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NASA NTRS1989

The inverse gravimetric problem in gravity modelling

One of the main purposes of geodesy is to determine the gravity field of the Earth in the space outside its physical surface. This purpose can be pursued without any particular knowledge of the internal density even if the exact shape of the physical surface of the Earth is not known, though this seems to entangle the two domains, as it was in the old Stoke's theory before the appearance of Molodensky's approach. Nevertheless, even when large, dense and homogeneous data sets are available, it was always recognized that subtracting from the gravity field the effect of the outer layer of the masses (topographic effect) yields a much smoother field. This is obviously more important when a sparse data set is bad so that any smoothing of the gravity field helps in interpolating between the data without raising the modeling error, this approach is generally followed because it has become very cheap in terms of computing time since the appearance of spectral techniques. The mathematical description of the Inverse Gravimetric Problem (IGP) is dominated mainly by two principles, which in loose terms can be formulated as follows: the knowledge of the external gravity field determines mainly the lateral variations of the density; and the deeper the density anomaly giving rise to a gravity anomaly, the more improperly posed is the problem of recovering the former from the latter. The statistical relation between rho and n (and its inverse) is also investigated in its general form, proving that degree cross-covariances have to be introduced to describe the behavior of rho. The problem of the simultaneous estimate of a spherical anomalous potential and of the external, topographic masses is addressed criticizing the choice of the mixed collection approach.

Sanso, F.↗

NASA NTRS2004

Unified Models of Turbulence and Nonlinear Wave Evolution in the Extended Solar Corona and Solar Wind

The PI (Cranmer) and Co-I (A. van Ballegooijen) made substantial progress toward the goal of producing a unified model of the basic physical processes responsible for solar wind acceleration. The approach outlined in the original proposal comprised two complementary pieces: (1) to further investigate individual physical processes under realistic coronal and solar wind conditions, and (2) to extract the dominant physical effects from simulations and apply them to a 1D model of plasma heating and acceleration. The accomplishments in Year 2 are divided into these two categories: 1a. Focused Study of Kinetic Magnetohydrodynamic (MHD) Turbulence. lb. Focused Study of Non - WKB Alfven Wave Rejection. and 2. The Unified Model Code. We have continued the development of the computational model of a time-study open flux tube in the extended corona. The proton-electron Monte Carlo model is being tested, and collisionless wave-particle interactions are being included. In order to better understand how to easily incorporate various kinds of wave-particle processes into the code, the PI performed a detailed study of the so-called "Ito Calculus", i.e., the mathematical theory of how to update the positions of particles in a probabilistic manner when their motions are governed by diffusion in velocity space.

Cranmer, Steven R.↗

NASA NTRS2010

Cognitive Assessment During Long-Duration Space Flight

The Space Flight Cognitive Assessment Tool for Windows (WinSCAT) is a computer-based, self-administered battery of five cognitive assessment tests developed for medical operations at NASA's Johnson Space Center in Houston, Texas. WinSCAT is a medical requirement for U.S. long-duration astronauts and has been implemented with U.S. astronauts from one NASA/Mir mission (NASA-7 mission) and all expeditions to date on the International Space Station (ISS). Its purpose is to provide ISS crew surgeons with an objective clinical tool after an unexpected traumatic event, a medical condition, or the cumulative effects of space flight that could negatively affect an astronaut's cognitive status and threaten mission success. WinSCAT was recently updated to add network capability to support a 6-person crew on the station support computers. Additionally, WinSCAT Version 2.0.28 has increased difficulty of items in Mathematics, increased number of items in Match-to-Sample, incorporates a moving rather than a fixed baseline, and implements stricter interpretation rules. ISS performance data were assessed to compare initial to modified interpretation rules for detecting potential changes in cognitive functioning during space flight. WinSCAT tests are routinely taken monthly during an ISS mission. Performance data from these ISS missions do not indicate significant cognitive decrements due to microgravity/space flight alone but have shown decrements. Applying the newly derived rules to ISS data results in a number of off-nominal performances at various times during and after flight.. Correlation to actual events is needed, but possible explanations for off-nominal performances could include actual physical factors such as toxic exposure, medication effects, or fatigue; emotional factors including stress from the mission or life events; or failure to exert adequate effort on the tests.

