation of customers with PVs. Then, to identify hourly BTM solar generation for these customers, their estimated monthly solar generation is decomposed into an hourly timescale; to do this, we have proposed a maximum likelihood estimation (MLE)-based technique that utilizes hourly typical solar exemplars. Leveraging the strong monthly native demand correlation and high PV generation similarity enhances our approach's robustness against the volatility of customers’ hourly load and enables highly-accurate disaggregation. Furthermore, the proposed approach has been verified using real native demand and PV generation data.
The degree of error expected in the measurement of widths of sea ice leads along a single transect are examined in a probabilistic sense under assumed orientation and width distributions, where both isotropic and anisotropic lead orientations are examined. Methods are developed for estimating the distribution of 'actual' widths (measured perpendicular to the local lead orientation) knowing the 'apparent' width distribution (measured along the transect), and vice versa. The distribution of errors, defined as the difference between the actual and apparent lead width, can be estimated from the two width distributions, and all moments of this distribution can be determined. The problem is illustrated with Landsat imagery and the procedure is applied to a submarine sonar transect. Results are determined for a range of geometries, and indicate the importance of orientation information if data sampled along a transect are to be used for the description of lead geometries. While the application here is to sea ice leads, the methodology can be applied to measurements of any linear feature.
The development of new products is dependent on product designs that incorporate high levels of reliability along with a design that meets predetermined levels of system cost. Additional constraints on the product include explicit and implicit performance requirements. Existing reliability and cost prediction methods result in no direct linkage between variables affecting these two dominant product attributes. A methodology to integrate reliability and cost estimates using a sequential linear approximation method is proposed. The sequential linear approximation method utilizes probability of failure sensitivities determined from probabilistic reliability methods as well a manufacturing cost sensitivities. The application of the sequential linear approximation method to a mechanical system is demonstrated.
To better understand the potential benefits and drawbacks of utilizing a probability-based method, a number of alternative approaches to the collision avoidance problem were examined and summarized in the paper "Survey of Conflict Detection and Resolution Modeling Methods" which was presented in August 1997 at the AIAA Guidance, Navigation, and Control Conference. The paper provides a summary and comparative evaluation of the many different approaches that have been used in the past to perform conflict analysis. Each method is categorized in its dynamic modeling approach and method of handling conflict detection and conflict resolution. For example, one category included the extrapolation method used to predict future trajectories of which 3 were defined: nominal, probabilistic, and worst-case. Another category listed the metrics and parameters used by each method to make conflict decisions (i.e. estimated time to closest point of approach, miss distance, current separation, expected maneuvering cost, probability of conflict). Other useful information such as the ability to handle multi-aircraft conflicts and cooperative and non-cooperative maneuvering is also included.
Although most asteroids and other near-Earth objects (NEOs) do not pose a threat to Earth’s inhabitants, impacts from objects that are just tens of meters in diameter can cause significant damage if they occur over a populated area. This paper forms the foundation of an effort at NASA Ames Research Center to quantify these risks and identify the greatest risk-driving parameters and uncertainties. An integrated risk model that couples dynamic probabilistic simulations of strike occurrences with physics-based models of NEO impact damage factors has been developed to generate casualty estimates for a range of NEO impact properties. Currently, the model focuses on the risk due to blast overpressure damage from airbursts and impacts on land. The model is first used to reproduce results from established sources, and then is extended to perform sensitivity studies that yield greater insights into risk driving parameters. Results show that meteor strength and entry angle play a role for small to mid-size NEOs, and that accounting for the specific target location significantly affects casualty estimates and dominates the risk. Future work will continue to refine and expand the models to better characterize key impact risk factors, include additional types of threats such as tsunamis and climate effects, and ultimately support assessments of potential asteroid mitigation strategies.
Floods and heavy precipitation have disruptive impacts worldwide, but their historical variability remains only partially understood at the global scale. This article aims at reducing this knowledge gap by jointly analyzing seasonal maxima of streamflow and precipitation at more than 3,000 stations over a 100‐year period. The analysis is based on Hidden Climate Indices (HCIs). Like standard climate indices (e.g., Nino 3.4, NAO), HCIs are used as covariates explaining the temporal variability of data, but unlike them, HCIs are estimated from the data. In this work, a distinction is made between common HCIs, that affect both heavy precipitation and floods, and specific HCIs, that exclusively affect one or the other. Overall, HCIs do not show noticeable autocorrelation, but some are affected by noticeable trends. In particular, strong and wide‐ranging trends are identified in precipitation‐specific HCIs, while trends affecting flood‐specific HCIs are weaker and have more localized effects. A probabilistic model is then derived to link HCIs and large‐scale atmospheric variables (pressure, wind, temperature) and to reconstruct HCIs since 1836 using the 20CRv3 reanalysis. In turn this allows estimating the probability of occurrence of floods and heavy precipitation at the global scale. This 180‐year reconstruction highlights flood hot‐spots and hot‐moments in the distant past, well before the establishment of perennial monitoring networks. Finally, the approach presented in this study is generic and paves the way for an improved characterization of historical variability by making a better use of long but highly irregular station data sets.