Low-thrust guidance - An optimal stochastic control problem
Space vehicle low thrust minimum terminal variance guidance problem reduced to stochastic bang-bang optimal control system
Ash, G. R.↗
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Design of optimal probing signals for vector parameter estimation.
In the design of optimal inputs or probing signals for parameter estimation, it is more natural to consider functions of the Fisher information matrix as the criterion of optimality instead of some function of the error covariance matrix. The input which maximizes the Fisher information measure for efficient estimation of a scalar parameter also provides the minimum error variance. The information is thus a logical choice for the optimality criterion in scalar problems. No such obvious choice is apparent for vector parameter estimation. A number of performance measures are examined and compared in the present study, and a useful criterion is selected. The design of an optimal probing signal using this criterion is shown to be equivalent to an optimal control problem in which certain equality constraints must be satisfied. This problem may be solved by conventional techniques of deterministic or stochastic optimal control.
Nahi, N. E.↗
Space transportation vehicle design evaluation using saturated designs
An important objective in the preliminary design and evaluation of space transportation vehicles is to find the best values of design variables that optimize the performance characteristic (e.g. dry weight). For a given configuration, the vehicle performance can be determined by the use of complex sizing and performance evaluation computer programs. These complex computer programs utilize iterative algorithms and they are generally too expensive and/or difficult to use directly in multidisciplinary design optimization. An alternative is to use response surface methodology (RSM) and obtain quadratic polynomial approximations to the functional relationships between performance characteristics and design variables. In RSM, these approximation models are then used to determine optimum design parameter values and for rapid sensitivity studies. Constructing a second-order model requires that 'n' design parameters be studied at least at 3 levels (values) so that the coefficients in the model can be estimated. There, 3(n) factorial experiments (point designs or observations) may be necessary. For small values of 'n' such as two or three, this design works well. However, when a large number of design parameters are under study, the number of design points required for a full-factorial design may become excessive. Fortunately, these quadratic polynomial approximations can be obtained by selecting an efficient design matrix using central composite designs (CCD) from design of experiments theory. Each unique point design from the CCD matrix is then conducted using computerized analysis tools (e.g. POST, CONSIZ, etc.). In the next step, least squares regression analysis is used to calculate the quadratic polynomial coefficients from the data. However, in some multidisciplinary applications involving a large number of design variables and several disciplines, the computerized performance synthesis programs may get too time consuming and expensive to run even with the use of efficient central composite designs. In such cases, it may be preferable to keep the number of design points to an absolute minimum and trade some model accuracy with cost. For this purpose, another class of experimental designs, called saturated D-optimal designs may be utilized for generating a matrix of vehicle designs. A design is called saturated when the number of design points is exactly equal to the number of terms in the model to be fitted. As a result, saturated designs require the absolute minimum number of design points ((n+1)(n+2)/s) to estimate the quadratic polynomial model coefficients. Saturated designs can be generated using the D-optimality criterion. A good saturated design should give rise to least squares estimates with minimum generalized variance.
Unal, Resit↗
The Variance of Solar Wind Magnetic Fluctuations: Solutions and Further Puzzles
We study the dependence of the variance directions of the magnetic field in the solar wind as a function of scale, radial distance, and Alfvenicity. The study resolves the question of why different studies have arrived at widely differing values for the maximum to minimum power (approximately equal to 3:1 up to approximately equal to 20:1). This is due to the decreasing anisotropy with increasing time interval chosen for the variance, and is a direct result of the "spherical polarization" of the waves which follows from the near constancy of |B|. The reason for the magnitude preserving evolution is still unresolved. Moreover, while the long-known tendency for the minimum variance to lie along the mean field also follows from this view (as shown by Barnes many years ago), there is no theory for why the minimum variance follows the field direction as the Parker angle changes. We show that this turning is quite generally true in Alfvenic regions over a wide range of heliocentric distances. The fact that nonAlfvenic regions, while still showing strong power anisotropies, tend to have a much broader range of angles between the minimum variance and the mean field makes it unlikely that the cause of the variance turning is to be found in a turbulence mechanism. There are no obvious alternative mechanisms, leaving us with another intriguing puzzle.
Roberts, D. A.↗
Mesoscale Gravity Wave Variances from AMSU-A Radiances
A variance analysis technique is developed here to extract gravity wave (GW) induced temperature fluctuations from NOAA AMSU-A (Advanced Microwave Sounding Unit-A) radiance measurements. By carefully removing the instrument/measurement noise, the algorithm can produce reliable GW variances with the minimum detectable value as small as 0.1 K2. Preliminary analyses with AMSU-A data show GW variance maps in the stratosphere have very similar distributions to those found with the UARS MLS (Upper Atmosphere Research Satellite Microwave Limb Sounder). However, the AMSU-A offers better horizontal and temporal resolution for observing regional GW variability, such as activity over sub-Antarctic islands.
middle atmosphere↗
RFI in hybrid loops - Simulation and experimental results.
