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At least 1,477 records · Page 82

Minimal Time Problem with Impulsive Controls

Time optimal control problems for systems with impulsive controls are investigated. Sufficient conditions for the existence of time optimal controls are given. A dynamical programming principle is derived and Lipschitz continuity of an appropriately defined value functional is established. The value functional satisfies a Hamilton–Jacobi–Bellman equation in the viscosity sense. A numerical example for a rider-swing system is presented and it is shown that the reachable set is enlargered by allowing for impulsive controls, when compared to nonimpulsive controls.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Techniques Optimized for Reducing Instabilities in Advanced Nickel-Base Superalloys for Turbine Blades

The High-Speed Research (HSR) Airfoil Alloy program developed fourth-generation single-crystal superalloys with up to an 85 F increase in creep rupture capability over current production airfoil alloys. Recent results have been generated at the NASA Glenn Research Center on these fourth-generation alloys, but in coated form, for subsonic turbine blade applications under NASA's Ultra-Efficient Engine Technology (UEET) Program. One goal for UEET is to optimize the airfoil alloy/thermal barrier coating system for 3100 F turbine inlet temperatures. The state-of-the art turbine blade airfoil system consists of a superalloy single crystal that provides the basic mechanical performance of the airfoil. A thermal barrier coating is used to reduce the temperature of the base superalloy, and a bondcoat is deposited between the base material and the thermal barrier coating. The bondcoat improves the oxidation and corrosion resistance of the base superalloy and improves the spallation resistance of the thermal barrier coating. A commercial platinum aluminide bondcoat was applied to the HSR-developed alloys, and a diffusion zone developed as a result of interaction between the bondcoat and the superalloy. Optimized strength is obtained for superalloys when the refractory element content is high and the limits of microstructural stability are approached or exceeded slightly. For fourthgeneration alloys, instability leads to the formation of topologically close packed (TCP) phases, which form internally in the superalloy, and a secondary reaction zone (SRZ), which forms under the diffusion zone. There was a concern that excessive quantities of either TCP or SRZ might decrease the mechanical properties of the superalloy, with SRZ thought to be particularly detrimental and its formation unpredictable. Thus, an SRZreduction effort was initiated in the NASA UEET Program so that methods developed during the HSR project could be optimized further to reduce or eliminate the SRZ. An SRZ is a three-phase constituent composed of TCP and stringers of gamma phase in a matrix of gamma prime. An incoherent grain boundary separates the SRZ from the gammagamma prime microstructure of the superalloy. The SRZ is believed to form as a result of local chemistry changes in the superalloy due to the application of the diffusion aluminide bondcoat. Locally high surface stresses also appear to promote the formation of the SRZ. Thus, techniques that change the local alloy chemistry or reduce surface stresses have been examined for their effectiveness in reducing SRZ. These SRZ-reduction steps are performed on the test specimen or the turbine blade before the bondcoat is applied. Stressrelief heat treatments developed at NASA Glenn have been demonstrated to reduce significantly the amount of SRZ that develops during subsequent high-temperature exposures. Stress-relief heat treatments reduce surface stresses by recrystallizing a thin surface layer of the superalloy. However, in alloys with very high propensities to form SRZ, stress relief heat treatments alone do not eliminate SRZ entirely. Thus, techniques that modify the local chemistry under the bondcoat have been emphasized and optimized successfully at Glenn. One such technique is carburization, which changes the local chemistry by forming submicron carbides near the surface of the superalloy. Detailed characterizations have demonstrated that the depth and uniform distribution of these carbides are enhanced when a stress relief treatment and an appropriate surface preparation are employed in advance of the carburization treatment. Even in alloys that have the propensity to develop a continuous SRZ layer beneath the diffusion zone, the SRZ has been completely eliminated or reduced to low, manageable levels when this combination of techniques is utilized. Now that the techniques to mitigate SRZ have been established at Glenn, TCP phase formation is being emphasized in ongoing work under the UEET Program. The limitsf stability of the fourth-generation alloys with respect to TCP phase formation are currently being defined along with high-temperature creep rupture properties. In addition, a regression model is being developed at Glenn for the prediction of the presence of TCP phase in the microstructure and SRZ under the diffusion zone. The model is based on a design-of-experiments methodology with emphasis on the potential synergistic effects of alloying elements.

