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NASA NTRS1990

Krylov subspace methods - Theory, algorithms, and applications

Projection methods based on Krylov subspaces for solving various types of scientific problems are reviewed. The main idea of this class of methods when applied to a linear system Ax = b, is to generate in some manner an approximate solution to the original problem from the so-called Krylov subspace span. Thus, the original problem of size N is approximated by one of dimension m, typically much smaller than N. Krylov subspace methods have been very successful in solving linear systems and eigenvalue problems and are now becoming popular for solving nonlinear equations. The main ideas in Krylov subspace methods are shown and their use in solving linear systems, eigenvalue problems, parabolic partial differential equations, Liapunov matrix equations, and nonlinear system of equations are discussed.

Sad, Youcef↗
NASA NTRS1992

Lunar optical telescopes: An historical perspective

There is a long history of thought and discussion on the possibilities of astronomical observatories on the Moon. Numerous ideas have been suggested and a variety of concepts have resulted for lunar optical telescopes. This paper reviews some of the ideas and efforts of individuals and working groups including Hershel, Clarke, Malina, Herbig, and Hess; working groups of the 1960s; and recent initiatives of Burke, Burns, and others. The enhanced technologies of the 1980s and 1990s can make past dreams of lunar observatories come to reality in the 21st century.

Johnson, Stewart W.↗
NASA NTRS1992

Approximation methods for stochastic petri nets

Stochastic Marked Graphs are a concurrent decision free formalism provided with a powerful synchronization mechanism generalizing conventional Fork Join Queueing Networks. In some particular cases the analysis of the throughput can be done analytically. Otherwise the analysis suffers from the classical state explosion problem. Embedded in the divide and conquer paradigm, approximation techniques are introduced for the analysis of stochastic marked graphs and Macroplace/Macrotransition-nets (MPMT-nets), a new subclass introduced herein. MPMT-nets are a subclass of Petri nets that allow limited choice, concurrency and sharing of resources. The modeling power of MPMT is much larger than that of marked graphs, e.g., MPMT-nets can model manufacturing flow lines with unreliable machines and dataflow graphs where choice and synchronization occur. The basic idea leads to the notion of a cut to split the original net system into two subnets. The cuts lead to two aggregated net systems where one of the subnets is reduced to a single transition. A further reduction leads to a basic skeleton. The generalization of the idea leads to multiple cuts, where single cuts can be applied recursively leading to a hierarchical decomposition. Based on the decomposition, a response time approximation technique for the performance analysis is introduced. Also, delay equivalence, which has previously been introduced in the context of marked graphs by Woodside et al., Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's is slower, but the accuracy is generally better. Delay equivalence often fails to converge, while flow equivalent aggregation can lead to potentially bad results if a strong dependence of the mean completion time on the interarrival process exists.

Jungnitz, Hauke Joerg↗
NASA NTRS1992

The KASE approach to domain-specific software systems

Designing software systems, like all design activities, is a knowledge-intensive task. Several studies have found that the predominant cause of failures among system designers is lack of knowledge: knowledge about the application domain, knowledge about design schemes, knowledge about design processes, etc. The goal of domain-specific software design systems is to explicitly represent knowledge relevant to a class of applications and use it to partially or completely automate various aspects of the designing systems within that domain. The hope is that this would reduce the intellectual burden on the human designers and lead to more efficient software development. In this paper, we present a domain-specific system built on top of KASE, a knowledge-assisted software engineering environment being developed at the Stanford Knowledge Systems Laboratory. We introduce the main ideas underlying the construction of domain specific systems within KASE, illustrate the application of the idea in the synthesis of a system for tracking aircraft from radar signals, and discuss some of the issues in constructing domain-specific systems.

Bhansali, Sanjay↗
NASA NTRS1992

A numerical field experiment approach for determining probabilities of microburst intensity

