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Trajectory-Based Complexity (TBX): A Modified Aircraft Count to Predict Sector Complexity During Trajectory-Based Operations

In this paper we introduce a new complexity metric to predict -in real-time- sector complexity for trajectory-based operations (TBO). TBO will be implemented in the Next Generation Air Transportation System (NextGen). Trajectory-Based Complexity (TBX) is a modified aircraft count that can easily be computed and communicated in a TBO environment based upon predictions of aircraft and weather trajectories. TBX is scaled to aircraft count and represents an alternate and additional means to manage air traffic demand and capacity with more consideration of dynamic factors such as weather, aircraft equipage or predicted separation violations, as well as static factors such as sector size. We have developed and evaluated TBX in the Airspace Operations Laboratory (AOL) at the NASA Ames Research Center during human-in-the-loop studies of trajectory-based concepts since 2009. In this paper we will describe the TBX computation in detail and present the underlying algorithm. Next, we will describe the specific TBX used in an experiment at NASA's AOL. We will evaluate the performance of this metric using data collected during a controller-inthe- loop study on trajectory-based operations at different equipage levels. In this study controllers were prompted at regular intervals to rate their current workload on a numeric scale. When comparing this real-time workload rating to the TBX values predicted for these time periods we demonstrate that TBX is a better predictor of workload than aircraft count. Furthermore we demonstrate that TBX is well suited to be used for complexity management in TBO and can easily be adjusted to future operational concepts.

trajectories

Multi Sector Planning Tools for Trajectory-Based Operations

This paper discusses a suite of multi sector planning tools for trajectory-based operations that were developed and evaluated in the Airspace Operations Laboratory (AOL) at the NASA Ames Research Center. The toolset included tools for traffic load and complexity assessment as well as trajectory planning and coordination. The situation assessment tools included an integrated suite of interactive traffic displays, load tables, load graphs, and dynamic aircraft filters. The planning toolset allowed for single and multi aircraft trajectory planning and data communication-based coordination of trajectories between operators. Also newly introduced was a real-time computation of sector complexity into the toolset that operators could use in lieu of aircraft count to better estimate and manage sector workload, especially in situations with convective weather. The tools were used during a joint NASA/FAA multi sector planner simulation in the AOL in 2009 that had multiple objectives with the assessment of the effectiveness of the tools being one of them. Current air traffic control operators who were experienced as area supervisors and traffic management coordinators used the tools throughout the simulation and provided their usefulness and usability ratings in post simulation questionnaires. This paper presents these subjective assessments as well as the actual usage data that was collected during the simulation. The toolset was rated very useful and usable overall. Many elements received high scores by the operators and were used frequently and successfully. Other functions were not used at all, but various requests for new functions and capabilities were received that could be added to the toolset.

Prevot, Thomas

Dynamic Weather Routes: A Weather Avoidance Concept for Trajectory-Based Operations

The integration of convective weather modeling with trajectory automation for conflict detection, trial planning, direct routing, and auto resolution has uncovered a concept that could help controllers, dispatchers, and pilots identify improved weather routes that result in significant savings in flying time and fuel burn. Trajectory automation continuously and automatically monitors aircraft in flight to find those that could potentially benefit from improved weather reroutes. Controllers, dispatchers, and pilots then evaluate reroute options to assess their suitability given current weather and traffic. In today's operations aircraft fly convective weather avoidance routes that were implemented often hours before aircraft approach the weather and automation does not exist to automatically monitor traffic to find improved weather routes that open up due to changing weather conditions. The automation concept runs in real-time and employs two keysteps. First, a direct routing algorithm automatically identifies flights with large dog legs in their routes and therefore potentially large savings in flying time. These are common - and usually necessary - during convective weather operations and analysis of Fort Worth Center traffic shows many aircraft with short cuts that indicate savings on the order of 10 flying minutes. The second and most critical step is to apply trajectory automation with weather modeling to determine what savings could be achieved by modifying the direct route such that it avoids weather and traffic and is acceptable to controllers and flight crews. Initial analysis of Fort Worth Center traffic suggests a savings of roughly 50% of the direct route savings could be achievable.The core concept is to apply trajectory automation with convective weather modeling in real time to identify a reroute that is free of weather and traffic conflicts and indicates enough time and fuel savings to be considered. The concept is interoperable with today's integrated FMS/datalink. Auxiliary(lat/long) waypoints define a minimum delay reroute between current position and a downstream capture fix beyond the weather. These auxiliary waypoints can be uplinked to equipped aircraft and auto-loaded into the FMS. Alternatively, for unequipped aircraft, auxiliary waypoints can be replaced by nearby named fixes, but this could reduce potential savings. The presentation includes an overview of the automation approach and focuses on several cases in terms of potential savings, reroute complexity, best auxiliary waypoint solution vs. named fix solution, and other metrics.

