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All sources NASA NTRS DOE OSTI

DOE OSTI2019

Study of Integrable and Quasi-Integrable Sextupole Lattice

In order to maximize beam lifetime in circular particle accelerators, the nonlinear beam optics are optimized to maximize the dynamic aperture of the beam. The dynamic aperture (DA), which is a 6-D phase space volume of stable trajectories, depends on the strength of the nonlinearities in the machine, and is calculated via particle tracking. Current DA optimization processes include multi-objective genetic algorithm optimizers, and relies on minimizing the magnitudes of resonance driving terms (RDT), which are calculated from the nonlinear contribution to the one-turn-map. The process of searching through the parameter space for an ideal combination that maximizes DA is computationally strenuous. By setting up the sextupole channel such that it is resembles a symplectic integrator of a smooth Hamiltonian, with only a few sextupoles we are able to closely reproduce phase space trajectories of a smooth Hamiltonian up to the hyperbolic point. No chaos and resonances are observed if phase advance per one sextupole magnet in the channel does not exceed ~0.12x2 pi. Therefore, an important property of the suggested approach is the intrinsic elimination of the resonances, and minimization of corresponding RDTs.

43 PARTICLE ACCELERATORS↗

NASA NTRS1986

Extensions to PIFCGT: Multirate output feedback and optimal disturbance suppression

New control synthesis procedures for digital flight control systems were developed. The theoretical developments are the solution to the problem of optimal disturbance suppression in the presence of windshear. Control synthesis is accomplished using a linear quadratic cost function, the command generator tracker for trajectory following and the proportional-integral-filter control structure for practical implementation. Extensions are made to the optimal output feedback algorithm for computing feedback gains so that the multirate and optimal disturbance control designs are computed and compared for the advanced transport operating system (ATOPS). The performance of the designs is demonstrated by closed-loop poles, frequency domain multiinput sigma and eigenvalue plots and detailed nonlinear 6-DOF aircraft simulations in the terminal area in the presence of windshear.

Broussard, J. R.↗

NASA NTRS2007

Impact to Space Shuttle Vehicle Trajectory on Day of Launch from change in Low Frequency Winds

The National Aeronautics and Space Administration's (NASA) Space Shuttle utilizes atmospheric winds on day of launch to develop throttle and steering commands to best optimize vehicle performance while keeping structural loading on the vehicle within limits. The steering commands and resultant trajectory are influenced by both the high and low frequency component of the wind. However, the low frequency component has a greater effect on the ascent design. Change in the low frequency wind content from the time of trajectory design until launch can induce excessive loading on the vehicle. Wind change limits have been derived to protect from launching in an environment where these temporal changes occur. Process of developing wind change limits are discussed followed by an observational study of temporal wind change in low frequency wind profiles at the NASA's Kennedy Space Center area are presented.

Decker, Ryan K.↗

NASA NTRSDate not supplied

Improving Multi-Model Trajectory Simulation Estimators using Model Selection and Tuning

Multi-model Monte Carlo methods have been demonstrated to be an efficient and accurate alternative to standard Monte Carlo (MC) in the model-based propagation of uncertainty in entry, descent, and landing (EDL) applications. These multi-model MC methods fuse predictions from low-fidelity models with the high-fidelity EDL model of interest to produce unbiased statistics with a fraction of the computational cost. The accuracy and efficiency of the multi-model MC methods are dependent upon the magnitude of correlations of the low-fidelity models with the high-fidelity model, but also upon the correlation amongst the low-fidelity models, and their relative computational cost. Because of this layer of complexity, the question of how to optimally select the set of low-fidelity models has remained open. In this work, methods for optimal model construction and tuning are investigated as a means to increase the speed and precision of trajectory simulation for EDL. Specifically, the focus is on the inclusion of low-fidelity model tuning within the sample allocation optimization that accompanies multi-model MC methods. Preliminary results indicate that low-fidelity model tuning can significantly improve efficiency and precision of trajectory simulations and provide an increased edge to multi-model MC methods when compared to standard MC. The challenges and potential benefits to exploring a fully iterative and comprehensive optimization strategy in future work are highlighted.

uncertainty quantification↗

NASA NTRS2007

Two-Stage Path Planning Approach for Designing Multiple Spacecraft Reconfiguration Maneuvers

