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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
NASA NTRS2010

Onboard Run-Time Goal Selection for Autonomous Operations

We describe an efficient, online goal selection algorithm for use onboard spacecraft and its use for selecting goals at runtime. Our focus is on the re-planning that must be performed in a timely manner on the embedded system where computational resources are limited. In particular, our algorithm generates near optimal solutions to problems with fully specified goal requests that oversubscribe available resources but have no temporal flexibility. By using a fast, incremental algorithm, goal selection can be postponed in a "just-in-time" fashion allowing requests to be changed or added at the last minute. This enables shorter response cycles and greater autonomy for the system under control.

Rabideau, Gregg↗
NASA NTRS2009

Tractable Goal Selection with Oversubscribed Resources

We describe an efficient, online goal selection algorithm and its use for selecting goals at runtime. Our focus is on the re-planning that must be performed in a timely manner on the embedded system where computational resources are limited. In particular, our algorithm generates near optimal solutions to problems with fully specified goal requests that oversubscribe available resources but have no temporal flexibility. By using a fast, incremental algorithm, goal selection can be postponed in a "just-in-time" fashion allowing requests to be changed or added at the last minute. This enables shorter response cycles and greater autonomy for the system under control.

Rabideau, Gregg↗
NASA NTRS2013

Optimal Integration of Departures and Arrivals in Terminal Airspace

Coordination of operations with spatially and temporally shared resources, such as route segments, fixes, and runways, improves the efficiency of terminal airspace management. Problems in this category are, in general, computationally difficult compared to conventional scheduling problems. This paper presents a fast time algorithm formulation using a non-dominated sorting genetic algorithm (NSGA). It was first applied to a test problem introduced in existing literature. An experiment with a test problem showed that new methods can solve the 20 aircraft problem in fast time with a 65% or 440 second delay reduction using shared departure fixes. In order to test its application in a more realistic and complicated problem, the NSGA algorithm was applied to a problem in LAX terminal airspace, where interactions between 28% of LAX arrivals and 10% of LAX departures are resolved by spatial separation in current operations, which may introduce unnecessary delays. In this work, three types of separations - spatial, temporal, and hybrid separations - were formulated using the new algorithm. The hybrid separation combines both temporal and spatial separations. Results showed that although temporal separation achieved less delay than spatial separation with a small uncertainty buffer, spatial separation outperformed temporal separation when the uncertainty buffer was increased. Hybrid separation introduced much less delay than both spatial and temporal approaches. For a total of 15 interacting departures and arrivals, when compared to spatial separation, the delay reduction of hybrid separation varied between 11% or 3.1 minutes and 64% or 10.7 minutes corresponding to an uncertainty buffer from 0 to 60 seconds. Furthermore, as a comparison with the NSGA algorithm, a First-Come-First-Serve based heuristic method was implemented for the hybrid separation. Experiments showed that the results from the NSGA algorithm have 9% to 42% less delay than the heuristic method with varied uncertainty buffer sizes.

terminal airspace↗
NASA NTRS2006

Algorithm for Rapid Searching Among Star-Catalog Entries

An algorithm searches a star catalog to identify guide stars within the field of view of a telescope or camera. The algorithm is fast: the number of computations needed to perform the search is approximately proportional to the logarithm of the number of stars in the catalog. The algorithm requires the prior organization of the star catalog into a hierarchy utilizing independent spherical coverings (see figure), such that each successively higher level contains fewer elements. In the lowest and most numerous level of the hierarchy, the elements are individual stars in the star catalog. The next higher level contains a spherical covering (a constellation of n points on a sphere that minimizes the maximum distance of any point on the sphere from the closest one of the n points), the next higher level contains a smaller spherical covering, and so forth, ending at the highest level, which contains one element representing the point of entry into the search structure. With necessary exceptions at the lowest and highest levels, each element at each level is labeled in terms of the element to which it is linked in the next higher level and the first element to which it is linked in the next lower level. Each element is also labeled in terms of (1) its coordinates on the celestial sphere and (2) the largest angular distance to any element in any lower level in the hierarchy. The elements at all levels of the hierarchy are numbered on a single list, such that the elements of each constellation at each level are numbered consecutively. The algorithm is recursive. The input required to start the algorithm comprises the coordinates of a point on the celestial sphere. Attention is then focused on individual elements of the hierarchy, starting from the topmost one, as follows: The angle between the input point and the element under consideration is calculated. If the calculated angle is larger than the sum of (1) the predetermined angle to the most distant element plus (2) the half field of view of the telescope, then no stars will be within the field of view and this recursive part of the algorithm is terminated.