A digital simulation of an imperfect second-order hybrid phase-locked loop (HPLL) operating in radio frequency interference (RFI) is described. Its performance is characterized in terms of phase error variance and phase error probability density function (PDF). Monte-Carlo simulation is used to show that the HPLL can be superior to the conventional phase-locked loops in RFI backgrounds when minimum phase error variance is the goodness criterion. Similar experimentally obtained data are given in support of the simulation data.
Ziemer, R. E.↗
Reproducibility and Repeatability of Tensile and Low-Cycle Fatigue Properties in Propulsion Grade Hydrogen
Hydrogen has the potential of increased use in the future as an environmentally friendly fuel. It has, however, shown a tendency to embrittle some materials. To be used in a safe manner and to exploit its full potential, it will be necessary to develop a database of material properties in hydrogen environment. The tests needed to produce this data are costly to perform (tensile test cost 25 times more and low cycle fatigue test are 55 times as expensive). Moreover, there is presently a lack of universal test methods to ensure standardized data within the hydrogen community. Each of the industries that work with hydrogen (aerospace, petroleum, fuel cells, etc.) performs tests by their own laboratory-developed methods, thus rendering cross- comparisons of material property data highly questionable. It is extremely important that data generated in a hydrogen environment be done to a standard that reduces variance to a minimum and allows direct comparison of test results from different laboratories. Doing so will assure that all data generated can be used to further our understanding of the hydrogen effects and to make sure components/products designed for hydrogen are the safest and most reliable possible. This paper reviews the results of two 'round-robin' programs conducted by NASA-MSFC. These two programs examined the reproducibility and repeatability of tensile and low-cycle fatigue test results in high-pressure hydrogen environments. The studies indicated that even with the tightest controls available from current commercial standards, the reproducibility (between different laboratories) and repeatability (within a laboratory) results of the tensile tests exhibited five times the variance as in standard ambient air tests. The variance with the LCF tests were on the same order as with air tests, but that was due to the large variation present in the last Interlaboratory air program. The paper concludes with a recommendation for a program that would allow the development of improved test methods, leading to lower variance in the generation of mechanical property data in the future.
Vesely, E. J.↗
Operational wind plants increase planetary boundary layer height: an observational study
As wind energy deployment grows, interactions between wind plants and the surrounding environment become more prevalent. The current investigation seeks to understand these interactions by characterizing the impact of wind plants on the planetary boundary layer height (PBLH), utilizing observations from the American WAKE experimeNt (AWAKEN) campaign. Given the ambiguity of the definition of PBLH under stable atmospheric conditions, where the impact of wind plants is expected to be strongest, a comparison of different methods for identifying PBLH is first conducted using data collected by multiple types of instruments. The Heffter method is selected as the thermodynamic method because it generates the most consistent results for the radiosonde and infrared spectrometer. A minimum vertical velocity variance method is used for a turbulence-based definition. Using both of these methods, the values of PBLH measured at spatially distributed sites are compared under a range of atmospheric conditions. Both methods show a clear increase in PBLH downstream of a wind plant for stable conditions. These impacts are strongest when the upstream PBLH is shallow (less than 0.25 km), with the thermodynamic method showing a PBLH increase of 35 %–39 % and the turbulence-based method showing a 143 % increase. At a site 20 km downstream of the wind plant, these effects are no longer observed, suggesting PBLH is not influenced by the wind plant at this distance. The results of this investigation show that wind plants can modify PBLH in their vicinity. As PBLH is a key parameter for numerical models, this insight into wind plant–atmosphere interactions can be used to validate and improve the accuracy of wind energy forecasts.
17 WIND ENERGY↗
Radiation exposure and performance of multiple burn LEO-GEO orbit transfer trajectories
Many potential strategies exist for the transfer of spacecraft from low Earth orbit (LEO) to geosynchronous (GEO) orbit. One strategy has generally been utilized, that being a single impulsive burn at perigee and a GEO insertion burn at apogee. Multiple burn strategies were discussed for orbit transfer vehicles (OTVs) but the transfer times and radiation exposure, particularly for potentially manned missions, were used as arguments against those options. Quantitative results concerning the trip time and radiation encountered by multiple burn orbit transfer missions in order to establish the feasibility of manned missions, the vulnerability of electronics, and the shielding requirements are presented. The performance of these multiple burn missions is quantified in terms of the payload and propellant variances from the minimum energy mission transfer. The missions analyzed varied from one to eight perigee burns and ranged from a high thrust, 1 g acceleration, cryogenic hydrogen-oxygen chemical prpulsion system to a continuous burn, 0.001 g acceleration, hydrogen fueled resistojet propulsion system with a trip time of 60 days.
