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.

SourceResearch connectionFrom yearThrough year

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

At least 595 records · Page 33

All sources NASA NTRS DOE OSTI

DOE OSTI2021

Dakota A Multilevel Parallel Object-Oriented Framework for Design Optimization Parameter Estimation Uncertainty Quantification and Sensitivity Analysis (V.6.14) (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 users 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↗

DOE OSTI2020

Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 6.13 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↗

DOE OSTI2021

Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 6.15 User's Manual

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis (V.6.16 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↗

DOE OSTI2021

Network-Level Optimization for Unbalanced Power Distribution System: Approximation and Relaxation

The nonlinear programming (NLP) problem to solve distribution-level optimal power flow (D-OPF) poses convergence issues and does not scale well for unbalanced distribution systems. The existing scalable D-OPF algorithms either use approximations that are not valid for an unbalanced power distribution system, or apply relaxation techniques to the nonlinear power flow equations that do not guarantee a feasible power flow solution. In this paper, we propose scalable D-OPF algorithms that simultaneously achieve optimal and feasible solutions by solving multiple iterations of approximate, or relaxed, D-OPF subproblems of low complexity. The first algorithm is based on a successive linear approximation of the nonlinear power flow equations around the current operating point, where the D-OPF solution is obtained by solving multiple iterations of a linear programming (LP) problem. The second algorithm is based on the relaxation of the nonlinear power flow equations as conic constraints together with directional constraints, which achieves optimal and feasible solutions over multiple iterations of a second-order cone programming (SOCP) problem. Finally, it is demonstrated that the proposed algorithms are able to reach an optimal and feasible solution while significantly reducing the computation time as compared to an equivalent NLPD-OPF model for the same distribution system.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS2009

Constructing LDPC Codes from Loop-Free Encoding Modules

A method of constructing certain low-density parity-check (LDPC) codes by use of relatively simple loop-free coding modules has been developed. The subclasses of LDPC codes to which the method applies includes accumulate-repeat-accumulate (ARA) codes, accumulate-repeat-check-accumulate codes, and the codes described in Accumulate-Repeat-Accumulate-Accumulate Codes (NPO-41305), NASA Tech Briefs, Vol. 31, No. 9 (September 2007), page 90. All of the affected codes can be characterized as serial/parallel (hybrid) concatenations of such relatively simple modules as accumulators, repetition codes, differentiators, and punctured single-parity check codes. These are error-correcting codes suitable for use in a variety of wireless data-communication systems that include noisy channels. These codes can also be characterized as hybrid turbolike codes that have projected graph or protograph representations (for example see figure); these characteristics make it possible to design high-speed iterative decoders that utilize belief-propagation algorithms. The present method comprises two related submethods for constructing LDPC codes from simple loop-free modules with circulant permutations. The first submethod is an iterative encoding method based on the erasure-decoding algorithm. The computations required by this method are well organized because they involve a parity-check matrix having a block-circulant structure. The second submethod involves the use of block-circulant generator matrices. The encoders of this method are very similar to those of recursive convolutional codes. Some encoders according to this second submethod have been implemented in a small field-programmable gate array that operates at a speed of 100 megasymbols per second. By use of density evolution (a computational- simulation technique for analyzing performances of LDPC codes), it has been shown through some examples that as the block size goes to infinity, low iterative decoding thresholds close to channel capacity limits can be achieved for the codes of the type in question having low maximum variable node degrees. The decoding thresholds in these examples are lower than those of the best-known unstructured irregular LDPC codes constrained to have the same maximum node degrees. Furthermore, the present method enables the construction of codes of any desired rate with thresholds that stay uniformly close to their respective channel capacity thresholds.

