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Waveform multigrid method is an efficient method for solving certain classes of time dependent PDEs. This paper studies the relationship between this method and the analogous multigrid method for steady-state problems. Using a Fourier-Laplace analysis, practical convergence rate estimates of the waveform multigrid iterations are obtained. Experimental results show that the analysis yields accurate performance prediction.
Recent work on minimum variances estimators based on Cauchy distributions appear relevant to orbital drag estimation. Samples form Cauchy distributions which are part of a class of heavy-tailed distributions, are characterized by long stretches of fairly small variation, punctuated by large variations that are many times larger than could be expected from a Gaussian. Such behavior can occur when solar storms perturb the atmosphere. In this context, the present work describes an embedding of the scalar Idan-Speyer Cauchy Estimator to estimate density corrections, within an Extended Kalman Filter that estimates the state of a low Earth orbiter. In contrast to the baseline Kalman approach, the larger formal errors of the present approach fully and conservatively bound the predictive error distribution, even in the face of unanticipated density disturbances of hundreds of percent.
The paper presents an over-parametrization free certainty equivalence state feedback backstepping adaptive control design method for systems of any relative degree with unmatched uncertainties and unknown virtual control coefficients. It uses a fast prediction model to estimate the unknown parameters, which is independent of the control design. It is shown that the system's input and output tracking errors can be systematically decreased by the proper choice of the design parameters. The benefits of the approach are demonstrated in numerical simulations.
On February 18th, 2021, the Mars 2020 entry system successfully delivered the Perseverance rover to the surface of Mars at Jezero Crater. The entry capsule carried instrumentation installed on the heatshield and backshell, named the Mars Entry, Descent, and Landing Instrumentation 2. The instruments included pressure transducers, thermocouples, heat flux gauges, and a radiometer to measure the aerodynamic and aerothermodynamic performance of the entry vehicle. Three of these sensors, a thermocouple plug, heat flux gauge, and a radiometer, were co-located on the backshell. The sensors were exposed to roughly the same aerodynamic heating, but measured these environments in different ways, each with its own set of modeling and measurement error complications. This paper develops a method for blending each of these measurements together in a single algorithm to produce estimates of the aerothermodynamic environments at that backshell location. The approach makes use of the Kalman-Schmidt filter/smoother methodology, where systematic measurement error parameters are modeled as multiplicative states that are estimated by the filter along with the aerothermal states. The results indicate peak convective and radiative heating values of 0.86 and 5.16 W/cm2, respectively, compared to the filter predictive model values of 0.67 and 4.83 W/cm2.
The Soil Moisture Active Passive (SMAP) mission is part of the NASA space-based Earth observation program, and consists of an L-band radar and radiometer scheduled for launch into sun synchronous orbit in late 2014. A joint effort of the Jet Propulsion Laboratory (JPL) and the Goddard Space Flight Center (GSFC), the SMAP mission draws heavily on the design and risk reduction heritage of the Hydrosphere State (Hydros) mission [1], [2]. The SMAP science and applications objectives are to: 1) understand processes that link the terrestrial water, energy and carbon cycles, 2) estimate global water and energy fluxes at the land surface, 3) quantify net carbon flux in boreal landscapes, 4) enhance weather and climate forecast skill, and 5) develop improved flood prediction and drought monitoring capability. To meet these science objectives, SMAP ground processing will combine the attributes of the radar and radiometer observations (in terms of their spatial resolution and sensitivity to soil moisture, surface roughness, and vegetation) to estimate soil moisture with 4% volumetric accuracy at a resolution of 10 km, and freeze-thaw state at a resolution of 1-3 km. Model sensitivities translate the soil moisture accuracy to a radar backscatter accuracy of 1 dB (1 sigma) at 3 km resolution and a brightness temperature accuracy of 1.3 K at 40 km resolution. This paper will describe the level 1 radar processing and calibration challenges and the choices made so far for the algorithms and software implementation.
This paper studies single-axis equations of motion that are applicable to a spacecraft or to a space experiment pointing assembly whose motion has been perfectly isolated from the carrier vehicle. It considers four state estimators for implementation in the control loop for a stellar observation experiment. The first three estimators are very general and do not make use of input torque in their prediction models, while the proposed fourth estimator utilizes this information. It is shown via closed-loop covariance analysis that the best achievable pointing performance with the best of the first three estimators is limited to about 0.125 arc-sec (rms) with the given rate-gyro and star-tracker inaccuracies. It is also shown that the fourth estimator has the capability of achieving a pointing performance far superior to the performance achievable using the first three estimators. The fourth estimator relies on the ability to accurately generate the desired control torque (i.e., low input noise).
