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NASA NTRS1987

Exact state reconstruction in deterministic digital control systems

A state reconstructor for deterministic digital systems is presented which is ideal in the following sense: if the plant parameters are known exactly, the output of the state reconstructor will exactly equal the true state of the plant, not just approximate it. Furthermore, this ideal state reconstructor adds no additional states or eigenvalues to the system. Nor does it affect the plant equation for the system in any way; it affects only the measurement equation. While there are countless ways of choosing the ideal state reconstructor parameters, two distinct methods are described here. An example is presented which illustrates the procedures to completely design the ideal state reconstructor using both methods.

Polites, Michael E.↗

NASA NTRS1987

Deterministic properties of the recursive separable median filter

The recursive separable median filter has been successfully used to extract features from noisy two-dimensional signals. In many applications, it gives better noise suppression and edge preservation than the standard separable median filter. In this paper, a new approach is used for studying the deterministic properties of separable median filters. In particular, using threshold decomposition, the root structure of the recursive separable median filter is derived, where a root is a signal invariant to further filtering. It is shown that these root structures differ from those of their nonrecursive counterparts. It is also shown that any two-dimensional signal will converge to a root after repeated passes of the recursive separable median filter.

Mcloughlin, Michael P.↗

NASA NTRS1988

Further developments in exact state reconstruction in deterministic digital control systems

A more general version of the ideal state reconstructor for deterministic digital control systems previously developed is presented. In the original version, measurements prefiltered by a multi-input/multi-output moving-average (MA) process were utilized in the state reconstruction process. In this version, the MA-prefiltered measurements can be supplemented by standard instantaneous measurements. The ideal state reconstructor is so named because: if the plant parameters are known exactly, its output will exactly equal the true state of the plant, not just approximate it. Furthermore, it adds no additional states or eigenvalues to the system. Nor does it affect the plant equation for the system in any way; it affects the measurement equation only. An example is presented which illustrates the procedure for choosing the parameters in it.

Polites, Michael E.↗

NASA NTRS1988

More on exact state reconstruction in deterministic digital control systems

Presented is a special form of the Ideal State Reconstructor for deterministic digital control systems which is simpler to implement than the most general form. The Ideal State Reconstructor is so named because, if the plant parameters are known exactly, its output will exactly equal, not just approximate, the true state of the plant and accomplish this without any knowledge of the plant's initial state. Besides this, it adds no new states or eigenvalues to the system. Nor does it affect the plant equation for the system in any way; it affects the measurement equation only. It is characterized by the fact that discrete measurements are generated every T/N seconds and input into a multi-input/multi-output moving-average (MA) process. The output of this process is sampled every T seconds and utilized in reconstructing the state of the system.

Polites, Michael E.↗

NASA NTRS1989

Deterministic errors in the Magellan orbit due to attitude control thruster activity

The pitch and yaw attitude control thrusters of the Magellan spacecraft generate uncoupled moments about the spacecraft center of mass, perturbing the spacecraft's orbit. A strategy to model these perturbing forces in the spacecraft equations of motion is presented. This strategy can model the thruster forces occurring in the nominal and contingency modes of attitude control operation. In the nominal mode, the thrusters fire only to balance the daily unloading of the momentum wheels. The contingency case will occur if a pitch or yaw axis momentum wheel fails, and the thrusters could fire up to 1200 times around the orbit to replace the failed wheel's momentum contribution. Deterministic errors are computed and shown to be under specified error requirements.

Engelhardt, Douglas B.↗

NASA NTRS1989

Deterministic photon bias in speckle imaging

A method for determining photo bias terms in speckle imaging is presented, and photon bias is shown to be a deterministic quantity that can be calculated without the use of the expectation operator. The quantities obtained are found to be identical to previous results. The present results have extended photon bias calculations to the important case of the bispectrum where photon events are assigned different weights, in which regime the bias is a frequency dependent complex quantity that must be calculated for each frame.

Beletic, James W.↗

NASA NTRS1989

Ideal state reconstructor for deterministic digital control systems

Polites, Michael E.↗

NASA NTRS1988

Ada programming guidelines for deterministic storage management

Previous reports have established that a program can be written in the Ada language such that the program's storage management requirements are determinable prior to its execution. Specific guidelines for ensuring such deterministic usage of Ada dynamic storage requirements are described. Because requirements may vary from one application to another, guidelines are presented in a most-restrictive to least-restrictive fashion to allow the reader to match appropriate restrictions to the particular application area under investigation.

