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NASA NTRS2021

An Information Theory Approach to Physical Domain Discovery

The project of physics discovery is often equivalent to finding the most concise description of a physical system. The description with optimum predictive capability for a dataset generated by a physical system is one that minimizes both predictive error on the dataset and the complexity of the description. The discovery of the governing physics of a system can therefore be viewed as a mathematical optimization problem. We outline here a method to optimize the description of arbitrarily complex physical systems by minimizing the entropy of the description of the system. The Recursive Domain Partitioning (RDP) procedure finds the optimum partitioning of each physical domain into subdomains, and the optimum predictive function within each subdomain. Penalty functions are introduced to limit the complexity of the predictive function within each domain. Examples are shown in 1D and 2D. In 1D, the technique effectively discovers the elastic and plastic regions within a stress-strain curve generated by simulations of amorphous carbon material, while in 2D the technique discovers the free-flow region and the inertially-obstructed flow region in the simulation of fluid flow across a plate.

Daniel Shea↗

NASA NTRS1992

Artificial Intelligence Research Branch future plans

This report contains information on the activities of the Artificial Intelligence Research Branch (FIA) at NASA Ames Research Center (ARC) in 1992, as well as planned work in 1993. These activities span a range from basic scientific research through engineering development to fielded NASA applications, particularly those applications that are enabled by basic research carried out in FIA. Work is conducted in-house and through collaborative partners in academia and industry. All of our work has research themes with a dual commitment to technical excellence and applicability to NASA short, medium, and long-term problems. FIA acts as the Agency's lead organization for research aspects of artificial intelligence, working closely with a second research laboratory at the Jet Propulsion Laboratory (JPL) and AI applications groups throughout all NASA centers. This report is organized along three major research themes: (1) Planning and Scheduling: deciding on a sequence of actions to achieve a set of complex goals and determining when to execute those actions and how to allocate resources to carry them out; (2) Machine Learning: techniques for forming theories about natural and man-made phenomena; and for improving the problem-solving performance of computational systems over time; and (3) Research on the acquisition, representation, and utilization of knowledge in support of diagnosis design of engineered systems and analysis of actual systems.

Stewart, Helen↗

NASA NTRS2014

MDO and Cross-Disciplinary Practice in R&D: A Portrait of Principles and Current Practice

For several decades, Multidisciplinary Design Optimization (MDO) has served an important role in aerospace engineering by incorporating physics based disciplinary models into integrated system or sub-system models for use in research, development, (R&D) and design. This paper examines MDO's role in facilitating the integration of the researchers from different single disciplines during R&D and early design of large-scale complex engineered systems (LaCES) such as aerospace systems. The findings in this paper are summarized from a larger study on interdisciplinary practices and perspectives that included considerable empirical data from surveys, interviews, and ethnography. The synthesized findings were derived by integrating the data with theories from organization science and engineering. The over-arching finding is that issues related to cognition, organization, and social interrelations mostly dominate interactions across disciplines. Engineering issues, such as the integration of hardware or physics-based models, are not as significant. Correspondingly, the data showed that MDO is not the primary integrator of researchers working across disciplines during R&D and early design of LaCES. Cognitive focus such as analysis versus design, organizational challenges such as incentives, and social opportunities such as personal networks often drove the human interactive practices among researchers from different disciplines. Facilitation of the inherent confusion, argument, and learning in crossdisciplinary research was identified as one of several needed elements of enabling successful research across disciplines.

Rivas McGowan, Anna-Maria↗

NASA NTRS1993

Linear, multivariable robust control with a mu perspective

The structured singular value is a linear algebra tool developed to study a particular class of matrix perturbation problems arising in robust feedback control of multivariable systems. These perturbations are called linear fractional, and are a natural way to model many types of uncertainty in linear systems, including state-space parameter uncertainty, multiplicative and additive unmodeled dynamics uncertainty, and coprime factor and gap metric uncertainty. The structured singular value theory provides a natural extension of classical SISO robustness measures and concepts to MIMO systems. The structured singular value analysis, coupled with approximate synthesis methods, make it possible to study the tradeoff between performance and uncertainty that occurs in all feedback systems. In MIMO systems, the complexity of the spatial interactions in the loop gains make it difficult to heuristically quantify the tradeoffs that must occur. This paper examines the role played by the structured singular value (and its computable bounds) in answering these questions, as well as its role in the general robust, multivariable control analysis and design problem.

