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At least 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Development of parallel algorithms for electrical power management in space applications

The application of parallel techniques for electrical power system analysis is discussed. The Newton-Raphson method of load flow analysis was used along with the decomposition-coordination technique to perform load flow analysis. The decomposition-coordination technique enables tasks to be performed in parallel by partitioning the electrical power system into independent local problems. Each independent local problem represents a portion of the total electrical power system on which a loan flow analysis can be performed. The load flow analysis is performed on these partitioned elements by using the Newton-Raphson load flow method. These independent local problems will produce results for voltage and power which can then be passed to the coordinator portion of the solution procedure. The coordinator problem uses the results of the local problems to determine if any correction is needed on the local problems. The coordinator problem is also solved by an iterative method much like the local problem. The iterative method for the coordination problem will also be the Newton-Raphson method. Therefore, each iteration at the coordination level will result in new values for the local problems. The local problems will have to be solved again along with the coordinator problem until some convergence conditions are met.

Berry, Frederick C.↗
NASA NTRS1986

On orbital allotments for geostationary satellites

The following satellite synthesis problem is addressed: communication satellites are to be allotted positions on the geostationary arc so that interference does not exceed a given acceptable level by enforcing conservative pairwise satellite separation. A desired location is specified for each satellite, and the objective is to minimize the sum of the deviations between the satellites' prescribed and desired locations. Two mixed integer programming models for the satellite synthesis problem are presented. Four solution strategies, branch-and-bound, Benders' decomposition, linear programming with restricted basis entry, and a switching heuristic, are used to find solutions to example synthesis problems. Computational results indicate the switching algorithm yields solutions of good quality in reasonable execution times when compared to the other solution methods. It is demonstrated that the switching algorithm can be applied to synthesis problems with the objective of minimizing the largest deviation between a prescribed location and the corresponding desired location. Furthermore, it is shown that the switching heuristic can use no conservative, location-dependent satellite separations in order to satisfy interference criteria.

Gonsalvez, David J. A.↗
NASA NTRS1993

Implementation of ADI: Schemes on MIMD parallel computers

In order to simulate the effects of the impingement of hot exhaust jets of High Performance Aircraft on landing surfaces a multi-disciplinary computation coupling flow dynamics to heat conduction in the runway needs to be carried out. Such simulations, which are essentially unsteady, require very large computational power in order to be completed within a reasonable time frame of the order of an hour. Such power can be furnished by the latest generation of massively parallel computers. These remove the bottleneck of ever more congested data paths to one or a few highly specialized central processing units (CPU's) by having many off-the-shelf CPU's work independently on their own data, and exchange information only when needed. During the past year the first phase of this project was completed, in which the optimal strategy for mapping an ADI-algorithm for the three dimensional unsteady heat equation to a MIMD parallel computer was identified. This was done by implementing and comparing three different domain decomposition techniques that define the tasks for the CPU's in the parallel machine. These implementations were done for a Cartesian grid and Dirichlet boundary conditions. The most promising technique was then used to implement the heat equation solver on a general curvilinear grid with a suite of nontrivial boundary conditions. Finally, this technique was also used to implement the Scalar Penta-diagonal (SP) benchmark, which was taken from the NAS Parallel Benchmarks report. All implementations were done in the programming language C on the Intel iPSC/860 computer.

Vanderwijngaart, Rob F.↗
NASA NTRS1993

The development of a scalable parallel 3-D CFD algorithm for turbomachinery

Two algorithms capable of computing a transonic 3-D inviscid flow field about rotating machines are considered for parallel implementation. During the study of these algorithms, a significant new method of measuring the performance of parallel algorithms is developed. The theory that supports this new method creates an empirical definition of scalable parallel algorithms that is used to produce quantifiable evidence that a scalable parallel application was developed. The implementation of the parallel application and an automated domain decomposition tool are also discussed.

Luke, Edward Allen↗
NASA NTRS1995

A CFD study of complex missile and store configurations in relative motion

An investigation was conducted from May 16, 1990 to August 31, 1994 on the development of computational fluid dynamics (CFD) methodologies for complex missiles and the store separation problem. These flowfields involved multiple-component configurations, where at least one of the objects was engaged in relative motion. The two most important issues that had to be addressed were: (1) the unsteadiness of the flowfields (time-accurate and efficient CFD algorithms for the unsteady equations), and (2) the generation of grid systems which would permit multiple and moving bodies in the computational domain (dynamic domain decomposition). The study produced two competing and promising methodologies, and their proof-of-concept cases, which have been reported in the open literature: (1) Unsteady solutions on dynamic, overlapped grids, which may also be perceived as moving, locally-structured grids, and (2) Unsteady solutions on dynamic, unstructured grids.

