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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records

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NASA NTRS1999

Fast Integer Ambiguity Resolution for GPS Attitude Determination

In this paper, a new algorithm for GPS (Global Positioning System) integer ambiguity resolution is shown. The algorithm first incorporates an instantaneous (static) integer search to significantly reduce the search space using a geometric inequality. Then a batch-type loss function is used to check the remaining integers in order to determine the optimal integer. This batch function represents the GPS sightline vectors in the body frame as the sum of two vectors, one depending on the phase measurements and the other on the unknown integers. The new algorithm has several advantages: it does not require an a-priori estimate of the vehicle's attitude; it provides an inherent integrity check using a covariance-type expression; and it can resolve the integers even when coplanar baselines exist. The performance of the new algorithm is tested on a dynamic hardware simulator.

Lightsey, E. Glenn↗

NASA NTRS1986

Discrete Dirac equation on a finite half-integer lattice

The formulation of the Dirac equation on a discrete lattice with half-integer spacing and periodic boundary conditions is investigated analytically. The importance of lattice formulations for problems in field theory and quantum mechanics is explained; the concept of half-integer Fourier representation is introduced; the discrete Dirac equation for the two-dimensional case is derived; dispersion relations for the four-dimensional case are developed; and the spinor formulation for the Dirac fields on the half-integer lattice and the discrete time variable for the four-dimensional time-dependent Dirac equation are obtained. It is argued that the half-integer lattice, because it takes the Dirac Lagrangian into account, is more than a mere relabeling of the integer lattice and may have fundamental physical meaning (e.g., for the statistics of fermions). It is noted that the present formulation does not lead to species doubling, except in the continuum limit.

Smalley, L. L.↗

NASA NTRS1998

A Polynomial Time, Numerically Stable Integer Relation Algorithm

Let x = (x1, x2...,xn be a vector of real numbers. X is said to possess an integer relation if there exist integers a(sub i) not all zero such that a1x1 + a2x2 + ... a(sub n)Xn = 0. Beginning in 1977 several algorithms (with proofs) have been discovered to recover the a(sub i) given x. The most efficient of these existing integer relation algorithms (in terms of run time and the precision required of the input) has the drawback of being very unstable numerically. It often requires a numeric precision level in the thousands of digits to reliably recover relations in modest-sized test problems. We present here a new algorithm for finding integer relations, which we have named the "PSLQ" algorithm. It is proved in this paper that the PSLQ algorithm terminates with a relation in a number of iterations that is bounded by a polynomial in it. Because this algorithm employs a numerically stable matrix reduction procedure, it is free from the numerical difficulties, that plague other integer relation algorithms. Furthermore, its stability admits an efficient implementation with lower run times oil average than other algorithms currently in Use. Finally, this stability can be used to prove that relation bounds obtained from computer runs using this algorithm are numerically accurate.

Ferguson, Helaman R. P.↗

NASA NTRS2010

Using Integer Clocks to Verify the Timing-Sync Sensor Network Protocol

We use the UPPAAL model checker for Timed Automata to verify the Timing-Sync time-synchronization protocol for sensor networks (TPSN). The TPSN protocol seeks to provide network-wide synchronization of the distributed clocks in a sensor network. Clock-synchronization algorithms for sensor networks such as TPSN must be able to perform arithmetic on clock values to calculate clock drift and network propagation delays. They must be able to read the value of a local clock and assign it to another local clock. Such operations are not directly supported by the theory of Timed Automata. To overcome this formal-modeling obstacle, we augment the UPPAAL specification language with the integer clock derived type. Integer clocks, which are essentially integer variables that are periodically incremented by a global pulse generator, greatly facilitate the encoding of the operations required to synchronize clocks as in the TPSN protocol. With this integer-clock-based model of TPSN in hand, we use UPPAAL to verify that the protocol achieves network-wide time synchronization and is devoid of deadlock. We also use the UPPAAL Tracer tool to illustrate how integer clocks can be used to capture clock drift and resynchronization during protocol execution

Huang, Xiaowan↗

NASA NTRS2019

Partition-based Feasible Integer Solution Pre-computation for Hybrid Model Predictive Control

For multiparametric mixed-integer convex programming problems such as those encountered in hybrid model predictive control, we propose an algorithm for generating a feasible partition of a subset of the parameter space. The result is a static map from the current parameter to a suboptimal integer solution such that the remaining convex program is feasible. Convergence is proved with a new insight that the overlap among the feasible parameter sets of each integer solution governs the partition complexity. The partition is stored as a tree which makes querying the feasible solution efﬁcient. The algorithm can be used to warm start a mixed integer solver with a real-time guarantee or to provide a reference integer solution in several suboptimal MPC schemes. The algorithm is tested on randomly generated systems with up to six states, demonstrating the effectiveness of the approach.