The paper presents a two-stage approach for designing optimal reconfiguration maneuvers for multiple spacecraft. These maneuvers involve well-coordinated and highly-coupled motions of the entire fleet of spacecraft while satisfying an arbitrary number of constraints. This problem is particularly difficult because of the nonlinearity of the attitude dynamics, the non-convexity of some of the constraints, and the coupling between the positions and attitudes of all spacecraft. As a result, the trajectory design must be solved as a single 6N DOF problem instead of N separate 6 DOF problems. The first stage of the solution approach quickly provides a feasible initial solution by solving a simplified version without differential constraints using a bi-directional Rapidly-exploring Random Tree (RRT) planner. A transition algorithm then augments this guess with feasible dynamics that are propagated from the beginning to the end of the trajectory. The resulting output is a feasible initial guess to the complete optimal control problem that is discretized in the second stage using a Gauss pseudospectral method (GPM) and solved using an off-the-shelf nonlinear solver. This paper also places emphasis on the importance of the initialization step in pseudospectral methods in order to decrease their computation times and enable the solution of a more complex class of problems. Several examples are presented and discussed.

Aoude, Georges S.↗

DOE OSTI2019

Direct construction of optimized stellarator shapes. Part 2. Numerical quasisymmetric solutions

Quasisymmetric stellarators are appealing intellectually and as fusion reactor candidates since the guiding-centre particle trajectories and neoclassical transport are isomorphic to those in a tokamak, implying good confinement. Previously, quasisymmetric magnetic fields have been identified by applying black-box optimization algorithms to minimize symmetry-breaking Fourier modes of the field strength $B$ . Here, instead, we directly construct magnetic fields in cylindrical coordinates that are quasisymmetric to leading order in the distance from the magnetic axis, without using optimization. The approach involves solution of a one-dimensional nonlinear ordinary differential equation, originally derived by Garren & Boozer ( Phys. Fluids B, vol. 3, 1991, p. 2805). We illustrate the usefulness and accuracy of this optimization-free approach by providing the results of this construction as input to the codes VMEC and BOOZ_XFORM, confirming the purity and scaling of the magnetic spectrum. The space of magnetic fields that are quasisymmetric to this order is parameterized by the magnetic axis shape along with three other real numbers, one of which reflects the on-axis toroidal current density, and another one of which is zero for stellarator symmetry. The method here could be used to generate good initial conditions for conventional optimization, and its speed enables exhaustive searches of parameter space.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1990

The 4-D descent trajectory generation techniques under realistic operating conditions

NASA-Langley has been conducting and sponsoring research in airborne energy management for a number of years. During the course of this research, two fundamental techniques for the generation of 4D (fixed time) descent trajectories have emerged as viable candidates for advanced flight management systems. The first technique utilizes speed schedules of constant Mach number transitioning to constant calibrated airspeed chosen empirically to produce minimum fuel usage. The second technique computes cost optimized speed schedules of variable airspeed developed through application of optimal control theory. Both techniques have been found to produce reasonable and flyable descent trajectories. The formulation of the algorithms for each technique is evaluated and their suitability for operations in realistic conditions is discussed. Operational factors considered include: airplace speed, thrust, and altitude rate constaints; wind, temperature, and pressure variations; Air Traffic Control altitude, speed, and time constaints; and pilot interface and guidance considerations. Time flexibility, fuel usage, and airborne computational requirements were the primary performance measures.

Williams, David H.↗

DOE OSTI2014

Optimal beam design on intensity-modulated radiation therapy with simultaneous integrated boost in nasopharyngeal cancer

