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NASA NTRS1993

Impact contribution of prebiotic reactants to Earth

A study was performed to explore the effectiveness of comets for chemical evolution. The concentration of amino acids in various terrestrial environments was mathematically explored as there is evidence that amino acids formed as a result of cometary impact. First, the initial concentration of amino acids in surface environment after cometary impact was estimated. The effect of hydrothermal vents, ultra-violet rays, and clays was taken into consideration. Next, the absorption of amino acids by clay particles before degradation by ultra-violet light was analyzed. Finally, the effectiveness of clays, ultra-violet, and hydrothermal vents as sinks for cometary amino acids was compared. A mathematical model was then developed for the production of impact deposits on Earth for the past 2 Ga, and the relative thickness distribution was computed for impact deposits produced in 2 Ga. The reported relative thickness distribution of tillites and diamicites of all ages agrees with the thickness calculated from this impact model. This suggests that many of the ancient tillites and diamicites could be of impact origin. The effectiveness of comets was explored on the chemical evolution of amino acids. The effect of sinks such as clays, submarine vents, and UV light on amino acid concentration was considered. Sites favorable to chemical evolution of amino acids were examined, and it was concluded that chemical evolution could have occurred at or above the surface even during periods of intense bombardment of the Earth more than 3.8 billion years ago.

Aggarwal, Hans R.↗
NASA NTRS1993

Use of high performance networks and supercomputers for real-time flight simulation

In order to meet the stringent time-critical requirements for real-time man-in-the-loop flight simulation, computer processing operations must be consistent in processing time and be completed in as short a time as possible. These operations include simulation mathematical model computation and data input/output to the simulators. In 1986, in response to increased demands for flight simulation performance, NASA's Langley Research Center (LaRC), working with the contractor, developed extensions to the Computer Automated Measurement and Control (CAMAC) technology which resulted in a factor of ten increase in the effective bandwidth and reduced latency of modules necessary for simulator communication. This technology extension is being used by more than 80 leading technological developers in the United States, Canada, and Europe. Included among the commercial applications are nuclear process control, power grid analysis, process monitoring, real-time simulation, and radar data acquisition. Personnel at LaRC are completing the development of the use of supercomputers for mathematical model computation to support real-time flight simulation. This includes the development of a real-time operating system and development of specialized software and hardware for the simulator network. This paper describes the data acquisition technology and the development of supercomputing for flight simulation.

Cleveland, Jeff I., II↗
NASA NTRS1992

SAVS: A Space Analysis and Visualization System

We propose to develop, test, demonstrate, and deliver to NASA a powerful and versatile data acquisition, manipulation, analysis and visualization system which will enhance scientific capabilities in the display and interpretation of diverse and distributed data within an integrated user-friendly environment. Our approach exploits existing technologies and combines three major elements into an easy-to-use interactive package: (1) innovative visualization software; (2) advanced database techniques; and (3) a rich set of mathematical and image processing tools. Visualization capabilities will include one-, two-, and three-dimensional displays, along with animation, compression, warping and slicing functions. Analysis tools will include generic mathematical and statistical techniques along with the ability to use large scale models for interactive interpretation of large volume data sets. Our system will be implemented on Sun and DEC UNIX workstations and on the Stardent Graphics Super computer. Our final deliverable will include complete documentation and a NASA/NSF-CDAW/SUNDIAL campaign demonstration.

Szuszczewicz, Edward P.↗
NASA NTRS1993

Multiscale Morphological Filtering for Analysis of Noisy and Complex Images

Images acquired with passive sensing techniques suffer from illumination variations and poor local contrasts that create major difficulties in interpretation and identification tasks. On the other hand, images acquired with active sensing techniques based on monochromatic illumination are degraded with speckle noise. Mathematical morphology offers elegant techniques to handle a wide range of image degradation problems. Unlike linear filters, morphological filters do not blur the edges and hence maintain higher image resolution. Their rich mathematical framework facilitates the design and analysis of these filters as well as their hardware implementation. Morphological filters are easier to implement and are more cost effective and efficient than several conventional linear filters. Morphological filters to remove speckle noise while maintaining high resolution and preserving thin image regions that are particularly vulnerable to speckle noise were developed and applied to SAR imagery. These filters used combination of linear (one-dimensional) structuring elements in different (typically four) orientations. Although this approach preserves more details than the simple morphological filters using two-dimensional structuring elements, the limited orientations of one-dimensional elements approximate the fine details of the region boundaries. A more robust filter designed recently overcomes the limitation of the fixed orientations. This filter uses a combination of concave and convex structuring elements. Morphological operators are also useful in extracting features from visible and infrared imagery. A multiresolution image pyramid obtained with successive filtering and a subsampling process aids in the removal of the illumination variations and enhances local contrasts. A morphology-based interpolation scheme was also introduced to reduce intensity discontinuities created in any morphological filtering task. The generality of morphological filtering techniques in extracting information from a wide variety of images obtained with active and passive sensing techniques is discussed. Such techniques are particularly useful in obtaining more information from fusion of complex images by different sensors such as SAR, visible, and infrared.

