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NASA NTRS2004

Model Checking Failed Conjectures in Theorem Proving: A Case Study

Interactive mechanical theorem proving can provide high assurance of correct design, but it can also be a slow iterative process. Much time is spent determining why a proof of a conjecture is not forthcoming. In some cases, the conjecture is false and in others, the attempted proof is insufficient. In this case study, we use the SAL family of model checkers to generate a concrete counterexample to an unproven conjecture specified in the mechanical theorem prover, PVS. The focus of our case study is the ROBUS Interactive Consistency Protocol. We combine the use of a mechanical theorem prover and a model checker to expose a subtle flaw in the protocol that occurs under a particular scenario of faults and processor states. Uncovering the flaw allows us to mend the protocol and complete its general verification in PVS.

Pike, Lee↗

NASA NTRS2019

Overview of the New Version 3 NASA Micro-Pulse Lidar Network (MPLNET) Automatic Precipitation Detection Algorithm

Precipitation modifies atmospheric column thermodynamics through the process of evaporation and serves as a proxy for latent heat modulation. For this reason, a correct precipitation parameterization (especially for low-intensity precipitation) within global scale models is crucial. In addition to improving our modeling of the hydrological cycle, this will reduce the associated uncertainty of global climate models in correctly forecasting future scenarios, and will enable the application of mitigation strategies. In this manuscript we present a proof of concept algorithm to automatically detect precipitation from lidar measurements obtained from the National Aeronautics and Space Administration Micropulse lidar network (MPLNET). The algorithm, once tested and validated against other remote sensing instruments, will be operationally implemented into the network to deliver a near real time (latency <1.5 h) rain masking variable that will be publicly available on MPLNET website as part of the new Version 3 data products. The methodology, based on an image processing technique, detects only light precipitation events (defined by intensity and duration) such as light rain, drizzle, and virga. During heavy rain events, the lidar signal is completely extinguished after a few meters in the precipitation or it is unusable because of water accumulated on the receiver optics. Results from the algorithm, in addition to filling a gap in light rain, drizzle, and virga detection by radars, are of particular interest for the scientific community as they help to fully characterize the aerosol cycle, from emission to deposition, as precipitation is a crucial meteorological phenomenon accelerating atmospheric aerosol removal through the scavenging effect. Algorithm results will also help the understanding of long term aerosol–cloud interactions, exploiting the multi-year database from several MPLNET permanent observational sites across the globe. The algorithm is also applicable to other lidar and/or ceilometer network infrastructures in the framework of the Global Aerosol Watch (GAW) aerosol lidar observation network (GALION).

Simone Lolli↗

NASA NTRS1989

Two-measured variable method for wall interference assessment/correction

An iterative method for wall interference assessment and/or correction is presented for transonic flow conditions in wind tunnels equipped with two component velocity measurements on a single interface. The iterative method does not require modeling of the test article and tunnel wall boundary conditions. Analytical proof for the convergence and stability of the iterative method is shown in the subsonic flow regime. The numerical solutions are given for both 2-D and axisymmetrical cases at transonic speeds with the application of global Mach number correction.

Lo, C. F.↗

NASA NTRS1983

Fast decoding of a d(min) = 6 RS code

A method for high speed decoding a d sub min = 6 Reed-Solomon (RS) code is presented. Properties of the two byte error correcting and three byte error detecting RS code are discussed. Decoding using a quadratic equation is shown. Theorems and concomitant proofs are included to substantiate this decoding method.

Deng, H.↗

NASA NTRS1990

Tutorial on Reed-Solomon error correction coding

This tutorial attempts to provide a frank, step-by-step approach to Reed-Solomon (RS) error correction coding. RS encoding and RS decoding both with and without erasing code symbols are emphasized. There is no need to present rigorous proofs and extreme mathematical detail. Rather, the simple concepts of groups and fields, specifically Galois fields, are presented with a minimum of complexity. Before RS codes are presented, other block codes are presented as a technical introduction into coding. A primitive (15, 9) RS coding example is then completely developed from start to finish, demonstrating the encoding and decoding calculations and a derivation of the famous error-locator polynomial. The objective is to present practical information about Reed-Solomon coding in a manner such that it can be easily understood.

