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Accelerated basis adaptation in homogeneous chaos spaces

Polynomial chaos expansions (PCE) provide an efficient approach to uncertainty quantification (UQ) and have been adapted to diverse applications across the spectrum of science and engineering. For situations involving large stochastic parameterizations, the curse of dimensionality renders PCE-based methods computationally prohibitive. A basis adaptation approach for PCE was proposed by Tipireddy and Ghanem (2014) which transforms the input random variables through an isometry such that sufficient probabilistic characterization of specific quantities of interest (QoI) is concentrated in an algebraic manifold embedded in the linear span of the dominant transformed variables. While quite versatile, that original version of the PCE basis adaptation exhibited slow convergence for a number of problems of practical significance. In the present paper, we propose two novel methods to accelerate the convergence of the original basis adaptation approach, thus expanding its reach while also providing insight into its performance. In the first method, information gained from a pilot PCE representation is used to correct the mean and Gaussian coefficients in the adapted space. By taking advantages of probabilistic information in higher dimensional adaptation gleaned from an initial adaptation, the second method updates the rotation matrix used to identify the dominant transformed variables. In this manner, the new rotation matrix concentrates even more probabilistic information in its first few dimensions. These two method can be combined to achieve even better performance, the combined method is referred to as sequentially optimized adaptation method. Here, the methods are demonstrated on an analytical test function and a model of a space structure with several sub-components and a non-smooth quantity of interest representing the maximum acceleration over time. Both methods achieve accelerated convergence of the basis adaptation approach with negligible additional costs.

Accelerated convergence↗

Nonylphenol in pregnant women and their matching fetuses: Placental transfer and potential risks of infants

As the predominant environmental biodegradation product of nonylphenol (NP) ethoxylates and with proven estrogenic effects, NP is formed during the alkylation process of phenols. The purposes of this study were (1) to examine maternal and prenatal exposure to NP in Taiwan, (2) to determine the level of placental protection against NP exposure as well as the level of NP in breast milk, and (3) to assess the potential risk for breastfed newborns exposed to NP through the milk. Thirty pairs of maternal and fetal blood samples, placenta, and breast milk during the 1st and the 3rd months of lactation were collected. External NP exposures of these specimens were then analyzed by using high-performance liquid chromatography coupling with fluorescence detection. Next, the socio-demographics, lifestyle, delivery method, dietary and work history were collected using a questionnaire. In addition, the daily intake of NP from consuming breast milk in the 1st and 3rd months for newborns was studied through deterministic and probabilistic risk assessment methods. The geometric means and geometric standard deviation of NP levels in maternal blood, fetal cord blood, placenta, and breast milk in the 1st and 3rd months were 14.6 (1.7) ng/ml, 18.8 (1.8) ng/ml, 19.8 (1.9) ng/g, 23.5 (3.2) ng/ml, and 57.3 (1.4) ng/ml, respectively. The probabilistic percentiles (50th, 75th, and 95th) of daily intake NP in breast milk were 4.33, 7.79, and 18.39 μg/kg-bw/day in the 1st month, respectively, and were 8.11, 10.78, 16.08 μg/kg-bw/day in the 3rd month, respectively. The probabilistic distributions (5th, 25th, and 50th) of risk for infants aged 1 month old were 0.27, 0.64, and 1.15, respectively, and that for infants aged 3 month old were 0.31, 0.46, and 0.62, respectively. Through repeated exposure from the dietary intake of expectant mothers, fetuses could encounter a high NP exposure level due to transplacental absorption, partitioning between the maternal and fetal compartments. Daily NP intake via breast milk in three month-old babies exceeded the tolerable daily intake (TDI) of 5 µg/kg bw/day indicated a potential risk for Taiwan infants. - Highlights: • A cohort of pregnant women was established and followed until delivery. • The pregnant and lactating mothers and their infants were exposed to NP. • Fetuses in Taiwan showed high NP milk level. • Daily NP intake via breast milk indicated a potential risk for Taiwan infants.

60 APPLIED LIFE SCIENCES↗

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↗

Reconstructing cerebrovascular networks under local physiological constraints by integer programming

We introduce a probabilistic approach to vessel network extraction that enforces physiological constraints on the vessel structure. The method accounts for both image evidence and geometric relationships between vessels by solving an integer program, which is shown to yield the maximum a posteriori (MAP) estimate to the probabilistic model. Starting from an over-connected network, it is pruning vessel stumps and spurious connections by evaluating the local geometry and the global connectivity of the graph. We utilize a high-resolution micro computed tomography (µCT) dataset of a cerebrovascular corrosion cast to obtain a reference network and learn the prior distributions of our probabilistic model. As a result, we perform experiments on micro magnetic resonance angiography (µMRA) images of mouse brains and discuss properties of the networks obtained under different tracking and pruning approaches.

