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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 1,099 records · Page 61
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

On the application of deterministic optimization methods to stochastic control problems.

A technique is presented by which one can apply the Minimum Principle of Pontryagin to stochastic optimal control problems formulated around linear systems with Gaussian noises and general cost criteria. Using this technique, the stochastic nature of the problem is suppressed but for two expectation operations, the optimization being essentially deterministic. The technique is applied to systems with quadratic and non-quadratic costs to illustrate its use.

Kramer, L. C.↗
NASA NTRS1974

On the application of deterministic optimization methods to stochastic control problems

A technique is presented by which deterministic optimization techniques, for example, the maximum principle of Pontriagin, can be applied to stochastic optimal control problems formulated around linear systems with Gaussian noises and general cost criteria. Using this technique, the stochastic nature of the problem is suppressed but for two expectation operations, the optimization being deterministic. The use of the technique in treating problems with quadratic and nonquadratic costs is illustrated.

Kramer, L. C.↗
DOE OSTI2022

Microgrid Assisted Design for Remote Areas

In this work, we present a three-stage multiobjective mixed-integer linear programming (MILP) for the optimal expansion planning and operation of isolated multienergy microgrids in remote areas. By selecting the optimal distributed generators (DGs) and energy storage systems (ESSs) mix selection, siting, sizing, and scheduling in the remote microgrid, the proposed model is targeted to minimize the annualized total cost of microgrids while enhancing the performance of the system, i.e., minimizing the voltage deviations and line power loss. To represent the electricity and heat flow between generation resources and various electrical, heating, and cooling loads in the isolated microgrid, linearized power flow, and heat flow constraints are employed in the proposed optimization model. The available capacity of DGs and ESSs are modeled as discrete constants instead of continuous variables for practical purpose. Numerical simulation results on a remote microgrid consisting of DGs, ESSs, and various loads validate the proposed method.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

A framework for discrete optimization of stellarator coils

Designing magnets for three-dimensional plasma confinement is a key task for advancing the stellarator as a fusion reactor concept. Stellarator magnets must produce an accurate field while leaving adequate room for other components and being reasonably simple to construct and assemble. In this paper, a framework for coil design and optimization is introduced that enables the attainment of sparse magnet solutions with arbitrary restrictions on where coils may be located. The solution space is formulated as a 'wireframe' consisting of a mesh of interconnected wire segments enclosing the plasma. Two methods are developed for optimizing the current distribution on a wireframe: Regularized Constrained Least Squares, which uses a linear least-squares approach to optimize the currents in each segment, and Greedy Stellarator Coil Optimization, a fully discrete procedure in which loops of current are added to the mesh one by one to achieve the desired magnetic field on the plasma boundary. Examples are presented of solutions obtainable with each method, some of which achieve high field accuracy while obeying spatial constraints that permit easy assembly.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1973

Constrained optimization of image restoration filters

A linear shift-invariant preprocessing technique is described which requires no specific knowledge of the image parameters and which is sufficiently general to allow the effective radius of the composite imaging system to be minimized while constraining other system parameters to remain within specified limits.

Riemer, T. E.↗
NASA NTRS1989

H(2)- and H(infinity)-design tools for linear time-invariant systems

Recent advances in optimal control have brought design techniques based on optimization of H(2) and H(infinity) norm criteria, closer to be attractive alternatives to single-loop design methods for linear time-variant systems. Significant steps forward in this technology are the deeper understanding of performance and robustness issues of these design procedures and means to perform design trade-offs. However acceptance of the technology is hindered by the lack of convenient design tools to exercise these powerful multivariable techniques, while still allowing single-loop design formulation. Presented is a unique computer tool for designing arbitrary low-order linear time-invarient controllers than encompasses both performance and robustness issues via the familiar H(2) and H(infinity) norm optimization. Application to disturbance rejection design for a commercial transport is demonstrated.

Ly, Uy-Loi↗
NASA NTRS1991

H(infinity) and H2 optimal controllers for periodic and multi-rate systems

The solutions to the optimal l2 to l2 disturbance rejection problem H(infinity) as well as to the LQG (linear quadratic Gaussian) H2 problem in periodic systems using the lifting technique are presented. Both problems involve a causality condition on the optimal LTI (linear time invariant) compensator when viewed in the lifted domain. The H(infinity) problem is solved using the Nehari's theorem, whereas in the H2 problem the solution is obtained using the projection theorem in Hilbert spaces. The authors demonstrate that exactly the same method of solution to the H(infinity) and H2 problems in periodic systems applies when considering the same problems in multirate sampled data systems.

