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At least 469 records · Page 26

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NASA NTRS1996

Application of Hybrid Optimization-Expert System for Optimal Power Management on Board Space Power Station

The space power system has two sources of energy: photo-voltaic blankets and batteries. The optimal power management problem on-board has two broad operations: off-line power scheduling to determine the load allocation schedule of the next several hours based on the forecast of load and solar power availability. The nature of this study puts less emphasis on speed requirement for computation and more importance on the optimality of the solution. The second category problem, on-line power rescheduling, is needed in the event of occurrence of a contingency to optimally reschedule the loads to minimize the 'unused' or 'wasted' energy while keeping the priority on certain type of load and minimum disturbance of the original optimal schedule determined in the first-stage off-line study. The computational performance of the on-line 'rescheduler' is an important criterion and plays a critical role in the selection of the appropriate tool. The Howard University Center for Energy Systems and Control has developed a hybrid optimization-expert systems based power management program. The pre-scheduler has been developed using a non-linear multi-objective optimization technique called the Outer Approximation method and implemented using the General Algebraic Modeling System (GAMS). The optimization model has the capability of dealing with multiple conflicting objectives viz. maximizing energy utilization, minimizing the variation of load over a day, etc. and incorporates several complex interaction between the loads in a space system. The rescheduling is performed using an expert system developed in PROLOG which utilizes a rule-base for reallocation of the loads in an emergency condition viz. shortage of power due to solar array failure, increase of base load, addition of new activity, repetition of old activity etc. Both the modules handle decision making on battery charging and discharging and allocation of loads over a time-horizon of a day divided into intervals of 10 minutes. The models have been extensively tested using a case study for the Space Station Freedom and the results for the case study will be presented. Several future enhancements of the pre-scheduler and the 'rescheduler' have been outlined which include graphic analyzer for the on-line module, incorporating probabilistic considerations, including spatial location of the loads and the connectivity using a direct current (DC) load flow model.

Momoh, James↗

DOE OSTI2018

Numerical approach based on fractional-order Lagrange polynomials for solving a class of fractional differential equations

In this study, we propose a new set of fractional functions based on the Lagrange polynomials to solve a class of fractional differential equations. Fractional differential equations are the best tools for modelling natural phenomenon that are elaborated by fractional calculus. Therefore, we need an accurate and efficient technique for solving them. The main purpose of this article is to generalize new functions based on Lagrange polynomials to the fractional calculus. At first, we present a new representation of Lagrange polynomials and in continue, we propose a new set of fractional-order functions which are called fractional-order Lagrange polynomials (FLPs). Besides, a general formulation for operational matrices of fractional integration and derivative of FLPs on arbitrary nodal points are extracted. These matrices are obtained using Laplace transform. The initial value problems is reduced to the system of algebraic equations using the operational matrix of fractional integration and collocation method. Also, we find the upper bound of error vector for the fractional integration operational matrix and we indicate convergence of approximations of FLPs. Illustrative examples are included to demonstrate the validity and applicability of the proposed technique.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2003

Intelligent machines in the twenty-first century: foundations of inference and inquiry

The last century saw the application of Boolean algebra to the construction of computing machines, which work by applying logical transformations to information contained in their memory. The development of information theory and the generalization of Boolean algebra to Bayesian inference have enabled these computing machines, in the last quarter of the twentieth century, to be endowed with the ability to learn by making inferences from data. This revolution is just beginning as new computational techniques continue to make difficult problems more accessible. Recent advances in our understanding of the foundations of probability theory have revealed implications for areas other than logic. Of relevance to intelligent machines, we recently identified the algebra of questions as the free distributive algebra, which will now allow us to work with questions in a way analogous to that which Boolean algebra enables us to work with logical statements. In this paper, we examine the foundations of inference and inquiry. We begin with a history of inferential reasoning, highlighting key concepts that have led to the automation of inference in modern machine-learning systems. We then discuss the foundations of inference in more detail using a modern viewpoint that relies on the mathematics of partially ordered sets and the scaffolding of lattice theory. This new viewpoint allows us to develop the logic of inquiry and introduce a measure describing the relevance of a proposed question to an unresolved issue. Last, we will demonstrate the automation of inference, and discuss how this new logic of inquiry will enable intelligent machines to ask questions. Automation of both inference and inquiry promises to allow robots to perform science in the far reaches of our solar system and in other star systems by enabling them not only to make inferences from data, but also to decide which question to ask, which experiment to perform, or which measurement to take given what they have learned and what they are designed to understand.

