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Results for “linear optimization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Cherenkov imaging method for rapid optimization of clinical treatment geometry in total skin electron beam therapy

Purpose: A method was developed utilizing Cherenkov imaging for rapid and thorough determination of the two gantry angles that produce the most uniform treatment plane during dual-field total skin electron beam therapy (TSET). Methods: Cherenkov imaging was implemented to gather 2D measurements of relative surface dose from 6 MeV electron beams on a white polyethylene sheet. An intensified charge-coupled device camera time-gated to the Linac was used for Cherenkov emission imaging at sixty-two different gantry angles (1° increments, from 239.5° to 300.5°). Following a modified Stanford TSET technique, which uses two fields per patient position for full body coverage, composite images were created as the sum of two beam images on the sheet; each angle pair was evaluated for minimum variation across the patient region of interest. Cherenkov versus dose correlation was verified with ionization chamber measurements. The process was repeated at source to surface distance (SSD) = 441, 370.5, and 300 cm to determine optimal angle spread for varying room geometries. In addition, three patients receiving TSET using a modified Stanford six-dual field technique with 6 MeV electron beams at SSD = 441 cm were imaged during treatment. Results: As in previous studies, Cherenkov intensity was shown to directly correlate with dose for homogenous flat phantoms (R{sup 2} = 0.93), making Cherenkov imaging an appropriate candidate to assess and optimize TSET setup geometry. This method provided dense 2D images allowing 1891 possible treatment geometries to be comprehensively analyzed from one data set of 62 single images. Gantry angles historically used for TSET at their institution were 255.5° and 284.5° at SSD = 441 cm; however, the angles optimized for maximum homogeneity were found to be 252.5° and 287.5° (+6° increase in angle spread). Ionization chamber measurements confirmed improvement in dose homogeneity across the treatment field from a range of 24.4% at the initial angles, to only 9.8% with the angles optimized. A linear relationship between angle spread and SSD was observed, ranging from 35° at 441 cm, to 39° at 300 cm, with no significant variation in percent-depth dose at midline (R{sup 2} = 0.998). For patient studies, factors influencing in vivo correlation between Cherenkov intensity and measured surface dose are still being investigated. Conclusions: Cherenkov intensity correlates to relative dose measured at depth of maximum dose in a uniform, flat phantom. Imaging of phantoms can thus be used to analyze and optimize TSET treatment geometry more extensively and rapidly than thermoluminescent dosimeters or ionization chambers. This work suggests that there could be an expanded role for Cherenkov imaging as a tool to efficiently improve treatment protocols and as a potential verification tool for routine monitoring of unique patient treatments.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2018

Multiphase Optimal and Non-Singular Power Flow by Successive Linear Approximations

We propose an optimal power flow method for multiphase power systems. The method works for both radial and meshed networks, and is able to accommodate different types of load/source connections such as wye, delta, and combination thereof. Moreover, the method generates a sequence of nonsingular points (i.e., associated with non-singular power-flow Jacobian) in the electrical state space and a corresponding sequence of power injections, which can be used in real-time control settings. Under certain conditions, the sequences attain the local minimum. The method has been tested using several typical networks, including the IEEE 37-bus and 123-bus test feeders.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2019

Large-scale quasi-Newton trust-region methods with low-dimensional linear equality constraints

We propose two limited-memory BFGS (L-BFGS) trust-region methods for large-scale optimization with linear equality constraints. Here, the methods are intended for problems where the number of equality constraints is small. By exploiting the structure of the quasi-Newton compact representation, both proposed methods solve the trust-region subproblems nearly exactly, even for large problems. We derive theoretical global convergence results of the proposed algorithms, and compare their numerical effectiveness and performance on a variety of large-scale problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

On the Efficacy and High-Performance Implementation of Quaternion Matrix Multiplication

Quaternion symmetry is ubiquitous in the physical sciences. As such, much work has been afforded over the years to the development of efficient schemes to exploit this symmetry using real and complex linear algebra. Recent years have also seen many advances in the formal theoretical development of explicitly quaternion linear algebra with promising applications in image processing and machine learning. Despite these advances, there do not currently exist optimized software implementations of quaternion linear algebra. The leverage of optimized linear algebra software is crucial in the achievement of high levels of performance on modern computing architectures, and thus provides a central tool in the development of high-performance scientific software. In this work, a case will be made for the efficacy of high-performance quaternion linear algebra software for appropriate problems. In this pursuit, an optimized software implementation of quaternion matrix multiplication will be presented and will be shown to outperform a vendor tuned implementation for the analogous complex matrix operation. The results of this work pave the path for further development of high-performance quaternion linear algebra software which will improve the performance of the next generation of applicable scientific applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Algebraic multigrid preconditioning of the Hessian in optimization constrained by a partial differential equation

