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NASA NTRS1993

Fractal image compression: A resolution independent representation for imagery

A deterministic fractal is an image which has low information content and no inherent scale. Because of their low information content, deterministic fractals can be described with small data sets. They can be displayed at high resolution since they are not bound by an inherent scale. A remarkable consequence follows. Fractal images can be encoded at very high compression ratios. This fern, for example is encoded in less than 50 bytes and yet can be displayed at resolutions with increasing levels of detail appearing. The Fractal Transform was discovered in 1988 by Michael F. Barnsley. It is the basis for a new image compression scheme which was initially developed by myself and Michael Barnsley at Iterated Systems. The Fractal Transform effectively solves the problem of finding a fractal which approximates a digital 'real world image'.

Sloan, Alan D.↗

NASA NTRS1993

Interactive Reliability Model for Whisker-toughened Ceramics

Wider use of ceramic matrix composites (CMC) will require the development of advanced structural analysis technologies. The use of an interactive model to predict the time-independent reliability of a component subjected to multiaxial loads is discussed. The deterministic, three-parameter Willam-Warnke failure criterion serves as the theoretical basis for the reliability model. The strength parameters defining the model are assumed to be random variables, thereby transforming the deterministic failure criterion into a probabilistic criterion. The ability of the model to account for multiaxial stress states with the same unified theory is an improvement over existing models. The new model was coupled with a public-domain finite element program through an integrated design program. This allows a design engineer to predict the probability of failure of a component. A simple structural problem is analyzed using the new model, and the results are compared to existing models.

Palko, Joseph L.↗

NASA NTRS1993

Narrow band noise as a model of time-dependent accelerations - Study of the stability of a fluid surface in a microgravity environment

We introduce a stochastic model to analyze in quantitative detail the effect of the high frequency components of the residual accelerations onboard spacecraft (often called g-jitter) on fluid motion. The residual acceleration field is modeled as a narrow band noise characterized by three independent parameters: its intensity G squared, a dominant frequency Omega, and a characteristic spectral width tau exp -1. The white noise limit corresponds to Omega tau goes to O, with G squared tau finite, and the limit of a periodic g-jitter (or deterministic limit) can be recovered for Omega tau goes to infinity, G squared finite. The analysis of the response of a fluid surface subjected to a fluctuating gravitational field leads to the stochastic Mathieu equation driven by both additive and multiplicative noise. We discuss the stability of the solutions of this equation in the two limits of white noise and deterministic forcing, and in the general case of narrow band noise. The results are then applied to typical microgravity conditions.

Casademunt, Jaume↗

NASA NTRS1993

The Application of Structural Reliability Techniques to Plume Impingement Loading of the Space Station Freedom Photovoltaic Array

A new aerospace application of structural reliability techniques is presented, where the applied forces depend on many probabilistic variables. This application is the plume impingement loading of the Space Station Freedom Photovoltaic Arrays. When the space shuttle berths with Space Station Freedom it must brake and maneuver towards the berthing point using its primary jets. The jet exhaust, or plume, may cause high loads on the photovoltaic arrays. The many parameters governing this problem are highly uncertain and random. An approach, using techniques from structural reliability, as opposed to the accepted deterministic methods, is presented which assesses the probability of failure of the array mast due to plume impingement loading. A Monte Carlo simulation of the berthing approach is used to determine the probability distribution of the loading. A probability distribution is also determined for the strength of the array. Structural reliability techniques are then used to assess the array mast design. These techniques are found to be superior to the standard deterministic dynamic transient analysis, for this class of problem. The results show that the probability of failure of the current array mast design, during its 15 year life, is minute.

Yunis, Isam S.↗

NASA NTRS1992

Response of launch pad structures to random acoustic excitation

Two solutions (probabilistic and deterministic) for the random vibration problem are presented in this paper from the standpoint of their applicability to predict the response of ground structures subjected to acoustic loading during the launch of a Space Shuttle. Deficiencies of the probabilistic method, especially to predict response in the low-frequency regime, prompted the development of the deterministic analysis, which offers a valid alternative. Challenges associated with the implementation of these response solutions in a commercially available Finite Element Method (FEM) code are briefly addressed.

