Description of the GDC program for the graphic display of three-dimensional models prepared by the combinatorial geometry technique
Computer programming for graphic display of combinatorial geometry
Guber, W.↗
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Solar Proton Transport within an ICRU Sphere Surrounded by a Complex Shield: Combinatorial Geometry
The 3DHZETRN code, with improved neutron and light ion (Z (is) less than 2) transport procedures, was recently developed and compared to Monte Carlo (MC) simulations using simplified spherical geometries. It was shown that 3DHZETRN agrees with the MC codes to the extent they agree with each other. In the present report, the 3DHZETRN code is extended to enable analysis in general combinatorial geometry. A more complex shielding structure with internal parts surrounding a tissue sphere is considered and compared against MC simulations. It is shown that even in the more complex geometry, 3DHZETRN agrees well with the MC codes and maintains a high degree of computational efficiency.
Wilson, John W.↗
The 3-D world modeling with updating capability based on combinatorial geometry
A 3-D world modeling technique using range data is discribed. Range data quantify the distances from the sensor focal plane to the object surface, i.e., the 3-D coordinates of discrete points on the object surface are known. The approach proposed herein for 3-D world modeling is based on the Combinatorial Geometry (CG) method which is widely used in Monte Carlo particle transport calculations. First, each measured point on the object surface is surrounded by a small sphere with a radius determined by the range to that point. Then, the 3-D shapes of the visible surfaces are obtained by taking the (Boolean) union of all the spheres. The result is an unambiguous representation of the object's boundary surfaces. The pre-learned partial knowledge of the environment can be also represented using the CG Method with a relatively small amount of data. Using the CG type of representation, distances in desired directions to boundary surfaces of various objects are efficiently calculated. This feature is particularly useful for continuously verifying the world model against the data provided by a range finder, and for integrating range data from successive locations of the robot during motion. The efficiency of the proposed approach is illustrated by simulations of a spherical robot in a 3-D room in the presence of moving obstacles and inadequate prelearned partial knowledge of the environment.
Goldstein, M.↗
Thermal analysis of combinatorial solid geometry models using SINDA
Algorithms have been developed using Monte Carlo techniques to determine the thermal network parameters necessary to perform a finite difference analysis on Combinatorial Solid Geometry (CSG) models. Orbital and laser fluxes as well as internal heat generation are modeled to facilitate satellite modeling. The results of the thermal calculations are used to model the infrared (IR) images of targets and assess target vulnerability. Sample analyses and validation are presented which demonstrate code products.
Gerencser, Diane↗
Solar Proton Transport Within an ICRU Sphere Surrounded by a Complex Shield: Ray-trace Geometry
A computationally efficient 3DHZETRN code with enhanced neutron and light ion (Z is less than or equal to 2) propagation was recently developed for complex, inhomogeneous shield geometry described by combinatorial objects. Comparisons were made between 3DHZETRN results and Monte Carlo (MC) simulations at locations within the combinatorial geometry, and it was shown that 3DHZETRN agrees with the MC codes to the extent they agree with each other. In the present report, the 3DHZETRN code is extended to enable analysis in ray-trace geometry. This latest extension enables the code to be used within current engineering design practices utilizing fully detailed vehicle and habitat geometries. Through convergence testing, it is shown that fidelity in an actual shield geometry can be maintained in the discrete ray-trace description by systematically increasing the number of discrete rays used. It is also shown that this fidelity is carried into transport procedures and resulting exposure quantities without sacrificing computational efficiency.
Slaba, Tony C.↗
Passive MMW camera for low visibility landings
A passive, millimeter wave imaging sensor for aircraft landing in low or poor visibility conditions is described. The sensor can be incorporated in a camera for future enhanced/synthetic vision systems. Contrast is provided by differences in material reflectivities, temperature, and sky illumination of the scene being imaged. Photographic images of the system's fog penetration capabilities are presented. A combinatorial geometry technique is used to construct the scene geometries. This technique uses eight basic geometric shapes which are used as building blocks for 3-D complex-shaped objects. The building blocks are then combined via union, intersection and exclusion operations to form 3-D scene objects and the combinatorial geometry package determines ray intercepts with scene objects, providing the specific surfaces and propagation distance for the scene.