Seaton, Kimberly↗

NASA NTRS1987

Slew maneuvers on the SCOLE Laboratory Facility

The Spacecraft Control Laboratory Experiment (SCOLE) was conceived to provide a physical test bed for the investigation of control techniques for large flexible spacecraft. The control problems studied are slewing maneuvers and pointing operations. The slew is defined as a minimum time maneuver to bring the antenna line-of-sight (LOS) pointing to within an error limit of the pointing target. The second objective is to rotate about the LOS within the 0.02 degree error limit. The SCOLE problem is defined as two design challenges: control laws for a mathematical model of a large antenna attached to the Space Shuttle by a long flexible mast; and a control scheme on a laboratory representation of the structure modelled on the control laws. Control sensors and actuators are typical of those which the control designer would have to deal with on an actual spacecraft. Computational facilities consist of microcomputer based central processing units with appropriate analog interfaces for implementation of the primary control system, and the attitude estimation algorithm. Preliminary results of some slewing control experiments are given.

Williams, Jeffrey P.↗

NASA NTRS1979

A new approach to the solution of large, full matrix equations: A two-dimensional potential flow feasibility study

An approach to the solution of matrix problems resulting from integral equations of mathematical physics is presented. Based on the inherent smoothness in such equations, the problem is reformulated using a set of orthogonal basis vectors, leading to an equivalent coefficient problem which can be of lower order without significantly impairing the accuracy of the solution. This approach was evaluated using a two-dimensional Neumann problem describing the inviscid, incompressible flow over an airfoil. Two different kinds of mode functions were investigated, namely eigenfunction series and Fourier series. The method using Fourier series was found preferable. It uses all of the coefficients from a Fast Fourier Transform algorithm in an approximate method which exploits the known structure of the transformed coefficient matrix and very promising results for the flow over a realistic airfoil are obtained. On the basis of the results presented here, an order of magnitude reduction in this computer time can be expected for such problems as compared with the time for a direct matrix solution.

James, R. M.↗

NASA NTRS1996

On the Boundary Conditions at an Oscillating Contact Line: A Physical/Numerical Experimental Program

We will pursue an improved physical understanding and mathematical model for the boundary condition at an oscillating contact line at high Reynolds number. We expect that the body force is locally unimportant for earth-based systems, and that the local behavior may dominate the mechanics of partially-filled reservoirs in the microgravity environment. One important space-based application for this contact-line study is for Faraday-waves. Oscillations in the direction of gravity (or acceleration) can dominate the fluid motion during take-off and reentry with large steady-state accelerations and in orbit, where fluctuations on the order of 10(exp -4)g occur about a zero mean. Our experience with Faraday waves has shown them to be 'cleaner' than those produced by vertical or horizontal oscillation of walls. They are easier to model analytically or computationally, and they do not have strong vortex formation at the bottom of the plate. Hence many, if not most, of the experiments will be performed in this manner. The importance of contact lines in the microgravity environment is well established. We will compare high resolution measurements of the velocity field (lO micro-m resolution) using particle-tracking and particle-image velocimetry as the fluid/fluid interface is approached from the lower fluid. The spatial gradients in the deviation provide additional means to determine an improved boundary condition and a measure of the slip region. Dissipation, the size of the eddy near the contact line, and hysteresis will be measured and compare to linear and nonlinear models of viscous and irrotational but dissipative models.