Margasahayam, Ravi↗

NASA NTRS1993

Total systems design analysis of high performance structures

Designer-control parameters were identified at interdiscipline interfaces to optimize structural systems performance and downstream development and operations with reliability and least life-cycle cost. Interface tasks and iterations are tracked through a matrix of performance disciplines integration versus manufacturing, verification, and operations interactions for a total system design analysis. Performance integration tasks include shapes, sizes, environments, and materials. Integrity integrating tasks are reliability and recurring structural costs. Significant interface designer control parameters were noted as shapes, dimensions, probability range factors, and cost. Structural failure concept is presented, and first-order reliability and deterministic methods, benefits, and limitations are discussed. A deterministic reliability technique combining benefits of both is proposed for static structures which is also timely and economically verifiable. Though launch vehicle environments were primarily considered, the system design process is applicable to any surface system using its own unique filed environments.

Verderaime, V.↗

NASA NTRS1993

Reliability-based structural optimization: A proposed analytical-experimental study

An analytical and experimental study for assessing the potential of reliability-based structural optimization is proposed and described. In the study, competing designs obtained by deterministic and reliability-based optimization are compared. The experimental portion of the study is practical because the structure selected is a modular, actively and passively controlled truss that consists of many identical members, and because the competing designs are compared in terms of their dynamic performance and are not destroyed if failure occurs. The analytical portion of this study is illustrated on a 10-bar truss example. In the illustrative example, it is shown that reliability-based optimization can yield a design that is superior to an alternative design obtained by deterministic optimization. These analytical results provide motivation for the proposed study, which is underway.

Stroud, W. Jefferson↗

NASA NTRS1994

Universal first-order reliability concept applied to semistatic structures

A reliability design concept was developed for semistatic structures which combines the prevailing deterministic method with the first-order reliability method. The proposed method surmounts deterministic deficiencies in providing uniformly reliable structures and improved safety audits. It supports risk analyses and reliability selection criterion. The method provides a reliability design factor derived from the reliability criterion which is analogous to the current safety factor for sizing structures and verifying reliability response. The universal first-order reliability method should also be applicable for air and surface vehicles semistatic structures.

Verderaime, V.↗

NASA NTRS1994

Magnetometer-only attitude and rate determination for a gyro-less spacecraft

Attitude determination algorithms that requires only the earth's magnetic field will be useful for contingency conditions. One way to determine attitude is to use the time derivative of the magnetic field as the second vector in the attitude determination process. When no gyros are available, however, attitude determination becomes difficult because the rates must be propagated via integration of Euler's equation, which in turn requires knowledge of the initial rates. The spacecraft state to be determined must then include not only the attitude but also rates. This paper describes a magnetometer-only attitude determination scheme with no a priori knowledge of the spacecraft state, which uses a deterministic algorithm to initialize an extended Kalman filter. The deterministic algorithm uses Euler's equation to relate the time derivatives of the magnetic field in the reference and body frames and solves the resultant transcendental equations for the coarse attitude and rates. An important feature of the filter is that its state vector also includes corrections to the propagated rates, thus enabling it to generate highly accurate solutions. The method was tested using in-flight data from the Solar, Anomalous, and Magnetospheric Particles Explorer (SAMPEX), a Small Explorer spacecraft. SAMPEX data using several eclipse periods were used to simulate conditions that may exist during the failure of the on-board digital sun sensor. The combined algorithm has been found effective, yielding accuracies of 1.5 deg in attitude (within even nominal mission requirements) and 0.01 degree per second (deg/sec) in the rates.

Natanson, G. A.↗

NASA NTRS1993

Trajectory design for the Deep Space Program Science Experiment (DSPSE) mission

In 1994, the Deep Space Program Science Experiment (DSPSE) spacecraft will become the first spacecraft to perform, in succession, both a lunar orbiting mission and a deep-space asteroid encounter mission. The primary mission objective is to perform a long-duration flight-test of various new-technology lightweight components, such as sensors, in a deep-space environment. The mission has two secondary science objectives: to provide high-resolution imaging of the entire lunar surface for mapping purposes and flyby imaging of the asteroid 1620 Geographos. The DSPSE mission is sponsored by the Strategic Defense Initiative Organization (SDIO). As prime contractor, the Naval Research Laboratory (NRL) is building the spacecraft and will conduct mission operations. The Goddard Space Flight Center's (GSFC) Flight Dynamics Division is supporting NRL in the areas of The Deep Space Network (DSN) will provide tracking support. The DSPSE mission will begin with a launch from the Western Test Range in late January 1994. Following a minimum 1.5-day stay in a low-Earth parking orbit, a solid kick motor burn will boost DSPSE into an 18-day, 2.5-revolution phasing orbit transfer trajectory to the Moon. Two burns to insert DSPSE into a lunar polar orbit suitable for the mapping mission will be followed by mapping orbit maintenance and adjustment operations over a period of 2 sidereal months. In May 1994, a lunar orbit departure maneuver, in conjunction with a lunar swingby 26 days later, will propel DSPSE onto a heliocentric transfer that will intercept Geographos on September 1, 1994. This paper presents the characteristics, deterministic delta-Vs, and design details of each trajectory phase of this unique mission, together with the requirements, constraints, and design considerations to which each phase is subject. Numerous trajectory plots and tables of significant trajectory events are included. Following a discussion of the results of a preliminary launch window analysis, a summary of the deterministic impulsive delta-V budget required to establish the baseline mission trajectory design is presented.