Gorland, S. H.↗
Radiation exposure and performance of multiple burn LEO-GEO orbit transfer trajectories
Many potential strategies exist for the transfer of spacecraft from low Earth orbit (LEO) to geosynchronous (GEO) orbit. One strategy has generally been utilized, that being a single impulsive burn at perigee and a GEO insertion burn at apogee. Multiple burn strategies were discussed for orbit transfer vehicles (OTVs) but the transfer times and radiation exposure, particularly for potentially manned missions, were used as arguments against those options. Quantitative results concerning the trip time and radiation encountered by multiple burn orbit transfer missions in order to establish the feasibility of manned missions, the vulnerability of electronics, and the shielding requirements are presented. The performance of these multiple burn missions is quantified in terms of the payload and propellant variances from the minimum energy mission transfer. The missions analyzed varied from one to eight perigee burns and ranged from a high thrust, 1 g, acceleration, cryogenic hydrogen-oxygen chemical propulsion system for a continuous burn, 0.001 g acceleration, hydrogen, fueled resistojet propulsion system with a trip time of 60 days.
Gorland, S. H.↗
Monitoring of Volcanogenic CO2-Induced Tree Kills with AVIRIS Image Data at Mammoth Mountain, California
Elevated cold CO2 emissions from the flank of Mammoth Mountain volcano on the southwest rim of the Long Valley Caldera, eastern California, have been the cause of over 100 acres of dead trees in that area since 1990. The source of the CO2 gas is thought to be from one or more magmatic intrusion(s) beneath Mammoth Mountain and is probably related to a period of seismic unrest that began in 1989. The gas rises to the surface probably from depths of a few kilometers, along faults and fracture zones. The gas is at ambient temperature and diffuses from the soil rather than discharging from distinct vents. Typically, soil gas concentrations in tree-kill areas range from 10% to over 90% CO2 by volume, as compared to normal background of < 1% in healthy forest. The gas composition is predominantly CO2 mixed with air (sulfur gases are not elevated), and C and He isotopic ratios are consistent with a magmatic origin for the gas. The total CO2 emission has been estimated at 1200 tons/day, comparable to the emissions at Kilauea. Some of the dead trees are as old as 250 years, suggesting that similar anomalous gas discharge has not occurred over the previous few hundred years. The delta C-13/12 ratio in the Mammoth Mountain CO2 emission averages about -4.5 (PDB standard). This is consistent with a mantle source for the carbon. However, the large volume of the emission suggests that not all of the CO2 is necessarily being generated from the 1989 intrusion. The voluminous gas could be leaking from a vapor-rich zone, capped by an impermeable layer, that was supplied CO2 from degassing of many small magma bodies that intruded beneath the mountain over a period of decades or centuries. Earthquakes in 1989 could have fractured the capping layer and provided pathways for the escape Of CO2 to the surface. Alternatively, some of the CO2 could be derived from contact metamorphism of carbonate rocks intruded by magma. Carbonate-bearing Paleozoic roof pendents crop out in close proximity to Mammoth Mountain. It is possible that similar rocks could occur at depth beneath Mammoth Mountain, and could have contributed CO2 from thermal decomposition caused from recent intrusions. We hope to determine the C-13/12 ratio of a suite of samples to demonstrate if the carbonate rocks could be the source of at least part of the 1990-97 CO2 emission. To better understand the behavior of the CO2 gas, we have used hyperspectral imagery data of Mammoth Mountain acquired from the Airborne Visual/Infrared Imaging Spectrometer (AVIRIS) to map out areas of dead trees. The areas of tree kill have increased in size from about 50 acres in 1994 to about 100 acres in 1997. Tree kill is the major surface manifestation of the carbon dioxide flux at Mammoth Mountain, is widely dispersed, and has been cursorily mapped by regular field mapping techniques in the area. Initial investigations using airborne digital imagery from the Thematic Mapper Simulator (NS001) and AVIRIS instruments have shown extremely encouraging results for complete delineation of the vegetation anomalies. The most successful maps (when compared with ground truth) were developed using AVIRIS data with spectral angle mapper and matched filter algorithms with a data set that was reduced to maximum variance via the minimum noise fraction transformation. The result of this work is a series of maps that show the tree kill areas occurring in an halo-pattern surrounding the base of Mammoth Mountain. We are applying these same techniques to earlier AVIRIS images of Mammoth Mountain to examine the progression of the tree kill areas over time. Temporal maps of the tree kill areas may assist in constructing a picture of the structure beneath Mammoth Mountain.
