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NASA NTRS1978

Two-dimensional radiative transfer. I - Planar geometry

Differential-equation methods for solving the transfer equation in two-dimensional planar geometries are developed. One method, which uses a Hermitian integration formula on ray segments through grid points, proves to be extremely well suited to velocity-dependent problems. An efficient elimination scheme is developed for which the computing time scales linearly with the number of angles and frequencies; problems with large velocity amplitudes can thus be treated accurately. A very accurate and efficient method for performing a formal solution is also presented. A discussion is given of several examples of periodic media and free-standing slabs, both in static cases and with velocity fields. For the free-standing slabs, two-dimensional transport effects are significant near boundaries, but no important effects were found in any of the periodic cases studied.

Mihalas, D.↗

NASA NTRS1975

Use of the Wigner representation in scattering problems

The basic equations of quantum scattering were translated into the Wigner representation, putting quantum mechanics in the form of a stochastic process in phase space, with real valued probability distributions and source functions. The interpretative picture associated with this representation is developed and stressed and results used in applications published elsewhere are derived. The form of the integral equation for scattering as well as its multiple scattering expansion in this representation are derived. Quantum corrections to classical propagators are briefly discussed. The basic approximation used in the Monte-Carlo method is derived in a fashion which allows for future refinement and which includes bound state production. Finally, as a simple illustration of some of the formalism, scattering is treated by a bound two body problem. Simple expressions for single and double scattering contributions to total and differential cross-sections as well as for all necessary shadow corrections are obtained.

Bemler, E. A.↗

NASA NTRS2003

A Comprehension Based Analysis of Autoflight System Interfaces

This cooperative agreement supported Dr. Peter Polson's participation in two interrelated research programs. The first was the development of the Situation-Goal-Behavior (SGB) Model that is both a formal description of an avionics system's logic and behavior and a representation of a system that can be understood by avionics designers, pilots, and training developers. The second was the development of a usability inspection method based on an approximate model, RAFIV, of pilot interactions with the Flight Management System (FMS). The main purpose of this report is to integrate the two models and provide a context in order to better characterize the accomplishments of this research program. A major focus of both the previous and this Cooperative Agreement was the development of usability evaluation methods that can be effectively utilized during all phases of the design, development, and certification process of modern avionics systems. The current efforts to validate these methods have involved showing that they generate useful analyses of known operational and training problems with the current generation of avionics systems in modern commercial airliners. This report is organized into seven sections. Following the overview, the second section describes the Goal-Situation-Behavior model and its applications. The next section summarizes the foundations of the RAFIV model and describes the model in some detail. The contents of both these sections are derived from previous reports referenced in footnotes. The fourth section integrates these two models into a complete design evaluation and training development framework. The fifth section contains conclusions and possible future directions for research. References are in Section 6. Section 7 contains the titles and abstracts of the papers paper describing in more detail the results of this research program.

Palmer, Everett↗

NASA NTRS2010

Verification and Validation of Flight-Critical Systems

For the first time in many years, the NASA budget presented to congress calls for a focused effort on the verification and validation (V&V) of complex systems. This is mostly motivated by the results of the VVFCS (V&V of Flight-Critical Systems) study, which should materialize as a a concrete effort under the Aviation Safety program. This talk will present the results of the study, from requirements coming out of discussions with the FAA and the Joint Planning and Development Office (JPDO) to technical plan addressing the issue, and its proposed current and future V&V research agenda, which will be addressed by NASA Ames, Langley, and Dryden as well as external partners through NASA Research Announcements (NRA) calls. This agenda calls for pushing V&V earlier in the life cycle and take advantage of formal methods to increase safety and reduce cost of V&V. I will present the on-going research work (especially the four main technical areas: Safety Assurance, Distributed Systems, Authority and Autonomy, and Software-Intensive Systems), possible extensions, and how VVFCS plans on grounding the research in realistic examples, including an intended V&V test-bench based on an Integrated Modular Avionics (IMA) architecture and hosted by Dryden.

Brat, Guillaume↗

NASA NTRS1997

Comparison of Several Numerical Methods for Simulation of Compressible Shear Layers

An investigation is conducted on several numerical schemes for use in the computation of two-dimensional, spatially evolving, laminar variable-density compressible shear layers. Schemes with various temporal accuracies and arbitrary spatial accuracy for both inviscid and viscous terms are presented and analyzed. All integration schemes use explicit or compact finite-difference derivative operators. Three classes of schemes are considered: an extension of MacCormack's original second-order temporally accurate method, a new third-order variant of the schemes proposed by Rusanov and by Kutier, Lomax, and Warming (RKLW), and third- and fourth-order Runge-Kutta schemes. In each scheme, stability and formal accuracy are considered for the interior operators on the convection-diffusion equation U(sub t) + aU(sub x) = alpha U(sub xx). Accuracy is also verified on the nonlinear problem, U(sub t) + F(sub x) = 0. Numerical treatments of various orders of accuracy are chosen and evaluated for asymptotic stability. Formally accurate boundary conditions are derived for several sixth- and eighth-order central-difference schemes. Damping of high wave-number data is accomplished with explicit filters of arbitrary order. Several schemes are used to compute variable-density compressible shear layers, where regions of large gradients exist.

