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At least 109 records · Page 6

Optimal Control Problems with Switching Points

The main idea of this report is to give an overview of the problems and difficulties that arise in solving optimal control problems with switching points. A brief discussion of existing optimality conditions is given and a numerical approach for solving the multipoint boundary value problems associated with the first-order necessary conditions of optimal control is presented. Two real-life aerospace optimization problems are treated explicitly. These are altitude maximization for a sounding rocket (Goddard Problem) in the presence of a dynamic pressure limit, and range maximization for a supersonic aircraft flying in the vertical, also in the presence of a dynamic pressure limit. In the second problem singular control appears along arcs with active dynamic pressure limit, which in the context of optimal control, represents a first-order state inequality constraint. An extension of the Generalized Legendre-Clebsch Condition to the case of singular control along state/control constrained arcs is presented and is applied to the aircraft range maximization problem stated above. A contribution to the field of Jacobi Necessary Conditions is made by giving a new proof for the non-optimality of conjugate paths in the Accessory Minimum Problem. Because of its simple and explicit character, the new proof may provide the basis for an extension of Jacobi's Necessary Condition to the case of the trajectories with interior point constraints. Finally, the result that touch points cannot occur for first-order state inequality constraints is extended to the case of vector valued control functions.

Seywald, Hans↗

Sizing and Location Selection of Medium‐Voltage Back‐to‐Back Converters for DER‐Dominated Distribution Systems

Medium‐voltage back‐to‐back (MVB2B) converters can connect two distribution systems and quantifiably transfer power between them. This function can enable the MVB2B converter to exchange distributed energy resource (DER)‐generated power between two systems and bring significant value to enhancing distribution system DER adoption. Our previous work analysed and demonstrated the value MVB2B converter can bring to DER integration. As continuous work, this paper presents a methodology that helps address the MVB2B converter sizing and location selection problem in distribution systems with high DER penetrations. The proposed methodology aims to address three critical problems for MVB2B converter implementation in the real world: (1) which distribution systems are better to be connected, (2) what converter size is appropriate for connecting the distribution systems, and (3) where the optimal connection points are in the systems for connecting the MVB2B converter. The proposed methodology has been demonstrated by case studies that include various scenarios involving distribution systems with different dominated load types and high photovoltaic penetrations. The results demonstrate that selecting the optimal converter size based on net revenue and time of return considerations leads to a balance between maximizing energy savings and minimizing financial payback periods. Furthermore, feeder pair selection based on load profile standard deviation effectively identifies systems that derive the greatest value from MVB2B integration. Finally, an optimized connection point selection approach using a voltage load sensitivity matrix ensures minimal system impact while facilitating efficient power exchange. These findings provide practical insights for the real‐world deployment of MVB2B converters to enhance DER hosting capacity and improve grid resilience.

14 SOLAR ENERGY↗

Two Point Exponential Approximation Method for structural optimization of problems with frequency constraints

The point exponential approximation method was introduced by Fadel et al. (Fadel, 1990), and tested on structural optimization problems with stress and displacement constraints. The reports in earlier papers were promising, and the method, which consists of correcting Taylor series approximations using previous design history, is tested in this paper on optimization problems with frequency constraints. The aim of the research is to verify the robustness and speed of convergence of the two point exponential approximation method when highly non-linear constraints are used.

Fadel, G. M.↗

Finding inputs that trigger floating-point exceptions in heterogeneous computing via Bayesian optimization

Testing code for floating-point exceptions is crucial as exceptions can quickly propagate and produce unreliable numerical answers. The state-of-the-art to test for floating-point exceptions in heterogeneous systems is quite limited and solutions require the application’s source code, which precludes their use in accelerated libraries where the source is not publicly available. We present an approach to find inputs that trigger floating-point exceptions in black-box CPU or GPU functions, i.e., functions where the source code and information about input bounds are unavailable. Our approach is the first to use Bayesian optimization (BO) to identify such inputs and uses novel strategies to overcome the challenges that arise in applying BO to this problem. Here, we implement our approach in the XSCOPE framework and demonstrate it on 58 functions from the CUDA Math Library and 81 functions from the Intel Math Library. XSCOPE is able to identify inputs that trigger exceptions in about 73% of the tested functions.

97 MATHEMATICS AND COMPUTING↗

P2P: Point Cloud to Panel Layout Optimization

Building envelope retrofits, despite their benefits on enhancing energy efficiency, progress slowly due to high operating costs. Overclad panelized systems present an attractive solution to make retrofits affordable and easy to install. However, several stages of the retrofit process remain disconnected, suboptimal, and require significant human intervention. This study aims to bridge the gap between digital twin generation and overclad panel installation by automating the design of an optimal panel layout directly from a building envelope point cloud. In this end-to-end approach, the dimensional twin is generated by segmenting the facade point cloud. The facade then undergoes a three-step process to generate an optimized panel layout for integration with automated placement systems.