Kher, A.↗
NASA NTRS1993

Uncertainty reasoning in expert systems

Intelligent control is a very successful way to transform the expert's knowledge of the type 'if the velocity is big and the distance from the object is small, hit the brakes and decelerate as fast as possible' into an actual control. To apply this transformation, one must choose appropriate methods for reasoning with uncertainty, i.e., one must: (1) choose the representation for words like 'small', 'big'; (2) choose operations corresponding to 'and' and 'or'; (3) choose a method that transforms the resulting uncertain control recommendations into a precise control strategy. The wrong choice can drastically affect the quality of the resulting control, so the problem of choosing the right procedure is very important. From a mathematical viewpoint these choice problems correspond to non-linear optimization and are therefore extremely difficult. In this project, a new mathematical formalism (based on group theory) is developed that allows us to solve the problem of optimal choice and thus: (1) explain why the existing choices are really the best (in some situations); (2) explain a rather mysterious fact that fuzzy control (i.e., control based on the experts' knowledge) is often better than the control by these same experts; and (3) give choice recommendations for the cases when traditional choices do not work.

Kreinovich, Vladik↗
NASA NTRS1992

Quantification of human responses

Human perception is a complex phenomenon which is difficult to quantify with instruments. For this reason, large panels of people are often used to elicit and aggregate subjective judgments. Print quality, taste, smell, sound quality of a stereo system, softness, and grading Olympic divers and skaters are some examples of situations where subjective measurements or judgments are paramount. We usually express what is in our mind through language as a medium but languages are limited in available choices of vocabularies, and as a result, our verbalizations are only approximate expressions of what we really have in mind. For lack of better methods to quantify subjective judgments, it is customary to set up a numerical scale such as 1, 2, 3, 4, 5 or 1, 2, 3, ..., 9, 10 for characterizing human responses and subjective judgments with no valid justification except that these scales are easy to understand and convenient to use. But these numerical scales are arbitrary simplifications of the complex human mind; the human mind is not restricted to such simple numerical variations. In fact, human responses and subjective judgments are psychophysical phenomena that are fuzzy entities and therefore difficult to handle by conventional mathematics and probability theory. The fuzzy mathematical approach provides a more realistic insight into understanding and quantifying human responses. This paper presents a method for quantifying human responses and subjective judgments without assuming a pattern of linear or numerical variation for human responses. In particular, quantification and evaluation of linguistic judgments was investigated.

Steinlage, R. C.↗
NASA NTRS1992

Methods of periodicity analysis - Relationship between the Rayleigh analysis and a maximum likelihood method

For periodicity analysis of occurrence rates of discrete events, one can use the maximum likelihood method or the 'Rayleigh analysis'. In a maximum likelihood analysis using a sinusoidal distribution, one tries various values of amplitude A and phase angle Theta(0) of the distribution function. We show that these two methods are essentially equivalent to one another in spite of their different mathematical origins. Using the Rayleigh analysis, therefore, we can simply calculate A and Theta(0) which maximize the likelihood. Using the cumulative nature of the logarithmic likelihood, we can identify time intervals during which the periodicity is in operation. When a periodicity operates only in certain time intervals, it is important to identify these intervals. Mathematically, the above technique is applicable only to discrete events. However, with slight modifications we can apply this technique to general cases - periodicity analysis of measurements of continuously varying quantities.

Bai, T.↗
NASA NTRS1992

On the correlated k-distribution method for radiative transfer in nonhomogeneous atmospheres

The paper discusses the correlated k(absorption coefficient)-distribution (CKD) method for radiative transfer in nonhomogeneous atmospheres, in terms of the physical and mathematical conditions under which this method is valid. The CKD approach is theoretically formulated, and the mathematical and physical conditions under which this method is valid are identified. The parameterization for incorporating pressure and temperature effects in the k distribution is presented. The errors of CKD for absorption bands in the solar and thermal infrared spectra are examined, and the errors due to both the CKD method and the use of the optimum number of quadrature points are identified. Finally, an overall treatment for various absorption bands is developed, which will provide high efficiency and accuracy.