Summary We construct an algebraic multigrid (AMG) based preconditioner for the reduced Hessian of a linear‐quadratic optimization problem constrained by an elliptic partial differential equation. While the preconditioner generalizes a geometric multigrid preconditioner introduced in earlier works, its construction relies entirely on a standard AMG infrastructure built for solving the forward elliptic equation, thus allowing for it to be implemented using a variety of AMG methods and standard packages. Our analysis establishes a clear connection between the quality of the preconditioner and the AMG method used. The proposed strategy has a broad and robust applicability to problems with unstructured grids, complex geometry, and varying coefficients. The method is implemented using the Hypre package and several numerical examples are presented.

Barker, Andrew T.↗
DOE OSTI2018

Cascade energy optimization for waste heat recovery in distributed energy systems

The efficiency of distributed energy systems can be significantly increased through waste heat recovery from industry or power generation. The technologies used for this process are typically dependent on the quality and temperature grades of waste heat. To maximize the efficiency of cascade heat utilization, it is important to optimize the choice of waste heat recovery technologies and their operation. Here, a detailed mixed integer linear programming optimization model is proposed for waste heat recovery in a district-scale microgrid. The model can distinguish waste heat quality for planning and operation optimization of distributed energy systems. Heat utilization technologies are formulated in this developed model and categorized in different temperature grades. The developed model is validated using four typical cases under different settings of system operation and business models. It is found that the optimization model, by distinguishing waste heat temperature, can increase energy cost savings by around 5%, compared to models that do not consider waste heat temperature grades. Additionally, the results indicate that the developed model can provide more realistic configuration and technologies dispatch.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Depot Charging Schedule Optimization for Medium- and Heavy-Duty Battery-Electric Trucks

Charge management, which lowers charging costs for fleets and prevents straining the electrical grid, is critical to the successful deployment of medium- and heavy-duty battery-electric trucks (MHD BETs). This study introduces an energy demand and cost management framework that optimizes depot charging for MHD BETs by combining an energy consumption machine learning model and a linear program optimization model. The framework considers key factors impacting real-world MHD BET operations, including vehicle and charger configurations, duty cycles, use cases, geographic and climate conditions, operation schedules, and utilities’ time-of-use (TOU) rates and demand charges. The framework was applied to a hypothetical fleet of 100 MHD BETs in California under three different utilities for 365 days, with results compared to unmanaged charging. The optimized charging solution avoided more than 90% of on-peak charging, reduced fleet charging peak load by 64–75%, and lowered fleet energy variable costs by 54–64%. This study concluded that the proposed charge management framework significantly reduces energy costs and peak loads for MHD BET fleets while making recommendations for fleet electrification infrastructure planning and the design of utility TOU rates and demand charges.

Song, Shuhan↗
DOE OSTI2024

Direct microstability optimization of stellarator devices

Turbulent transport is regarded as one of the key issues in magnetic confinement nuclear fusion, both for tokamaks and stellarators. Here, in this work, we show that a significant decrease in a microstability-based proxy, as opposed to a geometric one, for the turbulent heat flux, namely the quasilinear heat flux, can be obtained in an efficient manner by coupling stellarator optimization with linear gyrokinetic simulations. This is accomplished by computing the quasilinear heat flux at each step of the optimization process, as well as the deviation from quasisymmetry, and minimizing their sum, leading to a balance between neoclassical and the turbulent transport proxy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Optimal mode transformations for linear-optical cluster-state generation

In this paper, we analyze the generation of linear-optical cluster states (LOCSs) via sequential addition of one and two qubits. Existing approaches employ the stochastic linear-optical two-qubit controlled-Z (CZ) gate with success rate of 1/9 per operation. The question of optimality of the CZ gate with respect to LOCS generation has remained open. We report that there are alternative schemes to the CZ gate that are exponentially more efficient and show that sequential LOCS growth is indeed globally optimal. We find that the optimal cluster growth operation is a state transformation on a subspace of the full Hilbert space. Finally, we show that the maximal success rate of postselected entangling n photonic qubits or m Bell pairs into a cluster is (1/2) n-1 and (1/4) m-1 , respectively, with no ancilla photons, and we give an explicit optical description of the optimal mode transformations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Start-up Optimization Considering Integrated Power Electronic Systems

The startup of systems composed of power electronic systems is becoming more complex. As the systems grow, standard pre-configuration sequencing methods will struggle. This work proposes a linear programming optimization method to couple power electronic systems in a series of startup commands. This formulation is demonstrated in a real-time implementation on hardware.