Carrington, D.↗

NASA NTRS1997

Conflict Detection and Resolution for Future Air Transportation Management

With a Free Flight policy, the emphasis for air traffic control is shifting from active control to passive air traffic management with a policy of intervention by exception. Aircraft will be allowed to fly user preferred routes, as long as safety Alert Zones are not violated. If there is a potential conflict, two (or more) aircraft must be able to arrive at a solution for conflict resolution without controller intervention. Thus, decision aid tools are needed in Free Flight to detect and resolve conflicts, and several problems must be solved to develop such tools. In this report, we analyze and solve problems of proximity management, conflict detection, and conflict resolution under a Free Flight policy. For proximity management, we establish a system based on Delaunay Triangulations of aircraft at constant flight levels. Such a system provides a means for analyzing the neighbor relationships between aircraft and the nearby free space around air traffic which can be utilized later in conflict resolution. For conflict detection, we perform both 2-dimensional and 3-dimensional analyses based on the penetration of the Protected Airspace Zone. Both deterministic and non-deterministic analyses are performed. We investigate several types of conflict warnings including tactical warnings prior to penetrating the Protected Airspace Zone, methods based on the reachability overlap of both aircraft, and conflict probability maps to establish strategic Alert Zones around aircraft.

Krozel, Jimmy↗

NASA NTRS1997

Registration assisted mosaic generation

This paper presents a general strategy for assembling mosaics from numerous individual images where uncertainty exists in the position and orientation of those images. Both of the presented applications relate to remotely operated camera platforms, the first being the Galileo solid state imaging (SSI) camera presently in orbit around Jupiter, and the second being the Imager for Mars Pathfinder (IMP) stereo camera on Mars. A basic strategy in both applications is to determine the correct relative camera pointing followed by direct map projection of the images. It is assumed that approximate camera pointing exists sufficient to locate adjacent images and to place initial tiepoints within reach of the correlator. Spatial correlation is used to fix tiepoints whose initial locations are predicted by the camera pointing. We use either an fast fourier transform (fft) algorithm or a variant of Gruen's scheme permitting limited image rotation and skew. The Gruen correlator has three hierarchical modes: 1) A classical spatial least squares correlation on integral pixel boundaries used when rotation is small. 2) An annealing non-deterministic search used when rotations are unknown. A simplex deterministic search used for the end game. The correlation operation can be performed either interactively or autonomously. The final camera pointing solution relies upon a simplex downhill search in 2n or 3n dimensions where n is the number of images comprising the mosaic and the objective function to be minimized is the disagreement between tiepoint locations predicted from the camera pointing with those observed by the correlator. For Galileo the 3n unknowns are euler angles defining camera pointing in planet coordinates, and for Mars Pathfinder they are 2n unknowns representing commanded azimuth and elevation in the Lander coordinate system.

Lorre, Jean J.↗

NASA NTRS1989

Situated Control Rules

The plan net formalism presented in this paper is a language for expressing possible actions independent of any particular plan. Plan nets encode non-deterministic control programs which specify the local conditions under which actions may be taken. A two stage analysis synthesizes situated control rules which act to reduce this non-deterministic choice such that all remaining alternatives for action necessarily satisfy any given goals. Action execution can precede situated control rule synthesis: situated control rules simply help ensure that actions are first steps on the way to eventual goal satisfaction. Situated control rules inform action; they do not define it.

Drummond, Mark↗

NASA NTRS2000

Balanced Branching in Transcription Termination

The theory of stochastic transcription termination based on free-energy competition requires two or more reaction rates to be delicately balanced over a wide range of physical conditions. A large body of work on glasses and large molecules suggests that this should be impossible in such a large system in the absence of a new organizing principle of matter. We review the experimental literature of termination and find no evidence for such a principle but many troubling inconsistencies, most notably anomalous memory effects. These suggest that term ination has a deterministic component and may conceivably be not stochastic at all. We find that a key experiment by Wilson and von Hippel allegedly refuting deterministic termination was an incorrectly analyzed regulatory effect of Mg(2+) binding.

