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Algorithms for planning flight paths of autonomous aerobots (robotic blimps) to be deployed in scientific exploration of remote planets are undergoing development. These algorithms are also adaptable to terrestrial applications involving robotic submarines as well as aerobots and other autonomous aircraft used to acquire scientific data or to perform surveying or monitoring functions.
A candidate math model search algorithm was developed at Ames Research Center that determines a recommended math model for the multivariate regression analysis of experimental data. The search algorithm is applicable to classical regression analysis problems as well as wind tunnel strain gage balance calibration analysis applications. The algorithm compares the predictive capability of different regression models using the standard deviation of the PRESS residuals of the responses as a search metric. This search metric is minimized during the search. Singular value decomposition is used during the search to reject math models that lead to a singular solution of the regression analysis problem. Two threshold dependent constraints are also applied. The first constraint rejects math models with insignificant terms. The second constraint rejects math models with near-linear dependencies between terms. The math term hierarchy rule may also be applied as an optional constraint during or after the candidate math model search. The final term selection of the recommended math model depends on the regressor and response values of the data set, the user s function class combination choice, the user s constraint selections, and the result of the search metric minimization. A frequently used regression analysis example from the literature is used to illustrate the application of the search algorithm to experimental data.
Small spacecraft autonomous rendezvous and docking is an essential technology for future space structure assembly missions. A novel magnetic capture and latching mechanism is analyzed that allows for docking of two CubeSats without precise sensors and actuators. The proposed magnetic docking hardware not only provides the means to latch the CubeSats but it also significantly increases the likelihood of successful docking in the presence of relative attitude and position errors. The simplicity of the design allows it to be implemented on many CubeSat rendezvous missions. A CubeSat 3-DOF ground demonstration effort is on-going at NASA Langley Research Center that enables hardware-in-the loop testing of the autonomous approach and docking of a follower CubeSat to an identical leader CubeSat. The test setup consists of a 3 meter by 4 meter granite table and two nearly frictionless air bearing systems that support the two CubeSats. Four cold-gas on-off thrusters are used to translate the follower towards the leader, while a single reaction wheel is used to control the attitude of each CubeSat. An innovative modified pseudo inverse control allocation scheme was developed to address interactions between control effectors. The docking procedure requires relatively high actuator precision, a novel minimal impulse bit mitigation algorithm was developed to minimize the undesirable deadzone effects of the thrusters. Simulation of the ground demonstration shows that the Guidance, Navigation, and Control system along with the docking subsystem leads to successful docking under 3-sigma dispersions for all key system parameters. Extensive simulation and ground testing will provide sufficient confidence that the proposed docking mechanism along with the choosen suite of sensors and actuators will perform successful docking in the space environment.
The objective of the research is to apply selected FAA certification techniques to the NASA experimental wind shear radar system. Although there is no intent to certify the NASA system, the procedures developed may prove useful to manufacturers that plan to undergo the certification process. The certification methodology for forward-looking wind shear detection radars will require estimation of system performance in several FAA-specified microburst/clutter scenarios as well as the estimation of probabilities of missed and false hazard alerts under general operational conditions. Because of the near-impossibility of obtaining these results experimentally, analytical and simulation approaches must be used. Hazard detection algorithms were developed that derived predictive estimates of aircraft hazard from basic radar measurements of weather reflectivity and radial wind velocity. These algorithms were designed to prevent false alarms due to ground clutter while providing accurate predictions of hazard to the aircraft due to weather. A method of calculation of the probability of missed and false hazard alerts has been developed that takes into account the effect of the various algorithms used in the system and provides estimates of the probability of missed and false alerts per microburst encounter under weather conditions found at Denver, Kansas City, and Orlando. Simulation techniques have been developed that permit the proper merging of radar ground clutter data (obtained from flight tests) with simulated microburst data (obtained from microburst models) to estimate system performance using the microburst/clutter scenarios defined by the FAA.
