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Results for “Quadratic 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 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Advanced rotorcraft control using parameter optimization

A reliable algorithm for the evaluation of a quadratic performance index and its gradients with respect to the controller design parameters is presented. The algorithm is part of a design algorithm for an optimal linear dynamic output feedback controller that minimizes a finite time quadratic performance index. The numerical scheme is particularly robust when it is applied to the control law synthesis for systems with densely packed modes and where there is a high likelihood of encountering degeneracies in the closed loop eigensystem. This approach through the use of a accurate Pade series approximation does not require the closed loop system matrix to be diagonalizable. The algorithm has been included in a control design package for optimal robust low order controllers. Usefulness of the proposed numerical algorithm has been demonstrated using numerous practical design cases where degeneracies occur frequently in the closed loop system under an arbitrary controller design initialization and during the numerical search.

Vansteenwyk, Brett↗
NASA NTRS1981

Electro-optical processor for optimal control

An iterative optical processor has been developed for applications in the optimal control of advanced sensor systems. The processor is designed for the realization of the Richardson algorithm on bipolar data, using as input a linear array of LEDs. The usefulness of the processor has been demonstrated by the solution of the linear quadratic regulator problem for the optimal control signals of the F100 turbofan engine. In this case study, the algebraic Riccati equation matrix was solved by the use of a modified Kleinman algorithm along with the Richardson algorithm applied to a system of linear algebraic equations. Preliminary experimental results demonstrate the gradual convergence of the processor.

Casasent, D.↗
DOE OSTI2015

A Bound- and Equality-Constrained Quadratic Programming Method for Image Reconstruction

Image deblurring is modeled as an ill-posed, linear inverse problem and can be written in terms of an optimization problem. By adding bound and equality constraints and/or penalty terms to the objective function, the problem is regularized and a viable solution exists; however, there are few methods available for solving such constrained problems. Here we formulate two regularized solutions into constrained optimization problems and adapt an iterative augmented Lagrangian solver. Results are shown on synthetic data in one- and two-dimensions, as well as on a radiograph used to calibrate the transmission curve of a pulsed power X-ray source at a U.S. Department of Energy radiography facility.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS1989

Active vibration mitigation of distributed parameter, smart-type structures using Pseudo-Feedback Optimal Control (PFOC)

A new, near-optimal feedback control technique is introduced that is shown to provide excellent vibration attenuation for those distributed parameter systems that are often encountered in the areas of aeroservoelasticity and large space systems. The technique relies on a novel solution methodology for the classical optimal control problem. Specifically, the quadratic regulator control problem for a flexible vibrating structure is first cast in a weak functional form that admits an approximate solution. The necessary conditions (first-order) are then solved via a time finite-element method. The procedure produces a low dimensional, algebraic parameterization of the optimal control problem that provides a rigorous basis for a discrete controller with a first-order like hold output. Simulation has shown that the algorithm can successfully control a wide variety of plant forms including multi-input/multi-output systems and systems exhibiting significant nonlinearities. In order to firmly establish the efficacy of the algorithm, a laboratory control experiment was implemented to provide planar (bending) vibration attenuation of a highly flexible beam (with a first clamped-free mode of approximately 0.5 Hz).

Patten, W. N.↗
NASA NTRS1989

Design for steering accuracy in antenna arrays using shared optical phase shifters

Uniform linear phased arrays where many radiating elements share a relatively small number of phase shifters are investigated. Such architectures arise in arrays which derive the time delays in the signal paths from a small group of independent phase shifters. In particular, a true time-delay device which has been suggested recently for optically controlled arrays is used as the basic phase shifter. Different architectures, viz. alternative procedures of deriving the necessary time delay for each antenna in the face of phase-shifter inaccuracies, are examined. The variance of the steered beam's direction is used as the performance criterion. The direction-optimal architecture is obtained by means of quadratic programming, and is shown not to be unique. The nonuniqueness of the optimal architecture is exploited to improve other characteristics of the array's beam shape, and the optimal solution is shown to compare favorably with a suboptimal interleaved solution which is easier to implement.