Packard, Andy↗

NASA NTRS2002

Control of Initialized Fractional-Order Systems

Due to the importance of historical effects in fractional-order systems, this paper presents a general fractional-order control theory that includes the time-varying initialization response. Previous studies have not properly accounted for these historical effects. The initialization response, along with the forced response, for fractional-order systems is determined. Stability properties of fractional-order systems are presented in the complex Airplane, which is a transformation of the s-plane. Time responses are discussed with respect to pole positions in the complex Airplane and frequency response behavior is included. A fractional-order vector space representation, which is a generalization of the state space concept, is presented including the initialization response. Control methods for vector representations of initialized fractional-order systems are shown. Nyquist, root-locus, and other input-output control methods are adapted to the control of fractional-order systems. Finally, the fractional-order differintegral is generalized to continuous order-distributions that have the possibility of including a continuum of fractional orders in a system element.

Hartly, Tom T.↗

NASA NTRS2002

Control of Initialized Fractional-Order Systems

Due to the importance of historical effects in fractional-order systems, this paper presents a general fractional-order control theory that includes the time-varying initialization response. Previous studies have not properly accounted for these historical effects. The initialization response, along with the forced response, for fractional-order systems is determined. Stability properties of fractional-order systems are presented in the complex w-plane, which is a transformation of the s-plane. Time responses are discussed with respect to pole positions in the complex w-plane and frequency response behavior is included. A fractional-order vector space representation, which is a generalization of the state space concept, is presented including the initialization response. Control methods for vector representations of initialized fractional-order systems are shown. Nyquist, root-locus, and other input-output control methods are adapted to the control of fractional-order systems. Finally, the fractional-order differintegral is generalized to continuous order-distributions that have the possibility of including a continuum of fractional orders in a system element.

Hartley, Tom T.↗

NASA NTRS2002

Dynamical Models of the Solar System Formation and Evolution

Mark Lewis has extended his them is work by completing a series of N-body simulations of a narrow ring that: is in the location of Saturn's F-ring and is perturbed by a single satellite comparable to Prometheus, but on a circular orbit. We had previously shown how the satellite perturbations can cause a broadly distributed sparse population of ring particles to become concentrated into narrow rings that can be maintained outside of any resonance location. For low optical depths, the collisions between ring particles are highly localized in the peaks of the satellite wakes. The inelastic collisions therefore occur at a particular orbital phase angle so as to damp the azimuthal component of the relative velocities. Since particle positions are not changed by collisions, the semimajor axes of the particles are shifted toward the actual particle positions where the collisions occur. Thus, negative radial diffusion can occur while conserving orbital angular momentum so long as the forced eccentricity is continually re-excited by the satellite. We speculated that the separation between the final ringlets was largely determined by the magnitude of the forced eccentricities induced by the satellite at closest approach. We carried out a series of simulations with a variety of different satellite masses in order to vary the magnitude of the forced eccentricity. We found that indeed the final spacing of the ringlets does increase with the magnitude of the forced eccentricity (Lewis and Stewart 2002). This occurs because neighboring eccentric ringlets drift out of phase with one another due to Keplerian shear and eventually collide with one another, leading to a smaller number of more widely spaced ringlets, The time scale required to form narrow ringlets in these simulations is much shorter than one would expect from standard theories based upon the orbit-averaged torque produced by multiple passes by the satellite. We find that the initial ringlets form in less than two synodic periods and the final state is typically reached in 10 to 20 synodic periods. These studies move us closer to understanding the significantly more complex system of Saturn's F ring, where the perturbation magnitude varies over short temporal and spatial time scales due to the orbital eccentricities of the perturbing satellite. We are currently extending the simulation to allow for an eccentric orbit of the satellite.

Stewart, Glen R.↗

NASA NTRS1991

Expert system training and control based on the fuzzy relation matrix

Fuzzy knowledge, that for which the terms of reference are not crisp but overlapped, seems to characterize human expertise. This can be shown from the fact that an experienced human operator can control some complex plants better than a computer can. Proposed here is fuzzy theory to build a fuzzy expert relation matrix (FERM) from given rules or/and examples, either in linguistic terms or in numerical values to mimic human processes of perception and decision making. The knowledge base is codified in terms of many implicit fuzzy rules. Fuzzy knowledge thus codified may also be compared with explicit rules specified by a human expert. It can also provide a basis for modeling the human operator and allow comparison of what a human operator says to what he does in practice. Two experiments were performed. In the first, control of liquid in a tank, demonstrates how the FERM knowledge base is elicited and trained. The other shows how to use a FERM, build up from linguistic rules, and to control an inverted pendulum without a dynamic model.