Bayard, David S.↗

NASA NTRS1994

Algorithm For Integer Cosine Transforms

Algorithm computes coefficients of integer cosine transforms, containing only integer coefficients approximately proportional to floating-point coefficients of discrete cosine transforms. Used in compression of image data in blocks of N x N pixels, discrete cosine transforms involve large amounts of computation, typically amounting to 80 percent of computational load in data-compression scheme. In constructing integer approximations, competing requirements are to obtain data-compression and data-decompression performances comparable to those of corresponding descrete cosine transforms while taking advantage of simplicity afforded by integer arithmetic to reduce complexity and amount of computation.

Pollara, Fabrizio↗

NASA NTRS1982

Quadratic integer programming for large scale banded matrices

This paper is concerned with the integer quadratic program where the variables are constrained to belong to a given set of discrete values. This quadratic integer program is shown to be equivalent to a problem of finding the shortest path in a particular directed graph called a trellis when the matrix is a positive-definite symmetric banded matrix. An efficient procedure for solving this shortest path problem is presented which allows the solution of the integer quadratic program. This method is particularly effective when the half-bandwidth of the matrix is significantly smaller than its dimension.

Yan, T. Y.↗

NASA NTRS1986

A new VLSI complex integer multiplier which uses a quadratic-polynomial residue system with Fermat numbers

A quadratic-polynomial Fermat residue number system (QFNS) has been used to compute complex integer multiplications. The advantage of such a QFNS is that a complex integer multiplication requires only two integer multiplications. In this article, a new type Fermat number multiplier is developed which eliminates the initialization condition of the previous method. It is shown that the new complex multiplier can be implemented on a single VLSI chip. Such a chip is designed and fabricated in CMOS-pw technology.

Truong, T. K.↗

NASA NTRS1987

A new VLSI complex integer multiplier which uses a quadratic-polynomial residue system with Fermat numbers

Shyu, H. C.↗

NASA NTRS1992

Software For Integer Programming

Improved Exploratory Search Technique for Pure Integer Linear Programming Problems (IESIP) program optimizes objective function of variables subject to confining functions or constraints, using discrete optimization or integer programming. Enables rapid solution of problems up to 10 variables in size. Integer programming required for accuracy in modeling systems containing small number of components, distribution of goods, scheduling operations on machine tools, and scheduling production in general. Written in Borland's TURBO Pascal.

Fogle, F. R.↗

NASA NTRS1991

Integer cosine transform for image compression

This article describes a recently introduced transform algorithm called the integer cosine transform (ICT), which is used in transform-based data compression schemes. The ICT algorithm requires only integer operations on small integers and at the same time gives a rate-distortion performance comparable to that offered by the floating-point discrete cosine transform (DCT). The article addresses the issue of implementation complexity, which is of prime concern for source coding applications of interest in deep-space communications. Complexity reduction in the transform stage of the compression scheme is particularly relevant, since this stage accounts for most (typically over 80 percent) of the computational load.

Cheung, K.-M.↗

NASA NTRS2022

Foraging with MUSHROOMS: A Mixed-integer Linear Programming Scheduler for Multimessenger Target of Opportunity Searches with the Zwicky Transient Facility

Electromagnetic follow-up of gravitational-wave detections is very resource intensive, taking up hours of limited observation time on dozens of telescopes. Creating more efficient schedules for follow-up will lead to a commensurate increase in counterpart location efficiency without using more telescope time. Widely used in operations research and telescope scheduling, mixed-integer linear programming is a strong candidate to produce these higher-efficiency schedules, as it can make use of powerful commercial solvers that find globally optimal solutions to provided problems. We detail a new target-of-opportunity scheduling algorithm designed with Zwicky Transient Facility in mind that uses mixed-integer linear programming. We compare its performance to gwemopt, the tuned heuristic scheduler used by the Zwicky Transient Facility and other facilities during the third LIGO–Virgo gravitational-wave observing run. This new algorithm uses variable-length observing blocks to enforce cadence requirements and to ensure field observability, along with having a secondary optimization step to minimize slew time. We show that by employing a hybrid method utilizing both this scheduler and gwemopt, the previous scheduler used, in concert, we can achieve an average improvement in detection efficiency of 3%–11% over gwemopt alone for a simulated binary neutron star merger data set consistent with LIGO–Virgo's third observing run, highlighting the potential of mixed-integer target of opportunity schedulers for future multimessenger follow-up surveys.

B Parazin↗

NASA NTRS2012

Mixed Integer Programming and Heuristic Scheduling for Space Communication Networks

We developed framework and the mathematical formulation for optimizing communication network using mixed integer programming. The design yields a system that is much smaller, in search space size, when compared to the earlier approach. Our constrained network optimization takes into account the dynamics of link performance within the network along with mission and operation requirements. A unique penalty function is introduced to transform the mixed integer programming into the more manageable problem of searching in a continuous space. The constrained optimization problem was proposed to solve in two stages: first using the heuristic Particle Swarming Optimization algorithm to get a good initial starting point, and then feeding the result into the Sequential Quadratic Programming algorithm to achieve the final optimal schedule. We demonstrate the above planning and scheduling methodology with a scenario of 20 spacecraft and 3 ground stations of a Deep Space Network site. Our approach and framework have been simple and flexible so that problems with larger number of constraints and network can be easily adapted and solved.

