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At least 127 records · Page 7

Hierarchic Extensions in the Static and Dynamic Analysis of Elastic Beams

Approximate solutions of static and dynamic beam problems by the p-version of the finite element method are investigated. Within a hierarchy of engineering beam idealizations, rigorous formulations of the strain and kinetic energies for straight and circular beam elements are presented. These formulations include rotating coordinate system effects and geometric nonlinearities to allow for the evaluation of vertical axis wind turbines, the motivating problem for this research. Hierarchic finite element spaces, based on extensions of the polynomial orders used to approximate the displacement variables, are constructed. The developed models are implemented into a general purpose computer program for evaluation. Quality control procedures are examined for a diverse set of sample problems. These procedures include estimating discretization errors in energy norm and natural frequencies, performing static and dynamic equilibrium checks, observing convergence for qualities of interest, and comparison with more exacting theories and experimental data. It is demonstrated that p-extensions produce exponential rates of convergence in the approximation of strain energy and natural frequencies for the class of problems investigated.

Watson, Robert A.↗

Numerically exact generalized Green's function cluster expansions for electron-phonon problems

We generalize the family of approximate momentum average methods to formulate a numerically exact, convergent hierarchy of equations whose solution provides an efficient algorithm to compute the Green's function of a particle dressed by bosons suitable in the entire parameter regime. We use this approach to extract ground-state properties and spectral functions. Our approximation-free framework, dubbed the generalized Green's function cluster expansion (GGCE), allows access to exact numerical results in the extreme adiabatic limit, where many standard methods struggle or completely fail. We showcase the performance of the method, specializing three important models of charge-boson coupling in solids and molecular complexes: the molecular Holstein model, which describes coupling between charge density and local distortions, the Peierls model, which describes modulation of charge hopping due to intersite distortions, and a more complex Holstein + Peierls system with couplings to two different phonon modes, paradigmatic of charge-lattice interactions in organic crystals. Furthermore, the GGCE serves as an efficient approach that can be systematically extended to different physical scenarios, thus providing a tool to model the frequency dependence of dressed particles in realistic settings.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Deep reinforcement learning for dynamic control of fuel injection timing in multi-pulse compression ignition engines

Conventional compression-ignition (CI) engines have long offered high thermal efficiencies and torque across a wide range of loads, but often require extensive exhaust gas treatment that decreases efficiency to meet ever-increasing emissions regulations. One strategy to decrease emissions is to split the fuel injection into a series of smaller injections. In this paper, we explore a new way of discovering optimal control strategies for the next generation of CI engines using deep reinforcement learning (DRL). We outline a DRL procedure to maximize the weighted reward of engine work while minimizing end-of-cycle NO x emissions. Through the procedure outlined in this paper, we show that the DRL agent is able to reduce NO x emissions threefold while only decreasing network by 2%. We demonstrate the use of transfer learning (TL) across hierarchies of physical models to accelerate the learning process, making this approach feasible for a range of control problems within this space. This paper presents a framework and demonstration for using DRL to design control systems in technology areas such as multi-pulse engine control where a hierarchy of models combined with multi-objective rewards are used for optimal operation.

33 ADVANCED PROPULSION SYSTEMS↗

OpenMDAO: Framework for Flexible Multidisciplinary Design, Analysis and Optimization Methods

The OpenMDAO project is underway at NASA to develop a framework which simplifies the implementation of state-of-the-art tools and methods for multidisciplinary design, analysis and optimization. Foremost, OpenMDAO has been designed to handle variable problem formulations, encourage reconfigurability, and promote model reuse. This work demonstrates the concept of iteration hierarchies in OpenMDAO to achieve a flexible environment for supporting advanced optimization methods which include adaptive sampling and surrogate modeling techniques. In this effort, two efficient global optimization methods were applied to solve a constrained, single-objective and constrained, multiobjective version of a joint aircraft/engine sizing problem. The aircraft model, NASA's nextgeneration advanced single-aisle civil transport, is being studied as part of the Subsonic Fixed Wing project to help meet simultaneous program goals for reduced fuel burn, emissions, and noise. This analysis serves as a realistic test problem to demonstrate the flexibility and reconfigurability offered by OpenMDAO.