59 BASIC BIOLOGICAL SCIENCES↗

Bayesian learning with Gaussian processes for low-dimensional representations of time-dependent nonlinear systems

This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that poses the problem of learning low-dimensional model terms as a regression of state space data and corresponding time derivatives by minimizing the residual of reduced system equations. Standard operator inference models perform well with accurate training data that are dense in time, but producing stable and accurate models when the state data are noisy and/or sparse in time remains a challenge. Another challenge is the lack of uncertainty estimation for the predictions from the operator inference models. Our approach addresses these challenges by incorporating Gaussian process surrogates into the operator inference framework to (1) probabilistically describe uncertainties in the state predictions and (2) procure analytical time derivative estimates with quantified uncertainties. The formulation leads to a generalized least-squares regression and, ultimately, reduced-order models that are described probabilistically with a closed-form expression for the posterior distribution of the operators. The resulting probabilistic surrogate model propagates uncertainties from the observed state data to reduced-order predictions. Furthermore, we demonstrate the method is effective for constructing low-dimensional models of two nonlinear partial differential equations representing a compressible flow and a nonlinear diffusion–reaction process, as well as for estimating the parameters of a low-dimensional system of nonlinear ordinary differential equations representing compartmental models in epidemiology.

Data-driven model reduction↗

An efficient method to identify uncertainties of WRF-Solar variables in forecasting solar irradiance using a tangent linear sensitivity analysis

Uncertainty in predicting solar energy resources introduces major challenges in power system management and necessitates the development of reliable probabilistic solar forecasts. As the first part of the development of probabilistic forecasts based on the Weather Research and Forecasting model with solar extensions (WRF-Solar), this study presents a tangent linear approach to identify input variables responsible for the largest uncertainties in predicting surface solar irradiance and clouds. A tangent linear analysis is capable of efficiently investigating sensitivities of output variables with respect to various input variables of WRF-Solar because this approach avoids the computational burden of perturbing the initial conditions of individual input variables. We develop tangent linear models (TLMs) for six WRF-Solar physics packages that control the formation and dissipation of clouds and solar radiation, and we evaluate the validity of TLMs using a linearity test. The tangent linear sensitivity analysis is conducted under various scenarios based on satellite observations and model simulations to consider realistic input conditions. A simple method is used to quantify the impact of the uncertainty of input variables on the output variables from the TLMs. The results demonstrate that uncertainties in the output variables that are the focus of this study—including global horizontal irradiance, direct normal irradiance, cloud mixing ratio, cloud tendency, cloud fraction, and sensible and latent heat fluxes—are highly sensitive to uncertainties in 14 input variables. This study indicates that the tangent linear method can identify key variables of physics modules in WRF-Solar that can be stochastically perturbed to generate ensemble-based probabilistic forecasts.

14 SOLAR ENERGY↗

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↗

Multi-component background learning automates signal detection for spectroscopic data

Abstract Automated experimentation has yielded data acquisition rates that supersede human processing capabilities. Artificial Intelligence offers new possibilities for automating data interpretation to generate large, high-quality datasets. Background subtraction is a long-standing challenge, particularly in settings where multiple sources of the background signal coexist, and automatic extraction of signals of interest from measured signals accelerates data interpretation. Herein, we present an unsupervised probabilistic learning approach that analyzes large data collections to identify multiple background sources and establish the probability that any given data point contains a signal of interest. The approach is demonstrated on X-ray diffraction and Raman spectroscopy data and is suitable to any type of data where the signal of interest is a positive addition to the background signals. While the model can incorporate prior knowledge, it does not require knowledge of the signals since the shapes of the background signals, the noise levels, and the signal of interest are simultaneously learned via a probabilistic matrix factorization framework. Automated identification of interpretable signals by unsupervised probabilistic learning avoids the injection of human bias and expedites signal extraction in large datasets, a transformative capability with many applications in the physical sciences and beyond.

