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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 649 records · Page 36
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Maximum a posteriori CMB lensing reconstruction

Gravitational lensing of the CMB is a valuable cosmological signal that correlates to tracers of large-scale structure and acts as a important source of confusion for primordial B-mode polarization. State-of-the-art lensing reconstruction analyses use quadratic estimators, which are easily applicable to data. Yet, these estimators are known to be suboptimal, in particular for polarization, and large improvements are expected to be possible for high signal-to-noise polarization experiments. We develop a method and numerical code, LensIt, that is able to find efficiently the most probable lensing map, introducing no significant approximations to the lensed CMB likelihood, and applicable to beamed and masked data with inhomogeneous noise. It works by iteratively reconstructing the primordial unlensed CMB using a deflection estimate and its inverse, and removing residual lensing from these maps with quadratic estimator techniques. Roughly linear computational cost is maintained due to fast convergence of iterative searches, combined with the local nature of lensing. The technique achieves the maximal improvement in signal to noise expected from analytical considerations on the unmasked parts of the sky. Delensing with this optimal map leads to forecast tensor-to-scalar ratio parameter errors improved by a factor ≃2 compared to the quadratic estimator in a CMB stage IV configuration.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Online Optimization as a Feedback Controller: Stability and Tracking

This paper develops and analyzes feedback-based online optimization methods to regulate the output of a linear time-invariant (LTI) dynamical system to the optimal solution of a time-varying convex optimization problem. The design of the algorithm is based on continuous-time primal-dual dynamics, properly modified to incorporate feedback from the LTI dynamical system, applied to a proximal augmented Lagrangian function. The resultant closed-loop algorithm tracks the solution of the time-varying optimization problem without requiring knowledge of (time-varying) disturbances in the dynamical system. The analysis leverages integral quadratic constraints to provide linear matrix inequality (LMI) conditions that guarantee global exponential stability and bounded tracking error. Analytical results show that, under a sufficient time-scale separation between the dynamics of the LTI dynamical system and the algorithm, the LMI conditions can be always satisfied. The paper further proposes a modified algorithm that can track an approximate solution trajectory of the constrained optimization problem under less restrictive assumptions. As an illustrative example, the proposed algorithms are showcased for power transmission systems, to compress the time scales between secondary and tertiary control, and allow to simultaneously power re-balancing and tracking of DC optimal power flow points.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1988

Optimal discrete-time LQR problems for parabolic systems with unbounded input: Approximation and convergence

An abstract approximation and convergence theory for the closed-loop solution of discrete-time linear-quadratic regulator problems for parabolic systems with unbounded input is developed. Under relatively mild stabilizability and detectability assumptions, functional analytic, operator techniques are used to demonstrate the norm convergence of Galerkin-based approximations to the optimal feedback control gains. The application of the general theory to a class of abstract boundary control systems is considered. Two examples, one involving the Neumann boundary control of a one-dimensional heat equation, and the other, the vibration control of a cantilevered viscoelastic beam via shear input at the free end, are discussed.

Rosen, I. G.↗
NASA NTRS2004

A Study of Penalty Function Methods for Constraint Handling with Genetic Algorithm

COMETBOARDS (Comparative Evaluation Testbed of Optimization and Analysis Routines for Design of Structures) is a design optimization test bed that can evaluate the performance of several different optimization algorithms. A few of these optimization algorithms are the sequence of unconstrained minimization techniques (SUMT), sequential linear programming (SLP) and the sequential quadratic programming techniques (SQP). A genetic algorithm (GA) is a search technique that is based on the principles of natural selection or "survival of the fittest". Instead of using gradient information, the GA uses the objective function directly in the search. The GA searches the solution space by maintaining a population of potential solutions. Then, using evolving operations such as recombination, mutation and selection, the GA creates successive generations of solutions that will evolve and take on the positive characteristics of their parents and thus gradually approach optimal or near-optimal solutions. By using the objective function directly in the search, genetic algorithms can be effectively applied in non-convex, highly nonlinear, complex problems. The genetic algorithm is not guaranteed to find the global optimum, but it is less likely to get trapped at a local optimum than traditional gradient-based search methods when the objective function is not smooth and generally well behaved. The purpose of this research is to assist in the integration of genetic algorithm (GA) into COMETBOARDS. COMETBOARDS cast the design of structures as a constrained nonlinear optimization problem. One method used to solve constrained optimization problem with a GA to convert the constrained optimization problem into an unconstrained optimization problem by developing a penalty function that penalizes infeasible solutions. There have been several suggested penalty function in the literature each with there own strengths and weaknesses. A statistical analysis of some suggested penalty functions is performed in this study. Also, a response surface approach to robust design is used to develop a new penalty function approach. This new penalty function approach is then compared with the other existing penalty functions.