Several investigators had determined that some atmospheric parameters were related to the formation and severity of microbursts. For example, Caracena pointed out the relationship between a dry adiabatic lapse rate and microbursts in 'The crash of Delta Flight 191 at Dallas-Fort Worth international airport'. These early investigations led to the idea that numeric modeling of microbursts with varying atmospheric parameters might define 'signatures' that could lead to determining the probability of microburst intensity. The idea was that, by using already available sensors (such as static air temperature, pressure altitude, and radar reflectivity) onboard an aircraft, a reliable prediction of microburst existence and intensity could be formed. Such data could be used to create an 'expert meteorologist' using either artificial intelligence or other techniques that could be used in either reactive or look-ahead systems to vary sensitivity thresholds and coordinate the inputs from different detecting systems. To this end, Honeywell contracted to have the microburst simulations run. The questions to be addressed were the following: using the sensor set available to the aircraft (e.g. temperature, radar reflectivity, etc.), can we calculate the probability that (1) a microburst could be formed? and (2) that the resultant winds would be of sufficient magnitude to threaten the aircraft? Over a two year period, a data set of 1800 microburst simulations was accumulated. Verification of the microburst simulation was obtained using the results of other independent researchers and actual comparison to microburst events in Orlando and Denver. Some of the results from the simulation have already been incorporated into Honeywell's Windshear Detection and Guidance System with excellent results. Various aspects of this investigation are presented in viewgraph form.

Droegemeier, Kelvin K.↗
NASA NTRS1993

Certain and possible rules for decision making using rough set theory extended to fuzzy sets

Uncertainty may be caused by the ambiguity in the terms used to describe a specific situation. It may also be caused by skepticism of rules used to describe a course of action or by missing and/or erroneous data. To deal with uncertainty, techniques other than classical logic need to be developed. Although, statistics may be the best tool available for handling likelihood, it is not always adequate for dealing with knowledge acquisition under uncertainty. Inadequacies caused by estimating probabilities in statistical processes can be alleviated through use of the Dempster-Shafer theory of evidence. Fuzzy set theory is another tool used to deal with uncertainty where ambiguous terms are present. Other methods include rough sets, the theory of endorsements and nonmonotonic logic. J. Grzymala-Busse has defined the concept of lower and upper approximation of a (crisp) set and has used that concept to extract rules from a set of examples. We will define the fuzzy analogs of lower and upper approximations and use these to obtain certain and possible rules from a set of examples where the data is fuzzy. Central to these concepts will be the idea of the degree to which a fuzzy set A is contained in another fuzzy set B, and the degree of intersection of a set A with set B. These concepts will also give meaning to the statement; A implies B. The two meanings will be: (1) if x is certainly in A then it is certainly in B, and (2) if x is possibly in A then it is possibly in B. Next, classification will be looked at and it will be shown that if a classification will be looked at and it will be shown that if a classification is well externally definable then it is well internally definable, and if it is poorly externally definable then it is poorly internally definable, thus generalizing a result of Grzymala-Busse. Finally, some ideas of how to define consensus and group options to form clusters of rules will be given.

Dekorvin, Andre↗
NASA NTRS1989

Determination of design and operation parameters for upper atmospheric research instrumentation to yield optimum resolution with deconvolution, appendix 4

The power spectrum for a stationary random process can be defined with the Wiener-Khintchine Theorem, which says that the power spectrum and the auto correlation function are a Fourier transform pair. To implement this theorem for signals that are discrete and of finite length we can use the Blackman-Tukey method. Blackman and Tukey (1958) show that a function w(tau), called a lag window, can be applied to the auto correlation estimates to obtain power spectrum estimates that are statistically stable. The Fourier transform of w(r) is called a spectral window. Typical choices for spectral windows show a distinct trade-off between the main lobe width and side lobe strength. A new idea for designing windows by taking linear combinations of the standard windows to produce hybrid windows was introduced by Smith (1985). We implement Smith's idea to obtain spectral windows with narrow main lobes and smaller (compared with typical windows) near side lobes. One of the main contributions of this thesis is that we show that Smith's problem is equivalent to a Quadratic Programming (QP) problem with linear equality and inequality constraints. A computer program was written to produce hybrid windows by setting up and solving the QP problem. We also developed and solved two variations of the original problem. The two variations involved changing the inequality constraints in both cases from non negativity on the combination coefficients to non negativity on the hybrid lag window itself. For the second variation, the window functions used to construct the hybrid window were changed to a frequency-variable set of truncated cosinusoids. A series of tests was run with the three computer programs to investigate the behavior of the hybrid spectral and lag windows. Emphasis was put on obtaining spectral windows with both relatively narrow main lobes and the lowest possible (for these algorithms) near side lobes. Some success was achieved for this goal. A 10 dB peak side lobe reduction over the rectangular spectral window without significant main lobe broadening was achieved. Also, average side lobe levels of -117 dB were reached at a cost of doubling the main lobe width (at the -3 dB point).