Starke, Michael↗
DOE OSTI2019

An adjoint method for neoclassical stellarator optimization

Stellarators remain an enticing route to steady-state fusion power. However, to achieve the required confinement, the magnetic geometry must be highly optimized. This optimization requires navigating high-dimensional spaces, often necessitating the use of gradient-based methods. The gradient of the neoclassical fluxes is expensive to compute with classical methods, requiring $O(N)$ flux computations, where $N$ is the number of parameters. To reduce the cost of the gradient computation, we present an adjoint method for computing the derivatives of moments of the neoclassical distribution function for stellarator optimization. The linear adjoint method allows derivatives of quantities which depend on solutions of a linear system, such as moments of the distribution function, to be computed with respect to many parameters from the solution of only two linear systems. This reduces the cost of computing the gradient to the point that the finite-collisionality neoclassical fluxes can be used within an optimization loop. With the neoclassical adjoint method, we compute solutions of the drift kinetic equation and an adjoint drift kinetic equation to obtain derivatives of neoclassical quantities with respect to geometric parameters. When the number of parameters in the derivative is large ( $O(10^{2})$ ), this adjoint method provides up to a factor of 200 reduction in cost. We demonstrate adjoint-based optimization of the field strength to obtain minimal bootstrap current on a surface. With adjoint-based derivatives, we also compute the local sensitivity to magnetic perturbations on a flux surface and identify regions where tight tolerances on error fields are required for control of the bootstrap current or radial transport. Moreover, the solve for the ambipolar electric field is accelerated using a Newton method with derivatives obtained from the adjoint method.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Optically resonant magneto-electric cubic nanoantennas for ultra-directional light scattering

Cubic dielectric nanoparticles are promising candidates for futuristic low-loss, ultra-compact, nanophotonic applications owing to their larger optical coefficients, greater packing density, and relative ease of fabrication as compared to spherical nanoparticles; besides possessing negligible heating at nanoscale in contrast to their metallic counterparts. Here, we present the first theoretical demonstration of azimuthally symmetric, ultra-directional Kerker's-type scattering of simple dielectric nanocubes in visible and near-infrared regions via simultaneous excitation and interference of optically induced electric- and magnetic-resonances up to quadrupolar modes. Unidirectional forward-scattering by individual nanocubes is observed at the first generalized-Kerker's condition for backward-scattering suppression, having equal electric- and magnetic-dipolar responses. Both directionality and magnitude of these unidirectional-scattering patterns get enhanced where matching electric- and magnetic-quadrupolar responses spectrally overlap. While preserving azimuthal-symmetry and backscattering suppression, a nanocube homodimer provides further directionality improvement for increasing interparticle gap, but with reduced main-lobe magnitude due to emergence of side-scattering lobes from diffraction-grating effect. We thoroughly investigate the influence of interparticle gap on scattering patterns and propose optimal range of gap for minimizing side-scattering lobes. Besides suppressing undesired side-lobes, significant enhancement in scattering magnitude and directionality is attained with increasing number of nanocubes forming a linear chain. Optimal directionality, i.e., the narrowest main-scattering lobe, is found at the wavelength of interfering quadrupolar resonances; whereas the largest main-lobe magnitude is observed at the wavelength satisfying the first Kerker's condition. These unique optical properties of dielectric nanocubes thus can revolutionize their applications at visible and near-infrared regions in the fields of nanoantennas, nanolasers, photovoltaics, and even in biomedicine.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Iterative Linearization for Phasor-Defined Optimal Power Dispatch

Optimal power flow (OPF) problems, which dispatch power targets to controllable generating units across a network, must generally account for non-convex constraints on power flow. Furthermore, adapting those problems so as to make them solvable with convex optimization techniques is an area of much academic and operational interest. In this paper, we present a method for solving OPF as a quadratic program by iteratively refining and re-initializing a linearized model of power flow based on the outputs of an associated nonlinear solver. The linear model on which we demonstrate this method is an adapted version of an approximation designed for use with unbalanced distribution networks. As an important benefit, the model allows for the explicit inclusion of nodal voltage phasor values in both the OPF problem's objective and its constraints, which opens the door to the idea of phasor-based control (PBC) design. We show in simulations on the IEEE 13-node test feeder that our method quickly converges to a set of phasor targets that are sufficiently precise for use in operations at the distribution level.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2018