Shoucri, Merit↗
Update On the Status of the FLUKA Monte Carlo Transport Code*
The FLUKA Monte Carlo transport code is a well-known simulation tool in High Energy Physics. FLUKA is a dynamic tool in the sense that it is being continually updated and improved by the authors. We review the progress achieved since the last CHEP Conference on the physics models, some technical improvements to the code and some recent applications. From the point of view of the physics, improvements have been made with the extension of PEANUT to higher energies for p, n, pi, pbar/nbar and for nbars down to the lowest energies, the addition of the online capability to evolve radioactive products and get subsequent dose rates, upgrading of the treatment of EM interactions with the elimination of the need to separately prepare preprocessed files. A new coherent photon scattering model, an updated treatment of the photo-electric effect, an improved pair production model, new photon cross sections from the LLNL Cullen database have been implemented. In the field of nucleus-- nucleus interactions the electromagnetic dissociation of heavy ions has been added along with the extension of the interaction models for some nuclide pairs to energies below 100 MeV/A using the BME approach, as well as the development of an improved QMD model for intermediate energies. Both DPMJET 2.53 and 3 remain available along with rQMD 2.4 for heavy ion interactions above 100 MeV/A. Technical improvements include the ability to use parentheses in setting up the combinatorial geometry, the introduction of pre-processor directives in the input stream. a new random number generator with full 64 bit randomness, new routines for mathematical special functions (adapted from SLATEC). Finally, work is progressing on the deployment of a user-friendly GUI input interface as well as a CAD-like geometry creation and visualization tool. On the application front, FLUKA has been used to extensively evaluate the potential space radiation effects on astronauts for future deep space missions, the activation dose for beam target areas, dose calculations for radiation therapy as well as being adapted for use in the simulation of events in the ALICE detector at the LHC.
Ferrari, A.↗
A Dose of Reality: Radiation Analysis for Realistic Human Spacecraft
INTRODUCTION As with most computational analyses, a tradeoff exists between problem complexity, resource availability and response accuracy when modeling radiation transport from the source to a detector. The largest amount of analyst time for setting up an analysis is often spent ensuring that any simplifications made have minimal impact on the results. The vehicle shield geometry of interest is typically simplified from the original CAD design in order to reduce computation time, but this simplification requires the analyst to "re-draw" the geometry with a limited set of volumes in order to accommodate a specific radiation transport software package. The resulting low-fidelity geometry model cannot be shared with or compared to other radiation transport software packages, and the process can be error prone with increased model complexity. The work presented here demonstrates the use of the DAGMC (Direct Accelerated Geometry for Monte Carlo) Toolkit from the University of Wisconsin, to model the impacts of several space radiation sources on a CAD drawing of the US Lab module. METHODS The DAGMC toolkit workflow begins with the export of an existing CAD geometry from the native CAD to the ACIS format. The ACIS format file is then cleaned using SpaceClaim to remove small holes and component overlaps. Metadata is then assigned to the cleaned geometry file using CUBIT/Trelis from csimsoft (Registered Trademark). The DAGMC plugin script removes duplicate shared surfaces, facets the geometry to a specified tolerance, and ensures that the faceted geometry is water tight. This step also writes the material and scoring information to a standard input file format that the analyst can alter as desired prior to running the radiation transport program. The scoring results can be transformed, via python script, into a 3D format that is viewable in a standard graphics program. RESULTS The CAD model of the US Lab module of the International Space Station, inclusive of all the racks and components, was simplified to remove holes and volume overlaps. Problematic features within the drawing were also removed or repaired to prevent runtime issues. The cleaned drawing was then run through the DAGMC workflow to prepare for analysis. Pilot tests modeling transport of 1GeV proton and 800MeV/A oxygen sources show that reasonable results are converged upon in an acceptable amount of overall computation time from drawing preparation to data analysis. The FLUKA radiation transport code will next be used to model both a GCR and a trapped radiation source. These results will then be compared with measurements that have been made by the radiation instrumentation deployed inside the US Lab module. DISCUSSION Early analyses have indicated that the DAGMC workflow is a promising toolkit for running vehicle geometries of interest to NASA through multiple radiation transport codes. In addition, recent work has shown that a realistic human phantom, provided via a subcontract with the University of Florida, can be placed inside any vehicle geometry for a combinatorial analysis. This added functionality gives the user the ability to score various parameters at the organ level, and the results can then be used as input for cancer risk models.