Divsalar, Dariush↗

NASA NTRS2015

Automated Point Cloud Correspondence Detection for Underwater Mapping Using AUVs

An algorithm for automating correspondence detection between point clouds composed of multibeam sonar data is presented. This allows accurate initialization for point cloud alignment techniques even in cases where accurate inertial navigation is not available, such as iceberg profiling or vehicles with low-grade inertial navigation systems. Techniques from computer vision literature are used to extract, label, and match keypoints between "pseudo-images" generated from these point clouds. Image matches are refined using RANSAC and information about the vehicle trajectory. The resulting correspondences can be used to initialize an iterative closest point (ICP) registration algorithm to estimate accumulated navigation error and aid in the creation of accurate, self-consistent maps. The results presented use multibeam sonar data obtained from multiple overlapping passes of an underwater canyon in Monterey Bay, California. Using strict matching criteria, the method detects 23 between-swath correspondence events in a set of 155 pseudo-images with zero false positives. Using less conservative matching criteria doubles the number of matches but introduces several false positive matches as well. Heuristics based on known vehicle trajectory information are used to eliminate these.

Sonar↗

NASA NTRS2012

Assessment of Polarization Effect on Efficiency of Levenberg-Marquardt Algorithm in Case of Thin Atmosphere Over Black Surface

The Levenberg-Marquardt algorithm [1, 2] provides a numerical iterative solution to the problem of minimization of a function over a space of its parameters. In our work, the Levenberg-Marquardt algorithm retrieves optical parameters of a thin (single scattering) plane parallel atmosphere irradiated by collimated infinitely wide monochromatic beam of light. Black ground surface is assumed. Computational accuracy, sensitivity to the initial guess and the presence of noise in the signal, and other properties of the algorithm are investigated in scalar (using intensity only) and vector (including polarization) modes. We consider an atmosphere that contains a mixture of coarse and fine fractions. Following [3], the fractions are simulated using Henyey-Greenstein model. Though not realistic, this assumption is very convenient for tests [4, p.354]. In our case it yields analytical evaluation of Jacobian matrix. Assuming the MISR geometry of observation [5] as an example, the average scattering cosines and the ratio of coarse and fine fractions, the atmosphere optical depth, and the single scattering albedo, are the five parameters to be determined numerically. In our implementation of the algorithm, the system of five linear equations is solved using the fast Cramer s rule [6]. A simple subroutine developed by the authors, makes the algorithm independent from external libraries. All Fortran 90/95 codes discussed in the presentation will be available immediately after the meeting from sergey.v.korkin@nasa.gov by request.

Korkin, S.↗

DOE OSTI2025

Simulation of an inductively coupled plasma with a two-dimensional Darwin particle-in-cell code

A two-dimensional particle-in-cell code for the simulation of low-frequency electromagnetic processes in laboratory plasmas has been developed. The code uses the Darwin method omitting the electromagnetic wave propagation. The Darwin method separates the electric field into solenoidal and irrotational parts. The solenoidal electric field is calculated with a new algorithm based on the equation for the electric field vorticity. The system of linear equations in the new algorithm is readily solved using a standard iterative method. The irrotational electric field is the electrostatic field calculated with the direct implicit algorithm. The code is verified by reproducing the two-stream instability, electron electromagnetic waves, and shear Alfvén waves. The code is applied to simulate an inductively coupled plasma with the driving current flowing around the plasma region. In this simulation, a ring of dense plasma forms at the initial stage but then the density becomes maximal in the center and decays monotonically toward the walls. The skin effect is in the transitional mode between local and non-local, and the electron velocity distribution function is non-Maxwellian.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1995

Optimal Signal Processing of Frequency-Stepped CW Radar Data

An optimal signal processing algorithm is derived for estimating the time delay and amplitude of each scatterer reflection using a frequency-stepped CW system. The channel is assumed to be composed of abrupt changes in the reflection coefficient profile. The optimization technique is intended to maximize the target range resolution achievable from any set of frequency-stepped CW radar measurements made in such an environment. The algorithm is composed of an iterative two-step procedure. First, the amplitudes of the echoes are optimized by solving an overdetermined least squares set of equations. Then, a nonlinear objective function is scanned in an organized fashion to find its global minimum. The result is a set of echo strengths and time delay estimates. Although this paper addresses the specific problem of resolving the time delay between the two echoes, the derivation is general in the number of echoes. Performance of the optimization approach is illustrated using measured data obtained from an HP-851O network analyzer. It is demonstrated that the optimization approach offers a significant resolution enhancement over the standard processing approach that employs an IFFT. Degradation in the performance of the algorithm due to suboptimal model order selection and the effects of additive white Gaussion noise are addressed.