This study aims to determine the optimal beam design among various combinations of field numbers and beam trajectories for intensity-modulated radiation therapy (IMRT) with simultaneous integrated boost (SIB) technique for the treatment of nasopharyngeal cancer (NPC). We used 10 fields with gantry angles of 155°, 130°, 75°, 25°, 0° L, 0° R, 335°, 285°, 230°, and 205° denoted as F10. To decrease doses in the spinal cord, the F10 technique was designed by featuring 2 pairs of split-opposed beam fields at 155° to 335° and 205° to 25°, as well as one pair of manually split beam fields at 0°. The F10 technique was compared with 4 other common field arrangements: F7E, 7 fields with 50° equally spaced gantry angles; F7, the basis of F10 with 155°, 130°, 75°, 0°, 285°, 230°, and 205°; F9E, 9 fields with 40° equally spaced gantry angles; and FP, 7 posterior fields with 180°, 150°, 120°, 90°, 270°, 240°, and 210°. For each individual case of 10 patients, the customized constraints derived after optimization with the standard F10 technique were applied to 4 other field arrangements. The 4 new optimized plans of each individual case were normalized to achieve the same coverage of planning target volume (PTV){sub 63} {sub Gy} as that of the standard F10 technique. The F10 field arrangement exhibited the best coverage in PTV{sub 70} {sub Gy} and the least mean dose in the trachea-esophagus region. Furthermore, the F10 field arrangement demonstrated the highest level of conformity in the low-dose region and the least monitor unit. The F10 field arrangement performed more outstandingly than the other field arrangements in PTV{sub 70} {sub Gy} coverage and spared the central organ. This arrangement also exhibited the highest conformity and delivery efficiency. The F10 technique is recommended as the standard beam geometry for the SIB-IMRT of NPC.

61 RADIATION PROTECTION AND DOSIMETRY↗

NASA NTRSDate not supplied

Application of Tisserand's Criterion and the Lidov-Kozai Effect to STORM's Trajectory Design

The Solar-Terrestrial Observer for the Response of the Magnetosphere (STORM) concept recently completed its Phase A design funded by NASA's Heliophysics Medium-class Explorers program. The mission design required a lunar gravity assist to insert the single spacecraft into a 30-Earth-radii circular geocentric science orbit inclined 90 degrees to the ecliptic. STORM's trajectory design leveraged several interesting gravitational effects from third bodies. This paper describes our application of Tisserand's criterion for finding feasible transfers and lunar gravity assist trajectories, and the Lidov-Kozai effect to design a maneuver-free science orbit optimization and decommissioning strategy.

tisserand criterion↗

DOE OSTI2026

Automated Classification of Vehicle Movements at Signalized Intersections Using Vehicle Trajectories

Accurate vehicle movement classification through signalized intersections is of paramount importance to the analysis of intersection performance and the optimization of traffic control strategies. Conventional techniques for tracking vehicle turning movements depend on infrastructure-based strategies like human counts, loop detectors, and video analytics, all of which are costly, prone to errors, and spatially constrained. High-frequency trajectory data can be utilized to determine vehicle movement patterns in a scalable and infrastructure-independent method due to the adoption of connected vehicles (CVs). In recent years, several studies have utilized connected vehicle data to generate performance measures. Most of the trajectory-based performance measures approaches, however, require map matching-i.e., extracting geospatial references from maps to identify the movements that individual vehicles make at a signalized intersection. These approaches are often time-consuming and hinder scalability since geographic features need to be provided for an analysis to be conducted. Map matching methods are prone to errors as different map versions change these geographic features. This research presents a novel automatic classification pipeline that uses CV trajectory data to classify vehicle movements at signalized crossings, specifically pass-through left-turn and right-turn maneuvers. The process starts by filtering trips that cross a spatial bounding box that has been defined at the target intersection. Approach and departure headings for each trajectory crossing the boundary are computed and are clustered together to identify dominant movements. The proposed algorithm is used to classify the movement of vehicles at 10 intersections in the state of California, and the results indicate that the algorithm can classify movements at these intersections with varying traffic volumes and road network configurations, all in a map-less framework with no need for conflation of vehicle trajectories to a digital base map.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRSDate not supplied

Improving Multi-Model Trajectory Simulation Estimators using Model Selection and Tuning

Multi-model Monte Carlo methods have been demonstrated to be an efficient and accurate alternative to standard Monte Carlo (MC) in the model-based propagation of uncertainty in entry, descent, and landing (EDL) applications. These multi-model MC methods fuse predictions from low-fidelity models with the high-fidelity EDL model of interest to produce unbiased statistics with a fraction of the computational cost. The accuracy and efficiency of the multi-model MC methods are dependent upon the magnitude of correlations of the low-fidelity models with the high-fidelity model, but also upon the correlation among the low-fidelity models, and their relative computational cost. Because of this layer of complexity, the question of how to optimally select the set of low-fidelity models has remained open. In this work, methods for optimal model construction and tuning are investigated as a means to increase the speed and precision of trajectory simulation for EDL. Specifically, the focus is on the inclusion of low-fidelity model tuning within the sample allocation optimization that accompanies multi-model MC methods. Preliminary results indicate that low-fidelity model tuning can significantly improve efficiency and precision of trajectory simulations and provide an increased edge to multi-model MC methods when compared to standard MC. The challenges and potential benefits to exploring a fully iterative and comprehensive optimization strategy in future work are highlighted.

