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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Solving Stochastic Inverse Problems for Property–Structure Linkages Using Data-Consistent Inversion and Machine Learning

Determining process–structure–property linkages is one of the key objectives in material science, and uncertainty quantification plays a critical role in understanding both process–structure and structure–property linkages. In this work, we seek to learn a distribution of microstructure parameters that are consistent in the sense that the forward propagation of this distribution through a crystal plasticity finite element model matches a target distribution on materials properties. This stochastic inversion formulation infers a distribution of acceptable/consistent microstructures, as opposed to a deterministic solution, which expands the range of feasible designs in a probabilistic manner. Furthermore, to solve this stochastic inverse problem, we employ a recently developed uncertainty quantification framework based on push-forward probability measures, which combines techniques from measure theory and Bayes’ rule to define a unique and numerically stable solution. This approach requires making an initial prediction using an initial guess for the distribution on model inputs and solving a stochastic forward problem. To reduce the computational burden in solving both stochastic forward and stochastic inverse problems, we combine this approach with a machine learning Bayesian regression model based on Gaussian processes and demonstrate the proposed methodology on two representative case studies in structure–property linkages.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Optimal test selection for prediction uncertainty reduction

Economic factors and experimental limitations often lead to sparse and/or imprecise data used for the calibration and validation of computational models. This paper addresses resource allocation for calibration and validation experiments, in order to maximize their effectiveness within given resource constraints. When observation data are used for model calibration, the quality of the inferred parameter descriptions is directly affected by the quality and quantity of the data. This paper characterizes parameter uncertainty within a probabilistic framework, which enables the uncertainty to be systematically reduced with additional data. The validation assessment is also uncertain in the presence of sparse and imprecise data; therefore, this paper proposes an approach for quantifying the resulting validation uncertainty. Since calibration and validation uncertainty affect the prediction of interest, the proposed framework explores the decision of cost versus importance of data in terms of the impact on the prediction uncertainty. Often, calibration and validation tests may be performed for different input scenarios, and this paper shows how the calibration and validation results from different conditions may be integrated into the prediction. Then, a constrained discrete optimization formulation that selects the number of tests of each type (calibration or validation at given input conditions) is proposed. Furthermore, the proposed test selection methodology is demonstrated on a microelectromechanical system (MEMS) example.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Multi-Formalism Modeling for Disaster Resilience, Forecasting, and Response

Disaster response preparedness, risk mitigation, and effective post-event response are critical for national security, public health, and economic integrity. For areas impacted by extreme events, timely and accurate impact assessments of lifeline infrastructures are critical. Traditional disaster management and situational awareness platforms are not capable of handling the massive influx of available information from traditional and non-traditional sources. Next-generation analytic assessment approaches, where use of dynamically sourced, heterogeneous data with near real-time availability are integrated into a continually-updated analytics framework. The objective of this research was to develop a foundational multi-formalism modeling platform to integrate novel data sources for use in improving situational awareness after a disaster event. Specifically, to 1) provide an architecture for machine-learning based data fusion various multi-sensor datasets; 2) classify, geolocate, and temporally bin novel data sources for use in spatially-enabled machine-learning based data fusion; and 3) derive confidence-based observation data with machine-learning based prediction to fill spatial and temporal observation gaps. This project developed a reusable cloud-based pipeline architecture for ingesting, storing, and analyzing relevant data, executing a range of deep-learning models, and visualize the information geographically. The pipeline development was informed by previous PNNL investments (StreamKit) and built upon leading-edge technologies consisting of: 1) a raw datastore; 2) a data enrichment pipeline with custom and third-party analytics; 3) enriched data storage; and 4) a custom UI to display the enriched data. Machine learning/deep learning models were selected and tested to classify social media images for relevancy and presence of flood waters. Our custom trained relevance models were run on a validation dataset and the overall accuracy of the relevance classifiers ranged from 65% to 90%. We found that convolutional neural network (CNN) models were both faster and more accurate than more traditional machine learning models. We applied the relevance classifier to remove non-relevant images and then undertook a limited training of CNN models to detect flood on ~1,800 labeled images. The testing accuracy of the flood detection models were ~88%. To improve the geographic location of both social media and oblique aerial images we tested a multi-step workflow built on a pre-trained deep-learning model. To identify similarity features from test and reference scenes, we applied the Xception and Faiss models to a set of test images with inaccurate spatial locations, as well and precisely-located reference scenes from the general area. Matching reference scenes to the test scenes with the closest similarity index had limited success in improving the precision of test scene location and additional methods have been identified for testing. Data fusion between authoritative geographic data (satellite imaging) and non-authoritative crowdsourced data is an underlying theme throughout this research and methods are tested bring these data to a common geographic form through feature matching and transformations. The automated extraction of supporting information for disaster response from oblique aerial images or ground-level social media images is accomplished through semantic image segmentation and transformation. The non-authoritative data are used to validate the authoritative data collections and processing and optionally, t+0 flood models. In addition, the common form geographic data are combined with other static landscape features to develop spatially-explicit training vectors used in deep generative statistical inference models to develop complex non-linear relationships in static and dynamic data and ultimately derive a spatially continuous and probabilistic assessment of flood damage with the event domain.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2017

