Search NASA⌕ Search

SEARCH · Search NASA

Results for “Iterative algorithms”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 577 records · Page 32
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 6.16 Theory Manual

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota’s iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1983

An iterative approach to region growing using associative memories

Region growing, often given as a classical example of the recursive control structures used in image processing which are often awkward to implement in hardware where the intent is the segmentation of an image at raster scan rates, is addressed in light of the postulate that any computation which can be performed recursively can be performed easily and efficiently by iteration coupled with association. Attention is given to an algorithm and hardware structure able to perform region labeling iteratively at scan rates. Every pixel is individually labeled with an identifier which signifies the region to which it belongs. Difficulties otherwise requiring recursion are handled by maintaining an equivalence table in hardware transparent to the computer, which reads the labeled pixels. A simulation of the associative memory has demonstrated its effectiveness.

Snyder, W. E.↗
NASA NTRS1999

Real-time Adaptive Control Using Neural Generalized Predictive Control

The objective of this paper is to demonstrate the feasibility of a Nonlinear Generalized Predictive Control algorithm by showing real-time adaptive control on a plant with relatively fast time-constants. Generalized Predictive Control has classically been used in process control where linear control laws were formulated for plants with relatively slow time-constants. The plant of interest for this paper is a magnetic levitation device that is nonlinear and open-loop unstable. In this application, the reference model of the plant is a neural network that has an embedded nominal linear model in the network weights. The control based on the linear model provides initial stability at the beginning of network training. In using a neural network the control laws are nonlinear and online adaptation of the model is possible to capture unmodeled or time-varying dynamics. Newton-Raphson is the minimization algorithm. Newton-Raphson requires the calculation of the Hessian, but even with this computational expense the low iteration rate make this a viable algorithm for real-time control.

Haley, Pam↗
DOE OSTI2025

Distributed Coordination of Demand-side Flexible Resources in Microgrid with All-Time Feasibility

The prevalence of distributed renewable generators motivates microgrid operators to exploit demand-side flexible resources (DFRs). Due to their dispersed nature, distributed DFR coordination has been a vibrant research area, while there are several issues awaiting to be addressed. On one hand, DFR power is internally coupled through power flow, while DFR usually cannot access grid information. On the other hand, in time-restricted scenarios, solution feasibility cannot be guaranteed by conventional dual-based algorithms. To fill these gaps, we propose a distributed DFR coordination framework with all-time feasibility. The proposed framework accounts for the distinct access of microgrid entities to grid information. A distributed and all-time feasible algorithm is proposed for optimal DFR coordination, which allows DFRs to make local decisions without violating constraints throughout iterations. The effectiveness of the proposed algorithm is demonstrated through case studies. The impact of peer-to-peer communication links on algorithm convergence is also investigated, which emphasizes the balance between communication investment and algorithm performance.

Li, Hongyi [Iowa State Univ., Ames, IA (United Sta↗
NASA NTRS1983

Calculations of transonic potential flows by a parameter free procedure

A parameter-free computational procedure for transonic potential flows around an airfoil is presented. The method is based on an inexact, Newton-like iterative scheme, and a preconditioned minimal residual algorithm is used to solve the linear system of equations arising at each iterate. This iterative procedure is formulated so that the difficulties associated with the approximate factorization technique, namely the requirement of iteration parameters and the boundary conditions for the intermediate variable are eliminated. Numerical experiments are given for potential flows around NACA 0012 airfoil with different Mach numbers and different angles of attack. These results are then compared with those obtained by the approximate factorization techniques.

Wong, Y. S.↗
NASA NTRS1985

Solution of partial differential equations on vector and parallel computers

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed.

Ortega, J. M.↗
NASA NTRS1985

Solution of partial differential equations on vector and parallel computers

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed.