Philips, Nisha Deborah [ORNL]↗

Electromagnetic analysis for large reflector antennas

A comparison is made between the measured E and H plane patterns of the 35 GHz offset paraboloidal reflector and the calculated patterns for the same reflector using the 200 points to describe the surface. The accuracy of the computer prediction is quite good considering that the only description of the surface was the coordinates of a finite number of points on the reflector. The results indicate the possibility of acceptable accuracy in the prediction of electromagnetic performance for arbitrarily distorted reflectors using the coordinates of a practical number of measured points. An optimization of the number and distribution of points, and experimental verification for a distorted reflector are planned.

Bailey, M. C.↗

Fuel-optimal maneuvers of a spacecraft relative to a point in circular orbit

Fuel optimal maneuvers of spacecraft relative to a body in circular orbit are investigated using a point mass model in which the magnitude of the thrust vector is bounded. All nonsingular optimal maneuvers consist of intervals of full thrust and coast and are found to contain at most seven such intervals in one period. Only four boundary conditions where singular solutions occur are possible. Computer simulation of optimal flight path shapes and switching functions are found for various boundary conditions. Emphasis is placed on the problem of soft rendezvous with a body in circular orbit.

Carter, T. E.↗

A simulation study of test fixture attachment points for vibration test optimization (MEEN 5440 Final Project)

The aerospace industry uses vibration shaker tables to perform component durability testing. These dynamic environments tests often have a hard time replicating the service environment of a component due to a mismatch in the applied force or the boundary condition. Figure 1 shows the desired outcome of a dynamic environments test. The measured responses in a lab test, ideally, should match the measured response of the service environment field test. One way to address the mismatch between field environment and lab environment is with test fixture design. The test fixture attaches the component under test to the shaker table. Single-axis shakers are the industry standard type of shaker table, and, therefore, test fixtures are often rigid in order to minimize cross-axis responses.

42 ENGINEERING↗

High-Performance Reaction Wheel Optimization for Fine-Pointing Space Platforms: Minimizing Induced Vibration Effects on Jitter Performance plus Lessons Learned from Hubble Space Telescope for Current and Future Spacecraft Applications

The Hubble Space Telescope (HST) applies large-diameter optics (2.5-m primary mirror) for diffraction-limited resolution spanning an extended wavelength range (approx. 100-2500 nm). Its Pointing Control System (PCS) Reaction Wheel Assemblies (RWAs), in the Support Systems Module (SSM), acquired an unprecedented set of high-sensitivity Induced Vibration (IV) data for 5 flight-certified RWAs: dwelling at set rotation rates. Focused on 4 key ratios, force and moment harmonic values (in 3 local principal directions) are extracted in the RWA operating range (0-3000 RPM). The IV test data, obtained under ambient lab conditions, are investigated in detail, evaluated, compiled, and curve-fitted; variational trends, core causes, and unforeseen anomalies are addressed. In aggregate, these values constitute a statistically-valid basis to quantify ground test-to-test variations and facilitate extrapolations to on-orbit conditions. Accumulated knowledge of bearing-rotor vibrational sources, corresponding harmonic contributions, and salient elements of IV key variability factors are discussed. An evolved methodology is presented for absolute assessments and relative comparisons of macro-level IV signal magnitude due to micro-level construction-assembly geometric details/imperfections stemming from both electrical drive and primary bearing design parameters. Based upon studies of same-size/similar-design momentum wheels' IV changes, upper estimates due to transitions from ground tests to orbital conditions are derived. Recommended HST RWA choices are discussed relative to system optimization/tradeoffs of Line-Of-Sight (LOS) vector-pointing focal-plane error driven by higher IV transmissibilities through low-damped structural dynamics that stimulate optical elements. Unique analytical disturbance results for orbital HST accelerations are described applicable to microgravity efforts. Conclusions, lessons learned, historical context/insights, and perspectives on future applications are given; these previously unpublished data and findings represents a valuable resource for fine-pointing spacecraft or space-based platforms using RWAs, Control Moment Gyros (CMGs), Momentum Wheels, or other ball-bearing-based rotational units.