Liebe, Carl Christian↗
NASA NTRS2012

Optimal Integration of Departure and Arrivals in Terminal Airspace

Coordination of operations with spatially and temporally shared resources such as route segments, fixes, and runways improves the efficiency of terminal airspace management. Problems in this category include scheduling and routing, thus they are normally difficult to solve compared with pure scheduling problems. In order to reduce the computational time, a fast time algorithm formulation using a non-dominated sorting genetic algorithm (NSGA) was introduced in this work and applied to a test case based on existing literature. The experiment showed that new method can solve the whole problem in fast time instead of solving sub-problems sequentially with a window technique. The results showed a 60% or 406 second delay reduction was achieved by sharing departure fixes (more details on the comparison with MILP results will be presented in the final paper). Furthermore, the NSGA algorithm was applied to a problem in LAX terminal airspace, where interactions between 28% of LAX arrivals and 10% of LAX departures are resolved by spatial segregation, which may introduce unnecessary delays. In this work, spatial segregation, temporal segregation, and hybrid segregation were formulated using the new algorithm. Results showed that spatial and temporal segregation approaches achieved similar delay. Hybrid segregation introduced much less delay than the other two approaches. For a total of 9 interacting departures and arrivals, delay reduction varied from 4 minutes to 6.4 minutes corresponding flight time uncertainty from 0 to 60 seconds. Considering the amount of flights that could be affected, total annual savings with hybrid segregation would be significant.

high density terminal↗
NASA NTRS2011

Technique for Solving Electrically Small to Large Structures for Broadband Applications

Fast iterative algorithms are often used for solving Method of Moments (MoM) systems, having a large number of unknowns, to determine current distribution and other parameters. The most commonly used fast methods include the fast multipole method (FMM), the precorrected fast Fourier transform (PFFT), and low-rank QR compression methods. These methods reduce the O(N) memory and time requirements to O(N log N) by compressing the dense MoM system so as to exploit the physics of Green s Function interactions. FFT-based techniques for solving such problems are efficient for spacefilling and uniform structures, but their performance substantially degrades for non-uniformly distributed structures due to the inherent need to employ a uniform global grid. FMM or QR techniques are better suited than FFT techniques; however, neither the FMM nor the QR technique can be used at all frequencies. This method has been developed to efficiently solve for a desired parameter of a system or device that can include both electrically large FMM elements, and electrically small QR elements. The system or device is set up as an oct-tree structure that can include regions of both the FMM type and the QR type. The system is enclosed with a cube at a 0- th level, splitting the cube at the 0-th level into eight child cubes. This forms cubes at a 1st level, recursively repeating the splitting process for cubes at successive levels until a desired number of levels is created. For each cube that is thus formed, neighbor lists and interaction lists are maintained. An iterative solver is then used to determine a first matrix vector product for any electrically large elements as well as a second matrix vector product for any electrically small elements that are included in the structure. These matrix vector products for the electrically large and small elements are combined, and a net delta for a combination of the matrix vector products is determined. The iteration continues until a net delta is obtained that is within the predefined limits. The matrix vector products that were last obtained are used to solve for the desired parameter. The solution for the desired parameter is then presented to a user in a tangible form; for example, on a display.

Jandhyala, Vikram↗
NASA NTRS2015

Unsteady Solution of Non-Linear Differential Equations Using Walsh Function Series

Walsh functions form an orthonormal basis set consisting of square waves. The discontinuous nature of square waves make the system well suited for representing functions with discontinuities. The product of any two Walsh functions is another Walsh function - a feature that can radically change an algorithm for solving non-linear partial differential equations (PDEs). The solution algorithm of non-linear differential equations using Walsh function series is unique in that integrals and derivatives may be computed using simple matrix multiplication of series representations of functions. Solutions to PDEs are derived as functions of wave component amplitude. Three sample problems are presented to illustrate the Walsh function series approach to solving unsteady PDEs. These include an advection equation, a Burgers equation, and a Riemann problem. The sample problems demonstrate the use of the Walsh function solution algorithms, exploiting Fast Walsh Transforms in multi-dimensions (O(Nlog(N))). Details of a Fast Walsh Reciprocal, defined here for the first time, enable inversion of aWalsh Symmetric Matrix in O(Nlog(N)) operations. Walsh functions have been derived using a fractal recursion algorithm and these fractal patterns are observed in the progression of pairs of wave number amplitudes in the solutions. These patterns are most easily observed in a remapping defined as a fractal fingerprint (FFP). A prolongation of existing solutions to the next highest order exploits these patterns. The algorithms presented here are considered a work in progress that provide new alternatives and new insights into the solution of non-linear PDEs.