Perlin, Marc↗

NASA NTRS1989

Computer simulation of the mathematical modeling involved in constitutive equation development: Via symbolic computations

Development of new material models for describing the high temperature constitutive behavior of real materials represents an important area of research in engineering disciplines. Derivation of mathematical expressions (constitutive equations) which describe this high temperature material behavior can be quite time consuming, involved and error prone; thus intelligent application of symbolic systems to facilitate this tedious process can be of significant benefit. A computerized procedure (SDICE) capable of efficiently deriving potential based constitutive models, in analytical form is presented. This package, running under MACSYMA, has the following features: partial differentiation, tensor computations, automatic grouping and labeling of common factors, expression substitution and simplification, back substitution of invariant and tensorial relations and a relational data base. Also limited aspects of invariant theory were incorporated into SDICE due to the utilization of potentials as a starting point and the desire for these potentials to be frame invariant (objective). Finally not only calculation of flow and/or evolutionary laws were accomplished but also the determination of history independent nonphysical coefficients in terms of physically measurable parameters, e.g., Young's modulus, was achieved. The uniqueness of SDICE resides in its ability to manipulate expressions in a general yet predefined order and simplify expressions so as to limit expression growth. Results are displayed when applicable utilizing index notation.

Arnold, S. M.↗

NASA NTRS2023

Chemical Thermodynamics and the Mathematical Integration of Reaction Kinetics

Key advances in the development of numerical methods for non-reacting compressible flows have been enabled by translating physical requirements into concrete numerical guidelines, such as the satisfaction of entropy inequalities for shock-capturing techniques [Lax, Contributions to Nonlinear Functional Analysis (1971) 603-634]. In the present work, we present nonlinear numerical analysis tools that draw from Chemical Thermodynamics , the branch of Nonequilibrium Thermodynamics that deals with chemical reactions. Through Gibbs formalism, chemical thermodynamics provides a well-known theoretical expression for the chemical equilibrium constant of a reaction in terms of reduced chemical potentials. A less-known, yet extremely valuable result, due to [Krambeck, Arch. Ration. Mech. Anal. , 38 (1970) 317], states that when this expression is implemented, mass-action kinetic models are consistent with the dynamical prescriptions of the 2nd law of thermodynamics. For fixed-temperature ordinary differential equations modeling constant-volume reacting gas mixtures, this leads to a decreasing Helmholtz free energy. If the temperature is allowed to vary in accordance with conservation of energy (1st law), this leads to the statement of increasing entropy. These nonlinear prescriptions can, and should be, used to further develop temporal integration techniques for reaction kinetics. We demonstrate that Krambeck's result holds even when the equilibrium constants are approximated from data. We prove this result by constructing the implicit free energy and the implicit entropy inherent to a given approximation. This is first done for a 5-species, 17-reaction model problem for air. With this structure established, elements of discrete entropy-stability theory [Tadmor, Acta Numer. , 12 (2003) 451] are leveraged to examine the consistency of time-integration schemes with these prescriptions. Using chemical potentials, one can compute the respective contributions of the kinetics model and of the temporal scheme to free energy/entropy variations. We introduce a nonlinear-stable version of the Discontinuous-Galerkin (DG) scheme in time which shows robustness improvements over the standard linearly-stable version. Most notably, the maximum timestep that can be resolved with the nonlinearly-stable variant tends to grow with polynomial order, in contrast to the linearly-stable variant. We generalize our constructions to arbitrary systems of reversible chemical reactions, ultimately showing that the compressible reacting Euler system admits the opposite of the implicitly constructed thermodynamic entropy as a mathematical entropy . This lays important theoretical foundations towards robust scheme development [Harten, J. Comput. Phys. 49 (1983) 151-164].

