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At least 145 records · Page 8

Finite-dimensional approximation for optimal fixed-order compensation of distributed parameter systems

In controlling distributed parameter systems it is often desirable to obtain low-order, finite-dimensional controllers in order to minimize real-time computational requirements. Standard approaches to this problem employ model/controller reduction techniques in conjunction with LQG theory. In this paper we consider the finite-dimensional approximation of the infinite-dimensional Bernstein/Hyland optimal projection theory. This approach yields fixed-finite-order controllers which are optimal with respect to high-order, approximating, finite-dimensional plant models. The technique is illustrated by computing a sequence of first-order controllers for one-dimensional, single-input/single-output, parabolic (heat/diffusion) and hereditary systems using spline-based, Ritz-Galerkin, finite element approximation. Numerical studies indicate convergence of the feedback gains with less than 2 percent performance degradation over full-order LQG controllers for the parabolic system and 10 percent degradation for the hereditary system.

Bernstein, Dennis S.↗

Numerical methods for incompressible viscous flows with engineering applications

A numerical scheme has been developed to solve the incompressible, 3-D Navier-Stokes equations using velocity-vorticity variables. This report summarizes the development of the numerical approximation schemes for the divergence and curl of the velocity vector fields and the development of compact schemes for handling boundary and initial boundary value problems.

Rose, M. E.↗

Structure of scintillations in Neptune's occultation shadow

An exceptionally high-quality data set from a Neptune occultation is used here to derive a number of new results about the statistical properties of the fluctuations of the intensity distribution in various parts of Neptune's occultation shadow. An approximate numerical ray-tracing model which successfully accounts for many of the qualitative aspects of the observed intensity fluctuation distribution is introduced. Strong refractive scintillation is simulated by including the effects of 'turbulence' with projected atmospheric properties allowed to vary in both the direction perpendicular and parallel to the limb, and an explicit two-dimensional picture of a typical intensity distribution throughout an occulting planet's shadow is presented. The results confirm the existence of highly anisotropic turbulence.

Hubbard, W. B.↗

Modifying PASVART to solve singular nonlinear 2-point boundary problems

To study the buckling and post-buckling behavior of shells and various other structures, one must solve a nonlinear 2-point boundary problem. Since closed-form analytic solutions for such problems are virtually nonexistent, numerical approximations are inevitable. This makes the availability of accurate and reliable software indispensable. In a series of papers Lentini and Pereyra, expanding on the work of Keller, developed PASVART: an adaptive finite difference solver for nonlinear 2-point boundary problems. While the program does produce extremely accurate solutions with great efficiency, it is hindered by a major limitation. PASVART will only locate isolated solutions of the problem. In buckling problems, the solution set is not unique. It will contain singular or bifurcation points, where different branches of the solution set may intersect. Thus, PASVART is useless precisely when the problem becomes interesting. To resolve this deficiency we propose a modification of PASVART that will enable the user to perform a more complete bifurcation analysis. PASVART would be combined with the Thurston bifurcation solution: as adaptation of Newton's method that was motivated by the work of Koiter 3 are reinterpreted in terms of an iterative computational method by Thurston.

Fulton, James P.↗

Efficient optimization of integrated aerodynamic-structural design

Techniques for reducing the computational complexity of multidisciplinary design optimization (DO) of aerodynamic structures are described and demonstrated. The basic principles of aerodynamic and structural DO are reviewed; the formulation of the combined DO problem is outlined; and particular attention is given to (1) the application of perturbation methods to cross-sensitivity computations and (2) numerical approximation procedures. Trial DOs of a simple sailplane design are presented in tables and graphs and discussed in detail. The IBM 3090 CPU time for the entire integrated DO was reduced from an estimated 10 h to about 6 min.

Haftka, R. T.↗

A general numerical model for wave rotor analysis

Wave rotors represent one of the promising technologies for achieving very high core temperatures and pressures in future gas turbine engines. Their operation depends upon unsteady gas dynamics and as such, their analysis is quite difficult. This report describes a numerical model which has been developed to perform such an analysis. Following a brief introduction, a summary of the wave rotor concept is given. The governing equations are then presented, along with a summary of the assumptions used to obtain them. Next, the numerical integration technique is described. This is an explicit finite volume technique based on the method of Roe. The discussion then focuses on the implementation of appropriate boundary conditions. Following this, some results are presented which first compare the numerical approximation to the governing differential equations and then compare the overall model to an actual wave rotor experiment. Finally, some concluding remarks are presented concerning the limitations of the simplifying assumptions and areas where the model may be improved.

Paxson, Daniel W.↗

Things that go bump in the light - On the optical specification of contact severity

Psychologists are intrigued with the idea that optical variables can specify not only the time until an object impacts an observer but also the severity of the impact. However, the mapping between the optical variables and the kinematic variables has been misstated, erroneously implying that there exist critical values of the optical variables used for locomotion and control. In this commentary, the mathematical relationship between the optical and kinematic variables is reexamined and the erroneous assumptions that have led to the proposal of critical values are shown. Also examined are the empirical data on deceleration to approach to assess whether the proposed optical variables are likely candidates for control strategies. Finally, problems associated with numerical approximations to dynamic systems, particularly when analytic solutions exist, are discussed.

