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NASA NTRS2002

An Automated Method to Compute Orbital Re-Entry Trajectories with Heating Constraints

Determining how to properly manipulate the controls of a re-entering re-usable launch vehicle (RLV) so that it is able to safely return to Earth and land involves the solution of a two-point boundary value problem (TPBVP). This problem, which can be quite difficult, is traditionally solved on the ground prior to flight. If necessary, a nearly unlimited amount of time is available to find the "best" solution using a variety of trajectory design and optimization tools. The role of entry guidance during flight is to follow the pre-determined reference solution while correcting for any errors encountered along the way. This guidance method is both highly reliable and very efficient in terms of onboard computer resources. There is a growing interest in a style of entry guidance that places the responsibility of solving the TPBVP in the actual entry guidance flight software. Here there is very limited computer time. The powerful, but finicky, mathematical tools used by trajectory designers on the ground cannot in general be made to do the job. Nonconvergence or slow convergence can result in disaster. The challenges of designing such an algorithm are numerous and difficult. Yet the payoff (in the form of decreased operational costs and increased safety) can be substantial. This paper presents an algorithm that incorporates features of both types of guidance strategies. It takes an initial RLV orbital re-entry state and finds a trajectory that will safely transport the vehicle to a Terminal Area Energy Management (TAEM) region. During actual flight, the computed trajectory is used as the reference to be flown by a more traditional guidance method.

Zimmerman, Curtis↗

NASA NTRS2009

Direct Multiple Shooting Optimization with Variable Problem Parameters

Taking advantage of a novel approach to the design of the orbital transfer optimization problem and advanced non-linear programming algorithms, several optimal transfer trajectories are found for problems with and without known analytic solutions. This method treats the fixed known gravitational constants as optimization variables in order to reduce the need for an advanced initial guess. Complex periodic orbits are targeted with very simple guesses and the ability to find optimal transfers in spite of these bad guesses is successfully demonstrated. Impulsive transfers are considered for orbits in both the 2-body frame as well as the circular restricted three-body problem (CRTBP). The results with this new approach demonstrate the potential for increasing robustness for all types of orbit transfer problems.

Whitley, Ryan J.↗

NASA NTRS2013

Issues and Strategies in Solving Multidisciplinary Optimization Problems

Optimization research at NASA Glenn Research Center has addressed the design of structures, aircraft and airbreathing propulsion engines. The accumulated multidisciplinary design activity is collected under a testbed entitled COMETBOARDS. Several issues were encountered during the solution of the problems. Four issues and the strategies adapted for their resolution are discussed. This is followed by a discussion on analytical methods that is limited to structural design application. An optimization process can lead to an inefficient local solution. This deficiency was encountered during design of an engine component. The limitation was overcome through an augmentation of animation into optimization. Optimum solutions obtained were infeasible for aircraft and airbreathing propulsion engine problems. Alleviation of this deficiency required a cascading of multiple algorithms. Profile optimization of a beam produced an irregular shape. Engineering intuition restored the regular shape for the beam. The solution obtained for a cylindrical shell by a subproblem strategy converged to a design that can be difficult to manufacture. Resolution of this issue remains a challenge. The issues and resolutions are illustrated through a set of problems: Design of an engine component, Synthesis of a subsonic aircraft, Operation optimization of a supersonic engine, Design of a wave-rotor-topping device, Profile optimization of a cantilever beam, and Design of a cylindrical shell. This chapter provides a cursory account of the issues. Cited references provide detailed discussion on the topics. Design of a structure can also be generated by traditional method and the stochastic design concept. Merits and limitations of the three methods (traditional method, optimization method and stochastic concept) are illustrated. In the traditional method, the constraints are manipulated to obtain the design and weight is back calculated. In design optimization, the weight of a structure becomes the merit function with constraints imposed on failure modes and an optimization algorithm is used to generate the solution. Stochastic design concept accounts for uncertainties in loads, material properties, and other parameters and solution is obtained by solving a design optimization problem for a specified reliability. Acceptable solutions can be produced by all the three methods. The variation in the weight calculated by the methods was found to be modest. Some variation was noticed in designs calculated by the methods. The variation may be attributed to structural indeterminacy. It is prudent to develop design by all three methods prior to its fabrication. The traditional design method can be improved when the simplified sensitivities of the behavior constraint is used. Such sensitivity can reduce design calculations and may have a potential to unify the traditional and optimization methods. Weight versus reliability traced out an inverted-S-shaped graph. The center of the graph corresponded to mean valued design. A heavy design with weight approaching infinity could be produced for a near-zero rate of failure. Weight can be reduced to a small value for a most failure-prone design. Probabilistic modeling of load and material properties remained a challenge.