Ybarra, Gary A.↗

NASA NTRS1995

Optimal Signal Processing of Frequency-Stepped CW Radar Data

An optimal signal processing algorithm is derived for estimating the time delay and amplitude of each scatterer reflection using a frequency-stepped CW system. The channel is assumed to be composed of abrupt changes in the reflection coefficient profile. The optimization technique is intended to maximize the target range resolution achievable from any set of frequency-stepped CW radar measurements made in such an environment. The algorithm is composed of an iterative two-step procedure. First, the amplitudes of the echoes are optimized by solving an overdetermined least squares set of equations. Then, a nonlinear objective function is scanned in an organized fashion to find its global minimum. The result is a set of echo strengths and time delay estimates. Although this paper addresses the specific problem of resolving the time delay between the first two echoes, the derivation is general in the number of echoes. Performance of the optimization approach is illustrated using measured data obtained from an HP-X510 network analyzer. It is demonstrated that the optimization approach offers a significant resolution enhancement over the standard processing approach that employs an IFFT. Degradation in the performance of the algorithm due to suboptimal model order selection and the effects of additive white Gaussion noise are addressed.

Ybarra, Gary A.↗

NASA NTRS2000

A Parallel Genetic Algorithm for Automated Electronic Circuit Design

Parallelized versions of genetic algorithms (GAs) are popular primarily for three reasons: the GA is an inherently parallel algorithm, typical GA applications are very compute intensive, and powerful computing platforms, especially Beowulf-style computing clusters, are becoming more affordable and easier to implement. In addition, the low communication bandwidth required allows the use of inexpensive networking hardware such as standard office ethernet. In this paper we describe a parallel GA and its use in automated high-level circuit design. Genetic algorithms are a type of trial-and-error search technique that are guided by principles of Darwinian evolution. Just as the genetic material of two living organisms can intermix to produce offspring that are better adapted to their environment, GAs expose genetic material, frequently strings of 1s and Os, to the forces of artificial evolution: selection, mutation, recombination, etc. GAs start with a pool of randomly-generated candidate solutions which are then tested and scored with respect to their utility. Solutions are then bred by probabilistically selecting high quality parents and recombining their genetic representations to produce offspring solutions. Offspring are typically subjected to a small amount of random mutation. After a pool of offspring is produced, this process iterates until a satisfactory solution is found or an iteration limit is reached. Genetic algorithms have been applied to a wide variety of problems in many fields, including chemistry, biology, and many engineering disciplines. There are many styles of parallelism used in implementing parallel GAs. One such method is called the master-slave or processor farm approach. In this technique, slave nodes are used solely to compute fitness evaluations (the most time consuming part). The master processor collects fitness scores from the nodes and performs the genetic operators (selection, reproduction, variation, etc.). Because of dependency issues in the GA, it is possible to have idle processors. However, as long as the load at each processing node is similar, the processors are kept busy nearly all of the time. In applying GAs to circuit design, a suitable genetic representation 'is that of a circuit-construction program. We discuss one such circuit-construction programming language and show how evolution can generate useful analog circuit designs. This language has the desirable property that virtually all sets of combinations of primitives result in valid circuit graphs. Our system allows circuit size (number of devices), circuit topology, and device values to be evolved. Using a parallel genetic algorithm and circuit simulation software, we present experimental results as applied to three analog filter and two amplifier design tasks. For example, a figure shows an 85 dB amplifier design evolved by our system, and another figure shows the performance of that circuit (gain and frequency response). In all tasks, our system is able to generate circuits that achieve the target specifications.

Long, Jason D.↗

NASA NTRS2013

Mixed-Strategy Chance Constrained Optimal Control

This paper presents a novel chance constrained optimal control (CCOC) algorithm that chooses a control action probabilistically. A CCOC problem is to find a control input that minimizes the expected cost while guaranteeing that the probability of violating a set of constraints is below a user-specified threshold. We show that a probabilistic control approach, which we refer to as a mixed control strategy, enables us to obtain a cost that is better than what deterministic control strategies can achieve when the CCOC problem is nonconvex. The resulting mixed-strategy CCOC problem turns out to be a convexification of the original nonconvex CCOC problem. Furthermore, we also show that a mixed control strategy only needs to "mix" up to two deterministic control actions in order to achieve optimality. Building upon an iterative dual optimization, the proposed algorithm quickly converges to the optimal mixed control strategy with a user-specified tolerance.