Mixed Integer Programming↗

NASA NTRS1975

Two-dimensional convolute integers for optical image data processing and surface fitting

An approach toward low-pass, high-pass and band-pass filtering is presented. Convolution coefficients possessing the filtering speed associated with a moving smoothing average without suffering a loss of resolution are discussed. Resolution was retained because the coefficients represented the equivalance of applying high order two-dimensional regression calculations to an image without considering the time-consuming summations associated with the usual normal equations. The smoothing (low-pass) and roughing (high-pass) aspects of the filters are a result of being derived from regression theory. The coefficients are universal integer valves completely described by filter size and surface order, and possess a number of symmetry properties. Double convolution lead to a single set of coefficients with an expanded mask which can yield band-pass filtering and the surface normal. For low order surfaces (0,1), the two-dimensional convolute integers were equivalent to a moving smoothing average.

Edwards, T. R.↗

NASA NTRS1982

Two-dimensional convolute integers for analytical instrumentation

As new analytical instruments and techniques emerge with increased dimensionality, a corresponding need is seen for data processing logic which can appropriately address the data. Two-dimensional measurements reveal enhanced unknown mixture analysis capability as a result of the greater spectral information content over two one-dimensional methods taken separately. It is noted that two-dimensional convolute integers are merely an extension of the work by Savitzky and Golay (1964). It is shown that these low-pass, high-pass and band-pass digital filters are truly two-dimensional and that they can be applied in a manner identical with their one-dimensional counterpart, that is, a weighted nearest-neighbor, moving average with zero phase shifting, convoluted integer (universal number) weighting coefficients.

Edwards, T. R.↗

NASA NTRS1988

Two dimensional convolute integers for machine vision and image recognition

Machine vision and image recognition require sophisticated image processing prior to the application of Artificial Intelligence. Two Dimensional Convolute Integer Technology is an innovative mathematical approach for addressing machine vision and image recognition. This new technology generates a family of digital operators for addressing optical images and related two dimensional data sets. The operators are regression generated, integer valued, zero phase shifting, convoluting, frequency sensitive, two dimensional low pass, high pass and band pass filters that are mathematically equivalent to surface fitted partial derivatives. These operators are applied non-recursively either as classical convolutions (replacement point values), interstitial point generators (bandwidth broadening or resolution enhancement), or as missing value calculators (compensation for dead array element values). These operators show frequency sensitive feature selection scale invariant properties. Such tasks as boundary/edge enhancement and noise or small size pixel disturbance removal can readily be accomplished. For feature selection tight band pass operators are essential. Results from test cases are given.

Edwards, Thomas R.↗

NASA NTRS1990

An improved exploratory search technique for pure integer linear programming problems

The development is documented of a heuristic method for the solution of pure integer linear programming problems. The procedure draws its methodology from the ideas of Hooke and Jeeves type 1 and 2 exploratory searches, greedy procedures, and neighborhood searches. It uses an efficient rounding method to obtain its first feasible integer point from the optimal continuous solution obtained via the simplex method. Since this method is based entirely on simple addition or subtraction of one to each variable of a point in n-space and the subsequent comparison of candidate solutions to a given set of constraints, it facilitates significant complexity improvements over existing techniques. It also obtains the same optimal solution found by the branch-and-bound technique in 44 of 45 small to moderate size test problems. Two example problems are worked in detail to show the inner workings of the method. Furthermore, using an established weighted scheme for comparing computational effort involved in an algorithm, a comparison of this algorithm is made to the more established and rigorous branch-and-bound method. A computer implementation of the procedure, in PC compatible Pascal, is also presented and discussed.

Fogle, F. R.↗

NASA NTRS1991

Stacking-sequence optimization for buckling of laminated plates by integer programming

Integer-programming formulations for the design of symmetric and balanced laminated plates under biaxial compression are presented. Both maximization of buckling load for a given total thickness and the minimization of total thickness subject to a buckling constraint are formulated. The design variables that define the stacking sequence of the laminate are zero-one integers. It is shown that the formulation results in a linear optimization problem that can be solved on readily available software. This is in contrast to the continuous case, where the design variables are the thicknesses of layers with specified ply orientations, and the optimization problem is nonlinear. Constraints on the stacking sequence such as a limit on the number of contiguous plies of the same orientation and limits on in-plane stiffnesses are easily accommodated. Examples are presented for graphite-epoxy plates under uniaxial and biaxial compression using a commercial software package based on the branch-and-bound algorithm.

Haftka, Raphael T.↗