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NASA NTRSDate not supplied

Uncertainty Quantification of Inducer Eigenvalues using Conditional Assessment of Models and Modal Test of Simpler Systems

The low pressure fuel pump inducer of the new Space Launch System RS25 core stage engine operates in a highly complex environment that substantially affects its modal characteristics. Some of the more important effects are fluid-added mass resulting from operation within a light liquid (Hydrogen), and the magnification of this effect due to tight tip clearance. Since higher order cavitation has been identified as a significant harmonic driver, knowledge of the natural frequency of potentially excitable modes is critical for safe operation, but this frequency cannot be measured during the severe operational environment. A comprehensive testing and analysis program has therefore been performed over the last four years to identify the nominal value and uncertainty of the frequency by modeling and testing four simpler structures which share some of the characteristics of the operational inducer. This testing was used to assess and adjust modeling techniques and excellent correlation was achieved. Identification of the uncertainty in the inducer frequency itself was still problematic, however. This difficulty led to an investigation of Bayesian uncertainty quantification techniques, and to the application of the relatively simple technique of Multi-Variate Normal conditional distributions to calculate the inducer natural frequency uncertainty. Assumptions on prior distributions of uncertainty of the fluid-added mass and tip clearance effect are initially applied to models of each of the simple structures and the inducer itself, and these uncertainties are propagated to generate natural frequencies using design of experiments. Simple response surfaces are then created from this data in order to calculate a Covariance Matrix relating all of these natural frequencies. Finally, the results from modal test of the simple structures are considered to be observations and used to calculate the conditional variance of the desired inducer frequencies. As this method is less rigorous than more complicated Bayesian methods reported in the literature, a conservative factor is applied to the result, but the resulting uncertainty is still significantly less than originally estimated and will greatly assist certification of the inducer for use in the engine.

Uncertainty Quantification↗
DOE OSTI2024

Uncertainty quantification of graph convolution neural network models of evolving processes

The application of neural network models to scientific machine learning tasks has proliferated in recent years. In particular, neural networks have proved to be adept at modeling processes with spatial–temporal complexity. Nevertheless, these highly parameterized models have garnered skepticism in their ability to produce outputs with quantified error bounds over the regimes of interest. Hence there is a need to find uncertainty quantification methods that are suitable for neural networks. In this work we present comparisons of the parametric uncertainty quantification of neural networks modeling complex spatial–temporal processes with Hamiltonian Monte Carlo and Stein variational gradient descent and its projected variant. Specifically we apply these methods to graph convolutional neural network models of evolving systems modeled with recurrent neural network and neural ordinary differential equations architectures. We show that Stein variational inference is a viable alternative to Monte Carlo methods with some clear advantages for complex neural network models. For our exemplars, Stein variational interference gave similar pushed forward uncertainty profiles through time compared to Hamiltonian Monte Carlo, albeit with generally more generous variance. As a result, projected Stein variational gradient descent also produced similar uncertainty profiles to the non-projected counterpart, but large reductions in the active weight space were confounded by the stability of the neural network predictions and the convoluted likelihood landscape.

36 MATERIALS SCIENCE↗
NASA NTRSDate not supplied

Uncertainty Quantification of Inducer Natural Frequency using Conditional Assessment of Modeling and Modal Testing of Simpler Systems