Ament, Sebastian E.↗

National and subnational short-term forecasting of COVID-19 in Germany and Poland during early 2021

During the COVID-19 pandemic there has been a strong interest in forecasts of the short-term development of epidemiological indicators to inform decision makers. In this study we evaluate probabilistic real-time predictions of confirmed cases and deaths from COVID-19 in Germany and Poland for the period from January through April 2021. We evaluate probabilistic real-time predictions of confirmed cases and deaths from COVID-19 in Germany and Poland. These were issued by 15 different forecasting models, run by independent research teams. Moreover, we study the performance of combined ensemble forecasts. Evaluation of probabilistic forecasts is based on proper scoring rules, along with interval coverage proportions to assess calibration. The presented work is part of a pre-registered evaluation study. We find that many, though not all, models outperform a simple baseline model up to four weeks ahead for the considered targets. Ensemble methods show very good relative performance. The addressed time period is characterized by rather stable non-pharmaceutical interventions in both countries, making short-term predictions more straightforward than in previous periods. However, major trend changes in reported cases, like the rebound in cases due to the rise of the B.1.1.7 (Alpha) variant in March 2021, prove challenging to predict. Multi-model approaches can help to improve the performance of epidemiological forecasts. However, while death numbers can be predicted with some success based on current case and hospitalization data, predictability of case numbers remains low beyond quite short time horizons. Additional data sources including sequencing and mobility data, which were not extensively used in the present study, may help to improve performance.

60 APPLIED LIFE SCIENCES↗

Life Cycle Cost Analysis of Prestressed Concrete Poles Subjected to Wind, Surges, and Waves

Prestressed concrete (PC) poles are becoming popular choices to support coastal power transmission systems. However, the existing literature does not offer a detailed analysis of the effectiveness of PC poles in terms of long-term vulnerabilities and the direct and indirect costs. This is due to (1) lack of fragility models for PC poles and (2) lack of probabilistic wind, storm surge, and wave models in coastal settings. In this study, we address these gaps through a series of Monte Carlo simulations to estimate fragility of PC poles as a function of age and hazard (wind, surges, and waves) intensity, and the development of a probabilistic hazard model based on 10,000 years of synthetic tropical cyclone data. The probabilistic hazard model is used in conjunction with high-resolution hydrodynamic models to generate realizations of coastal wind, storm surges, and waves for the Louisiana and Mississippi coasts. A comprehensive life cycle cost analysis for a service life of 70 years considering direct and indirect losses is conducted to compare the performance of a transmission line located in Pascagoula, Mississippi, when wood poles are replaced by PC poles. Results showed that aging has a minor effect on the reliability of PC poles, highlighting the advantages of replacing wood poles with PC poles, especially in coastal areas. In addition, PC poles are significantly more cost-effective compared with wood poles over their life cycle, leading to an estimated saving of $11.55 million (68.17% reduction). The results of this study provide key insight to inform decision-making processes to keep the coastal power grids resilient and cost-effective against future storm hazards.

natural disasters↗

Three-dimensional microstructure-explicit and void-explicit mesoscale simulations of detonation of HMX at millimeter sample size scale

Fully three-dimensional (3D) microstructure-explicit and void-explicit mesoscale simulations of the shock-to-detonation (SDT) process of pressed granular HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) are performed. The overall size scale of the models is up to 3 × 3 × 15 mm3, with ∼30 000 grains and 206 265 voids. The models account for the heterogeneous material microstructure, constituent distribution, constituent morphology, and voids. Loading conditions considered involve piston velocities in the range of 600–1200 m/s or pressures in the range of 4–8 GPa. The focus is on analyzing the SDT process and the effects of microstructure and voids on the run-to-detonation distance (RDD). Companion two-dimensional (2D) simulations are also carried out to assess the differences between 2D and 3D. Statistically equivalent microstructure sample sets (SEMSSs) are generated and used for both 2D and 3D, allowing the prediction of the statistical and probabilistic Pop plots (PPs). The predictions are in general agreement with trends in available experimental data in the literature. It is found that both the microstructure (heterogeneous grain size, morphology, and size distribution) and voids significantly affect the RDD and the PPs. These effects are systematically delineated and quantified via the use of SEMSSs with different combinations of attributes. A recently developed probabilistic formulation for the PPs is used to characterize the results, allowing uncertainties in the relations between the shock pressure and RDD arising from material heterogeneities to be quantified. The probabilistic formulation is further used to quantify the confidence levels in the ranked order of influences of different combinations of microstructure and voids on the PPs.