Ortega, J. M.↗
NASA NTRS1992

An implementation of the QMR method based on coupled two-term recurrences

The authors have proposed a new Krylov subspace iteration, the quasi-minimal residual algorithm (QMR), for solving non-Hermitian linear systems. In the original implementation of the QMR method, the Lanczos process with look-ahead is used to generate basis vectors for the underlying Krylov subspaces. In the Lanczos algorithm, these basis vectors are computed by means of three-term recurrences. It has been observed that, in finite precision arithmetic, vector iterations based on three-term recursions are usually less robust than mathematically equivalent coupled two-term vector recurrences. This paper presents a look-ahead algorithm that constructs the Lanczos basis vectors by means of coupled two-term recursions. Implementation details are given, and the look-ahead strategy is described. A new implementation of the QMR method, based on this coupled two-term algorithm, is described. A simplified version of the QMR algorithm without look-ahead is also presented, and the special case of QMR for complex symmetric linear systems is considered. Results of numerical experiments comparing the original and the new implementations of the QMR method are reported.

Freund, Roland W.↗
NASA NTRS1974

Rapid finite-difference computation of subsonic and transonic aerodynamic flows

Rapid iterative (or semidirect) computation methods are developed for the finite-difference solution of the nonlinear equations of subsonic and transonic aerodynamics. At each iteration, a fast, direct elliptic algorithm solves the entire computation field. In an application to subsonic flow over a lifting airfoil, the full nonlinear stream-function equation is solved. Finally, a direct Cauchy-Riemann solver is used for the nonlinear transonic small-disturbance equations for a biconvex airfoil. At M = 0.7, t/c = 0.1 (subcritical), three iterations on a 39 x 32 mesh (totaling 2.45 sec on an IBM 360/67 computer) obtain convergence within 0.1%. A slightly supercritical case requires seven iterations (6.75 sec) for convergence within 1%.

Martin, E. D.↗
NASA NTRS1993

Uniform convergence of multigrid V-cycle iterations for indefinite and nonsymmetric problems

In this paper, we present an analysis of a multigrid method for nonsymmetric and/or indefinite elliptic problems. In this multigrid method various types of smoothers may be used. One type of smoother which we consider is defined in terms of an associated symmetric problem and includes point and line, Jacobi, and Gauss-Seidel iterations. We also study smoothers based entirely on the original operator. One is based on the normal form, that is, the product of the operator and its transpose. Other smoothers studied include point and line, Jacobi, and Gauss-Seidel. We show that the uniform estimates for symmetric positive definite problems carry over to these algorithms. More precisely, the multigrid iteration for the nonsymmetric and/or indefinite problem is shown to converge at a uniform rate provided that the coarsest grid in the multilevel iteration is sufficiently fine (but not depending on the number of multigrid levels).

Bramble, James H.↗
NASA NTRS1986

An efficient algorithm for solution of the unsteady transonic small-disturbance equation

A time accurate approximate factorization (AF) algorithm is formulated for solution of the three dimensional unsteady transonic small-disturbance equation. The AF algorithm consists of a time linearization procedure coupled with a Newton iteration technique. Superior stability characteristics of the new algorithm are demonstrated through applications to steady and oscillatory flows at subsonic and supersonic freestream conditions for an F-5 fighter wing. For steady flow calculations, the size of the time step is cycled to achieve rapid convergence. For unsteady flow calculations, the AF algorithm is sufficiently robust to allow the step size to be selected based on accuracy rather than on stability considerations. Therefore, accurate solutions are obtained in only several hundred time steps yielding a significant computational cost savings when compared to alternative methods.

Batina, John T.↗
NASA NTRS1987

An efficient algorithm for solution of the unsteady transonic small-disturbance equation

A time accurate approximation factorization (AF) algorithm is formulated for solution of the three-dimensional unsteady transonic small-disturbance equation. The AF algorithm consists of a time linearization procedure coupled with a Newton iteration technique. Superior stability characteristics of the new algorithm are demonstrated through applications to steady and oscillatory flows at subsonic and supersonic freestream conditions for an F-5 fighter wing. For steady flow calculations, the size of the time step is cycled to achieve rapid convergence. For unsteady flow calculations, the AF algorithm is sufficiently robust to allow the step size to be selected based on accuracy rather than on stability considerations. Therefore, accurate solutions are obtained in only several hundred time steps yielding a significant computational cost savings when compared to alternative methods.