Geisel, William A.↗

NASA NTRS1976

Exospheric density measurements from the drag-free satellite Triad

The Triad satellite is maintained within 1 mm of its proof mass (a small metal ball) in a purely gravitational orbit, using a drag-free control system, named Discos, as the disturbance compensation system. The Discos proof mass is surrounded by an outer shell which holds fuel tanks and cold gas jets. The shell shields the proof mass from such nongravitational forces as radiation pressure, atmospheric drag, and micrometeorite impact. Whenever these forces displace the outer shell relative to the proof mass, an error signal is generated by a capacitive bridge sensor, and the satellite is propelled by gas jets to remain centered on the proof mass when the error reaches 1 mm. Local atmospheric densities near 800 km were measured, using ball position data, and the observed accelerations were corrected for the effects of solar radiation pressure. The measured densities reveal a greater dependence on latitude than that indicated by balloon satellites, and also a dependence on longitude. Only a small dependence on Kp, however, was observed in the region where the measurements were made.

Moe, K.↗

NASA NTRS2005

Assume-Guarantee Testing

Verification techniques for component-based systems should ideally be able to predict properties of the assembled system through analysis of individual components before assembly. This work introduces such a modular technique in the context of testing. Assume-guarantee testing relies on the (automated) decomposition of key system-level requirements into local component requirements at design time. Developers can verify the local requirements by checking components in isolation; failed checks may indicate violations of system requirements, while valid traces from different components compose via the assume-guarantee proof rule to potentially provide system coverage. These local requirements also form the foundation of a technique for efficient predictive testing of assembled systems: given a correct system run, this technique can predict violations by alternative system runs without constructing those runs. We discuss the application of our approach to testing a multi-threaded NASA application, where we treat threads as components.

Blundell, Colin↗

NASA NTRS2011

Differential Deposition to Correct Surface Figure Deviations in Astronomical Grazing-Incidence X-Ray Optics

A coating technique is being developed to correct the surface figure deviations in reflective-grazing-incidence X-ray optics. These optics are typically designed to have precise conic profiles, and any deviation in this profile, as a result of fabrication, results in a degradation of the imaging performance. To correct the mirror profiles, physical vapor deposition has been utilized to selectively deposit a filler material inside the mirror shell. The technique, termed differential deposition, has been implemented as a proof of concept on miniature X-ray optics developed at MSFC for medical-imaging applications. The technique is now being transferred to larger grazing-incidence optics suitable for astronomy and progress to date is reported.

Kilaru, Kiranmayee↗

NASA NTRS2012

Frequency Domain Beamforming for a Deep Space Network Downlink Array

This paper describes a frequency domain beamformer to array up to 8 antennas of NASA's Deep Space Network currently in development. The objective of this array is to replace and enhance the capability of the DSN 70m antennas with multiple 34m antennas for telemetry, navigation and radio science use. The array will coherently combine the entire 500 MHz of usable bandwidth available to DSN receivers. A frequency domain beamforming architecture was chosen over a time domain based architecture to handle the large signal bandwidth and efficiently perform delay and phase calibration. The antennas of the DSN are spaced far enough apart that random atmospheric and phase variations between antennas need to be calibrated out on an ongoing basis in real-time. The calibration is done using measurements obtained from a correlator. This DSN Downlink Array expands upon a proof of concept breadboard array built previously to develop the technology and will become an operational asset of the Deep Space Network. Design parameters for frequency channelization, array calibration and delay corrections will be presented as well a method to efficiently calibrate the array for both wide and narrow bandwidth telemetry.

Filterbank↗

NASA NTRSDate not supplied

Discontinuous Galerkin and Related Methods for ODE

A defining feature of the discontinuous Galerkin (DG) method for ODE is that the piecewise polynomial solution can have a jump discontinuity at the beginning of each step. Starting from the standard integral formulation, the DG method is derived here in differential form. The key ingredient is a polynomial called the correction function, which helps ‘correct’ the discontinuous solution by approximating the jump and yields a continuous one. Under the right Radau quadrature, this continuous solution is identical to the solutions by the right Radau collocation and the continuous Galerkin (CG) methods. Next, the correction function facilitates the construction of the associated implicit Runge-Kutta schemes (IRK-DG). Different quadratures for DG result in different IRK-DG methods: left Radau quadrature in Radau IA, right Radau quadrature in Radau IIA or right Radau collocation, and Gauss quadrature in a method called DG-Gauss. The construction of IRK-DG clarifies the meaning and facilitates the proofs of various 𝐵(𝑝), 𝐶(𝜂), and 𝐷(𝜁) conditions for accuracy. The two consequences of these conditions are that all 𝑠-stage IRK-DG methods are accurate to order 2𝑠 − 1, and the IRK-DG methods of Radau type are unique. Numerical examples showing the behavior of the DG solutions are provided. In all, the correction function plays a key role and helps establish the relations among the DG, IRK-DG, collocation, and CG schemes.