Kaiser, Mary K.↗

Non equilibrium flow in an arc-jet

A method for simulating the flow of a nitrogen plasma in thermodynamic nonequilibrium is described. The method relies on the modeling of the relevant physical and chemical phenomena and on a fully coupled implicit finite volume upwind numerical approximation of the governing equations. The results agree with experimental data.

Rostand, P.↗

Linear quadratic tracking problems in Hilbert space - Application to optimal active noise suppression

A unified treatment of the linear quadratic tracking (LQT) problem, in which a control system's dynamics are modeled by a linear evolution equation with a nonhomogeneous component that is linearly dependent on the control function u, is presented; the treatment proceeds from the theoretical formulation to a numerical approximation framework. Attention is given to two categories of LQT problems in an infinite time interval: the finite energy and the finite average energy. The behavior of the optimal solution for finite time-interval problems as the length of the interval tends to infinity is discussed. Also presented are the formulations and properties of LQT problems in a finite time interval.

Banks, H. T.↗

Stalling of Helicopter Blades

Theoretical studies have predicted that operation of helicopter rotor beyond certain combinations of thrust, forward speed, and rotational speed might be prevented by rapidly increasing stalling of the retreating blade. The same studies also indicate that the efficiency of the rotor will increase until these limits are reached or closely approached, so that it is desirable to design helicopter rotors for operation close to the limits imposed by blade stalling. Inasmuch as the theoretical predictions of blade stalling involve numerous approximations and assumptions, an experimental investigation was needed to determine whether, in actual practice, the stall did occur and spread as predicted and to establish the amount of stalling that could be present without severe vibration or control difficulties being introduced. This report presents the results of such an investigation.

Gustafson, F B↗

On the design of structural components using materials with time-dependent properties

The application of the elastic-viscoelastic correspondence principle is presented as a design tool for structural design engineers for composite material applications. The classical problem of cantilever beams is used as the illustration problem. Both closed-form and approximate numerical solutions are presented for several different problems. The application of the collocation method is presented as a viable and simple design tool to determine the time-dependent behavior and response of viscoelastic composite beams under load.

Rodriguez, Pedro I.↗

A stable penalty method for the compressible Navier-Stokes equations. 1: Open boundary conditions

The purpose of this paper is to present asymptotically stable open boundary conditions for the numerical approximation of the compressible Navier-Stokes equations in three spatial dimensions. The treatment uses the conservation form of the Navier-Stokes equations and utilizes linearization and localization at the boundaries based on these variables. The proposed boundary conditions are applied through a penalty procedure, thus ensuring correct behavior of the scheme as the Reynolds number tends to infinity. The versatility of this method is demonstrated for the problem of a compressible flow past a circular cylinder.

Hesthaven, J. S.↗

Quantum propagation in single mode fiber

This paper presents a theory for quantum light propagation in a single-mode fiber which includes the effects of the Kerr nonlinearity, group-velocity dispersion, and linear loss. The theory reproduces the results of classical self-phase modulation, quantum four-wave mixing, and classical solution physics, within their respective regions of validity. It demonstrates the crucial role played by the Kerr-effect material time constant, in limiting the quantum phase shifts caused by the broadband zero-point fluctuations that accompany any quantized input field. Operator moment equations - approximated, numerically, via a terminated cumulant expansion - are used to obtain results for homodyne-measurement noise spectra when dispersion is negligible. More complicated forms of these equations can be used to incorporate dispersion into the noise calculations.

Joneckis, Lance G.↗

Numerical Computation of Sensitivities and the Adjoint Approach

We discuss the numerical computation of sensitivities via the adjoint approach in optimization problems governed by differential equations. We focus on the adjoint problem in its weak form. We show how one can avoid some of the problems with the adjoint approach, such as deriving suitable boundary conditions for the adjoint equation. We discuss the convergence of numerical approximations of the costate computed via the weak form of the adjoint problem and show the significance for the discrete adjoint problem.

Lewis, Robert Michael↗

Trajectories for High Specific Impulse High Specific Power Deep Space Exploration

Flight times and deliverable masses for electric and fusion propulsion systems are difficult to approximate. Numerical integration is required for these continuous thrust systems. Many scientists are not equipped with the tools and expertise to conduct interplanetary and interstellar trajectory analysis for their concepts. Several charts plotting the results of well-known trajectory simulation codes were developed and are contained in this paper. These charts illustrate the dependence of time of flight and payload ratio on jet power, initial mass, specific impulse and specific power. These charts are intended to be a tool by which people in the propulsion community can explore the possibilities of their propulsion system concepts. Trajectories were simulated using the tools VARITOP and IPOST. VARITOP is a well known trajectory optimization code that involves numerical integration based on calculus of variations. IPOST has several methods of trajectory simulation; the one used in this paper is Cowell's method for full integration of the equations of motion. An analytical method derived in the companion paper was also evaluated. The accuracy of this method is discussed in the paper.

