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Optimal transfer trajectories from earth parking orbit to various terminal conic constraints, and ROBOT computer program modifications
The nonlinear programming (NLP) problem to solve distribution-level optimal power flow (D-OPF) poses convergence issues and does not scale well for unbalanced distribution systems. The existing scalable D-OPF algorithms either use approximations that are not valid for an unbalanced power distribution system, or apply relaxation techniques to the nonlinear power flow equations that do not guarantee a feasible power flow solution. In this paper, we propose scalable D-OPF algorithms that simultaneously achieve optimal and feasible solutions by solving multiple iterations of approximate, or relaxed, D-OPF subproblems of low complexity. The first algorithm is based on a successive linear approximation of the nonlinear power flow equations around the current operating point, where the D-OPF solution is obtained by solving multiple iterations of a linear programming (LP) problem. The second algorithm is based on the relaxation of the nonlinear power flow equations as conic constraints together with directional constraints, which achieves optimal and feasible solutions over multiple iterations of a second-order cone programming (SOCP) problem. Finally, it is demonstrated that the proposed algorithms are able to reach an optimal and feasible solution while significantly reducing the computation time as compared to an equivalent NLPD-OPF model for the same distribution system.
In this paper, we consider a distributionally robust partially observable Markov decision process (DR-POMDP), where the distribution of the transition-observation probabilities is unknown at the beginning of each decision period, but their realizations can be inferred using side information at the end of each period after an action being taken. We build an ambiguity set of the joint distribution using bounded moments via conic constraints and seek an optimal policy to maximize the worst-case (minimum) reward for any distribution in the set. We show that the value function of DR-POMDP is piecewise linear convex with respect to the belief state and propose a heuristic search value iteration method for obtaining lower and upper bounds of the value function. We conduct numerical studies and demonstrate the computational performance of our approach via testing instances of a dynamic epidemic control problem. Our results show that DR-POMDP can produce more robust policies under misspecified distributions of transition-observation probabilities as compared to POMDP but has less costly solutions than robust POMDP. The DR-POMDP policies are also insensitive to varying parameter in the ambiguity set and to noise added to the true transition-observation probability values obtained at the end of each decision period.
Edge constraint effect on buckling of sandwich and ring stiffened conical shells under external pressure
Experimental and analytical investigations of the vibratory behavior of ring-stiffened truncated-cone shells are described. Vibration tests were conducted on 60 deg conical shells having up to four ring stiffeners and for free-free and clamped-free edge constraints and 9 deg conical shells, for two thicknesses, each with two angle rings and for free-free, free-clamped, and clamped-clamped edge constraints. The analytical method is based on linear thin shell theory, employing the Rayleigh-Ritz method. Discrete rings are represented as composed of one or more segments, each of which is a short truncated-cone shell of uniform thickness. Equations of constraint are used to join a ring and shell along a circumferential line connection. Excellent agreement was obtained for comparisons of experimental and calculated frequencies.
Here, this paper studies two-stage distributionally robust conic linear programming under constraint uncertainty over type-1 Wasserstein balls. We present optimality conditions for the dual of the worst-case expectation problem, which characterizes worst-case uncertain parameters for its inner maximization problem. This condition offers an alternative proof, a counterexample, and an extension to previous works. Additionally, the condition highlights the potential advantage of a specific distance metric for out-of-sample performance, as exemplified in a numerical study on a facility location problem with demand uncertainty. Furthermore, cutting-plane-based algorithms, equipped with a unified scenario generation framework, are proposed for addressing both unbounded support and second-stage dual feasible regions, with a finite convergence proof under less stringent assumptions.
The M51 system (NGC 5194/5195) provides an excellent problem both in spiral structure and in galaxy interactions. The authors present an analytic study of a computer experiment on the excitation mechanisms for M51's spiral arms and whether or not a halo is important for these mechanisms. This work extends previous numerical studies of the M51 system by including self-gravitation in a two component disk: gas and stars, and a dark halo. The analytic study provides two new observational constraints: the time (approx. 70 to 84 million years ago) and position angle of perigalacticon (300 degrees). By using these constraints and a simple conic approximation, the search for the companion's possible orbit is greatly simplified. This requires fewer N-body simulations than a fully self-gravitating orbit search.
A computer program calculates a best conic fit of a given spacecraft trajectory. Spacecraft trajectories are often propagated as conics onboard. The conic-section parameters as a result of the best-conic-fit are uplinked to computers aboard the spacecraft for use in updating predictions of the spacecraft trajectory for operational purposes. In the initial application for which this program was written, there is a requirement to fit a single conic section (necessitated by onboard memory constraints) accurate within 200 microradians to a sequence of positions measured over a 4.7-hour interval. The present program supplants a prior one that could not cover the interval with fewer than four successive conic sections. The present program is based on formulating the best-fit conic problem as a parameter-optimization problem and solving the problem numerically, on the ground, by use of a modified steepest-descent algorithm. For the purpose of this algorithm, optimization is defined as minimization of the maximum directional propagation error across the fit interval. In the specific initial application, the program generates a single 4.7-hour conic, the directional propagation of which is accurate to within 34 microradians easily exceeding the mission constraints by a wide margin.