Patnaik, Surya↗

NASA NTRS2013

X-Ray Detection and Processing Models for Spacecraft Navigation and Timing

The current primary method of deepspace navigation is the NASA Deep Space Network (DSN). High-performance navigation is achieved using Delta Differential One-Way Range techniques that utilize simultaneous observations from multiple DSN sites, and incorporate observations of quasars near the line-of-sight to a spacecraft in order to improve the range and angle measurement accuracies. Over the past four decades, x-ray astronomers have identified a number of xray pulsars with pulsed emissions having stabilities comparable to atomic clocks. The x-ray pulsar-based navigation and time determination (XNAV) system uses phase measurements from these sources to establish autonomously the position of the detector, and thus the spacecraft, relative to a known reference frame, much as the Global Positioning System (GPS) uses phase measurements from radio signals from several satellites to establish the position of the user relative to an Earth-centered fixed frame of reference. While a GPS receiver uses an antenna to detect the radio signals, XNAV uses a detector array to capture the individual xray photons from the x-ray pulsars. The navigation solution relies on detailed xray source models, signal processing, navigation and timing algorithms, and analytical tools that form the basis of an autonomous XNAV system. Through previous XNAV development efforts, some techniques have been established to utilize a pulsar pulse time-of-arrival (TOA) measurement to correct a position estimate. One well-studied approach, based upon Kalman filter methods, optimally adjusts a dynamic orbit propagation solution based upon the offset in measured and predicted pulse TOA. In this delta position estimator scheme, previously estimated values of spacecraft position and velocity are utilized from an onboard orbit propagator. Using these estimated values, the detected arrival times at the spacecraft of pulses from a pulsar are compared to the predicted arrival times defined by the pulsar s pulse timing model. A discrepancy provides an estimate of the spacecraft position offset, since an error in position will relate to the measured time offset of a pulse along the line of sight to the pulsar. XNAV researchers have been developing additional enhanced approaches to process the photon TOAs to arrive at an estimate of spacecraft position, including those using maximum-likelihood estimation, digital phase locked loops, and "single photon processing" schemes that utilize all available time data associated with each photon. Using pulsars from separate, non-coplanar locations provides range and range-rate measurements in each pulsar s direction. Combining these different pulsar measurements solves for offsets in position and velocity in three dimensions, and provides accurate overall navigation for deep space vehicles.