The low pressure fuel pump inducer of the new Space Launch System RS25 core stage engine operates in a highly complex environment that substantially affects its modal characteristics. Some of the more important effects are fluid-added mass resulting from operation within a light liquid (Hydrogen), and the magnification of this effect due to tight tip clearance. Since higher order cavitation has been identified as a significant harmonic driver, knowledge of the natural frequency of potentially excitable modes is critical for safe operation, but this frequency cannot be measured during the severe operational environment. A comprehensive testing and analysis program has therefore been performed over the last four years to identify the nominal value and uncertainty of the frequency by modeling and testing four simpler structures which share some of the characteristics of the operational inducer. This testing was used to assess and adjust modeling techniques and excellent correlation was achieved. Identification of the uncertainty in the inducer frequency itself was still problematic, however. This difficulty led to an investigation of Bayesian uncertainty quantification techniques, and to the application of the relatively simple technique of Multi-Variate Normal conditional distributions to calculate the inducer natural frequency uncertainty. Assumptions on prior distributions of uncertainty of the fluid-added mass and tip clearance effect are initially applied to models of each of the simple structures and the inducer itself, and these uncertainties are propagated to generate natural frequencies using design of experiments. Simple response surfaces are then created from this data in order to calculate a Covariance Matrix relating all of these natural frequencies. Finally, the results from modal test of the simple structures are considered to be observations and used to calculate the conditional variance of the desired inducer frequencies. As this method is less rigorous than more complicated Bayesian methods reported in the literature, a conservative factor is applied to the result, but the resulting uncertainty is still significantly less than originally estimated and will greatly assist certification of the inducer for use in the engine.

Uncertainty Quantification↗
NASA NTRS2009

Convective Weather Avoidance with Uncertain Weather Forecasts

Convective weather events have a disruptive impact on air traffic both in terminal area and in en-route airspaces. In order to make sure that the national air transportation system is safe and efficient, it is essential to respond to convective weather events effectively. Traffic flow control initiatives in response to convective weather include ground delay, airborne delay, miles-in-trail restrictions as well as tactical and strategic rerouting. The rerouting initiatives can potentially increase traffic density and complexity in regions neighboring the convective weather activity. There is a need to perform rerouting in an intelligent and efficient way such that the disruptive effects of rerouting are minimized. An important area of research is to study the interaction of in-flight rerouting with traffic congestion or complexity and developing methods that quantitatively measure this interaction. Furthermore, it is necessary to find rerouting solutions that account for uncertainties in weather forecasts. These are important steps toward managing complexity during rerouting operations, and the paper is motivated by these research questions. An automated system is developed for rerouting air traffic in order to avoid convective weather regions during the 20- minute - 2-hour time horizon. Such a system is envisioned to work in concert with separation assurance (0 - 20-minute time horizon), and longer term air traffic management (2-hours and beyond) to provide a more comprehensive solution to complexity and safety management. In this study, weather is dynamic and uncertain; it is represented as regions of airspace that pilots are likely to avoid. Algorithms are implemented in an air traffic simulation environment to support the research study. The algorithms used are deterministic but periodically revise reroutes to account for weather forecast updates. In contrast to previous studies, in this study convective weather is represented as regions of airspace that pilots are likely to avoid. The automated system periodically updates forecasts and reassesses rerouting decisions in order to account for changing weather predictions. The main objectives are to reroute flights to avoid convective weather regions and determine the resulting complexity due to rerouting. The eventual goal is to control and reduce complexity while rerouting flights during the 20 minute - 2 hour planning period. A three-hour simulation is conducted using 4800 flights in the national airspace. The study compares several metrics against a baseline scenario using the same traffic and weather but with rerouting disabled. The results show that rerouting can have a negative impact on congestion in some sectors, as expected. The rerouting system provides accurate measurements of the resulting complexity in the congested sectors. Furthermore, although rerouting is performed only in the 20-minute - 2-hour range, it results in a 30% reduction in encounters with nowcast weather polygons (100% being the ideal for perfectly predictable and accurate weather). In the simulations, rerouting was performed for the 20-minute - 2-hour flight time horizon, and for the en-route segment of air traffic. The implementation uses CWAM, a set of polygons that represent probabilities of pilot deviation around weather. The algorithms were implemented in a software-based air traffic simulation system. Initial results of the system's performance and effectiveness were encouraging. Simulation results showed that when flights were rerouted in the 20-minute - 2-hour flight time horizon of air traffic, there were fewer weather encounters in the first 20 minutes than for flights that were not rerouted. Some preliminary results were also obtained that showed that rerouting will also increase complexity. More simulations will be conducted in order to report conclusive results on the effects of rerouting on complexity. Thus, the use of the 20-minute - 2-hour flight time horizon weather avoidance teniques performed in the simulation is expected to provide benefits for short-term weather avoidance.