Ortiz, Francisco↗
NASA NTRS1981

Antenna optimization and cost consideration for the Solar Power Satellite microwave system

The sizing, criteria, cost analysis, and optimized taper of the Solar Power Satellite (SPS) transmitting antenna are discussed. The sizing parameters considered were a thermal limit of 23 kW/sq m in the antenna, a peak power density of 23 mW/sq cm in the ionosphere, and cost effectiveness. Cost schedules and equations are presented for the SPS, and four antenna tapers are analyzed and compared, including the reference 10 dB Gaussian taper. An even powered quadratic series is formulated to minimize electricity cost and stay within thermal and ionospheric power level limits. The optimized Johnson Space Center taper is found to display the lowest energy costs, 4% below the 10 dB Gaussian, and can deliver 5.69 GW at 45.4 mills/kWh to the grid. Further studies are indicated for the optimal antenna and rectenna sizes

Kerwin, E. M.↗
NASA NTRS1989

Locally optimal-digital redesign of continuous-time systems

This paper presents a new optimal digital redesign technique for finding a dynamic digital control law from the given continuous-time counterpart by minimizing a local quadratic performance index. The quadratic performance index is chosen as the integral of the weighted squared difference between the states of the original closed-loop system and those of the digitally controlled closed-loop system at any instant between each sampling period. The developed optimal digital redesign control law enables the states of the digitally controlled closed-loop system 10 closely match those of the original closed-loop system at any instant between each sampling period, and it can easily be implemented using microcomputers with a relatively large sampling period.

Shieh, Leang-San↗
NASA NTRSDate not supplied

Path Planning: Differential Dynamic Programming and Model Predictive Path Integral Control on VTOL Aircraft

This paper explores two optimal control approaches, widely used in robotics, to establish their viability as real-time trajectory planners for vehicle configurations envisioned for the emerging aviation sector of Urban Air Mobility (UAM). Differential Dynamic Programming (DDP) enables planning over highly nonlinear dynamics using second-order approximations along a nominal trajectory, and displays quadratic convergence to a local solution. Model Predictive Path Integral (MPPI) is a stochastic sampling-based algorithm that can optimize for general cost criteria, including potentially highly nonlinear formulations, and supports parallel computation through the use of modern GPU hardware. In this work, DDP and MPPI were implemented using model predictive control (MPC), and the results indicate they are able to successfully transition the aircraft over different flight envelopes and generate trajectories unique to UAM vehicles.

Differential Dynamic Programming↗
DOE OSTI2016

TH-CD-207B-09: Task-Driven Fluence Field Modulation Design for Model-Based Iterative Reconstruction in CT

Purpose: There has been increasing interest in integrating fluence field modulation (FFM) devices with diagnostic CT scanners for dose reduction purposes. Conventional FFM strategies, however, are often either based on heuristics or the analysis of filtered-backprojection (FBP) performance. This work investigates a prospective task-driven optimization of FFM for model-based iterative reconstruction (MBIR) in order to improve imaging performance at the same total dose as conventional strategies. Methods: The task-driven optimization framework utilizes an ultra-low dose 3D scout as a patient-specific anatomical model and a mathematical formation of the imaging task. The MBIR method investigated is quadratically penalized-likelihood reconstruction. The FFM objective function uses detectability index, d’, computed as a function of the predicted spatial resolution and noise in the image. To optimize performance throughout the object, a maxi-min objective was adopted where the minimum d’ over multiple locations is maximized. To reduce the dimensionality of the problem, FFM is parameterized as a linear combination of 2D Gaussian basis functions over horizontal detector pixels and projection angles. The coefficients of these bases are found using the covariance matrix adaptation evolution strategy (CMA-ES) algorithm. The task-driven design was compared with three other strategies proposed for FBP reconstruction for a calcification cluster discrimination task in an abdomen phantom. Results: The task-driven optimization yielded FFM that was significantly different from those designed for FBP. Comparing all four strategies, the task-based design achieved the highest minimum d’ with an 8–48% improvement, consistent with the maxi-min objective. In addition, d’ was improved to a greater extent over a larger area within the entire phantom. Conclusion: Results from this investigation suggests the need to re-evaluate conventional FFM strategies for MBIR. The task-based optimization framework provides a promising approach that maximizes imaging performance under the same total dose constraint.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Optimality and Noise Resilience of Critical Quantum Sensing