Systematic parameter inference in stochastic mesoscopic modeling

We propose a method to efficiently determine the optimal coarse-grained force field in mesoscopic stochastic simulations of Newtonian fluid and polymer melt systems modeled by dissipative particle dynamics (DPD) and energy conserving dissipative particle dynamics (eDPD). The response surfaces of various target properties (viscosity, diffusivity, pressure, etc.) with respect to model parameters are constructed based on the generalized polynomial chaos (gPC) expansion using simulation results on sampling points (e.g., individual parameter sets). To alleviate the computational cost to evaluate the target properties, we employ the compressive sensing method to compute the coefficients of the dominant gPC terms given the prior knowledge that the coefficients are “sparse”. The proposed method shows comparable accuracy with the standard probabilistic collocation method (PCM) while it imposes a much weaker restriction on the number of the simulation samples especially for systems with high dimensional parametric space. Fully access to the response surfaces within the confidence range enables us to infer the optimal force parameters given the desirable values of target properties at the macroscopic scale. Moreover, it enables us to investigate the intrinsic relationship between the model parameters, identify possible degeneracies in the parameter space, and optimize the model by eliminating model redundancies. The proposed method provides an efficient alternative approach for constructing mesoscopic models by inferring model parameters to recover target properties of the physics systems (e.g., from experimental measurements), where those force field parameters and formulation cannot be derived from the microscopic level in a straight forward way.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Scalable and efficient learning from crowds with Gaussian processes

Over the last few years, multiply-annotated data has become a very popular source of information. Online platforms such as Amazon Mechanical Turk have revolutionized the labelling process needed for any classification task, sharing the effort between a number of annotators (instead of the classical single expert). This crowdsourcing approach has introduced new challenging problems, such as handling disagreements on the annotated samples or combining the unknown expertise of the annotators. Probabilistic methods, such as Gaussian Processes (GP), have proven successful to model this new crowdsourcing scenario. However, GPs do not scale up well with the training set size, which makes them prohibitive for medium-to-large datasets (beyond 10K training instances). This constitutes a serious limitation for current real-world applications. In this work, we introduce two scalable and efficient GP-based crowdsourcing methods that allow for processing previously-prohibitive datasets. The first one is an efficient and fast approximation to GP with squared exponential (SE) kernel. The second allows for learning a more flexible kernel at the expense of a heavier training (but still scalable to large datasets). Since the latter is not a GP-SE approximation, it can be also considered as a whole new scalable and efficient crowdsourcing method, useful for any dataset size. Both methods use Fourier features and variational inference, can predict the class of new samples, and estimate the expertise of the involved annotators. A complete experimentation compares them with state-of-the-art probabilistic approaches in synthetic and real crowdsourcing datasets of different sizes. Finally, they stand out as the best performing approach for large scale problems. Moreover, the second method is competitive with the current state-of-the-art for small datasets.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
NASA NTRS2017

Near Real-Time Probabilistic Damage Diagnosis Using Surrogate Modeling and High Performance Computing