An efficient computational algorithm for estimating the noise covariance matrices of large linear discrete stochatic-dynamic systems is presented. Such systems arise typically by discretizing distributed-parameter systems, and their size renders computational efficiency a major consideration. The proposed adaptive filtering algorithm is based on the ideas of Belanger, and is algebraically equivalent to his algorithm. The earlier algorithm, however, has computational complexity proportional to p to the 6th, where p is the number of observations of the system state, while the new algorithm has complexity proportional to only p-cubed. Further, the formulation of noise covariance estimation as a secondary filter, analogous to state estimation as a primary filter, suggests several generalizations of the earlier algorithm. The performance of the proposed algorithm is demonstrated for a distributed system arising in numerical weather prediction.
Two triglycine sulphate crystals were grown from an aqueous solution on the Spacelab 3 mission. Using a diffusion coefficient of 0.00002 sq cm/sec, a computer simulation gave reasonable agreement between experimental and theoretical crystal sizes and interferometric lines in the solution near the growing crystal. This diffusion coefficient is larger than most measured values, possibly due to fluctuating accelerations on the order of 0.001 g. The average acceleration was estimated to be less than 10 to the -6th g. At this level buoyancy-driven convection is predicted to add approximately 20 percent to the steady-state growth rate.
Models are foundational for estimating states of the earth's climate system, both as tools to extrapolate information in time and space, and as observation 'operators' used to relate what is analyzed and predicted to what is observed. Expanding the simulation approach further, observing system simulation experiments (OSSEs) are designed to mimic the complete process of analyzing the climate state by replacing real observations with entirely simulated ones determined from a model-based depiction of nature. OSSEs provide a framework to 'fly' simulated satellite instruments through a synthetic atmosphere and investigate the trade-spaces of measurements for various satellite configurations and sampling strategies, and assess their measurement impact on modeling and forecasting capabilities. Such a tool is a crucial but as yet unfulfilled need for future mission selection and design. The components of a state-of-the-art OSSE system are being assembled at the Global Modeling and Assimilation Office (GMAO, Code 610.1) at NASA/GSFC, leveraging on the GMAO's existing modeling and data assimilation infrastructure for numerical weather prediction (NWP). The OSSE framework is based on the GMAO's Goddard Earth Observing System atmospheric general circulation model, version 5 (GEOS-5) and the Gridpoint Statistical Interpolation (GSI) observational analysis scheme, combined with the Goddard Chemistry, Aerosol, Radiation, and Transport (GOCART) model developed by the Atmospheric Chemistry and Dynamics Branch (Code 613.3). This system is an evolving, key component of Goddard's planned development of an Integrated Earth System Analysis (IESA) capability, which will bring together into a single, fully interactive system Goddard's modeling and assimilation efforts in atmosphere, ocean and chemistry and aerosols to provide a comprehensive analysis and prediction system for weather and climate In addition to providing a state-of-the-art capability for assimilating current observation types, GEOS-5, and the future IESA, provide the capability to identify the need for, and assess the potential impact of, future observing systems under consideration for improving weather and climate prediction.
On February 18th, 2021, the Mars 2020 entry system successfully delivered the Perseverance rover to the surface of Mars at Jezero Crater. The entry capsule carried instrumentation installed on the heatshield and backshell, named the Mars Entry, Descent, and Landing Instrumentation 2. The instruments included pressure transducers, thermocouples, heat flux gauges, and a radiometer to measure the aerodynamic and aerothermodynamic performance of the entry vehicle. Three of these sensors, a thermocouple plug, heat flux gauge, and a radiometer, were co-located on the backshell. The sensors were exposed to roughly the same aerodynamic heating, but measured these environments in different ways, each with its own set of modeling and measurement error complications. This paper develops a method for blending each of these measurements together in a single algorithm to produce estimates of the aerothermodynamic environments at that backshell location. The approach makes use of the Kalman-Schmidt filter/smoother methodology, where systematic measurement error parameters are modeled as multiplicative states that are estimated by the filter along with the aerothermal states. The results indicate peak convective and radiative heating values of 0.86 and 5.16 W/cm$^2$, respectively, compared to the filter predictive model values of 0.67 and 4.83 W/cm$^2$.