Karahan, Sinan↗
NASA NTRS1997

The Role of Global Hydrologic Processes in Interannual and Long-Term Climate Variability

The earth's climate and its variability is linked inextricably with the presence of water on our planet. El Nino / Southern Oscillation-- the major mode of interannual variability-- is characterized by strong perturbations in oceanic evaporation, tropical rainfall, and radiation. On longer time scales, the major feedback mechanism in CO2-induced global warming is actually that due to increased water vapor holding capacity of the atmosphere. The global hydrologic cycle effects on climate are manifested through influence of cloud and water vapor on energy fluxes at the top of atmosphere and at the surface. Surface moisture anomalies retain the "memory" of past precipitation anomalies and subsequently alter the partitioning of latent and sensible heat fluxes at the surface. At the top of atmosphere, water vapor and cloud perturbations alter the net amount of radiation that the earth's climate system receives. These pervasive linkages between water, radiation, and surface processes present major complexities for observing and modeling climate variations. Major uncertainties in the observations include vertical structure of clouds and water vapor, surface energy balance, and transport of water and heat by wind fields. Modeling climate variability and change on a physical basis requires accurate by simplified submodels of radiation, cloud formation, radiative exchange, surface biophysics, and oceanic energy flux. In the past, we m safely say that being "data poor' has limited our depth of understanding and impeded model validation and improvement. Beginning with pre-EOS data sets, many of these barriers are being removed. EOS platforms with the suite of measurements dedicated to specific science questions are part of our most cost effective path to improved understanding and predictive capability. This talk will highlight some of the major questions confronting global hydrology and the prospects for significant progress afforded by EOS-era measurements.

Robertson, Franklin R.↗
DOE OSTI2024

A Roadmap for a Lightning Modeling Grand Challenge

This document is a roadmap for building an interconnected model of the physical processes that produce a lightning discharge, and its observable optical and radio signals. We call this a Lightning Modeling Grand Challenge, recognizing that significant effort and coordination of human and financial resources is required to realize the capability. The roadmap serves to outline the coordination of resources necessary to enable stitching together existing knowledge and model components to make a lightning prediction, and to test these predictions with observations. Such a capability does not currently exist. The roadmap is motivated not only by a spirit of scientific inquiry, but by practical challenges faced by US Federal and societal stakeholders. Advancements in lightning observations have outpaced our tests of integrated understanding, leaving many stakeholders unsure how to design their missions to properly detect and discriminate lightning, and unsure how to apply the sometimes-disagreeing lightning signals from diverse instruments. The time is right to connect existing theories and models to support stakeholders in understanding the signals they observe, for needs as diverse as climate monitoring, national security, weather forecasting, public safety, and protection of natural and built environments. The roadmap’s two main technical sections describe the components of a linked physical model, followed by a description of models of lightning signals and sensors that are driven by outputs from the physical model. The goal is to predict the time-varying physical properties of lightning that are self-consistent with the thunderstorm’s structure and dynamics. These lightning signals then propagate through the storm, with realistic dispersion and attenuation, to receivers on the ground or in space. At a high level, the model begins with weather (cloud) model output, including explicit prediction of the electrification of cloud particles. The cloud’s electrical structure drives a model of lightning physics, from initiation, through channel development, and discharges along those channels. Key lightning parameters, such as the temperature and currents in the channel, and their space and time distribution, are then used to produce optical and electromagnetic signal sources that propagate to modeled receivers. This architecture therefore generates a dataset suitable for comparison to existing and envisioned observing systems. The need for additional measurements and field campaigns to support model development is described. In each model sub-component, inputs, outputs, uncertainties, evaluation methods, and next steps are summarized, interleaved with references to the scientific literature. Identifying boundaries between the model sub-components aids in segmenting an integrated, complex model into practical work packages and system sub-components, allowing a diverse team to contribute and maintain the system. We estimate that at least five years of effort and a $\$$10M initial investment is necessary to make a significant step forward. Mechanisms to facilitate community coordination, including annual workshops and open-source code repositories, are described.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