STMD↗

NASA NTRS1989

Towards real-time simulation of large space structures: Stabilization of fluid/thermal/structure interactions and implementation on high performance supercomputers

Within the Center for Space Construction, the SIMSTRUC project's objectives center around the development of simulation tools for the realistic analysis of large space structures. The word 'tools' is the broad sense; it designates mathematical models, finite element/finite difference formulations, computational algorithms, implementations on advanced computer architectures, and visualization capabilities. The results of our activities during the first year within the SIMSTRUC project are reported. On the modeling side, an alternative approach to fluid/thermal/structure interaction analysis that is a departure from the 'loosely coupled' and 'unified' approaches that are being currently practiced are described. The advantages of our approach both in terms of accuracy and computational efficiency were demonstrated. On the computational side, a software architecture for parallel/vector and massively parallel supercomputers that speeds up finite element and finite difference computations by several orders of magnitude is presented. As an example, the simulation of the deployment of a space structure that used to require over six hours of a workstation using a conventional finite element software, now runs on a multiprocessor using a parallel computation strategy in less than three seconds. In order to promote the physical understanding of the simulation behavior, a real-time visualization capability on the Connection Machine, which allows the analyst to watch the graphical animation of the results at the same time these are generated, was also developed. It is believed that by combining efficient analytical formulations with the state-of-the-art high performance computer implementations and superfast visualization capabilities, SIMSTRUC is moving fast towards the real-time simulation of large space structures. The designers as well as the researchers will certainly benefit from this technology.

Farhat, C.↗

NASA NTRS2014

Elastic Model Transitions: A Hybrid Approach Utilizing Quadratic Inequality Constrained Least Squares (LSQI) and Direct Shape Mapping (DSM)

A method for transitioning linear time invariant (LTI) models in time varying simulation is proposed that utilizes a hybrid approach for determining physical displacements by augmenting the original quadratically constrained least squares (LSQI) algorithm with Direct Shape Mapping (DSM) and modifying the energy constraints. The approach presented is applicable to simulation of the elastic behavior of launch vehicles and other structures that utilize discrete LTI finite element model (FEM) derived mode sets (eigenvalues and eigenvectors) that are propagated throughout time. The time invariant nature of the elastic data presents a problem of how to properly transition elastic states from the prior to the new model while preserving motion across the transition and ensuring there is no truncation or excitation of the system. A previous approach utilizes a LSQI algorithm with an energy constraint to effect smooth transitions between eigenvector sets with no requirement that the models be of similar dimension or have any correlation. This approach assumes energy is conserved across the transition, which results in significant non-physical transients due to changing quasi-steady state energy between mode sets, a phenomenon seen when utilizing a truncated mode set. The computational burden of simulating a full mode set is significant so a subset of modes is often selected to reduce run time. As a result of this truncation, energy between mode sets may not be constant and solutions across transitions could produce non-physical transients. In an effort to abate these transients an improved methodology was developed based on the aforementioned approach, but this new approach can handle significant changes in energy across mode set transitions. It is proposed that physical velocities due to elastic behavior be solved for using the LSQI algorithm, but solve for displacements using a two-step process that independently addresses the quasi-steady-state and non-steady-state contributions to the elastic displacement. For structures subject to large external forces, such as thrust or atmospheric drag, it is imperative to capture these forces when solving for elastic displacement. To simplify the mathematical formulation, assumptions are made regarding mass matrix normalization, constant external forcing, and constant viscous damping. These simplifications allow for direct solutions to the quasi-steady-state displacements through a process titled Direct Shape Mapping. DSM solves for the displacements using the eigenvalues of the elastic modes and the external forcing and returns a set of elastic displacements dictated by the eigenvectors of the post-transition mode set. For the non-steady-state contributions to displacement we formulate a LSQI problem that is constrained by energy of the non-steady state terms. The contributions from the quasi-steady-state and non-steady state solutions are then combined to obtain the physical displacements associated with the new set of eigenvectors. Results for the LSQI-DSM approach show significant reduction/complete removal of transients across mode set transitions while maintaining elastic motion from the prior state. For time propagation applications employing discrete elastic models that need to be transitioned in time and where running with full a full mode set is not feasible, the method developed offers a practical solution to simulating vehicle elasticity.