McNally, B. David

Airborne Tactical Intent-Based Conflict Resolution Capability

Trajectory-based operations with self-separation involve the aircraft taking the primary role in the management of its own trajectory in the presence of other traffic. In this role, the flight crew assumes the responsibility for ensuring that the aircraft remains separated from all other aircraft by at least a minimum separation standard. These operations are enabled by cooperative airborne surveillance and by airborne automation systems that provide essential monitoring and decision support functions for the flight crew. An airborne automation system developed and used by NASA for research investigations of required functionality is the Autonomous Operations Planner. It supports the flight crew in managing their trajectory when responsible for self-separation by providing monitoring and decision support functions for both strategic and tactical flight modes. The paper focuses on the latter of these modes by describing a capability for tactical intent-based conflict resolution and its role in a comprehensive suite of automation functions supporting trajectory-based operations with self-separation.

Wing, David J.

A Near-Term Concept for Trajectory Based Operations with Air/Ground Data Link Communication

An operating concept and required system components for trajectory-based operations with air/ground data link for today's en route and transition airspace is proposed. Controllers are fully responsible for separation as they are today, and no new aircraft equipage is required. Trajectory automation computes integrated solutions to problems like metering, weather avoidance, traffic conflicts and the desire to find and fly more time/fuel efficient flight trajectories. A common ground-based system supports all levels of aircraft equipage and performance including those equipped and not equipped for data link. User interface functions for the radar controller's display make trajectory-based clearance advisories easy to visualize, modify if necessary, and implement. Laboratory simulations (without human operators) were conducted to test integrated operation of selected system components with uncertainty modeling. Results are based on 102 hours of Fort Worth Center traffic recordings involving over 37,000 individual flights. The presence of uncertainty had a marginal effect (5%) on minimum-delay conflict resolution performance, and windfavorable routes had no effect on detection and resolution metrics. Flight plan amendments and clearances were substantially reduced compared to today s operations. Top-of-descent prediction errors are the largest cause of failure indicating that better descent predictions are needed to reliably achieve fuel-efficient descent profiles in medium to heavy traffic. Improved conflict detections for climbing flights could enable substantially more continuous climbs to cruise altitude. Unlike today s Conflict Alert, tactical automation must alert when an altitude amendment is entered, but before the aircraft starts the maneuver. In every other failure case tactical automation prevented losses of separation. A real-time prototype trajectory trajectory-automation system is running now and could be made ready for operational testing at an en route Center in 1-2 years.

McNally, David

Complexity Science Applications to Dynamic Trajectory Management: Research Strategies

The promise of the Next Generation Air Transportation System (NextGen) is strongly tied to the concept of trajectory-based operations in the national airspace system. Existing efforts to develop trajectory management concepts are largely focused on individual trajectories, optimized independently, then de-conflicted among each other, and individually re-optimized, as possible. The benefits in capacity, fuel, and time are valuable, though perhaps could be greater through alternative strategies. The concept of agent-based trajectories offers a strategy for automation of simultaneous multiple trajectory management. The anticipated result of the strategy would be dynamic management of multiple trajectories with interacting and interdependent outcomes that satisfy multiple, conflicting constraints. These constraints would include the business case for operators, the capacity case for the Air Navigation Service Provider (ANSP), and the environmental case for noise and emissions. The benefits in capacity, fuel, and time might be improved over those possible under individual trajectory management approaches. The proposed approach relies on computational agent-based modeling (ABM), combinatorial mathematics, as well as application of "traffic physics" concepts to the challenge, and modeling and simulation capabilities. The proposed strategy could support transforming air traffic control from managing individual aircraft behaviors to managing systemic behavior of air traffic in the NAS. A system built on the approach could provide the ability to know when regions of airspace approach being "full," that is, having non-viable local solution space for optimizing trajectories in advance.