We compare critical quantum sensing to passive quantum strategies to perform frequency estimation, in the case of single-mode quadratic Hamiltonians. We show that, while in the unitary case both strategies achieve precision scaling quadratic with the number of photons, in the presence of dissipation this is true only for critical strategies. We also establish that working at the exceptional point or beyond threshold provides suboptimal performance. This critical enhancement is due to the emergence of a transient regime in the open critical dynamics, and is invariant to temperature changes. When considering both time and system size as resources, for both strategies the precision scales linearly with the product of the total time and the number of photons, in accordance with fundamental bounds. However, we show that critical protocols outperform optimal passive strategies if preparation and measurement times are not negligible. Our results are applicable to a broad variety of critical sensors whose phenomenology can be reduced to that of a single-mode quadratic Hamiltonian, including systems described by finite-component and fully connected models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

A neuro approach to solve fuzzy Riccati differential equations

There are many applications of optimal control theory especially in the area of control systems in engineering. In this paper, fuzzy quadratic Riccati differential equation is estimated using neural networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). The solution can be achieved by solving the 1st Order Non-linear Differential Equation (ODE) that is found commonly in Riccati differential equation. Research has shown improved results relatively to the RK4 method. It can be said that NN approach shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over RK4.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Calibration of Car-Following Models Using a Dual Genetic Algorithm with Central Composite Design

We report the calibration of microscopic traffic simulation models has received much attention in the simulation field. Although no standard has been established for it, a genetic algorithm (GA) has been widely employed in recent literature because of its high efficiency to find solutions in such optimization problems. However, the performance still falls short in simulation analyses to support fast decision making. This paper proposes a new calibration procedure using a dual GA and central composite design (CCD) in order to improve the efficiency. The calibration exercise goes through three major sequential steps: (1) experimental design using CCD for a quadratic response surface model (RSM) estimation, (2) 1st GA procedure using the RSM with CCD to find a near-optimal initial population for a next step, and (3) 2nd GA procedure to find a final solution. The proposed method was applied in calibrating the Gipps car-following model with respect to maximizing the likelihood of a spacing distribution between a lead and following vehicle. In order to evaluate the performance of the proposed method, a conventional calibration approach using a single GA was compared under both simulated and real vehicle trajectory data. It was found that the proposed approach enhances the optimization speed by starting to search from an initial population that is closer to the optimum than that of the other approach. This result implies the proposed approach has benefits for a large-scale traffic network simulation analysis. Finally, this method can be extended to other optimization tasks using GA in transportation studies.

42 ENGINEERING↗
NASA NTRS1988

Efficient approximation concepts using second order information

The application of second derivative information for solving structural optimization problems is considered. In the present method, rather than building approximate nonlinear forms for the objective function and constraints, only linear approximations are used. A separable quadratic approximation of the Lagrangian function is included in the subproblem statement. The method has been successfully used for simple problems that can be solved in closed form, in addition to the sizing optimization of trusses, and it is shown to converge faster than the convex linearization method or the method of moving asymptotes.