Gnoffo, Peter A.↗
NASA NTRS1994

A new algorithm for attitude-independent magnetometer calibration

A new algorithm is developed for inflight magnetometer bias determination without knowledge of the attitude. This algorithm combines the fast convergence of a heuristic algorithm currently in use with the correct treatment of the statistics and without discarding data. The algorithm performance is examined using simulated data and compared with previous algorithms.

Alonso, Roberto↗
NASA NTRS1990

Using Strassen's algorithm to accelerate the solution of linear systems

Strassen's algorithm for fast matrix-matrix multiplication has been implemented for matrices of arbitrary shapes on the CRAY-2 and CRAY Y-MP supercomputers. Several techniques have been used to reduce the scratch space requirement for this algorithm while simultaneously preserving a high level of performance. When the resulting Strassen-based matrix multiply routine is combined with some routines from the new LAPACK library, LU decomposition can be performed with rates significantly higher than those achieved by conventional means. We succeeded in factoring a 2048 x 2048 matrix on the CRAY Y-MP at a rate equivalent to 325 MFLOPS.

Bailey, David H.↗
DOE OSTI2021

Absolute contrast estimation for soft X-ray photon fluctuation spectroscopy using a variational droplet model

Abstract X-ray photon fluctuation spectroscopy using a two-pulse mode at the Linac Coherent Light Source has great potential for the study of quantum fluctuations in materials as it allows for exploration of low-energy physics. However, the complexity of the data analysis and interpretation still prevent recovering real-time results during an experiment, and can even complicate post-analysis processes. This is particularly true for high-spatial resolution applications using CCDs with small pixels, which can decrease the photon mapping accuracy resulting from the large electron cloud generation at the detector. Droplet algorithms endeavor to restore accurate photon maps, but the results can be altered by their hyper-parameters. We present numerical modeling tools through extensive simulations that mimic previous x-ray photon fluctuation spectroscopy experiments. By modification of a fast droplet algorithm, our results demonstrate how to optimize the precise parameters that lift the intrinsic counting degeneracy impeding accuracy in extracting the speckle contrast. These results allow for an absolute determination of the summed contrast from multi-pulse x-ray speckle diffraction, the modus operandi by which the correlation time for spontaneous fluctuations can be measured.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS2003

A Fast Implementation of the ISOCLUS Algorithm

Unsupervised clustering is a fundamental building block in numerous image processing applications. One of the most popular and widely used clustering schemes for remote sensing applications is the ISOCLUS algorithm, which is based on the ISODATA method. The algorithm is given a set of n data points in d-dimensional space, an integer k indicating the initial number of clusters, and a number of additional parameters. The general goal is to compute the coordinates of a set of cluster centers in d-space, such that those centers minimize the mean squared distance from each data point to its nearest center. This clustering algorithm is similar to another well-known clustering method, called k-means. One significant feature of ISOCLUS over k-means is that the actual number of clusters reported might be fewer or more than the number supplied as part of the input. The algorithm uses different heuristics to determine whether to merge lor split clusters. As ISOCLUS can run very slowly, particularly on large data sets, there has been a growing .interest in the remote sensing community in computing it efficiently. We have developed a faster implementation of the ISOCLUS algorithm. Our improvement is based on a recent acceleration to the k-means algorithm of Kanungo, et al. They showed that, by using a kd-tree data structure for storing the data, it is possible to reduce the running time of k-means. We have adapted this method for the ISOCLUS algorithm, and we show that it is possible to achieve essentially the same results as ISOCLUS on large data sets, but with significantly lower running times. This adaptation involves computing a number of cluster statistics that are needed for ISOCLUS but not for k-means. Both the k-means and ISOCLUS algorithms are based on iterative schemes, in which nearest neighbors are calculated until some convergence criterion is satisfied. Each iteration requires that the nearest center for each data point be computed. Naively, this requires O(kn) time, where k denotes the current number of centers. Traditional techniques for accelerating nearest neighbor searching involve storing the k centers in a data structure. However, because of the iterative nature of the algorithm, this data structure would need to be rebuilt with each new iteration. Our approach is to store the data points in a kd-tree data structure. The assignment of points to nearest neighbors is carried out by a filtering process, which successively eliminates centers that can not possibly be the nearest neighbor for a given region of space. This algorithm is significantly faster, because large groups of data points can be assigned to their nearest center in a single operation. Preliminary results on a number of real Landsat datasets show that our revised ISOCLUS-like scheme runs about twice as fast.

