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At least 703 records · Page 39
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

How to detect lensing rotation

Gravitational lensing rotation of images is predicted to be negligible at linear order in density perturbations, but can be produced by the post-Born lens-lens coupling at second order. This rotation is somewhat enhanced for Cosmic Microwave Background (CMB) lensing due to the large source path length, but remains small and very challenging to detect directly by CMB lensing reconstruction alone. We show the rotation may be detectable at high significance as a cross-correlation signal between the curl reconstructed with Simons Observatory (SO) or CMB-S4 data, and a template constructed from quadratic combinations of large-scale structure (LSS) tracers. Equivalently, the lensing rotation-tracer-tracer bispectrum can also be detected, where LSS tracers considered include the CMB lensing convergence, galaxy density, and the Cosmic Infrared Background (CIB), or optimal combinations thereof. We forecast that an optimal combination of these tracers can probe post-Born rotation at the level of 5.7σ–6.1σ with SO and 13.6σ–14.7σ for CMB-S4, depending on whether standard quadratic estimators or maximum a posteriori iterative methods are deployed. We also show possible improvement up to 21.3σ using a CMB-S4 deep patch observation with polarization-only iterative lensing reconstruction. However, these cross-correlation signals have non-zero bias because the rotation template is quadratic in the tracers, and exists even if the lensing is rotation free. We estimate this bias analytically, and test it using simple null-hypothesis simulations to confirm that the bias remains subdominant to the rotation signal of interest. Detection and then measurement of the lensing rotation cross-spectrum is therefore a realistic target for future observations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Quadratic general rotary unitized design for doping concentrations and up-conversion luminescence properties of Er{sup 3+}/Yb{sup 3+} co-doped NaLa(MoO{sub 4}){sub 2} phosphors

Highlights: • NaLa(MoO4)2: Er3+/Yb3+ phosphor is synthesized by solid state method. • QGRUD is first applied to the codoping concentration option. • Optimized phosphor presents more stable UC emissions than the commercial phosphor. - Abstract: It is still a great challenge that designing proper codoping concentrations of rare earth ions for achieving intensest expected emission from the studied phosphor. In this work, the quadratic general rotary unitized design (QGRUD) was introduced into the codoping concentration option of NaLa(MoO{sub 4}){sub 2}: Er{sup 3+}/Yb{sup 3+} phosphor for upconversion (UC) applications, and the optimum doping concentrations of Er{sup 3+} and Yb{sup 3+} for achieving maximum UC luminescence intensity, which is close to commercial NaYF{sub 4}:Er{sup 3+}/Yb{sup 3+} phosphor, were obtained. The two-photon process was assigned to the green UC emissions in the optimized NaLa(MoO{sub 4}){sub 2}: Er{sup 3+}/Yb{sup 3+} phosphor. It was also demonstrated that the optimized phosphor presented more stable upconversion emissions than the commercial NaYF{sub 4}:Er{sup 3+}/Yb{sup 3+} phosphor.

36 MATERIALS SCIENCE↗
NASA NTRS1990

Optimal Regulator Algorithms For The Control Of Linear Systems (ORACLS)

Control theory design package offers engineer full range of subroutines to manipulate and solve Linear-Quadratic-Gaussian types of problems. ORACLS is rigorous tool, intended for multi-input and multi-output dynamic systems in both continuous and discrete form. Written in FORTRAN.