EnergyPlus Interior Radiant Heat Exchange Runtime Performance Improvements

EnergyPlus is the flagship whole-building energy simulation program developed by the US Department of Energy. This paper describes the various approaches to improve the performance of the interior radiant heat exchange algorithm. Vectorization, optimized Basic Linear Algebra Subprograms (BLAS) library, multithreading, and Graphical Processing Unit (GPU) computation are all investigated. The approach with the best performance, while maintaining drop-in compatibility with existing EnergyPlus code, is the optimized BLAS library. However, GPU computing has the potential to reduce simulation time by orders of magnitude with major refactoring to EnergyPlus.

Adams, Mark↗
DOE OSTI2021

Parallelized POD-based suboptimal economic model predictive control of a state-constrained Boussinesq approximation

Motivated by an energy efficient building application, we want to optimize a quadratic cost functional subject to the Boussinesq approximation of the Navier-Stokes equations and to bilateral state and control constraints. Since the computation of such an optimal solution is numerically costly, we design an efficient strategy to compute a sub-optimal (but applicationally acceptable) solution with significantly reduced computational effort. We employ an economic Model Predictive Control (MPC) strategy to obtain a feedback control. The MPC sub-problems are based on a linear-quadratic optimal control problem subjected to mixed control and state constraints and a convection-diffusion equation, reduced with proper orthogonal decomposition. Finally, to solve each sub-problem, we apply a primal-dual active set strategy. The method can be fully parallelized, which enables the solution of large problems with real-world parameters.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Multiphase Optimal and Non-Singular Power Flow by Successive Linear Approximations: Preprint

We propose an optimal power flow method for multiphase power systems. The method works for both radial and meshed networks, and is able to accommodate different types of load/source connections such as wye, delta, etc. Moreover, the method generates a sequence of non-singular points in the electrical state space and a corresponding sequence of power injections, which can be used in real-time control settings. Under certain conditions, the sequences attain the local minimum. The method has been tested using several typical networks, including the IEEE 37-bus and 123-bus test feeders.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2015

Numerical optimization of three-dimensional coils for NSTX-U

A tool for the calculation of optimal three-dimensional (3D) perturbative magnetic fields in tokamaks has been developed. The IPECOPT code builds upon the stellarator optimization code STELLOPT to allow for optimization of linear ideal magnetohydrodynamic perturbed equilibrium (IPEC). This tool has been applied to NSTX-U equilibria, addressing which fields are the most effective at driving NTV torques. The NTV torque calculation is performed by the PENT code. Optimization of the normal field spectrum shows that fields with n = 1 character can drive a large core torque. It is also shown that fields with n = 3 features are capable of driving edge torque and some core torque. Coil current optimization (using the planned in-vessel and existing RWM coils) on NSTX-U suggest the planned coils set is adequate for core and edge torque control. In conclusion, comparison between error field correction experiments on DIII-D and the optimizer show good agreement.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders

Nearly all model-reduction techniques project the governing equations onto a linear subspace of the original state space. Such subspaces are typically computed using methods such as balanced truncation, rational interpolation, the reduced-basis method, and (balanced) proper orthogonal decomposition (POD). Unfortunately, restricting the state to evolve in a linear subspace imposes a fundamental limitation to the accuracy of the resulting reduced-order model (ROM). In particular, linear-subspace ROMs can be expected to produce low-dimensional models with high accuracy only if the problem admits a fast decaying Kolmogorov n -width (e.g., diffusion-dominated problems). Unfortunately, many problems of interest exhibit a slowly decaying Kolmogorov n-width (e.g., advection-dominated problems). To address this, we propose a novel framework for projecting dynamical systems onto nonlinear manifolds using minimum-residual formulations at the time-continuous and time-discrete levels; the former leads to manifold Galerkin projection, while the latter leads to manifold least-squares Petrov–Galerkin (LSPG) projection. We perform analyses that provide insight into the relationship between these proposed approaches and classical linear-subspace reduced-order models; we also derive a posteriori discrete-time error bounds for the proposed approaches. In addition, we propose a computationally practical approach for computing the nonlinear manifold, which is based on convolutional autoencoders from deep learning. Lastly, we demonstrate the ability of the method to significantly outperform even the optimal linear-subspace ROM on benchmark advection-dominated problems, thereby demonstrating the method's ability to overcome the intrinsic n -width limitations of linear subspaces.

97 MATHEMATICS AND COMPUTING↗