Baysal, Oktay↗
NASA NTRS2000

Airbreathing Propulsion System Analysis Using Multithreaded Parallel Processing

In this paper, parallel processing is used to analyze the mixing, and combustion behavior of hypersonic flow. Preliminary work for a sonic transverse hydrogen jet injected from a slot into a Mach 4 airstream in a two-dimensional duct combustor has been completed [Moon and Chung, 1996]. Our aim is to extend this work to three-dimensional domain using multithreaded domain decomposition parallel processing based on the flowfield-dependent variation theory. Numerical simulations of chemically reacting flows are difficult because of the strong interactions between the turbulent hydrodynamic and chemical processes. The algorithm must provide an accurate representation of the flowfield, since unphysical flowfield calculations will lead to the faulty loss or creation of species mass fraction, or even premature ignition, which in turn alters the flowfield information. Another difficulty arises from the disparity in time scales between the flowfield and chemical reactions, which may require the use of finite rate chemistry. The situations are more complex when there is a disparity in length scales involved in turbulence. In order to cope with these complicated physical phenomena, it is our plan to utilize the flowfield-dependent variation theory mentioned above, facilitated by large eddy simulation. Undoubtedly, the proposed computation requires the most sophisticated computational strategies. The multithreaded domain decomposition parallel processing will be necessary in order to reduce both computational time and storage. Without special treatments involved in computer engineering, our attempt to analyze the airbreathing combustion appears to be difficult, if not impossible.

Schunk, Richard Gregory↗
NASA NTRS1998

Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes

A code trellis is a graphical representation of a code, block or convolutional, in which every path represents a codeword (or a code sequence for a convolutional code). This representation makes it possible to implement Maximum Likelihood Decoding (MLD) of a code with reduced decoding complexity. The most well known trellis-based MLD algorithm is the Viterbi algorithm. The trellis representation was first introduced and used for convolutional codes [23]. This representation, together with the Viterbi decoding algorithm, has resulted in a wide range of applications of convolutional codes for error control in digital communications over the last two decades. There are two major reasons for this inactive period of research in this area. First, most coding theorists at that time believed that block codes did not have simple trellis structure like convolutional codes and maximum likelihood decoding of linear block codes using the Viterbi algorithm was practically impossible, except for very short block codes. Second, since almost all of the linear block codes are constructed algebraically or based on finite geometries, it was the belief of many coding theorists that algebraic decoding was the only way to decode these codes. These two reasons seriously hindered the development of efficient soft-decision decoding methods for linear block codes and their applications to error control in digital communications. This led to a general belief that block codes are inferior to convolutional codes and hence, that they were not useful. Chapter 2 gives a brief review of linear block codes. The goal is to provide the essential background material for the development of trellis structure and trellis-based decoding algorithms for linear block codes in the later chapters. Chapters 3 through 6 present the fundamental concepts, finite-state machine model, state space formulation, basic structural properties, state labeling, construction procedures, complexity, minimality, and sectionalization of trellises. Chapter 7 discusses trellis decomposition and subtrellises for low-weight codewords. Chapter 8 first presents well known methods for constructing long powerful codes from short component codes or component codes of smaller dimensions, and then provides methods for constructing their trellises which include Shannon and Cartesian product techniques. Chapter 9 deals with convolutional codes, puncturing, zero-tail termination and tail-biting.Chapters 10 through 13 present various trellis-based decoding algorithms, old and new. Chapter 10 first discusses the application of the well known Viterbi decoding algorithm to linear block codes, optimum sectionalization of a code trellis to minimize computation complexity, and design issues for IC (integrated circuit) implementation of a Viterbi decoder. Then it presents a new decoding algorithm for convolutional codes, named Differential Trellis Decoding (DTD) algorithm. Chapter 12 presents a suboptimum reliability-based iterative decoding algorithm with a low-weight trellis search for the most likely codeword. This decoding algorithm provides a good trade-off between error performance and decoding complexity. All the decoding algorithms presented in Chapters 10 through 12 are devised to minimize word error probability. Chapter 13 presents decoding algorithms that minimize bit error probability and provide the corresponding soft (reliability) information at the output of the decoder. Decoding algorithms presented are the MAP (maximum a posteriori probability) decoding algorithm and the Soft-Output Viterbi Algorithm (SOVA) algorithm. Finally, the minimization of bit error probability in trellis-based MLD is discussed.