numerical methods↗

NASA NTRSDate not supplied

Discontinuous Galerkin and Related Methods for ODE

Starting from the standard integral formulation, the DG method is derived here in differential form. The key ingredient is a polynomial called the correction function, which helps ‘correct’ the discontinuous solution by approximating the jump and yields a continuous one. Under the right Radau quadrature, this continuous solution is identical to the solutions by the right Radau collocation and the continuous Galerkin (CG) methods. Next, the correction function facilitates the construction of the associated implicit Runge-Kutta schemes (IRK-DG). Different quadratures for DG result in different IRK-DG methods: left Radau quadrature in Radau IA, right Radau quadrature in Radau IIA or right Radau collocation, and Gauss quadrature in a method called DG-Gauss. The construction of IRK-DG clarifies the meaning and facilitates the proofs of various 𝐵(𝑝), 𝐶(𝜂), and 𝐷(𝜁) conditions for accuracy. The two consequences of these conditions are that all 𝑠-stage IRK-DG methods are accurate to order 2𝑠− 1, and the IRK-DG methods of Radau type are unique. Numerical examples showing the behavior of the DG solutions are provided. In all, the correction function plays a key role and helps establish the relations among the DG, IRK DG, collocation, and CG methods.

Numerical Methods for Ordinary Differential Equati↗

NASA NTRS1961

Chemical and Thermodynamic Properties at High Temperatures: A Symposium

This book contains the program and all available abstracts of the 90' invited and contributed papers to be presented at the TUPAC Symposium on Chemical and Thermodynamic Properties at High Temperatures. The Symposium will be held in conjunction with the XVIIIth IUPAC Congress, Montreal, August 6 - 12, 1961. It has been organized, by the Subcommissions on Condensed States and on Gaseous States of the Commission on High Temperatures and Refractories and by the Subcommission on Experimental Thermodynamics of the Commission on Chemical Thermodynamics, acting in conjunction with the Organizing Committee of the IUPAC Congress. All inquiries concerning participation In the Symposium should be directed to: Secretary, XVIIIth International Congress of Pure and Applied Chemistry, National Research Council, Ottawa, 'Canada. Owing to the limited time and facilities available for the preparation and printing of the book, it has not been possible to refer the proofs of the abstracts to the authors for checking. Furthermore, it has not been possible to subject the manuscripts to a very thorough editorial examination. Some obvious errors in the manuscripts have been corrected; other errors undoubtedly have been introduced. Figures have been redrawn only when such a step was essential for reproduction purposes. Sincere apologies are offered to authors and readers for any errors which remain; however, in the circumstances neither the IUPAC Commissions who organized the Symposium, nor the U. S. Government Agencies who assisted in the preparation of this book can accept responsibility for the errors.

Walker, Raymond F.↗

NASA NTRS1989

Advanced technology satellite demodulator development

Ford Aerospace has developed a proof-of-concept satellite 8 phase shift keying (PSK) modulation and coding system operating in the Time Division Multiple Access (TDMA) mode at a data range of 200 Mbps using rate 5/6 forward error correction coding. The 80 Msps 8 PSK modem was developed in a mostly digital form and is amenable to an ASIC realization in the next phase of development. The codec was developed as a paper design only. The power efficiency goal was to be within 2 dB of theoretical at a bit error rate (BER) of 5x10(exp 7) while the measured implementation loss was 4.5 dB. The bandwidth efficiency goal was 2 bits/sec/Hz while the realized bandwidth efficiency was 1.8 bits/sec/Hz. The burst format used a preamble of only 40 8 PSK symbol times including 32 symbols of all zeros and an eight symbol unique word. The modem and associated special test equipment (STE) were fabricated mostly on a specially designed stitch-weld board although a few of the highest rate circuits were built on printed circuit cards. All the digital circuits were ECL to support the clock rates of from 80 MHz to 360 MHz. The transmitter and receiver matched filters were square-root Nyquist bandpass filters realized at the 3.37 GHz i.f. The modem operated as a coherent system although no analog phase locked (PLL) loop was employed. Within the budgetary constraints of the program, the approach to the demodulator has been proven and is eligible to proceed to the next phase of development of a satellite demodulator engineering model. This would entail the development of an ASIC version of the digital portion of the demodulator, and MMIC version of the quadrature detector, and SAW Nyquist filters to realize the bandwidth efficiency.