This work investigates novel approaches to probabilistic damage diagnosis that utilize surrogate modeling and high performance computing (HPC) to achieve substantial computational speedup. Motivated by Digital Twin, a structural health management (SHM) paradigm that integrates vehicle-specific characteristics with continual in-situ damage diagnosis and prognosis, the methods studied herein yield near real-time damage assessments that could enable monitoring of a vehicle's health while it is operating (i.e. online SHM). High-fidelity modeling and uncertainty quantification (UQ), both critical to Digital Twin, are incorporated using finite element method simulations and Bayesian inference, respectively. The crux of the proposed Bayesian diagnosis methods, however, is the reformulation of the numerical sampling algorithms (e.g. Markov chain Monte Carlo) used to generate the resulting probabilistic damage estimates. To this end, three distinct methods are demonstrated for rapid sampling that utilize surrogate modeling and exploit various degrees of parallelism for leveraging HPC. The accuracy and computational efficiency of the methods are compared on the problem of strain-based crack identification in thin plates. While each approach has inherent problem-specific strengths and weaknesses, all approaches are shown to provide accurate probabilistic damage diagnoses and several orders of magnitude computational speedup relative to a baseline Bayesian diagnosis implementation.

Warner, James E.↗
DOE OSTI2016

Phylogenetically resolving epidemiologic linkage

The use of phylogenetic trees in epidemiological investigations has become commonplace, but their epidemiological interpretation has not been systematically evaluated. Here, we use an HIV-1 within-host coalescent model to probabilistically evaluate transmission histories of two epidemiologically linked hosts. Previous critique of phylogenetic reconstruction has claimed that direction of transmission is difficult to infer, and that the existence of unsampled intermediary links or common sources can never be excluded. The phylogenetic relationship between the HIV populations of epidemiologically linked hosts can be classified into six types of trees, based on cladistic relationships and whether the reconstruction is consistent with the true transmission history or not. We show that the direction of transmission and whether unsampled intermediary links or common sources existed make very different predictions about expected phylogenetic relationships: (i) Direction of transmission can often be established when paraphyly exists, (ii) intermediary links can be excluded when multiple lineages were transmitted, and (iii) when the sampled individuals’ HIV populations both are monophyletic a common source was likely the origin. Inconsistent results, suggesting the wrong transmission direction, were generally rare. In addition, the expected tree topology also depends on the number of transmitted lineages, the sample size, the time of the sample relative to transmission, and how fast the diversity increases after infection. Typically, 20 or more sequences per subject give robust results. Moreover, we confirm our theoretical evaluations with analyses of real transmission histories and discuss how our findings should aid in interpreting phylogenetic results.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Imprecise global sensitivity analysis using bayesian multimodel inference and importance sampling

Global Sensitivity Analysis (GSA) aims to understand the relative importance of uncertain input variables to model response. Conventional GSA involves calculating sensitivity (Sobol’) indices for a model with known model parameter distributions. However, model parameters are affected by aleatory and epistemic uncertainty, with the latter often caused by lack of data. In this paper, we propose a new framework to quantify uncertainty in probability model-form and model parameters resulting from small datasets and integrate these uncertainties into Sobol’ index estimates. First, the process establishes, through Bayesian multimodel inference, a set of candidate probability models and their associated probabilities. Imprecise Sobol’ indices are calculated from these probability models using an importance sampling reweighting approach. This results in probabilistic Sobol’ indices, whose distribution characterizes uncertainty in the sensitivity resulting from small dataset size. The imprecise Sobol’ indices thus provide a measure of confidence in the sensitivity estimate and, moreover, can be used to inform data collection efforts targeted to minimize the impact of uncertainties. Through an example studying the parameters of a Timoshenko beam, we show that these probabilistic Sobol’ indices converge to the true/deterministic Sobol’ indices as the dataset size increases and hence, distribution-form uncertainty reduces. The approach is then applied to assess the sensitivity of the out-of-plane properties of an E-glass fiber composite material to its constituent properties. This second example illustrates the approach for an important class of materials with wide-ranging applications when data may be lacking for some input parameters.

42 ENGINEERING↗
NASA NTRS2002

Classification image analysis: estimation and statistical inference for two-alternative forced-choice experiments

We consider estimation and statistical hypothesis testing on classification images obtained from the two-alternative forced-choice experimental paradigm. We begin with a probabilistic model of task performance for simple forced-choice detection and discrimination tasks. Particular attention is paid to general linear filter models because these models lead to a direct interpretation of the classification image as an estimate of the filter weights. We then describe an estimation procedure for obtaining classification images from observer data. A number of statistical tests are presented for testing various hypotheses from classification images based on some more compact set of features derived from them. As an example of how the methods we describe can be used, we present a case study investigating detection of a Gaussian bump profile.

