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NASA NTRS1990

Theory of biaxial graded-index optical fiber

A biaxial graded-index fiber with a homogeneous cladding is studied. Two methods, wave equation and matrix differential equation, of formulating the problem and their respective solutions are discussed. For the wave equation formulation of the problem it is shown that for the case of a diagonal permittivity tensor the longitudinal electric and magnetic fields satisfy a pair of coupled second-order differential equations. Also, a generalized dispersion relation is derived in terms of the solutions for the longitudinal electric and magnetic fields. For the case of a step-index fiber, either isotropic or uniaxial, these differential equations can be solved exactly in terms of Bessel functions. For the cases of an istropic graded-index and a uniaxial graded-index fiber, a solution using the Wentzel, Krammers and Brillouin (WKB) approximation technique is shown. Results for some particular permittivity profiles are presented. Also the WKB solutions is compared with the vector solution found by Kurtz and Streifer. For the matrix formulation it is shown that the tangential components of the electric and magnetic fields satisfy a system of four first-order differential equations which can be conveniently written in matrix form. For the special case of meridional modes, the system of equations splits into two systems of two equations. A general iterative technique, asymptotic partitioning of systems of equations, for solving systems of differential equations is presented. As a simple example, Bessel's differential equation is written in matrix form and is solved using this asymptotic technique. Low order solutions for particular examples of a biaxial and uniaxial graded-index fiber are presented. Finally numerical results obtained using the asymptotic technique are presented for particular examples of isotropic and uniaxial step-index fibers and isotropic, uniaxial and biaxial graded-index fibers.

Kawalko, Stephen F.↗
NASA NTRS1990

Component model reduction via the projection and assembly method

This paper explains the projection and assembly model reduction method which has been used to derive reduced order component models for the Galileo spacecraft. Assembly of reduced order component models produces a reduced order system model which can then be used in multibody simulation codes for efficient run times. The methodology is explained and a proof is given showing the exact reproduction of selected significant system modes. Frequency bounds are obtained for all modes produced when the reduced order components are assembled. The projection and assembly method is demonstrated on two examples. The first example is a simplified model of the Galileo spacecraft, while the second example is the model of the Galileo spacecraft in its early mission configuration. When articulation of components is allowed, the method may not reproduce all system modes precisely. Remedies for this problem are suggested.

Kissel, Glen J.↗
NASA NTRS1990

A first-order Lyapunov robustness method for linear systems with uncertain parameters

A method for stability-robustness analysis based on a quadratic Liapunov function that varies linearly with uncertainty parameters is derived. Linear time-invariant systems with structured uncertainties are discussed. The Liapunov function is optimized numerically to maximize the robustness region in parameter space. Numerical results are given for four examples in which the first-order method is compared to previous Liapunov methods. While the zero-order method is slightly better than the first-order method for one example, the first-order method is clearly superior in the other three (more realistic) examples. The first-order method is especially superior for the active control of flexible structures, where robustness with respect to (1) unmodeled coupling between modeled modes and (2) unmodeled modes is important. For such applications, the first-order method is much better at detecting the increased robustness associated with increased separation between frequencies.

Leal, M. A.↗
NASA NTRS1990

Procedural error monitoring and smart checklists

Human beings make and usually detect errors routinely. The same mental processes that allow humans to cope with novel problems can also lead to error. Bill Rouse has argued that errors are not inherently bad but their consequences may be. He proposes the development of error-tolerant systems that detect errors and take steps to prevent the consequences of the error from occurring. Research should be done on self and automatic detection of random and unanticipated errors. For self detection, displays should be developed that make the consequences of errors immediately apparent. For example, electronic map displays graphically show the consequences of horizontal flight plan entry errors. Vertical profile displays should be developed to make apparent vertical flight planning errors. Other concepts such as energy circles could also help the crew detect gross flight planning errors. For automatic detection, systems should be developed that can track pilot activity, infer pilot intent and inform the crew of potential errors before their consequences are realized. Systems that perform a reasonableness check on flight plan modifications by checking route length and magnitude of course changes are simple examples. Another example would be a system that checked the aircraft's planned altitude against a data base of world terrain elevations. Information is given in viewgraph form.