Memarsadeghi, Nargess↗
DOE OSTI2020

Gradient-Based Multi-Area Distribution System State Estimation

The increasing distributed and renewable energy resources and controllable devices in distribution systems make fast distribution system state estimation (DSSE) crucial in system monitoring and control. We consider a large multi-phase distribution system and formulate DSSE as a weighted least squares (WLS) problem. We divide the large distribution system into smaller areas of subtree structure, and by jointly exploring the linearized power flow model and the network topology, we propose a gradient-based multi-area algorithm to exactly and efficiently solve the WLS problem. The proposed algorithm enables distributed and parallel computation of the state estimation problem without compromising any performance. Numerical results on a 4,521-node test feeder show that the designed algorithm features fast convergence and accurate estimation results. Comparison with traditional Gauss-Newton method shows that the proposed method has much better performance in distribution systems with a limited amount of reliable measurement. The real-time implementation of the algorithm tracks time-varying system states with high accuracy.

41 EE - Solar Energy Technologies Office (EE-4S)↗
NASA NTRS2014

Next Generation Aura-OMI SO2 Retrieval Algorithm: Introduction and Implementation Status

We introduce our next generation algorithm to retrieve SO2 using radiance measurements from the Aura Ozone Monitoring Instrument (OMI). We employ a principal component analysis technique to analyze OMI radiance spectral in 310.5-340 nm acquired over regions with no significant SO2. The resulting principal components (PCs) capture radiance variability caused by both physical processes (e.g., Rayleigh and Raman scattering, and ozone absorption) and measurement artifacts, enabling us to account for these various interferences in SO2 retrievals. By fitting these PCs along with SO2 Jacobians calculated with a radiative transfer model to OMI-measured radiance spectra, we directly estimate SO2 vertical column density in one step. As compared with the previous generation operational OMSO2 PBL (Planetary Boundary Layer) SO2 product, our new algorithm greatly reduces unphysical biases and decreases the noise by a factor of two, providing greater sensitivity to anthropogenic emissions. The new algorithm is fast, eliminates the need for instrument-specific radiance correction schemes, and can be easily adapted to other sensors. These attributes make it a promising technique for producing long-term, consistent SO2 records for air quality and climate research. We have operationally implemented this new algorithm on OMI SIPS for producing the new generation standard OMI SO2 products.

Sulfur dioxide↗
DOE OSTI2020

Assessing Historical Variability of South Asian Monsoon Lows and Depressions With an Optimized Tracking Algorithm

Abstract Cyclonic low‐pressure systems (LPS) produce abundant rainfall in South Asia, where they are traditionally categorized as monsoon lows, monsoon depressions, and more intense cyclonic storms. The India Meteorological Department (IMD) has tracked monsoon depressions for over a century, finding a large decline in their number in recent decades, but their methods have changed over time and do not include monsoon lows. This study presents a fast, objective algorithm for identifying monsoon LPS and uses it to assess interannual variability and trends in reanalyses. Variables and thresholds used in the algorithm are selected to best match a subjectively analyzed LPS data set while minimizing disagreement between four reanalyses in a training period. The stream function of 850 hPa horizontal wind is found to be optimal in this sense; it is less noisy than vorticity and represents the complete nondivergent wind, even when flow is not geostrophic. Using this algorithm, LPS statistics are computed for five reanalyses, and none show a detectable trend in monsoon depression counts since 1979. Both the Japanese 55‐year Reanalysis (JRA‐55) and the IMD data set show a step‐like reduction in depression counts when they began using geostationary satellite data, in 1979 and 1982, respectively; the 1958–2018 linear trend in JRA‐55, however, is smaller than in the IMD data set, and its error bar includes 0. There are more LPS in seasons with above‐average monsoon rainfall and in La Niña years, but few other large‐scale modes of interannual variability are found to modulate LPS counts, lifetimes, or track length consistently across reanalyses.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1975