The rising number of small unmanned aerial vehicles (UAVs) expected in the next decade will enable a new series of commercial, service, and military operations in low altitude airspace as well as above densely populated areas. These operations may include on-demand delivery, medical transportation services, law enforcement operations, traffic surveillance and many more. Such unprecedented scenarios create the need for robust, efficient ways to monitor the UAV state in time to guarantee safety and mitigate contingencies throughout the operations. This work proposes a generalized monitoring and prediction methodology that utilizes realtime measurements of an autonomous UAV following a series of way-points. Two different methods, based on sinusoidal acceleration profiles and high-order splines, are utilized to generate the predicted path. The monitoring approach includes dynamic trajectory re-planning in the event of unexpected detour or hovering of the UAV during flight. It can be further extended to different vehicle types, to quantify uncertainty affecting the state variables, e.g., aerodynamic and other environmental effects, and can also be implemented to prognosticate safety-critical metrics which depend on the estimated flight path and required thrust. The proposed framework is implemented on a simplified, scalable UAV modeling and control system traversing 3D trajectories. Results presented include examples of real-time predictions of the UAV trajectories during flight and a critical analysis of the proposed scenarios under uncertainty constraints.
Magnitude estimates by each of 31 listeners were obtained for a variety of noise sources under three methods of stimuli presentation: loudspeaker presentation in an anechoic chamber, loudspeaker presentation in a normal semi-reverberant room, and earphone presentation. Comparability of ratings obtained in these environments were evaluated with respect to predictability of ratings from physical measures, reliability of ratings, and to the scale values assigned to various noise stimuli. Acoustic environment was found to have little effect upon physical predictive measures and ratings of perceived noisiness were little affected by the acoustic environment in which they were obtained. The need for further study of possible differing interactions between judged noisiness of steady state sound and the methods of magnitude estimation and paired comparisons is indicated by the finding that in these tests the subjects, though instructed otherwise, apparently judged the maximum rather than the effective magnitude of steady-state noises.
The existence of methane in Titan's atmosphere (approx. 6% level at the surface) presents a unique enigma, as photochemical models predict that the current inventory will be entirely depleted by photochemistry in a timescale of approx 20 Myr. In this paper, we examine the clues available from isotopic ratios (C-12/C-13 and D/H) in Titan's methane as to the past atmosphere history of this species. We first analyze recent infrared spectra of CH4 collected by the Cassini Composite Infrared Spectrometer, measuring simultaneously for the first time the abundances of all three detected minor isotopologues: (13)CH4, (12)CH3D, and (13)CH3D. From these we compute estimates of C-12/C-13 = 86.5 +/- 8.2 and D/H = (1.59 +/- 0.33) x 10(exp -4) , in agreement with recent results from the Huygens GCMS and Cassini INMS instruments. We also use the transition state theory to estimate the fractionation that occurs in carbon and hydrogen during a critical reaction that plays a key role in the chemical depletion of Titan's methane: CH4 + C2H yields CH3 + C2H2. Using these new measurements and predictions we proceed to model the time evolution of C-12/C-13 and D/H in Titan's methane under several prototypical replenishment scenarios. In our Model 1 (no resupply of CH4), we find that the present-day C-12/C-13 implies that the CH4 entered the atmosphere 60-1600 Myr ago if methane is depleted by chemistry and photolysis alone, but much more recently-most likely less than 10 Myr ago-if hydrodynamic escape is also occurring. On the other hand, if methane has been continuously supplied at the replenishment rate then the isotopic ratios provide no constraints, and likewise for the case where atmospheric methane is increasing, We conclude by discussing how these findings may be combined with other evidence to constrain the overall history of the atmospheric methane.
The goal of this program was to combine modern control concepts with new identification techniques to develop a comprehensive package for estimation of 'robust flutter boundaries' based on experimental data. The goal was to use flight data, combined with a fundamental physical understanding of flutter dynamics, to generate a prediction of flutter speed and an estimate of the accuracy of the prediction. This report is organized as follows: the specific contributions of this project will be listed first. Then, the problem under study will be stated and the general approach will be outlined. Third, the specific system under study (F- 18 SRA) will be described and a preliminary data analysis will be performed. Then, the various steps of the flutter boundary determination will be outlined and applied to tile F-18 SRA data and others.
System reliability assessment is a methodology which incorporates reliability analyses performed at parts and components level such as Reliability Prediction, Failure Modes and Effects Analysis (FMEA) and Fault Tree Analysis (FTA) to assess risks, perform design tradeoffs, and therefore, to ensure effective productivity and/or mission success. The system reliability is used to optimize the product design to accommodate today?s mandated budget, manpower, and schedule constraints. Stand ard based reliability assessment is an effective approach consisting of reliability predictions together with other reliability analyses for electronic, electrical, and electro-mechanical (EEE) complex parts and components of large systems based on failure rate estimates published by the United States (U.S.) military or commercial standards and handbooks. Many of these standards are globally accepted and recognized. The reliability assessment is especially useful during the initial stages when the system design is still in the development and hard failure data is not yet available or manufacturers are not contractually obliged by their customers to publish the reliability estimates/predictions for their parts and components. This paper presents a methodology to assess system reliability using parts and components reliability estimates to ensure effective productivity and/or mission success in an efficient manner, low cost, and tight schedule.