Sawhill, Bruce

Comparison of Ground-Based and Airborne Function Allocation Concepts for NextGen Using Human-In-The-Loop Simulations

Investigation of function allocation for the Next Generation Air Transportation System is being conducted by the National Aeronautics and Space Administration (NASA). To provide insight on comparability of different function allocations for separation assurance, two human-in-the-loop simulation experiments were conducted on homogeneous airborne and ground-based approaches to four-dimensional trajectory-based operations, one referred to as ground-based automated separation assurance (groundbased) and the other as airborne trajectory management with self-separation (airborne). In the coordinated simulations at NASA s Ames and Langley Research Centers, controllers for the ground-based concept at Ames and pilots for the airborne concept at Langley managed the same traffic scenarios using the two different concepts. The common scenarios represented a significant increase in airspace demand over current operations. Using common independent variables, the simulations varied traffic density, scheduling constraints, and the timing of trajectory change events. Common metrics were collected to enable a comparison of relevant results. Where comparisons were possible, no substantial differences in performance or operator acceptability were observed. Mean schedule conformance and flight path deviation were considered adequate for both approaches. Conflict detection warning times and resolution times were mostly adequate, but certain conflict situations were detected too late to be resolved in a timely manner. This led to some situations in which safety was compromised and/or workload was rated as being unacceptable in both experiments. Operators acknowledged these issues in their responses and ratings but gave generally positive assessments of the respective concept and operations they experienced. Future studies will evaluate technical improvements and procedural enhancements to achieve the required level of safety and acceptability and will investigate the integration of airborne and ground-based capabilities within the same airspace to leverage the benefits of each concept.

Wing, David J.

Modeling Off-Nominal Recovery in NextGen Terminal-Area Operations

Robust schedule-based arrival management requires efficient recovery from off-nominal situations. This paper presents research on modeling off-nominal situations and plans for recovering from them using TRAC, a route/airspace design, fast-time simulation, and analysis tool for studying NextGen trajectory-based operations. The paper provides an overview of a schedule-based arrival-management concept and supporting controller tools, then describes TRAC implementations of methods for constructing off-nominal scenarios, generating trajectory options to meet scheduling constraints, and automatically producing recovery plans.

Callantine, Todd J.

Airborne Precision Spacing: A Trajectory-based Approach to Improve Terminal Area Operations

Airborne Precision Spacing has been developed by the National Aeronautics and Space Administration (NASA) over the past seven years as an attempt to benefit from the capabilities of the flight deck to precisely space their aircraft relative to another aircraft. This development has leveraged decades of work on improving terminal area operations, especially the arrival phase. With APS operations, the air traffic controller instructs the participating aircraft to achieve an assigned inter-arrival spacing interval at the runway threshold, relative to another aircraft. The flight crew then uses airborne automation to manage the aircraft s speed to achieve the goal. The spacing tool is designed to keep the speed within acceptable operational limits, promote system-wide stability, and meet the assigned goal. This reallocation of tasks with the controller issuing strategic goals and the flight crew managing the tactical achievement of those goals has been shown to be feasible through simulation and flight test. A precision of plus or minus 2-3 seconds is generally achievable. Simulations of long strings of arriving traffic show no signs of instabilities or compression waves. Subject pilots have rated the workload to be similar to current-day operations and eye-tracking data substantiate this result. This paper will present a high-level review of research results over the past seven years from a variety of tests and experiments. The results will focus on the precision and accuracy achievable, flow stability and some major sources of uncertainty. The paper also includes a summary of the flight crew s procedures and interface and a brief concept overview.