Kennedy, Christopher A.↗

NASA NTRS2007

Synthesis from Design Requirements of a Hybrid System for Transport Aircraft Longitudinal Control

Volume I of this report presents a new method for synthesizing hybrid systems directly from desi gn requirements, and applies the method to design of a hybrid system for longitudinal control of transport aircraft. The resulting system satisfies general requirement for safety and effectiveness specified a priori, enabling formal validation to be achieved. Volume II contains seven appendices intended to make the report accessible to readers with backgrounds in human factors, flight dynamics and control, and formal logic. Major design goals are (1) system design integrity based on proof of correctness at the design level, (2) significant simplification and cost reduction in system development and certification, and (3) improved operational efficiency, with significant alleviation of human-factors problems encountered by pilots in current transport aircraft. This report provides for the first time a firm technical basis for criteria governing design and certification of avionic systems for transport aircraft. It should be of primary interest to designers of next-generation avionic systems.

Hynes, Charles S.↗

NASA NTRSDate not supplied

Proof Mate: An Interactive Proof Helper for PVS (Tool Paper)

This paper presents Proof Mate, an interactive proof helper for the PVS verification system. The helper is integrated in VSCode-PVS, the Visual Studio Code extension for PVS. It extends the capabilities of VSCode-PVS by introducing new functionalities for suggesting proof commands, sketching proof attempts, and repairing broken proofs during interactive proof sessions. This work further aligns VSCode-PVS to the functionalities provided by modern development tools, with the ultimate aim to facilitate the adoption of formal methods in engineering practices and education.

Interactive Theorem Proving↗

NASA NTRSDate not supplied

Proof Mate: An Interactive Proof Helper for PVS

Formal Methods↗

NASA NTRS1995

Flight test validation of a frequency-based system identification method on an F-15 aircraft

A frequency-based performance identification approach was evaluated using flight data from the NASA F-15 Highly Integrated Digital Electronic Control aircraft. The approach used frequency separation to identify the effectiveness of multiple controls simultaneously as an alternative to independent control identification methods. Fourier transformations converted measured control and response data into frequency domain representations. Performance gradients were formed using multiterm frequency matching of control and response frequency domain models. An objective function was generated using these performance gradients. This function was formally optimized to produce a coordinated control trim set. This algorithm was applied to longitudinal acceleration and evaluated using two control effectors: nozzle throat area and inlet first ramp. Three criteria were investigated to validate the approach: simultaneous gradient identification, gradient frequency dependency, and repeatability. This report describes the flight test results. These data demonstrate that the approach can accurately identify performance gradients during simultaneous control excitation independent of excitation frequency.

Schkolnik, Gerard S.↗

NASA NTRS2006

Hard and Soft Constraints in Reliability-Based Design Optimization

This paper proposes a framework for the analysis and design optimization of models subject to parametric uncertainty where design requirements in the form of inequality constraints are present. Emphasis is given to uncertainty models prescribed by norm bounded perturbations from a nominal parameter value and by sets of componentwise bounded uncertain variables. These models, which often arise in engineering problems, allow for a sharp mathematical manipulation. Constraints can be implemented in the hard sense, i.e., constraints must be satisfied for all parameter realizations in the uncertainty model, and in the soft sense, i.e., constraints can be violated by some realizations of the uncertain parameter. In regard to hard constraints, this methodology allows (i) to determine if a hard constraint can be satisfied for a given uncertainty model and constraint structure, (ii) to generate conclusive, formally verifiable reliability assessments that allow for unprejudiced comparisons of competing design alternatives and (iii) to identify the critical combination of uncertain parameters leading to constraint violations. In regard to soft constraints, the methodology allows the designer (i) to use probabilistic uncertainty models, (ii) to calculate upper bounds to the probability of constraint violation, and (iii) to efficiently estimate failure probabilities via a hybrid method. This method integrates the upper bounds, for which closed form expressions are derived, along with conditional sampling. In addition, an l(sub infinity) formulation for the efficient manipulation of hyper-rectangular sets is also proposed.