Hannan, Mike R.↗

NASA NTRS1996

Adjustment of Sensor Locations During Thermal Property Parameter Estimation

The temperature dependent thermal properties of a material may be evaluated from transient temperature histories using nonlinear parameter estimation techniques. The usual approach is to minimize the sum of the squared errors between measured and calculated temperatures at specific locations in the body. Temperature measurements are usually made with thermocouples and it is customary to take thermocouple locations as known and fixed during parameter estimation computations. In fact, thermocouple locations are never known exactly. Location errors on the order of the thermocouple wire diameter are intrinsic to most common instrumentation procedures (e.g., inserting a thermocouple into a drilled hole) and additional errors can be expected for delicate materials, difficult installations, large thermocouple beads, etc.. Thermocouple location errors are especially significant when estimating thermal properties of low diffusively materials which can sustain large temperature gradients during testing. In the present work, a parameter estimation formulation is presented which allows for the direct inclusion of thermocouple positions into the primary parameter estimation procedure. It is straightforward to set bounds on thermocouple locations which exclude non-physical locations and are consistent with installation tolerances. Furthermore, bounds may be tightened to an extent consistent with any independent verification of thermocouple location, such as x-raying, and so the procedure is entirely consonant with experimental information. A mathematical outline of the procedure is given and its implementation is illustrated through numerical examples characteristic of light-weight, high-temperature ceramic insulation during transient heating. The efficacy and the errors associated with the procedure are discussed.

Milos, Frank S.↗

NASA NTRS1987

Investigation of hypersonic rarefied flow on a spherical nose of the AOTV

The Navier-Stokes (NS) equations were integrated numerically for investigating the flow characteristics on the forepart of the spherical nose of a space vehicle such as the AOTV or AFE by a modified Accelerated Successive Replacement (ASR) scheme under hypersonic rarefied conditions. Technical feasibility of the mathematical approach was demonstrated by computing the flowfield on a spherical nose under conditions that the AFE encounters at times t = 15 and 20 seconds after its reentry into the atmosphere. Local similar solutions for the merged layer flow along the stagnation line of the sphere were developed. These are correct to the same degree of accuracy as the NS equations. These solutions provided stagnation line boundary conditions for the domain of integration on the spherical noise. Also, a parametric study of the stagnation line solution was made with a view to understand the flow characteristics in tunnels with different ambient fluids. Analytical expressions for surface slip temperature, jump conditions, and concentration level in the presence of the real gas effects at the top of the Knudsen layer were derived and used to calculate the stagnation line flowfield with nonequilibrium dissociation and ionization. A number of graphics were drawn to illustrate the basic physics of the flowfields. The present analysis can be extended to include real gas effects and to bodies of arbitrary shapes. It can further provide boundary conditions for integrating the NS equations in the near wake region.

Jain, Amolak C.↗

NASA NTRS2001

General Multimechanism Reversible-Irreversible Time-Dependent Constitutive Deformation Model Being Developed

Since most advanced material systems (for example metallic-, polymer-, and ceramic-based systems) being currently researched and evaluated are for high-temperature airframe and propulsion system applications, the required constitutive models must account for both reversible and irreversible time-dependent deformations. Furthermore, since an integral part of continuum-based computational methodologies (be they microscale- or macroscale-based) is an accurate and computationally efficient constitutive model to describe the deformation behavior of the materials of interest, extensive research efforts have been made over the years on the phenomenological representations of constitutive material behavior in the inelastic analysis of structures. From a more recent and comprehensive perspective, the NASA Glenn Research Center in conjunction with the University of Akron has emphasized concurrently addressing three important and related areas: that is, 1) Mathematical formulation; 2) Algorithmic developments for updating (integrating) the external (e.g., stress) and internal state variables; 3) Parameter estimation for characterizing the model. This concurrent perspective to constitutive modeling has enabled the overcoming of the two major obstacles to fully utilizing these sophisticated time-dependent (hereditary) constitutive models in practical engineering analysis. These obstacles are: 1) Lack of efficient and robust integration algorithms; 2) Difficulties associated with characterizing the large number of required material parameters, particularly when many of these parameters lack obvious or direct physical interpretations.