Voulgaris, Petros G.↗
DOE OSTI2017

Quantified Gamow shell model interaction for p s d -shell nuclei

Background: The structure of weakly bound and unbound nuclei close to particle drip lines is one of the major science drivers of nuclear physics. A comprehensive understanding of these systems goes beyond the traditional configuration interaction approach formulated in the Hilbert space of localized states (nuclear shell model) and requires an open quantum system description. The complex-energy Gamow shell model (GSM) provides such a framework as it is capable of describing resonant and nonresonant many-body states on equal footing. Purpose: To make reliable predictions, quality input is needed that allows for the full uncertainty quantification of theoretical results. In this study, we carry out the optimization of an effective GSM (one-body and two-body) interaction in the psdf-shell-model space. The resulting interaction is expected to describe nuclei with 5 ≤ A ≲ 12 at the p-sd-shell interface. Method: The one-body potential of the 4 He core is modeled by a Woods-Saxon + spin-orbit + Coulomb potential, and the finite-range nucleon-nucleon interaction between the valence nucleons consists of central, spin-orbit, tensor, and Coulomb terms. The GSM is used to compute key fit observables. The χ 2 optimization is performed using the Gauss-Newton algorithm augmented by the singular value decomposition technique. The resulting covariance matrix enables quantification of statistical errors within the linear regression approach. Results: The optimized one-body potential reproduces nucleon- 4 He scattering phase shifts up to an excitation energy of 20 MeV. The two-body interaction built on top of the optimized one-body field is adjusted to the bound and unbound ground-state binding energies and selected excited states of the helium, lithium, and beryllium isotopes up to A = 9 . A very good agreement with experimental results was obtained for binding energies. First applications of the optimized interaction include predictions for two-nucleon correlation densities and excitation spectra of light nuclei with quantified uncertainties. In conclusion: The new interaction will enable comprehensive and fully quantified studies of structure and reactions aspects of nuclei from the psd region of the nuclear chart.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Optimization of transformer ratio and beam loading in a plasma wakefield accelerator with a structure-exploiting algorithm

Plasma-based acceleration has emerged as a promising candidate as an accelerator technology for a future linear collider or a next-generation light source. We consider the plasma wakefield accelerator (PWFA) concept where a plasma wave wake is excited by a particle beam and a trailing beam surfs on the wake. For a linear collider, the energy transfer efficiency from the drive beam to the wake and from the wake to the trailing beam must be large, while the emittance and energy spread of the trailing bunch must be preserved. One way to simultaneously achieve this when accelerating electrons is to use longitudinally shaped bunches and nonlinear wakes. In the linear regime, there is an analytical formalism to obtain the optimal shapes. In the nonlinear regime, however, the optimal shape of the driver to maximize the energy transfer efficiency cannot be precisely obtained because currently no theory describes the wake structure and excitation process for all degrees of nonlinearity. In addition, the ion channel radius is not well defined at the front of the wake where the plasma electrons are not fully blown out by the drive beam. We present results using a novel optimization method to effectively determine a current profile for the drive and trailing beam in PWFA that provides low energy spread, low emittance, and high acceleration efficiency. We parameterize the longitudinal beam current profile as a piecewise-linear function and define optimization objectives. For the trailing beam, the algorithm converges quickly to a nearly inverse trapezoidal trailing beam current profile similar to that predicted by the ultrarelativistic limit of the nonlinear wakefield theory. For the drive beam, the beam profile found by the optimization in the nonlinear regime that maximizes the transformer ratio also resembles that predicted by linear theory. Furthermore, the current profiles found from the optimization method provide higher transformer ratios compared with the linear ramp predicted by the relativistic limit of the nonlinear theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2021

Nonlinear Navigation Analysis for a Europa Lander Mission Concept

Navigation strategies typically use linearized techniques to predict maneuver statistics. This method has been successfully employed on numerous high-energy trajectories, but may not be valid for low-energy ones due to the highly non-linear environment. We explore nonlinear navigational techniques applied to a Europa Lander concept by assessing trajectory sensitivity. The linearity assumption is tested at different phases of the endgame trajectory. Maneuver strategies and placement are considered to improve the delivery to Europa. Several cases of non-linear statistical maneuver Monte Carlo simulations are conducted to optimize maneuvers and compare ∆V statistics against conventional linear simulations.

Hernandez, Sonia↗
DOE OSTI2024

Improving cosmological analyses of HI clustering by reducing stochastic noise

High-number-density tracers of large-scale structure, such as the HI-rich galaxies measured by 21 cm intensity mapping, have low sampling noise, making them particularly promising as cosmological probes. At large scales, this sampling noise can be subdominant to other scale-independent contributions to the power spectrum; such contributions arise from nonlinear bias, and exceed the sampling noise if at least one of the associated bias coefficients is sufficiently large. This has important consequences for cosmological constraints obtained from such tracers, since it indicates that using the power spectrum does not lead to optimal constraints even in the linear regime. In this paper, we provide a conservative estimate of the possible improvement in constraining power of a 21 cm survey if one were to use an optimal analysis strategy (such as field-level analysis), where only the true sampling noise enters the error budget. We find that improvements in uncertainties on some cosmological parameters can be as large as 50%, depending on redshift, foreground cleaning efficiency, scales used in the analysis, and instrumental noise. One byproduct of our work is measurements of bias parameters and stochasticity for neutral hydrogen in the IllustrisTNG simulation over a wide range of redshifts; we provide simple fitting formulas for these measurements. Furthermore, our results motivate further exploration of new optimal analysis techniques and provide important insights into the constraining power of current and future 21 cm surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Structure optimization with stochastic density functional theory