Kriging↗

Parallel Element-based Algebraic Multigrid for H (c url ) and H (div) Problems Using the ParELAG Library

This paper presents the use of element-based algebraic multigrid (AMGe) hierarchies, implemented in the ParELAG (Parallel Element Agglomeration Algebraic Multigrid Upscaling and Solvers) library, to produce multilevel preconditioners and solvers for H (c url ) and H (div) formulations. ParELAG constructs hierarchies of compatible nested spaces, forming an exact de Rham sequence on each level. This allows the application of hybrid smoothers on all levels and AMS (Auxiliary-space Maxwell Solver) or ADS (Auxiliary-space Divergence Solver) on the coarsest levels, obtaining complete multigrid cycles. Numerical results are presented, showing the parallel performance of the proposed methods. As a part of the exposition, this paper demonstrates some of the capabilities of ParELAG and outlines some of the components and procedures within the library.

97 MATHEMATICS AND COMPUTING↗

A BBGKY framework for fluid turbulence

A framework is presented for a systematic kinetic theory of turbulence originating from the Liouville equation for the Fourier coefficients of fluid variables. The real and imaginary parts of these Fourier coefficients play the role that particle coordinates (positions and momenta) play in the BBGKY theory. The basic relations of the problem are the incompressible Navier-Stokes equations in two dimensions with zero viscosity, with the probability distributions of Fourier coefficients rather than moments being the basic variables of the theory. A kinetic equation is derived and shown to possess a number of requirements that any reasonable kinetic equation must have: conservation laws, positive-definite spectral densities, and an H-theorem. The major lack in the theory is any reliable information on the relaxation predicted by the complicated linear operator H. Closure of the hierarchy is achieved by the hypothesis that the five-coefficient correlation function is negligible. Problems associated with inclusion of viscosity and external driving forces are discussed.

Montgomery, D.↗

Bayesian inference of Stochastic reaction networks using Multifidelity Sequential Tempered Markov Chain Monte Carlo

Stochastic reaction network models are often used to explain and predict the dynamics of gene regulation in single cells.These models usually involve several parameters, such as the kinetic rates of chemical reactions, that are not directly measurable and must be inferred from experimental data. Bayesian inference provides a rigorous probabilistic frame-work for identifying these parameters by finding a posterior parameter distribution that captures their uncertainty.Traditional computational methods for solving inference problems such as Markov Chain Monte Carlo methods based on classical Metropolis-Hastings algorithm involve numerous serial evaluations of the likelihood function, which in turn requires expensive forward solutions of the chemical master equation (CME). We propose an alternate approach based on a multifidelity extension of the Sequential Tempered Markov Chain Monte Carlo (ST-MCMC) sampler. This algorithm is built upon Sequential Monte Carlo and solves the Bayesian inference problem by decomposing it into a sequence of efficiently solved subproblems that gradually increase both model fidelity and the influence of the observed data. We reformulate the finite state projection (FSP) algorithm, a well-known method for solving the CME, to produce a hierarchy of surrogate master equations to be used in this multifidelity scheme. To determine the appropriate fidelity, we introduce a novel information-theoretic criteria that seeks to extract the most information about the ultimate Bayesian posterior from each model in the hierarchy without inducing significant bias. This novel sampling scheme is tested with high performance computing resources using biologically relevant problems.

97 MATHEMATICS AND COMPUTING↗

Optimal Planning and Problem-Solving

CTAEMS MDP Optimal Planner is a problem-solving software designed to command a single spacecraft/rover, or a team of spacecraft/rovers, to perform the best action possible at all times according to an abstract model of the spacecraft/rover and its environment. It also may be useful in solving logistical problems encountered in commercial applications such as shipping and manufacturing. The planner reasons around uncertainty according to specified probabilities of outcomes using a plan hierarchy to avoid exploring certain kinds of suboptimal actions. Also, planned actions are calculated as the state-action space is expanded, rather than afterward, to reduce by an order of magnitude the processing time and memory used. The software solves planning problems with actions that can execute concurrently, that have uncertain duration and quality, and that have functional dependencies on others that affect quality. These problems are modeled in a hierarchical planning language called C_TAEMS, a derivative of the TAEMS language for specifying domains for the DARPA Coordinators program. In realistic environments, actions often have uncertain outcomes and can have complex relationships with other tasks. The planner approaches problems by considering all possible actions that may be taken from any state reachable from a given, initial state, and from within the constraints of a given task hierarchy that specifies what tasks may be performed by which team member.

