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Results for “Numerical 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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

The use of singular value gradients and optimization techniques to design robust controllers for multiloop systems

A method for designing robust feedback controllers for multiloop systems is presented. Robustness is characterized in terms of the minimum singular value of the system return difference matrix at the plant input. Analytical gradients of the singular values with respect to design variables in the controller are derived. A cumulative measure of the singular values and their gradients with respect to the design variables is used with a numerical optimization technique to increase the system's robustness. Both unconstrained and constrained optimization techniques are evaluated. Numerical results are presented for a two output drone flight control system.

Newsom, J. R.↗
DOE OSTI2024

Continuously bounds-preserving discontinuous Galerkin methods for hyperbolic conservation laws

For finite element approximations of transport phenomena, it is often necessary to apply a form of limiting to ensure that the discrete solution remains well-behaved and satisfies physical constraints. However, these limiting procedures are typically performed at discrete nodal locations, which is not sufficient to ensure the robustness of the scheme when the solution must be evaluated at arbitrary locations (e.g., for adaptive mesh refinement, remapping in arbitrary Lagrangian–Eulerian solvers, overset meshes, etc.). In this work, a novel limiting approach for discontinuous Galerkin methods is presented which ensures that the solution is continuously bounds-preserving (i.e., across the entire solution polynomial) for any arbitrary choice of basis, approximation order, and mesh element type. Through a modified formulation for the constraint functionals, the proposed approach requires only the solution of a single spatial scalar minimization problem per element for which a highly efficient numerical optimization procedure is presented. Here, the efficacy of this approach is shown in numerical experiments by enforcing continuous constraints in high-order unstructured discontinuous Galerkin discretizations of hyperbolic conservation laws, ranging from scalar transport with maximum principle preserving constraints to compressible gas dynamics with positivity-preserving constraints.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1986

Weight estimation of unconventional structures by structural optimization

Automated techniques are presented that are used in structural optimization technology, with emphasis on modifications of finite element models to obtain an optimal material distribution for minimum weight while satisfying the prescribed design requirements. It is anticipated that the future development of computer aided engineering (CAE) system will provide environments where structural analysis, a design optimization, and weight evaluation modules are integrated, sharing a common data base. Structural optimization capabilities obtained by integrating a finite element structural analysis program and a numerical optimization code are developed and applied to two illustrative examples: marine gear housing structural weight minimization and joined wing structures.

Miura, Hirokazu↗
NASA NTRS1988

A near optimal guidance algorithm for aero-assisted orbit transfer

The paper presents a near optimal guidance algorithm for aero-assited orbit plane change, based on minimizing the energy loss during the atmospheric portion of the maneuver. The guidance algorithm makes use of recent results obtained from energy state approximations and singular perturbation analysis of optimal heading change for a hypersonic gliding vehicle. This earlier work ignored the terminal constraint on altitude needed to insure that the vehicle exits that atmosphere. Thus, the resulting guidance algorithm was only appropriate for maneuvering reentry vehicle guidance. In the context of singular perturbation theory, a constraint on final altitude gives rise to a difficult terminal boundary layer problem, which cannot be solved in closed form. This paper will demonstrate the near optimality of a predictive/corrective guidance algorithm for the terminal maneuver. Comparisons are made to numerically optimized trajectories for a range or orbit plane angles.

Calise, Anthony J.↗
DOE OSTI2019

Optimized quasisymmetric stellarators are consistent with the Garren–Boozer construction

The majority of quasisymmetric stellarators to date have been designed by numerically optimizing the plasma boundary shape to minimize symmetry-breaking Fourier modes of the magnetic field strength B. At high aspect ratio, a faster approach is to directly construct the plasma shape from the equations of quasisymmetry near the magnetic axis derived by Garren and Boozer [Phys Fluids B 3, 2805 (1991)]. Here we demonstrate that the core shape and rotational transform of many optimization-based configurations can be accurately described by this direct-construction approach. This consistency supports use of the near-axis construction as an accurate analytical model for modern stellarator configurations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Combining the synergistic control capabilities of modeling and experiments: Illustration of finding a minimum-time quantum objective

A common way to manipulate a quantum system, for example spins or artificial atoms, is to use properly tailored control pulses. In order to accomplish quantum information tasks before coherence is lost, it is crucial to implement the control in the shortest possible time. Here we report the near time-optimal preparation of a Bell state with fidelity higher than 99% in an NMR experiment, which is feasible by combining the synergistic capabilities of modeling and experiments operating in tandem. In this work, the pulses preparing the Bell state are found by experiments that are recursively assisted with a gradient-based optimization algorithm working with a model. Thus, we exploit the interplay between model-based numerical optimal design and experimental-based learning control. Utilizing the balanced synergism between the dual approaches, as dictated by the case specific capabilities of each approach, should have broad applications for accelerating the search for optimal quantum controls.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1969

Trajectory optimization using regularized variables

Regularized equations for a particular optimal trajectory are compared with unregularized equations with respect to computational characteristics, using perturbation type numerical optimization. In the case of the three dimensional, low thrust, Earth-Jupiter rendezvous, the regularized equations yield a significant reduction in computer time.