Harrington, K. J.↗

NASA NTRS2001

The Constitutive Modeling of Thin Films with Randon Material Wrinkles

Material wrinkles drastically alter the structural constitutive properties of thin films. Normally linear elastic materials, when wrinkled, become highly nonlinear and initially inelastic. Stiffness' reduced by 99% and negative Poisson's ratios are typically observed. This paper presents an effective continuum constitutive model for the elastic effects of material wrinkles in thin films. The model considers general two-dimensional stress and strain states (simultaneous bi-axial and shear stress/strain) and neglects out of plane bending. The constitutive model is derived from a traditional mechanics analysis of an idealized physical model of random material wrinkles. Model parameters are the directly measurable wrinkle characteristics of amplitude and wavelength. For these reasons, the equations are mechanistic and deterministic. The model is compared with bi-axial tensile test data for wrinkled Kaptong(Registered Trademark) HN and is shown to deterministically predict strain as a function of stress with an average RMS error of 22%. On average, fitting the model to test data yields an RMS error of 1.2%

Murphey, Thomas W.↗

NASA NTRS2001

Interrelation Between Safety Factors and Reliability

An evaluation was performed to establish relationships between safety factors and reliability relationships. Results obtained show that the use of the safety factor is not contradictory to the employment of the probabilistic methods. In many cases the safety factors can be directly expressed by the required reliability levels. However, there is a major difference that must be emphasized: whereas the safety factors are allocated in an ad hoc manner, the probabilistic approach offers a unified mathematical framework. The establishment of the interrelation between the concepts opens an avenue to specify safety factors based on reliability. In cases where there are several forms of failure, then the allocation of safety factors should he based on having the same reliability associated with each failure mode. This immediately suggests that by the probabilistic methods the existing over-design or under-design can be eliminated. The report includes three parts: Part 1-Random Actual Stress and Deterministic Yield Stress; Part 2-Deterministic Actual Stress and Random Yield Stress; Part 3-Both Actual Stress and Yield Stress Are Random.

Elishakoff, Isaac↗

NASA NTRS2001

Design of Critical Components

Critical component design is based on minimizing product failures that results in loss of life. Potential catastrophic failures are reduced to secondary failures where components removed for cause or operating time in the system. Issues of liability and cost of component removal become of paramount importance. Deterministic design with factors of safety and probabilistic design address but lack the essential characteristics for the design of critical components. In deterministic design and fabrication there are heuristic rules and safety factors developed over time for large sets of structural/material components. These factors did not come without cost. Many designs failed and many rules (codes) have standing committees to oversee their proper usage and enforcement. In probabilistic design, not only are failures a given, the failures are calculated; an element of risk is assumed based on empirical failure data for large classes of component operations. Failure of a class of components can be predicted, yet one can not predict when a specific component will fail. The analogy is to the life insurance industry where very careful statistics are book-kept on classes of individuals. For a specific class, life span can be predicted within statistical limits, yet life-span of a specific element of that class can not be predicted.

Hendricks, Robert C.↗

NASA NTRS1995

The Dripping Handrail Model: Transient Chaos in Accretion Systems

We define and study a simple dynamical model for accretion systems, the "dripping handrail" (DHR). The time evolution of this spatially extended system is a mixture of periodic and apparently random (but actually deterministic) behavior. The nature of this mixture depends on the values of its physical parameters - the accretion rate, diffusion coefficient, and density threshold. The aperiodic component is a special kind of deterministic chaos called transient chaos. The model can simultaneously exhibit both the quasiperiodic oscillations (QPO) and very low frequency noise (VLFN) that characterize the power spectra of fluctuations of several classes of accretion systems in astronomy. For this reason, our model may be relevant to many such astrophysical systems, including binary stars with accretion onto a compact object - white dwarf, neutron star, or black hole - as well as active galactic nuclei. We describe the systematics of the DHR's temporal behavior, by exploring its physical parameter space using several diagnostics: power spectra, wavelet "scalegrams," and Lyapunov exponents. In addition, we note that for large accretion rates the DHR has periodic modes; the effective pulse shapes for these modes - evaluated by folding the time series at the known period - bear a resemblance to the similarly- determined shapes for some x-ray pulsars. The pulsing observed in some of these systems may be such periodic-mode accretion, and not due to pure rotation as in the standard pulsar model.

Young, Karl↗