Ono, Masahiro↗

DOE OSTI2023

Fast Multigrid Reduction-in-Time for Advection via Modified Semi-Lagrangian Coarse-Grid Operators

Many iterative parallel-in-time algorithms have been shown to be highly efficient for diffusion-dominated partial differential equations (PDEs) but are inefficient or even divergent when applied to advection-dominated PDEs. We consider the application of the multigrid reduction-in-time (MGRIT) algorithm to linear advection PDEs. Here, the key to efficient time integration with this method is using a coarse-grid operator that provides a sufficiently accurate approximation to the so-called ideal coarse-grid operator. For certain classes of semi-Lagrangian discretizations, we present a novel semi-Lagrangian-based coarse-grid operator that leads to fast and scalable multilevel time integration of linear advection PDEs. The coarse-grid operator is composed of a semi-Lagrangian discretization followed by a correction term, with the correction designed so that the leading-order truncation error of the composite operator is approximately equal to that of the ideal coarse-grid operator. Parallel results show substantial speed-ups over sequential time integration for variable-wave-speed advection problems in one and two spatial dimensions, and using high-order discretizations up to order five. The proposed approach establishes the first practical method that provides small and scalable MGRIT iteration counts for advection problems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Benders Cut Classification via Support Vector Machines for Solving Two-Stage Stochastic Programs

In this work, we consider Benders decomposition for solving two-stage stochastic programs with complete recourse based on finite samples of the uncertain parameters. We define the Benders cuts binding at the final optimal solution or the ones significantly improving bounds over iterations as valuable cuts. We propose a learning-enhanced Benders decomposition (LearnBD) algorithm, which adds a cut classification step in each iteration to selectively generate cuts that are more likely to be valuable cuts. The LearnBD algorithm includes two phases: (i) sampling cuts and collecting information from training problems and (ii) solving testing problems with a support vector machine (SVM) cut classifier. We run the LearnBD algorithm on instances of capacitated facility location and multicommodity network design under uncertain demand. Our results show that SVM cut classifier works effectively for identifying valuable cuts, and the LearnBD algorithm reduces the total solving time of all instances for different problems with various sizes and complexities.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1989

Conjugate gradient type methods for linear systems with complex symmetric coefficient matrices

We consider conjugate gradient type methods for the solution of large sparse linear system Ax equals b with complex symmetric coefficient matrices A equals A(T). Such linear systems arise in important applications, such as the numerical solution of the complex Helmholtz equation. Furthermore, most complex non-Hermitian linear systems which occur in practice are actually complex symmetric. We investigate conjugate gradient type iterations which are based on a variant of the nonsymmetric Lanczos algorithm for complex symmetric matrices. We propose a new approach with iterates defined by a quasi-minimal residual property. The resulting algorithm presents several advantages over the standard biconjugate gradient method. We also include some remarks on the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.

Freund, Roland↗

NASA NTRS1986

Communications oriented programming of parallel iterative solutions of sparse linear systems

Parallel algorithms are developed for a class of scientific computational problems by partitioning the problems into smaller problems which may be solved concurrently. The effectiveness of the resulting parallel solutions is determined by the amount and frequency of communication and synchronization and the extent to which communication can be overlapped with computation. Three different parallel algorithms for solving the same class of problems are presented, and their effectiveness is analyzed from this point of view. The algorithms are programmed using a new programming environment. Run-time statistics and experience obtained from the execution of these programs assist in measuring the effectiveness of these algorithms.

Patrick, M. L.↗

NASA NTRS1989

Upwind relaxation methods for the Navier-Stokes equations using inner iterations

A supersonic and subsonic test problem is solved using an upwind line relaxation algorithm for the Navier-Stokes equations which employs inner iterations. In the supersonic test case, the inner iteration method was found to require only about 65 percent of the CPU time which was required by the most efficient line relaxation method without inner iterations. In the subsonic test case, poor matrix conditioning resulted in less efficiency than line relaxation methods employing a more conventional CPU-saving strategy.

Taylor, Arthur C., III↗