The goal of any modeling methodology is to develop a mathematical description of a system that is accurate in its representation and also permits analysis of structural and/or performance properties. Inherently, trade-offs exist between the level detail in the model and the ease with which analysis can be performed. Petri nets (PN's), a highly graphical modeling methodology for Discrete Event Dynamic Systems, permit representation of shared resources, finite capacities, conflict, synchronization, concurrency, and timing between state changes. By restricting the state transition time delays to the family of exponential density functions, Markov chain analysis of performance problems is possible. One major drawback of PN's is the tendency for the state-space to grow rapidly (exponential complexity) compared to increases in the PN constructs. It is the state space, or the Markov chain obtained from it, that is needed in the solution of many problems. The theory of state-space size estimation for PN's is introduced. The problem of state-space size estimation is defined, its complexities are examined, and estimation algorithms are developed. Both top-down and bottom-up approaches are pursued, and the advantages and disadvantages of each are described. Additionally, the author's research in non-exponential transition modeling for PN's is discussed. An algorithm for approximating non-exponential transitions is developed. Since only basic PN constructs are used in the approximation, theory already developed for PN's remains applicable. Comparison to results from entropy theory show the transition performance is close to the theoretic optimum. Inclusion of non-exponential transition approximations improves performance results at the expense of increased state-space size. The state-space size estimation theory provides insight and algorithms for evaluating this trade-off.
Three algorithms are developed for designing finite impulse response digital filters to be used for pulse shaping and channel equalization. The first is the Minimax algorithm which uses linear programming to design a frequency-sampling filter with a pulse shape that approximates the specification in a minimax sense. Design examples are included which accurately approximate a specified impulse response with a maximum error of 0.03 using only six resonators. The second algorithm is an extension of the Minimax algorithm to design preset equalizers for channels with known impulse responses. Both transversal and frequency-sampling equalizer structures are designed to produce a minimax approximation of a specified channel output waveform. Examples of these designs are compared as to the accuracy of the approximation, the resultant intersymbol interference (ISI), and the required transmitted energy. While the transversal designs are slightly more accurate, the frequency-sampling designs using six resonators have smaller ISI and energy values.
The author has identified the following significant results. Algorithms were developed to permit correction of scattering coefficient and brightness temperature for the Skylab S193 Radscat for the effects of cloud attenuation. These algorithms depend upon a measurement of the vertically polarized excess brightness temperature at 50 deg incidence angle. This excess temperature is converted to an equivalent 50 deg attenuation, which may then be used to estimate the horizontally polarized excess brightness temperature and reduced scattering coefficient at 50 deg. For angles other than 50 deg, the correction also requires use of the variation of emissivity with salinity and water temperature.
Algorithms are developed for computing stresses in a semi-infinite body when loaded by a uniform pressure acting over a circular area. The algorithm allows easy determination of any stress component in a semi-infinite body having a known Poisson's ratio. Example curves are plotted for Portland cement grout and metal representative values.
The measurements of wind speed and rain rate over a large dynamic range has been demonstrated by using passive microwave remote sensing measurements by a C-band radiometer flying above a hurricane. The measurements were obtained by using a unique variable frequency radiometer, the Stepped Frequency Microwave Radiometer (SFMR), which is capable of near simultaneous measurements at several widely spaced frequencies in a near octave bandwidth in the C-band microwave frequency region. In addition, an algorithm was developed which computes the surface wind speed and rain rate from the SFMR measured radiometric brightness temperature at two frequencies, and this algorithm was tested using experimental data collected during flights into Hurricane Allen during 1980. Results showed a reasonable agreement between the SFMR measured data and measurements obtained by weather radar.
The atmospheric backscatter coefficient, beta, measured with an airborne CO Laser Doppler Velocimeter (LDV) system operating in a continuous wave, focussed model is discussed. The Single Particle Mode (SPM) algorithm, was developed from concept through analysis of an extensive amount of data obtained with the system on board a NASA aircraft. The SPM algorithm is intended to be employed in situations where one particle at a time appears in the sensitive volume of the LDV. In addition to giving the backscatter coefficient, the SPM algorithm also produces as intermediate results the aerosol density and the aerosol backscatter cross section distribution. A second method, which measures only the atmospheric backscatter coefficient, is called the Volume Mode (VM) and was simultaneously employed. The results of these two methods differed by slightly less than an order of magnitude. The measurement uncertainties or other errors in the results of the two methods are examined.
A conventional prime factor discrete Fourier transform (DFT) algorithm is used to realize a discrete Fourier-like transform on the finite field, GF(q sub n). A pipeline structure is used to implement this prime factor DFT over GF(q sub n). This algorithm is developed to compute cyclic convolutions of complex numbers and to decode Reed-Solomon codes. Such a pipeline fast prime factor DFT algorithm over GF(q sub n) is regular, simple, expandable, and naturally suitable for VLSI implementation. An example illustrating the pipeline aspect of a 30-point transform over GF(q sub n) is presented.