Sheikh, Suneel↗

NASA NTRS2022

PAAV Concept Document

The Pathfinding for Airspace with Autonomous Vehicles (PAAV) Concept Document, version 1.0, lays out the key challenges and potential solutions for the use of uncrewed aircraft (UA) technology for future regional air cargo operations. The challenges and solutions described in this document were informed by communications with the UA industry community (e.g., RTCA, the Federal Aviation Administration, and regional air cargo business operators), as well as the PAAV team’s research activities during the last two years including four tabletop exercises, a human-in-the-loop simulation study, a numerical simulation study, a functional allocation study, and flight data analysis (Appendix A). This document first describes the expected operational context of PAAV (Section 2), such as the flight mission, baseline UAS components, nominal operations, m:N operations (i.e., "m" remote pilots per "N" aircraft), and off-nominal operations. This context sets the scope for the PAAV concept development work. PAAV concept development assumes that UA operations will be increasingly autonomous. Thus, near- and far-term assumptions are defined (Section 3). PAAV identified seven key challenges for UA operations (Section 4): - Flight route planning - Separation and flow management - Traffic pattern integration - Contingency management - Taxi, takeoff, and landing - m:N operations - Communications operations The following 13 potential solutions to these challenges are then described (Section 5): - Scalable communications architecture - Data link - Designated UAS corridors - Crew planning for m:N operations - Flight route optimization - Traffic load-level control - Trajectory solutions with data link - Automated hazard avoidance for m:N operations - Traffic pattern integration (TPI) tool - Standard lost command and control (C2) link (LC2L) procedures - Automated hazard avoidance under LC2L - Auto-taxi, auto-takeoff, and auto-land - Ground control station (GCS) user interface for m:N operations The document attempts to link each of these solutions to one or more of the challenge areas. Novel solutions involving numerous automation technologies are needed to mitigate traffic and airspace management challenges, especially for realizing m:N operations and ensuring safety under LC2L conditions. The purpose of this document is to help understand alternatives and tradeoffs among potential solutions and provide a foundation for a cohesive PAAV concept that will be described and refined in subsequent concept versions.

Unmanned aircraft, uncrewed aircraft, regional air↗

DOE OSTI2024

High-Throughput Computing: Case Study of Medical Image Processing Applications

HPC is designed for large-scale simulations using monolithic codes of tightly coupled processes highly optimized to deliver decreased time to solution. Medical image processing is not a traditional field of HPC. Similar to AI applications, medical image processing parses large datasets, typically multiple times, to support a variety of studies for classification, diagnosis or monitoring purposes. The convergence of AI, HPC and Big Data encouraged more fields using image processing to transition to HPC. However, not all applications benefit from the same optimizations. In this paper we focus on high throughput medical image processing applications that analyze a huge dataset of small MRI images and that require HPC systems to decrease the time of parsing the entire dataset and not individual MRIs. We show in this research the performance of running SLANT, an image processing application for a whole brain segmentation, on large-scale systems and highlight performance limitations. We present optimizations prioritizing throughput that exhibit a 3.5x speed-up on the Summit Supercomputer that can be used as a baseline for building a high-throughput execution framework for other HPC systems.

Predescu, Maria↗

DOE OSTI2025

MetaHeuristic Feature Selection for Energy Group Optimization and Analysis

Energy discretization is a crucial component of deterministic neutron transport simulations. Metaheuristic (MH) optimizers are effective algorithms to determine group structures that maximize both solution accuracy and computational efficiency. This project establishes a framework for optimizing group structures for PARTISN simulations using the Python library MEALPY. Group structure optimization is formulated as a binary feature selection problem, and results are investigated with permutation and material importance techniques to determine physically relevant energy bounds. We conclude that MH optimizers find group structures that drastically improve flux calculations while preserving k-effective accuracy. Further, we find that individual energy bounds are not necessarily physically relevant, but rather specific energy ranges are.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1989

Recursive multibody dynamics and discrete-time optimal control

A recursive algorithm is developed for the solution of the simulation dynamics problem for a chain of rigid bodies. Arbitrary joint constraints are permitted, that is, joints may allow translational and/or rotational degrees of freedom. The recursive procedure is shown to be identical to that encountered in a discrete-time optimal control problem. For each relevant quantity in the multibody dynamics problem, there exists an analog in the context of optimal control. The performance index that is minimized in the control problem is identified as Gibbs' function for the chain of bodies.

Deleuterio, G. M. T.↗

NASA NTRS1987

Problem size, parallel architecture and optimal speedup

The communication and synchronization overhead inherent in parallel processing can lead to situations where adding processors to the solution method actually increases execution time. Problem type, problem size, and architecture type all affect the optimal number of processors to employ. The numerical solution of an elliptic partial differential equation is examined in order to study the relationship between problem size and architecture. The equation's domain is discretized into n sup 2 grid points which are divided into partitions and mapped onto the individual processor memories. The relationships between grid size, stencil type, partitioning strategy, processor execution time, and communication network type are analytically quantified. In so doing, the optimal number of processors was determined to assign to the solution, and identified (1) the smallest grid size which fully benefits from using all available processors, (2) the leverage on performance given by increasing processor speed or communication network speed, and (3) the suitability of various architectures for large numerical problems.