Ioup, George E.↗
NASA NTRS1991

Monte-Carlo methods make Dempster-Shafer formalism feasible

One of the main obstacles to the applications of Dempster-Shafer formalism is its computational complexity. If we combine m different pieces of knowledge, then in general case we have to perform up to 2(sup m) computational steps, which for large m is infeasible. For several important cases algorithms with smaller running time were proposed. We prove, however, that if we want to compute the belief bel(Q) in any given query Q, then exponential time is inevitable. It is still inevitable, if we want to compute bel(Q) with given precision epsilon. This restriction corresponds to the natural idea that since initial masses are known only approximately, there is no sense in trying to compute bel(Q) precisely. A further idea is that there is always some doubt in the whole knowledge, so there is always a probability p(sub o) that the expert's knowledge is wrong. In view of that it is sufficient to have an algorithm that gives a correct answer a probability greater than 1-p(sub o). If we use the original Dempster's combination rule, this possibility diminishes the running time, but still leaves the problem infeasible in the general case. We show that for the alternative combination rules proposed by Smets and Yager feasible methods exist. We also show how these methods can be parallelized, and what parallelization model fits this problem best.

Kreinovich, Vladik YA.↗
NASA NTRS1991

What procedure to choose while designing a fuzzy control? Towards mathematical foundations of fuzzy control

Fuzzy control has been successfully applied in industrial systems. However, there is some caution in using it. The reason is that it is based on quite reasonable ideas, but each of these ideas can be implemented in several different ways, and depending on which of the implementations chosen different results are achieved. Some implementations lead to a high quality control, some of them not. And since there are no theoretical methods for choosing the implementation, the basic way to choose it now is experimental. But if one chooses a method that is good for several examples, there is no guarantee that it will work fine in all of them. Hence the caution. A theoretical basis for choosing the fuzzy control procedures is provided. In order to choose a procedure that transforms a fuzzy knowledge into a control, one needs, first, to choose a membership function for each of the fuzzy terms that the experts use, second, to choose operations of uncertainty values that corresponds to 'and' and 'or', and third, when a membership function for control is obtained, one must defuzzy it, that is, somehow generate a value of the control u that will be actually used. A general approach that will help to make all these choices is described: namely, it is proved that under reasonable assumptions membership functions should be linear or fractionally linear, defuzzification must be described by a centroid rule and describe all possible 'and' and 'or' operations. Thus, a theoretical explanation of the existing semi-heuristic choices is given and the basis for the further research on optimal fuzzy control is formulated.

Kreinovich, Vladik YA.↗
NASA NTRS1991

Controls for space structures

Assembly and operation of large space structures (LSS) in orbit will require robot-assisted docking and berthing of partially-assembled structures. These operations require new solutions to the problems of controls. This is true because of large transient and persistent disturbances, controller-structure interaction with unmodeled modes, poorly known structure parameters, slow actuator/sensor dynamical behavior, and excitation of nonlinear structure vibrations during control and assembly. For on-orbit assembly, controllers must start with finite element models of LSS and adapt on line to the best operating points, without compromising stability. This is not easy to do, since there are often unmodeled dynamic interactions between the controller and the structure. The indirect adaptive controllers are based on parameter estimation. Due to the large number of modes in LSS, this approach leads to very high-order control schemes with consequent poor stability and performance. In contrast, direct model reference adaptive controllers operate to force the LSS to track the desirable behavior of a chosen model. These schemes produce simple control algorithms which are easy to implement on line. One problem with their use for LSS has been that the model must be the same dimension as the LSS - i.e., quite large. A control theory based on the command generator tracker (CGT) ideas of Sobel, Mabins, Kaufman and Wen, Balas to obtain very low-order models based on adaptive algorithms was developed. Closed-loop stability for both finite element models and distributed parameter models of LSS was proved. In addition, successful numerical simulations on several LSS databases were obtained. An adaptive controller based on our theory was also implemented on a flexible robotic manipulator at Martin Marietta Astronautics. Computation schemes for controller-structure interaction with unmodeled modes, the residual mode filters or RMF, were developed. The RMF theory was modified to compensate slow actuator/sensor dynamics. These new ideas are being applied to LSS simulations to demonstrate the ease with which one can incorporate slow actuator/sensor effects into our design. It was also shown that residual mode filter compensation can be modified for small nonlinearities to produce exponentially stable closed-loop control. A theory for disturbance accommodating controllers based on reduced order models of structures was developed, and stability results for these controllers in closed-loop with large-scale finite element models of structures were obtained.