AEOLUS: Advances in Experimental Design, Optimal Control, and Learning for Uncertain Complex Systems

Sustained advances in the mathematics of modeling and simulation have resulted in the capability today for routine simulation of a number of large scale complex DOE-relevant systems. As remarkable as this capability for solving the so-called forward problem is, it is typically only the first step-an inner loop within an outer loop that explores the simulation model's parameter space and decision space to characterize uncertainty in the model's predictions, learn unknown model parameters from data, design the most informative experiments, determine optimal control strategies, and create optimal designs. Broadly, what unifies all of these outer loop problems is that they are, in one form or another, optimization problems over parameter/control/design space that are constrained by complex uncertain models. To fully realize the power of scientific simulation as a basis for scientific discovery, technological innovation, and rational decision-making, it is imperative to move beyond simulation to tackle the outer loop of optimization for learning from data, experimental design, and control with complex uncertain models. When the models under consideration are large-scale and complex, and when the optimization variable and uncertain parameter spaces are high (or infinite) dimensional, this constitutes a grand challenge of the highest order, and is intractable with conventional methods. To overcome these challenges, the AEOLUS Center was established to develop a unified mathematical, computational, and statistical framework for (1) Learning predictive models from complex data via Bayesian inference and optimization, and (2) Optimizing experiments, processes, and designs using the resulting uncertain models. These problems are intractable with conventional methods, for several reasons: (1) The simulation problems that govern the inner loops of the optimization problems are expensive to execute (due to severe nonlinearity, heterogeneity, multiphysics/multiscale coupling); (2) The optimization variable and uncertain parameter spaces are high dimensional, often stemming from discretizations of infinite dimensional fields such as initial conditions, sources, or material properties. We argue that the key to overcoming these challenges is to develop new mathematical, computational, and statistical methods that exploit the structure of the Bayesian inference and optimization problems mediated by their underlying complex uncertain models. This structure includes the regularity, sparsity, geometry, low intrinsic dimensionality, and multifidelity nature of the maps from uncertain parameter/optimization variable spaces to the specific objectives targeted: Bayesian inference, optimal experimental design, and optimal control design. Black box methods developed as generic tools are incapable of exploiting this structure. To be successful, we must create, integrate, and cross-fertilize ideas across multiple areas of applied math--including approximation theory, Bayesian inference, data science, experimental design, information theory, machine learning, model reduction, optimal control theory, parallel algorithms, PDE-constrained optimization, randomized algorithms, stochastic optimization, and uncertainty quantification--all while exploiting the structure of the problems at hand. With this goal in mind, we have marshaled a team of leading authorities in these areas. While the methods we develop will be broadly applicable across a wide spectrum of DOE problems in which experiments inform models and the systems those models describe must be optimized under uncertainty, we have chosen a specific area, advanced manufacturing and materials, to drive our work. AMM is characterized by complex models across multiple scales, and is a rich source of challenging problems in inference, experimental design, and optimal control, requiring multifaceted and integrated advances in applied mathematics. As such, AMM serves as an excellent vehicle to motivate and demonstrate the advances in applied mathematics developed by our center.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Quantum surrogate models for uncertainty quantification

Surrogate models are a critical ingredient to computation-based design and validation of many DOE mission-relevant physical systems. When first-principles computation of properties of a physical systems becomes pro hibitive, surrogate models are the only path towards achieving tasks such as uncertainty quantification (UQ), exploration of design space, and validation of design choices. In this project we have developed and demonstrated a new surro gate modeling paradigm for complex models that is data-driven, non-intrusive, and has the potential to be versatile and equipped with performance guaran tees. This combination of features is absent in existing surrogate modeling tools. The framework we have developed in this project exploits a quantum-classical correspondence to establish a quantum system that mimics the dynamics of the classical Hamiltonian system from which data in the form of temporal snapshots is provided. Since quantum dynamics propagates distributions over observables, the framework is naturally suited to propagation of epistemic uncertainties in the form of distributions over initial state and parametric uncertainties. In this project, we take the first step in establishing this novel framework by deriving a quantization and de-quantization procedure, demonstrating the accuracy of the quantum surrogate models these define using two model systems, and defining the next steps in maturing the framework towards a tool applicable to Sandia mission-relevant problems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2011