Saleeb, A. F.↗

NASA NTRS1961

THEORETICAL STUDY OF ATOMIC AND MOLECULAR GASES AND THEIR REACTIONS IN THE UPPER ATMOSPHERE. SUMMARY OF WORK DONE IN THE PERIOD NOV. 1, 1960 TO APR. 30, 1961

In the previous report it was stated that the major mathematical problems of computations were nearly solved and an attempt is being made to start application of "Tables of Integrals" to the computation of the different states of atoms and molecules. In this respect I like to report that the computation of a number of states of atoms and molecules has been carried out. The results are so far confined only to the equilibrium distance of molecules. We are extending the calculation to other distances so as to compute potential energy curves of different states of molecules. We are also developing Thomas Fermi Statistical model of the atom to verify our results of more accurate calculation. The results so far have been very encouraging and I hope to report some of these results in the next paper.

Gas↗

NASA NTRS1998

Investigation of Coronal Large Scale Structures Utilizing Spartan 201 Data

Two telescopes aboard Spartan 201, a small satellite has been launched from the Space Shuttles, on April 8th, 1993, September 8th, 1994, September 7th, 1995 and November 20th, 1997. The main objective of the mission was to answer some of the most fundamental unanswered questions of solar physics-What accelerates the solar wind and what heats the corona? The two telescopes are 1) Ultraviolet Coronal Spectrometer (UVCS) provided by the Smithsonian Astrophysical Observatory which uses ultraviolet emissions from neutral hydrogen and ions in the corona to determine velocities of the coronal plasma within the solar wind source region, and the temperature and density distributions of protons and 2) White Light Coronagraph (WLC) provided by NASA's Goddard Space Flight Center which measures visible light to determine the density distribution of coronal electrons within the same region. The PI has had the primary responsibility in the development and application of computer codes necessary for scientific data analysis activities, end instrument calibration for the white-light coronagraph for the entire Spartan mission. The PI was responsible for the science output from the WLC instrument. PI has also been involved in the investigation of coronal density distributions in large-scale structures by use of numerical models which are (mathematically) sufficient to reproduce the details of the observed brightness and polarized brightness distributions found in SPARTAN 201 data.

Guhathakurta, Madhulika↗

NASA NTRS1996

Uncertainty and Intelligence in Computational Stochastic Mechanics

Classical structural reliability assessment techniques are based on precise and crisp (sharp) definitions of failure and non-failure (survival) of a structure in meeting a set of strength, function and serviceability criteria. These definitions are provided in the form of performance functions and limit state equations. Thus, the criteria provide a dichotomous definition of what real physical situations represent, in the form of abrupt change from structural survival to failure. However, based on observing the failure and survival of real structures according to the serviceability and strength criteria, the transition from a survival state to a failure state and from serviceability criteria to strength criteria are continuous and gradual rather than crisp and abrupt. That is, an entire spectrum of damage or failure levels (grades) is observed during the transition to total collapse. In the process, serviceability criteria are gradually violated with monotonically increasing level of violation, and progressively lead into the strength criteria violation. Classical structural reliability methods correctly and adequately include the ambiguity sources of uncertainty (physical randomness, statistical and modeling uncertainty) by varying amounts. However, they are unable to adequately incorporate the presence of a damage spectrum, and do not consider in their mathematical framework any sources of uncertainty of the vagueness type. Vagueness can be attributed to sources of fuzziness, unclearness, indistinctiveness, sharplessness and grayness; whereas ambiguity can be attributed to nonspecificity, one-to-many relations, variety, generality, diversity and divergence. Using the nomenclature of structural reliability, vagueness and ambiguity can be accounted for in the form of realistic delineation of structural damage based on subjective judgment of engineers. For situations that require decisions under uncertainty with cost/benefit objectives, the risk of failure should depend on the underlying level of damage and the uncertainties associated with its definition. A mathematical model for structural reliability assessment that includes both ambiguity and vagueness types of uncertainty was suggested to result in the likelihood of failure over a damage spectrum. The resulting structural reliability estimates properly represent the continuous transition from serviceability to strength limit states over the ultimate time exposure of the structure. In this section, a structural reliability assessment method based on a fuzzy definition of failure is suggested to meet these practical needs. A failure definition can be developed to indicate the relationship between failure level and structural response. In this fuzzy model, a subjective index is introduced to represent all levels of damage (or failure). This index can be interpreted as either a measure of failure level or a measure of a degree of belief in the occurrence of some performance condition (e.g., failure). The index allows expressing the transition state between complete survival and complete failure for some structural response based on subjective evaluation and judgment.