Balas, Mark↗
NASA NTRS1993

Horizon Mission Methodology - A tool for the study of technology innovation and new paradigms

The Horizon Mission (HM) methodology was developed to provide a means of identifying and evaluating highly innovative, breakthrough technology concepts (BTCs) and for assessing their potential impact on advanced space missions. The methodology is based on identifying new capabilities needed by hypothetical 'horizon' space missions having performance requirements that cannot be met even by extrapolating known space technologies. Normal human evaluation of new ideas such as BTCs appears to be governed (and limited) by 'inner models of reality' defined as paradigms. Thus, new ideas are evaluated by old models. This paper describes the use of the HM Methodology to define possible future paradigms that would provide alternatives to evaluation by current paradigms. The approach is to represent a future paradigm by a set of new BTC-based capabilities - called a paradigm abstract. The paper describes methods of constructing and using the abstracts for evaluating BTCs for space applications and for exploring the concept of paradigms and paradigm shifts as a representation of technology innovation.

Anderson, John L.↗
NASA NTRS1992

Are coronal type II shocks piston driven?

Flare blast waves and shocks piston driven by coronal mass ejections (CMEs) have been proposed to be responsible for generating type II radio bursts in the solar corona. The idea for piston-driven shocks came primarily from temporal association of shocks and CMEs. Our compilation of CME events with simultaneous radio observations with positional information supports idea of flare blast waves.

Gopalswamy, N.↗
NASA NTRS1992

The theory of sunspots

This review covers the present state of our theoretical understanding of the physics of sunspots, along with the principal observational results that need to be explained. The topics covered range from the detailed structure of an individual sunspot to the broad connection between sunspots and the global solar magnetic field and the solar cycle. Our aim is to give a critical discussion of the theoretical ideas and models without presenting mathematical details. After outlining the historical development of the basic concepts associated with the magnetohydrodynamic theory of sunspots, we discuss recent treatments of their properties and structure, placing special emphasis on developments that have occurred within the last ten years. There have been remarkable improvements in the theoretical modelling of sunspots, led by new ideas and by more elaborate and realistic numerical simulations. At the same time, new observations have raised new theoretical questions or caused old ones to be reconsidered. In particular, measurements of oscillations in and around sunspots have opened up the new field of sunspot seismology, while recent high-resolution observations have forced us to rethink the structure of a sunspot penumbra.

Thomas, John H.↗
NASA NTRS1993

Hubble Space Telescope ultraviolet spectroscopy of the highly polarized but quiescent quasar OI 287

The quasar OI 287 has a unique combination of properties, including a high and constant optical polarization oriented parallel to the radio axis, a quiescent optical flux, and a lobe-dominant radio source. Previous studies have led to the picture of an edge-on thin dusty torus occulting a featureless continuum (FC) source and a broad line region (BLR) in this object. The FC source and the BLR are seen only in reflected (polarized) light. In the unified models, this makes OI 287 a 'quasar 2', analogous to the type 2 Seyfert galaxies and the narrow-line radio galaxies. Our UV spectrum adds two bits of information consistent with the above ideas. First, the spectrum neither turns up in the UV, as expected for optically thin dust scattering, nor turns down as expected for polarization by dust transmission. It is consistent with reflection by free electrons or optically thick dust. Second, there are in fact blueshifted absorption troughs associated with the C IV 1549 A line, supporting the analogy with BALs, as well as the idea that the BALs are objects which present a nearly edge-on view of a disk structure.

Antonucci, Robert↗
NASA NTRS1990

Frequency domain FIR and IIR adaptive filters

A discussion of the LMS adaptive filter relating to its convergence characteristics and the problems associated with disparate eigenvalues is presented. This is used to introduce the concept of proportional convergence. An approach is used to analyze the convergence characteristics of block frequency-domain adaptive filters. This leads to a development showing how the frequency-domain FIR adaptive filter is easily modified to provide proportional convergence. These ideas are extended to a block frequency-domain IIR adaptive filter and the idea of proportional convergence is applied. Experimental results illustrating proportional convergence in both FIR and IIR frequency-domain block adaptive filters is presented.