Advances in Application of Fast Semidirect Computational Methods in Transonic Flow

This paper is intended as a review and summary of the advances made in a recently developed approach for rapid numerical solution of the equations of inviscid transonic aerodynamics. The investigation has been limited to two-dimensional, steady, inviscid flow over airfoils in a subsonic free stream, with emphasis on development of a rapid computational technique, rather than on generality of application. The approach uses finite-difference algorithms called "fast direct elliptic solvers" within an iteration scheme. "Direct" means that the entire computation field is solved at once, rather than in successive traverses over the field as in a point- or line-relaxation method. Such an iterative method is referred to as "semidirect." The iterative convergence can be faster than in other relaxation methods because changes are felt simultaneously at all points in each succeeding iteration. Direct elliptic solvers and semidirect methods have restrictions, but these are gradually being removed. Direct solvers were first developed for solving Poisson's equation on a rectangle without interior boundaries. A method to treat first-order systems, a direct Cauchy-Riemann solver has also been developed. Numerical treatment of part of a system of nonlinear equations by a Poisson solver has been reported. Also Poisson solvers in semidirect methods were used for nonseparable elliptic equations. The semidirect method was extended to the solution of a problem of mixed type, where the improved Murman-Cole transonic small-disturbance difference equations were solved. A slightly supercritical flow over a biconvex airfoil was treated successfully, but the iterations did not converge for more strongly supercritical conditions In another work the addition of terms ot both sides of the difference equations stabilized the iteration for supercritical conditions with large supersonic zones. For this, the Cauchy-Riemann solver was revised to incl,ude the needed terms. Most recently, the evaluation of parameters for rapid convergence and comparisons, with Murman's line-relaxation method was described. The method was extended to full second order accuracy in a fully conservative formulation in another work.

Martin, E. Dale↗
DOE OSTI2024

Lattice Green’s Functions for High-Order Finite Difference Stencils

Lattice Green's Functions (LGFs) are fundamental solutions to discretized linear operators, and as such they are a useful tool for solving discretized elliptic PDEs on domains that are unbounded in one or more directions. The majority of existing numerical solvers that make use of LGFs rely on a second-order discretization and operate on domains with free-space boundary conditions in all directions. Under these conditions, fast expansion methods are available that enable precomputation of 2D or 3D LGFs in linear time, avoiding the need for brute-force multi-dimensional quadrature of numerically unstable integrals. Here we focus on higher-order discretizations of the Laplace operator on domains with more general boundary conditions, by (1) providing an algorithm for fast and accurate evaluation of the LGFs associated with high-order dimension-split centered finite differences on unbounded domains, and (2) deriving closed-form expressions for the LGFs associated with both dimension-split and Mehrstellen discretizations on domains with one unbounded dimension. Through numerical experiments we demonstrate that these techniques provide LGF evaluations with near machine-precision accuracy, and that the resulting LGFs allow for numerically consistent solutions to high-order discretizations of the Poisson's equation on fully or partially unbounded 3D domains.

97 MATHEMATICS AND COMPUTING↗
NASA NTRSDate not supplied

Quantum-Accelerated Distributed Algorithms for Approximate Steiner Trees and Directed Minimum Spanning Trees

We present two algorithms in the Quantum CONGEST-CLIQUE model of distributed computation that succeed with high probability; one for producing an approximately optimal Steiner Tree, and one for producing an exact spanning arborescence of minimum weight, the analog of a Minimum Spanning Tree in a directed graph, each of which uses O~(n^(1/4)) rounds of communication and O~(n^(9/4)) messages, achieving a lower round and message complexity than any known algorithms in the classical CONGEST-CLIQUE model. The CONGEST distributed computational model allows limited-sized messages to be transmitted within a network described by a communication graph of size n in a series of rounds to address a computational problem. The size limitation for such messages isO(log(n)) bits at each edge of the communication graph per round. The communication graph in the CONGEST-CLIQUE model is fully connected. In the Quantum CONGEST-CLIQUE model, at most O(log(n)) classical and quantum bits (qubits) can be communicated across each edge of the communication graph per round. At a high level, we achieve these results by combining classical algorithms with fast quantum subroutines. These speedups further contribute to understanding what problems can be solved more efficiently when we allow quantum communication in this CONGEST-CLIQUE model of distributed computation.

quantum distributed algorithms↗