Lin, Shu↗
DOE OSTI2022

Quantum annealing algorithms for Boolean tensor networks

Abstract Quantum annealers manufactured by D-Wave Systems, Inc., are computational devices capable of finding high-quality heuristic solutions of NP-hard problems. In this contribution, we explore the potential and effectiveness of such quantum annealers for computing Boolean tensor networks. Tensors offer a natural way to model high-dimensional data commonplace in many scientific fields, and representing a binary tensor as a Boolean tensor network is the task of expressing a tensor containing categorical (i.e., $$\{0, 1\}$$ { 0 , 1 } ) values as a product of low dimensional binary tensors. A Boolean tensor network is computed by Boolean tensor decomposition, and it is usually not exact. The aim of such decomposition is to minimize the given distance measure between the high-dimensional input tensor and the product of lower-dimensional (usually three-dimensional) tensors and matrices representing the tensor network. In this paper, we introduce and analyze three general algorithms for Boolean tensor networks: Tucker, Tensor Train, and Hierarchical Tucker networks. The computation of a Boolean tensor network is reduced to a sequence of Boolean matrix factorizations, which we show can be expressed as a quadratic unconstrained binary optimization problem suitable for solving on a quantum annealer. By using a novel method we introduce called parallel quantum annealing, we demonstrate that Boolean tensor’s with up to millions of elements can be decomposed efficiently using a DWave 2000Q quantum annealer.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Parallel physics-informed neural networks via domain decomposition

Here we develop a distributed framework for the physics-informed neural networks (PINNs) based on two recent extensions, namely conservative PINNs (cPINNs) and extended PINNs (XPINNs), which employ domain decomposition in space and in time-space, respectively. This domain decomposition endows cPINNs and XPINNs with several advantages over the vanilla PINNs, such as parallelization capacity, large representation capacity, efficient hyperparameter tuning, and is particularly effective for multi-scale and multi-physics problems. Here, we present a parallel algorithm for cPINNs and XPINNs constructed with a hybrid programming model described by MPI + X, where X ∈ {CPUs, GPUs}. The main advantage of cPINN and XPINN over the more classical data and model parallel approaches is the flexibility of optimizing all hyperparameters of each neural network separately in each subdomain. We compare the performance of distributed cPINNs and XPINNs for various forward problems, using both weak and strong scalings. Our results indicate that for space domain decomposition, cPINNs are more efficient in terms of communication cost but XPINNs provide greater flexibility as they can also handle time-domain decomposition for any differential equations, and can deal with any arbitrarily shaped complex subdomains. To this end, we also present an application of the parallel XPINN method for solving an inverse diffusion problem with variable conductivity on the United States map, using ten regions as subdomains.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2013

An Efficient Model-based Diagnosis Engine for Hybrid Systems Using Structural Model Decomposition

Complex hybrid systems are present in a large range of engineering applications, like mechanical systems, electrical circuits, or embedded computation systems. The behavior of these systems is made up of continuous and discrete event dynamics that increase the difficulties for accurate and timely online fault diagnosis. The Hybrid Diagnosis Engine (HyDE) offers flexibility to the diagnosis application designer to choose the modeling paradigm and the reasoning algorithms. The HyDE architecture supports the use of multiple modeling paradigms at the component and system level. However, HyDE faces some problems regarding performance in terms of complexity and time. Our focus in this paper is on developing efficient model-based methodologies for online fault diagnosis in complex hybrid systems. To do this, we propose a diagnosis framework where structural model decomposition is integrated within the HyDE diagnosis framework to reduce the computational complexity associated with the fault diagnosis of hybrid systems. As a case study, we apply our approach to a diagnostic testbed, the Advanced Diagnostics and Prognostics Testbed (ADAPT), using real data.

Structural Decomposition↗
DOE OSTI2025

Sylvester-preconditioned adaptive-rank implicit time integrators for advection-diffusion equations with variable coefficients

Here, we consider the adaptive-rank integration of multi-dimensional time-dependent advection-diffusion partial differential equations (PDEs) with variable coefficients. We employ a standard finite-difference method for spatial discretization coupled with high-order diagonally implicit Runge-Kutta temporal schemes. The discrete equation is a generalized Sylvester equation (GSE), which we solve with a projection-based adaptive-rank algorithm structured around two key strategies: (i) constructing dimension-wise subspaces using a novel atypical extended Krylov strategy, and (ii) efficiently solving the basis coefficient matrix with a preconditioned GMRES solver. The low-rank decomposition is performed in 2D using SVD and with high-order SVD (HOSVD) in 3D to represent the tensor in a compressed Tucker format. For d-dimensional problems (here, d = 2 or 3), the computational complexity and memory storage of the approach are found numerically to scale as and $\mathscr{O}(Nr^2) + \mathscr{O} (r^{d+1})$ and $\mathscr{O}(Nr) + \mathscr{O} (r^{d})$, respectively, with the one-dimensional resolution and the maximal rank during the Krylov iteration (which we find to be largely independent of on our numerical examples). We present numerical examples that illustrate the advertised properties of the algorithm.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2009