Review↗

NASA NTRS1974

HAL/S - The programming language for Shuttle

HAL/S is a higher order language and system, now operational, adopted by NASA for programming Space Shuttle on-board software. Program reliability is enhanced through language clarity and readability, modularity through program structure, and protection of code and data. Salient features of HAL/S include output orientation, automatic checking (with strictly enforced compiler rules), the availability of linear algebra, real-time control, a statement-level simulator, and compiler transferability (for applying HAL/S to additional object and host computers). The compiler is described briefly.

Martin, F. H.↗

NASA NTRS1974

REDUCE 2: A computer program for the symbolic reduction of large block diagrams

REDUCE 2 is reported as a FORMAC program which symbolically calculates the transfer function(s) of any linear-block-diagram output variable to any or all input variables. The program requires as input a set of algebraic expressions representing the block diagram, the desired transfer function(s), and a string of variables indicating the desired order of reduction. The solution is presented in the compact form of a set of nested functions (super G's). The program can handle systems as large as 600 equations and is intended as a tool for the analysis of complex control and dynamic systems. A companion FORTRAN program, EVAL 2, which numerically evaluates the solution set to obtain amplitude ratio and phase angle as functions of frequency is also presented.

Lorenzo, C. F.↗

DOE OSTI2016

Infrared computations of defect Schur indices

We conjecture a formula for the Schur index of four-dimensional N = 2 theories in the presence of boundary conditions and/or line defects, in terms of the low-energy effective Seiberg-Witten description of the system together with massive BPS excitations. We test our proposal in a variety of examples for SU(2) gauge theories, either conformal or asymptotically free. We use the conjecture to compute these defect-enriched Schur indices for theories which lack a Lagrangian description, such as Argyres-Douglas theories. We demonstrate in various examples that line defect indices can be expressed as sums of characters of the associated two-dimensional chiral algebra and that for Argyres-Douglas theories the line defect OPE reduces in the index to the Verlinde algebra.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Thermodynamic efficiency limits of classical and bifacial multi-junction tandem solar cells: An analytical approach

Bifacial tandem cells promise to reduce three fundamental losses (i.e., above-bandgap, below bandgap, and the uncollected light between panels) inherent in classical single junction photovoltaic (PV) systems. The successive filtering of light through the bandgap cascade and the requirement of current continuity make optimization of tandem cells difficult and accessible only to numerical solution through computer modeling. The challenge is even more complicated for bifacial design. In this paper, we use an elegantly simple analytical approach to show that the essential physics of optimization is intuitively obvious, and deeply insightful results can be obtained with a few lines of algebra. This powerful approach reproduces, as special cases, all of the known results of conventional and bifacial tandem cells and highlights the asymptotic efficiency gain of these technologies.

Alam, Muhammad Ashraful (ORCID:0000000187756043)↗

NASA NTRS1982

Numerical grid generation; Proceedings of the Symposium on Numerical Generation of Curvilinear Coordinate Systems and Their Use in the Numerical Solution of Partial Differential Equations, Nashville, TN, April 13-16, 1982

General curvilinear coordinate systems are considered along with the error induced by coordinate systems, basic differential models for coordinate generation, elliptic grid generation, conformal grid generation, algebraic grid generation, orthogonal grid generation, patched coordinate systems, and solid mechanics applications of boundary fitted coordinate systems. Attention is given to coordinate system control and adaptive meshes, the application of body conforming curvilinear grids for finite difference solution of external flow, the use of solution adaptive grids in solving partial differential equations, adaptive gridding for finite difference solutions to heat and mass transfer problems, and the application of curvilinear coordinate generation techniques to the computation of internal flows. Other topics explored are related to the solution of nonlinear water wave problems using boundary-fitted coordinate systems, the numerical modeling of estuarine hydrodynamics on a boundary-fitted coordinate system, and conformal grid generation for multielement airfoils.

Thompson, J. F.↗

NASA NTRS1976

Computation and sensitivity considerations of the Ricatti equation in spacecraft CMG steering laws

The steady-state matrix Ricatti equation is studied with respect to sensitivity and computational burden for a linear regulator controller in spacecraft. The class of systems studied use control moment gyros (CMGs) as the torque driver, assuming that the CMGs are free of gimbal stops. Different solution techniques are evaluated relative to computation time and accuracy to determine which solution method is most acceptable with respect to the prescribed requirements. It is shown that it is not feasible to eliminate off-diagonal Ricatti equation terms in the relevent updata equation due to their high sensitivity, that Potter's algebraic technique requires the least computation time of the methods studied, and that the simple Euler method yields the best results when accuracy and computation time are equally weighted. If an optimal linear regulator formulation is employed, a full Ricatti equation solution of n(n + 1)2 elements of the symmetric positive definite gain matrix which is the solution to the matrix Ricatti equation must be computed at each update cycle.