Ames, Stephen A.↗

NASA NTRS1994

Capacitive Edge Sensor Design for Selene Segmented Primary Mirror

The objective of this project is to produce a proof-of-concept demonstration of an edge sensor for the Space Laser Energy (SELENE) program. In the SELENE telescope, the primary mirror design sonsists of more than 200,000 segments which must be precisely aligned to correct for distortions in the optical train

SELENE↗

NASA NTRS2015

Software Validation via Model Animation

This paper explores a new approach to validating software implementations that have been produced from formally-verified algorithms. Although visual inspection gives some confidence that the implementations faithfully reflect the formal models, it does not provide complete assurance that the software is correct. The proposed approach, which is based on animation of formal specifications, compares the outputs computed by the software implementations on a given suite of input values to the outputs computed by the formal models on the same inputs, and determines if they are equal up to a given tolerance. The approach is illustrated on a prototype air traffic management system that computes simple kinematic trajectories for aircraft. Proofs for the mathematical models of the system's algorithms are carried out in the Prototype Verification System (PVS). The animation tool PVSio is used to evaluate the formal models on a set of randomly generated test cases. Output values computed by PVSio are compared against output values computed by the actual software. This comparison improves the assurance that the translation from formal models to code is faithful and that, for example, floating point errors do not greatly affect correctness and safety properties.

Dutle, Aaron M.↗

NASA NTRS2009

Design and Verification of a Distributed Communication Protocol

The safety of remotely operated vehicles depends on the correctness of the distributed protocol that facilitates the communication between the vehicle and the operator. A failure in this communication can result in catastrophic loss of the vehicle. To complicate matters, the communication system may be required to satisfy several, possibly conflicting, requirements. The design of protocols is typically an informal process based on successive iterations of a prototype implementation. Yet distributed protocols are notoriously difficult to get correct using such informal techniques. We present a formal specification of the design of a distributed protocol intended for use in a remotely operated vehicle, which is built from the composition of several simpler protocols. We demonstrate proof strategies that allow us to prove properties of each component protocol individually while ensuring that the property is preserved in the composition forming the entire system. Given that designs are likely to evolve as additional requirements emerge, we show how we have automated most of the repetitive proof steps to enable verification of rapidly changing designs.

Munoz, Cesar A.↗

NASA NTRS1939

Full-Scale Wind-Tunnel Investigation of Wing-Cooling Ducts Effects of Propeller Slipstream, Special Report

Nickle, F. R.↗

NASA NTRS2010

Intelligent Flexible Materials for Space Structures: Expandable Habitat Engineering Development Unit

Expandable habitable elements are an enabling technology for human exploration in space and on planetary surfaces. Large geometries can be deployed from a small launch volume, allowing greater mission capability while reducing mass and improving robustness over traditional rigid shells. This report describes research performed by ILC Dover under the Intelligent Flexible Materials for Space Structures program on the design and manufacture of softgoods for LaRC's Expandable Habitat Engineering Development Unit (EDU). The EDU is a full-scale structural test article of an expandable hybrid habitat, integrating an expandable softgoods center section with two rigid end caps. The design of the bladder, restraint layer and a mock-up Thermal Micrometeoroid Cover is detailed together with the design of the interface hardware used to attach them to the end caps. The integration and design of two windows and a floor are also covered. Analysis was performed to study the effects of the open weave design, and to determine the correct webbing and fabric configuration. Stress analyses were also carried out on the interfaces between the softgoods and the end caps and windows. Testing experimentally determined the strength of the fabric and straps, and component testing was used to proof several critical parts of the design. This program established new manufacturing and design techniques that can be applied to future applications in expandable structures.

Hinkle, Jon↗