Linear Quadratic Tracking Design for a Generic Transport Aircraft with Structural Load Constraints

When designing control laws for systems with constraints added to the tracking performance, control allocation methods can be utilized. Control allocations methods are used when there are more command inputs than controlled variables. Constraints that require allocators are such task as; surface saturation limits, structural load limits, drag reduction constraints or actuator failures. Most transport aircraft have many actuated surfaces compared to the three controlled variables (such as angle of attack, roll rate & angle of side slip). To distribute the control effort among the redundant set of actuators a fixed mixer approach can be utilized or online control allocation techniques. The benefit of an online allocator is that constraints can be considered in the design whereas the fixed mixer cannot. However, an online control allocator mixer has a disadvantage of not guaranteeing a surface schedule, which can then produce ill defined loads on the aircraft. The load uncertainty and complexity has prevented some controller designs from using advanced allocation techniques. This paper considers actuator redundancy management for a class of over actuated systems with real-time structural load limits using linear quadratic tracking applied to the generic transport model. A roll maneuver example of an artificial load limit constraint is shown and compared to the same no load limitation maneuver.

Burken, John J.↗
NASA NTRS2022

Uncertainty Models for the Hybrid Parametric Variation Method of Uncertainty Quantification; Analysis

There is some level of uncertainty in every finite element model (FEM), which flows to a level of uncertainty in predicted results. The purpose of uncertainty quantification (UQ) is to provide statistical bounds on prediction accuracy based on model uncertainty. This is distinct from model updating, which attempts to modify models to improve their accuracy. UQ does not improve the accuracy of models, but accepts that the models are inherently inaccurate and attempts to quantify the impact of that inaccuracy on predicted results. Previously, an alternate method for UQ, called the Hybrid Parametric Variation (HPV) method, was applied to Space Launch System (SLS) Hurty/Craig-Bampton (HCB) components to predict system-level statistics for launch vehicle attitude control transfer functions and core stage section loads due to buffet. The HPV method combines a parametric variation of the HCB fixed-interface (FI) modal frequencies with a nonparametric variation (NPV) method that randomly varies the HCB mass and stiffness matrices as Wishart random matrix distributions using random matrix theory (RMT). Alternatively, the most common method for modeling uncertainty in the structural dynamics community is a parametric approach, which varies physical parameters in the model. However, there are several disadvantages associated with the parametric method. Determining a reduced set of parameters that have a significant impact on the system response can be time consuming, and the selected parameter probability distributions are rarely reliably known. Therefore, in practice, the parameters are surrogates for the actual errors, and the link to parameter uncertainty is unknown. Another major drawback is that the uncertainty that can be represented is limited to the form of the nominal FEM. It is the experience of the authors that based on numerous aerospace programs, almost all FEM errors are in form rather than parameter values. This hypothesis is supported by the observation of the authors that it is almost never possible to ‘tune’ a FEM to match modal test results by only modifying model parameters. Model-form uncertainty cannot be directly represented by FEM input parameters nor included in a parametric approach. However, model-form uncertainty can be modeled using RMT, where a probability distribution is developed for the matrix ensemble of interest. The major advantage of the NPV method is that it covers errors in model form. The HPV method anchors uncertainty at the HCB component level to component modal test results by matching the HCB and test modes based on mode descriptions or other methods, and then applying differing levels of frequency variation. The specific variations depend on the confidence to which a component FEM has been validated through modal testing. The NPV method is layered on the frequency variation to match modal test self-orthogonality and cross-orthogonality (XO) results. Once the component uncertainty models are identified, they are assembled, and the uncertainty is propagated to the system level using a Monte Carlo (MC) analysis approach that generates statistics for system-level predictions This provides a UQ method that can be traced to test data, which can be updated as additional data and improved correlated models become available. The purpose of this paper is to collect and present all of the theory for HPV that has been previously published in reports and papers and to present examples of its application. Specifically, component uncertainty models based on the dispersion of corresponding mass and stiffness matrices using proposed test/analysis correlation metrics are investigated. The first example is purely academic so that the true answers are known, and the validity of the HPV method and the corresponding uncertainty models can be determined. The purpose of this paper is to collect and present all of the theory for HPV that has been previously published in reports and papers and to present examples of its application. Specifically, component uncertainty models based on the dispersion of corresponding mass and stiffness matrices using proposed test/analysis correlation metrics are investigated. The first example is purely academic so that the true answers are known, and the validity of the HPV method and the corresponding uncertainty models can be determined. The second example is an application to a component that is design specific to the SLS. Based on this work and other assessments, the HPV method provides another tool to the toolset used for complex system UQ analysis. From experience gathered to date using the HPV method, additional design specific applications must be investigated to provide further confidence in the validity of the HPV method of UQ analysis.