Frisch, Harold P.↗
DOE OSTI2018

SEMI-ACTIVE CONTROL FOR TWO-BODY OCEAN WAVE ENERGY CONVERTER BY USING HYBRID MODEL PREDICTIVE CONTROL

Model predictive control (MPC) has been considered as one important feed-forward optimal control strategy for ocean wave energy converter (WEC) targeted on power maximization. The capability of MPC to handle system constraints (ex. stroke, velocity, actuator limitations), and the availability to provide optimal solution for linear system provide potential for the implementation of such algorithm in the WEC control. However, currently, only active MPC control has been introduced for single and two-body WECs. Such control strategy may introduce negative power during the optimization process, since the power take-off (PTO) damping has no constraint. In this paper, we proposed a hybrid MPC strategy in limiting both the PTO damping force and PTO damping to avoid negative power generation during cost function minimization (negative power minimization) for the two-body WEC. The problem is formulated into a quadratic programming (QP) problem targeted at power maximization. However, the standard QP problem formulation cannot be directly applied to the semi-active control problem due to the PTO damping constraints. Therefore, the problem is reformulated as a Mixed-integer Quadratic Programming (MIQP) problem, which contains logical switch to select constraint matrices based on the sign of the relative velocity between the buoy and submerged body. The optimal solution is compared with those of the active MPC control strategy and the passive model with the same irregular wave input.

16 TIDAL AND WAVE POWER↗
NASA NTRS1981

Application of constrained optimization to active control of aeroelastic response

Active control of aeroelastic response is a complex in which the designer usually tries to satisfy many criteria which are often conflicting. To further complicate the design problem, the state space equations describing this type of control problem are usually of high order, involving a large number of states to represent the flexible structure and unsteady aerodynamics. Control laws based on the standard Linear-Quadratic-Gaussian (LQG) method are of the same high order as the aeroelastic plant. To overcome this disadvantage of the LQG mode, an approach developed for designing low order optimal control laws which uses a nonlinear programming algorithm to search for the values of the control law variables that minimize a composite performance index, was extended to the constrained optimization problem. The method involves searching for the values of the control law variables that minimize a basic performance index while satisfying several inequality constraints that describe the design criteria. The method is applied to gust load alleviation of a drone aircraft.

Newsom, J. R.↗
DOE OSTI2017

A QCQP Approach for OPF in Multiphase Radial Networks with Wye and Delta Connections: Preprint

This paper examines the AC Optimal Power Flow (OPF) problem for multiphase distribution networks featuring renewable energy resources (RESs). We start by outlining a power flow model for radial multiphase systems that accommodates wye-connected and delta-connected RESs and non-controllable energy assets. We then formalize an AC OPF problem that accounts for both types of connections. Similar to various AC OPF renditions, the resultant problem is a non convex quadratically-constrained quadratic program. However, the so-called Feasible Point Pursuit-Successive Convex Approximation algorithm is leveraged to obtain a feasible and yet locally-optimal solution. The merits of the proposed solution approach are demonstrated using two unbalanced multiphase distribution feeders with both wye and delta connections.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2026

Classical combinatorial optimization scaling for random Ising models on 2D heavy-hex graphs

Motivated by near term quantum computing hardware limitations, combinatorial optimization problems that can be addressed by current quantum algorithms and noisy hardware with little or no overhead are used to probe capabilities of quantum algorithms such as the quantum approximate optimization algorithm. In this study, a specific class of near term quantum computing hardware defined combinatorial optimization problems, Ising models on heavy-hex graphs both with and without geometrically local cubic terms, are examined for their classical computational hardness via empirical computation time scaling quantification. Specifically the time-to-solution (TTS) metric using the classical heuristic simulated annealing is measured for finding optimal variable assignments (ground states), as well as the time required for the optimization software Gurobi to find an optimal variable assignment. Because of the sparsity of these Ising models, the classical algorithms are able to find optimal solutions efficiently even for large instances (i.e. 100 000 spin variables). The Ising models both with and without geometrically local cubic terms exhibit average-case linear-time or weakly quadratic scaling when solved exactly using Gurobi, and the Ising models with no cubic terms show evidence of exponential-time TTS scaling when sampled using simulated annealing. These findings point to the necessity of developing and testing more complex, namely more densely connected, optimization problems in order for quantum computing to ever have a practical advantage over classical computing. Our results are another illustration that different classical algorithms can indeed have exponentially different running times, thus making the identification of the best practical classical technique important in any quantum computing vs. classical computing comparison.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2009

Sensitivity Analysis of Linear Programming and Quadratic Programming Algorithms for Control Allocation