Kam, Moshe↗
DOE OSTI2025

Alternative mixed integer linear programming optimization for joint job scheduling and data allocation in grid computing

This paper presents a novel approach to the joint optimization of job scheduling and data allocation in grid computing environments. We formulate this joint optimization problem as a mixed integer quadratically constrained program. To tackle the nonlinearity in the constraint, we alternatively fix a subset of decision variables and optimize the remaining ones via Mixed Integer Linear Programming (MILP). We solve the MILP problem at each iteration via an off-the-shelf MILP solver. Our experimental results show that our method significantly outperforms existing heuristic methods, employing either independent optimization or joint optimization strategies. We have also verified the generalization ability of our method over grid environments with various sizes and its high robustness to the algorithm setting.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

The potential of quantum annealing for rapid solution structure identification

Abstract The recent emergence of novel computational devices, such as quantum computers, coherent Ising machines, and digital annealers presents new opportunities for hardware-accelerated hybrid optimization algorithms. Unfortunately, demonstrations of unquestionable performance gains leveraging novel hardware platforms have faced significant obstacles. One key challenge is understanding the algorithmic properties that distinguish such devices from established optimization approaches. Through the careful design of contrived optimization tasks, this work provides new insights into the computation properties of quantum annealing and suggests that this model has the potential to quickly identify the structure of high-quality solutions. A meticulous comparison to a variety of algorithms spanning both complete and local search suggests that quantum annealing’s performance on the proposed optimization tasks is distinct. This result provides new insights into the time scales and types of optimization problems where quantum annealing has the potential to provide notable performance gains over established optimization algorithms and suggests the development of hybrid algorithms that combine the best features of quantum annealing and state-of-the-art classical approaches.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1976

Trends in modern system theory

The topics considered are related to linear control system design, adaptive control, failure detection, control under failure, system reliability, and large-scale systems and decentralized control. It is pointed out that the design of a linear feedback control system which regulates a process about a desirable set point or steady-state condition in the presence of disturbances is a very important problem. The linearized dynamics of the process are used for design purposes. The typical linear-quadratic design involving the solution of the optimal control problem of a linear time-invariant system with respect to a quadratic performance criterion is considered along with gain reduction theorems and the multivariable phase margin theorem. The stumbling block in many adaptive design methodologies is associated with the amount of real time computation which is necessary. Attention is also given to the desperate need to develop good theories for large-scale systems, the beginning of a microprocessor revolution, the translation of the Wiener-Hopf theory into the time domain, and advances made in dynamic team theory, dynamic stochastic games, and finite memory stochastic control.

Athans, M.↗
DOE OSTI2016

Coronary artery analysis: Computer-assisted selection of best-quality segments in multiple-phase coronary CT angiography

Purpose: The authors are developing an automated method to identify the best-quality coronary arterial segment from multiple-phase coronary CT angiography (cCTA) acquisitions, which may be used by either interpreting physicians or computer-aided detection systems to optimally and efficiently utilize the diagnostic information available in multiple-phase cCTA for the detection of coronary artery disease. Methods: After initialization with a manually identified seed point, each coronary artery tree is automatically extracted from multiple cCTA phases using our multiscale coronary artery response enhancement and 3D rolling balloon region growing vessel segmentation and tracking method. The coronary artery trees from multiple phases are then aligned by a global registration using an affine transformation with quadratic terms and nonlinear simplex optimization, followed by a local registration using a cubic B-spline method with fast localized optimization. The corresponding coronary arteries among the available phases are identified using a recursive coronary segment matching method. Each of the identified vessel segments is transformed by the curved planar reformation (CPR) method. Four features are extracted from each corresponding segment as quality indicators in the original computed tomography volume and the straightened CPR volume, and each quality indicator is used as a voting classifier for the arterial segment. A weighted voting ensemble (WVE) classifier is designed to combine the votes of the four voting classifiers for each corresponding segment. The segment with the highest WVE vote is then selected as the best-quality segment. In this study, the training and test sets consisted of 6 and 20 cCTA cases, respectively, each with 6 phases, containing a total of 156 cCTA volumes and 312 coronary artery trees. An observer preference study was also conducted with one expert cardiothoracic radiologist and four nonradiologist readers to visually rank vessel segment quality. The performance of our automated method was evaluated by comparing the automatically identified best-quality segments identified by the computer to those selected by the observers. Results: For the 20 test cases, 254 groups of corresponding vessel segments were identified after multiple phase registration and recursive matching. The AI-BQ segments agreed with the radiologist’s top 2 ranked segments in 78.3% of the 254 groups (Cohen’s kappa 0.60), and with the 4 nonradiologist observers in 76.8%, 84.3%, 83.9%, and 85.8% of the 254 groups. In addition, 89.4% of the AI-BQ segments agreed with at least two observers’ top 2 rankings, and 96.5% agreed with at least one observer’s top 2 rankings. In comparison, agreement between the four observers’ top ranked segment and the radiologist’s top 2 ranked segments were 79.9%, 80.7%, 82.3%, and 76.8%, respectively, with kappa values ranging from 0.56 to 0.68. Conclusions: The performance of our automated method for selecting the best-quality coronary segments from a multiple-phase cCTA acquisition was comparable to the selection made by human observers. This study demonstrates the potential usefulness of the automated method in clinical practice, enabling interpreting physicians to fully utilize the best available information in cCTA for diagnosis of coronary disease, without requiring manual search through the multiple phases and minimizing the variability in image phase selection for evaluation of coronary artery segments across the diversity of human readers with variations in expertise.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2018