Uncertainty quantification↗
DOE OSTI2020

A systems engineering vision for floating offshore wind cost optimization

The U.S. offshore wind resource potential is immense, and often in close proximity to densely-populated coastal load centers. In many U.S. coastal areas, water depths favor the deployment of floating over fixed-bottom offshore wind technology. Floating offshore wind plants have the potential to be cost-competitive with fixed-bottom installations, but because the technology has not yet been deployed at commercial scale, it is not clear when and with what configurations this potential cost parity can be achieved. This article first reviews the state of floating offshore wind technology and deployments to identify key gaps that must be addressed to bring down the overall cost of energy produced. The article then puts forth a long-term vision for a research program and design methodology that may be able to push floating wind plants toward a lower levelized cost of energy than fixed-bottom offshore wind. The method involves a fully integrated systems-engineering and techno-economic design approach to capture the complex interactions between the physics, manufacturing, installation, and operation of floating wind turbines to achieve transformational cost reductions. The approach also envisions multifidelity and uncertainty management strategies to examine the most robust and viable concepts in the design trade-space. To better focus the computational resources, engineering lessons learned from existing offshore wind systems and concept studies are used to develop a set of criteria that can be applied to prefilter candidate technology building blocks that have the greatest cost reduction potential.

17 WIND ENERGY↗
NASA NTRS2015

Rigging Test Bed Enables Development of Multi-Stage Decelerator Extraction

The Low Density Supersonic Decelerator (LDSD) project developed a Parachute Deployment System (PDS) for use on its Supersonic Flight Dynamics Tests (SFDT). The PDS involves a multi-stage pilot driven extraction of a supersonic parachute. The uncertainties and complexities of developing the design for the lines and rigging of the PDS were addressed through testing in the Rigging Test Bed (RTB). The RTB provided a facility capable of simulating a variety of extraction scenarios with full scale hardware on the ground. Through more than 100 tests conducted in the facility, a wealth of data and experience were gained that fueled the PDS development. The utility of this testing and the lessons learned are presented in this paper. The goal is to inform the development of similar systems in the future and highlight the value and flexibility this type of testing offers rapid hardware development. The RTB provided a great compliment to the analytical models greatly compressing what would have otherwise been a very lengthy analytical effort or potentially much expanded flight test campaign.

Kenig, Sivan J.↗
DOE OSTI2020

Systems Theory Principles and Complex Systems Engineering Concepts for Protection and Resilience in Critical Infrastructure: Lessons from the Nuclear Sector