Fu, Qiang↗
NASA NTRS1993

DUKSUP - A high thrust trajectory optimization code

Designing missions on expendable launch vehicles (ELV's) includes determining launch vehicle performance capabilities and trajectory characteristics over the range of mission requirements for suitable launch periods. This analysis depends on mathematically modeling both the launch vehicle and the mission requirements. Generally the result is a mathematical model that is described by an objective function to be optimized subject to an assortment of algebraic and dynamic constraints. About 30 years ago, engineers at Lewis Research Center (LeRC) undertook the task of creating a software code to solve 3D versions of such problems and based it on the Calculus of Variations/Optimal Control Theory. One of these codes, DUKSUP, has been in use at LeRC for nearly 25 years, during which time it has played an important role in a large number of studies and actual missions. Currently it is being used by about 12 analysts in the Center's Advanced Space Analysis Office (ASAO) to do mission design, feasibility studies, corroboration of contractor data and planning studies for the Space Exploration Initiative (SEI). Today, it is one of the few ELV mission analysis production codes based on variational methods. With future ELV missions in mind, ASAO is presently creating a new code to upgrade DUKSUP's capabilities.

Balkanyi, Leslie R.↗
NASA NTRS1993

An optimal GPS data processing technique for precise positioning

A mathematical formula to optimally combine dual-frequency GPS pseudorange and carrier phase (integrated Doppler) data streams into a single data stream is derived in closed form. The data combination reduces the data volume and computing time in the filtering process for parameter estimation by a factor of 4 while preserving the full data strength for precise positioning. The resulting single data stream is that of carrier phase measurements with both data noise and bias uncertainty strictly defined. With this mathematical formula the single stream of optimally combined GPS measurements can be efficiently formed by simple numerical calculations. Carrier phase ambiguity resolution, when feasible, is strengthened due to the preserved full data strength with the optimally combined data and the resulting longer wavelength for the ambiguity to be resolved.

Wu, Sien-Chong↗
NASA NTRS1993

Ratchetting behavior in viscoplasticity - A technical note

Viscoplastic models that use the Armstrong and Frederick (1966) kinematic hardening relationship are known to generally overpredict the observed accumulation of ratchet strains. The reason for this behavior is a consequence of the mathematics used to describe Hooke's law and the evolution equations for plastic strain and back stress. Conditions for ratchetting exist whenever there is a cycle-averaged mean stress present over a cyclic loading path. Two types of controlled loading paths are often studied: cyclic relaxation is the ratchet mechanism associated with displacement (strain) control, while cyclic creep is the ratchet mechanism associated with load (stress) control. Overcoming the possible adverse trends in predicted ratchetting behavior is a difficult task, and how one ought to go about doing this is not yet completely clear. We therefore choose to discuss the mathematical cause of ratchetting and how it has been dealt with to date, but make no attempt to correct this flaw.

Freed, Alan D.↗
NASA NTRS1992

Data integration in multi-sensor based robotic workstations

A relaxation labeling algorithm is developed. The major advantage of this algorithm over the existing ones is that the mathematic operation is simplified. The simplification eases the analysis of the convergence properties. Both the theoretical and application aspects of the proposed algorithm are investigated. The local convergence properties of a labeling process with n labels and m labels are established. The investigation of the interaction among the nodes in a multinode labeling process reveals some insight into the mathematical issues involved in the relaxation operations.

Chen, Qin↗
NASA NTRS1993

Analysis of the distribution of pitch angles in model galactic disks - Numerical methods and algorithms

An automated mathematical method capable of successfully isolating the many different features in prototype and observed spiral galaxies and of accurately measuring the pitch angles and lengths of these individual features is developed. The method is applied to analyze the evolution of specific features in a prototype galaxy exhibiting flocculent spiral structure. The mathematical-computational method was separated into two components. Initially, the galaxy was partitioned into dense regions constituting features using two different methods. The results obtained using these two partitioning algorithms were very similar, from which it is inferred that no numerical biasing was evident and that capturing of the features was consistent. Standard least-squares methods underestimated the true slope of the cloud distribution and were incapable of approximating an orientation of 45 deg. The problems were overcome by introducing a superior fit least-squares method, developed with the intention of calculating true orientation rather than a regression line.