MacKay, Rebecca A.↗

Optimization methods applied to the aerodynamic design of helicopter rotor blades

This paper describes a formal optimization procedure for helicopter rotor blade designs which minimizes hover horsepower while assuring satisfactory forward flight performance. The approach is to couple hover and forward flight analysis programs with a general purpose optimization procedure. The resulting optimization system provides a systematic evaluation of the rotor blade design variables and their interaction, thus reducing the time and cost of designing advanced rotor blades. The paper discusses the basis for and details of the overall procedure, describes the generation of advanced blade designs for representative Army helicopters, and compares designs and design effort with those from the conventional approach which is based on parametric studies and extensive cross-plots.

Walsh, J. L.↗

Interior Point Algorithms for Optimization Problems (Final Technical Report)

Over the period of this award we developed an algorithmic framework for constraint reduction in linear programming (LP) and convex quadratic programming (QP), proved convergence of our algorithms, and applied them to a variety of applications, including entropy-based moment closure in gas dynamics.

97 MATHEMATICS AND COMPUTING↗

An analytic model for footprint dispersions and its application to mission design

This is the final report on our recent research activities that are complementary to those conducted by our colleagues, Professor Farrokh Mistree and students, in the context of the Taguchi method. We have studied the mathematical model that forms the basis of the Simulation and Optimization of Rocket Trajectories (SORT) program and developed an analytic method for determining mission reliability with a reduced number of flight simulations. This method can be incorporated in a design algorithm to mathematically optimize different performance measures of a mission, thus leading to a robust and easy-to-use methodology for mission planning and design.

Rao, J. R. Jagannatha↗

Rooftop Unit Replacement: Target's Rooftop Unit Replacement Program

This case study describes how Target developed an optimized, re-engineered process that integrates several energy-efficiency measures such as reduced lighting loads, improved roof insulation, optimized ventilation, and more accurate load calculations through its rooftop unit (RTU) replacement program. Target's approach achieved ongoing energy reduction, operations and maintenance reduction, and improved heating, ventilating, and air-conditioning (HVAC) performance by reducing equipment cycling.

HVAC, Rooftop Unit, RTU, commercial, retail, air c↗

The New Weather Radar for America's Space Program in Florida: A Temperature Profile Adaptive Scan Strategy

A new weather radar is being acquired for use in support of America s space program at Cape Canaveral Air Force Station, NASA Kennedy Space Center, and Patrick AFB on the east coast of central Florida. This new radar replaces the modified WSR-74C at Patrick AFB that has been in use since 1984. The new radar is a Radtec TDR 43-250, which has Doppler and dual polarization capability. A new fixed scan strategy was designed to best support the space program. The fixed scan strategy represents a complex compromise between many competing factors and relies on climatological heights of various temperatures that are important for improved lightning forecasting and evaluation of Lightning Launch Commit Criteria (LCC), which are the weather rules to avoid lightning strikes to in-flight rockets. The 0 C to -20 C layer is vital since most generation of electric charge occurs within it and so it is critical in evaluating Lightning LCC and in forecasting lightning. These are two of the most important duties of 45 WS. While the fixed scan strategy that covers most of the climatological variation of the 0 C to -20 C levels with high resolution ensures that these critical temperatures are well covered most of the time, it also means that on any particular day the radar is spending precious time scanning at angles covering less important heights. The goal of this project is to develop a user-friendly, Interactive Data Language (IDL) computer program that will automatically generate optimized radar scan strategies that adapt to user input of the temperature profile and other important parameters. By using only the required scan angles output by the temperature profile adaptive scan strategy program, faster update times for volume scans and/or collection of more samples per gate for better data quality is possible, while maintaining high resolution at the critical temperature levels. The temperature profile adaptive technique will also take into account earth curvature and refraction when geo-locating the radar beam (i.e., beam height and arc distance), including non-standard refraction based on the user-input temperature profile. In addition to temperature profile adaptivity, this paper will also summarize the other requirements for this scan strategy program such as detection of low-level boundaries, detection of anvil clouds, reducing the Cone Of Silence, and allowing for times when deep convective clouds will not occur. The adaptive technique will be carefully compared to and benchmarked against the new fixed scan strategy. Specific environmental scenarios in which the adaptive scan strategy is able to optimize and improve coverage and resolution at critical heights, scan time, and/or sample numbers relative to the fixed scan strategy will be presented.