Non-NASA Center↗
NASA NTRS2011

Thoughts Without Content are Empty, Intuitions Without Concepts are Blind - Determinism and Contingency Revisited

Was the emergence of life a predictable outcome of chemical evolution on earth? Could evolution produce life very different from ours? These are one of the oldest questions in the field of the origin of life that not only have broad philosophical implications but also impact how we approach the problem from the methodological standpoint. Framing the issue in terms of the dichotomy between contingency and determinism is not a fortunate because these two terms in their conventional meaning are neither mutually exclusive nor jointly exhaustive. Determinism, represented in natural sciences by Newtonian physics, relies on the assumption that every event is causally determined by a chain of previous events. In the context of the origin of life it means that once the initial conditions on the early earth have been specified further evolution follows inevitably. Considering uncertainties about conditions on the prebiotic earth, many plausible sets of initial conditions can be defined, each followed by a separate deterministic trajectory. This conventional understanding of determinism does not admit contingency. Further, it has no implications for evaluating how many sets of initial conditions lead to the emergence of life. It appears that a better framing of the problem is as follows: given plausible sets of initial conditions on the early earth how probable and broadly spread are evolutionary trajectories that lead to life? Instead of undertaking an impossible task of specifying microscopic initial conditions for all components of the system one uses a reduced representation of this system and specify only a small set of essential macroscopic parameters, values (or ranges of values) of which can be identified, inferred or estimated from experiment, theory or historical record. The following evolutionary trajectories are still governed by laws of physics and chemistry but become probabilistic and "contingency" is admitted as variations in other variables in the system. A similar reasoning is common in other fields of science, for example in statistical mechanics. Some trajectories lead to life, perhaps in different forms, whereas others do not. Of our true interest is the ratio of these two outcomes. The issue of determinism does not directly enter the picture. The debate about the likelihood of the emergence of life is quite old. One view holds that the origin of life is an event governed by chance, and the result of so many random events (contingencies) is unpredictable. This view was eloquently expressed by Monod. In his book "Chance or Necessity" he argued that life was a product of "nature's roulette." In an alternative view, expressed in particular by deDuve and Morowitz, the origin of life is considered a highly probable or even inevitable event (although its details need not be determined in every respect). Only in this sense the origin of life can be considered a "deterministic event".

Pohorille, Andrew↗
NASA NTRS2017

Near Earth Asteroid Characterization for Threat Assessment

Physical characteristics of NEAs are an essential input to modeling behavior during atmospheric entry and to assess the risk of impact but determining these properties requires a non-trivial investment of time and resources. The characteristics relevant to these models include size, density, strength and ablation coefficient. Some of these characteristics cannot be directly measured, but rather must be inferred from related measurements of asteroids and/or meteorites. Furthermore, for the majority of NEAs, only the basic measurements exist so often properties must be inferred from statistics of the population of more completely characterized objects. The Asteroid Threat Assessment Project at NASA Ames Research Center has developed a probabilistic asteroid impact risk (PAIR) model in order to assess the risk of asteroid impact. Our PAIR model and its use to develop probability distributions of impact risk are discussed in other contributions to PDC 2017 (e.g., Mathias et al.). Here we utilize PAIR to investigate which NEA characteristics are important for assessing the impact threat by investigating how changes in these characteristics alter the damage predicted by PAIR. We will also provide an assessment of the current state of knowledge of the NEA characteristics of importance for asteroid threat assessment. The relative importance of different properties as identified using PAIR will be combined with our assessment of the current state of knowledge to identify potential high impact investigations. In addition, we will discuss an ongoing effort to collate the existing measurements of NEA properties of interest to the planetary defense community into a readily accessible database.