This work presents the results of an experimental study on supercooled droplet deformation and breakup near the leading edge of an airfoil. The results are compared to prior room temperature droplet deformation results to explore the effects of droplet supercooling. The experiments were conducted in the Adverse Environment Rotor Test Stand (AERTS) at The Pennsylvania State University. An airfoil model placed at the end of the rotor blades mounted onto the hub in the AERTS chamber was moved at speeds ranging between 50 and 80 m/sec. The temperature of the chamber was set at -20˚C. A monotonic droplet generator was used to produce droplets that fell from above, perpendicular to the path of the airfoil. The supercooled state of the droplets was determined by measurement of the temperature of the drops at various locations below the droplet generator exit. A temperature prediction code was also used to estimate the temperature of the droplets based on vertical velocity and the distance traveled by droplets from the droplet generator to the airfoil stagnation line. High speed imaging was employed to observe the interaction between the droplets and the airfoil. The high speed imaging provided droplet deformation information as the droplet approached the airfoil near the stagnation line. A tracking software program was used to measure the horizontal and vertical displacement of the droplet against time. It was demonstrated that to compare the effects of water supercooling on droplet deformation, the ratio of the slip velocity and the initial droplet velocity must be equal. A case with equal slip velocity to initial velocity ratios was selected for room temperature and supercooled droplet conditions. The airfoil velocity was 60 m/s and the slip velocity for both sets of data was 40 m/s. In these cases, the deformation of the weakly supercooled and warm droplets did not present different trends. The similar behavior for both environmental conditions indicates that water supercooling has no effect on particle deformation for the limited range of the weak supercooling of the droplets tested and the selected impact velocity. The assumption of a constant surface tension value was further supported by the equal trend of the Bond number obtained for supercooled and room temperature droplets.
Kalman filtering techniques usually compare a known dynamic model with some process noise to an updated, noisy measurement. Both sources of noise are generally assumed to be Gaussian and are filtered to obtain a more accurate estimate of the state of the system of interest. However, these methods assume that a relatively accurate dynamical model already exists. By including discriminative methodology to interpret differences in the predictive model and the measured states over time, an incorrect model can be corrected overtime, allowing a spacecraft to learn about its environment and adapt to changing conditions. In this paper, a discriminative unscented Kalman filter (DUKF) is introduced on the special Euclidean group SE(3) formulation framework. A spacecraft is initialized near a small body with no knowledge of its parameters, and using several consecutive conditional models the environment is studied and the filter is updated. The case study of a spacecraft in a slightly elliptical, inclined, relatively tight orbit around the irregular moon Phobos is simulated and discussed. The accuracy of this approach is quantifying the differences between the true state, the UKF with a poor model, and the DUKF.
An experimental and analytical study of the thermal behavior of spiral bevel gears is presented. Experimental data were taken using thermocoupled test hardware and an infrared microscope. Many operational parameters were varied to investigate their effects on the thermal behavior. The data taken were also used to validate the boundary conditions applied to the analytical model. A finite element-based solution sequence was developed. The three-dimensional model was developed based on the manufacturing process for these gears. Contact between the meshing gears was found using tooth contact analysis to describe the location, curvatures, orientations, and surface velocities. This information was then used in a three-dimensional Hertzian contact analysis to predict contact ellipse size and maximum pressure. From these results, an estimate of the heat flux magnitude and the location on the finite element model was made. The finite element model used time-averaged boundary conditions to permit the solution to attain steady state in a computationally efficient manner.Then time- and position-varying boundary conditions were applied to the model to analyze the cyclic heating and cooling due to the gears meshing and transferring heat to the surroundings, respectively. The model was run in this mode until the temperature behavior stabilized. The transient flash temperature on the surface was therefore described. The analysis can be used to predict the overall expected thermal behavior of spiral bevel gears. The experimental and analytical results were compared for this study and also with a limited number of other studies. The experimental and analytical results attained in the current study were basically within 10% of each other for the cases compared. The experimental comparison was for bulk thermocouple locations and data taken with an infrared microscope. The results of a limited number of other studies were compared with those obtained herein and predicted the same basic behavior.