Regression Model Optimization for the Analysis of Experimental Data

A candidate math model search algorithm was developed at Ames Research Center that determines a recommended math model for the multivariate regression analysis of experimental data. The search algorithm is applicable to classical regression analysis problems as well as wind tunnel strain gage balance calibration analysis applications. The algorithm compares the predictive capability of different regression models using the standard deviation of the PRESS residuals of the responses as a search metric. This search metric is minimized during the search. Singular value decomposition is used during the search to reject math models that lead to a singular solution of the regression analysis problem. Two threshold dependent constraints are also applied. The first constraint rejects math models with insignificant terms. The second constraint rejects math models with near-linear dependencies between terms. The math term hierarchy rule may also be applied as an optional constraint during or after the candidate math model search. The final term selection of the recommended math model depends on the regressor and response values of the data set, the user s function class combination choice, the user s constraint selections, and the result of the search metric minimization. A frequently used regression analysis example from the literature is used to illustrate the application of the search algorithm to experimental data.

Ulbrich, N.↗
NASA NTRS1995

Development of Fast Algorithms Using Recursion, Nesting and Iterations for Computational Electromagnetics

In the first phase of our work, we have concentrated on laying the foundation to develop fast algorithms, including the use of recursive structure like the recursive aggregate interaction matrix algorithm (RAIMA), the nested equivalence principle algorithm (NEPAL), the ray-propagation fast multipole algorithm (RPFMA), and the multi-level fast multipole algorithm (MLFMA). We have also investigated the use of curvilinear patches to build a basic method of moments code where these acceleration techniques can be used later. In the second phase, which is mainly reported on here, we have concentrated on implementing three-dimensional NEPAL on a massively parallel machine, the Connection Machine CM-5, and have been able to obtain some 3D scattering results. In order to understand the parallelization of codes on the Connection Machine, we have also studied the parallelization of 3D finite-difference time-domain (FDTD) code with PML material absorbing boundary condition (ABC). We found that simple algorithms like the FDTD with material ABC can be parallelized very well allowing us to solve within a minute a problem of over a million nodes. In addition, we have studied the use of the fast multipole method and the ray-propagation fast multipole algorithm to expedite matrix-vector multiplication in a conjugate-gradient solution to integral equations of scattering. We find that these methods are faster than LU decomposition for one incident angle, but are slower than LU decomposition when many incident angles are needed as in the monostatic RCS calculations.

Chew, W. C.↗
DOE OSTI2022

A Hybrid Method for Tensor Decompositions that Leverages Stochastic and Deterministic Optimization

In this paper, we propose a hybrid method that uses stochastic and deterministic search to compute the maximum likelihood estimator of a low-rank count tensor with Poisson loss via state-of-theart local methods. Our approach is inspired by Simulated Annealing for global optimization and allows for fine-grain parameter tuning as well as adaptive updates to algorithm parameters. We present numerical results that indicate our hybrid approach can compute better approximations to the maximum likelihood estimator with less computation than the state-of-the-art methods by themselves.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2021

Small UAV Flight Planning in Urban Environments

This work proposes a fast algorithm for generating obstacle-free and wind-efficient flight paths at a constant above-ground-level altitude in urban environments because a fast flight path planning algorithm is an essential function or service needed for enabling small unmanned aerial vehicle (sUAV) to operate in urban environments within Class G airspace. The proposed method first converts the 3D path planning problem to a 2D problem by constructing an obstacle map at a given above-ground-level altitude. A quad-tree decomposition is then used to build a search space in terms of obstacle occupancy and wind difference. The wind cost of traveling through each cell is defined based on energy consumption under various wind conditions. A repulsive potential is also adopted to make sure that the flight plans stay away from obstacles. The Theta* search algorithm, a variant of A* algorithm, is applied to mitigate the path angle change constraints introduced by grid-based graphs. With the Theta* and postsmoothing techniques, an obstacle-free, wind efficient, and constant above-ground-level flight plan can be quickly generated for sUAV operations in urban environments while meeting the lateral path angle constraints. The results showed that the path planning algorithm is efficient and can be finished within several seconds. With a proper choice of wind coefficient, the proposed path planning algorithm outperforms the multiple-shooting trajectory optimization method even in an obstacle-free environment. With the flexibility of incorporating other geo-related costs and computation efficiency, the proposed algorithm shows the potential for real-time flight path planning in complex urban environments.