Buckling strength of truncated conical shell at uniform external pressure on small edge
This paper discusses theoretical foundations of quantitative image-based measurements for extracting and reconstructing geometric, kinematic and dynamic properties of observed objects. New results are obtained by using a combination of methods in perspective geometry, differential geometry. radiometry, kinematics and dynamics. Specific topics include perspective projection transformation. perspective developable conical surface, perspective projection under surface constraint, perspective invariants, the point correspondence problem. motion fields of curves and surfaces. and motion equations of image intensity. The methods given in this paper arc useful for determining morphology and motion fields of deformable bodies such as elastic bodies. viscoelastic mediums and fluids.
The trajectory design process for the Galilean satellite probe, expected to be launched in January 1982, is examined and its interplanetary path, emphasizing arrival dates and the Mars flyby, is presented. The Galileo spacecraft is of dual spin design, combining features of Pioneer, a spinning craft, and Voyager which was 3-axis stabilized. The design of the initial orbit from Orbiter deflection through Jupiter to the beginning of the satellite tour is discussed as well as the use of an Io gravity assist flyby to achieve Jupiter orbit insertion, and the effects of solar perturbation on the initial orbit. Detail is given to the entire satellite tour trajectory design process, starting from the requirements and constraints placed on the tour through the conic design to the final numerically integrated trajectories.
Designing interplanetary missions is an iterative process, with a tight coupling between mission analysis and vehicle design. The ability to simultaneously process both analyses early on can provide significant benefits in both the concept formulation and in overall mission feasibility. To implement such a simultaneous analysis process, there is a need to model interplanetary trajectories rapidly while maintaining an acceptable level of fidelity. Many simple patched conics tools make too many assumptions to satisfactorily address all relevant constraints and objectives, while full-fidelity trajectory design tools often require more time and expertise than is available in early conceptual studies. Hence, some form of middle-ground modeling tool would provide value. This paper introduces the development of such a tool using Python. This tool, Keplerian Analysis for Versatile Evaluation of Arbitrary Trajectories (KAVEAT), implements a patched conics method that enforces continuity of state (time, mass, position, velocity) through all transitions between various spheres of influence on the trajectory. The trajectory is constructed in an object-oriented manner, dynamically assembling unique maneuvers such as departure burns, heliocentric transfers (ballistic or with electric propulsion), and planetary flybys (powered or unpowered). Each maneuver has its own specific set of basic inputs needed to define it. The tool then takes these defined maneuvers, strings them together creating all the interdependencies required, and solves for the ideal trajectory using a gradient-based optimizer.
The NASA High-Altitude Imaging Wind and Rain Airborne Profiler (HIWRAP) is a solid-state transmitter-based, dual-frequency (Ka- and Ku-band), dual-beam (30 degree and 40 degree incidence angle), conical scan Doppler radar system, designed for operation on the NASA high-altitude (20 km) aircrafts, such as the Global Hawk Unmanned Aerial System (UAS). Supported by the NASA Instrument Incubator Program (IIP), HIWRAP was developed to provide high spatial and temporal resolution 3D wind and reflectivity data for the research of tropical cyclone and severe storms. With the simultaneous measurements at both Ku- and Ka-band two different incidence angles, HIWRAP is capable of imaging Doppler winds and volume backscattering from clouds and precipitation associated with tropical storms. In addition, HIWRAP is able to obtain ocean surface backscatter measurements for surface wind retrieval using an approach similar to QuikScat. There are three key technology advances for HIWRAP. Firstly, a compact dual-frequency, dual-beam conical scan antenna system was designed to fit the tight size and weight constraints of the aircraft platform. Secondly, The use of solid state transmitters along with a novel transmit waveform and pulse compression scheme has resulted in a system with improved performance to size, weight, and power ratios compared to typical tube based Doppler radars currently in use for clouds and precipitation measurements. Tube based radars require high voltage power supply and pressurization of the transmitter and radar front end that complicates system design and implementation. Solid state technology also significantly improves system reliability. Finally, HIWRAP technology advances also include the development of a high-speed digital receiver and processor to handle the complex receiving pulse sequences and high data rates resulting from multi receiver channels and conical scanning. This paper describes HIWRAP technology development for dual-frequency operation at high-altitudes using low peak power transmitters and pulse compression. The hardware will be described along with the methods and concepts for the system design. Finally, we will present recent preliminary results from flights on the NASA Global Hawk in support of the NASA Genesis and Rapid Intensification Processes (GRIP) field campaign, and on the NASA ER-2 as fixed nadir pointing mode for the NASA Global Precipitation Measurement (GPM) ground validation (GV) mission - Midlatitude Continental Convective Cloud Experiment (MC3E)
Reflector antenna of the parabolic type offers complete control of its aperature illumination function. The antennas beam width can be changed easily by excitation of various amounts of the line-source feed. The conical reflector collimates a beam when the feed complies with certain geometric constraints.