Gaussian process based optimization of molecular geometries using statistically sampled energy surfaces from quantum Monte Carlo

Optimization of atomic coordinates and lattice parameters remains a significant challenge to the wide use of stochastic electronic structure methods such as quantum Monte Carlo (QMC). Measurements of the forces and stress tensor by these methods contain statistical errors, challenging conventional gradient-based numerical optimization methods that assume deterministic results. Additionally, forces are not yet available for some methods, wavefunctions, and basis sets and when available may be expensive to compute to sufficiently high statistical accuracy near energy minima, where the energy surfaces are flat. Here, we explore the use of Gaussian process based techniques to sample the energy surfaces and reduce sensitivity to the statistical nature of the problem. We utilize Latin hypercube sampling, with the number of sampled energy points scaling quadratically with the number of optimized parameters. Furthermore, we show these techniques may be successfully applied to systems consisting of tens of parameters, demonstrating QMC optimization of a benzene molecule starting from a randomly perturbed, broken symmetry geometry.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1987

Approximation of discrete-time LQG compensators for distributed systems with boundary input and unbounded measurement

The approximation of optimal discrete-time linear quadratic Gaussian (LQG) compensators for distributed parameter control systems with boundary input and unbounded measurement is considered. The approach applies to a wide range of problems that can be formulated in a state space on which both the discrete-time input and output operators are continuous. Approximating compensators are obtained via application of the LQG theory and associated approximation results for infinite dimensional discrete-time control systems with bounded input and output. Numerical results for spline and modal based approximation schemes used to compute optimal compensators for a one dimensional heat equation with either Neumann or Dirichlet boundary control and pointwise measurement of temperature are presented and discussed.

Gibson, J. S.↗
NASA NTRS1988

Approximation of discrete-time LQG compensators for distributed systems with boundary input and unbounded measurement

The approximation of optimal discrete-time linear quadratic Gaussian (LQG) compensators for distributed parameter control systems with boundary input and unbounded measurement is considered. The approach applies to a wide range of problems that can be formulated in a state space on which both the discrete-time input and output operators are continuous. Approximating compensators are obtained via application of the LQG theory and associated approximation results for infinite dimensional discrete-time control systems with bounded input and output. Numerical results for spline and modal based approximation schemes used to compute optimal compensators for a one-dimensional heat equation with either Neumann or Dirichlet boundary control and pointwise measurement of temperature are presented and discussed.

Gibson, J. S.↗
NASA NTRS1988

Modeling and control of flexible structures

This monograph presents integrated modeling and controller design methods for flexible structures. The controllers, or compensators, developed are optimal in the linear-quadratic-Gaussian sense. The performance objectives, sensor and actuator locations and external disturbances influence both the construction of the model and the design of the finite dimensional compensator. The modeling and controller design procedures are carried out in parallel to ensure compatibility of these two aspects of the design problem. Model reduction techniques are introduced to keep both the model order and the controller order as small as possible. A linear distributed, or infinite dimensional, model is the theoretical basis for most of the text, but finite dimensional models arising from both lumped-mass and finite element approximations also play an important role. A central purpose of the approach here is to approximate an optimal infinite dimensional controller with an implementable finite dimensional compensator. Both convergence theory and numerical approximation methods are given. Simple examples are used to illustrate the theory.