Carey, L. D.↗

iGeoT v1.0

iGeoT v1.0 automates into a stand-alone computer program the multicomponent chemical geothermometry code GeoT v2.1 and the numerical optimization engine of iTOUGH2. iGeoT allows for optimizations of GeoT runs using multiple water chemical analyses. The underlying geothermometry method is that previously developed by Reed and Spycher (1984) using the computed saturation indices of multiple minerals. GeoT automatically reconstitutes deep fluid compositions and estimates reservoir temperature from statistical evaluation of computed mineral saturation indices. The output include estimated temperatures following various statistical methods and their range of uncertainty. The computer program also outputs temperatures predicted using classical geothermometers. Input parameters include water composition and, optionally, gas composition, fraction of gas discharge, dilution/evaporation factor (in case of boiling or mixing with dilute waters), and end-member water composition (in case of mixing with other non-dilute waters). The dilution/evaporation factor, fraction of gas discharge, and concentration of various aqueous and gas species can be automatically estimated by numerical optimization. This program was designed for geothermal applications.

Spycher, Nicolas↗

An across-the-bay flight support structure designed specifically for the Spartan program

The preliminary design of an across-the-bay Flight Support Structure optimized to the specific requirements of the Spartan program has been completed. Although approximately 15 percent heavier than the initial goal, preliminary analysis indicate very low stress levels and significant reduction in weight should be possible in the final design. This structure is capable of supporting two Spartan 200-class spacecraft or attached payloads of equivalent total weight. The inherent structural efficiency of monocoque type construction is utilized. The minimization of fabrication and assembly costs and provision for simple and versatile payload interfacing where given significant considerations. Modularity of this structure allows it to be readily adapted for use as the primary structure of an Aries-class Spartan free-flyer utilizing the Orbit trunning latch mechanisms, thus eliminating the need for a flight support structure.

Rast, J. J.↗

A parallel hub-and-spoke system for large-scale scenario-based optimization under uncertainty

Practical solution of stochastic programming problems generally requires the use of parallel computing resources. Here, we describe the open source package mpi-sppy, in which efficient and scalable parallelization is a central feature. We report computational experiments that demonstrate the ability to solve very large stochastic programming problems - including mixed-integer variants - in minutes of wall clock time, efficiently leveraging significant parallel computing resources. We report results for the largest publicly available instances of stochastic mixed-integer unit commitment problems, solving to provably tight optimality gaps. In addition, we introduce a novel software architecture that facilitates combinations of methods for accelerating convergence that can be combined in plug-and-play manner. Finally, the mpi-sppy package is written in Python, leverages the widely used Pyomo (http://www.pyomo.org) library for modeling mathematical programs, builds on existing MPI implementations to ensure efficiency and scalability, and is available via http://github.com/Pyomo/mpi-sppy.

97 MATHEMATICS AND COMPUTING↗

Modeling the AC Power Flow Equations with Optimally Compact Neural Networks: Application to Unit Commitment

Nonlinear power flow constraints render a variety of power system optimization problems computationally intractable. Emerging research shows, however, that the nonlinear AC power flow equations can be successfully modeled using neural networks. These neural networks can be exactly transformed into mixed integer linear programs and embedded inside challenging optimization problems, thus replacing nonlinearities that are intractable for many applications with tractable piecewise linear approximations. Such approaches, though, suffer from an explosion of the number of binary variables needed to represent the neural network. Accordingly, this paper develops a technique for training an "optimally compact'' neural network, i.e., one that can represent the power flow equations with a sufficiently high degree of accuracy while still maintaining a tractable number of binary variables. We demonstrate the use of this neural network as an approximator of the nonlinear power flow equations by embedding it in the AC unit commitment problem, transforming the problem from a mixed integer nonlinear program into a more manageable mixed integer linear program. We use the 14-, 57-, and 89-bus networks as test cases and compare the AC-feasibility of commitment decisions resulting from the neural network, DC, and linearized power flow approximations. Our results show that the neural network model outperforms both the DC and linearized power flow approximations when embedded in the unit commitment problem. The neural network formulation most often selects a feasible unit commitment schedule, and furthermore, it only s

AC power flow↗

Machine-learning-aided cognitive reconfiguration for flexible-bandwidth HPC and data center networks [Invited]

This paper proposes a machine-learning (ML)-aided cognitive approach for effective bandwidth reconfiguration in optically interconnected datacenter/high-performance computing (HPC) systems. The proposed approach relies on a Hyper-X-like architecture augmented with flexible-bandwidth photonic interconnections at large scales using a hierarchical intra/inter-POD photonic switching layout. We first formulate the problem of the connectivity graph and routing scheme optimization as a mixed-integer linear programming model. A two-phase heuristic algorithm and a joint optimization approach are devised to solve the problem with low time complexity. Then, we propose an ML-based end-to-end performance estimator design to assist the network control plane with intelligent decision making for bandwidth reconfiguration. Numerical simulations using traffic distribution profiles extracted from HPC applications traces as well as random traffic matrices verify the accuracy performance of the ML design estimator ( < <#comment/> 9 % <#comment/> error) and demonstrate up to 5 × <#comment/> throughput gain from the proposed approach compared with the baseline Hyper-X network using fixed all-to-all intra/inter-portable data center interconnects.