Hausback, Brian P.↗
Solar Drivers of 11-yr and Long-Term Cosmic Ray Modulation
In the current paradigm for the modulation of galactic cosmic rays (GCRs), diffusion is taken to be the dominant process during solar maxima while drift dominates at minima. Observations during the recent solar minimum challenge the pre-eminence of drift: at such times. In 2009, the approx.2 GV GCR intensity measured by the Newark neutron monitor increased by approx.5% relative to its maximum value two cycles earlier even though the average tilt angle in 2009 was slightly larger than that in 1986 (approx.20deg vs. approx.14deg), while solar wind B was significantly lower (approx.3.9 nT vs. approx.5.4 nT). A decomposition of the solar wind into high-speed streams, slow solar wind, and coronal mass ejections (CMEs; including postshock flows) reveals that the Sun transmits its message of changing magnetic field (diffusion coefficient) to the heliosphere primarily through CMEs at solar maximum and high-speed streams at solar minimum. Long-term reconstructions of solar wind B are in general agreement for the approx. 1900-present interval and can be used to reliably estimate GCR intensity over this period. For earlier epochs, however, a recent Be-10-based reconstruction covering the past approx. 10(exp 4) years shows nine abrupt and relatively short-lived drops of B to < or approx.= 0 nT, with the first of these corresponding to the Sporer minimum. Such dips are at variance with the recent suggestion that B has a minimum or floor value of approx.2.8 nT. A floor in solar wind B implies a ceiling in the GCR intensity (a permanent modulation of the local interstellar spectrum) at a given energy/rigidity. The 30-40% increase in the intensity of 2.5 GV electrons observed by Ulysses during the recent solar minimum raises an interesting paradox that will need to be resolved.
Cliver, E. W.↗
The Impact of Truth Surrogate Variance on Quality Assessment/Assurance in Wind Tunnel Testing
Minimum data volume requirements for wind tunnel testing are reviewed and shown to depend on error tolerance, response model complexity, random error variance in the measurement environment, and maximum acceptable levels of inference error risk. Distinctions are made between such related concepts as quality assurance and quality assessment in response surface modeling, as well as between precision and accuracy. Earlier research on the scaling of wind tunnel tests is extended to account for variance in the truth surrogates used at confirmation sites in the design space to validate proposed response models. A model adequacy metric is presented that represents the fraction of the design space within which model predictions can be expected to satisfy prescribed quality specifications. The impact of inference error on the assessment of response model residuals is reviewed. The number of sites where reasonably well-fitted response models actually predict inadequately is shown to be considerably less than the number of sites where residuals are out of tolerance. The significance of such inference error effects on common response model assessment strategies is examined.
DeLoach, Richard↗
The Interaction Between Dynamics and Chemistry of Ozone in the Set-up Phase of the Northern Hemisphere Polar Vortex
The morphology and evolution of the stratospheric ozone (O3) distribution at high latitudes in the Northern Hemisphere (NH) are examined for the late summer and fall seasons of 1999. This time period sets the O3 initial condition for the SOLVE/THESEO field mission performed during winter 1999-2000. In situ and satellite data are used along with a three-dimensional model of chemistry and transport (CTM) to determine the key processes that control the distribution of O3 in the lower-to-middle stratosphere. O3 in the vortex at the beginning of the winter season is found to be nearly constant from 500 to above 800 K with a value at 3 ppmv +/- approx. 10%. Values outside the vortex are up to a factor of 2 higher and increase significantly with potential temperature. The seasonal time series of data from POAM shows that relatively low O3 mixing ratios, which characterize the vortex in late fall, are already present at high latitudes at the end of summer before the vortex circulation sets up. Analysis of the CTM output shows that the minimum O3 and increase in variance in late summer are the result of: 1) stirring of polar concentric O3 gradients by nascent wave-driven transport, and 2) an acceleration of net photochemical loss with decreasing solar illumination. The segregation of low O3 mixing ratios into the vortex as the circulation strengthens through the fall suggests a possible feedback role between O3 chemistry and the vortex formation dynamics. Trajectory calculations from O3 sample points early in the fall, however, show only a weak correlation between initial O3 mixing ratio and potential vorticity later in the season consistent with order-of-magnitude calculations for the relative importance of O3 in the fall radiative balance at high latitudes. The possible connection between O3 chemistry and the dynamics of vortex formation does suggest that these feedbacks and sensitivities need to be better understood in order to make confident predictions of the recovery of NH O3.