Miller, Christopher (ORCID:0000000206844381)↗

On the Language of Reliability: A System Engineer Perspective

In its classical definition, risk is defined by three elements: what can go wrong, what are its consequences, and how likely is it to occur? While this definition makes sense in a regulatory-based framework where for the current fleet of operating light water reactors (LWRs), the risks associated with nuclear power plants typically are characterized in terms of core damage and large early release frequency (LERF), this approach does not provide a useful snapshot of the health of the plant from a broader perspective. This is due to the very narrow context in which the term “risk” typically is defined as nuclear safety aspects that have the potential to impact public health. In this paper, we take the viewpoint of nuclear safety that is reflective of the current fleet of operating LWRs for which core damage frequency and LERF are appropriate metrics. For other advanced reactor designs, other more applicable technology neutral metrics of reactor safety metrics would be specified. A possible alternate path would start by redefining the word risk with a broader meaning that better reflects the needs of a system health and asset management decision-making process. Rather than asking how likely an event could occur (in probabilistic terms), we can ask how far this event is from occurring. Our approach starts by defining and quantifying component and system health in terms of a “distance” between its actual and limiting conditions, i.e., determination of the margin that exists between the current state/condition and the state where the component/system is no longer capable of achieving its intended function. A margin is a measure that is more reflective of the current state or performance of a component, and therefore more closely tied to decisions that are made on an ongoing basis. Further, we will show how, given the data available from plant equipment reliability and monitoring (e.g., pump vibration data) and prognostic (e.g., component remaining useful life estimation) data, a margin can be described and determined for all types of maintenance approaches (e.g., corrective or predictive maintenance). We show how classical reliability models (e.g., fault trees) can be used to quantify the system margin provided component margin values. In the approach described in this paper, the propagation of margin values through classical reliability models are not performed using classical probabilistic calculations applied to sets (as performed in a typical plant probabilistic risk assessment). Instead, we show how it is possible to propagate margin values through Boolean logic gates (i.e., AND and OR operators) through distance-based operations.

97 MATHEMATICS AND COMPUTING↗

Assessment of doses in contaminated urban areas: modelling exercise based on Fukushima data

State-of-the-art dose assessment models were applied to estimate doses to the population in urban areas contaminated by the Fukushima Daiichi Nuclear Power Plant accident. Assessment results were compared among five models, and comparisons of model predictions with actual measurements were also made. Assessments were performed using both probabilistic and deterministic approaches. Predicted dose distributions for indoor and outdoor workers from a probabilistic approach were in good agreement with the actual measurements. In addition, when the models were applied to assess the doses to the representative person, based on a concept recommended by the International Commission on Radiological Protection and in the International Atomic Energy Agency Safety Standards, it was evident that doses to the representative person obtained with a deterministic approach were always higher than those obtained with a probabilistic approach using the same model.

dose assessment↗

Extending Performance and Evaluating Risks of PV Systems Failure Using a Fault Tree and Event Tree Approach: Analysis of the Possible Application

Performance and reliability of photovoltaic (PV) systems are important issues in the overall evaluation of a PV plant and its components. While performance is connected to the amount of energy produced by the PV installation in the working environmental conditions, reliability impacts the availability of the system to produce the expected amount of energy. In both cases, the evaluation should be done considering information and data coming from indoor as well as outdoor tests. In this paper a way of re-thinking performance, giving it a probabilistic connotation, and connecting the two concepts of performance and reliability is proposed. The paper follows a theoretical approach and discusses the way to obtaining such information, facing benefits and problems. The proposed probabilistic performance accounts for the probability of the system to function correctly, thus passing through the complementary evaluation of the probability of system malfunctions and consequences. Scenarios have to be identified where the system is not functioning properly or at all. They are expected to be combined in a probabilistic safety analysis (PSA) based approach, providing not only the required probability, but also being capable of giving a prioritization of the risks and the most dominant scenario associated to a specific situation. This approach can offer the possibility to highlight the most critical parts of a PV system, as well as providing support in design activities identifying weak connections.