Barmore, Bryan

An Overview of a Trajectory-Based Solution for En Route and Terminal Area Self-Spacing to Include Parallel Runway Operations

This paper presents an overview of an algorithm specifically designed to support NASA's Airborne Precision Spacing concept. This airborne self-spacing concept is trajectory-based, allowing for spacing operations prior to the aircraft being on a common path. This implementation provides the ability to manage spacing against two traffic aircraft, with one of these aircraft operating to a parallel dependent runway. Because this algorithm is trajectory-based, it also has the inherent ability to support required-time-of-arrival (RTA) operations

Abbott, Terence S.

Experimental Evaluation of an Integrated Datalink and Automation-Based Strategic Trajectory Concept

This paper presents research on the interoperability of trajectory-based automation concepts and technologies with modern Flight Management Systems and datalink communication available on many of today s commercial aircraft. A tight integration of trajectory-based ground automation systems with the aircraft Flight Management System through datalink will enable mid-term and far-term benefits from trajectory-based automation methods. A two-way datalink connection between the trajectory-based automation resident in the Center/TRACON Automation System and the Future Air Navigation System-1 integrated FMS/datalink in NASA Ames B747-400 Level D simulator has been established and extensive simulation of the use of datalink messages to generate strategic trajectories completed. A strategic trajectory is defined as an aircraft deviation needed to solve a conflict or honor a route request and then merge the aircraft back to its nominal preferred trajectory using a single continuous trajectory clearance. Engineers on the ground side of the datalink generated lateral and vertical trajectory clearances and transmitted them to the Flight Management System of the 747; the airborne automation then flew the new trajectory without human intervention, requiring the flight crew only to review and to accept the trajectory. This simulation established the protocols needed for a significant majority of the trajectory change types required to solve a traffic conflict or deviate around weather. This demonstration provides a basis for understanding the requirements for integration of trajectory-based automation with current Flight Management Systems and datalink to support future National Airspace System operations.

Mueller, Eric

Polariton spectra under the collective coupling regime. I. Efficient simulation of linear spectra and quantum dynamics

We outline two general theoretical techniques to simulate polariton quantum dynamics and optical spectra under the collective coupling regimes described by a Holstein–Tavis–Cummings (HTC) model Hamiltonian. The first one takes advantage of sparsity of the HTC Hamiltonian, which allows one to reduce the cost of acting polariton Hamiltonian onto a state vector to the linear order of the number of states, instead of the quadratic order. The second one is applying the well-known Chebyshev series expansion approach for quantum dynamics propagation and to simulate the polariton dynamics in the HTC system; this approach allows us to use a much larger time step for propagation and only requires a few recursive operations of the polariton Hamiltonian acting on state vectors. These two theoretical approaches are general and can be applied to any trajectory-based non-adiabatic quantum dynamics methods. We apply these two techniques with our previously developed Lindblad-partially linearized density matrix approach to simulate the linear absorption spectra of the HTC model system, with both inhomogeneous site energy disorders and dipolar orientational disorders. Our numerical results agree well with the previous analytic and numerical work.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Design and Evaluation of the Terminal Area Precision Scheduling and Spacing System

This paper describes the design, development and results from a high fidelity human-in-the-loop simulation of an integrated set of trajectory-based automation tools providing precision scheduling, sequencing and controller merging and spacing functions. These integrated functions are combined into a system called the Terminal Area Precision Scheduling and Spacing (TAPSS) system. It is a strategic and tactical planning tool that provides Traffic Management Coordinators, En Route and Terminal Radar Approach Control air traffic controllers the ability to efficiently optimize the arrival capacity of a demand-impacted airport while simultaneously enabling fuel-efficient descent procedures. The TAPSS system consists of four-dimensional trajectory prediction, arrival runway balancing, aircraft separation constraint-based scheduling, traffic flow visualization and trajectory-based advisories to assist controllers in efficient metering, sequencing and spacing. The TAPSS system was evaluated and compared to today's ATC operation through extensive series of human-in-the-loop simulations for arrival flows into the Los Angeles International Airport. The test conditions included the variation of aircraft demand from a baseline of today's capacity constrained periods through 5%, 10% and 20% increases. Performance data were collected for engineering and human factor analysis and compared with similar operations both with and without the TAPSS system. The engineering data indicate operations with the TAPSS show up to a 10% increase in airport throughput during capacity constrained periods while maintaining fuel-efficient aircraft descent profiles from cruise to landing.