uncertainty quantification↗

DOE OSTI2018

Direct construction of optimized stellarator shapes. Part 1. Theory in cylindrical coordinates

The confinement of the guiding-centre trajectories in a stellarator is determined by the variation of the magnetic field strength $B$ in Boozer coordinates $(r,\unicode[STIX]{x1D703},\unicode[STIX]{x1D711})$ , but $B(r,\unicode[STIX]{x1D703},\unicode[STIX]{x1D711})$ depends on the flux surface shape in a complicated way. Here we derive equations relating $B(r,\unicode[STIX]{x1D703},\unicode[STIX]{x1D711})$ in Boozer coordinates and the rotational transform to the shape of flux surfaces in cylindrical coordinates, using an expansion in distance from the magnetic axis. A related expansion was done by Garren and Boozer ( Phys. Fluids B, vol. 3, 1991 a , 2805) based on the Frenet–Serret frame, which can be discontinuous anywhere the magnetic axis is straight, a situation that occurs in the interesting case of omnigenity with poloidally closed $B$ contours. Our calculation in contrast does not use the Frenet–Serret frame. The transformation between the Garren–Boozer approach and cylindrical coordinates is derived, and the two approaches are shown to be equivalent if the axis curvature does not vanish. The expressions derived here help enable optimized plasma shapes to be constructed that can be provided as input to VMEC and other stellarator codes, or to generate initial configurations for conventional stellarator optimization.

Physics↗

NASA NTRS1984

Approximate solutions to minimax optimal control problems for aeroassisted orbital transfer

The maneuver considered in the present investigation involves the coplanar transfer of a spacecraft from a high earth orbit (HEO) to a low earth orbit (LEO). HEO can be a geosynchronous earth orbit (GEO). The basic concept utilized involves the hybrid combination of propulsive maneuvers in space and aerodynamic maneuvers in the sensible atmosphere. The considered type of flight is also called synergetic space flight. With respect to the atmospheric part of the maneuver, trajectory control is achieved by means of lift modulation. The Bolza problem of optimal control is stated, and the first-order optimality conditions for this problem are given. The one-arc approach, the two-arc approach, and the three-subarc approach are discussed. Attention is given to the Chebyshev problem of optimal control, details concerning aeroassisted orbital transfer (AOT), AOT optimization problems, and numerical experiments.

Miele, A.↗

DOE OSTI2018

Mass, momentum, and energy transfer in supersonic aerosol deposition processes

Aerosol deposition (AD) can lead to the formation of dense coatings via deposition of particles from a gas flow; in AD the aerosol is passed through a converging-diverging nozzle, facilitating inertial particle impaction on a desired substrate at supersonic particle velocities. Unique from thermal spray methods, AD can be applied near room temperature and unique from cold spray, in AD the aerosol is typically at atmospheric pressure upstream of the nozzle. Though AD has been successfully demonstrated previously, a number of aspects related to particle motion in AD systems remain poorly understood. In this work, we simulated compressible flow field profiles and particle trajectories for typical AD working conditions for a slit type converging-diverging nozzle with a planar substrate. In examining the fluid flow profile, we show that the velocity and pressure profiles, as well as the shock structure are sensitive to the upstream and downstream operating pressures of the nozzle. These ultimately affect particle impaction speed. Importantly, in AD, the particle drag regime is dynamic; both particle Knudsen numbers and Mach numbers can vary by orders of magnitude. To aid particle trajectory simulations, we trained a neural network to predict the drag force on the particles based on existing experimental data, theoretical limits, and new direct simulation Monte Carlo (DMSC) results. The neural network based drag law, which depends upon both Mach and Knudsen numbers, shows better agreement with the DSMC simulation data than pre-existing correlations. With it, particle trajectory simulation results reveal that for a given particle density, there exists an optimal particle diameter to maximize particle impaction speed. We also find that in AD particles undergo size dependent inertial focusing, i.e. there is a particular particle diameter where the particle deposition linewidth is minimized. Particles smaller than this diameter are underfocused, and particles larger than this are overfocused, and hence have larger deposition linewidths in both cases. Using trajectory simulations, we additionally develop a framework that can be used to evaluate the position-dependent mass, momentum and kinetic energy fluxes to the deposition substrate for any aerosol size distribution function upstream the nozzle. It is shown for typical aerosol concentrations achievable in the laboratory, the kinetic energy flux can approach a magnitude normally observed in convective heat transfer with phase change, hence translational kinetic energy to thermal energy transfer in AD is likely the key contributor to the formation of dense coatings.