14 SOLAR ENERGY↗

FunM2C: A Filter for Uncertainty Visualization of Multivariate Data on Multi-Core Devices

Uncertainty visualization is an emerging research topic in data visualization because neglecting uncertainty in visualization can lead to inaccurate assessments. In this paper, we study the propagation of multivariate data uncertainty in visualization. Although there have been a few advancements in probabilistic uncertainty visualization of multivariate data, three critical challenges remain to be addressed. First, the state-of-the-art probabilistic uncertainty visualization framework is limited to bivariate data (two variables). Second, existing uncertainty visualization algorithms use computationally intensive techniques and lack support for cross-platform portability. Third, as a consequence of the computational expense, integration into production visualization tools is impractical. In this work, we address all three issues and make a threefold contribution. First, we take a step to generalize the state-of-the-art probabilistic framework for bivariate data to multivariate data with an arbitrary number of variables. Second, through utilization of VTK-m’s shared-memory parallelism and cross-platform compatibility features, we demonstrate acceleration of multivariate uncertainty visualization on different many-core architectures, including OpenMP and AMD GPUs. Third, we demonstrate the integration of our algorithms with the ParaView software. We demonstrate the utility of our algorithms through experiments on multivariate simulation data with three and four variables.

Hari, Gautam↗

SURROGATE MODEL DEVELOPMENT AND VALIDATION FOR RELIABILITY ANALYSIS OF REACTOR PRESSURE VESSELS

In nuclear light water reactors (LWRs), the reactor coolant, core and shroud are contained within a massive, thick walled steel vessel known as a reactor pressure vessel (RPV). Given the tremendous size of these structures, RPVs typically contain a large population of pre-existing flaws introduced in the manufacturing process. After many years of operation, irradiation-induced embrittlement makes these vessels increasingly susceptible to fracture initiation at the locations of the pre-existing flaws. Because of the uncertainty in the loading conditions, flaw characteristics and material properties, probabilistic methods are widely accepted and used in assessing RPV integrity. The Fracture Analysis of Vessels – Oak Ridge (FAVOR) computer program developed by researchers at Oak Ridge National Laboratory is widely used for this purpose. This program can be used in order to perform deterministic and probabilistic risk-informed analyses of the structural integrity of an RPV subjected to a range of thermal-hydraulic events. FAVOR uses a one-dimensional representation of the global response of the RPV, which is appropriate for the beltline region, which experiences the most embrittlement, and employs an influence coefficient technique to rapidly compute stress intensity factors for axis-aligned surface-breaking flaws. The Grizzly code is currently under development at Idaho National Laboratory (INL) to be used as a general multiphysics simulation tool to study a variety of degradation mechanisms in nuclear power plant components. The first application of Grizzly has been to study fracture in embrittled RPVs. Grizzly can be used to model the thermo-mechanical response of an RPV under transient conditions observed in a pressurized thermal shock (PTS) scenario. The global response of the vessel provides boundary conditions for local 3D 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. To use Grizzly for probabilistic analysis, it is necessary to have a way to rapidly evaluate stress intensity factors. To accomplish this goal, a reduced order model (ROM) has been developed to efficiently represent the behavior of a detailed 3D Grizzly model used to calculate fracture parameters. This approach uses the stress intensity factor influence coefficient method that has been used with great success in FAVOR. Instead of interpolating between tabulated solutions, as FAVOR does, the ROM approach uses a response surface methodology to compute fracture solutions based on a sampled set of results used to train the ROM. The main advantages of this approach are that the process of generating the training data can be fully automated, and the procedure can be readily used to consider more general flaw configurations. This paper demonstrates the procedure used to generate a ROM to rapidly compute stress intensity factors for axis-aligned flaws. The results from this procedure are in good agreement with those produced using the traditional influence coefficient interpolation procedure, which gives confidence in this method. This paves the way for applying this procedure for more general flaw configurations.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Building and using dynamic risk-informed diagnosis procedures for complex system accidents

Accidents pose unique challenges for operating crews in complex systems such as nuclear power plants, presenting limitations in plant status information and lack of detailed monitoring, diagnosis, and response planning support. Advances in severe accident simulation and dynamic probabilistic risk assessment provide an opportunity to garner detailed insight into accident scenarios. In this article, we demonstrate how to build and use a framework which leverages dynamic probabilistic risk assessment, simulation, and dynamic Bayesian networks to provide real-time monitoring and diagnostic support for severe accidents in a nuclear power plant. We use general purpose modeling technology, the dynamic Bayesian network, and adapt it for risk management of complex engineering systems. This article presents a prototype model for monitoring and diagnosing system states associated with loss of flow and transient overpower accidents in a generic sodium fast reactor. We discuss using this framework to create a risk-informed accident management framework called Safely Managing Accidental Reactor Transients procedures. This represents a new application of risk assessment, expanding probabilistic risk assessment techniques beyond static decision support into dynamic, real-time models which support accident diagnosis and management.

Groth, Katrina M.↗