Hasha, Martin D.↗

An optimally tuned range-separated hybrid starting point for ab initio GW plus Bethe–Salpeter equation calculations of molecules

The ab initio GW plus Bethe–Salpeter equation (GW-BSE, where G is the one particle Green's function and W is the screened Coulomb interaction) approach has emerged as a leading method for predicting excitations in both solids and molecules with a predictive power contingent upon several factors. Among these factors are the (1) generalized Kohn–Sham eigensystem used to construct the GW self-energy and to solve the BSE and (2) the efficacy and suitability of the Tamm–Dancoff approximation. Here, we present a detailed benchmark study of low-lying singlet excitations from a generalized Kohn–Sham (gKS) starting point based on an optimally tuned range-separated hybrid (OTRSH) functional. We show that the use of this gKS starting point with one-shot G0W0 and G0W0-BSE leads to the lowest mean absolute errors (MAEs) and mean signed errors (MSEs), with respect to high-accuracy reference values, demonstrated in the literature thus far for the ionization potentials of the GW100 benchmark set and for low-lying neutral excitations of Thiel’s set molecules in the gas phase, without the need for self-consistency. The MSEs and MAEs of one-shot G0W0-BSE@OTRSH excitation energies are comparable to or lower than those obtained with other functional starting points after self-consistency. Additionally, we compare these results with linear-response time-dependent density functional theory (TDDFT) calculations and find GW-BSE to be superior to TDDFT when calculations are based on the same exchange-correlation functional. This work demonstrates tuned range-separated hybrids used in combination with GW and GW-BSE can greatly suppress starting point dependence for molecules, leading to accuracy similar to that for higher-order wavefunction-based theories for molecules without the need for costlier iterations to self-consistency.

McKeon, Caroline A. (ORCID:0000000217373503)↗

Runtime Systems for Energy Efficiency in Advanced Computing Systems

As heterogeneous systems become increasingly popular for both mobile and high-performance computing, conventional efficiency techniques such as dynamic voltage and frequency scaling (DVFS) fail to account for the tightly coupled and varied nature of systems on a chip (SoCs). In this work, we explore the impact of system unaware DVFS techniques on a mobile SoC under three benchmark suites: Chai, Rodinia, and Antutu. We then analyze performance trends across the suites to identify a set of consistent operating points that optimally balance power and performance across the system. The consistent operating points are then constructed into a dependency graph which can be leveraged to produce a more effective, SoC-wide governor.

97 MATHEMATICS AND COMPUTING↗

Autonomous Energy Management Software System for Small Commercial Buildings in Support of Decarbonization (Abstract)

The primary goal for the project is to develop and validate an autonomous energy management software (AEMS) system that will continuously optimize small commercial building operations by minimizing energy consumption and cost, providing a solution for maximizing decarbonization benefits from electrification of buildings. The work will leverage vast experience of Pacific Northwest National Laboratory (PNNL) research and development staff who have over two decades of experience in developing and successfully transferring software technologies to the private sector. This solution will be jointly developed with Intellimation LLC who plans to use it to scale their building energy efficiency offering. The project plan will include collaboratively working with Intellimation to package a set of solutions into the AEMS system, validate and demonstrate their capability, and value proposition through field demonstrations. If the deployment of the AEMS system optimizes RTUs’ set points, schedules, setbacks and optimal start and results in energy consumption reduction of 20%, the technical potential savings is approximately 675 trillion Btus of site energy savings and 2,000 trillion Btus of source energy. It will also result in carbon reductions of approximately 2.4 MMTCO2 and contribute to the climate change mitigation plans of many cities and states across the United States. Additional cost savings and emissions reduction are possible from management of peak electricity demand. The primary outcome will be an AEMS system that can be deployed at scale on small commercial buildings to improve operating efficiency.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Effects of Planetary Gear Ratio on Mean Service Life

Planetary gear transmissions are compact, high-power speed reductions which use parallel load paths. The range of possible reduction ratios is bounded from below and above by limits on the relative size of the planet gears. For a single plane transmission, the planet gear has no size at a ratio of two. As the ratio increases, so does the size of the planets relative to the sizes of the sun and ring. Which ratio is best for a planetary reduction can be resolved by studying a series of optimal designs. In this series, each design is obtained by maximizing the service life for a planetary with a fixed size, gear ratio, input speed power and materials. The planetary gear reduction service life is modeled as a function of the two-parameter Weibull distributed service lives of the bearings and gears in the reduction. Planet bearing life strongly influences the optimal reduction lives which point to an optimal planetary reduction ratio in the neighborhood of four to five.

Savage, M.↗

Effects of Planetary Speed Reduction Ratio on Mean Service Life

Planetary gear transmissions are compact speed reductions which use parallel-load paths to transmit high power. The range of possible reduction ratios is bounded from below and above by limits on the relative size of the planet gears. For a single plane planetary transmission, the speed-reduction ratio must be greater than two for planet gears to exist. As the ratio increase, so does the size of the planets relative to the sizes of the sun and ring. Which ratio is best for a planetary reduction can be resolved by studying a series of optimal designs. In this series, each design is obtained by maximizing the service life for a spur-gear planetary with a fixed size, speed reduction ratio, input speed, power and materials. The planetary gear reduction service life is modeled as a function of the two-parameter Weibull distributed service lives of the ball bearings and spur gears in the reduction. Planet-bearing life strongly influences the optimal reduction lives which point to an optimal planetary reduction ratio in the neighborhood of four to five.

Savage, M.↗