Ren, Jie↗

NASA NTRS1995

Large HAWT wake measurement and analysis

From the theoretical fluid dynamics point of view, the wake region of a large horizontal-axis wind turbine has been defined and described, and numerical models of wake behavior have been developed. Wind tunnel studies of single turbine wakes and turbine array wakes have been used to verify the theory and further refine the numerical models. However, the effects of scaling, rotor solidity, and topography on wake behavior are questions that remain unanswered. In the wind tunnel studies, turbines were represented by anything from scaled models to tea strainers or wire mesh disks whose solidity was equivalent to that of a typical wind turbine. The scale factor compensation for the difference in Reynolds number between the scale model and an actual turbine is complex, and not typically accounted for. Though it is wise to study the simpler case of wakes in flat topography, which can be easily duplicated in the wind tunnel, current indications are that wind turbine farm development is actually occurring in somewhat more complex terrain. Empirical wake studies using large horizontal-axis wind turbines have not been thoroughly composited, and, therefore, the results have not been applied to the well-developed theory of wake structure. The measurement programs have made use of both in situ sensor systems, such as instrumented towers, and remote sensors, such as kites and tethered, balloonborne anemometers. We present a concise overview of the work that has been performed, including our own, which is based on the philosophy that the MOD-2 turbines are probably their own best detector of both the momentum deficit and the induced turbulence effect downwind. Only the momentum deficit aspects of the wake/machine interactions have been addressed. Both turbine power output deficits and wind energy deficits as measured by the onsite meteorological towers have been analyzed from a composite data set. The analysis has also evidenced certain topographic influences on the operation of spatially diverse wind turbines.

Miller, A. H.↗

NASA NTRS1991

Bayesian classification theory

The task of inferring a set of classes and class descriptions most likely to explain a given data set can be placed on a firm theoretical foundation using Bayesian statistics. Within this framework and using various mathematical and algorithmic approximations, the AutoClass system searches for the most probable classifications, automatically choosing the number of classes and complexity of class descriptions. A simpler version of AutoClass has been applied to many large real data sets, has discovered new independently-verified phenomena, and has been released as a robust software package. Recent extensions allow attributes to be selectively correlated within particular classes, and allow classes to inherit or share model parameters though a class hierarchy. We summarize the mathematical foundations of AutoClass.

Hanson, Robin↗

NASA NTRS2003

The Ionization History of The Intergalactic Medium:

The funded project seeked a unified description of the ionization, physical structure, and evolution of the intergalactic medium (IGM) and quasar intervening absorption systems. We proposed to conduct theoretical studies of the IGM and QSO absorbers in the context of current theories of galaxy formation, developing and using numerical and analytical techniques aimed at a detailed modeling of cosmological radiative transfer, gas dynamics, and thermal and ionization evolution. The ionization history of the IGM has important implications for the metagalactic UV background, intergalactic helium absorption 21-cm tomography, metal absorption systems, fluctuations in the microwave background, and the cosmic rate of structure and star formation. All the original objectives of our program have been achieved, and the results widely used and quoted by the community. Indeed, they remain relevant as the level and complexity of research in this area has increased substantially since our proposal was submitted, due to new discoveries on galaxy formation and evolution, a flood of high-quality data on the distant universe, new theoretical ideas and direct numerical simulations of structure formation in hierarchical clustering theories.

Madau, Piero↗

NASA NTRS1984

GCKP84--General Chemical Kinetics Code for Gas-Phase Flow and Batch Processes Including Heat Transfer Effects

A general chemical kinetics code is described for complex, homogeneous ideal gas reactions in any chemical system. The main features of the GCKP84 code are flexibility, convenience, and speed of computation for many different reaction conditions. The code, which replaces the GCKP code published previously, solves numerically the differential equations for complex reaction in a batch system or one dimensional inviscid flow. It also solves numerically the nonlinear algebraic equations describing the well stirred reactor. A new state of the art numerical integration method is used for greatly increased speed in handling systems of stiff differential equations. The theory and the computer program, including details of input preparation and a guide to using the code are given.

David A Bittker↗

NASA NTRS1993

The theory of interface slicing

Interface slicing is a new tool which was developed to facilitate reuse-based software engineering, by addressing the following problems, needs, and issues: (1) size of systems incorporating reused modules; (2) knowledge requirements for program modification; (3) program understanding for reverse engineering; (4) module granularity and domain management; and (5) time and space complexity of conventional slicing. The definition of a form of static program analysis called interface slicing is addressed.

Beck, Jon↗

NASA NTRS1998

Context in Models of Human-Machine Systems

All human-machine systems models represent context. This paper proposes a theory of context through which models may be usefully related and integrated for design. The paper presents examples of context representation in various models, describes an application to developing models for the Crew Activity Tracking System (CATS), and advances context as a foundation for integrated design of complex dynamic systems.

Callantine, Todd J.↗

NASA NTRS2004

Renormalization Group Tutorial

Complex physical systems sometimes have statistical behavior characterized by power- law dependence on the parameters of the system and spatial variability with no particular characteristic scale as the parameters approach critical values. The renormalization group (RG) approach was developed in the fields of statistical mechanics and quantum field theory to derive quantitative predictions of such behavior in cases where conventional methods of analysis fail. Techniques based on these ideas have since been extended to treat problems in many different fields, and in particular, the behavior of turbulent fluids. This lecture will describe a relatively simple but nontrivial example of the RG approach applied to the diffusion of photons out of a stellar medium when the photons have wavelengths near that of an emission line of atoms in the medium.