Palmer, Everett↗
NASA NTRS1990

A flight expert system for on-board fault monitoring and diagnosis

An architecture for a flight expert system (FLES) to assist pilots in monitoring, diagnosing, and recovering from inflight faults is described. A prototype was implemented and an attempt was made to automate the knowledge acquisition process by employing a learning by being told methodology. The scope of acquired knowledge ranges from domain knowledge, including the information about objects and their relationships, to the procedural knowledge associated with the functionality of the mechanisms. AKAS (automatic knowledge acquisition system) is the constructed prototype for demonstration proof of concept, in which the expert directly interfaces with the knowledge acquisition system to ultimately construct the knowledge base for the particular application. The expert talks directly to the system using a natural language restricted only by the extent of the definitions in an analyzer dictionary, i.e., the interface understands a subset of concepts related to a given domain. In this case, the domain is the electrical system of the Boeing 737. Efforts were made to define and employ heuristics as well as algorithmic rules to conceptualize data produced by normal and faulty jet engine behavior examples. These rules were employed in developing the machine learning system (MLS). The input to MLS is examples which contain data of normal and faulty engine behavior and which are obtained from an engine simulation program. MLS first transforms the data into discrete selectors. Partial descriptions formed by those selectors are then generalized or specialized to generate concept descriptions about faults. The concepts are represented in the form of characteristic and discriminant descriptions, which are stored in the knowledge base and are employed to diagnose faults. MLS was successfully tested on jet engine examples.

Ali, Moonis↗
NASA NTRS1990

Dynamic modeling, property investigation, and adaptive controller design of serial robotic manipulators modeled with structural compliance

Research results on general serial robotic manipulators modeled with structural compliances are presented. Two compliant manipulator modeling approaches, distributed and lumped parameter models, are used in this study. System dynamic equations for both compliant models are derived by using the first and second order influence coefficients. Also, the properties of compliant manipulator system dynamics are investigated. One of the properties, which is defined as inaccessibility of vibratory modes, is shown to display a distinct character associated with compliant manipulators. This property indicates the impact of robot geometry on the control of structural oscillations. Example studies are provided to illustrate the physical interpretation of inaccessibility of vibratory modes. Two types of controllers are designed for compliant manipulators modeled by either lumped or distributed parameter techniques. In order to maintain the generality of the results, neither linearization is introduced. Example simulations are given to demonstrate the controller performance. The second type controller is also built for general serial robot arms and is adaptive in nature which can estimate uncertain payload parameters on-line and simultaneously maintain trajectory tracking properties. The relation between manipulator motion tracking capability and convergence of parameter estimation properties is discussed through example case studies. The effect of control input update delays on adaptive controller performance is also studied.

Tesar, Delbert↗
NASA NTRS1989

Size distribution of dust grains: A problem of self-similarity

Distribution functions describing the results of natural processes frequently show the shape of power laws, e.g., mass functions of stars and molecular clouds, velocity spectrum of turbulence, size distributions of asteroids, micrometeorites and also interstellar dust grains. It is an open question whether this behavior is a result simply coming about by the chosen mathematical representation of the observational data or reflects a deep-seated principle of nature. The authors suppose the latter being the case. Using a dust model consisting of silicate and graphite grains Mathis et al. (1977) showed that the interstellar extinction curve can be represented by taking a grain radii distribution of power law type n(a) varies as a(exp -p) with 3.3 less than or equal to p less than or equal to 3.6 (example 1) as a basis. A different approach to understanding power laws like that in example 1 becomes possible by the theory of self-similar processes (scale invariance). The beta model of turbulence (Frisch et al., 1978) leads in an elementary way to the concept of the self-similarity dimension D, a special case of Mandelbrot's (1977) fractal dimension. In the frame of this beta model, it is supposed that on each stage of a cascade the system decays to N clumps and that only the portion beta N remains active further on. An important feature of this model is that the active eddies become less and less space-filling. In the following, the authors assume that grain-grain collisions are such a scale-invarient process and that the remaining grains are the inactive (frozen) clumps of the cascade. In this way, a size distribution n(a) da varies as a(exp -(D+1))da (example 2) results. It seems to be highly probable that the power law character of the size distribution of interstellar dust grains is the result of a self-similarity process. We can, however, not exclude that the process leading to the interstellar grain size distribution is not fragmentation at all. It could be, e.g., diffusion-limited growth discussed by Sander (1986), who applied the theory of fractal geometry to the classification of non-equilibrium growth processes. He received D=2.4 for diffusion-limited aggregation in 3d-space.