Clemet, Bradley↗

Multilevel Spectral Coarsening for Graph Laplacian Problems with Application to Reservoir Simulation

We extend previously developed two-level coarsening procedures for graph Laplacian problems written in a mixed saddle point form to the fully recursive multilevel case. The resulting hierarchy of discretizations gives rise to a hierarchy of upscaled models, in the sense that they provide approximation in the natural norms (in the mixed setting). This property enables us to utilize them in three applications: (i) as an accurate reduced model, (ii) as a tool in multilevel Monte Carlo simulations (in application to finite volume discretizations), and (iii) for providing a sequence of nonlinear operators in a full approximation scheme for solving nonlinear pressure equations discretized by the conservative two-point flux approximation. Finally, we illustrate the potential of the proposed multilevel technique in all three applications on a number of popular benchmark problems used in reservoir simulation.

multilevel Monte Carlo↗

Development of an intelligent interface for adding spatial objects to a knowledge-based geographic information system

Earth Scientists lack adequate tools for quantifying complex relationships between existing data layers and studying and modeling the dynamic interactions of these data layers. There is a need for an earth systems tool to manipulate multi-layered, heterogeneous data sets that are spatially indexed, such as sensor imagery and maps, easily and intelligently in a single system. The system can access and manipulate data from multiple sensor sources, maps, and from a learned object hierarchy using an advanced knowledge-based geographical information system. A prototype Knowledge-Based Geographic Information System (KBGIS) was recently constructed. Many of the system internals are well developed, but the system lacks an adequate user interface. A methodology is described for developing an intelligent user interface and extending KBGIS to interconnect with existing NASA systems, such as imagery from the Land Analysis System (LAS), atmospheric data in Common Data Format (CDF), and visualization of complex data with the National Space Science Data Center Graphics System. This would allow NASA to quickly explore the utility of such a system, given the ability to transfer data in and out of KBGIS easily. The use and maintenance of the object hierarchies as polymorphic data types brings, to data management, a while new set of problems and issues, few of which have been explored above the prototype level.

Campbell, William J.↗

Understanding the Impact of Memory Access Patterns in Intel Processors

Because of increasing complexity in the memory hierarchy, predicting the performance of a given application in a given processor is becoming more difficult. The problem is worsened by the fact that the hardware needed to deal with more complex memory traffic also affects energy consumption. Moreover, in a heterogeneous system with shared main memory, the memory traffic between the last level cache (LLC) and the memory creates contention between other processors and accelerator devices. For these reasons, it is important to investigate and understand the impact of different memory access patterns on the memory system. This study investigates the interplay between Intel processors' memory hierarchy and different memory access patterns in applications. The authors explore sequential streaming and strided memory access patterns with the objective of predicting LLC-dynamic random access memory (DRAM) traffic for a given application in given Intel architectures. Moreover, the impact of prefetching is also investigated in this study. Experiments with different Intel micro-architectures uncover mechanisms to predict LLC-DRAM traffic that can yield up to 99% accuracy for sequential streaming access patterns and up to 95% accuracy for strided access patterns.

Alaul haque monil, Mohammad↗

Mathematical concepts for modeling human behavior in complex man-machine systems

Many human behavior (e.g., manual control) models have been found to be inadequate for describing processes in certain real complex man-machine systems. An attempt is made to find a way to overcome this problem by examining the range of applicability of existing mathematical models with respect to the hierarchy of human activities in real complex tasks. Automobile driving is chosen as a baseline scenario, and a hierarchy of human activities is derived by analyzing this task in general terms. A structural description leads to a block diagram and a time-sharing computer analogy.