Chen, Xiaoliang (ORCID:0000000278056237)↗

Analyzing Millimeter-Wave Mixers

Series of computer programs developed to serve as tool in understanding behavior and subsequent optimization of millimeter-wave mixers. Major program in collection is general mixer-analysis program that performs complete large- and small-signal analysis of mixer with known diode and mount characteristics. Primary objective behind programs to gain better understanding of factors that affect performance of room-temperature, single-ended Schottky-diode mixers operating above 100 GHz.

Siegel, P.↗

A design optimization process for Space Station Freedom

The Space Station Freedom Program is used to develop and implement a process for design optimization. Because the relative worth of arbitrary design concepts cannot be assessed directly, comparisons must be based on designs that provide the same performance from the point of view of station users; such designs can be compared in terms of life cycle cost. Since the technology required to produce a space station is widely dispersed, a decentralized optimization process is essential. A formulation of the optimization process is provided and the mathematical models designed to facilitate its implementation are described.

Chamberlain, Robert G.↗

Optimal Network-Topology Design

Candidate network designs tested for acceptability and cost. Optimal Network Topology Design computer program developed as part of study on topology design and analysis of performance of Space Station Information System (SSIS) network. Uses efficient algorithm to generate candidate network designs consisting of subsets of set of all network components, in increasing order of total costs and checks each design to see whether it forms acceptable network. Technique gives true cost-optimal network and particularly useful when network has many constraints and not too many components. Program written in PASCAL.

Li, Victor O. K.↗

TH-E-17A-05: Optimizing Four Dimensional Cone Beam Computed Tomography Projection Allocation to Respiratory Bins

Purpose: Four dimensional cone beam computed tomography (4DCBCT) is an emerging image guidance strategy but it can suffer from poor image quality. To avoid repeating scans it is beneficial to make the best use of the imaging data obtained. For conventional 4DCBCT the location and size of respiratory bins is fixed and projections are allocated to the respiratory bin within which it falls. Strictly adhering to this rule is unnecessary and can compromise image quality. In this study we optimize the size and location of respiratory bins and allow projections to be sourced from adjacent phases of the respiratory cycle. Methods: A mathematical optimization framework using mixed integer quadratic programming has been developed that determines when to source projections from adjacent respiratory bins and optimizes the size and location of the bins. The method, which we will call projection sharing, runs in under 2 seconds of CPU time. Five 4DCBCT datasets of stage III-IV lung cancer patients were used to test the algorithm. The standard deviation of the angular separation between projections (SD-A) and the standard deviation in the volume of the reconstructed fiducial gold coil (SD-V) were used as proxies to measure streaking artefacts and motion blur respectively. Results: The SD-A using displacement binning and projection sharing was 30%–50% smaller than conventional phase based binning and 59%–76% smaller than conventional displacement binning indicating more uniformly spaced projections and fewer streaking artefacts. The SD-V was 20–90% smaller when using projection sharing than using conventional phase based binning suggesting more uniform marker segmentation and less motion blur. Conclusion: Image quality was visibly and significantly improved with projection sharing. Projection sharing does not require any modifications to existing hardware and offers a more robust replacement to phase based binning, or, an option if phase based reconstruction is not of a suitable quality. This project is supported by an NHMRC Australia Fellowship and NHMRC project grant number 1034060.

60 APPLIED LIFE SCIENCES↗

Computer simulation for time optimal or energy optimal attitude control of spin-stabilized spacecraft.

An original technique for determining the optimal magnetic torque strategy for control of the attitude of spin stabilized spacecraft is presented. By employing Lagrange multipliers and the Calculus of Variations, optimal control equations are derived which define minimum time and minimum energy attitude maneuvers. Computer program algorithms to numerically solve these optimal control equations are also described. The performance of this technique is compared with a commonly employed planning method.

Woolley, R. D.↗