Barzilla, J. E.↗
The Topology of Symmetric Tensor Fields
Combinatorial topology, also known as "rubber sheet geometry", has extensive applications in geometry and analysis, many of which result from connections with the theory of differential equations. A link between topology and differential equations is vector fields. Recent developments in scientific visualization have shown that vector fields also play an important role in the analysis of second-order tensor fields. A second-order tensor field can be transformed into its eigensystem, namely, eigenvalues and their associated eigenvectors without loss of information content. Eigenvectors behave in a similar fashion to ordinary vectors with even simpler topological structures due to their sign indeterminacy. Incorporating information about eigenvectors and eigenvalues in a display technique known as hyperstreamlines reveals the structure of a tensor field. The simplify and often complex tensor field and to capture its important features, the tensor is decomposed into an isotopic tensor and a deviator. A tensor field and its deviator share the same set of eigenvectors, and therefore they have a similar topological structure. A a deviator determines the properties of a tensor field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of tensor fields. In 2-D tensor fields, there are only two types of degenerate points; while in 3-D, the degenerate points can be characterized in a Q'-R' plane. Compressible and incompressible flows share similar topological feature due to the similarity of their deviators. In the case of the deformation tensor, the singularities of its deviator represent the area of vortex core in the field. In turbulent flows, the similarities and differences of the topology of the deformation and the Reynolds stress tensors reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions.
Levin, Yingmei↗
Implementation of Combinatorial Optimization Techniques for Automated Fiber Placement Through Thickness Defect Stack-Up Minimization
The Computer Aided Process Planning (CAPP) module was developed to facilitate and accelerate the process planning workflow for Automated Fiber Placement (AFP). CAPP assists process planners in identifying optimal starting point locations and layup strategies for each ply of a laminate. Ply optimization operates on measurement and scoring of geometry-based defects such as gaps, overlaps, angle deviation, and steering. This paper expands on the established framework for analyzing defect stack-up through thickness of a laminate. Four different combinatorial optimization algorithms are implemented and evaluated: (1) genetic algorithm, (2) differential evolution, (3) particle swarm, and (4) greedy search. The algorithms identify the optimal combination of ply-level layup strategies, by scoring potential laminates on defect stacking, using two different objective functions. A final optimization approach is also presented which trades some performance for a large gain in efficiency. These approaches are compared to a randomized combination using a complex tool surface in a virtual case study. The result is a streamlined methodology for comparing different laminate-level manufacturing strategies and minimizing the through thickness defect stack up.
CAPP↗
Introducing Tropical Geometric Approaches to Delay Tolerant Networking Optimization
Delay Tolerant Networking (DTN) is the standard approach to the networking of space systems with the goal of supporting the Solar System Internet (SSI). Current space networks have a small scale and often depend on rigorously scheduled (pre-determined) contact opportunities; this manual approach inhibits scalability. The goal of this paper is to recast these scheduling problems in order to apply the optimization machinery of tropical geometry. Contact opportunities in space are dependent on such factors as orbital mechanics and asset availability, which induce time-varying connectivity; indeed, end-to-end connectivity might never occur. Routing optimization within this structure is classically difficult and typically utilizes Dijkstra's algorithm as applied to contact graphs. Alternatively, we follow the successes of tropical geometry in train schedule optimization, job assignments, and even traditional networking, by extending this approach to this more general (i.e. disconnected) problem space. These successes imply tropical geometry provides a useful framework in the context of DTNs, starting with applications to queuing theory and long-haul links. Recently, tropical geometry has been applied to parametric path optimization on graphs with variable edge weights. In this work, we extend these advances to account for the problem of routing in a space network, and find that tropical geometry is well-suited to the challenges offered by this new setting, including contact schedules featuring probabilities. Our approach leverages the combinatorial nature of the problem to give feasible shortest path trees in the presence of variable channel conditions and latency, evolving topologies, and uncertainty inherent in space routing. We discuss our tropical approach to DTN for two Python implementations, a Verilog Tropical ALU implementation, tropical frameworks for other parametric graph problems, and solution stability. Lastly, a program for future work is included to illuminate the path ahead.