Johannsen, G.↗

Tree-oriented interactive processing with an application to theorem-proving, appendix E

The concept of unstructured structure editing and ted, an editor for unstructured trees, is described. Ted is used to manipulate hierarchies of information in an unrestricted manner. The tool was implemented and applied to the problem of organizing formal proofs. As a proof management tool, it maintains the validity of a proof and its constituent lemmas independently from the methods used to validate the proof. It includes an adaptable interface which may be used to invoke theorem provers and other aids to proof construction. Using ted, a user may construct, maintain, and verify formal proofs using a variety of theorem provers, proof checkers, and formatters.

Hammerslag, David↗

Dynamic resource allocation in a hierarchical multiprocessor system: A preliminary study

An integrated system approach to dynamic resource allocation is proposed. Some of the problems in dynamic resource allocation and the relationship of these problems to system structures are examined. A general dynamic resource allocation scheme is presented. A hierarchial system architecture which dynamically maps between processor structure and programs at multiple levels of instantiations is described. Simulation experiments were conducted to study dynamic resource allocation on the proposed system. Preliminary evaluation based on simple dynamic resource allocation algorithms indicates that with the proposed system approach, the complexity of dynamic resource management could be significantly reduced while achieving reasonable effective dynamic resource allocation.

Ngai, Tin-Fook↗

Management of space networks

NASA has proposed missions to the Moon and Mars that reflect three areas of emphasis: human presence, exploration, and space resource development for the benefit of Earth. A major requirement for such missions is a robust and reliable communications architecture. Network management--the ability to maintain some degree of human and automatic control over the span of the network from the space elements to the end users on Earth--is required to realize such robust and reliable communications. This article addresses several of the architectural issues associated with space network management. Round-trip delays, such as the 5- to 40-min delays in the Mars case, introduce a host of problems that must be solved by delegating significant control authority to remote nodes. Therefore, management hierarchy is one of the important architectural issues. The following article addresses these concerns, and proposes a network management approach based on emerging standards that covers the needs for fault, configuration, and performance management, delegated control authority, and hierarchical reporting of events. A relatively simple approach based on standards was demonstrated in the DSN 2000 Information Systems Laboratory, and the results are described.

Markley, R. W.↗

Assessment models

The types of models used in assessment of possible chemical perturbations to the stratosphere are reviewed. The statue of one and two dimensional models are discussed. The problem of model validation is covered before the status of photochemical modeling efforts is discussed. A hierarchy of tests for photochemical models is presented.

Pyle, J. A.↗

Safety Analysis of FMS/CTAS Interactions During Aircraft Arrivals

This grant funded research on human-computer interaction design and analysis techniques, using future ATC environments as a testbed. The basic approach was to model the nominal behavior of both the automated and human procedures and then to apply safety analysis techniques to these models. Our previous modeling language, RSML, had been used to specify the system requirements for TCAS II for the FAA. Using the lessons learned from this experience, we designed a new modeling language that (among other things) incorporates features to assist in designing less error-prone human-computer interactions and interfaces and in detecting potential HCI problems, such as mode confusion. The new language, SpecTRM-RL, uses "intent" abstractions, based on Rasmussen's abstraction hierarchy, and includes both informal (English and graphical) specifications and formal, executable models for specifying various aspects of the system. One of the goals for our language was to highlight the system modes and mode changes to assist in identifying the potential for mode confusion. Three published papers resulted from this research. The first builds on the work of Degani on mode confusion to identify aspects of the system design that could lead to potential hazards. We defined and modeled modes differently than Degani and also defined design criteria for SpecTRM-RL models. Our design criteria include the Degani criteria but extend them to include more potential problems. In a second paper, Leveson and Palmer showed how the criteria for indirect mode transitions could be applied to a mode confusion problem found in several ASRS reports for the MD-88. In addition, we defined a visual task modeling language that can be used by system designers to model human-computer interaction. The visual models can be translated into SpecTRM-RL models, and then the SpecTRM-RL suite of analysis tools can be used to perform formal and informal safety analyses on the task model in isolation or integrated with the rest of the modeled system. We had hoped to be able to apply these modeling languages and analysis tools to a TAP air/ground trajectory negotiation scenario, but the development of the tools took more time than we anticipated.

Nancy G. Leveson↗