Polsgrove, Tara↗

Automatic Generation of Algorithms for the Statistical Analysis of Planetary Nebulae Images

Analyzing data sets collected in experiments or by observations is a Core scientific activity. Typically, experimentd and observational data are &aught with uncertainty, and the analysis is based on a statistical model of the conjectured underlying processes, The large data volumes collected by modern instruments make computer support indispensible for this. Consequently, scientists spend significant amounts of their time with the development and refinement of the data analysis programs. AutoBayes [GF+02, FS03] is a fully automatic synthesis system for generating statistical data analysis programs. Externally, it looks like a compiler: it takes an abstract problem specification and translates it into executable code. Its input is a concise description of a data analysis problem in the form of a statistical model as shown in Figure 1; its output is optimized and fully documented C/C++ code which can be linked dynamically into the Matlab and Octave environments. Internally, however, it is quite different: AutoBayes derives a customized algorithm implementing the given model using a schema-based process, and then further refines and optimizes the algorithm into code. A schema is a parameterized code template with associated semantic constraints which define and restrict the template s applicability. The schema parameters are instantiated in a problem-specific way during synthesis as AutoBayes checks the constraints against the original model or, recursively, against emerging sub-problems. AutoBayes schema library contains problem decomposition operators (which are justified by theorems in a formal logic in the domain of Bayesian networks) as well as machine learning algorithms (e.g., EM, k-Means) and nu- meric optimization methods (e.g., Nelder-Mead simplex, conjugate gradient). AutoBayes augments this schema-based approach by symbolic computation to derive closed-form solutions whenever possible. This is a major advantage over other statistical data analysis systems which use numerical approximations even in cases where closed-form solutions exist. AutoBayes is implemented in Prolog and comprises approximately 75.000 lines of code. In this paper, we take one typical scientific data analysis problem-analyzing planetary nebulae images taken by the Hubble Space Telescope-and show how AutoBayes can be used to automate the implementation of the necessary anal- ysis programs. We initially follow the analysis described by Knuth and Hajian [KHO2] and use AutoBayes to derive code for the published models. We show the details of the code derivation process, including the symbolic computations and automatic integration of library procedures, and compare the results of the automatically generated and manually implemented code. We then go beyond the original analysis and use AutoBayes to derive code for a simple image segmentation procedure based on a mixture model which can be used to automate a manual preproceesing step. Finally, we combine the original approach with the simple segmentation which yields a more detailed analysis. This also demonstrates that AutoBayes makes it easy to combine different aspects of data analysis.

Fischer, Bernd↗

An Uncertainty Structure Matrix for Models and Simulations

Software that is used for aerospace flight control and to display information to pilots and crew is expected to be correct and credible at all times. This type of software is typically developed under strict management processes, which are intended to reduce defects in the software product. However, modeling and simulation (M&S) software may exhibit varying degrees of correctness and credibility, depending on a large and complex set of factors. These factors include its intended use, the known physics and numerical approximations within the M&S, and the referent data set against which the M&S correctness is compared. The correctness and credibility of an M&S effort is closely correlated to the uncertainty management (UM) practices that are applied to the M&S effort. This paper describes an uncertainty structure matrix for M&S, which provides a set of objective descriptions for the possible states of UM practices within a given M&S effort. The columns in the uncertainty structure matrix contain UM elements or practices that are common across most M&S efforts, and the rows describe the potential levels of achievement in each of the elements. A practitioner can quickly look at the matrix to determine where an M&S effort falls based on a common set of UM practices that are described in absolute terms that can be applied to virtually any M&S effort. The matrix can also be used to plan those steps and resources that would be needed to improve the UM practices for a given M&S effort.

Green, Lawrence L.↗

AutoBayes Program Synthesis System Users Manual

Program synthesis is the systematic, automatic construction of efficient executable code from high-level declarative specifications. AutoBayes is a fully automatic program synthesis system for the statistical data analysis domain; in particular, it solves parameter estimation problems. It has seen many successful applications at NASA and is currently being used, for example, to analyze simulation results for Orion. The input to AutoBayes is a concise description of a data analysis problem composed of a parameterized statistical model and a goal that is a probability term involving parameters and input data. The output is optimized and fully documented C/C++ code computing the values for those parameters that maximize the probability term. AutoBayes can solve many subproblems symbolically rather than having to rely on numeric approximation algorithms, thus yielding effective, efficient, and compact code. Statistical analysis is faster and more reliable, because effort can be focused on model development and validation rather than manual development of solution algorithms and code.

Schumann, Johann↗