Nicol, David M.↗

NASA NTRS1988

Problem size, parallel architecture, and optimal speedup

Nicol, David M.↗

NASA NTRS1990

Optimum structural design of robotic manipulators with fiber reinforced composite materials

High-speed robotic arms with advanced structural characteristics can be fabricated from optimally tailored fiber reinforced composites. An integrated design methodology is presented for the optimal structural synthesis of composite robotic manipulators. Optimum configurations of ply angles and ply thicknesses are predicted for maximum structural end-effector stiffness and maximum end-effector load carrying capacity, without altering the geometric dimensions of the links. Multiple posture finite element-based static performance criteria are implemented. A new finite element has been developed for the modeling of tubular composite links. Unique features are the inclusion of shear effects and coupling between stretching and flexure. Numerical solutions are obtained via an efficient optimization algorithm. Applications to an existing SCARA-class manipulator illustrate the effectiveness of the method and demonstrate the dramatic influence of the multi-postural design criteria on the optimal design. For a filament wound structure using a high strength carbon fiber in a thermoplastic matrix, the resultant optimum ply configurations have increased the specific stiffness and specific load capacity by factors of 1.5 and 16, respectively, in comparison to identically sized aluminum links.

Saravanos, D. A.↗

NASA NTRS1970

A high speed, automated solution for physical network or system parameters based on sensitivity analysis and hybrid computer optimization techniques

High speed automated network design method for optimum value determination of system parameters, using sensitivity analysis and hybrid computer optimization techniques

Beck, C. H.↗

NASA NTRS1973

First-order corrections to approximate solutions to two-point boundary-condition problems

A method, applicable to real time guidance, is developed for accurate solution to exo-atmospheric space flight optimization problems. In principle the method is applicable to many other two-point boundary-condition (TPBC) problems. The first step of the method is the iterative solution (using a shooting method) of a TPBC problem with differential equations simplified so that they may be solved analytically by means of a single closed-form solution over each stage of the flight. The second step is the addition of a closed-form correction to the solution to the TPBC problem obtained in the first step. The correction accounts (to first-order accuracy) for the errors due to the aforementioned simplifications. Numerical results are given for several orbital injection problems.

Andrus, J. F.↗

DOE OSTI2025

An Optimization-Based Law of Mass Action Precipitation/Dissolution Model

Rare earth elements (REE) and many other critical minerals are necessary for the manufacturing of modern everyday technologies, including microchips, batteries and electric motors. Recovery of these materials typically involves aqueous systems which can be modeled as chemical equilibrium problems. One common method for solving these problems is the law of mass action approach (LMA), where a system of non-linear equations involving the equilibrium constants is solved. However, despite being theoretically simple, these problems are in practice very difficult to solve. Currently, the use of iterative heuristics based on saturation indices to decide on which species and reactions to include in the calculations is the state of the art to arrive at a solution. Here, we present an optimization-based alternative to solve chemical equilibria problems involving precipitation/dissolution reactions without the need for such heuristics. Our approach is first validated against the LMA software MINTEQ and PHREEQC for a number of case studies, and then applied to a novel REE recovery process reported in the literature. Overall, our approach was found to have close agreement with MINTEQ and PHREEQC, and we were able to successfully replicate the reported yield and purity for the published REE process.

42 ENGINEERING↗

NASA NTRS1987

Precise near-earth navigation with GPS: A survey of techniques

The tracking accuracy of the low earth orbiters (below about 3000 km altitude) can be brought below 10 cm with a variety of differential techniques that exploit the Global Positioning System (GPS). All of these techniques require a precisely known global network of GPS ground receivers and a receiver aboard the user satellite, and all simultaneously estimate the user and GPS satellite orbits. Three basic approaches are the geometric, dynamic, and nondynamic strategies. The last combines dynamic GPS solutions with a geometric user solution. Two powerful extensions of the nondynamic strategy show considerable promise. The first uses an optimized synthesis of dynamics and geometry in the user solution, while the second uses a novel gravity-adjustment method to exploit data from repeat ground tracks. These techniques will offer sub-decimeter accuracy for dynamically unpredictable satellites down to the lowesst possible altitudes.