Kawa, S. R.↗
Atmosphere Explorer observations of the geocoronal H Balmer alpha nightglow
The Balmer alpha nightglow emission of geocoronal atomic hydrogen has been investigated using photometric data obtained by the Visible Airglow Experiment on board the Atmosphere Explorer E satellite. The measured H Balmer alpha intensities are presented as a function of solar depression angle, observation zenith angle, and azimuth relative to the sun for solar minimum conditions. The results are at variance with the earlier D2A satellite observations but in better agreement with previous ground-based studies. As a result of comparison with theoretical predictions, the present observations reaffirm the findings of the ground-based investigations in implying that values for the Lyman beta line center flux are a factor of 2 greater than those derived from direct measurements.
Burrage, M. D.↗
Constraints on the power spectrum of the primordial density field from large-scale data - Microwave background and predictions of inflation
It is shown here that, by using galaxy catalog correlation data as input, measurements of microwave background radiation (MBR) anisotropies should soon be able to test two of the inflationary scenario's most basic predictions: (1) that the primordial density fluctuations produced were scale-invariant and (2) that the universe is flat. They should also be able to detect anisotropies of large-scale structure formed by gravitational evolution of density fluctuations present at the last scattering epoch. Computations of MBR anisotropies corresponding to the minimum of the large-scale variance of the MBR anisotropy are presented which favor an open universe with P(k) significantly different from the Harrison-Zeldovich spectrum predicted by most inflationary models.
Kashlinsky, A.↗
Trends in Human Spaceflight: Failure Tolerance, High Reliability and Correlated Failure History
In a half century of human spaceflight, NASA has continuously refined agency safety and reliability requirements in response to mission demands, critical failures, and technology development. Early spacecraft, including Mercury, Gemini and Apollo vehicles, were highly reliant on dissimilar redundancy and demonstrated test margins. Later programs, such as the reusable Space Transportation System (STS) and International Space Station (ISS), introduced probabilistic studies and isolated two-failure tolerance to improve robustness at the expense of added complexity. More recently, the Orion Multi-Program Crew Vehicle (MPCV) program adopted universal single-failure tolerance with two categorical exceptions; Zero-Failure Tolerant (0FT) and Design for Minimum Risk (DFMR) hardware. Failure tolerance variances are defined and managed in accordance with agency human-rating requirements, and require concurrence from program Technical Authorities (TA) as well as the MPCV Safety and Mission Assurance Safety and Engineering Review Panel (MSERP). To understand and reaffirm standards applied to Apollo, Space Shuttle and Orion vehicles, Orion and Deep Space Gateway Safety and Mission Assurance (S&MA) representatives conducted accelerated research to compare unique safety and reliability criteria against ground and flight anomalies, based on information contained in post-mission reports and the Problem Reporting and Corrective Action (PRACA) database. In some cases, high-profile failures and narrow escapes have reinforced decisions to maintain or adapt safety requirements. In others, empirical trends have highlighted the need for vigilance and innovative safety guidelines. Given the inability to achieve absolute compliance with evolving safety and reliability requirements, the team conducted a targeted review of DFMR and 0FT propulsion elements within the framework of changing system design, inspection, materials and process developments to formulate conclusions on technological maturity, failure density, and net changes in safety risk. Based on the aggregate performance of high-reliability and failure-tolerant systems, the authors have attempted to establish best practices and guidelines to inform future program decisions. On a somewhat cautionary note, this study is not intended to direct a universal set of requirements for future missions based on prior lessons learned. Spacecraft safety is a multi-variable problem, and attempts to mitigate past failures will not guarantee future success. However, this assessment offers a retrospective review of policy changes, implementation and effectiveness. In the future, NASA, European Space Agency (ESA) and industry partners may benefit from a more robust correlation between requirements and performance, as space-faring nations work toward more challenging, complex and long-duration commercial and deep-space ventures.
Green, Carrie↗
Quantizing and sampling considerations in digital phased-locked loops
The quantizer problem is first considered. The conditions under which the uniform white sequence model for the quantizer error is valid are established independent of the sampling rate. An equivalent spectral density is defined for the quantizer error resulting in an effective SNR value. This effective SNR may be used to determine quantized performance from infinitely fine quantized results. Attention is given to sampling rate considerations. Sampling rate characteristics of the digital phase-locked loop (DPLL) structure are investigated for the infinitely fine quantized system. The predicted phase error variance equation is examined as a function of the sampling rate. Simulation results are presented and a method is described which enables the minimum required sampling rate to be determined from the predicted phase error variance equations.
Hurst, G. T.↗