The buckling of a truncated elastic conical shell subjected to an axial compression is a classical problem in shell structures. The paper reinvestigates the buckling of an axially compressed truncated conical shell with rigid bulkheads. Two improvements are achieved. First, the condition that the total horizontal displacement must vanish due to rigid bulkhead and axisymmetry is treated as a constraint. This constraint is incorporated into the system through the use of the Lagrange multiplier; then the variational method is used to derive a complete set of boundary conditions for conical shells. Second, the stability is evaluated in the deformed state using the asymptotic solutions of the pair of Donnell-type equations for axisymmetric configuration. The results indicate that the buckling strength of conical shells depends mainly on the condition of the smaller end. In addition to the vertex angle, the distance ratio plays, at least, an equally important role.
The Global Precipitation Measurement (GPM) Mission is an international satellite mission specifically designed to unify and advance precipitation measurements from a constellation of research and operational microwave sensors. The cornerstone of the GPM mission is the deployment of a Core Observatory in a 65 deg non-Sun-synchronous orbit to serve as a physics observatory and a transfer standard for inter-calibration of constellation radiometers. The GPM Core Observatory will carry a Ku/Ka-band Dual-frequency Precipitation Radar (DPR) and a conical-scanning multi-channel (10-183 GHz) GPM Microwave Radiometer (GMI). The first space-borne dual-frequency radar will provide not only measurements of 3-D precipitation structures but also quantitative information on microphysical properties of precipitating particles needed for improving precipitation retrievals from passive microwave sensors. The combined use of DPR and GMI measurements will place greater constraints on radiometer retrievals to improve the accuracy and consistency of precipitation estimates from all constellation radiometers. The GPM constellation is envisioned to comprise five or more conical-scanning microwave radiometers and four or more cross-track microwave sounders on operational satellites. NASA and the Japan Aerospace Exploration Agency (JAXA) plan to launch the GPM Core in July 2013. NASA will provide a second radiometer to be flown on a partner-provided GPM Low-Inclination Observatory (L10) to improve near real-time monitoring of hurricanes and mid-latitude storms. NASA and the Brazilian Space Program (AEB/IPNE) are currently engaged in a one-year study on potential L10 partnership. JAXA will contribute to GPM data from the Global Change Observation Mission-Water (GCOM-W) satellite. Additional partnerships are under development to include microwave radiometers on the French-Indian Megha-Tropiques satellite and U.S. Defense Meteorological Satellite Program (DMSP) satellites, as well as cross-track scanning humidity sounders on operational satellites such as the National Polar-orbiting Operational Environmental Satellite System (NPOESS) Preparatory Project (NPP), POES, the NASA/NOAA Joint Polar Satellite System (JPSS), and EUMETSAT MetOp satellites. Data from Chinese and Russian microwave radiometers may also become available through international collaboration under the auspices of the Committee on Earth Observation Satellites (CEOS) and Group on Earth Observations (GEO). The current generation of global rainfall products combines observations from a network of uncoordinated satellite missions using a variety of merging techniques. Relative to current data products, GPM's "nextgeneration" precipitation products will be characterized by: (1) more accurate instantaneous precipitation estimate (especially for light rain and cold-season solid precipitation), (2) more frequent sampling by an expanded constellation of microwave radiometers including operational humidity sounders over land, (3) intercalibrated microwave brightness temperatures from constellation radiometers within a unified framework, and (4) physical-based precipitation retrievals from constellation radiometers using a common a priori hydrometeor database constrained by combined radar/radiometer measurements provided by the GPM Core Observatory. An overview of the GPM mission concept, the U.S. GPM program status and updates on international science collaborations on GPM will be presented.
For a hypersonic vehicle, propelled by scramjet engines, integration of the engines and airframe is highly desirable. Thus, the forward capture shape of the engine inlet should conform to the vehicle body shape. Furthermore, the use of modular engines places a constraint on the shape of the inlet sidewalls. Finally, one may desire a combustor cross- section shape that is different from that of the inlet. These shape constraints for the inlet can be accommodated by employing a streamline-tracing and lofting technique. This design technique was developed by Smart for inlets with a rectangular-to-elliptical shape transition. In this paper, we generalise that technique to produce inlets that conform to arbitrary shape requirements. As an example, we show the design of a body-integrated hypersonic inlet on a winged-cone vehicle, typical of what might be used in a three-stage orbital launch system. The special challenge of inlet design for this conical vehicle at an angle-of-attack is also discussed. That challenge is that the bow shock sits relatively close to the vehicle body.
The International Solar Polar Mission is sponsored jointly by NASA and the European Space Agency to study the sun and the solar environment from a new vantage point. Trajectories far out of the ecliptic plane are achieved by a gravity assist from Jupiter which sends the spacecraft back over the poles of the sun. The process for optimizing these trajectories is described. From the point of view of trajectory design, performance is measured by the time spent at high heliographic latitudes, but many trajectory constraints must be met to ensure spacecraft integrity and good scientific return. The design problem is tractable by closely approximating integrated trajectories with specially calibrated conics. Then the optimum trajectory is found primarily by graphical methods, which were easy to develop and use and are highly adaptable to changes in the plan of the mission.