Lynn, D. W.↗
NASA NTRS1993

Possible solutions to the problem of channel formation on early Mars

A warm climate on early Mars would provide a natural, although not unique, explanation for the presence of fluvial networks on the ancient, heavily cratered terrains. Explaining how the climate could have been kept warm, however, is not easy. The idea that the global average surface temperature, T(sub s), could have been kept warm by a dense, CO2 atmosphere supplied by volcanism or impacts is no longer viable. It was shown that CO2 cloud formation should have kept T(sub s) well below freezing until approximately 2 b.y. ago, when the Sun had brightened to at least 86 percent of its present value. Warm equatorial regions on an otherwise cold planet seem unlikely because atmospheric CO2 would probably condense out at the poles. Warming by impact-produced dust in the atmosphere seems unlikely because the amount of warming expected for silicate dust particles is relatively small. Greenhouse warming by high altitude CO2 ice clouds seems unlikely because such are poor absorbers of infrared radiation at most wavelengths. Warming by atmospheric NH3 seems unlikely because NH3 is readily photodissociated and because N may have been in short supply as consequence of impact erosion and the high solubility of NH3. A brighter, mass-losing young Sun seems unlikely because stellar winds of the required strength were not observed on other solar-type stars. In short, most of the explanations for a warm Martian paleoclimate that were proposed in the past seem unlikely. One possibility that seems feasible from radiative/photochemical standpoint is that CH4 and associated hydrocarbon gases and particles contributed substantially to the greenhouse effect on early Mars. Methane is photochemically more stable than NH3 and the gases and particles that can be formed from it are all good absorbers of infrared radiation. The idea of a CH4-rich Martian paleoatmosphere was suggested a long time ago but has fallen out of favor because of perceived difficulties in maintaining a CH4-rich atmosphere. In particular, it is not obvious where the CH4 might come from, since volcanic gases (on Earth, at least) contain very little CH4. This difficulty could be largely overcome if early Mars was inhabited by microorganisms. Then, methanogenic bacteria living in sediments could presumably have supplied CH4 to the atmosphere in copious quantities.

Kasting, J. F.↗
NASA NTRS1994

Third order LPF type compensator for flexible rotor suspension

The tuning job of the compensator for levitating flexible rotors supported by active magnetic bearings (AMB) concerns providing a good damping effect to the critical speed modes while avoiding the spillover problem on the instability of higher bending modes. In this paper, an idea for design of the control law of the compensator based on utilizing a third order low pass filter (LPF) is proposed to essentially enable elimination of the spillover instability. According to the proposed design method, good damping effects for the critical speeds are obtained by the usual phase lead/lag function. Stabilization for all of higher bending modes is completed by the additional function of the 3rd order LPF due to its phase lag approaching about -270 degrees in the high frequency domain. This idea is made clear by experiments and simulations.

Matsushita, Osami↗
NASA NTRS1994

An efficient system for reliably transmitting image and video data over low bit rate noisy channels

This research project is intended to develop an efficient system for reliably transmitting image and video data over low bit rate noisy channels. The basic ideas behind the proposed approach are the following: employ statistical-based image modeling to facilitate pre- and post-processing and error detection, use spare redundancy that the source compression did not remove to add robustness, and implement coded modulation to improve bandwidth efficiency and noise rejection. Over the last six months, progress has been made on various aspects of the project. Through our studies of the integrated system, a list-based iterative Trellis decoder has been developed. The decoder accepts feedback from a post-processor which can detect channel errors in the reconstructed image. The error detection is based on the Huber Markov random field image model for the compressed image. The compression scheme used here is that of JPEG (Joint Photographic Experts Group). Experiments were performed and the results are quite encouraging. The principal ideas here are extendable to other compression techniques. In addition, research was also performed on unequal error protection channel coding, subband vector quantization as a means of source coding, and post processing for reducing coding artifacts. Our studies on unequal error protection (UEP) coding for image transmission focused on examining the properties of the UEP capabilities of convolutional codes. The investigation of subband vector quantization employed a wavelet transform with special emphasis on exploiting interband redundancy. The outcome of this investigation included the development of three algorithms for subband vector quantization. The reduction of transform coding artifacts was studied with the aid of a non-Gaussian Markov random field model. This results in improved image decompression. These studies are summarized and the technical papers included in the appendices.

Costello, Daniel J., Jr.↗