Asteroid characterization↗
DOE OSTI2015

Comparing probabilistic and descriptive analyses of time–dose–toxicity relationship for determining no-observed-adverse-effect level in drug development

The no-observed-adverse-effect level (NOAEL) of a drug defined from animal studies is important for inferring a maximal safe dose in human. However, several issues are associated with its concept, determination and application. It is confined to the actual doses used in the study; becomes lower with increasing sample size or dose levels; and reflects the risk level seen in the experiment rather than what may be relevant for human. We explored a pharmacometric approach in an attempt to address these issues. We first used simulation to examine the behaviour of the NOAEL values as determined by current common practice; and then fitted the probability of toxicity as a function of treatment duration and dose to data collected from all applicable toxicology studies of a test compound. Our investigation was in the context of an irreversible toxicity that is detected at the end of the study. Simulations illustrated NOAEL's dependency on experimental factors such as dose and sample size, as well as the underlying uncertainty. Modelling the probability as a continuous function of treatment duration and dose simultaneously to data from multiple studies allowed the estimation of the dose, along with its confidence interval, for a maximal risk level that might be deemed as acceptable for human. The model-based data integration also reconciled between-study inconsistency and explicitly provided maximised estimation confidence. Such alternative NOAEL determination method should be explored for its more efficient data use, more quantifiable insight to toxic doses, and the potential for more relevant animal-to-human translation. - Highlights: • Simulations revealed issues with NOAEL concept, determination and application. • Probabilistic modelling was used to address these issues. • The model integrated time-dose-toxicity data from multiple studies. • The approach uses data efficiently and may allow more meaningful human translation.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1987

NESSUS/expert and NESSUS/FPI in the Probabilistic Structural Analysis Methods (PSAM) program

The Numerical Evaluation of Stochastic Structures under Stress (NESSUS) is the primary computer code being developed in the NASA Probabilistic Structural Analysis Methods (PSAM) project. It consists of four modules NESSUS/EXPERT, NESSUS/FPI, NESSUS/PRE and NESSUS/FEM. This presentation concentrates on EXPERT and FPI. To provide an effective interface between NESSUS and the user, an expert system module called NESSUS/EXPERT is being developed. That system uses the CLIPS artificial intelligence code developed to NASA-JSC. The code is compatible with FORTRAN, the standard language for codes in PSAM. The user interacts with the CLIPS inference engine, which is linked to the knowledge database. The perturbation database generated by NESSUS/FEM and managed in EXPERT is used to develop the so-called response or performance model in the random variables. Two independent probabilistic methods are available in PSAM for the computation of the probabilistic structural response. These are the Fast Probability Integration (FPI) method and Monte Carlo simulation. FPI is classified as an advanced reliability method and has been developed over the past ten years by researchers addressing the reliability of civil engineering structures. Monte Carlo is a well-established technique for computing probabilities by conducting a number of deterministic analyses with specified input distributional information.

Burnside, O. H.↗
DOE OSTI2019

ENSEMBLE KALMAN FILTERS FOR RELIABILITY ESTIMATION IN PERFUSION INFERENCE

We consider the solution of inverse problems in dynamic contrast–enhanced imaging by means of ensemble Kalman filters. Our quantity of interest is blood perfusion, i.e., blood flow rates in tissue. While existing approaches to compute blood perfusion parameters for given time series of radiological measurements mainly rely on deterministic, deconvolution–based methods, we aim at recovering probabilistic solution information for given noisy measurements. To this end, we model radiological image capturing as a sequential data assimilation process and solve it by an ensemble Kalman filter. Thereby, we recover deterministic results as an ensemble–based mean and are able to compute reliability information such as probabilities for the perfusion to be in a given range. Our target application is the inference of blood perfusion parameters in the human brain. A numerical study shows promising results for artificial measurements generated by a digital perfusion phantom.