Gibson, J. S.↗
NASA NTRS1973

Optimization of structures to satisfy a flutter velocity constraint by use of quadratic equation fitting

Using the first and the second derivative of flutter velocity with respect to the parameters, the velocity hypersurface is made quadratic. This greatly simplifies the numerical procedure developed for determining the values of the design parameters such that a specified flutter velocity constraint is satisfied and the total structural mass is near a relative minimum. A search procedure is presented utilizing two gradient search methods and a gradient projection method. The procedure is applied to the design of a box beam, using finite-element representation. The results indicate that the procedure developed yields substantial design improvement satisfying the specified constraint and does converge to near a local optimum.

Motiwalla, S. K.↗
DOE OSTI2022

Machine Learning with Gradient-Based Optimization of Nuclear Waste Vitrification with Uncertainties and Constraints

Gekko is an optimization suite in Python that solves optimization problems involving mixed-integer, nonlinear, and differential equations. The purpose of this study is to integrate common Machine Learning (ML) algorithms such as Gaussian Process Regression (GPR), support vector regression (SVR), and artificial neural network (ANN) models into Gekko to solve data based optimization problems. Uncertainty quantification (UQ) is used alongside ML for better decision making. These methods include ensemble methods, model-specific methods, conformal predictions, and the delta method. An optimization problem involving nuclear waste vitrification is presented to demonstrate the benefit of ML in this field. ML models are compared against the current partial quadratic mixture (PQM) model in an optimization problem in Gekko. GPR with conformal uncertainty was chosen as the best substitute model as it had a lower mean squared error of 0.0025 compared to 0.018 and more confidently predicted a higher waste loading of 37.5 wt% compared to 34 wt%. The example problem shows that these tools can be used in similar industry settings where easier use and better performance is needed over classical approaches. Future works with these tools include expanding them with other regression models and UQ methods, and exploration into other optimization problems or dynamic control.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2025

Impact and mitigation of polarized extragalactic foregrounds on Bayesian cosmic microwave background lensing

Future low-noise cosmic microwave background (CMB) lensing measurements from e.g., CMB-S4 will be polarization dominated, rather than temperature dominated. In this new regime, statistically optimal lensing reconstructions outperform the standard quadratic estimator, but their sensitivity to extragalactic polarized foregrounds has not been quantified. Using realistic simulations of polarized radio and infrared point sources, we show for the first time that optimal Bayesian lensing from a CMB-S4-like experiment is insensitive to the expected level of polarized extragalactic foregrounds after masking, as long as an accurate foreground power spectrum is included in the analysis. For more futuristic experiments where these foregrounds could cause a detectable bias, we propose a new method to jointly fit for lensing and the Poisson foregrounds, generalizing the bias hardening from the standard quadratic estimator to Bayesian lensing.

cosmic microwave background↗
DOE OSTI2018

Control of Three Degrees-of-Freedom Wave Energy Converters Using Pseudo-Spectral Methods

This study presents a solution to the optimal control problem of a three degrees-of-freedom (3DOF) wave energy converter (WEC). The three modes are the heave, pitch, and surge. The dynamic model is characterized by a coupling between the pitch and surge modes, while the heave is decoupled. The heave, however, excites the pitch motion through nonlinear parametric excitation in the pitch mode. This paper uses Fourier series (FS) as basis functions to approximate the states and the control. A simplified model is first used where the parametric excitation term is neglected and a closed-form solution for the optimal control is developed. For the parametrically excited case, a sequential quadratic programming approach is implemented to solve for the optimal control numerically. Numerical results show that the harvested energy from three modes is greater than three times the harvested energy from the heave mode alone. Moreover, the harvested energy using a control that accounts for the parametric excitation is significantly higher than the energy harvested when neglecting this nonlinear parametric excitation term.

16 TIDAL AND WAVE POWER↗