Swenson, Harry N.

Dissipative ground state preparation in ab initio electronic structure theory

Dissipative engineering is a powerful tool for quantum state preparation, and has drawn significant attention in quantum algorithms and quantum many-body physics in recent years. In this work, we introduce a novel approach using the Lindblad dynamics to efficiently prepare the ground state for general ab initio electronic structure problems on quantum computers, without variational parameters. These problems often involve Hamiltonians that lack geometric locality or sparsity structures, which we address by proposing two generic types of jump operators for the Lindblad dynamics. Type-I jump operators break the particle number symmetry and should be simulated in the Fock space. Type-II jump operators preserves the particle number symmetry and can be simulated more efficiently in the full configuration interaction space. For both types of jump operators, we prove that in a simplified Hartree-Fock framework, the spectral gap of our Lindbladian is lower bounded by a universal constant. For physical observables such as energy and reduced density matrices, the convergence rate of our Lindblad dynamics with Type-I jump operators remains universal, while the convergence rate with Type-II jump operators only depends on coarse grained information such as the number of orbitals and the number of electrons. To validate our approach, we employ a Monte Carlo trajectory-based algorithm for simulating the Lindblad dynamics for full ab initio Hamiltonians, demonstrating its effectiveness on molecular systems amenable to exact wavefunction treatment.

Quantum chemistry

Trajectory-Based Takeoff Time Predictions Applied to Tactical Departure Scheduling: Concept Description, System Design, and Initial Observations

Current aircraft departure release times are based on manual estimates of aircraft takeoff times. Uncertainty in takeoff time estimates may result in missed opportunities to merge into constrained en route streams and lead to lost throughput. However, technology exists to improve takeoff time estimates by using the aircraft surface trajectory predictions that enable air traffic control tower (ATCT) decision support tools. NASA s Precision Departure Release Capability (PDRC) is designed to use automated surface trajectory-based takeoff time estimates to improve en route tactical departure scheduling. This is accomplished by integrating an ATCT decision support tool with an en route tactical departure scheduling decision support tool. The PDRC concept and prototype software have been developed, and an initial test was completed at air traffic control facilities in Dallas/Fort Worth. This paper describes the PDRC operational concept, system design, and initial observations.

Engelland, Shawn A.

Complexity Management Using Metrics for Trajectory Flexibility Preservation and Constraint Minimization

The growing demand for air travel is increasing the need for mitigating air traffic congestion and complexity problems, which are already at high levels. At the same time new surveillance, navigation, and communication technologies are enabling major transformations in the air traffic management system, including net-based information sharing and collaboration, performance-based access to airspace resources, and trajectory-based rather than clearance-based operations. The new system will feature different schemes for allocating tasks and responsibilities between the ground and airborne agents and between the human and automation, with potential capacity and cost benefits. Therefore, complexity management requires new metrics and methods that can support these new schemes. This paper presents metrics and methods for preserving trajectory flexibility that have been proposed to support a trajectory-based approach for complexity management by airborne or ground-based systems. It presents extensions to these metrics as well as to the initial research conducted to investigate the hypothesis that using these metrics to guide user and service provider actions will naturally mitigate traffic complexity. The analysis showed promising results in that: (1) Trajectory flexibility preservation mitigated traffic complexity as indicated by inducing self-organization in the traffic patterns and lowering traffic complexity indicators such as dynamic density and traffic entropy. (2)Trajectory flexibility preservation reduced the potential for secondary conflicts in separation assurance. (3) Trajectory flexibility metrics showed potential application to support user and service provider negotiations for minimizing the constraints imposed on trajectories without jeopardizing their objectives.