The Next Generation (NextGen) transport aircraft configurations being investigated as part of the NASA Aeronautics Subsonic Fixed Wing Project have more control surfaces, or control effectors, than existing transport aircraft configurations. Conventional flight control is achieved through two symmetric elevators, two antisymmetric ailerons, and a rudder. The five effectors, reduced to three command variables, produce moments along the three main axes of the aircraft and enable the pilot to control the attitude and flight path of the aircraft. The NextGen aircraft will have additional redundant control effectors to control the three moments, creating a situation where the aircraft is over-actuated and where a simple relationship does not exist anymore between the required effector deflections and the desired moments. NextGen flight controllers will incorporate control allocation algorithms to determine the optimal effector commands and attain the desired moments, taking into account the effector limits. Approaches to solving the problem using linear programming and quadratic programming algorithms have been proposed and tested. It is of great interest to understand their relative advantages and disadvantages and how design parameters may affect their properties. In this paper, we investigate the sensitivity of the effector commands with respect to the desired moments and show on some examples that the solutions provided using the l2 norm of quadratic programming are less sensitive than those using the l1 norm of linear programming.

Frost, Susan A.↗
DOE OSTI2017

Causal control design for wave energy converters with finite stroke

Control design is of central importance in the optimization of power generation from ocean wave energy converters (WECs). The problem is made challenging by the fact that the resource is vibratory and stochastic, with a low quality factor. It has recently been shown that when constrained to causality, the optimal feedback controller for a WEC is solvable in closed-form as a sign-indefinite LQG problem, for the case in which the WEC exhibits linear dynamics and quadratic power transmission dissipation. However, most WECs exhibit stroke limits, which must be explicitly accounted for in control design to avoid end-stop collisions. This is important because such collisions lead to damage, and also because the introduction of unmodeled stroke limits can actually destabilize the otherwise-optimal closed loop. We illustrate a control design technique to address this issue, which consists of two design steps. In the first step, LMI techniques are used to optimize the mean power harvested from waves with a known power spectral density, subject to several competing objectives. In the second step, the controller is augmented via a nonlinear passivity-based outer-loop design which guarantees to prevent stroke saturation while also guaranteeing to preserve closed-loop stability. Furthermore, the technique is illustrated using a model of a simple heaving point absorber, and verified in simulation.

16 TIDAL AND WAVE POWER↗
NASA NTRSDate not supplied

Fast Aircraft Separation Calculations for Gradient Based Optimization of Airspace Simulations

Simulations of airspace operational concepts can play a significant role in determining future paradigms that would allow for a safe increase in airspace density. In particular, airspace simulations which are capable of handling large numbers of aircraft act as an enabling capability for the testing of proposed airspace operational concepts. Simulations allowing for gradient based optimization methods are particularly attractive, since they would potentially allow for an efficient and empirical means to derive best operational practices. These could also allow for vehicle multidisciplinary design and optimization studies to include air traffic management considerations as a discipline. But any large scale simulation of airspace operations must include some methodology for addressing airspace separation requirements, which in the most direct sense would be tracked in a manner that computationally grows as a quadratic function of the number of simulated aircraft. Efficient indirect methods have been developed in certain contexts to address this limitation. However, any means of addressing separation requirements in a gradient based optimization context should be implemented by functions which provide analytic derivative information to maximize numerical precision and computational efficiency. In this paper, a fast and differentiable separation metric is described in application to gradient based optimization of airspace operations. Rather than computing the separation distance between every pair of aircraft in a simulation, this method effectively reduces the problem to a smaller relevant set using a geometric decomposition. This method guarantees that the smallest distance at all points in simulated time is determined exactly. When used in an optimization constraint context, this guarantees that a minimum separation is maintained between all pairs of aircraft. The presented metric has logarithmic computational growth with respect to the number of simulated aircraft, and is shown to perform well in a series of notional 2D airspace optimization problems when used to enforce specified airborne separation constraints. Results show that this is notably faster than a direct pairwise distance computing metric for optimizations involving both small and large numbers of aircraft, yet enforce separation requirements to the same tolerance. It is shown that this favorable scalability is an enabling capability for more sophisticated air traffic management conceptual studies.