42 ENGINEERING↗

DOE OSTI2015

Statistical behaviour of adaptive multilevel splitting algorithms in simple models

Adaptive multilevel splitting algorithms have been introduced rather recently for estimating tail distributions in a fast and efficient way. In particular, they can be used for computing the so-called reactive trajectories corresponding to direct transitions from one metastable state to another. The algorithm is based on successive selection–mutation steps performed on the system in a controlled way. It has two intrinsic parameters, the number of particles/trajectories and the reaction coordinate used for discriminating good or bad trajectories. We investigate first the convergence in law of the algorithm as a function of the timestep for several simple stochastic models. Second, we consider the average duration of reactive trajectories for which no theoretical predictions exist. The most important aspect of this work concerns some systems with two degrees of freedom. They are studied in detail as a function of the reaction coordinate in the asymptotic regime where the number of trajectories goes to infinity. We show that during phase transitions, the statistics of the algorithm deviate significatively from known theoretical results when using non-optimal reaction coordinates. In this case, the variance of the algorithm is peaking at the transition and the convergence of the algorithm can be much slower than the usual expected central limit behaviour. The duration of trajectories is affected as well. Moreover, reactive trajectories do not correspond to the most probable ones. Such behaviour disappears when using the optimal reaction coordinate called committor as predicted by the theory. We finally investigate a three-state Markov chain which reproduces this phenomenon and show logarithmic convergence of the trajectory durations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1985

Energy management of three-dimensional minimum-time intercept

A real-time computer algorithm to control and optimize aircraft flight profiles is described and applied to a three-dimensional minimum-time intercept mission. The proposed scheme has roots in two well known techniques: singular perturbations and neighboring-optimal guidance. Use of singular-perturbation ideas is made in terms of the assumed trajectory-family structure. A heading/energy family of prestored point-mass-model state-Euler solutions is used as the baseline in this scheme. The next step is to generate a near-optimal guidance law that will transfer the aircraft to the vicinity of this reference family. The control commands fed to the autopilot (bank angle and load factor) consist of the reference controls plus correction terms which are linear combinations of the altitude and path-angle deviations from reference values, weighted by a set of precalculated gains. In this respect the proposed scheme resembles neighboring-optimal guidance. However, in contrast to the neighboring-optimal guidance scheme, the reference control and state variables as well as the feedback gains are stored as functions of energy and heading in the present approach. Some numerical results comparing open-loop optimal and approximate feedback solutions are presented.

Kelley, H. J.↗

NASA NTRS2022

Stability Analysis of Streaks Induced by Optimized Vortex Generators

Numerical computations are performed to investigate the potential for transition control in an axisymmetric boundary layer via fully realizable, streamwise stationary streaks induced by an azimuthally periodic array of surface mounted vortex generators (VGs). Previous work has shown that suitable streaks of this type can significantly reduce the growth of Mack’s second mode instabilities, but large streak amplitudes can make the flow susceptible to previously absent streak instabilities that can become the leading cause of transition. Here, we use the adjoint capabilities of the SU2 flow solver to optimize the VG shape to maximize the reduction in the growth of second-mode disturbances while also preventing the streak amplitudes from reaching large enough values to precipitate an earlier onset of transition via streak instabilities. The geometry and the freestream flow conditions are selected to match a relevant trajectory lo-cation from the HIFiRE-1 flight experiment. Results show that the optimized VGs can increase the mean streak amplitude by 117% with respect to a manually developed baseline design. The stability of this optimized basic state is analyzed via the plane-marching parabolized stability equations, predicting a fully laminar flow over the entire cone, or equivalently, yielding transition delay of 130% versus the 17% for the baseline VGs.

Boundary layer transition↗

NASA NTRS2022

Stability Analysis of Streaks Induced By Optimized Vortex Generators

Boundary layer transition↗