Bell, Thomas L.↗

NASA NTRS2002

An Experimental Investigation of Incompressible Richtmyer-Meshkov Instability

Richtmyer-Meshkov (RM) instability occurs when two different density fluids are impulsively accelerated in the direction normal to their nearly planar interface. The instability causes small perturbations on the interface to grow and eventually become a turbulent flow. It is closely related to Rayleigh-Taylor instability, which is the instability of a planar interface undergoing constant acceleration, such as caused by the suspension of a heavy fluid over a lighter one in the earth's gravitational field. Like the well-known Kelvin-Helmholtz instability, RM instability is a fundamental hydrodynamic instability which exhibits many of the nonlinear complexities that transform simple initial conditions into a complex turbulent flow. Furthermore, the simplicity of RM instability (in that it requires very few defining parameters), and the fact that it can be generated in a closed container, makes it an excellent test bed to study nonlinear stability theory as well as turbulent transport in a heterogeneous system. However, the fact that RM instability involves fluids of unequal densities which experience negligible gravitational force, except during the impulsive acceleration, requires RM instability experiments to be carried out under conditions of microgravity. This experimental study investigates the instability of an interface between incompressible, miscible liquids with an initial sinusoidal perturbation. The impulsive acceleration is generated by bouncing a rectangular tank containing two different density liquids off a retractable vertical spring. The initial perturbation is produced prior to release by oscillating the tank in the horizontal direction to produce a standing wave. The instability evolves in microgravity as the tank travels up and then down the vertical rails of a drop tower until hitting a shock absorber at the bottom. Planar Laser Induced Fluorescence (PLIF) is employed to visualize the flow. PLIF images are captured by a video camera that travels with the tank. Figure 1 is as sequence of images showing the development of the instability from the initial sinusoidal disturbance far into the nonlinear regime which is characterized by the appearance of mushroom structures resulting from the coalescence of baroclinic vorticity produced by the impulsive acceleration. At later times in this sequence the vortex cores are observed to become unstable showing the beginnings of the transition to turbulence in this flow. The amplitude of the growing disturbance after the impulsive acceleration is measured and found to agree well with theoretical predictions. The effects of Reynolds number (based on circulation) on the development of the vortices and the transition to turbulence are also determined.

Jacobs, J. W.↗

NASA NTRS1998

Trajectory design strategies that incorporate invariant manifolds and swingby

Libration point orbits serve as excellent platforms for scientific investigations involving the Sun as well as planetary environments. Trajectory design in support of such missions is increasingly challenging as more complex missions are envisioned in the next few decades. Software tools for trajectory design in this regime must be further developed to incorporate better understanding of the solution space and, thus, improve the efficiency and expand the capabilities of current approaches. Only recently applied to trajectory design, dynamical systems theory now offers new insights into the natural dynamics associated with the multi-body problem. The goal of this effort is the blending of analysis from dynamical systems theory with the well established NASA Goddard software program SWINGBY to enhance and expand the capabilities for mission design. Basic knowledge concerning the solution space is improved as well.

Guzman, J. J.↗

NASA NTRS2011

Initiating Molecular Growth in the Interstellar Medium via Dimeric Complexes of Observed Ions and Molecules

A feasible initiation step for particle growth in the interstellar medium (ISM) is simulated by means of ab quantum chemistry methods. The systems studied are dimer ions formed by pairing nitrogen containing small molecules known to exist in the ISM with ions of unsaturated hydrocarbons or vice versa. Complexation energies, structures of ensuing complexes and electronic excitation spectra of the encounter complexes are estimated using various quantum chemistry methods. Moller-Plesset perturbation theory (MP2, Z-averaged perturbation theory (ZAP2), coupled cluster singles and doubles with perturbative triples corrections (CCSD(T)), and density functional theory (DFT) methods (B3LYP) were employed along with the correlation consistent cc-pVTZ and aug-cc-pVTZ basis sets. Two types of complexes are predicted. One type of complex has electrostatic binding with moderate (7-20 kcal per mol) binding energies, that are nonetheless significantly stronger than typical van der Waals interactions between molecules of this size. The other type of complex develops strong covalent bonds between the fragments. Cyclic isomers of the nitrogen containing complexes are produced very easily by ion-molecule reactions. Some of these complexes show intense ultraviolet visible spectra for electronic transitions with large oscillator strengths at the B3LYP, omegaB97, and equations of motion coupled cluster (EOM-CCSD) levels. The open shell nitrogen containing carbonaceous complexes especially exhibit a large oscillator strength electronic transition in the visible region of the electromagnetic spectrum.

Bera, Partha P.↗