Optimization↗
DOE OSTI2017

Optimal Bandwidth for Multitaper Spectrum Estimation

A systematic method for bandwidth parameter selection is desired for Thomson multitaper spectrum estimation. We give a method for determining the optimal bandwidth based on a mean squared error (MSE) criterion. When the true spectrum has a second-order Taylor series expansion, one can express quadratic local bias as a function of the curvature of the spectrum, which can be estimated by using a simple spline approximation. This is combined with a variance estimate, obtained by jackknifing over individual spectrum estimates, to produce an estimated MSE for the log spectrum estimate for each choice of time-bandwidth product. The bandwidth that minimizes the estimated MSE then gives the desired spectrum estimate. Additionally, the bandwidth obtained using our method is also optimal for cepstrum estimates. We give an example of a damped oscillatory (Lorentzian) process in which the approximate optimal bandwidth can be written as a function of the damping parameter. Furthermore, the true optimal bandwidth agrees well with that given by minimizing estimated the MSE in these examples.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1990

Optical neural network system for pose determination of spinning satellites

An optical neural network architecture and algorithm based on a Hopfield optimization network are presented for multitarget tracking. This tracker utilizes a neuron for every possible target track, and a quadratic energy function of neural activities which is minimized using gradient descent neural evolution. The neural net tracker is demonstrated as part of a system for determining position and orientation (pose) of spinning satellites with respect to a robotic spacecraft. The input to the system is time sequence video from a single camera. Novelty detection and filtering are utilized to locate and segment novel regions from the input images. The neural net multitarget tracker determines the correspondences (or tracks) of the novel regions as a function of time, and hence the paths of object (satellite) parts. The path traced out by a given part or region is approximately elliptical in image space, and the position, shape and orientation of the ellipse are functions of the satellite geometry and its pose. Having a geometric model of the satellite, and the elliptical path of a part in image space, the three-dimensional pose of the satellite is determined. Digital simulation results using this algorithm are presented for various satellite poses and lighting conditions.

Lee, Andrew↗
NASA NTRS1990

Second-order design sensitivities for linear elastic problems

The subject of this paper is the efficient and accurate determination of second-order design sensitivities in elastic bodies. The approach being carried out here is the direct differentiation of the governing derivative boundary element method (DBEM) formulation of the problem. Second-order sensitivities of boundary stresses are obtained in an elegant manner. A numerical implementation of the method is carried out with isoparametric quadratic boundary elements and numerical results are presented for several sample problems. Considerable savings in computational effort for an optimization procedure is possible through the use of efficiently determined accurate second-order design sensitivities.

Zhang, Qing↗
NASA NTRS1989

Integrated control-system design via generalized LQG (GLQG) theory

Thirty years of control systems research has produced an enormous body of theoretical results in feedback synthesis. Yet such results see relatively little practical application, and there remains an unsettling gap between classical single-loop techniques (Nyquist, Bode, root locus, pole placement) and modern multivariable approaches (LQG and H infinity theory). Large scale, complex systems, such as high performance aircraft and flexible space structures, now demand efficient, reliable design of multivariable feedback controllers which optimally tradeoff performance against modeling accuracy, bandwidth, sensor noise, actuator power, and control law complexity. A methodology is described which encompasses numerous practical design constraints within a single unified formulation. The approach, which is based upon coupled systems or modified Riccati and Lyapunov equations, encompasses time-domain linear-quadratic-Gaussian theory and frequency-domain H theory, as well as classical objectives such as gain and phase margin via the Nyquist circle criterion. In addition, this approach encompasses the optimal projection approach to reduced-order controller design. The current status of the overall theory will be reviewed including both continuous-time and discrete-time (sampled-data) formulations.