Yunck, T. P.↗

NASA NTRS2001

Power and Efficiency Optimized in Traveling-Wave Tubes Over a Broad Frequency Bandwidth

A traveling-wave tube (TWT) is an electron beam device that is used to amplify electromagnetic communication waves at radio and microwave frequencies. TWT's are critical components in deep space probes, communication satellites, and high-power radar systems. Power conversion efficiency is of paramount importance for TWT's employed in deep space probes and communication satellites. A previous effort was very successful in increasing efficiency and power at a single frequency (ref. 1). Such an algorithm is sufficient for narrow bandwidth designs, but for optimal designs in applications that require high radiofrequency power over a wide bandwidth, such as high-density communications or high-resolution radar, the variation of the circuit response with respect to frequency must be considered. This work at the NASA Glenn Research Center is the first to develop techniques for optimizing TWT efficiency and output power over a broad frequency bandwidth (ref. 2). The techniques are based on simulated annealing, which has the advantage over conventional optimization techniques in that it enables the best possible solution to be obtained (ref. 3). Two new broadband simulated annealing algorithms were developed that optimize (1) minimum saturated power efficiency over a frequency bandwidth and (2) simultaneous bandwidth and minimum power efficiency over the frequency band with constant input power. The algorithms were incorporated into the NASA coupled-cavity TWT computer model (ref. 4) and used to design optimal phase velocity tapers using the 59- to 64-GHz Hughes 961HA coupled-cavity TWT as a baseline model. In comparison to the baseline design, the computational results of the first broad-band design algorithm show an improvement of 73.9 percent in minimum saturated efficiency (see the top graph). The second broadband design algorithm (see the bottom graph) improves minimum radiofrequency efficiency with constant input power drive by a factor of 2.7 at the high band edge (64 GHz) and increases simultaneous bandwidth by 500 MHz.

Wilson, Jeffrey D.↗

NASA NTRS1971

Approximate optimal atmospheric entry trajectories.

For a reentry glider, approximate solutions are found in closed form for the problem of maximizing a function of the terminal velocity, altitude, flight-path angle and heading angle subject to, at most, three terminal nonlinear constraints. The results given here extend the previous results in two important ways: (1) the second-order approximation of the entry dynamics of Loh is used instead of the first-order approximation of Allen and Eggers. This approximation is found to compare extremely well with an exact numerical optimal path. (2) A three-dimensional optimization problem is solved which includes Loh's second-order approximation where the roll angle as well as the lift coefficient are determined subject to constraints which include the terminal heading angle. Furthermore, closed-form solutions can also be obtained subject to in-flight constraints on the lift coefficient and roll angle.

Speyer, J. L.↗

NASA NTRS1998

Attitude Determination Using Two Vector Measurements

Many spacecraft attitude determination methods use exactly two vector measurements. The two vectors are typically the unit vector to the Sun and the Earth's magnetic field vector for coarse "sun-mag" attitude determination or unit vectors to two stars tracked by two star trackers for fine attitude determination. TRIAD, the earliest published algorithm for determining spacecraft attitude from two vector measurements, has been widely used in both ground-based and onboard attitude determination. Later attitude determination methods have been based on Wahba's optimality criterion for n arbitrarily weighted observations. The solution of Wahba's problem is somewhat difficult in the general case, but there is a simple closed-form solution in the two-observation case. This solution reduces to the TRIAD solution for certain choices of measurement weights. This paper presents and compares these algorithms as well as sub-optimal algorithms proposed by Bar-Itzhack, Harman, and Reynolds. Some new results will be presented, but the paper is primarily a review and tutorial.

Markley, F. Landis↗