Batina, John T.↗
DOE OSTI2020

GNET2: an R package for constructing gene regulatory networks from transcriptomic data

Abstract Motivation The Gene Network Estimation Tool (GNET) is designed to build gene regulatory networks (GRNs) from transcriptomic gene expression data with a probabilistic graphical model. The data preprocessing, model construction and visualization modules of the original GNET software were developed on different programming platforms, which were inconvenient for users to deploy and use. Results Here, we present GNET2, an improved implementation of GNET as an integrated R package. GNET2 provides more flexibility for parameter initialization and regulatory module construction based on the core iterative modeling process of the original algorithm. The data exchange interface of GNET2 is handled within an R session automatically. Given the growing demand for regulatory network reconstruction from transcriptomic data, GNET2 offers a convenient option for GRN inference on large datasets. Availability and implementation The source code of GNET2 is available at https://github.com/jianlin-cheng/GNET2. Supplementary information Supplementary data are available at Bioinformatics online.

59 BASIC BIOLOGICAL SCIENCES↗
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↗
NASA NTRS1990

On domains of convergence in optimization problems

Numerical optimization algorithms require the knowledge of an initial set of design variables. Starting from an initial design x(sup 0), improved solutions are obtained by updating the design iteratively in a way prescribed by the particular algorithm used. If the algorithm is successful, convergence is achieved to a local optimal solution. Let A denote the iterative procedure that characterizes a typical optimization algorithm, applied to the problem: Find x belonging to R(sup n) that maximizes f(x) subject to x belonging to Omega contained in R(sup n). We are interested in problems with several local maxima (x(sub j))(sup *), j=1, ..., m, in the feasible design space Omega. In general, convergence of the algorithm A to a specific solution (x(sub j))(sup *) is determined by the choice of initial design x(sup 0). The domain of convergence D(sub j) of A associated with a local maximum (x(sub j))(sup *) is a subset of initial designs x(sup 0) in Omega such that the sequence (x(sup k)), k=0,1,2,... defined by x(sup k+1) = A(x(sup k)), k=0,1,... converges to (x(sub j))(sup *). The set D(sub j) is also called the basin of attraction of (x(sub j))(sup *). Cayley first proposed the problem of finding the basin of attraction for Newton's method in 1897. It has been shown that the basin of attraction for Newton's method exhibits chaotic behavior in problems with polynomial objective. This implies that there may be regions in the feasible design space where arbitrarily close starting points will converge to different local optimal solutions. Furthermore, the boundaries of the domains of convergence may have a very complex, even fractal structure. In this paper we show that even simple structural optimization problems solved using standard gradient based (first order) algorithms exhibit similar features.

Diaz, Alejandro R.↗
DOE OSTI2020

Iterative Learning Control for Video-rate Atomic Force Microscopy

We present a control scheme for video-rate atomic force microscopy with rosette pattern. The controller structure involves a feedback internal-model-based controller and a feedforward iterative learning controller. The iterative learning controller is designed to improve tracking performance of the feedback-controlled scanner by rejecting the repetitive disturbances arising from the system nonlinearities. We investigate the performance of two inversion techniques for constructing the learning filter. We conduct tracking experiments using a two-degree-of-freedom microelectromechanical system (MEMS) nanopositioner at frame rates ranging from 5 to 20 frames per second. Furthermore, the results reveal that the algorithm converges rapidly and the iterative learning controller significantly reduces both the transient and steady-state tracking errors. We acquire and report a series of high-resolution time-lapsed video-rate AFM images with the rosette pattern.

42 ENGINEERING↗
DOE OSTI2021

Randomized algorithms for generalized singular value decomposition with application to sensitivity analysis

The generalized singular value decomposition (GSVD) is a valuable tool that has many applications in computational science. However, computing the GSVD for large-scale problems is challenging. Motivated by applications in hyper-differential sensitivity analysis (HDSA), in this work we propose new randomized algorithms for computing the GSVD which use randomized subspace iteration and weighted QR factorization. Detailed error analysis is given which provides insight into the accuracy of the algorithms and the choice of the algorithmic parameters. We demonstrate the performance of our algorithms on test matrices and a large-scale model problem where HDSA is used to study subsurface flow.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization Parameter Estimation Uncertainty Quantification and Sensitivity Analysis: Version 6.12 User's Manual

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a user's manual for the Dakota software and provides capability overviews and procedures for software execution, as well as a variety of example studies.

97 MATHEMATICS AND COMPUTING↗