Bernstein, Dennis S.↗
DOE OSTI2019

Optimizing multi-modal, non-axisymmetric plasma response metrics with additional coil rows on DIII-D

The expansion of the DIII-D tokamak operational space via the addition of new non-axisymmetric coil rows is investigated using the linear MHD plasma response code MARS-F. The plasma response to magnetic perturbations imposed by five distinct low- and high-field side coil geometries is modeled for toroidal mode numbers up to n = 6. A set of linear (~δB^2: resonant, kink mode amplitude) and quadratic (~δB: core and edge integrated NTV torque) plasma metrics are defined and compared directly for the various coil geometries. Coil size is also scanned as a secondary optimization variable. An in-vessel coil located at the low-field side midplane is identified as the most efficient plasma response actuator across all metrics and toroidal mode numbers. The multi-row combination of this new midplane (M) coil with the existing DIII-D non-axisymmetric coil set is considered in numerical optimization studies to quantify the impact of this new coil on modeled plasma response metrics. The addition of the M coil is shown to significantly increase the actuator efficiency in maximizing individual plasma response metrics as well as maximizing multi-modal ratios of response metrics, e.g. maximizing resonant modes or edge NTV torque while minimizing kink modes or core NTV torque. The ex-vessel midplane (C) coil is also observed to have an outsize effect on multi-modal optimization due to its uniquely narrow poloidal spectra, and the expansion of optimization space due to the combined use of the two existing in-vessel coil rows with both the M and C coils is notably larger than either coil's individual contribution even though both share similar poloidal locations. This four-row system is expected to greatly extend abilities to understand and optimize the control of transients and rotation on the DIII-D tokamak.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1986

Optimal control laws for microburst encounter

Simplified structures for longitudinal control laws that reduce an aircraft's response to the strong head-tailwind and downdraft variations associated with microbursts are presented. They are based on non-zero-set-point linear-quadratic regulators that command throttle setting and angle of attack as functions of velocity and flight path angle, and they can incorporate direct measurements of the wind profile if available. Selection of cost functions to be minimized by feedback control has been aided by a prior study of classical control laws and exact nonlinear-optimal flight paths through realistic microburst wind profiles. The resulting optimal control laws have an adaptive, dual-mode structure that can be implemented either in flight-director logic or in an autopilot.

Stengel, R. F.↗
NASA NTRS1972

Davidon-Broyden rank-one minimization methods in Hilbert space with application to optimal control problems

The Davidon-Broyden class of rank one, quasi-Newton minimization methods is extended from Euclidean spaces to infinite-dimensional, real Hilbert spaces. For several techniques of choosing the step size, conditions are found which assure convergence of the associated iterates to the location of the minimum of a positive definite quadratic functional. For those techniques, convergence is achieved without the problem of the computation of a one-dimensional minimum at each iteration. The application of this class of minimization methods for the direct computation of the solution of an optimal control problem is outlined. The performance of various members of the class are compared by solving a sample optimal control problem. Finally, the sample problem is solved by other known gradient methods, and the results are compared with those obtained with the rank one quasi-Newton methods.

Straeter, T. A.↗
NASA NTRS1984

Application of optimization techniques to the design of a flutter suppression control law for the DAST ARW-2

The design of a candidate flutter suppression (FS) control law for the symmetric degrees of freedom for the DAST ARW-2 aircraft is discussed. The results illustrate the application of several currently employed control law design techniques. Subsequent designs, obtained as the mathematical model of the ARW-2 is updated, are expected to employ similar methods and to provide a control law whose performance will be flight tested. This study represents one of the steps necessary to provide an assessment of the validity of applying current control law synthesis and analysis techniques in the design of actively controlled aircraft. Mathematical models employed in the control law design and evaluation phases are described. The control problem is specified by presenting the flutter boundary predicted for the uncontrolled aircraft and by defining objectives and constraints that the controller should satisfy. A full-order controller is obtained by using Linear Quadratic Gaussian (LQG) techniques. The process of obtaining an implementable reduced-order controller is described. One example is also shown in which constrained optimization techniques are utilized to explicitly include robustness criteria within the design algorithm.

Adams, W. M., Jr.↗