Part of the Presidential Policy Directive 21 (PPD-21) (PPD 2013) mandate includes evaluating safety, security, and safeguards (or nonproliferation) mechanisms traditionally implemented within the nuclear reactors, materials, and waste sector of critical infrastructure—including a complex, dynamic set of risks and threats within an all-hazards approach. In response, research out of Sandia National Laboratories (Sandia) explores the ability of systems theory principles (hierarchy and emergence) and complex systems engineering concepts (multidomain interdependence) to better understand and address these risks and threats. Herein, this Sandia research explores the safety, safeguards, and security risks of three different nuclear sector-related activities—spent nuclear fuel transportation, small modular reactors, and portable nuclear power reactors—to investigate the complex and dynamic risk related to the PPD-21-mandated all-hazards approach. This research showed that a systems-theoretic approach can better identify inter-dependencies, conflicts, gaps, and leverage points across traditional safety, security, and safeguards hazard mitigation strategies in the nuclear reactors, materials, and waste sector. Resulting from this, mitigation strategies from applying systems theoretic principles and complex systems engineering concepts can be (1) designed to better capture interdependencies, (2) implemented to better align with real-world operational uncertainties, and (3) evaluated as a systems-level whole to better identify, characterize, and manage PPD-21's all hazards strategies.

42 ENGINEERING↗
DOE OSTI2020

Recent advances in computational mathematics and applications

We are honored to bring you this special issue dedicated to recent advances in computational mathematics and applications in science and engineering. The papers in this special issue were presented in ”Conference on Computational Mathematics and Applications (CCMA)” held at the University of Nevada Las Vegas (UNLV) during October 25–27, 2019. The conference has attracted about 90 attendees from six countries. The 15 papers in the special issue comprise a diverse collection of theoretical numerical analysis as well as applications in various subjects. Topics cover optimal control of PDEs, discontinuous Galerkin methods, fluid flow in porous media, turbulence flow, static and moving interface problems, complex fluids composed by the mixture of Newtonian fluid and nematic (liquid crystal) flows, modeling of ocean–atmosphere system, image segmentation algorithm, uncertainty quantification problems for turbulence model and Maxwell’s equations, iterative solver for systems resulting from mixed methods, and novel methods for solving systems of nonlinear equations. As the Guest Editors we would like to thank Dr. Leland Jameson at NSF (National Science Foundation) for kindly supporting our conference proposal which made this conference possible. We would also like to thank Darren Sugrue from Elsevier who provided partial support for our conference, and Thennarasu Gunasekaran and his production team from Elsevier who produced this nice special issue. We are grateful to many people (Dr. Zhijian Wu, Lori Ornelas, Elsa Juarez, and many Ph.D. students) at the Department of Mathematical Sciences of UNLV who provided tremendous support for the conference. Finally, we very much appreciate all authors who contributed their precious results to this special issue.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2004

Scale-Free Networks and Commercial Air Carrier Transportation in the United States

Network science, or the art of describing system structure, may be useful for the analysis and control of large, complex systems. For example, networks exhibiting scale-free structure have been found to be particularly well suited to deal with environmental uncertainty and large demand growth. The National Airspace System may be, at least in part, a scalable network. In fact, the hub-and-spoke structure of the commercial segment of the NAS is an often-cited example of an existing scale-free network After reviewing the nature and attributes of scale-free networks, this assertion is put to the test: is commercial air carrier transportation in the United States well explained by this model? If so, are the positive attributes of these networks, e.g. those of efficiency, flexibility and robustness, fully realized, or could we effect substantial improvement? This paper first outlines attributes of various network types, then looks more closely at the common carrier air transportation network from perspectives of the traveler, the airlines, and Air Traffic Control (ATC). Network models are applied within each paradigm, including discussion of implied strengths and weaknesses of each model. Finally, known limitations of scalable networks are discussed. With an eye towards NAS operations, utilizing the strengths and avoiding the weaknesses of scale-free networks are addressed.