Colburn, B. K.↗

NASA NTRS2007

Development of a Linear Stirling Model with Varying Heat Inputs

The linear model of the Stirling system developed by NASA Glenn Research Center (GRC) has been extended to include a user-specified heat input. Previously developed linear models were limited to the Stirling convertor and electrical load. They represented the thermodynamic cycle with pressure factors that remained constant. The numerical values of the pressure factors were generated by linearizing GRC s non-linear System Dynamic Model (SDM) of the convertor at a chosen operating point. The pressure factors were fixed for that operating point, thus, the model lost accuracy if a transition to a different operating point were simulated. Although the previous linear model was used in developing controllers that manipulated current, voltage, and piston position, it could not be used in the development of control algorithms that regulated hot-end temperature. This basic model was extended to include the thermal dynamics associated with a hot-end temperature that varies over time in response to external changes as well as to changes in the Stirling cycle. The linear model described herein includes not only dynamics of the piston, displacer, gas, and electrical circuit, but also the transient effects of the heater head thermal inertia. The linear version algebraically couples two separate linear dynamic models, one model of the Stirling convertor and one model of the thermal system, through the pressure factors. The thermal system model includes heat flow of heat transfer fluid, insulation loss, and temperature drops from the heat source to the Stirling convertor expansion space. The linear model was compared to a nonlinear model, and performance was very similar. The resulting linear model can be implemented in a variety of computing environments, and is suitable for analysis with classical and state space controls analysis techniques.

Regan, Timothy F.↗

NASA NTRS2007

Development of a Linear Stirling System Model with Varying Heat Inputs

The linear model of the Stirling system developed by NASA Glenn Research Center (GRC) has been extended to include a user-specified heat input. Previously developed linear models were limited to the Stirling convertor and electrical load. They represented the thermodynamic cycle with pressure factors that remained constant. The numerical values of the pressure factors were generated by linearizing GRC's nonlinear System Dynamic Model (SDM) of the convertor at a chosen operating point. The pressure factors were fixed for that operating point, thus, the model lost accuracy if a transition to a different operating point were simulated. Although the previous linear model was used in developing controllers that manipulated current, voltage, and piston position, it could not be used in the development of control algorithms that regulated hot-end temperature. This basic model was extended to include the thermal dynamics associated with a hot-end temperature that varies over time in response to external changes as well as to changes in the Stirling cycle. The linear model described herein includes not only dynamics of the piston, displacer, gas, and electrical circuit, but also the transient effects of the heater head thermal inertia. The linear version algebraically couples two separate linear dynamic models, one model of the Stirling convertor and one model of the thermal system, through the pressure factors. The thermal system model includes heat flow of heat transfer fluid, insulation loss, and temperature drops from the heat source to the Stirling convertor expansion space. The linear model was compared to a nonlinear model, and performance was very similar. The resulting linear model can be implemented in a variety of computing environments, and is suitable for analysis with classical and state space controls analysis techniques.

Regan, Timothy F.↗

DOE OSTI2018

Brochure on Basic Research Needs for Scientific Machine Learning: Core Technologies for Artificial Intelligence [Slides]

Scientific Machine Learning (SciML) and Artificial Intelligence (AI) will have broad use and transformative effects across the Department of Energy. Accordingly, the January 2018 Basic Research Needs workshop identified six Priority Research Directions (PRDs). The first three PRDs describe foundational research themes that correspond to the need for domain-awareness (PRD #1), interpretability (PRD #2), and robustness (PRD #3). The other three PRDs describe capability research themes and correspond to the three major use cases for massive scientific data analysis (PRD #4), machine learning-enhanced modeling and simulation (PRD #5), and intelligent automation and decision-support for complex systems (PRD #6). The Priority Research Directions provide a sound basis for a coherent, long-term research and development strategy in SciML and AI. Over the last decade, DOE investments in applied mathematics have laid the groundwork for the type of basic research that will underpin key advances in the six PRDs. Such advances will build on the work from leading researchers in optimization, linear algebra, high-performance solvers and algorithms, multiscale modeling and simulation, complex systems research, uncertainty quantification, and the new basic research areas that will emerge from the pursuit of transformative technologies.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Block smoothers and generalized ideal interpolation in AMG (Final Report)

The Pennsylvania State University (“Subcontractor”) worked on developing new parallel algebraic multilevel methods suitable for solving PDEs. Specifically, work on the design of multigrid solvers for coupled systems of partial differential equations arising in numerical modeling of various applications was completed. A main emphasis was on the design of new ideal algebraic multigrid interpolation for problems such as Maxwell’s equations where block smoothers are needed and the standard form of ideal interpolation is not an effective choice.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Statistical and machine learning models for optimizing energy in parallel applications