Idris, Husni

Investigation of a geodesy coexperiment to the Gravity Probe B relativity gyroscope program

Geodesy is the science of measuring the gravitational field of and positions on the Earth. Estimation of the gravitational field via gravitation gradiometry, the measurement of variations in the direction and magnitude of gravitation with respect to position, is this dissertation's focus. Gravity Probe B (GP-B) is a Stanford satellite experiment in gravitational physics. GP-B will measure the precession the rotating Earth causes on the space time around it by observing the precessions of four gyroscopes in a circular, polar, drag-free orbit at 650 km altitude. The gyroscopes are nearly perfect niobium-coated spheres of quartz, operating at 1.8 K to permit observations with extremely low thermal noise. The permissible gyroscope drift rate is miniscule, so the torques on the gyros must be tiny. A drag-free control system, by canceling accelerations caused by nongravitational forces, minimizes the support forces and hence torques. The GP-B system offers two main possibilities for geodesy. One is as a drag-free satellite to be used in trajectory-based estimates of the Earth's gravity field. We described calculations involving that approach in our previous reports, including comparison of laser only, GPS only, and combined tracking and a preliminary estimate of the possibility of estimating relativistic effects on the orbit. The second possibility is gradiometry. This technique has received a more cursory examination in previous reports, so we concentrate on it here. We explore the feasibility of using the residual suspension forces centering the GP-B gyros as gradiometer signals for geodesy. The objective of this work is a statistical prediction of the formal uncertainty in an estimate of the Earth's gravitation field using data from GP-B. We perform an instrument analysis and apply two mathematical techniques to predict uncertainty. One is an analytical approach using a flat-Earth approximation to predict geopotential information quality as a function of spatial wavelength. The second estimates the covariance matrix arising in a least-squares estimate of a spherical harmonic representation of the geopotential using GP-B gradiometer data. The results show that the GP-B data set can be used to create a consistent estimate of the geopotential up to spherical harmonic degree and order 60. The formal uncertainty of all coefficients between degrees 5 and 50 is reduced by factors of up to 30 over current satellite-only estimates and up to 7 over estimates which include surface data. The primary conclusion resulting from this study is that the gravitation gradiometer geodesy coexperiment to GP-B is both feasible and attractive.

Everitt, C. W. F.

Parallel-in-Time Solution of Allen-Cahn Equations by Integrating Operator Learning into the Parareal Method

While recent advances in deep learning have shown promising efficiency gains in solving time-dependent partial differential equations (PDEs), matching the accuracy of conventional numerical solvers still remains a challenge. One strategy to improve the accuracy of deep learning-based solutions for time-dependent PDEs is to use the learned model as the coarse propagator in the Parareal method and a traditional numerical method as the fine solver. However, successful integration of deep learning into the Parareal method requires consistency between the coarse and fine solvers, particularly for PDEs exhibiting rapid changes such as sharp transitions. Here, to ensure this consistency, we propose using convolutional neural networks (CNNs) to learn the fully discrete time-stepping operator defined by the same numerical scheme employed as the fine solver. We demonstrate the effectiveness of the proposed method in solving the classical and mass-conservative Allen–Cahn (AC) equations. Through iterative updates in the Parareal algorithm, our approach achieves a significant computational speedup compared to traditional fine solvers while converging to high-accuracy solutions. Our results highlight that the proposed hybrid Parareal algorithm effectively accelerates simulations, particularly when implemented on multiple GPUs, and converges to the desired accuracy in only a few iterations. Another advantage of our method is that the CNN model is trained on trajectory-based data generated from random initial conditions, such that the trained model can be used to solve the AC equations with various initial conditions without retraining. This work demonstrates the potential of integrating neural network methods into parallel-in-time frameworks for efficient and accurate simulations of time-dependent PDEs.

97 MATHEMATICS AND COMPUTING