Likelihood estimation for distributed parameter models for NASA Mini-MAST truss

A maximum likelihood estimation for distributed parameter models of large flexible structures was formulated. Distributed parameter models involve far fewer unknown parameters than independent modal characteristics or finite element models. The closed form solutions for the partial differential equations with corresponding boundary conditions were derived. The closed-form expressions of sensitivity functions led to highly efficient algorithms for analyzing ground or on-orbit test results. For an illustration of this approach, experimental data of the NASA Mini-MAST truss was used. The estimations of modal properties involve lateral bending modes and torsional modes. The results show that distributed parameter models are promising in the parameter estimation of large flexible structures

Resonant Geometric Phases for Soliton Equations

The goal of the present paper is to introduce a multidimensional generalization of asymptotic reduction given in a paper by Alber and Marsden [1992], to use this to obtain a new class of solutions that we call resonant solitons, and to study the corresponding geometric phases. The term "resonant solitons" is used because those solutions correspond to a spectrum with multiple points, and they also represent a dividing solution between two different types of solitons. In this sense, these new solutions are degenerate and, as such, will be considered as singular points in the moduli space of solitons

An adaptive pseudospectral method for discontinuous problems

The accuracy of adaptively chosen, mapped polynomial approximations is studied for functions with steep gradients or discontinuities. It is shown that, for steep gradient functions, one can obtain spectral accuracy in the original coordinate system by using polynomial approximations in a transformed coordinate system with substantially fewer collocation points than are necessary using polynomial expansion directly in the original, physical, coordinate system. It is also shown that one can avoid the usual Gibbs oscillation associated with steep gradient solutions of hyperbolic pde's by approximation in suitably chosen coordinate systems. Continuous, high gradient solutions are computed with spectral accuracy (as measured in the physical coordinate system). Discontinuous solutions associated with nonlinear hyperbolic equations can be accurately computed by using an artificial viscosity chosen to smooth out the solution in the mapped, computational domain. Thus, shocks can be effectively resolved on a scale that is subgrid to the resolution available with collocation only in the physical domain. Examples with Fourier and Chebyshev collocation are given

Efficient implementations of 2-D noncausal IIR filters

Includes bibliographical references (p. 34-35).Supported by the Office of Naval Research. N00014-91-J-1004 Supported by the Air Force Office of Scientific Research. F49620-95-1-0083 Supported by the Army Research Office. DAAL03-92-G-0115Michael M. Daniel, Alan S. Willsky

Climate control of a bulk storage room for foodstuffs

A storage room contains a bulk of potatoes that produce heat due to respiration. A ventilator blows cooled air around to keep the potatoes cool and prevent spoilage. The aim is to design a control law such that the product temperature is kept at a constant, desired level. This physical system is modelled by a set of nonlinear coupled partial differential equations (pde's) with nonlinear input. Due to their complex form, standard control design will not be adequate. A novel modelling procedure is proposed. The input is considered to attain only discrete values. Analysis of the transfer functions of the system in the frequency domain leads to a simplification of the model into a set of static ordinary differential equations ode's). The desired control law is now the optimal time to switch between the discrete input values on an intermediate time interval. The switching time can be written as a symbolic expression of all physical parameters of the system. Finally, a dynamic controller can be designed that regulates the air temperature on a large time interval, by means of adjustment of the switching time

Spectral methods for partial differential equations

Origins of spectral methods, especially their relation to the Method of Weighted Residuals, are surveyed. Basic Fourier, Chebyshev, and Legendre spectral concepts are reviewed, and demonstrated through application to simple model problems. Both collocation and tau methods are considered. These techniques are then applied to a number of difficult, nonlinear problems of hyperbolic, parabolic, elliptic, and mixed type. Fluid dynamical applications are emphasized

Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's

We have designed a cubic spline wavelet decomposition for the Sobolev space H(sup 2)(sub 0)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's

Space structure vibration modes: How many exist? Which ones are important?

This report attempts to shed some light on the two issues raised in the title, namely, how many vibration modes does a real structure have, and which of these modes are important? The surprise-free answers to these two questions are, respectively, an infinite number and the first several modes. The author argues that the absurd subspace (all but the first billion modes) is not a strength of continuum modeling, but, in fact, a weakness. Partial differential equations are not real structures, only mathematical models. This note also explains (1) that the PDE model and the finite element model are, in fact, the same model, the latter being a numerical method for dealing with the former, (2) that modes may be selected on dynamical grounds other than frequency alone, and (3) that long slender rods are useful as primitive cases but dangerous to extrapolate from

Progress in local preconditioning of the Euler and Navier-Stokes equations

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76116/1/AIAA-1993-3328-321.pd

Linear and nonlinear PSE for compressible boundary layers

Compressible stability of growing boundary layers is studied by numerically solving the partial differential equations under a parabolizing approximation. The resulting parabolized stability equations (PSE) account for nonparallel as well as nonlinear effects. Evolution of disturbances in compressible flat-plate boundary layers are studied for freestream Mach numbers ranging from 0 to 4.5. Results indicate that the effect of boundary-layer growth is important for linear disturbances. Nonlinear calculations are performed for various Mach numbers. Two-dimensional nonlinear results using the PSE approach agree well with those from direct numerical simulations using the full Navier-Stokes equations while the required computational time is less by an order of magnitude. Spatial simulation using PSE were carried out for both the fundamental and subharmonic type breakdown for a Mach 1.6 boundary layer. The promising results obtained show that the PSE method is a powerful tool for studying boundary-layer instabilities and for predicting transition over a wide range of Mach numbers