Delay Tolerant Networking↗
Combinatorial communications - The target lemma
Target lemma in combinatorial communications - proof of geometric property of multivariate Gaussian distribution
TELECOMMUNICATION↗
ACES M and S: Unmitigated Factorial Encounter Study on DAA/TCAS Interoperability
Realization of the expected proliferation of Unmanned Aircraft System (UAS) operations in the National Airspace System (NAS) depends on the development and validation of standards for UAS Detect and Avoid (DAA) Systems. The RTCA Special Committee 228 is charged with leading the development of draft Minimum Operational Performance Standards (MOPS) for UAS DAA Systems. NASA, as a participating member of RTCA SC-228 is committed to supporting the development and validation of draft requirements for DAA alerting and guidance systems. This presentation contains the results of two combinatorial encounter analysis studies using NASA's SAA Control fast-time simulation capability for this purpose. In these studies, encounters between two aircraft were simulated one at a time for the full factorial combination of encounter geometries (e.g., encounter angle, CPA offset) and aircraft performance (e.g., ownership and intruder ground speeds and vertical rates). The first study analyzes the relationships (e.g., timeline) between the different alerting-safety regions in the SC-228 MOPS (in order of increasing severity): 1) DAA warning alert, 2) well clear recovery (WCR) guidance, 3) DAA-Collision Avoidance (CA), and 4) TCAS RA. This study will focus primarily on encounter situations in which TCAS RA occurs prior to any of the other alerting-safety boundaries. In particular, this study will investigate whether using vertical distance or vertical distance at closest point of approach (i.e., vertical miss distance or VMD) is more appropriate for the definition of the DAA-CA region. In addition, cases where transitions between different regions skip an intermediate region will be analyzed. The second study in this presentation explores a proposal to use an altitude rate error threshold to determine if vertical maneuvers are acceptable for DAA WCR guidance against non-cooperative intruders. This study incorporates the radar from the Honeywell sensor model and examines a series of pairwise encounters between a non-cooperative intruder and a UAS ownship, with different combinations of intruder states and ownship performance levels. The study uses SAA Control as a simulation platform and pilot model, and Omnibands to provide DWC recovery guidance. Two simulation sets, one that allows vertical DWC recovery guidance and one that does not, are compared to determine if encounters with altitude rate errors above 250 feet-per-minute are more likely to have more severe losses of well clear, as determined by the Loss of Well-Clear Severity metric.
SaaControl↗
Initial Results of Heuristic Guided Orbit Selection for a Low Frequency Radio Interferometric Spacecraft Constellation
A constellation of radio telescope spacecraft can leverage interferometry to accurately image distant objects throughout the universe, but mission design must balance among many interrelated constraints. In particular, the number of craft and the selection of time-varying orbital parameters play a pivotal role in determining what interferometric baselines are feasible with respect to different targets, and thus drives the breadth and quality of data available to the constellation. The large combinatorial orbit configuration space and competing concerns present a challenging problem that is not well addressed by traditional mission design processes. This paper describes application of automated optimization methods to help direct mission design effort to the most promising dynamic constellation geometries: those that achieve broad interferometric coverage but remain cost-effective and resilient to failures. Several automatic heuristic-driven optimization algorithms representing complementary search strategies were created to explore among concrete constellation configuration plans. Evaluation of each candidate constellation plan was accelerated by efficiently combining precomputed caches of orbital and interferometric data. Results indicate that leveraging automated optimization for constellation mission design is both practical and illuminating: generated solutions provided both evidence for existing design intuitions as well as fresh insights into novel configurations.
Hernandez, Sonia↗
A Method for Aircraft Concept Selection Using Multicriteria Interactive Genetic Algorithms
The problem of aircraft concept selection has become increasingly difficult in recent years as a result of a change from performance as the primary evaluation criteria of aircraft concepts to the current situation in which environmental effects, economics, and aesthetics must also be evaluated and considered in the earliest stages of the decision-making process. This has prompted a shift from design using historical data regression techniques for metric prediction to the use of physics-based analysis tools that are capable of analyzing designs outside of the historical database. The use of optimization methods with these physics-based tools, however, has proven difficult because of the tendency of optimizers to exploit assumptions present in the models and drive the design towards a solution which, while promising to the computer, may be infeasible due to factors not considered by the computer codes. In addition to this difficulty, the number of discrete options available at this stage may be unmanageable due to the combinatorial nature of the concept selection problem, leading the analyst to arbitrarily choose a sub-optimum baseline vehicle. These concept decisions such as the type of control surface scheme to use, though extremely important, are frequently made without sufficient understanding of their impact on the important system metrics because of a lack of computational resources or analysis tools. This paper describes a hybrid subjective/quantitative optimization method and its application to the concept selection of a Small Supersonic Transport. The method uses Genetic Algorithms to operate on a population of designs and promote improvement by varying more than sixty parameters governing the vehicle geometry, mission, and requirements. In addition to using computer codes for evaluation of quantitative criteria such as gross weight, expert input is also considered to account for criteria such as aeroelasticity or manufacturability which may be impossible or too computationally expensive to consider explicitly in the analysis. Results indicate that concepts resulting from the use of this method represent designs which are promising to both the computer and the analyst, and that a mapping between concepts and requirements that would not otherwise be apparent is revealed.