Henning, TH.↗
NASA NTRS1991

SAM 2 measurements of the polar stratospheric aerosol. Volume 9: October 1982 - April 1983

The Stratospheric Aerosol Measurement (SAM) II sensor aboard Nimbus 7 is providing 1.0 micron extinction measurements of Antarctic and Arctic stratospheric aerosols with a vertical resolution of 1 km. Representative examples and weekly averages including corresponding temperature profiles provided by NOAA for the time and place of each SAM II measurement are presented. Contours of aerosol extinction as a function of altitude and longitude or time are plotted, and aerosol optical depths are calculated for each week. Typical values of aerosol extinction and stratospheric optical depth in the Arctic are unusually large due to the presence of material from the El Chichon volcano eruption in the Spring of 1982. For example, the optical depth peaked at 0.068, more than 50 times background values. Typical values of aerosol extinction and stratospheric optical depth in the Antarctic varied considerably during this period due to the transport and arrival of the material from the El Chichon eruption. For example, the stratospheric optical depth varied from 0.002 in October 1982, to 0.021 in January 1983. Polar stratospheric clouds were observed during the Arctic winter, as expected. A representative sample is provided of the ninth 6-month period of data to be used in atmospheric and climatic studies.

Mcmaster, L. R.↗
NASA NTRS1991

A summary of existing and planned experiment hardware for low-gravity fluids research

An overview is presented of (1) existing ground-based, low gravity research facilities, with examples of hardware capabilities, and (2) existing and planned space-based research facilities, with examples of current and past flight hardware. Low-gravity, ground-based facilities, such as drop towers and aircraft, provide the experimenter with quick turnaround time, easy access to equipment, gravity levels ranging from 10(exp -2) to 10(exp -6) G, and low-gravity durations ranging from 2 to 30 sec. Currently, the only operational space-based facility is the Space Shuttle. The Shuttle's payload bay and middeck facilities are described. Existing and planned low-gravity fluids research facilities are also described with examples of experiments and hardware capabilities.

Hill, Myron E.↗
NASA NTRS1990

Strike-slip faulting, wrinkle ridges, and time variable stress states in the Coprates Region of Mars

The existence of strike-slip faults was recently documented in two locations on Mars. Two clear examples are reviewed located southeast of Valles Marineris and preliminary evidence is presented for more widespread strike-slip deformation elsewhere in Coprates. The first two examples show that strike-slip faulting occurred in a broad zone east of the Coprates Rise spanning approximately 400 km east-west by perhaps 1000 km north-south. The last example suggests that the growth of major wrinkle ridges throughout Coprates may have been influenced by horizontally directed shear stresses and that more than one generation of ridges was produced. Thus, 'compressional' deformation of ridged plains south of Valles Marineris was spatially heterogeneous and a temporal change in stress may have been involved.

Schultz, Richard A.↗
NASA NTRS1991

Alternative smoothing algorithms for on-line estimation problems

In recent years, much emphasis has been placed on the Kalman filter to solve on-line estimation problems. Smoothers, which determine state estimates at a certain time t using measurements between 0 and T, have been used primarily in off-line estimation schemes. This paper presents alternative forms of smoothers that can be used for on-line estimation problems. The alternative smoothing algorithms provide state estimates which are more refined than Kalman filtered state estimates. The alternative smoothing algorithms are illustrated in two examples. The first example considers a linear discrete-time system while the second example considers a nonlinear continuous-time system with discrete-time measurements.

Baumgartner, Eric T.↗
NASA NTRS1990

A design algorithm using Z-plane closed loop pole placement

It is argued that the design of a single input single output (SISO) control system is simplified if the designer has direct control over the closed loop poles. A space-laser-communications design example utilizing a two-transform algorithm that constructs a generic discrete compensator is presented. The plant in the example has an anti-aliasing filter, a double integrator, a torquer time constant, and a sample-and-hold as continuous elements, and a discrete proportional plus integral module. This fifth-order system is representative of many instrument pointing control systems. Poles resulting from the compensator are placed near the origin of the Z-plane so that the response is dominated by the closed loop poles from the plant. Root locus, time response, and frequency response data are given. Normalization by the sample interval is used to provide a dimensionless example.

Gatlin, James A.↗
NASA NTRS1992

An introduction to high speed aircraft noise prediction

The Aircraft Noise Prediction Program's High Speed Research prediction system (ANOPP-HSR) is introduced. This mini-manual is an introduction which gives a brief overview of the ANOPP system and the components of the HSR prediction method. ANOPP information resources are given. Twelve of the most common ANOPP-HSR control statements are described. Each control statement's purpose and format are stated and relevant examples are provided. More detailed examples of the use of the control statements are presented in the manual along with ten ANOPP-HSR templates. The purpose of the templates is to provide the user with working ANOPP-HSR programs which can be modified to serve particular prediction requirements. Also included in this manual is a brief discussion of common errors and how to solve these problems. The appendices include the following useful information: a summary of all ANOPP-HSR functional research modules, a data unit directory, a discussion of one of the more complex control statements, and input data unit and table examples.