Auty, David↗

NASA NTRS1991

Deterministic multi-zone ice accretion modeling

The study focuses on a deterministic model of the surface roughness transition behavior of glaze ice and analyzes the initial smooth/rough transition location, bead formation, and the propagation of the transition location. Based on a hypothesis that the smooth/rough transition location coincides with the laminar/turbulent boundary-layer transition location, a multizone model is implemented in the LEWICE code. In order to verify the effectiveness of the model, ice accretion predictions for simple cylinders calculated by the multizone LEWICE are compared to experimental ice shapes. The glaze ice shapes are found to be sensitive to the laminar surface roughness and bead thickness parameters controlling the transition location, while the ice shapes are found to be insensitive to the turbulent surface roughness.

Yamaguchi, K.↗

NASA NTRS1991

Deterministic multi-zone ice accretion modeling

The focus here is on a deterministic model of the surface roughness transition behavior of glaze ice. The initial smooth/rough transition location, bead formation, and the propagation of the transition location are analyzed. Based on the hypothesis that the smooth/rough transition location coincides with the laminar/turbulent boundary layer transition location, a multizone model is implemented in the LEWICE code. In order to verify the effectiveness of the model, ice accretion predictions for simple cylinders calculated by the multizone LEWICE are compared to experimental ice shapes. The glaze ice shapes are found to be sensitive to the laminar surface roughness and bead thickness parameters controlling the transition location, while the ice shapes are found to be insensitive to the turbulent surface roughness.

Yamaguchi, K.↗

NASA NTRS1992

A deterministic method for estimating attitude from magnetometer data only

A new deterministic algorithm which estimates spacecraft attitude utilizing magnetometer data only is presented. This algorithm exploits the dynamic equations of motion to propagate attitude and thus requires knowledge of both internal and external torques, except in the special case of a spacecraft rotating with constant angular velocity. Preliminary results obtained for the uncontrolled Relay Mirror Experiment satellite utilizing real telemetry data are reported.

Natanson, G. A.↗

NASA NTRS1990

The behavior of elastic anisotropic laminated composite flat structures subjected to deterministic and random loadings

Within this research project, the following topics were studied: (1) foundation of the refined theory of flat cross-ply laminated composite flat and curved panels as well as their static and dynamic response analysis; (2) foundation of a geometrically-nonlinear shear-deformable theory of composite laminated flat panels including the effect of initial geometric imperfections and its application in the postbuckling analysis; (3) the study of the dynamic response of shear deformable elastic laminated composite panels to deterministic time-dependent external excitations as the sonic boom and explosive blast type-loadings; (4) the study of the dynamic response of shear deformable elastic laminated composite panels to random excitation as e.g. the one produced by a jet noise or by any time-dependent external excitation whose characteristics are expressed in a statistical sense; and (5) the dynamic stability of fiber-reinforced composite flat panels whose materials (due to e.g. an ambient high temperature field) exhibit a time-dependent physical behavior.

Librescu, Liviu↗

NASA NTRS1992

Search for deterministic pulse trends in gamma ray burst temporal profiles

Most cosmic gamma-ray burst temporal profiles appear to be comprised of several individual pulses, many of which overlap. It is advantageous to deconvolve the temporal structures into their constituent pulses, and thereby investigate the shape, intensity and temporal distributions of the pulses as a function of energy. Such fundamental pulse descriptors would provide constraints for theoretical modeling of the burst emission process, such as indications of source size, optical depth and geometry, as a function of time. We have developed a deconvolution algorithm which treats sequences of pulse shapes that change deterministically. The algorithm, a generalization of autoregressive techniques, has been applied to a few bright bursts observed by BATSE. Results indicate that, even within short intervals, constituent pulses are not self-similarly shaped, nor do pulse shapes evolve in a simple manner throughout a burst. Hence, the direction of our future work on pulse deconvolution will focus on analysis methods which allow pulse shape to vary.