Conway, Sheila R.↗
NASA NTRSDate not supplied

Medium-Range River Flood Forecasts Using a Long Short-Term Memory Network

River flooding and the impacts are a concern for decision makers throughout the United States. Accurate medium-range forecasts (~3-7 days) are critical for providing advanced outlooks to emergency management officials. Unfortunately, accurately forecasting rainfall-runoff and the subsequent rise and fall within rivers remain a challenge in hydrological modeling. While complex physical modeling systems are the standard for representing the hydrological processes, they are computationally demanding and can require extensive calibration. Further, uncertainties remain in the model parameters and input data. The use of machine learning can reduce some of the computational demand while maintaining high accuracy. Therefore, this project makes use of a Long Short-Term Memory (LSTM) network which explicitly accounts for the time-dependent nature of rainfall-runoff modeling. The developed LSTM was trained to predict river gauge height, or stage height, based on time-lagged input features which include: gauge height to initialize the model, the NASA Short-term Prediction Research and Transition Center’s instance of the Land Information System (SPoRT-LIS) relative soil moisture to describe the rainfall infiltration rate, and 6-hr Multi-Radar Multi-Sensor quantitative precipitation estimate (MRMS QPE). The developed LSTM based system is then used to produce 7-day forecasts with a 6-hr temporal resolution using three different quantitative precipitation forecasts (QPF) from the NWS’s Weather Prediction Center (WPC), the NCEP Global Forecast System (GFS) model and the National Blend of Models (NBM). This trained modeling system has been implemented as an experimental product at over 100 different rivers in collaboration with at multiple National Weather Service (NWS) Forecast Offices and River Forecast Centers (RFC) across the eastern half of the United States. The developed LSTM model achieved average Nash-Sutcliffe efficiency (NSE) 0.89 higher than the equivalent medium-range National Water Model ensemble member forecast over a 7-day forecast. In addition to the initial development and evaluation, this project has continued to expand. While the initial model was developed for precipitation dominated basins, expansion of the project has taken it to basins effected by snow melt. This presentation will provide an overview of the project with focus on recent developments on incorporating snow melt processes into the model.

Andrew T. White↗
NASA NTRS2019

Method for Tracking and Communicating Aggregate Risk Through the Use of Model-Based Systems Engineering (MBSE) Tools

Large, complex projects can identify a significant number and variety of risks, throughout the project life cycle. These risks are analyzed, mitigated, closed or accepted as independent uncertainties. Once closed or accepted, it is easy for projects to lose awareness of their impact. In reality, each of these risks contributes some amount to the overall risk posture of the project. The ability to track and effectively communicate this aggregate risk has represented a challenge to project management. There have been previous attempts to create a schema to communicate the aggregate effect of risks, without notable success. Most of these attempts have centered on some additive metric derived from the scoring of likelihood and consequence values. This, in and of itself, is a logical approach, but all too often the scores were then aggregated to a level where all context was lost. One weakness has been a lack of attempt to create linkages or logical groups of the risks upon which useful aggregation could then occur. The overall move to model-based (systems) engineering (MBSE) has opened up a vast frontier of opportunities to better integrate all project data. MBSE provides an underlying layer that links data items to each other. Objectives link to requirements, which then link to functions, functions to physical architecture items, and so on, as far down as projects want to model. While it started with a focus on modeling requirements based on things like use cases, efforts are now underway to integrate safety and mission assurance (S&MA) information and analyses, such as risks. This effort, called Model Based Mission Assurance (MBMA), is yielding models that are more useful and are a more accurate representations of the systems. MBSE models, with this ability to link related items, provide a new means of tracking and communicating aggregate risks. In the proposed method, risks are added into the models as distinct items, having attributes that communicate a scoring derived from the likelihood and consequence values as charted on the standard NASA 5x5 risk matrix. Like earlier efforts, each box in the 5x5 has an associated scoring, which may include both a current score and potential post-mitigation/control score. The risk items are then linked to elements of the model, such as system objectives/goals, requirements, functions, or physical architecture items, with "Risk to" relationships. These risks will then be communicated by use of reports generated from the model, detailing all risks and/or hazards linked to model elements. These reports can include aggregate impacts, including a current scoring and potential future state scoring based on the planned mitigations and/or controls. These reports will show all risks, open, accepted, and closed, linked to project objectives or requirements. When run as part of an upcoming risk acceptance discussion, these reports will serve to remind the team of all previous risks that relate to the effected portion of the system. When included as part of periodic program or project reviews, risk reviews, and safety reviews, this method can improve the overall understanding of the system's true risk posture. This proposed method takes full advantage of the advances that modern modeling techniques provide, with a minimal investment of additional time. Utilizing the model environment also enables a near constant access to current state of aggregate risks.

model based mission assurance↗