Linear-scaling techniques for Kohn–Sham density functional theory are essential to describe the ground state properties of extended systems. Still, these techniques often rely on the localization of the density matrix or accurate embedding approaches, limiting their applicability. In contrast, stochastic density functional theory (sDFT) achieves linear- and sub-linear scaling by statistically sampling the ground state density without relying on embedding or imposing localization. In return, ground state observables, such as the forces on the nuclei, fluctuate in sDFT, making optimizing the nuclear structure a highly non-trivial problem. In this work, we combine the most recent noise-reduction schemes for sDFT with stochastic optimization algorithms to perform structure optimization within sDFT. We compare the performance of the stochastic gradient descent approach and its variations (stochastic gradient descent with momentum) with stochastic optimization techniques that rely on the Hessian, such as the stochastic Broyden–Fletcher–Goldfarb–Shanno algorithm. In conclusion, we further provide a detailed assessment of the computational efficiency and its dependence on the optimization parameters of each method for determining the ground state structure of bulk silicon with varying supercell dimensions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Efficient numerical methods to solve sparse linear equations with application to PageRank

Over the last two decades, the PageRank problem has received increased interest from the academic community as an efficient tool to estimate web-page importance in information retrieval. Despite numerous developments, the design of efficient optimization algorithms for the PageRank problem is still a challenge. Here, we propose three new algorithms with a linear time complexity for solving the problem over a bounded-degree graph. The idea behind them is to set up the PageRank as a convex minimization problem over a unit simplex, and then solve it using iterative methods with small iteration complexity. Our theoretical results are supported by an extensive empirical justification using real-world and simulated data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

The Recommendations for Linear Measurement Techniques on the Measurements of Nonlinear System Parameters of a Joint.

In the study of the dynamics of nonlinear systems, experimental measurements often convolute the response of the nonlinearity of interest and the effects of the experimental setup. To reduce the influence of the experimental setup on the deduction of the parameters of the nonlinearity, the response of a mechanical joint is investigated under various experimental setups. These experiments first focus on quantifying how support structures and measurement techniques affect the natural frequency and damping of a linear system. The results indicate that support structures created from bungees have negligible influence on the system in terms of frequency and damping ratio variations. The study then focuses on the effects of the excitation technique on the response for a linear system. The findings suggest that thinner stingers should not be used, because under the high force requirements the stinger bending modes are excited adding unwanted torsional coupling. The optimal configuration for testing the linear system is then applied to a nonlinear system in order to assess the robustness of the test configuration. Finally, recommendations are made for conducting experiments on nonlinear systems using conventional/linear testing techniques.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Substation-Level Grid Topology Optimization Using Bus Splitting: Preprint

Operations of substation circuit breakers are of high significance for performing system maintenance and topology optimization. Bus splitting is one type of topology changes where the two bus-bars at a substation become electrically disconnected after certain actions of circuit breakers. As these events involve detailed substation modeling, they are not typically considered in power system routine operation and control. In this paper, an improved substation-level topology optimization is developed by expanding traditional line switching with breaker-level bus splitting, which can further reduce grid congestion and generation costs. A tight McCormick relaxation is proposed to reformulate the bi-linear terms in the resultant topology optimization model. Thus, a tractable mixed-integer linear program formulation is presented which can be efficiently solved for real-time control. Numerical studies on the IEEE 14-bus and 118-bus systems demonstrate the performance and economic benefits of the proposed topology optimization approach.

bus split↗
DOE OSTI2019

An Efficient Parallel-in-Time Method for Optimization with Parabolic PDEs

To solve optimization problems with parabolic PDE constraints, often methods working on the reduced objective functional are used. They are computationally expensive due to the necessity of solving both the state equation and a backward-in-time adjoint equation to evaluate the reduced gradient in each iteration of the optimization method. In this study, we investigate the use of the parallel-in-time method PFASST in the setting of PDE-constrained optimization. In order to develop an efficient fully time-parallel algorithm, we discuss different options for applying PFASST to adjoint gradient computation, including the possibility of doing PFASST iterations on both the state and the adjoint equations simultaneously. Here, we also explore the additional gains in efficiency from reusing information from previous optimization iterations when solving each equation. Numerical results for both a linear and a nonlinear reaction-diffusion optimal control problem demonstrate the parallel speedup and efficiency of different approaches.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1974

On the quadratic sampled-data regulator with unstable random disturbances

This paper is concerned with the design of a digital controller, optimizing a quadratic cost function, for a linear system subjected to plant disturbance. The disturbance is viewed as a Gaussian random process generated by a linear system which may be unstable. It is shown that the optimal control consists of the sum of two terms: the optimal control when no disturbance is present and a term depending on the estimates of the disturbance. Necessary and sufficient conditions for the convergence of the gain matrices is given.

Halyo, N.↗