Norris, J. P.↗

NASA NTRS1995

Fabrication of the Advanced X-ray Astrophysics Facility (AXAF) Optics: A Deterministic, Precision Engineering Approach to Optical Fabrication

The mirror assembly of the AXAF observatory consists of four concentric, confocal, Wolter type 1 telescopes. Each telescope includes two conical grazing incidence mirrors, a paraboloid followed by a hyperboloid. Fabrication of these state-or-the-art optics is now complete, with predicted performance that surpasses the goals of the program. The fabrication of these optics, whose size and requirements exceed those of any previous x-ray mirrors, presented a challenging task requiring the use of precision engineering in many different forms. Virtually all of the equipment used for this effort required precision engineering. Accurate metrology required deterministic support of the mirrors in order to model the gravity distortions which will not be present on orbit. The primary axial instrument, known as the Precision Metrology Station (PMS), was a unique scanning Fizeau interferometer. After metrology was complete, the optics were placed in specially designed Glass Support Fixtures (GSF's) for installation on the Automated Cylindrical Grinder/Polishers (ACG/P's). The GSF's were custom molded for each mirror element to match the shape of the outer surface to minimize distortions of the inner surface. The final performance of the telescope is expected to far exceed the original goals and expectations of the program.

Gordon, T. E.↗

NASA NTRS1995

Development of a Probabilistic Component Mode Synthesis Method for the Analysis of Non-Deterministic Substructures

Standard methods of structural dynamic analysis assume that the structural characteristics are deterministic. Recognizing that these characteristics are actually statistical in nature, researchers have recently developed a variety of methods that use this information to determine probabilities of a desired response characteristic, such as natural frequency, without using expensive Monte Carlo simulations. One of the problems in these methods is correctly identifying the statistical properties of primitive variables such as geometry, stiffness, and mass. This paper presents a method where the measured dynamic properties of substructures are used instead as the random variables. The residual flexibility method of component mode synthesis is combined with the probabilistic methods to determine the cumulative distribution function of the system eigenvalues. A simple cantilever beam test problem is presented that illustrates the theory.

Brown, Andrew M.↗

NASA NTRS1997

Validation of a Deterministic Vibroacoustic Response Prediction Model

This report documents the recently completed effort involving validation of a deterministic theory for the random vibration problem of predicting the response of launch pad structures in the low-frequency range (0 to 50 hertz). Use of the Statistical Energy Analysis (SEA) methods is not suitable in this range. Measurements of launch-induced acoustic loads and subsequent structural response were made on a cantilever beam structure placed in close proximity (200 feet) to the launch pad. Innovative ways of characterizing random, nonstationary, non-Gaussian acoustics are used for the development of a structure's excitation model. Extremely good correlation was obtained between analytically computed responses and those measured on the cantilever beam. Additional tests are recommended to bound the problem to account for variations in launch trajectory and inclination.

Caimi, Raoul E.↗

NASA NTRS1997

On the Use of Statistics in Design and the Implications for Deterministic Computer Experiments

Perhaps the most prevalent use of statistics in engineering design is through Taguchi's parameter and robust design -- using orthogonal arrays to compute signal-to-noise ratios in a process of design improvement. In our view, however, there is an equally exciting use of statistics in design that could become just as prevalent: it is the concept of metamodeling whereby statistical models are built to approximate detailed computer analysis codes. Although computers continue to get faster, analysis codes always seem to keep pace so that their computational time remains non-trivial. Through metamodeling, approximations of these codes are built that are orders of magnitude cheaper to run. These metamodels can then be linked to optimization routines for fast analysis, or they can serve as a bridge for integrating analysis codes across different domains. In this paper we first review metamodeling techniques that encompass design of experiments, response surface methodology, Taguchi methods, neural networks, inductive learning, and kriging. We discuss their existing applications in engineering design and then address the dangers of applying traditional statistical techniques to approximate deterministic computer analysis codes. We conclude with recommendations for the appropriate use of metamodeling techniques in given situations and how common pitfalls can be avoided.

Simpson, Timothy W.↗

NASA NTRS2002

A Deterministic Interfacial Cyclic Oxidation Spalling Model: Model Development and Parametric Response - Part 1

An equation has been developed to model the iterative scale growth and spalling process that occurs during cyclic oxidation of high temperature materials. Parabolic scale growth and spalling of a constant surface area fraction have been assumed. Interfacial spallation of the only the thickest segments was also postulated. This simplicity allowed for representation by a simple deterministic summation series. Inputs are the parabolic growth rate constant, the spall area fraction, oxide stoichiometry, and cycle duration. Outputs include the net weight change behavior, as well as the total amount of oxygen and metal consumed, the total amount of oxide spalled, and the mass fraction of oxide spalled. The outputs all follow typical well-behaved trends with the inputs and are in good agreement with previous interfacial models.

Smialek, James L.↗