Crespo, L.uis G.↗

NASA NTRS2007

Synthesis from Design Requirements of a Hybrid System for Transport Aircraft Longitudinal Control

Volume I of this report presents a new method for synthesizing hybrid systems directly from design requirements, and applies the method to design of a hybrid system for longitudinal control of transport aircraft. The resulting system satisfies general requirement for safety and effectiveness specified a priori, enabling formal validation to be achieved. Volume II contains seven appendices intended to make the report accessible to readers with backgrounds in human factors, fli ght dynamics and control. and formal logic. Major design goals are (1) system desi g n integrity based on proof of correctness at the design level, (2), significant simplification and cost reduction in system development and certification, and (3) improved operational efficiency, with significant alleviation of human-factors problems encountered by pilots in current transport aircraft. This report provides for the first time a firm technical basis for criteria governing design and certification of avionic systems for transport aircraft. It should be of primary interest to designers of next-generation avionic systems.

Hynes, Charles S.↗

NASA NTRS1995

Formal Methods Specification and Verification Guidebook for Software and Computer Systems: Planning and Technology Insertion - Volume 1

The Formal Methods Specification and Verification Guidebook for Software and Computer Systems describes a set of techniques called Formal Methods (FM), and outlines their use in the specification and verification of computer systems and software. Development of increasingly complex systems has created a need for improved specification and verification techniques. NASA's Safety and Mission Quality Office has supported the investigation of techniques such as FM, which are now an accepted method for enhancing the quality of aerospace applications. The guidebook provides information for managers and practitioners who are interested in integrating FM into an existing systems development process. Information includes technical and administrative considerations that must be addressed when establishing the use of FM on a specific project. The guidebook is intended to aid decision makers in the successful application of FM to the development of high-quality systems at reasonable cost. This is the first volume of a planned two-volume set. The current volume focuses on administrative and planning considerations for the successful application of FM.

Source record↗

NASA NTRSDate not supplied

NASA Aeronautics Research Mission Directorate System Security Engineering Approaches

System security engineering (SSE) is a set of formal engineering methods and is considered a subset of systems engineering. It is a relatively new development in systems engineering with the initial NIST (National Institute of Standards) standard published in November of 2016 with updates in 2018, and 2022. The guiding principles in our methodology are based in NIST Special Publication 800-160 Vol. 1 “Systems Security Engineering: Considerations For A Multidisciplinary Approach In The Engineering Of Trustworthy Secure Systems” and integrate methodologies from common IT (Information Technology) threat modeling approaches utilizing MBSE (Model-Based Systems Engineering). The presentation will discuss how our teams utilize SSE and MBSE (Model-Based Systems Engineering) to develop secure architectures for systems under development in our NASA aeronautics research environment. This includes the activities to develop Protection Needs (PN) that, in turn result in security requirements in the design context and policies for the future state operational context for system protection. The process of applying SSE to analyze project architectures and ConOps (Concept of Operations) is intended to ensure the transferred research is both secure and securable in a “real-world” setting.

Systems Security Engineering↗

NASA NTRS1995

Modeling of collision-induced infrared absorption spectra of H2 pairs in the first overtone band at temperatures from 20 to 500 K

A simple formalism is presented that permits quick computations of the low-resolution, rotovibrational collision-induced absorption (RV CIA) spectra of H2 pairs in the first overtone band of hydrogen, at temperatures from 20 to 500 K. These spectra account for the free-free transitions. The sharp dimer features, originating from the bound-free, free-bound, and bound-bound transitions are ignored, though their integrated intensities are properly accounted for. The method employs spectral model line- shapes with parameters computed from the three lowest spectral moments. The moments are obtained from first principles expressed as analytical functions of temperature. Except for the sharp dimer features, which are absent in this model, the computed spectra reproduce closely the results of exact quantum mechanical lineshape computations. Comparisons of the computed spectra with existing experimental data also show good agreement. The work interest for the modeling of the atmospheres of the outer planets in the near-infrared region of the spectrum. The user-friendly Fortran program developed here is available on request from the authors.

Zheng, Chunguang↗

NASA NTRS2004

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition: Inclusion of Exchange - 2

The development of a practical method of accurately calculating the full scattering amplitude, without making a partial wave decomposition is continued. The method is developed in the context of electron-hydrogen scattering, and here exchange is dealt with by considering e-H scattering in the static exchange approximation. The Schroedinger equation in this approximation can be simplified to a set of coupled integro-differential equations. The equations are solved numerically for the full scattering wave function. The scattering amplitude can most accurately be calculated from an integral expression for the amplitude; that integral can be formally simplified, and then evaluated using the numerically determined wave function. The results are essentially identical to converged partial wave results.