Lewallen, J. M.↗
NASA NTRS2018

Jig-Shape Optimization of a Low-Boom Supersonic Aircraft

A simple approach for optimizing the jig-shape is proposed in this study. This simple approach is based on an unconstrained optimization problem and applied to a low-boom supersonic aircraft. In this study, the jig-shape optimization is performed using the two-step approach. First, starting design variables are computed using the least squares surface fitting technique. Next, the jig-shape is further tuned using a numerical optimization procedure based on in-house object-oriented optimization tool.

numerical analysi↗
NASA NTRS2018

Jig-Shape Optimization of a Low-Boom Supersonic Aircraft

A simple approach for optimizing the jig-shape is proposed in this study. This simple approach is based on an unconstrained optimization problem and applied to a low-boom supersonic aircraft. In this study, the jig-shape optimization is performed using the two-step approach. First, starting design variables are computed using the least squares surface fitting technique. Next, the jig-shape is further tuned using a numerical optimization procedure based on in-house object-oriented optimization tool.

numerical analysis↗
NASA NTRS1986

Supersonic airfoil optimization

A procedure for the optimization of supersonic airfoils is presented. A nonlinear, full-potential solver (NCOREL) is coupled with a numerical optimizer (CONMIN). The NCOREL code is a three-dimensional supersonic marching method, however, only two-dimensional (conical) results are used for the airfoil problem. Each airfoil evaluated in the NCOREL aerodynamic code is composed of a linear combination of user-specified basis airfoils. The weighting factors of the basis airfoils plus the angle of attack form the design variable vector. The inviscid drag coefficient is minimized subject to lift and crossflow Mach number gradient constraints. The optimization strategy is found to be extremely important for the efficient determination of an optimum airfoil.

Pittman, J. L.↗
NASA NTRS1988

The Sizing and Optimization Language, (SOL): Computer language for design problems

The Sizing and Optimization Language, (SOL), a new high level, special purpose computer language was developed to expedite application of numerical optimization to design problems and to make the process less error prone. SOL utilizes the ADS optimization software and provides a clear, concise syntax for describing an optimization problem, the OPTIMIZE description, which closely parallels the mathematical description of the problem. SOL offers language statements which can be used to model a design mathematically, with subroutines or code logic, and with existing FORTRAN routines. In addition, SOL provides error checking and clear output of the optimization results. Because of these language features, SOL is best suited to model and optimize a design concept when the model consits of mathematical expressions written in SOL. For such cases, SOL's unique syntax and error checking can be fully utilized. SOL is presently available for DEC VAX/VMS systems. A SOL package is available which includes the SOL compiler, runtime library routines, and a SOL reference manual.

Lucas, Stephen H.↗
NASA NTRS2015

Full-Carpet Design of a Low-Boom Demonstrator Concept

The Cart3D adjoint-based design framework is used to mitigate the undesirable o -track sonic boom properties of a demonstrator concept designed for low-boom directly under the flight path. First, the requirements of a Cart3D design mesh are determined using a high-fidelity mesh adapted to minimize the discretization error of the CFD analysis. Low-boom equivalent area targets are then generated at the under-track and one off-track azimuthal position for the baseline configuration. The under-track target is generated using a trim- feasible low-boom target generation process, ensuring that the final design is not only low-boom, but also trimmed at the specified flight condition. The o -track equivalent area target is generated by minimizing the A-weighted loudness using an efficient adjoint-based approach. The configuration outer mold line is then parameterized and optimized to match the off-body pressure distributions prescribed by the low-boom targets. The numerical optimizer uses design gradients which are calculated using the Cart3D adjoint- based design capability. Optimization constraints are placed on the geometry to satisfy structural feasibility. The low-boom properties of the final design are verified using the adaptive meshing approach. This analysis quantifies the error associated with the CFD mesh that is used for design. Finally, an alternate mesh construction and target positioning approach offering greater computational efficiency is demonstrated and verified.