The objective of the advanced detection, isolation, and accommodation (ADIA) program is to improve the overall demonstrated reliability of digital electronic control systems for turbine engines. For this purpose, algorithms were developed which detect, isolate, and accommodate sensor failures using analytical redundancy. Preliminary results of a full scale engine demonstration of the ADIA algorithm are presented. Minimum detectable levels of sensor failures for an F100 turbofan engine control system are determined and compared to those obtained during a previous evaluation of this algorithm using a real-time hybrid computer simulation of the engine.
The objective of the advanced detection, isolation, and accommodation (ADIA) program is to improve the overall demonstrated reliability of digital electronic control systems for turbine engines. For this purpose, algorithms were developed which detect, isolate, and accommodate sensor failures using analytical redundancy. Preliminary results of a full scale engine demonstration of the ADIA algorithm are presented. Minimum detectable levels of sensor failures for an F100 turbofan engine control system are determined and compared to those obtained during a previous evaluation of this algorithm using a real-time hybrid computer simulation of the engine.
A conventional prime factor discrete Fourier transform (DFT) algorithm is used to realize a discrete Fourier-like transform on the finite field, GF(q sub n). This algorithm is developed to compute cyclic convolutions of complex numbers and to decode Reed-Solomon codes. Such a pipeline fast prime factor DFT algorithm over GF(q sub n) is regular, simple, expandable, and naturally suitable for VLSI implementation. An example illustrating the pipeline aspect of a 30-point transform over GF(q sub n) is presented.
A large portion of the earth is covered by thin semi-transparent cirrus cloud. The cirrus results from the natural injection of moisture into the upper troposphere by deep convection (i.e., anvils) and from man-made moisture injected into the upper troposphere by jet aircraft. Although most cirrus clouds are semi-transparent to infrared wavelengths, their heights, thicknesses, and spectral absorption properties must be known in order to retrieve atmospheric temperature and moisture profiles from the data. An algorithm is developed for accounting for the radiative properties of semi-transparent cloud in the retrieval of vertical temperature and moisture profiles. The algorithm is to be applied to the NASA ER2 HIS data collected during the FIRE cirrus field program.
Two algorithms were developed which utilized multi-sensor analysis techniques to complement the current Space Shuttle Main Engine (SSME) safety monitoring system. The first algorithm analyzed the accumulative error between actual and predicted values of the engine parameter set, while the second algorithm combined these error terms into a response pattern and correlated each pattern with a standard pattern. These algorithms were applied to twelve SSME anomalous test firings and were found to produce improved failure detection times in eight of those twelve compared to the current engine safety monitoring system. Of the eight detected anomalous test firings, the first algorithm detected all eight, while the second algorithm detected seven of the eight. No false alarms were indicated by either algorithm for twelve nominal test firings. An initial parametric study of these algorithms for optimized parameter selection is presented and algorithm robustness to sensor failure is demonstrated.
A method has been developed to determine the oceanic daily mean mixed layer depth from satellite observations and a mixed layer thermal inertia (MLTI) model. The algorithms were developed to use remotely-sensed values of sea surface temperature, albedo, and surface wind speeds to calculate the thermal inertia and to predict changes in subsurface diurnal mixed layer depth. The MLTI model, based on a mixed layer model of the upper ocean, has been used to simulate the diurnal mixing process and thermal inertia distribution in the Sargasso Sea around 34 deg N, 70 deg W. Sea surface temperature and albedo have been obtained from the NOAA7-AVHRR images. Surface wind speeds have been derived from the Scanning Multichannel Microwave Radiometer (SMMR) aboard Nimbus 7. Image processing was performed for images gathered between June and July 1982. The daily mean mixed layer depths predicted by the MLTI model agree well with data gathered at the LOTUS mooring located in the Sargasso Sea. This suggests that vertical mixing is the dominant physical process that controls the thermal inertia distribution in the midocean, far from major current systems, and that remote sensing is a promising tool to study such upper ocean processes.
The application of probability density function (pdf) turbulence models is addressed. For the purpose of accurate prediction of turbulent combustion, an algorithm that combines a conventional computational fluid dynamic (CFD) flow solver with the Monte Carlo simulation of the pdf evolution equation was developed. The algorithm was validated using experimental data for a heated turbulent plane jet. The study of H2-F2 diffusion flames was carried out using this algorithm. Numerical results compared favorably with experimental data. The computations show that the flame center shifts as the equivalence ratio changes, and that for the same equivalence ratio, similarity solutions for flames exist.