Path planning↗
DOE OSTI2023

Granger Causality for prediction in Dynamic Mode Decomposition: Application to power systems

Here, the dynamic mode decomposition (DMD) technique extracts the dominant modes characterizing the innate dynamical behavior of the system within the measurement data. For appropriate identification of dominant modes from the measurement data, the DMD algorithm necessitates ensuring the quality of the input measurement data sequences. On that account, for validating the usability of the dataset for the DMD algorithm, the paper proposed two conditions: Persistence of excitation (PE) and the Granger Causality Test (GCT). The virtual data sequences are designed with the hankel matrix representation such that the dimensions of the subspace spanning the essential system modes are increased with the addition of new state variables. The PE condition provides the lower bound for the trajectory length, and the GCT provides the order of the model. Satisfying the PE condition enables estimating an approximate linear model, but the predictability with the identified model is only assured with the temporal causation among data searched with GCT. The proposed methodology is validated with the application for coherency identification (CI) in a multi-machine power system (MMPS), an essential phenomenon in transient stability analysis. The significance of PE condition and GCT is demonstrated through various case studies implemented on 22 bus six generator system.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS2022

Alternative regularizations for Outer-Approximation algorithms for convex MINLP

In this work, we extend the regularization framework from Kronqvist et al. (Math Program 180(1):285–310, 2020) by incorporating several new regularization functions and develop a regularized single-tree search method for solving convex mixed-integer nonlinear programming (MINLP) problems. We propose a set of regularization functions based on distance metrics and Lagrangean approximations, used in the projection problem for finding new integer combinations to be used within the Outer-Approximation (OA) method. The new approach, called Regularized Outer-Approximation (ROA), has been implemented as part of the open-source Mixed-integer nonlinear decomposition toolbox for Pyomo—MindtPy. We compare the OA method with seven regularization function alternatives for ROA. Moreover, we extend the LP/NLP Branch and Bound method proposed by Quesada and Grossmann (Comput Chem Eng 16(10–11):937–947, 1992) to include regularization in an algorithm denoted RLP/NLP. We provide convergence guarantees for both ROA and RLP/NLP. Finally, we perform an extensive computational experiment considering all convex MINLP problems in the benchmark library MINLPLib. The computational results show clear advantages of using regularization combined with the OA method.

Convex Mixed-integer nonlinear programming↗
DOE OSTI2022

A Mountaintop View Requires Minimal Sorting: A Faster Contour Tree Algorithm

Consider a scalar field f : M → R, where M is a triangulated simplicial mesh in R d . A level set, or contour, at value v is a connected component of f –1 (v). As v is changed, these contours change topology, merge into each other, or split. Contour trees are concise representations of f that track this contour behavior. The vertices of these trees are the critical points of f, where the gradient is zero. The edges represent changes in the topology of contours. It is a fundamental data structure in data analysis and visualization, and there is significant previous work (both theoretical and practical) on algorithms for constructing contour trees. Suppose M has n vertices, N facets, and t critical points. A classic result of Carr, Snoeyink, and Axen (2000) gives an algorithm that takes O(n log n+Nα(N)) time (where α(·) is the inverse Ackermann function). A further improvement to O(t log t + N) time was given by Chiang et al. All these algorithms involve a global sort of the critical points, a significant computational bottleneck. Unfortunately, lower bounds of Ω(t log t) also exist. We present the first algorithm that can avoid the global sort and has a refined time complexity that depends on the contour tree structure. Intuitively, if the tree is short and fat, we get significant improvements in running time. For a partition of the contour tree into a set of descending paths, P, our algorithm runs in O($\Sigma$ pϵP |p| log |p| + tα(t) + N). This is at most O(t log D + N), where D is the diameter of the contour tree. Moreover, it is O(tα(t) + N) for balanced trees, a significant improvement over the previous complexity. Our algorithm requires numerous ideas: partitioning the contour tree into join and split trees, a local growing procedure to iteratively build contour trees, and the use of heavy path decompositions for the time complexity analysis. There is a crucial use of a family of binomial heaps to maintain priorities, ensuring that any comparison made is between comparable nodes of the contour tree. We also prove lower bounds showing that the $\Sigma$ pϵP |p| log |p| complexity is inherent to computing contour trees.

97 MATHEMATICS AND COMPUTING↗