Fleury, Claude↗
DOE OSTI2024

Projective Integral Updates for High-Dimensional Variational Inference

Variational inference is an approximation framework for Bayesian inference that seeks to improve quantified uncertainty in predictions by optimizing a simplified distribution over parameters to stand in for the full posterior. Capturing model variations that remain consistent with training data enables more robust predictions by reducing parameter sensitivity. This work introduces a fixed-point optimization for variational inference that is applicable when every feasible log density can be expressed as a linear combination of functions from a given basis. In such cases, the optimizer becomes a fixed-point of projective integral updates. When the basis spans univariate quadratics in each parameter, the feasible distributions are Gaussian mean-fields and the projective integral updates yield quasi-Newton variational Bayes (QNVB). Other bases and updates are also possible. Since these updates require high-dimensional integration, this work begins by proposing an efficient quasirandom sequence of quadratures for mean-field distributions. Each iterate of the sequence contains two evaluation points that combine to correctly integrate all univariate quadratic functions and, if the mean-field factors are symmetric, all univariate cubics. More importantly, averaging results over short subsequences achieves periodic exactness on a much larger space of multivariate polynomials of quadratic total degree. The corresponding variational updates require four loss evaluations with standard (not second-order) backpropagation to eliminate error terms from over half of all multivariate quadratic basis functions. Furthermore, this integration technique is motivated by first proposing stochastic blocked mean-field quadratures, which may be useful in other contexts. A PyTorch implementation of QNVB allows for better control over model uncertainty during training than competing methods. Experiments demonstrate superior generalizability for multiple learning problems and architectures.

Gaussian mean-field↗
NASA NTRS1984

Development and testing of stable, invariant, isoparametric curvilinear 2- and 3-D hybrid-stress elements

Linear and quadratic Serendipity hybrid-stress elements are examined in respect of stability, coordinate invariance, and optimality. A formulation based upon symmetry group theory successfully addresses these issues in undistorted geometries and is fully detailed for plane elements. The resulting least-order stable invariant stress polynomials can be applied as astute approximations in distorted cases through a variety of tensor components and variational principles. A distortion sensitivity study for two- and three-dimensional elements provides favorable numerical comparisons with the assumed displacement method.

Punch, E. F.↗
NASA NTRS1978

Design of a compensation for an ARMA model of a discrete time system

The design of an optimal dynamic compensator for a multivariable discrete time system is studied. Also the design of compensators to achieve minimum variance control strategies for single input single output systems is analyzed. In the first problem the initial conditions of the plant are random variables with known first and second order moments, and the cost is the expected value of the standard cost, quadratic in the states and controls. The compensator is based on the minimum order Luenberger observer and it is found optimally by minimizing a performance index. Necessary and sufficient conditions for optimality of the compensator are derived. The second problem is solved in three different ways; two of them working directly in the frequency domain and one working in the time domain. The first and second order moments of the initial conditions are irrelevant to the solution. Necessary and sufficient conditions are derived for the compensator to minimize the variance of the output.

Mainemer, C. I.↗
NASA NTRS1999

Optimized System Identification

In system identification, one usually cares most about finding a model whose outputs are as close as possible to the true system outputs when the same input is applied to both. However, most system identification algorithms do not minimize this output error. Often they minimize model equation error instead, as in typical least-squares fits using a finite-difference model, and it is seen here that this distinction is significant. Here, we develop a set of system identification algorithms that minimize output error for multi-input/multi-output and multi-input/single-output systems. This is done with sequential quadratic programming iterations on the nonlinear least-squares problems, with an eigendecomposition to handle indefinite second partials. This optimization minimizes a nonlinear function of many variables, and hence can converge to local minima. To handle this problem, we start the iterations from the OKID (Observer/Kalman Identification) algorithm result. Not only has OKID proved very effective in practice, it minimizes an output error of an observer which has the property that as the data set gets large, it converges to minimizing the criterion of interest here. Hence, it is a particularly good starting point for the nonlinear iterations here. Examples show that the methods developed here eliminate the bias that is often observed using any system identification methods of either over-estimating or under-estimating the damping of vibration modes in lightly damped structures.

Juang, Jer-Nan↗
DOE OSTI2013

Adiabatic Quantum Programming: Minor Embedding With Hard Faults

Adiabatic quantum programming defines the time-dependent mapping of a quantum algorithm into the hardware or logical fabric. An essential programming step is the embedding of problem-specific information into the logical fabric to define the quantum computational transformation. We present algorithms for embedding arbitrary instances of the adiabatic quantum optimization algorithm into a square lattice of specialized unit cells. Our methods are shown to be extensible in fabric growth, linear in time, and quadratic in logical footprint. In addition, we provide methods for accommodating hard faults in the logical fabric without invoking approximations to the original problem. These hard fault-tolerant embedding algorithms are expected to prove useful for benchmarking the adiabatic quantum optimization algorithm on existing quantum logical hardware. We illustrate this versatility through numerical studies of embeddabilty versus hard fault rates in square lattices of complete bipartite unit cells.

graph theory↗