Ayyub, Bilal M.↗

NASA NTRS1989

Global models: Robot sensing, control, and sensory-motor skills

Robotics research has begun to address the modeling and implementation of a wide variety of unstructured tasks. Examples include automated navigation, platform servicing, custom fabrication and repair, deployment and recovery, and science exploration. Such tasks are poorly described at onset; the workspace layout is partially unfamiliar, and the task control sequence is only qualitatively characterized. The robot must model the workspace, plan detailed physical actions from qualitative goals, and adapt its instantaneous control regimes to unpredicted events. Developing robust representations and computational approaches for these sensing, planning, and control functions is a major challenge. The underlying domain constraints are very general, and seem to offer little guidance for well-bounded approximation of object shape and motion, manipulation postures and trajectories, and the like. This generalized modeling problem is discussed, with an emphasis on the role of sensing. It is also discussed that unstructured tasks often have, in fact, a high degree of underlying physical symmetry, and such implicit knowledge should be drawn on to model task performance strategies in a methodological fashion. A group-theoretic decomposition of the workspace organization, task goals, and their admissible interactions are proposed. This group-mechanical approach to task representation helps to clarify the functional interplay of perception and control, in essence, describing what perception is specifically for, versus how it is generically modeled. One also gains insight how perception might logically evolve in response to needs of more complex motor skills. It is discussed why, of the many solutions that are often mathematically admissible to a given sensory motor-coordination problem, one may be preferred over others.

Schenker, Paul S.↗

NASA NTRS2003

Discrete Abstractions of Hybrid Systems: Verification of Safety and Application to User-Interface Design

Human interaction with a complex control system involves the user, the automation’s discrete mode logic, and the underlying continuous dynamics of the physical system. The user-interface of such systems always displays a reduced set of information about the entire system. Designing interfaces such that all the pertinent information is available and assuring that this information is correct is important for any user-interface, but especially so for safety-critical systems such as automotive systems and autopilots. Here we describe a methodology for the analysis of hybrid control systems that incorporate user interaction, with the goal of assuring that the information provided to the user is correct. That is, the user-interface must contain all information necessary to safely complete a desired procedure or task. We begin with a hybrid system model which incorporates discrete mode logic as well as nonlinear continuous dynamics. Using a hybrid computational tool for reachability, we find the largest region of the state-space in which we can guarantee the state of the system can always remain – this is the safe region of operation. By implementing a controller for safety which arises from this computation, we mathematically guarantee that this safe region is invariant, meaning that the system will always remain within the safe region if the determined controller is used on the boundary of the safe region. Verification within a hybrid framework allows us to account for the continuous dynamics underlying the discrete representations displayed to the user. Using the computed invariant regions as discrete states, we can abstract a discrete event system from this hybrid system with safety restrictions. This abstraction can be used to determine what information must be provided on the display. Furthermore, in cases in which an interface already exists, the abstraction provides the necessary input into existing interface verification methods. We provide two examples: a car traveling through a yellow light at an intersection and an aircraft autopilot in an automatic landing/go-around maneuver. The examples demonstrate the applicability of this methodology to hybrid systems that have operational constraints we can pose in terms of safety. This methodology differs from existing work in hybrid system verification in that we directly account for the user’s interactions with the system.

Meeko Oishi↗