Ordaz, Irian↗
DOE OSTI2021

Quantum optimal control for pure-state preparation using one initial state

This paper presents a framework for solving the pure-state preparation problem using numerical optimal control. As an example, we consider the case where a number of qubits are dispersively coupled to a readout cavity. Herein, we model open system quantum dynamics using the Markovian Lindblad master equation driven by external control pulses. The main result of this paper develops a basis of density matrices (a parameterization) where each basis element is a density matrix by itself. Utilizing a specific objective function, we show how an ensemble of the basis elements can be used as a single initial state throughout the optimization process—independent of the system dimension. We apply the general framework to the specific application of ground-state reset of one and two qubits coupled to a readout cavity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2005

Evolutionary optimization of a Genetically Refined Truss

Structural optimization is a field of research that has experienced noteworthy growth for many years. Researchers in this area have developed optimization tools to successfully design and model structures, typically minimizing mass while maintaining certain deflection and stress constraints. Numerous optimization studies have been performed to minimize mass, deflection and stress on a benchmark cantilever truss problem. Predominantly traditional optimization theory is applied to this problem. The cross-sectional area of each member is optimized to minimize the aforementioned objectives. This paper will present a structural optimization technique that has been previously applied to compliant mechanism design. This technique demonstrates a method that combines topology optimization, geometric refinement, finite element analysis, and two forms of evolutionary computation: Genetic Algorithms and Differential Evolution to successfully optimize a benchmark structural optimization problem. An non-traditional solution to the benchmark problem is presented in this paper, specifically a geometrically refined topological solution. The design process begins with an alternate control mesh formulation, multilevel geometric smoothing operation, and an elastostatic structural analysis. The design process is wrapped in an evolutionary computing optimization toolset.

Hull, Patrick V.↗
NASA NTRS2007

Evolutionary Optimization of a Geometrically Refined Truss

Structural optimization is a field of research that has experienced noteworthy growth for many years. Researchers in this area have developed optimization tools to successfully design and model structures, typically minimizing mass while maintaining certain deflection and stress constraints. Numerous optimization studies have been performed to minimize mass, deflection, and stress on a benchmark cantilever truss problem. Predominantly traditional optimization theory is applied to this problem. The cross-sectional area of each member is optimized to minimize the aforementioned objectives. This Technical Publication (TP) presents a structural optimization technique that has been previously applied to compliant mechanism design. This technique demonstrates a method that combines topology optimization, geometric refinement, finite element analysis, and two forms of evolutionary computation: genetic algorithms and differential evolution to successfully optimize a benchmark structural optimization problem. A nontraditional solution to the benchmark problem is presented in this TP, specifically a geometrically refined topological solution. The design process begins with an alternate control mesh formulation, multilevel geometric smoothing operation, and an elastostatic structural analysis. The design process is wrapped in an evolutionary computing optimization toolset.

Hull, P. V.↗
NASA NTRSDate not supplied

Study of a Plug Nozzle for Supersonic Aircraft Concepts

Nozzles with external plugs are candidates for the exhaust system of supersonic aircraft concepts in an ongoing research effort at NASA. As part of that effort a fundamental study is being conducted at NASA Glenn Research Center (GRC). Experimental and limited numerical simulation results from this study, for a plug nozzle with a convergent nozzle (cowl),have been reported in recent publications[1,2]. Conventional method-of-characteristics (MoC) design for the plug requires that the flow is choked at the nozzle exit. This is why a sharp convergence of the cowl is invoked in such a design in most previous studies [3-5], leading to the earlier choice of the convergent cowl. Such a nozzle, however, is not suitable for supersonic flights because of large boat tail drag suffered by its outer surface. The boat tail drag consideration dictates that the cowl be more or less cylindrical in shape. While various other shapes have been studied in the past [6], essentially a cylindrical shape is adopted in the larger research program at NASA. The cylindrical shape has certain advantages. With the plug crown located somewhat inside the nozzle, the flow experiences convergence and divergence as with a C-D nozzle. By translating the plug, different throat-to-exit area ratio could be achieved to obtain fully expanded condition at different values of NPR. This offers a relatively easy active control strategy for the nozzle geometry throughout the flight regime from landing and takeoff (LTO) to cruise conditions. A plug nozzle model mimicking the geometry being considered in the NASA program, i.e., having a cylindrical exit, have been fabricated recently for continued fundamental studies. Some of the plugs used with the earlier convergent cowl [1] are readily adopted to this model. In addition, a few other plugs have been obtained following a numerical optimization study [7]. The various configurations are to be investigated for thrust, noise and flow fields, with complementing numerical simulations. Thrust data for a variety of configurations as well as limited noise data are in hand. Further explorations including schlieren visualization are to be conducted in the near future. The proposed paper is to summarize all these results. In the following, a few key results obtained so far are described.

jets↗