Buonanno, Michael↗
Automated Fiber Placement Through Thickness Defect Stacking Optimization
In its 2022 commercial market outlook, Boeing forecasted an 80% increase in the global fleet through 2041 compared to 2019 pre-pandemic levels. This sharp rise in demand will drive pressure onto airframe manufacturers to ramp up production and find more efficient ways to design and manufacture airplanes. Complicating this challenge is the industry’s recent transformation from traditional metal-based airframes towards hybrid composite-metal aircraft. While composites have been used in aviation for decades, aircraft manufacturers are still struggling to design and manufacture quality parts at a high rate. Automated Fiber Placement (AFP) is one of the main manufacturing techniques used to produce large-scale composite parts. After a design has been created, a manufacturing strategy has to be developed based on the working material, part geometry, and machine capabilities. This process planning stage is essential to the AFP workflow and currently requires a high level of manual input from an experienced process planner. In an effort to automate and optimize this stage, the Computer Aided Process Planning (CAPP) module was developed. CAPP assists process planners in identifying optimal starting point location and layup strategy for each ply of a laminate. This Ply-Level Optimization (PLO) phase operates on the quantification of ply quality through predictable geometry-based defects such as gaps, overlaps, angle deviation, and steering. As you move from PLO to Laminate-Level Optimization (LLO) the design space grows exponentially, emphasizing the need for automated optimization. The work presented in this thesis expands CAPP’s functionality by comparing the planned fiber paths through the thickness of the laminate to mitigate stacked area defects and achieve an optimal laminate-level manufacturing strategy. Within CAPP, predicted gap and overlap defects are imported from Vericut Composites Programming (VCP) and then discretized to streamline the through-thickness comparison. Two objective functions are used to score different combinations of ply layup strategies based on defect stacking both globally and locally. Four combinatorial optimization algorithms were coupled with these objective functions to investigate the laminate-level manufacturing strategy design space and converge on the optimal plan. These algorithms were evaluated based on accuracy and efficiency through virtual testing on a complex tool surface. A separate LLO approach was developed to achieve near-optimal laminates in significantly less time. The end result is a software package which greatly reduces the required input from process planners, shortening the design-build cycle time and improving part quality.
AFP↗
Runway Configuration Management with Offline Reinforcement Learning
Runway configuration management (RCM) is a challenging task, and it affects the efficiency of the National Airspace System (NAS) and airport surface operations significantly. Each airport, depending on the geometry, capacity, local climate patterns, etc. has multiple configurations for the runway usage for arriving and departing flights. Many factors such as the incoming/outgoing traffic load, wind direction and speed, convective weather, cloud ceiling and other environmental factors might affect the choice of a runway configuration at any point in time. However, other factors such as safety measures and regulations, noise abatement, capacity of each configuration, and preference of the air traffic controllers (ATCs) can also play a significant role in selecting the configuration. A sub-optimal selection of the runway configuration, or delay in making configuration changes might result in significant increase in taxi times for aircraft on the surface of the airport, fuel and energy use of the aircraft, and maintenance costs. It can also lead to safety concerns, such as an aircraft performing one or more go-arounds before being able to land. All these factors make RCM an extremely important and challenging decision-making process for the ATCs. The current state of practice sets the runway configuration by the ATCs based on relevant information available at the time including weather, traffic, noise abatement, safety bounds, etc. This makes the decision-making process subjective based on the accuracy of the available information and the bias in human decision making. Unfortunately, this approach yields poor results (e.g., significant delays) if the predicted outcomes are uncertain and their relative impact is not well understood. This is especially evident when the uncertainty increases the size of possible predicted outcomes (combinatorial explosion in possible scenarios) that cannot be handled by human reasoning. On the other hand, an automated approach based on machine intelligence can make use of historical data and search through all (or significant amount of) possible scenarios under uncertainty and make well-informed decisions.
Milad Memarzadeh↗