Rising power costs and constraints are driving a growing focus on the energy efficiency of high performance computing systems. The unique characteristics of a particular system and workload and their effect on performance and energy efficiency are typically difficult for application users to assess and to control. Settings for optimum performance and energy efficiency can also diverge, so we need to identify trade-off options that guide a suitable balance between energy use and performance. We present statistical and machine learning models that only require a small number of runs to make accurate Pareto-optimal trade-off predictions using parameters that users can control. We study model training and validation using several parallel kernels and more complex workloads, including Algebraic Multigrid (AMG), Large-scale Atomic Molecular Massively Parallel Simulator, and Livermore Unstructured Lagrangian Explicit Shock Hydrodynamics. Here, we demonstrate that we can train the models using as few as 12 runs, with prediction error of less than 10%. Our AMG results identify trade-off options that provide up to 45% improvement in energy efficiency for around 10% performance loss. We reduce the sample measurement time required for AMG by 90%, from 13 h to 74 min.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1999

Metrics for Labeled Markov Systems

Partial Labeled Markov Chains are simultaneously generalizations of process algebra and of traditional Markov chains. They provide a foundation for interacting discrete probabilistic systems, the interaction being synchronization on labels as in process algebra. Existing notions of process equivalence are too sensitive to the exact probabilities of various transitions. This paper addresses contextual reasoning principles for reasoning about more robust notions of "approximate" equivalence between concurrent interacting probabilistic systems. The present results indicate that:We develop a family of metrics between partial labeled Markov chains to formalize the notion of distance between processes. We show that processes at distance zero are bisimilar. We describe a decision procedure to compute the distance between two processes. We show that reasoning about approximate equivalence can be done compositionally by showing that process combinators do not increase distance. We introduce an asymptotic metric to capture asymptotic properties of Markov chains; and show that parallel composition does not increase asymptotic distance.

Desharnais, Josee↗

DOE OSTI2022

Compressed basis GMRES on high-performance graphics processing units

Krylov methods provide a fast and highly parallel numerical tool for the iterative solution of many large-scale sparse linear systems. To a large extent, the performance of practical realizations of these methods is constrained by the communication bandwidth in current computer architectures, motivating the investigation of sophisticated techniques to avoid, reduce, and/or hide the message-passing costs (in distributed platforms) and the memory accesses (in all architectures). This article leverages Ginkgo’s memory accessor in order to integrate a communication-reduction strategy into the (Krylov) GMRES solver that decouples the storage format (i.e., the data representation in memory) of the orthogonal basis from the arithmetic precision that is employed during the operations with that basis. Given that the execution time of the GMRES solver is largely determined by the memory accesses, the cost of the datatype transforms can be mostly hidden, resulting in the acceleration of the iterative step via a decrease in the volume of bits being retrieved from memory. Together with the special properties of the orthonormal basis (whose elements are all bounded by 1), this paves the road toward the aggressive customization of the storage format, which includes some floating-point as well as fixed-point formats with mild impact on the convergence of the iterative process. We develop a high-performance implementation of the “compressed basis GMRES” solver in the Ginkgo sparse linear algebra library using a large set of test problems from the SuiteSparse Matrix Collection. We demonstrate robustness and performance advantages on a modern NVIDIA V100 graphics processing unit (GPU) of up to 50% over the standard GMRES solver that stores all data in IEEE double-precision.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Hybrid Finite Element--Spectral Method for the Fractional Laplacian: Approximation Theory and Efficient Solver

Here, a numerical scheme is presented for approximating fractional order Poisson problems in two and three dimensions. The scheme is based on reformulating the original problem posed over $\Omega$ on the extruded domain $\mathcal{C}=\Omega\times[0,\infty)$ following. The resulting degenerate elliptic integer order PDE is then approximated using a hybrid FEM-spectral scheme. Finite elements are used in the direction parallel to the problem domain $\Omega$, and an appropriate spectral method is used in the extruded direction. The spectral part of the scheme requires that we approximate the true eigenvalues of the integer order Laplacian over $\Omega$. We derive an a priori error estimate which takes account of the error arising from using an approximation in place of the true eigenvalues. We further present a strategy for choosing approximations of the eigenvalues based on Weyl's law and finite element discretizations of the eigenvalue problem. The system of linear algebraic equations arising from the hybrid FEM-spectral scheme is decomposed into blocks which can be solved effectively using standard iterative solvers such as multigrid and conjugate gradient. Numerical examples in two and three dimensions suggest that the approach is quasi-optimal in terms of complexity.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Workshop Report on Basic Research Needs for Scientific Machine Learning: Core Technologies for Artificial Intelligence

97 MATHEMATICS AND COMPUTING↗