Shertzer, Janine↗

NASA NTRS2004

A Survey of Formal Methods for Intelligent Swarms

Swarms of intelligent autonomous spacecraft, involving complex behaviors and interactions, are being proposed for future space exploration missions. Such missions provide greater flexibility and offer the possibility of gathering more science data than traditional single spacecraft missions. The emergent properties of swarms make these missions powerful, but simultaneously far more difficult to design, and to assure that the proper behaviors will emerge. These missions are also considerably more complex than previous types of missions, and NASA, like other organizations, has little experience in developing or in verifying and validating these types of missions. A significant challenge when verifying and validating swarms of intelligent interacting agents is how to determine that the possible exponential interactions and emergent behaviors are producing the desired results. Assuring correct behavior and interactions of swarms will be critical to mission success. The Autonomous Nano Technology Swarm (ANTS) mission is an example of one of the swarm types of missions NASA is considering. The ANTS mission will use a swarm of picospacecraft that will fly from Earth orbit to the Asteroid Belt. Using an insect colony analogy, ANTS will be composed of specialized workers for asteroid exploration. Exploration would consist of cataloguing the mass, density, morphology, and chemical composition of the asteroids, including any anomalous concentrations of specific minerals. To perform this task, ANTS would carry miniaturized instruments, such as imagers, spectrometers, and detectors. Since ANTS and other similar missions are going to consist of autonomous spacecraft that may be out of contact with the earth for extended periods of time, and have low bandwidths due to weight constraints, it will be difficult to observe improper behavior and to correct any errors after launch. Providing V&V (verification and validation) for this type of mission is new to NASA, and represents the cutting edge in system correctness, and requires higher levels of assurance than other (traditional) missions that use a single or small number of spacecraft that are deterministic in nature and have near continuous communication access. One of the highest possible levels of assurance comes from the application of formal methods. Formal methods are mathematics-based tools and techniques for specifying and verifying (software and hardware) systems. They are particularly useful for specifying complex parallel systems, such as exemplified by the ANTS mission, where the entire system is difficult for a single person to fully understand, a problem that is multiplied with multiple developers. Once written, a formal specification can be used to prove properties of a system (e.g., the underlying system will go from one state to another or not into a specific state) and check for particular types of errors (e.g., race or livelock conditions). A formal specification can also be used as input to a model checker for further validation. This report gives the results of a survey of formal methods techniques for verification and validation of space missions that use swarm technology. Multiple formal methods were evaluated to determine their effectiveness in modeling and assuring the behavior of swarms of spacecraft using the ANTS mission as an example system. This report is the first result of the project to determine formal approaches that are promising for formally specifying swarm-based systems. From this survey, the most promising approaches were selected and are discussed relative to their possible application to the ANTS mission. Future work will include the application of an integrated approach, based on the selected approaches identified in this report, to the formal specification of the ANTS mission.

Truszkowski, Walt↗

NASA NTRS1995

DRS: Derivational Reasoning System

The high reliability requirements for airborne systems requires fault-tolerant architectures to address failures in the presence of physical faults, and the elimination of design flaws during the specification and validation phase of the design cycle. Although much progress has been made in developing methods to address physical faults, design flaws remain a serious problem. Formal methods provides a mathematical basis for removing design flaws from digital systems. DRS (Derivational Reasoning System) is a formal design tool based on advanced research in mathematical modeling and formal synthesis. The system implements a basic design algebra for synthesizing digital circuit descriptions from high level functional specifications. DRS incorporates an executable specification language, a set of correctness preserving transformations, verification interface, and a logic synthesis interface, making it a powerful tool for realizing hardware from abstract specifications. DRS integrates recent advances in transformational reasoning, automated theorem proving and high-level CAD synthesis systems in order to provide enhanced reliability in designs with reduced time and cost.

Bose, Bhaskar↗

NASA NTRS1983

Derivation of the fundamental equation of sound generated by moving aerodynamic surfaces

Ffowcs Williams and Hawkings (1969) based their derivation of the fundamental equation of the sound generated by arbitrarily moving aerodynamic surfaces on the study of mass and momentum balance of a control volume imbedding a mathematical surface(s) exactly corresponding to real surface(s). These investigators also sketched an alternative method, employing generalized functions, for its derivation. This latter method, which was later developed by Farassat (1975), is purely mathematical and formal. Goldstein (1976) used the free-space Green function to produce an implicit derivation of the Ffowcs Williams and Hawkings equation. In the study presented here, Lowson's (1965) concept of moving point singularities is generalized to moving surface singularities, and a new derivation is given of the fundamental equation. The derivation is based on topological considerations of the underlying space, the fluid medium, and the integral properties of the Dirac delta function.

Aggarwal, H. R.↗