Russell, William S.↗
NASA NTRS1988

Evaluation of structural integrity using integrated testing and analysis

An integrated approach to dynamic testing and mathematical model analysis is described. The overall approach addresses four key tasks, namely, pretest planning and analysis, test data acquisition, data reduction and analysis, and test/analysis correlation and mathematical model updates. Several key software programs are employed to accomplish this task. They are a leading finite element code, a sophisticated data analysis processor and a graphical pre- and post-processor along with an advanced interface utility. Several practical structures are used to illustrate tools and concepts employed in the integrated test analysis process.

Coppolino, Robert N.↗
NASA NTRS1988

Experimental facilities for system identification

Future space vehicles will differ significantly from the space systems used in the past. The planned spacecraft configurations will include extremely large structures, up to 100-200 meters across. Because the allowable launch weights are limited, the large space structures must be constructed of lightweight, flexible elements, and active control of the shape and attitude of the spacecraft will be required. The behavior of large structures is characterized by many closely spaced natural modes, and some applications may also include large on-board disturbances. Consequently, the control and disturbance forces will invariably spill over to a large number of modes. Structural identification will be necessary for precision pointing and shape controls to be effective. An accurate mathematical model of a structure is essential for the success of precision control system design. However, the currently available analytical modeling codes, such as NASTRAN, are incapable of producing numerical models of the required precision. The favored approach for model determination is to refine the mathematical model based on experiments in the orbital environment. It is to this effect that we must develop techniques to reliably generate the accurate models required for future missions, and the arena in which these methods will be developed and proved is through ground-based system identification experiments and demonstrations. The Air Force Astronautics Laboratory (AFAL) has expanded the on-site ground-test facilities in recent years, and additional sites are planned for the immediate future. We shall review the plans for laboratory growth at AFAL with regard to the type of experiments proposed and the availability of the new facilities.

Das, Alok↗
NASA NTRS1988

Parameter identification of material constants in a composite shell structure

One of the basic requirements in engineering analysis is the development of a mathematical model describing the system. Frequently comparisons with test data are used as a measurement of the adequacy of the model. An attempt is typically made to update or improve the model to provide a test verified analysis tool. System identification provides a systematic procedure for accomplishing this task. The terms system identification, parameter estimation, and model correlation all refer to techniques that use test information to update or verify mathematical models. The goal of system identification is to improve the correlation of model predictions with measured test data, and produce accurate, predictive models. For nonmetallic structures the modeling task is often difficult due to uncertainties in the elastic constants. A finite element model of the shell was created, which included uncertain orthotropic elastic constants. A modal survey test was then performed on the shell. The resulting modal data, along with the finite element model of the shell, were used in a Bayes estimation algorithm. This permitted the use of covariance matrices to weight the confidence in the initial parameter values as well as confidence in the measured test data. The estimation procedure also employed the concept of successive linearization to obtain an approximate solution to the original nonlinear estimation problem.

Martinez, David R.↗
NASA NTRS1930

Strength in Shear of the Thin Curved Sheets of Alclad

This note is on an investigation made to obtain information on the strength of thin curved sheets of Alclad in shear. Designers may utilize this material as a strength member as well as for a covering for the wings and fuselages. A reduction may then be made in the size of the internal strength members. These experiments were undertaken with the object of securing the maximum value from the metal in this respect. The point at which buckling occurs is of primary importance. The buckling shear of a curved thin plate was determined mathematically and also experimentally. The following formula was obtained mathematically: s=K E t/r in which s is the unit shear, K is a constant, E is the modulus of elasticity, t is the thickness of the material, and r is the radius of curvature. The value of K as determined by the experiments was found to be .075. This formula applies only when s is within the elastic limit of the material. The breaking point of the material was obtained in most of the tests as a matter of information and the results are included in this report. The effect of the supporting ribs was determined by varying the number used.

Smith, George Michael↗
NASA NTRS1946

On laminar and turbulent friction

Report deals, first with the theory of the laminar friction flow, where the basic concepts of Prandtl's boundary layer theory are represented from mathematical and physical points of view, and a method is indicated by means of which even more complicated cases can be treated with simple mathematical means, at least approximately. An attempt is also made to secure a basis for the computation of the turbulent friction by means of formulas through which the empirical laws of the turbulent pipe resistance can be applied to other problems on friction drag. (author)

Von Karman, TH↗