Wilson, Mark R.↗
NASA NTRS1991

Spatial vision within egocentric and exocentric frames of reference

It is remarkable that we are able to perceive a stable visual world and judge the directions, orientations, and movements of visual objects given that images move on the retina, the eyes move in the head, the head moves on the body, and the body moves in space. An understanding of the mechanisms underlying perceptual stability and spatial judgements requires precise definitions of relevant coordinate systems. An egocentric frame of reference is defined with respect to some part of the observer. There are four principal egocentric frames of reference, a station-point frame associated with the nodal point of the eye, an retinocentric frame associated with the retina, a headcentric frame associated with the head, and a bodycentric frame (torsocentric) associated with the torso. Additional egocentric frames can be identified with respect to any segment of the body. An egocentric task is one in which the position, orientation, or motion of an object is judged with respect to an egocentric frame of reference. A proprioceptive is a special kind of egocentric task in which the object being judged is also part of the body. An example of a proprioceptive task is that of directing the gaze toward the seen or unseen toe. An exocentric frame of reference is external to the observer. Geographical coordinates and the direction of gravity are examples of exocentric frames of reference. These various frames are listed in tabular form, together with examples of judgements of each type.

Howard, Ian P.↗
NASA NTRS1991

Extracting fuzzy rules under uncertainty and measuring definability using rough sets

Although computers have come a long way since their invention, they are basically able to handle only crisp values at the hardware level. Unfortunately, the world we live in consists of problems which fail to fall into this category, i.e., uncertainty is all too common. A problem is looked at which involves uncertainty. To be specific, attributes are dealt with which are fuzzy sets. Under this condition, knowledge is acquired by looking at examples. In each example, a condition as well as a decision is made available. Based on the examples given, two sets of rules are extracted, certain and possible. Furthermore, measures are constructed of how much these rules are believed in, and finally, the decisions are defined as a function of the terms used in the conditions.

Culas, Donald E.↗
NASA NTRS1991

A parallel-vector equation solver for unsymmetric matrices on supercomputers

A parallel-vector unsymmetric equation solver is presented. The solver exploits both vector and parallel capabilities provided by modern, high-performance supercomputers. A special storage scheme and loop-unrolling technique are used to optimize the vector performance. A parallel FORTRAN language is used to develop the solver on the CRAY 2 and CRAY Y-MP multiple processing computer environment. Three numerical examples are presented which demonstrate the efficiency and accuracy of this equation solver. The first two examples demonstrate the improved performance, and the third example utilizes the proposed solver to solve a highly nonlinear, unsymmetric finite element formulation for panel flutter.

Qin, J.↗
NASA NTRS1992

Error analysis of finite element results on plates with nonuniform grids

Discrete Dirac delta functions in two dimensions and the governing plate differential equations are used to produce continuous approximations from discrete finite-element data on nonuniform grids. The resulting continuous approximation when compared to the discrete data provides an error analysis. Moreover, the continuous approximation can be differentiated to compute continuous stresses needed for component failure prediction. Stresses can then be calculated accurately at boundaries and at interfaces where finite-element analysis alone may not provide reliable results. The continuous solution along with the differential equations also provides a residual error which is used in the error analysis. This is a unique feature of this approach. Two application examples of the procedure are provided. One example involves the linear response of a clamped square plate under uniform transverse load. Results from finite-element analysis and the continuous solution from the present analysis are compared to a closed-form elasticity solution. The continuous solution is used in a Zienkiewicz-Zhu error estimator to assess the performance of the present analysis. The continuous solution is observed to dramatically correct the finite-element results. In a second example, results for the nonlinear response of a stiffened panel are compared to the finite-element solution.

Sistla, Rajaram↗
NASA NTRS1991

Earth benefits from NASA research and technology. Life sciences applications

This document provides a representative sampling of examples of Earth benefits in life-sciences-related applications, primarily in the area of medicine and health care, but also in agricultural productivity, environmental monitoring and safety, and the environment. This brochure is not intended as an exhaustive listing, but as an overview to acquaint the reader with the breadth of areas in which the space life sciences have, in one way or another, contributed a unique perspective to the solution of problems on Earth. Most of the examples cited were derived directly from space life sciences research and technology. Some examples resulted from other space technologies, but have found important life sciences applications on Earth. And, finally, we have included several areas in which Earth benefits are anticipated from biomedical and biological research conducted in support of future human exploration missions.

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