Engineering↗
DOE OSTI2020

Statistical Treatment of Inverse Problems Constrained by Differential Equations-based Models with Stochastic Terms

This paper introduces a statistical treatment of inverse problems constrained by models with stochastic terms. The solution of the forward problem is given by a distribution represented numerically by an ensemble of simulations. The goal is to formulate the inverse problem, in particular the objective function, to find the closest forward distribution (i.e., the output of the stochastic forward problem) that best explains the distribution of the observations in a certain metric. We use proper scoring rules, a concept employed in statistical forecast verification, namely energy, variogram, and hybrid (i.e., combination of the two) scores. We study the performance of the proposed formulation in the context of two applications: a coefficient field inversion for subsurface flow governed by an elliptic partial differential equation with a stochastic source and a parameter inversion for power grid governed by differential-algebraic equations. In both cases we show that the variogram and the hybrid scores produce better parameter inversion results than does the energy score, whereas the energy score leads to better probabilistic predictions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

A Bayesian Approach to Real-Time Dynamic Parameter Estimation Using Phasor Measurement Unit Measurement

Here, we develop a polynomial-chaos-expansion (PCE)-based approach for decentralized dynamic parameter estimation through Bayesian inference. Using this approach, the non-Gaussian distribution of the inverted parameters is obtained. More specifically, we first represent the decentralized generator model with the PCE-based surrogate. This surrogate allows us to efficiently evaluate the time-consuming dynamic solver at parameter values through Metropolis-Hastings (M-H)-based Markov chain Monte Carlo (MCMC). Then, we propose a two-stage hybrid Markov chain Monte Carlo (MCMC) to recover a posteriori distribution of the decentralized generator model parameters. In the first stage, we use the gradient-enhanced Langevin MCMC algorithm to characterize an intermediate posterior parameter distribution. This algorithm is computationally scalable to the high-dimensional parameter space. Based on the intermediate posterior distribution, during the second stage, we use the adaptive MCMC algorithm to fine-tune the strong correlations between the parameters. Finally, the fully recovered a posterior distribution is obtained in the end. The simulation results show that the proposed PCE-based hybrid MCMC algorithm can accurately and efficiently estimate the high-dimensional generator dynamic model parameters with full probabilistic distribution provided.

42 ENGINEERING↗
DOE OSTI2018

Learning from crowds with variational Gaussian processes

Solving a supervised learning problem requires to label a training set. This task is traditionally performed by an expert, who provides a label for each sample. The proliferation of social web services (e.g., Amazon Mechanical Turk) has introduced an alternative crowdsourcing approach. Anybody with a computer can register in one of these services and label, either partially or completely, a dataset. The effort of labeling is then shared between a great number of annotators. However, this approach introduces scientifically challenging problems such as combining the unknown expertise of the annotators, handling disagreements on the annotated samples, or detecting the existence of spammer and adversarial annotators. All these problems require probabilistic sound solutions which go beyond the naive use of majority voting plus classical classification methods. In this work we introduce a new crowdsourcing model and inference procedure which trains a Gaussian Process classifier using the noisy labels provided by the annotators. Variational Bayes inference is used to estimate all unknowns. The proposed model can predict the class of new samples and assess the expertise of the involved annotators. Moreover, the Bayesian treatment allows for a solid uncertainty quantification. Since when predicting the class of a new sample we might have access to some annotations for it, we also show how our method can naturally incorporate this additional information. Furthermore, a comprehensive experimental section evaluates the proposed method with synthetic and real experiments, showing that it consistently outperforms other state-of-the-art crowdsourcing approaches.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2014

Aviation Safety Risk Modeling: Lessons Learned From Multiple Knowledge Elicitation Sessions

Aviation safety risk modeling has elements of both art and science. In a complex domain, such as the National Airspace System (NAS), it is essential that knowledge elicitation (KE) sessions with domain experts be performed to facilitate the making of plausible inferences about the possible impacts of future technologies and procedures. This study discusses lessons learned throughout the multiple KE sessions held with domain experts to construct probabilistic safety risk models for a Loss of Control Accident Framework (LOCAF), FLightdeck Automation Problems (FLAP), and Runway Incursion (RI) mishap scenarios. The intent of these safety risk models is to support a portfolio analysis of NASA's Aviation Safety Program (AvSP). These models use the flexible, probabilistic approach of Bayesian Belief Networks (BBNs) and influence diagrams to model the complex interactions of aviation system risk factors. Each KE session had a different set of experts with diverse expertise, such as pilot, air traffic controller, certification, and/or human factors knowledge that was elicited to construct a composite, systems-level risk model. There were numerous "lessons learned" from these KE sessions that deal with behavioral aggregation, conditional probability modeling, object-oriented construction, interpretation of the safety risk results, and model verification/validation that are presented in this paper.

Luxhoj, J. T.↗